// Electronic appendix to "Ranks of elliptic curves over function fields",
// by Alan G.B. Lauder. Published in LMS JCM.

FpXY<X,Y>:=PolynomialRing(GF(7),2);
QT<T>:=PolynomialRing(Rationals());

// List of 1250 pairs [*f,P*] where P is the unitarised L-function of the
// elliptic curve Z^2 = f(X,Y) over the function field F_7(Y), where F_7 is the
// finite field with 7 elements. Thus P(7T) is the L-function of Z^2 = f(X,Y).

ULp7d30:=[ [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 
        3*X*Y^8 + 3*X*Y^7 + X*Y^6 + 2*X*Y^5 + X*Y^4 + X*Y^3 + 3*X*Y^2 + 5*X*Y + 2*X 
        + 5*Y^30 + 2*Y^29 + Y^28 + 6*Y^27 + 2*Y^26 + 4*Y^25 + 2*Y^24 + 2*Y^23 + 
        2*Y^22 + 2*Y^20 + 3*Y^19 + Y^18 + 4*Y^17 + 5*Y^16 + 2*Y^15 + 2*Y^14 + 6*Y^13
        + 2*Y^12 + 4*Y^11 + 2*Y^10 + 6*Y^7 + 3*Y^6 + 5*Y^5 + 2*Y^4 + Y^3 + 6*Y,
    -T^56 - 11/7*T^55 - 4/7*T^54 + 293/343*T^53 + 496/343*T^52 + 3435/2401*T^51 + 
        310/2401*T^50 - 3538/2401*T^49 - 1815/2401*T^48 + 563/2401*T^47 - 
        100/2401*T^46 - 727/2401*T^45 - 793/2401*T^44 - 1808/2401*T^43 - 
        1012/2401*T^42 + 1305/2401*T^41 + 1651/2401*T^40 + 1212/2401*T^39 + 
        855/2401*T^38 + 180/2401*T^37 - 1314/2401*T^36 - 1394/2401*T^35 + 
        1599/2401*T^34 + 1878/2401*T^33 - 632/2401*T^32 - 1978/2401*T^31 - 
        3035/2401*T^30 - 594/343*T^29 + 594/343*T^27 + 3035/2401*T^26 + 
        1978/2401*T^25 + 632/2401*T^24 - 1878/2401*T^23 - 1599/2401*T^22 + 
        1394/2401*T^21 + 1314/2401*T^20 - 180/2401*T^19 - 855/2401*T^18 - 
        1212/2401*T^17 - 1651/2401*T^16 - 1305/2401*T^15 + 1012/2401*T^14 + 
        1808/2401*T^13 + 793/2401*T^12 + 727/2401*T^11 + 100/2401*T^10 - 
        563/2401*T^9 + 1815/2401*T^8 + 3538/2401*T^7 - 310/2401*T^6 - 3435/2401*T^5 
        - 496/343*T^4 - 293/343*T^3 + 4/7*T^2 + 11/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        3*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 4*X*Y + X + Y^30
        + 4*Y^29 + 2*Y^28 + 4*Y^27 + 4*Y^26 + 3*Y^23 + 6*Y^22 + 3*Y^21 + 2*Y^20 + 
        6*Y^19 + 5*Y^17 + 6*Y^15 + Y^13 + Y^12 + Y^11 + 5*Y^9 + 4*Y^7 + 3*Y^6 + 
        2*Y^5 + Y^4 + 4*Y^3 + 5*Y^2 + 5*Y + 1,
    -T^56 + 5/7*T^55 - 17/49*T^54 + 257/343*T^53 - 23/343*T^52 - 1461/2401*T^51 + 
        3582/2401*T^50 - 2983/2401*T^49 + 2143/2401*T^48 - 2218/2401*T^47 + 
        1229/2401*T^46 + 1619/2401*T^45 - 3190/2401*T^44 + 1979/2401*T^43 - 
        1852/2401*T^42 + 299/343*T^41 - 752/2401*T^40 - 2427/2401*T^39 + 
        2650/2401*T^38 - 2202/2401*T^37 + 53/49*T^36 - 942/2401*T^35 - 317/2401*T^34
        + 3006/2401*T^33 - 659/343*T^32 + 3838/2401*T^31 - 4024/2401*T^30 + 
        2673/2401*T^29 - 2673/2401*T^27 + 4024/2401*T^26 - 3838/2401*T^25 + 
        659/343*T^24 - 3006/2401*T^23 + 317/2401*T^22 + 942/2401*T^21 - 53/49*T^20 +
        2202/2401*T^19 - 2650/2401*T^18 + 2427/2401*T^17 + 752/2401*T^16 - 
        299/343*T^15 + 1852/2401*T^14 - 1979/2401*T^13 + 3190/2401*T^12 - 
        1619/2401*T^11 - 1229/2401*T^10 + 2218/2401*T^9 - 2143/2401*T^8 + 
        2983/2401*T^7 - 3582/2401*T^6 + 1461/2401*T^5 + 23/343*T^4 - 257/343*T^3 + 
        17/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 
        + 5*X*Y^8 + 6*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 3*X*Y^3 + 4*X*Y^2 + 3*X*Y + 6*X + 
        4*Y^30 + 3*Y^29 + 3*Y^28 + 4*Y^27 + 3*Y^26 + 5*Y^25 + 5*Y^24 + 5*Y^23 + 
        4*Y^21 + 6*Y^20 + Y^18 + 4*Y^16 + 3*Y^15 + 6*Y^14 + 5*Y^13 + 3*Y^12 + 3*Y^11
        + 5*Y^10 + 3*Y^9 + 4*Y^8 + 6*Y^7 + 4*Y^6 + 3*Y^5 + 6*Y^4 + 6*Y^3 + 2*Y^2 + 
        6*Y + 2,
    T^56 - 4/7*T^55 - 13/49*T^54 + 117/343*T^53 - 1783/2401*T^52 + 2309/2401*T^51 - 
        1366/2401*T^50 - 730/2401*T^49 + 2252/2401*T^48 - 195/343*T^47 + 
        965/2401*T^46 - 311/2401*T^45 - 1041/2401*T^44 + 265/343*T^43 - 
        1513/2401*T^42 + 440/2401*T^41 + 365/2401*T^40 - 1511/2401*T^39 + 
        1121/2401*T^38 - 750/2401*T^37 - 99/2401*T^36 + 347/2401*T^35 - 
        565/2401*T^34 + 481/2401*T^33 + 1011/2401*T^32 - 432/2401*T^31 - 
        475/2401*T^30 + 157/2401*T^29 - 1142/2401*T^28 + 157/2401*T^27 - 
        475/2401*T^26 - 432/2401*T^25 + 1011/2401*T^24 + 481/2401*T^23 - 
        565/2401*T^22 + 347/2401*T^21 - 99/2401*T^20 - 750/2401*T^19 + 
        1121/2401*T^18 - 1511/2401*T^17 + 365/2401*T^16 + 440/2401*T^15 - 
        1513/2401*T^14 + 265/343*T^13 - 1041/2401*T^12 - 311/2401*T^11 + 
        965/2401*T^10 - 195/343*T^9 + 2252/2401*T^8 - 730/2401*T^7 - 1366/2401*T^6 +
        2309/2401*T^5 - 1783/2401*T^4 + 117/343*T^3 - 13/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 +
        4*X*Y^7 + 3*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 5*X*Y + 5*X + 
        3*Y^30 + 3*Y^29 + 5*Y^28 + 6*Y^27 + 2*Y^26 + 4*Y^25 + 4*Y^24 + Y^23 + Y^22 +
        3*Y^20 + 5*Y^19 + 2*Y^18 + 2*Y^17 + 3*Y^16 + 2*Y^15 + 2*Y^14 + 3*Y^13 + Y^12
        + 2*Y^10 + Y^9 + 2*Y^8 + 6*Y^6 + 4*Y^5 + 2*Y^4 + 6*Y^3 + 3*Y^2 + Y + 1,
    T^56 - 4/7*T^55 + 36/49*T^54 + 100/343*T^53 - 2414/2401*T^52 + 2063/2401*T^51 - 
        2407/2401*T^50 + 1292/2401*T^49 - 1213/2401*T^48 - 116/2401*T^47 + 
        649/2401*T^46 - 1290/2401*T^45 + 803/2401*T^44 - 1621/2401*T^43 + 
        1212/2401*T^42 - 1695/2401*T^41 + 1243/2401*T^40 - 314/2401*T^39 + 
        29/2401*T^38 + 1195/2401*T^37 - 248/343*T^36 + 2144/2401*T^35 - 
        1770/2401*T^34 + 1419/2401*T^33 - 662/2401*T^32 - 90/2401*T^31 + 
        1259/2401*T^30 - 1765/2401*T^29 + 57/49*T^28 - 1765/2401*T^27 + 
        1259/2401*T^26 - 90/2401*T^25 - 662/2401*T^24 + 1419/2401*T^23 - 
        1770/2401*T^22 + 2144/2401*T^21 - 248/343*T^20 + 1195/2401*T^19 + 
        29/2401*T^18 - 314/2401*T^17 + 1243/2401*T^16 - 1695/2401*T^15 + 
        1212/2401*T^14 - 1621/2401*T^13 + 803/2401*T^12 - 1290/2401*T^11 + 
        649/2401*T^10 - 116/2401*T^9 - 1213/2401*T^8 + 1292/2401*T^7 - 2407/2401*T^6
        + 2063/2401*T^5 - 2414/2401*T^4 + 100/343*T^3 + 36/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 5*X*Y^7 + X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 6*X*Y + 2*X + 6*Y^30 + 
        3*Y^28 + 3*Y^27 + 2*Y^26 + 2*Y^25 + 2*Y^24 + 4*Y^22 + 3*Y^21 + Y^20 + 5*Y^18
        + Y^17 + 3*Y^16 + 2*Y^15 + 3*Y^14 + 5*Y^13 + 5*Y^12 + 2*Y^11 + 3*Y^10 + 
        4*Y^9 + 6*Y^8 + 3*Y^7 + 6*Y^6 + Y^4 + 5*Y^3 + 2*Y^2 + 2*Y + 1,
    -T^56 + 5/7*T^55 + 17/49*T^54 - 100/343*T^53 + 733/2401*T^52 - 1/343*T^51 - 
        844/2401*T^50 - 136/2401*T^49 + 236/2401*T^48 - 212/2401*T^47 + 4/343*T^46 +
        645/2401*T^45 + 732/2401*T^44 - 302/2401*T^43 - 282/2401*T^42 + 96/343*T^41 
        - 1226/2401*T^40 + 53/2401*T^39 - 4/49*T^38 + 432/2401*T^37 + 432/2401*T^36 
        - 657/2401*T^35 + 820/2401*T^34 - 335/2401*T^33 - 61/343*T^32 + 
        122/2401*T^31 - 199/2401*T^30 - 914/2401*T^29 + 914/2401*T^27 + 
        199/2401*T^26 - 122/2401*T^25 + 61/343*T^24 + 335/2401*T^23 - 820/2401*T^22 
        + 657/2401*T^21 - 432/2401*T^20 - 432/2401*T^19 + 4/49*T^18 - 53/2401*T^17 +
        1226/2401*T^16 - 96/343*T^15 + 282/2401*T^14 + 302/2401*T^13 - 732/2401*T^12
        - 645/2401*T^11 - 4/343*T^10 + 212/2401*T^9 - 236/2401*T^8 + 136/2401*T^7 + 
        844/2401*T^6 + 1/343*T^5 - 733/2401*T^4 + 100/343*T^3 - 17/49*T^2 - 5/7*T + 
        1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 
        6*X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 4*X*Y 
        + 4*X + 6*Y^30 + 6*Y^29 + 2*Y^28 + 2*Y^26 + 2*Y^25 + Y^24 + 3*Y^23 + 3*Y^22 
        + 6*Y^21 + 4*Y^20 + 2*Y^19 + Y^18 + 5*Y^17 + 5*Y^16 + 5*Y^15 + 5*Y^14 + 
        2*Y^12 + Y^10 + 4*Y^9 + Y^8 + 4*Y^7 + 6*Y^6 + Y^5 + 5*Y^4 + Y^3 + 2*Y^2 + 1,
    T^56 + 5/7*T^55 + 8/49*T^54 - 47/343*T^53 - 1143/2401*T^52 - 2336/2401*T^51 - 
        2048/2401*T^50 - 2105/2401*T^49 - 2844/2401*T^48 - 1555/2401*T^47 + 
        975/2401*T^46 + 2194/2401*T^45 + 3039/2401*T^44 + 88/49*T^43 + 435/343*T^42 
        + 1646/2401*T^41 + 130/343*T^40 - 951/2401*T^39 - 2136/2401*T^38 - 
        3131/2401*T^37 - 4055/2401*T^36 - 4125/2401*T^35 - 2294/2401*T^34 - 
        1002/2401*T^33 + 376/2401*T^32 + 975/2401*T^31 + 2504/2401*T^30 + 
        3572/2401*T^29 + 4140/2401*T^28 + 3572/2401*T^27 + 2504/2401*T^26 + 
        975/2401*T^25 + 376/2401*T^24 - 1002/2401*T^23 - 2294/2401*T^22 - 
        4125/2401*T^21 - 4055/2401*T^20 - 3131/2401*T^19 - 2136/2401*T^18 - 
        951/2401*T^17 + 130/343*T^16 + 1646/2401*T^15 + 435/343*T^14 + 88/49*T^13 + 
        3039/2401*T^12 + 2194/2401*T^11 + 975/2401*T^10 - 1555/2401*T^9 - 
        2844/2401*T^8 - 2105/2401*T^7 - 2048/2401*T^6 - 2336/2401*T^5 - 
        1143/2401*T^4 - 47/343*T^3 + 8/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + X*Y^13 + 2*X*Y^11 + 4*X*Y^9 + 3*X*Y^8 + 3*X*Y^7 + 6*X*Y^6 + 
        5*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 3*X*Y + 4*X + 5*Y^30 + 4*Y^29 + 
        3*Y^28 + 4*Y^27 + 2*Y^26 + 6*Y^25 + 2*Y^24 + Y^23 + 4*Y^20 + 5*Y^19 + 6*Y^17
        + 6*Y^16 + 4*Y^15 + 3*Y^14 + 4*Y^13 + 4*Y^12 + 3*Y^11 + 6*Y^10 + 5*Y^9 + 
        4*Y^8 + 6*Y^7 + 6*Y^6 + Y^5 + Y^4 + 2*Y^3 + 2*Y^2 + 2*Y + 6,
    -T^56 + 8/7*T^55 + 3/7*T^54 - 681/343*T^53 + 3373/2401*T^52 + 878/2401*T^51 - 
        3587/2401*T^50 + 2462/2401*T^49 + 793/2401*T^48 - 2907/2401*T^47 + 
        2573/2401*T^46 - 79/2401*T^45 - 279/343*T^44 + 1590/2401*T^43 - 
        109/2401*T^42 - 271/2401*T^41 + 874/2401*T^40 - 895/2401*T^39 + 
        451/2401*T^38 + 116/343*T^37 - 229/343*T^36 + 2357/2401*T^35 - 457/2401*T^34
        - 2479/2401*T^33 + 2992/2401*T^32 + 68/343*T^31 - 4504/2401*T^30 + 
        4553/2401*T^29 - 4553/2401*T^27 + 4504/2401*T^26 - 68/343*T^25 - 
        2992/2401*T^24 + 2479/2401*T^23 + 457/2401*T^22 - 2357/2401*T^21 + 
        229/343*T^20 - 116/343*T^19 - 451/2401*T^18 + 895/2401*T^17 - 874/2401*T^16 
        + 271/2401*T^15 + 109/2401*T^14 - 1590/2401*T^13 + 279/343*T^12 + 
        79/2401*T^11 - 2573/2401*T^10 + 2907/2401*T^9 - 793/2401*T^8 - 2462/2401*T^7
        + 3587/2401*T^6 - 878/2401*T^5 - 3373/2401*T^4 + 681/343*T^3 - 3/7*T^2 - 
        8/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + X*Y^8 + 2*X*Y^7 + 
        4*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + 6*X + 5*Y^30 + 5*Y^29 + 
        4*Y^28 + 6*Y^27 + 2*Y^26 + 5*Y^25 + 3*Y^22 + 2*Y^21 + 5*Y^20 + 3*Y^19 + 
        6*Y^18 + 2*Y^17 + Y^16 + 6*Y^15 + Y^14 + 3*Y^13 + 3*Y^12 + 5*Y^11 + 2*Y^9 + 
        2*Y^8 + 2*Y^6 + 4*Y^4 + 6*Y^3 + 3*Y^2 + 2*Y + 3,
    T^56 - 5/7*T^55 - 41/49*T^54 + 149/343*T^53 + 1915/2401*T^52 - 71/343*T^51 - 
        1562/2401*T^50 + 814/2401*T^49 + 447/2401*T^48 + 263/2401*T^47 + 
        64/2401*T^46 - 118/343*T^45 - 605/2401*T^44 + 621/2401*T^43 + 1228/2401*T^42
        - 743/2401*T^41 - 674/2401*T^40 + 506/2401*T^39 - 405/2401*T^38 + 
        731/2401*T^37 - 421/2401*T^36 + 68/2401*T^35 - 562/2401*T^34 - 285/2401*T^33
        + 782/2401*T^32 + 388/2401*T^31 - 1075/2401*T^30 - 404/2401*T^29 + 
        1105/2401*T^28 - 404/2401*T^27 - 1075/2401*T^26 + 388/2401*T^25 + 
        782/2401*T^24 - 285/2401*T^23 - 562/2401*T^22 + 68/2401*T^21 - 421/2401*T^20
        + 731/2401*T^19 - 405/2401*T^18 + 506/2401*T^17 - 674/2401*T^16 - 
        743/2401*T^15 + 1228/2401*T^14 + 621/2401*T^13 - 605/2401*T^12 - 
        118/343*T^11 + 64/2401*T^10 + 263/2401*T^9 + 447/2401*T^8 + 814/2401*T^7 - 
        1562/2401*T^6 - 71/343*T^5 + 1915/2401*T^4 + 149/343*T^3 - 41/49*T^2 - 5/7*T
        + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 4*X*Y^8 + 
        X*Y^7 + 5*X*Y^6 + X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 5*X*Y + 6*Y^30 + 6*Y^29 + 
        4*Y^28 + 5*Y^27 + 5*Y^25 + 3*Y^24 + 2*Y^23 + 6*Y^22 + 3*Y^21 + 2*Y^20 + Y^19
        + Y^17 + 5*Y^16 + 2*Y^15 + 2*Y^14 + 2*Y^13 + Y^12 + 4*Y^11 + 6*Y^10 + 3*Y^9 
        + 5*Y^8 + 3*Y^7 + 5*Y^6 + 2*Y^5 + 2*Y^4 + 4*Y^3 + 2*Y^2 + Y + 4,
    T^56 + 15/7*T^55 + 15/7*T^54 + 65/343*T^53 - 4475/2401*T^52 - 3392/2401*T^51 + 
        2097/2401*T^50 + 5210/2401*T^49 + 88/343*T^48 - 702/343*T^47 - 580/343*T^46 
        + 2273/2401*T^45 + 825/343*T^44 + 1002/2401*T^43 - 2*T^42 - 4717/2401*T^41 +
        1644/2401*T^40 + 6033/2401*T^39 + 414/343*T^38 - 4143/2401*T^37 - 
        152/49*T^36 - 2699/2401*T^35 + 4245/2401*T^34 + 6289/2401*T^33 + 
        1100/2401*T^32 - 4909/2401*T^31 - 4687/2401*T^30 + 803/2401*T^29 + 
        4230/2401*T^28 + 803/2401*T^27 - 4687/2401*T^26 - 4909/2401*T^25 + 
        1100/2401*T^24 + 6289/2401*T^23 + 4245/2401*T^22 - 2699/2401*T^21 - 
        152/49*T^20 - 4143/2401*T^19 + 414/343*T^18 + 6033/2401*T^17 + 
        1644/2401*T^16 - 4717/2401*T^15 - 2*T^14 + 1002/2401*T^13 + 825/343*T^12 + 
        2273/2401*T^11 - 580/343*T^10 - 702/343*T^9 + 88/343*T^8 + 5210/2401*T^7 + 
        2097/2401*T^6 - 3392/2401*T^5 - 4475/2401*T^4 + 65/343*T^3 + 15/7*T^2 + 
        15/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 
        2*X*Y^8 + 2*X*Y^5 + 2*X*Y^4 + X*Y^2 + X + 4*Y^30 + 5*Y^28 + 6*Y^26 + 5*Y^24 
        + 3*Y^23 + 2*Y^22 + 5*Y^21 + 5*Y^20 + 5*Y^19 + 2*Y^14 + 3*Y^12 + 5*Y^11 + 
        Y^10 + 3*Y^9 + 4*Y^8 + 5*Y^7 + 5*Y^6 + 2*Y^5 + 6*Y^4 + 3*Y^3 + 4*Y^2 + 4*Y +
        4,
    T^56 - 4/7*T^55 - 26/49*T^54 + 193/343*T^53 - 1552/2401*T^52 - 165/343*T^51 - 
        611/2401*T^50 + 186/343*T^49 - 752/2401*T^48 + 295/2401*T^47 + 
        1226/2401*T^46 + 674/2401*T^45 + 731/2401*T^44 - 710/2401*T^43 + 
        2026/2401*T^42 - 1154/2401*T^41 - 556/2401*T^40 + 295/2401*T^39 - 
        699/2401*T^38 - 75/2401*T^37 - 1885/2401*T^36 + 5/49*T^35 - 705/2401*T^34 + 
        884/2401*T^33 - 877/2401*T^32 + 354/2401*T^31 + 1781/2401*T^30 - 
        1055/2401*T^29 + 1734/2401*T^28 - 1055/2401*T^27 + 1781/2401*T^26 + 
        354/2401*T^25 - 877/2401*T^24 + 884/2401*T^23 - 705/2401*T^22 + 5/49*T^21 - 
        1885/2401*T^20 - 75/2401*T^19 - 699/2401*T^18 + 295/2401*T^17 - 
        556/2401*T^16 - 1154/2401*T^15 + 2026/2401*T^14 - 710/2401*T^13 + 
        731/2401*T^12 + 674/2401*T^11 + 1226/2401*T^10 + 295/2401*T^9 - 752/2401*T^8
        + 186/343*T^7 - 611/2401*T^6 - 165/343*T^5 - 1552/2401*T^4 + 193/343*T^3 - 
        26/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + X*Y^10 + 6*X*Y^9 + 
        3*X*Y^8 + 4*X*Y^7 + 4*X*Y^5 + X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 4*X*Y + 5*X + 
        2*Y^30 + 3*Y^29 + 3*Y^28 + 4*Y^27 + 6*Y^26 + Y^25 + 3*Y^24 + 4*Y^23 + 3*Y^22
        + 6*Y^21 + Y^20 + 2*Y^19 + 5*Y^18 + 5*Y^17 + Y^16 + 6*Y^15 + 2*Y^14 + 3*Y^13
        + 3*Y^11 + 5*Y^10 + 5*Y^9 + 6*Y^8 + 4*Y^7 + 3*Y^6 + 6*Y^5 + 5*Y^2 + 4*Y + 2,
    T^56 + 2/7*T^55 - 47/49*T^54 + 23/343*T^53 - 480/2401*T^52 + 974/2401*T^51 + 
        2586/2401*T^50 - 444/343*T^49 - 1480/2401*T^48 + 1353/2401*T^47 - 
        141/343*T^46 + 3340/2401*T^45 + 929/2401*T^44 - 4096/2401*T^43 + 20/343*T^42
        - 635/2401*T^41 + 809/2401*T^40 + 592/343*T^39 - 2216/2401*T^38 - 
        2344/2401*T^37 + 781/2401*T^36 - 957/2401*T^35 + 262/343*T^34 + 
        1058/2401*T^33 - 355/343*T^32 - 668/2401*T^31 - 925/2401*T^30 + 
        176/2401*T^29 + 2985/2401*T^28 + 176/2401*T^27 - 925/2401*T^26 - 
        668/2401*T^25 - 355/343*T^24 + 1058/2401*T^23 + 262/343*T^22 - 957/2401*T^21
        + 781/2401*T^20 - 2344/2401*T^19 - 2216/2401*T^18 + 592/343*T^17 + 
        809/2401*T^16 - 635/2401*T^15 + 20/343*T^14 - 4096/2401*T^13 + 929/2401*T^12
        + 3340/2401*T^11 - 141/343*T^10 + 1353/2401*T^9 - 1480/2401*T^8 - 
        444/343*T^7 + 2586/2401*T^6 + 974/2401*T^5 - 480/2401*T^4 + 23/343*T^3 - 
        47/49*T^2 + 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + 6*X*Y^10 + X*Y^9 + 4*X*Y^8 + 
        3*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 2*X + Y^30 + 
        5*Y^28 + 3*Y^27 + 3*Y^26 + Y^25 + 5*Y^24 + 3*Y^23 + Y^22 + 5*Y^21 + 2*Y^20 +
        6*Y^19 + Y^18 + 5*Y^17 + Y^16 + 4*Y^15 + Y^14 + Y^12 + 4*Y^11 + Y^9 + 6*Y^6 
        + 3*Y^5 + 2*Y^4,
    T^56 - 4/7*T^55 + 33/49*T^54 - 145/343*T^53 - 919/2401*T^52 + 165/2401*T^51 - 
        1072/2401*T^50 + 1089/2401*T^49 + 449/2401*T^48 + 398/2401*T^47 - 
        241/2401*T^46 - 198/2401*T^45 + 1/2401*T^44 - 1135/2401*T^43 + 717/2401*T^42
        - 305/2401*T^41 + 99/343*T^40 - 911/2401*T^39 + 634/2401*T^38 + 13/2401*T^37
        - 110/343*T^36 + 1161/2401*T^35 - 1171/2401*T^34 + 1203/2401*T^33 - 
        254/2401*T^32 - 699/2401*T^31 + 1073/2401*T^30 - 1305/2401*T^29 + 
        58/343*T^28 - 1305/2401*T^27 + 1073/2401*T^26 - 699/2401*T^25 - 
        254/2401*T^24 + 1203/2401*T^23 - 1171/2401*T^22 + 1161/2401*T^21 - 
        110/343*T^20 + 13/2401*T^19 + 634/2401*T^18 - 911/2401*T^17 + 99/343*T^16 - 
        305/2401*T^15 + 717/2401*T^14 - 1135/2401*T^13 + 1/2401*T^12 - 198/2401*T^11
        - 241/2401*T^10 + 398/2401*T^9 + 449/2401*T^8 + 1089/2401*T^7 - 
        1072/2401*T^6 + 165/2401*T^5 - 919/2401*T^4 - 145/343*T^3 + 33/49*T^2 - 
        4/7*T + 1
*], [*
    X^3 + X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 5*X*Y^8 + 
        5*X*Y^7 + X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + X*Y^2 + 6*X*Y + X + 6*Y^30 +
        6*Y^29 + 5*Y^28 + 4*Y^27 + Y^25 + 6*Y^23 + Y^22 + Y^20 + 6*Y^19 + 4*Y^16 + 
        Y^15 + Y^14 + 3*Y^13 + Y^12 + 6*Y^11 + 3*Y^10 + 6*Y^9 + 4*Y^8 + 4*Y^7 + 
        4*Y^6 + 5*Y^5 + Y^4 + 5*Y^3 + 4*Y^2 + 6*Y + 4,
    T^56 - 1/7*T^55 + 32/49*T^54 - 174/343*T^53 + 317/2401*T^52 - 2140/2401*T^51 - 
        1797/2401*T^50 - 206/343*T^49 - 1147/2401*T^48 + 808/2401*T^47 + 
        967/2401*T^46 + 1501/2401*T^45 + 1809/2401*T^44 + 1276/2401*T^43 + 
        331/2401*T^42 + 117/2401*T^41 - 978/2401*T^40 + 38/343*T^39 - 227/343*T^38 -
        137/2401*T^37 - 1108/2401*T^36 - 813/2401*T^35 - 558/2401*T^34 - 58/343*T^33
        - 103/2401*T^32 + 429/2401*T^31 - 57/2401*T^30 + 1906/2401*T^29 + 
        40/343*T^28 + 1906/2401*T^27 - 57/2401*T^26 + 429/2401*T^25 - 103/2401*T^24 
        - 58/343*T^23 - 558/2401*T^22 - 813/2401*T^21 - 1108/2401*T^20 - 
        137/2401*T^19 - 227/343*T^18 + 38/343*T^17 - 978/2401*T^16 + 117/2401*T^15 +
        331/2401*T^14 + 1276/2401*T^13 + 1809/2401*T^12 + 1501/2401*T^11 + 
        967/2401*T^10 + 808/2401*T^9 - 1147/2401*T^8 - 206/343*T^7 - 1797/2401*T^6 -
        2140/2401*T^5 + 317/2401*T^4 - 174/343*T^3 + 32/49*T^2 - 1/7*T + 1
*], [*
    X^3 + X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 3*X*Y^8 + X*Y^7 + 
        6*X*Y^6 + X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 6*X*Y + 5*X + 4*Y^30 + 
        2*Y^29 + 3*Y^28 + 6*Y^27 + 2*Y^26 + 3*Y^25 + 4*Y^24 + 3*Y^23 + Y^22 + 3*Y^21
        + 6*Y^20 + 4*Y^19 + 3*Y^18 + 5*Y^17 + Y^16 + 2*Y^15 + 6*Y^14 + 3*Y^12 + 
        5*Y^10 + 5*Y^8 + 2*Y^7 + Y^6 + 6*Y^5 + 5*Y^4 + 3*Y^3 + 2*Y^2 + Y + 6,
    T^56 + 9/7*T^55 + 73/49*T^54 + 270/343*T^53 - 78/343*T^52 - 1044/2401*T^51 - 
        2599/2401*T^50 - 4015/2401*T^49 - 4206/2401*T^48 - 4586/2401*T^47 - 
        2358/2401*T^46 - 283/2401*T^45 + 2221/2401*T^44 + 3533/2401*T^43 + 
        2713/2401*T^42 + 458/2401*T^41 - 1098/2401*T^40 - 1276/2401*T^39 - 
        766/2401*T^38 - 103/343*T^37 + 398/2401*T^36 + 1409/2401*T^35 + 
        3189/2401*T^34 + 571/343*T^33 + 2070/2401*T^32 + 124/343*T^31 - 
        1768/2401*T^30 - 83/49*T^29 - 533/343*T^28 - 83/49*T^27 - 1768/2401*T^26 + 
        124/343*T^25 + 2070/2401*T^24 + 571/343*T^23 + 3189/2401*T^22 + 
        1409/2401*T^21 + 398/2401*T^20 - 103/343*T^19 - 766/2401*T^18 - 
        1276/2401*T^17 - 1098/2401*T^16 + 458/2401*T^15 + 2713/2401*T^14 + 
        3533/2401*T^13 + 2221/2401*T^12 - 283/2401*T^11 - 2358/2401*T^10 - 
        4586/2401*T^9 - 4206/2401*T^8 - 4015/2401*T^7 - 2599/2401*T^6 - 
        1044/2401*T^5 - 78/343*T^4 + 270/343*T^3 + 73/49*T^2 + 9/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 5*X*Y^8 + 
        3*X*Y^7 + 2*X*Y^6 + 6*X*Y^4 + 6*X*Y^3 + X*Y^2 + 6*X + 3*Y^30 + Y^29 + 3*Y^28
        + Y^26 + 6*Y^25 + 3*Y^23 + 3*Y^22 + 3*Y^21 + 2*Y^20 + 4*Y^19 + 2*Y^18 + 
        3*Y^17 + Y^16 + Y^15 + 6*Y^14 + Y^13 + 5*Y^10 + 4*Y^9 + 5*Y^8 + 4*Y^7 + 
        2*Y^6 + Y^5 + 2*Y^4 + 6*Y^3 + 3*Y^2 + 4*Y + 1,
    T^56 - 5/7*T^55 + 8/49*T^54 - 48/343*T^53 + 198/2401*T^52 - 416/2401*T^51 - 
        544/2401*T^50 + 780/2401*T^49 - 839/2401*T^48 + 593/2401*T^47 - 118/343*T^46
        + 155/343*T^45 - 1156/2401*T^44 + 93/343*T^43 - 1667/2401*T^42 + 
        509/2401*T^41 + 144/343*T^40 - 948/2401*T^39 + 1557/2401*T^38 - 
        121/2401*T^37 + 1392/2401*T^36 - 1254/2401*T^35 + 677/2401*T^34 - 
        557/2401*T^33 - 607/2401*T^32 + 580/2401*T^31 - 1291/2401*T^30 + 
        1028/2401*T^29 - 164/343*T^28 + 1028/2401*T^27 - 1291/2401*T^26 + 
        580/2401*T^25 - 607/2401*T^24 - 557/2401*T^23 + 677/2401*T^22 - 
        1254/2401*T^21 + 1392/2401*T^20 - 121/2401*T^19 + 1557/2401*T^18 - 
        948/2401*T^17 + 144/343*T^16 + 509/2401*T^15 - 1667/2401*T^14 + 93/343*T^13 
        - 1156/2401*T^12 + 155/343*T^11 - 118/343*T^10 + 593/2401*T^9 - 839/2401*T^8
        + 780/2401*T^7 - 544/2401*T^6 - 416/2401*T^5 + 198/2401*T^4 - 48/343*T^3 + 
        8/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + X*Y^10 + 4*X*Y^9 + 
        4*X*Y^8 + 2*X*Y^6 + X*Y^5 + X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 6*X + 6*Y^30 + 
        4*Y^29 + 6*Y^27 + Y^26 + 4*Y^25 + 2*Y^24 + 6*Y^23 + 3*Y^22 + 2*Y^21 + Y^20 +
        3*Y^19 + 3*Y^18 + Y^17 + 5*Y^16 + 6*Y^15 + Y^14 + 3*Y^13 + 4*Y^12 + 6*Y^11 +
        4*Y^10 + 4*Y^9 + 4*Y^7 + 2*Y^6 + Y^5 + 3*Y^4 + 2*Y^3 + 5*Y^2 + 6*Y + 5,
    -T^56 + 5/7*T^55 - 11/7*T^54 + 73/49*T^53 - 3466/2401*T^52 + 5536/2401*T^51 - 
        4075/2401*T^50 + 5673/2401*T^49 - 4169/2401*T^48 + 5472/2401*T^47 - 
        5512/2401*T^46 + 4418/2401*T^45 - 4972/2401*T^44 + 2000/2401*T^43 - 
        3051/2401*T^42 + 751/2401*T^41 - 880/2401*T^40 + 44/2401*T^39 + 
        1972/2401*T^38 - 439/2401*T^37 + 2873/2401*T^36 - 2206/2401*T^35 + 
        62/49*T^34 - 540/343*T^33 + 2497/2401*T^32 - 3184/2401*T^31 + 1271/2401*T^30
        - 1595/2401*T^29 + 1595/2401*T^27 - 1271/2401*T^26 + 3184/2401*T^25 - 
        2497/2401*T^24 + 540/343*T^23 - 62/49*T^22 + 2206/2401*T^21 - 2873/2401*T^20
        + 439/2401*T^19 - 1972/2401*T^18 - 44/2401*T^17 + 880/2401*T^16 - 
        751/2401*T^15 + 3051/2401*T^14 - 2000/2401*T^13 + 4972/2401*T^12 - 
        4418/2401*T^11 + 5512/2401*T^10 - 5472/2401*T^9 + 4169/2401*T^8 - 
        5673/2401*T^7 + 4075/2401*T^6 - 5536/2401*T^5 + 3466/2401*T^4 - 73/49*T^3 + 
        11/7*T^2 - 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + X*Y^12 + 5*X*Y^10 + 3*X*Y^9 + 4*X*Y^8 + 
        6*X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 4*X*Y + 6*X + 
        3*Y^30 + Y^29 + 6*Y^27 + 3*Y^26 + 3*Y^25 + 5*Y^24 + 4*Y^23 + 5*Y^22 + 6*Y^21
        + 2*Y^20 + 4*Y^19 + Y^18 + 6*Y^17 + 6*Y^16 + 2*Y^15 + 6*Y^14 + 2*Y^13 + 
        3*Y^12 + 3*Y^11 + 3*Y^10 + 2*Y^8 + 2*Y^7 + Y^6 + 5*Y^5 + 2*Y^3 + 5*Y^2 + 4*Y
        + 2,
    T^56 - 16/7*T^55 + 131/49*T^54 - 278/343*T^53 - 4268/2401*T^52 + 6789/2401*T^51 
        - 5009/2401*T^50 + 3124/2401*T^49 - 3910/2401*T^48 + 3643/2401*T^47 - 
        717/2401*T^46 - 2930/2401*T^45 + 3221/2401*T^44 - 1465/2401*T^43 + 
        57/2401*T^42 - 292/2401*T^41 + 79/343*T^40 - 865/2401*T^39 + 2118/2401*T^38 
        - 4842/2401*T^37 + 6247/2401*T^36 - 3880/2401*T^35 - 1208/2401*T^34 + 
        5013/2401*T^33 - 4430/2401*T^32 + 1489/2401*T^31 - 29/2401*T^30 + 
        1434/2401*T^29 - 346/343*T^28 + 1434/2401*T^27 - 29/2401*T^26 + 
        1489/2401*T^25 - 4430/2401*T^24 + 5013/2401*T^23 - 1208/2401*T^22 - 
        3880/2401*T^21 + 6247/2401*T^20 - 4842/2401*T^19 + 2118/2401*T^18 - 
        865/2401*T^17 + 79/343*T^16 - 292/2401*T^15 + 57/2401*T^14 - 1465/2401*T^13 
        + 3221/2401*T^12 - 2930/2401*T^11 - 717/2401*T^10 + 3643/2401*T^9 - 
        3910/2401*T^8 + 3124/2401*T^7 - 5009/2401*T^6 + 6789/2401*T^5 - 
        4268/2401*T^4 - 278/343*T^3 + 131/49*T^2 - 16/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + X*Y^9 + 2*X*Y^8 + 
        5*X*Y^7 + 5*X*Y^6 + X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 6*X*Y + 5*X + 
        3*Y^30 + 5*Y^29 + 3*Y^28 + 6*Y^27 + 3*Y^26 + 2*Y^25 + 5*Y^24 + 5*Y^23 + 
        2*Y^18 + 3*Y^17 + 2*Y^16 + 5*Y^15 + 4*Y^13 + 2*Y^12 + 3*Y^11 + 6*Y^10 + 
        3*Y^9 + 3*Y^8 + 5*Y^5 + 2*Y^4 + 4*Y^3 + 6*Y^2 + 4*Y + 6,
    T^56 - 6/7*T^55 + 17/49*T^54 - 218/343*T^53 + 1034/2401*T^52 + 848/2401*T^51 - 
        2600/2401*T^50 + 1321/2401*T^49 - 1154/2401*T^48 + 2438/2401*T^47 - 
        2067/2401*T^46 - 10/49*T^45 + 250/343*T^44 + 802/2401*T^43 + 485/2401*T^42 -
        2434/2401*T^41 + 549/2401*T^40 + 808/2401*T^39 + 1431/2401*T^38 - 
        2164/2401*T^37 - 949/2401*T^36 + 687/2401*T^35 + 478/2401*T^34 - 
        668/2401*T^33 - 1810/2401*T^32 + 1192/2401*T^31 + 1951/2401*T^30 - 
        162/2401*T^29 - 1851/2401*T^28 - 162/2401*T^27 + 1951/2401*T^26 + 
        1192/2401*T^25 - 1810/2401*T^24 - 668/2401*T^23 + 478/2401*T^22 + 
        687/2401*T^21 - 949/2401*T^20 - 2164/2401*T^19 + 1431/2401*T^18 + 
        808/2401*T^17 + 549/2401*T^16 - 2434/2401*T^15 + 485/2401*T^14 + 
        802/2401*T^13 + 250/343*T^12 - 10/49*T^11 - 2067/2401*T^10 + 2438/2401*T^9 -
        1154/2401*T^8 + 1321/2401*T^7 - 2600/2401*T^6 + 848/2401*T^5 + 1034/2401*T^4
        - 218/343*T^3 + 17/49*T^2 - 6/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 2*X*Y^10 + 4*X*Y^9 + 2*X*Y^8 + 6*X*Y^6 + 6*X*Y^5 + 
        4*X*Y^4 + X*Y^3 + X*Y^2 + 5*X*Y + 4*X + 6*Y^30 + Y^29 + 5*Y^28 + Y^27 + 
        6*Y^25 + 3*Y^24 + Y^23 + 5*Y^22 + 4*Y^21 + 6*Y^20 + 2*Y^19 + 3*Y^18 + 6*Y^17
        + Y^16 + 2*Y^15 + 4*Y^13 + Y^11 + 5*Y^10 + 4*Y^9 + 4*Y^7 + Y^6 + 4*Y^4 + 
        4*Y^3 + 4*Y + 6,
    T^56 + T^55 + 10/49*T^54 + 267/343*T^53 + 754/2401*T^52 - 2957/2401*T^51 - 
        1604/2401*T^50 + 1146/2401*T^49 - 1408/2401*T^48 - 1273/2401*T^47 + 
        1749/2401*T^46 + 223/2401*T^45 - 2118/2401*T^44 - 594/2401*T^43 + 5/49*T^42 
        - 1872/2401*T^41 - 200/343*T^40 + 664/2401*T^39 - 347/2401*T^38 - 
        1472/2401*T^37 - 19/2401*T^36 + 1174/2401*T^35 + 1133/2401*T^34 + 
        234/343*T^33 + 2346/2401*T^32 + 1234/2401*T^31 - 137/343*T^30 - 
        1431/2401*T^29 - 143/343*T^28 - 1431/2401*T^27 - 137/343*T^26 + 
        1234/2401*T^25 + 2346/2401*T^24 + 234/343*T^23 + 1133/2401*T^22 + 
        1174/2401*T^21 - 19/2401*T^20 - 1472/2401*T^19 - 347/2401*T^18 + 
        664/2401*T^17 - 200/343*T^16 - 1872/2401*T^15 + 5/49*T^14 - 594/2401*T^13 - 
        2118/2401*T^12 + 223/2401*T^11 + 1749/2401*T^10 - 1273/2401*T^9 - 
        1408/2401*T^8 + 1146/2401*T^7 - 1604/2401*T^6 - 2957/2401*T^5 + 754/2401*T^4
        + 267/343*T^3 + 10/49*T^2 + T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 6*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 3*X*Y^7 +
        X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 2*X*Y + 4*X + 6*Y^30 + Y^28 + 3*Y^27 +
        3*Y^26 + 6*Y^25 + 2*Y^24 + 2*Y^23 + 3*Y^22 + 6*Y^21 + 2*Y^20 + 6*Y^19 + 
        5*Y^18 + 6*Y^17 + 4*Y^16 + 5*Y^15 + 4*Y^11 + 3*Y^9 + 4*Y^7 + 3*Y^6 + 2*Y^5 +
        5*Y^4 + 5*Y^3 + 5*Y^2 + 3*Y + 4,
    T^56 - 9/7*T^55 + 18/49*T^54 - 62/343*T^53 + 961/2401*T^52 + 670/2401*T^51 - 
        2046/2401*T^50 + 865/2401*T^49 - 1342/2401*T^48 + 367/343*T^47 - 
        1509/2401*T^46 - 614/2401*T^45 + 1434/2401*T^44 - 2021/2401*T^43 + 
        542/343*T^42 - 3651/2401*T^41 + 1609/2401*T^40 - 363/2401*T^39 + 
        466/2401*T^38 + 606/2401*T^37 - 3268/2401*T^36 + 3466/2401*T^35 - 
        3076/2401*T^34 + 2791/2401*T^33 - 849/2401*T^32 - 1627/2401*T^31 + 
        2740/2401*T^30 - 3502/2401*T^29 + 4631/2401*T^28 - 3502/2401*T^27 + 
        2740/2401*T^26 - 1627/2401*T^25 - 849/2401*T^24 + 2791/2401*T^23 - 
        3076/2401*T^22 + 3466/2401*T^21 - 3268/2401*T^20 + 606/2401*T^19 + 
        466/2401*T^18 - 363/2401*T^17 + 1609/2401*T^16 - 3651/2401*T^15 + 
        542/343*T^14 - 2021/2401*T^13 + 1434/2401*T^12 - 614/2401*T^11 - 
        1509/2401*T^10 + 367/343*T^9 - 1342/2401*T^8 + 865/2401*T^7 - 2046/2401*T^6 
        + 670/2401*T^5 + 961/2401*T^4 - 62/343*T^3 + 18/49*T^2 - 9/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + X*Y^10 + X*Y^9 + 
        2*X*Y^8 + 6*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 5*X*Y + X + 
        6*Y^30 + Y^29 + 5*Y^28 + 2*Y^27 + 2*Y^26 + 3*Y^25 + 2*Y^24 + 4*Y^23 + 2*Y^21
        + 5*Y^20 + Y^19 + 4*Y^18 + 2*Y^17 + 6*Y^16 + 2*Y^15 + 2*Y^14 + 3*Y^13 + 
        3*Y^12 + 2*Y^10 + 5*Y^9 + 2*Y^8 + 5*Y^7 + 3*Y^6 + 2*Y^5 + Y^3 + 5*Y^2 + 3*Y 
        + 3,
    -T^56 + 1/7*T^55 + 68/343*T^53 - 839/2401*T^52 + 71/343*T^51 + 1048/2401*T^50 + 
        16/2401*T^49 + 423/2401*T^48 - 11/2401*T^47 + 111/343*T^46 - 1590/2401*T^45 
        - 905/2401*T^44 + 867/2401*T^43 + 132/2401*T^42 + 478/2401*T^41 - 
        1590/2401*T^40 + 57/2401*T^39 + 188/2401*T^38 + 139/2401*T^37 - 
        306/2401*T^36 - 145/2401*T^35 + 323/2401*T^34 + 235/2401*T^33 + 
        723/2401*T^32 + 755/2401*T^31 + 761/2401*T^30 - 229/2401*T^29 + 
        229/2401*T^27 - 761/2401*T^26 - 755/2401*T^25 - 723/2401*T^24 - 
        235/2401*T^23 - 323/2401*T^22 + 145/2401*T^21 + 306/2401*T^20 - 
        139/2401*T^19 - 188/2401*T^18 - 57/2401*T^17 + 1590/2401*T^16 - 
        478/2401*T^15 - 132/2401*T^14 - 867/2401*T^13 + 905/2401*T^12 + 
        1590/2401*T^11 - 111/343*T^10 + 11/2401*T^9 - 423/2401*T^8 - 16/2401*T^7 - 
        1048/2401*T^6 - 71/343*T^5 + 839/2401*T^4 - 68/343*T^3 - 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + X*Y^13 + X*Y^12 + 5*X*Y^11 + X*Y^10 + X*Y^8 + 
        6*X*Y^7 + 3*X*Y^6 + 3*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 4*X*Y + 5*X + 4*Y^30 + 
        4*Y^27 + Y^26 + 5*Y^25 + 6*Y^24 + Y^23 + 6*Y^22 + 5*Y^21 + 3*Y^20 + 3*Y^17 +
        4*Y^16 + 4*Y^15 + 2*Y^14 + 3*Y^13 + 4*Y^12 + Y^11 + 6*Y^10 + 3*Y^9 + Y^8 + 
        5*Y^7 + Y^6 + 4*Y^5 + 4*Y^4 + 3*Y^2 + 3*Y + 2,
    T^56 + 9/7*T^55 + 20/49*T^54 + 106/343*T^53 + 197/343*T^52 + 500/2401*T^51 + 
        1395/2401*T^50 + 1938/2401*T^49 + 351/2401*T^48 - 1146/2401*T^47 - 
        2068/2401*T^46 - 1756/2401*T^45 - 135/2401*T^44 - 48/2401*T^43 - 
        1158/2401*T^42 - 2531/2401*T^41 - 2837/2401*T^40 - 2041/2401*T^39 - 
        135/343*T^38 - 80/2401*T^37 - 40/343*T^36 - 1548/2401*T^35 - 1562/2401*T^34 
        + 727/2401*T^33 + 2458/2401*T^32 + 2824/2401*T^31 + 3380/2401*T^30 + 
        2167/2401*T^29 + 1068/2401*T^28 + 2167/2401*T^27 + 3380/2401*T^26 + 
        2824/2401*T^25 + 2458/2401*T^24 + 727/2401*T^23 - 1562/2401*T^22 - 
        1548/2401*T^21 - 40/343*T^20 - 80/2401*T^19 - 135/343*T^18 - 2041/2401*T^17 
        - 2837/2401*T^16 - 2531/2401*T^15 - 1158/2401*T^14 - 48/2401*T^13 - 
        135/2401*T^12 - 1756/2401*T^11 - 2068/2401*T^10 - 1146/2401*T^9 + 
        351/2401*T^8 + 1938/2401*T^7 + 1395/2401*T^6 + 500/2401*T^5 + 197/343*T^4 + 
        106/343*T^3 + 20/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 5*X*Y^9 + 2*X*Y^8 +
        4*X*Y^7 + 6*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + X*Y^2 + 5*X*Y + 2*X + 3*Y^30 + Y^29 
        + 3*Y^28 + 4*Y^27 + Y^26 + 4*Y^25 + Y^24 + 4*Y^22 + 6*Y^20 + 4*Y^19 + 2*Y^18
        + 6*Y^17 + 4*Y^16 + 2*Y^15 + Y^14 + 2*Y^13 + 5*Y^11 + 2*Y^10 + 6*Y^9 + 6*Y^8
        + 6*Y^7 + 3*Y^6 + 3*Y^5 + 5*Y^3 + Y^2 + 3*Y,
    -T^56 + 11/7*T^55 - 39/49*T^54 + 209/343*T^53 - 2655/2401*T^52 + 2566/2401*T^51 
        - 1349/2401*T^50 - 269/2401*T^49 + 229/343*T^48 - 2070/2401*T^47 + 
        2647/2401*T^46 - 2918/2401*T^45 + 1282/2401*T^44 - 138/2401*T^43 - 
        183/2401*T^42 + 99/343*T^41 - 1194/2401*T^40 + 1807/2401*T^39 - 323/343*T^38
        + 1273/2401*T^37 + 671/2401*T^36 - 135/343*T^35 + 250/343*T^34 - 
        3121/2401*T^33 + 313/343*T^32 - 1735/2401*T^31 + 47/49*T^30 - 1320/2401*T^29
        + 1320/2401*T^27 - 47/49*T^26 + 1735/2401*T^25 - 313/343*T^24 + 
        3121/2401*T^23 - 250/343*T^22 + 135/343*T^21 - 671/2401*T^20 - 
        1273/2401*T^19 + 323/343*T^18 - 1807/2401*T^17 + 1194/2401*T^16 - 
        99/343*T^15 + 183/2401*T^14 + 138/2401*T^13 - 1282/2401*T^12 + 
        2918/2401*T^11 - 2647/2401*T^10 + 2070/2401*T^9 - 229/343*T^8 + 269/2401*T^7
        + 1349/2401*T^6 - 2566/2401*T^5 + 2655/2401*T^4 - 209/343*T^3 + 39/49*T^2 - 
        11/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        3*X*Y^8 + X*Y^7 + X*Y^6 + 5*X*Y^5 + X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + X*Y + 2*Y^30
        + 2*Y^29 + 4*Y^28 + 4*Y^27 + 6*Y^26 + 5*Y^25 + Y^24 + 3*Y^23 + 5*Y^22 + 
        4*Y^21 + 4*Y^20 + 6*Y^19 + 3*Y^18 + Y^17 + 2*Y^16 + 4*Y^15 + Y^14 + 6*Y^13 +
        2*Y^11 + 6*Y^10 + 2*Y^9 + 2*Y^8 + 2*Y^7 + 2*Y^6 + 3*Y^5 + 3*Y^4 + Y^3 + 
        5*Y^2 + 5*Y + 3,
    -T^56 + 11/7*T^55 - 37/49*T^54 + 6/343*T^53 + 746/2401*T^52 - 1919/2401*T^51 + 
        3398/2401*T^50 - 1922/2401*T^49 - 45/2401*T^48 - 1424/2401*T^47 + 
        2096/2401*T^46 - 1744/2401*T^45 + 3679/2401*T^44 - 4548/2401*T^43 + 
        891/2401*T^42 + 3154/2401*T^41 - 3127/2401*T^40 + 3312/2401*T^39 - 
        621/343*T^38 + 2438/2401*T^37 + 456/2401*T^36 + 530/2401*T^35 - 
        2231/2401*T^34 + 346/2401*T^33 - 50/2401*T^32 + 2288/2401*T^31 - 
        1073/2401*T^30 - 171/343*T^29 + 171/343*T^27 + 1073/2401*T^26 - 
        2288/2401*T^25 + 50/2401*T^24 - 346/2401*T^23 + 2231/2401*T^22 - 
        530/2401*T^21 - 456/2401*T^20 - 2438/2401*T^19 + 621/343*T^18 - 
        3312/2401*T^17 + 3127/2401*T^16 - 3154/2401*T^15 - 891/2401*T^14 + 
        4548/2401*T^13 - 3679/2401*T^12 + 1744/2401*T^11 - 2096/2401*T^10 + 
        1424/2401*T^9 + 45/2401*T^8 + 1922/2401*T^7 - 3398/2401*T^6 + 1919/2401*T^5 
        - 746/2401*T^4 - 6/343*T^3 + 37/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 
        6*X*Y^8 + 4*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 5*X*Y 
        + 5*Y^30 + 5*Y^29 + 6*Y^28 + 4*Y^27 + 2*Y^26 + 5*Y^25 + Y^24 + 2*Y^23 + Y^22
        + 4*Y^21 + 3*Y^20 + 6*Y^19 + Y^18 + Y^17 + 2*Y^16 + 3*Y^15 + 3*Y^14 + 5*Y^13
        + 4*Y^12 + 6*Y^11 + 5*Y^10 + Y^9 + 4*Y^8 + 3*Y^7 + Y^5 + 3*Y^4 + Y^3 + 3*Y +
        6,
    T^56 + 10/7*T^55 + 6/49*T^54 + 8/343*T^53 + 1038/2401*T^52 - 3221/2401*T^51 - 
        3177/2401*T^50 + 1510/2401*T^49 - 1345/2401*T^48 - 2267/2401*T^47 + 
        3851/2401*T^46 + 1667/2401*T^45 - 390/343*T^44 + 1697/2401*T^43 + 
        152/343*T^42 - 3135/2401*T^41 + 893/2401*T^40 + 284/343*T^39 - 374/343*T^38 
        - 995/2401*T^37 + 858/2401*T^36 - 2413/2401*T^35 - 2173/2401*T^34 + 
        310/2401*T^33 - 195/2401*T^32 + 120/2401*T^31 + 1895/2401*T^30 + 25/49*T^29 
        + 88/2401*T^28 + 25/49*T^27 + 1895/2401*T^26 + 120/2401*T^25 - 195/2401*T^24
        + 310/2401*T^23 - 2173/2401*T^22 - 2413/2401*T^21 + 858/2401*T^20 - 
        995/2401*T^19 - 374/343*T^18 + 284/343*T^17 + 893/2401*T^16 - 3135/2401*T^15
        + 152/343*T^14 + 1697/2401*T^13 - 390/343*T^12 + 1667/2401*T^11 + 
        3851/2401*T^10 - 2267/2401*T^9 - 1345/2401*T^8 + 1510/2401*T^7 - 
        3177/2401*T^6 - 3221/2401*T^5 + 1038/2401*T^4 + 8/343*T^3 + 6/49*T^2 + 
        10/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 5*X*Y^12 + 4*X*Y^11 + 2*X*Y^9 + 6*X*Y^8 + 3*X*Y^7 + 
        5*X*Y^5 + 4*X*Y^3 + 3*X*Y^2 + 5*X*Y + 6*X + 4*Y^30 + 6*Y^29 + 2*Y^28 + 
        6*Y^27 + 6*Y^26 + 3*Y^25 + 5*Y^24 + 5*Y^22 + 4*Y^21 + 3*Y^20 + 6*Y^18 + 
        3*Y^17 + Y^16 + 3*Y^15 + 6*Y^14 + 5*Y^13 + 6*Y^12 + 5*Y^11 + 4*Y^10 + 4*Y^9 
        + 2*Y^8 + Y^7 + 6*Y^6 + Y^5 + 4*Y^4 + 4*Y^3 + 5*Y^2 + 5*Y + 4,
    T^56 + 8/7*T^55 - 25/49*T^54 - 451/343*T^53 - 1565/2401*T^52 - 677/2401*T^51 - 
        53/2401*T^50 + 1982/2401*T^49 + 2665/2401*T^48 + 1474/2401*T^47 - 
        349/2401*T^46 - 1712/2401*T^45 - 1139/2401*T^44 - 89/343*T^43 - 
        900/2401*T^42 + 762/2401*T^41 + 1684/2401*T^40 + 33/2401*T^39 + 
        178/2401*T^38 + 475/2401*T^37 - 1062/2401*T^36 - 925/2401*T^35 + 
        275/2401*T^34 - 55/2401*T^33 - 725/2401*T^32 - 590/2401*T^31 - 790/2401*T^30
        + 458/2401*T^29 + 284/343*T^28 + 458/2401*T^27 - 790/2401*T^26 - 
        590/2401*T^25 - 725/2401*T^24 - 55/2401*T^23 + 275/2401*T^22 - 925/2401*T^21
        - 1062/2401*T^20 + 475/2401*T^19 + 178/2401*T^18 + 33/2401*T^17 + 
        1684/2401*T^16 + 762/2401*T^15 - 900/2401*T^14 - 89/343*T^13 - 
        1139/2401*T^12 - 1712/2401*T^11 - 349/2401*T^10 + 1474/2401*T^9 + 
        2665/2401*T^8 + 1982/2401*T^7 - 53/2401*T^6 - 677/2401*T^5 - 1565/2401*T^4 -
        451/343*T^3 - 25/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 
        X*Y^8 + 3*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + X*Y^2 + 2*X*Y + 
        6*X + 6*Y^30 + 2*Y^29 + Y^28 + Y^27 + 5*Y^26 + 2*Y^25 + Y^24 + 3*Y^22 + 
        5*Y^21 + 3*Y^19 + 5*Y^18 + 3*Y^17 + 6*Y^14 + 6*Y^13 + 2*Y^12 + 4*Y^11 + 
        6*Y^10 + Y^9 + 4*Y^8 + 4*Y^7 + Y^6 + 5*Y^5 + 6*Y^4 + 2*Y^3 + 6*Y^2 + 4*Y + 
        3,
    -T^56 - 8/7*T^55 - 9/49*T^54 - 11/49*T^53 - 128/2401*T^52 + 230/2401*T^51 - 
        1629/2401*T^50 - 1493/2401*T^49 - 265/2401*T^48 + 1049/2401*T^47 + 
        228/343*T^46 + 67/2401*T^45 - 596/2401*T^44 - 958/2401*T^43 - 1534/2401*T^42
        + 661/2401*T^41 + 517/2401*T^40 - 194/343*T^39 - 221/343*T^38 - 
        1587/2401*T^37 + 141/2401*T^36 + 918/2401*T^35 - 83/343*T^34 - 649/2401*T^33
        - 1213/2401*T^32 - 222/2401*T^31 + 2013/2401*T^30 + 1065/2401*T^29 - 
        1065/2401*T^27 - 2013/2401*T^26 + 222/2401*T^25 + 1213/2401*T^24 + 
        649/2401*T^23 + 83/343*T^22 - 918/2401*T^21 - 141/2401*T^20 + 1587/2401*T^19
        + 221/343*T^18 + 194/343*T^17 - 517/2401*T^16 - 661/2401*T^15 + 
        1534/2401*T^14 + 958/2401*T^13 + 596/2401*T^12 - 67/2401*T^11 - 228/343*T^10
        - 1049/2401*T^9 + 265/2401*T^8 + 1493/2401*T^7 + 1629/2401*T^6 - 
        230/2401*T^5 + 128/2401*T^4 + 11/49*T^3 + 9/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 3*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + X*Y^8 + 
        X*Y^7 + 3*X*Y^5 + X*Y^4 + 3*X*Y^3 + 4*X*Y + 2*X + 6*Y^30 + 4*Y^29 + 4*Y^28 +
        4*Y^26 + 6*Y^25 + 5*Y^24 + 3*Y^23 + 5*Y^22 + 2*Y^21 + 5*Y^20 + 5*Y^19 + 
        3*Y^18 + 4*Y^17 + 6*Y^16 + Y^15 + 2*Y^14 + 4*Y^13 + 3*Y^12 + 2*Y^11 + 4*Y^10
        + 5*Y^9 + Y^8 + 5*Y^7 + 3*Y^6 + 6*Y^3 + Y^2 + 2*Y,
    T^56 + 2*T^55 + 114/49*T^54 + 564/343*T^53 + 1399/2401*T^52 - 1591/2401*T^51 - 
        4461/2401*T^50 - 4703/2401*T^49 - 4721/2401*T^48 - 3028/2401*T^47 - 
        1452/2401*T^46 + 92/2401*T^45 + 1884/2401*T^44 + 419/343*T^43 + 453/343*T^42
        + 1384/2401*T^41 + 116/343*T^40 - 2/343*T^39 - 514/2401*T^38 + 449/2401*T^37
        + 1493/2401*T^36 + 3212/2401*T^35 + 3054/2401*T^34 + 2497/2401*T^33 - 
        1/49*T^32 - 2095/2401*T^31 - 2461/2401*T^30 - 3386/2401*T^29 - 437/343*T^28 
        - 3386/2401*T^27 - 2461/2401*T^26 - 2095/2401*T^25 - 1/49*T^24 + 
        2497/2401*T^23 + 3054/2401*T^22 + 3212/2401*T^21 + 1493/2401*T^20 + 
        449/2401*T^19 - 514/2401*T^18 - 2/343*T^17 + 116/343*T^16 + 1384/2401*T^15 +
        453/343*T^14 + 419/343*T^13 + 1884/2401*T^12 + 92/2401*T^11 - 1452/2401*T^10
        - 3028/2401*T^9 - 4721/2401*T^8 - 4703/2401*T^7 - 4461/2401*T^6 - 
        1591/2401*T^5 + 1399/2401*T^4 + 564/343*T^3 + 114/49*T^2 + 2*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + X*Y^11 + X*Y^10 + 3*X*Y^9 + 
        5*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 6*X*Y^3 + X*Y^2 + X*Y + X + 3*Y^30 + 5*Y^29 + 
        Y^28 + 6*Y^27 + 3*Y^26 + 3*Y^25 + 3*Y^24 + 6*Y^23 + 2*Y^22 + 5*Y^19 + Y^18 +
        3*Y^17 + 5*Y^16 + Y^15 + 4*Y^14 + Y^13 + 2*Y^12 + 2*Y^11 + Y^10 + 5*Y^8 + 
        Y^7 + 5*Y^5 + 3*Y^4 + 3*Y^3 + 6*Y^2 + 1,
    T^56 - 11/7*T^55 + 86/49*T^54 - 664/343*T^53 + 4002/2401*T^52 - 6943/2401*T^51 +
        8340/2401*T^50 - 9641/2401*T^49 + 11090/2401*T^48 - 9788/2401*T^47 + 
        11852/2401*T^46 - 12717/2401*T^45 + 14579/2401*T^44 - 15688/2401*T^43 + 
        14689/2401*T^42 - 14874/2401*T^41 + 13520/2401*T^40 - 15315/2401*T^39 + 
        16529/2401*T^38 - 17133/2401*T^37 + 2323/343*T^36 - 13451/2401*T^35 + 
        13590/2401*T^34 - 12837/2401*T^33 + 14627/2401*T^32 - 14608/2401*T^31 + 
        13431/2401*T^30 - 12858/2401*T^29 + 10923/2401*T^28 - 12858/2401*T^27 + 
        13431/2401*T^26 - 14608/2401*T^25 + 14627/2401*T^24 - 12837/2401*T^23 + 
        13590/2401*T^22 - 13451/2401*T^21 + 2323/343*T^20 - 17133/2401*T^19 + 
        16529/2401*T^18 - 15315/2401*T^17 + 13520/2401*T^16 - 14874/2401*T^15 + 
        14689/2401*T^14 - 15688/2401*T^13 + 14579/2401*T^12 - 12717/2401*T^11 + 
        11852/2401*T^10 - 9788/2401*T^9 + 11090/2401*T^8 - 9641/2401*T^7 + 
        8340/2401*T^6 - 6943/2401*T^5 + 4002/2401*T^4 - 664/343*T^3 + 86/49*T^2 - 
        11/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 3*X*Y^8 + 4*X*Y^7 +
        4*X*Y^6 + 2*X*Y^5 + X*Y^4 + X*Y^3 + 2*X*Y + 5*X + 4*Y^30 + 5*Y^29 + 5*Y^28 +
        3*Y^27 + 3*Y^26 + Y^25 + 2*Y^24 + 2*Y^23 + 4*Y^22 + Y^21 + 2*Y^20 + 2*Y^19 +
        3*Y^18 + 2*Y^17 + 2*Y^16 + Y^15 + 6*Y^14 + 4*Y^13 + 6*Y^11 + 4*Y^9 + 3*Y^8 +
        2*Y^7 + 2*Y^5 + 3*Y^4 + 4*Y^3 + Y^2 + 4*Y + 5,
    T^56 + 6/7*T^55 - 40/49*T^54 - 402/343*T^53 - 2518/2401*T^52 - 76/2401*T^51 + 
        2927/2401*T^50 + 4124/2401*T^49 + 170/343*T^48 - 4374/2401*T^47 - 
        4414/2401*T^46 - 205/343*T^45 + 2432/2401*T^44 + 5224/2401*T^43 + 
        4106/2401*T^42 - 184/343*T^41 - 5051/2401*T^40 - 3047/2401*T^39 - 12/49*T^38
        + 2141/2401*T^37 + 432/343*T^36 + 557/2401*T^35 - 160/343*T^34 - 
        1699/2401*T^33 - 1447/2401*T^32 - 617/2401*T^31 + 688/2401*T^30 + 
        1282/2401*T^29 + 988/2401*T^28 + 1282/2401*T^27 + 688/2401*T^26 - 
        617/2401*T^25 - 1447/2401*T^24 - 1699/2401*T^23 - 160/343*T^22 + 
        557/2401*T^21 + 432/343*T^20 + 2141/2401*T^19 - 12/49*T^18 - 3047/2401*T^17 
        - 5051/2401*T^16 - 184/343*T^15 + 4106/2401*T^14 + 5224/2401*T^13 + 
        2432/2401*T^12 - 205/343*T^11 - 4414/2401*T^10 - 4374/2401*T^9 + 170/343*T^8
        + 4124/2401*T^7 + 2927/2401*T^6 - 76/2401*T^5 - 2518/2401*T^4 - 402/343*T^3 
        - 40/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 +
        5*X*Y^7 + 3*X*Y^6 + 4*X*Y^5 + 2*X*Y^3 + 3*X*Y^2 + 5*X*Y + 4*Y^30 + Y^29 + 
        5*Y^28 + 4*Y^27 + 4*Y^26 + Y^25 + 3*Y^24 + 2*Y^23 + 4*Y^22 + 3*Y^21 + 3*Y^20
        + Y^19 + 3*Y^18 + 6*Y^17 + 2*Y^16 + 2*Y^15 + 2*Y^14 + 3*Y^13 + 2*Y^12 + 
        3*Y^11 + 4*Y^10 + 5*Y^9 + 5*Y^8 + 6*Y^6 + 4*Y^5 + 3*Y^4 + 2*Y^3 + Y^2 + 6,
    -T^56 - 2*T^55 - 79/49*T^54 - 223/343*T^53 - 347/2401*T^52 + 467/2401*T^51 + 
        3177/2401*T^50 + 4549/2401*T^49 + 372/343*T^48 + 195/2401*T^47 - 
        1182/2401*T^46 - 1735/2401*T^45 - 2581/2401*T^44 - 1802/2401*T^43 + 
        342/2401*T^42 + 1703/2401*T^41 + 365/343*T^40 + 3089/2401*T^39 + 
        3380/2401*T^38 + 2011/2401*T^37 + 12/343*T^36 - 1366/2401*T^35 - 
        2197/2401*T^34 - 1602/2401*T^33 + 75/2401*T^32 + 1649/2401*T^31 + 
        1886/2401*T^30 + 972/2401*T^29 - 972/2401*T^27 - 1886/2401*T^26 - 
        1649/2401*T^25 - 75/2401*T^24 + 1602/2401*T^23 + 2197/2401*T^22 + 
        1366/2401*T^21 - 12/343*T^20 - 2011/2401*T^19 - 3380/2401*T^18 - 
        3089/2401*T^17 - 365/343*T^16 - 1703/2401*T^15 - 342/2401*T^14 + 
        1802/2401*T^13 + 2581/2401*T^12 + 1735/2401*T^11 + 1182/2401*T^10 - 
        195/2401*T^9 - 372/343*T^8 - 4549/2401*T^7 - 3177/2401*T^6 - 467/2401*T^5 + 
        347/2401*T^4 + 223/343*T^3 + 79/49*T^2 + 2*T + 1
*], [*
    X^3 + 4*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + X*Y^11 + 3*X*Y^9 + 3*X*Y^8 + 3*X*Y^7 + 
        6*X*Y^6 + 6*X*Y^4 + 2*X*Y^3 + X + 4*Y^30 + Y^29 + Y^28 + 4*Y^27 + Y^26 + 
        Y^25 + 6*Y^24 + 2*Y^23 + Y^21 + 2*Y^19 + 4*Y^18 + 4*Y^16 + 3*Y^13 + 5*Y^12 +
        2*Y^11 + 6*Y^10 + 5*Y^9 + 4*Y^8 + Y^7 + 5*Y^6 + Y^5 + 4*Y^4 + 3*Y^3 + Y^2 + 
        4*Y + 3,
    T^56 - 4/7*T^55 + 3/49*T^54 + 50/343*T^53 + 139/2401*T^52 - 951/2401*T^51 - 
        989/2401*T^50 + 1244/2401*T^49 - 37/2401*T^48 - 1025/2401*T^47 + 
        708/2401*T^46 + 472/2401*T^45 + 417/2401*T^44 - 1398/2401*T^43 + 
        457/2401*T^42 + 545/2401*T^41 - 1233/2401*T^40 + 281/2401*T^39 + 
        600/2401*T^38 + 453/2401*T^37 - 226/2401*T^36 - 908/2401*T^35 + 
        177/2401*T^34 - 1142/2401*T^33 - 214/2401*T^32 + 554/2401*T^31 - 
        361/2401*T^30 + 1041/2401*T^29 + 416/2401*T^28 + 1041/2401*T^27 - 
        361/2401*T^26 + 554/2401*T^25 - 214/2401*T^24 - 1142/2401*T^23 + 
        177/2401*T^22 - 908/2401*T^21 - 226/2401*T^20 + 453/2401*T^19 + 
        600/2401*T^18 + 281/2401*T^17 - 1233/2401*T^16 + 545/2401*T^15 + 
        457/2401*T^14 - 1398/2401*T^13 + 417/2401*T^12 + 472/2401*T^11 + 
        708/2401*T^10 - 1025/2401*T^9 - 37/2401*T^8 + 1244/2401*T^7 - 989/2401*T^6 -
        951/2401*T^5 + 139/2401*T^4 + 50/343*T^3 + 3/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 
        + X*Y^8 + 5*X*Y^7 + 3*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 2*X*Y 
        + X + 4*Y^30 + 6*Y^29 + 4*Y^28 + 4*Y^27 + 6*Y^26 + 4*Y^25 + 2*Y^24 + 2*Y^23 
        + Y^22 + 4*Y^21 + 3*Y^20 + 5*Y^19 + Y^18 + Y^17 + 5*Y^16 + 2*Y^13 + 6*Y^11 +
        4*Y^9 + 5*Y^8 + 6*Y^7 + 6*Y^6 + 6*Y^5 + 5*Y^3,
    -T^56 + 6/7*T^55 + 15/49*T^54 - 453/343*T^53 + 85/2401*T^52 + 492/343*T^51 - 
        319/343*T^50 - 3324/2401*T^49 + 2866/2401*T^48 + 1599/2401*T^47 - 
        4293/2401*T^46 + 494/2401*T^45 + 3901/2401*T^44 - 1996/2401*T^43 - 
        443/343*T^42 + 3254/2401*T^41 + 1447/2401*T^40 - 4318/2401*T^39 + 
        946/2401*T^38 + 4497/2401*T^37 - 3161/2401*T^36 - 1853/2401*T^35 + 
        3867/2401*T^34 + 235/2401*T^33 - 4512/2401*T^32 + 2607/2401*T^31 + 
        3408/2401*T^30 - 722/343*T^29 + 722/343*T^27 - 3408/2401*T^26 - 
        2607/2401*T^25 + 4512/2401*T^24 - 235/2401*T^23 - 3867/2401*T^22 + 
        1853/2401*T^21 + 3161/2401*T^20 - 4497/2401*T^19 - 946/2401*T^18 + 
        4318/2401*T^17 - 1447/2401*T^16 - 3254/2401*T^15 + 443/343*T^14 + 
        1996/2401*T^13 - 3901/2401*T^12 - 494/2401*T^11 + 4293/2401*T^10 - 
        1599/2401*T^9 - 2866/2401*T^8 + 3324/2401*T^7 + 319/343*T^6 - 492/343*T^5 - 
        85/2401*T^4 + 453/343*T^3 - 15/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        3*X*Y^8 + 4*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 4*X*Y 
        + X + Y^30 + 4*Y^28 + 4*Y^27 + 6*Y^26 + 5*Y^25 + Y^24 + 3*Y^22 + 2*Y^21 + 
        2*Y^20 + 2*Y^19 + 3*Y^18 + 4*Y^17 + 3*Y^16 + 3*Y^15 + 3*Y^14 + Y^13 + Y^12 +
        3*Y^11 + 3*Y^10 + 5*Y^9 + Y^8 + 3*Y^6 + 2*Y^4 + 5*Y^3 + 5*Y^2 + 6,
    T^56 - 3/7*T^55 - 36/49*T^54 + 33/343*T^53 + 975/2401*T^52 - 213/2401*T^51 - 
        243/343*T^50 - 134/2401*T^49 + 1860/2401*T^48 - 423/2401*T^47 - 
        909/2401*T^46 + 1846/2401*T^45 - 474/2401*T^44 + 899/2401*T^43 - 
        1356/2401*T^42 - 58/2401*T^41 - 664/2401*T^40 + 118/2401*T^39 - 
        592/2401*T^38 + 48/2401*T^37 - 736/2401*T^36 + 1579/2401*T^35 + 
        1341/2401*T^34 - 830/2401*T^33 + 16/49*T^32 - 912/2401*T^31 + 797/2401*T^30 
        - 1178/2401*T^29 + 27/343*T^28 - 1178/2401*T^27 + 797/2401*T^26 - 
        912/2401*T^25 + 16/49*T^24 - 830/2401*T^23 + 1341/2401*T^22 + 1579/2401*T^21
        - 736/2401*T^20 + 48/2401*T^19 - 592/2401*T^18 + 118/2401*T^17 - 
        664/2401*T^16 - 58/2401*T^15 - 1356/2401*T^14 + 899/2401*T^13 - 
        474/2401*T^12 + 1846/2401*T^11 - 909/2401*T^10 - 423/2401*T^9 + 
        1860/2401*T^8 - 134/2401*T^7 - 243/343*T^6 - 213/2401*T^5 + 975/2401*T^4 + 
        33/343*T^3 - 36/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^13 + 5*X*Y^12 + X*Y^11 + X*Y^10 + X*Y^9 + 2*X*Y^8 + X*Y^7
        + 5*X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 4*X*Y^2 + 3*X + 4*Y^30 + 3*Y^29 + 5*Y^28 + 
        Y^27 + 5*Y^26 + 2*Y^25 + 6*Y^24 + 4*Y^23 + 6*Y^22 + 2*Y^21 + 4*Y^19 + 3*Y^18
        + 4*Y^17 + 6*Y^16 + 5*Y^14 + 3*Y^13 + 4*Y^12 + 6*Y^10 + 3*Y^9 + 2*Y^8 + 
        6*Y^7 + 2*Y^6 + 4*Y^4 + 6*Y^3 + 5*Y^2 + 4*Y + 6,
    T^56 + 4/7*T^55 - 5/49*T^54 + 16/343*T^53 - 1542/2401*T^52 - 1625/2401*T^51 - 
        1534/2401*T^50 - 1502/2401*T^49 - 388/2401*T^48 - 16/2401*T^47 + 57/343*T^46
        + 1181/2401*T^45 + 794/2401*T^44 + 365/2401*T^43 - 592/2401*T^42 - 
        2/343*T^41 + 442/2401*T^40 - 1/49*T^39 + 629/2401*T^38 - 162/2401*T^37 + 
        46/343*T^36 + 769/2401*T^35 + 1002/2401*T^34 + 228/343*T^33 + 97/343*T^32 - 
        213/2401*T^31 - 1503/2401*T^30 - 1878/2401*T^29 - 208/343*T^28 - 
        1878/2401*T^27 - 1503/2401*T^26 - 213/2401*T^25 + 97/343*T^24 + 228/343*T^23
        + 1002/2401*T^22 + 769/2401*T^21 + 46/343*T^20 - 162/2401*T^19 + 
        629/2401*T^18 - 1/49*T^17 + 442/2401*T^16 - 2/343*T^15 - 592/2401*T^14 + 
        365/2401*T^13 + 794/2401*T^12 + 1181/2401*T^11 + 57/343*T^10 - 16/2401*T^9 -
        388/2401*T^8 - 1502/2401*T^7 - 1534/2401*T^6 - 1625/2401*T^5 - 1542/2401*T^4
        + 16/343*T^3 - 5/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + X*Y^10 + 5*X*Y^9 + X*Y^7 + 5*X*Y^6 + 
        4*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 2*X*Y + 5*X + 5*Y^30 + 2*Y^29 + 
        3*Y^28 + 6*Y^27 + 3*Y^26 + 5*Y^25 + 2*Y^24 + Y^23 + 2*Y^22 + 6*Y^21 + 2*Y^20
        + 6*Y^19 + 4*Y^18 + 5*Y^17 + 3*Y^16 + 5*Y^15 + 6*Y^14 + 6*Y^13 + 3*Y^12 + 
        3*Y^11 + 5*Y^10 + Y^9 + 4*Y^7 + 3*Y^6 + 2*Y^4 + Y^3 + 3*Y^2 + 3*Y + 5,
    -T^56 + 8/7*T^55 - 5/49*T^54 + 6/343*T^53 - 862/2401*T^52 - 689/2401*T^51 + 
        1096/2401*T^50 + 137/2401*T^49 + 1419/2401*T^48 - 794/2401*T^47 - 
        1588/2401*T^46 + 1108/2401*T^45 - 377/2401*T^44 + 159/343*T^43 - 
        594/2401*T^42 + 366/2401*T^41 - 205/343*T^40 + 319/2401*T^39 + 55/343*T^38 +
        82/343*T^37 + 894/2401*T^36 - 1308/2401*T^35 - 887/2401*T^34 - 4/49*T^33 + 
        1275/2401*T^32 + 730/2401*T^31 - 820/2401*T^30 - 1518/2401*T^29 + 
        1518/2401*T^27 + 820/2401*T^26 - 730/2401*T^25 - 1275/2401*T^24 + 4/49*T^23 
        + 887/2401*T^22 + 1308/2401*T^21 - 894/2401*T^20 - 82/343*T^19 - 55/343*T^18
        - 319/2401*T^17 + 205/343*T^16 - 366/2401*T^15 + 594/2401*T^14 - 
        159/343*T^13 + 377/2401*T^12 - 1108/2401*T^11 + 1588/2401*T^10 + 
        794/2401*T^9 - 1419/2401*T^8 - 137/2401*T^7 - 1096/2401*T^6 + 689/2401*T^5 +
        862/2401*T^4 - 6/343*T^3 + 5/49*T^2 - 8/7*T + 1
*], [*
    X^3 + X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + X*Y^8 + 2*X*Y^7 + 6*X*Y^3 + X*Y^2
        + 3*X*Y + X + Y^30 + 5*Y^29 + 2*Y^28 + 6*Y^27 + 3*Y^26 + 2*Y^25 + 5*Y^24 + 
        2*Y^23 + 3*Y^22 + 4*Y^21 + 5*Y^20 + 4*Y^19 + 5*Y^17 + 6*Y^16 + 3*Y^15 + 
        2*Y^14 + 4*Y^13 + 5*Y^12 + 6*Y^11 + 3*Y^10 + 5*Y^9 + 4*Y^8 + 6*Y^7 + 6*Y^6 +
        5*Y^3 + 5*Y^2 + 4*Y + 1,
    -T^56 + 13/7*T^55 - 115/49*T^54 + 932/343*T^53 - 6088/2401*T^52 + 5863/2401*T^51
        - 2729/2401*T^50 - 144/343*T^49 + 3881/2401*T^48 - 6193/2401*T^47 + 
        6407/2401*T^46 - 6017/2401*T^45 + 5521/2401*T^44 - 3691/2401*T^43 + 
        2354/2401*T^42 - 223/343*T^41 + 440/2401*T^40 - 1055/2401*T^39 - 
        387/2401*T^38 + 1817/2401*T^37 - 3599/2401*T^36 + 5664/2401*T^35 - 
        671/343*T^34 + 5631/2401*T^33 - 814/343*T^32 + 4523/2401*T^31 - 
        2943/2401*T^30 + 482/2401*T^29 - 482/2401*T^27 + 2943/2401*T^26 - 
        4523/2401*T^25 + 814/343*T^24 - 5631/2401*T^23 + 671/343*T^22 - 
        5664/2401*T^21 + 3599/2401*T^20 - 1817/2401*T^19 + 387/2401*T^18 + 
        1055/2401*T^17 - 440/2401*T^16 + 223/343*T^15 - 2354/2401*T^14 + 
        3691/2401*T^13 - 5521/2401*T^12 + 6017/2401*T^11 - 6407/2401*T^10 + 
        6193/2401*T^9 - 3881/2401*T^8 + 144/343*T^7 + 2729/2401*T^6 - 5863/2401*T^5 
        + 6088/2401*T^4 - 932/343*T^3 + 115/49*T^2 - 13/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 2*X*Y^10 + 6*X*Y^9 + 3*X*Y^8 +
        3*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 5*X*Y + 4*Y^30 +
        6*Y^29 + 4*Y^28 + 6*Y^25 + Y^24 + 4*Y^23 + 5*Y^21 + 3*Y^20 + 3*Y^19 + 2*Y^17
        + 5*Y^16 + Y^15 + 3*Y^14 + 2*Y^13 + 4*Y^12 + 4*Y^11 + Y^10 + 3*Y^9 + 2*Y^7 +
        5*Y^6 + 2*Y^5 + 4*Y^4 + 5*Y^3 + 4*Y^2 + 3,
    T^56 + 5/7*T^55 - 78/49*T^54 - 306/343*T^53 + 4695/2401*T^52 + 2300/2401*T^51 - 
        2721/2401*T^50 + 118/2401*T^49 + 1985/2401*T^48 - 979/2401*T^47 - 
        565/2401*T^46 + 1496/2401*T^45 - 51/2401*T^44 - 356/2401*T^43 + 
        1605/2401*T^42 + 697/2401*T^41 - 642/2401*T^40 - 134/343*T^39 - 
        724/2401*T^38 + 1118/2401*T^37 + 1644/2401*T^36 - 1227/2401*T^35 - 
        435/2401*T^34 + 2120/2401*T^33 - 1220/2401*T^32 - 2553/2401*T^31 + 
        2629/2401*T^30 + 1478/2401*T^29 - 2708/2401*T^28 + 1478/2401*T^27 + 
        2629/2401*T^26 - 2553/2401*T^25 - 1220/2401*T^24 + 2120/2401*T^23 - 
        435/2401*T^22 - 1227/2401*T^21 + 1644/2401*T^20 + 1118/2401*T^19 - 
        724/2401*T^18 - 134/343*T^17 - 642/2401*T^16 + 697/2401*T^15 + 
        1605/2401*T^14 - 356/2401*T^13 - 51/2401*T^12 + 1496/2401*T^11 - 
        565/2401*T^10 - 979/2401*T^9 + 1985/2401*T^8 + 118/2401*T^7 - 2721/2401*T^6 
        + 2300/2401*T^5 + 4695/2401*T^4 - 306/343*T^3 - 78/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 6*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 + 4*X*Y^7 + 
        2*X*Y^5 + 3*X*Y^4 + X*Y^3 + 2*X*Y^2 + 4*X + 2*Y^30 + 3*Y^29 + 6*Y^28 + 
        6*Y^27 + 2*Y^26 + 5*Y^25 + 3*Y^24 + 3*Y^23 + Y^22 + 2*Y^21 + 6*Y^20 + Y^19 +
        3*Y^18 + 2*Y^17 + 5*Y^16 + 4*Y^15 + 5*Y^14 + 4*Y^13 + 6*Y^12 + 3*Y^11 + 
        2*Y^10 + 6*Y^8 + 3*Y^7 + Y^4 + Y^3 + 5*Y^2,
    T^56 + 13/7*T^55 + 39/49*T^54 - 255/343*T^53 - 1231/2401*T^52 + 572/2401*T^51 + 
        398/2401*T^50 - 1205/2401*T^49 - 3432/2401*T^48 - 99/49*T^47 - 118/343*T^46 
        + 5231/2401*T^45 + 5316/2401*T^44 + 487/2401*T^43 - 1942/2401*T^42 - 
        551/2401*T^41 + 2530/2401*T^40 + 4055/2401*T^39 + 528/2401*T^38 - 
        5599/2401*T^37 - 842/343*T^36 - 1150/2401*T^35 + 1982/2401*T^34 + 
        1371/2401*T^33 - 788/2401*T^32 - 2927/2401*T^31 - 1843/2401*T^30 + 
        3526/2401*T^29 + 150/49*T^28 + 3526/2401*T^27 - 1843/2401*T^26 - 
        2927/2401*T^25 - 788/2401*T^24 + 1371/2401*T^23 + 1982/2401*T^22 - 
        1150/2401*T^21 - 842/343*T^20 - 5599/2401*T^19 + 528/2401*T^18 + 
        4055/2401*T^17 + 2530/2401*T^16 - 551/2401*T^15 - 1942/2401*T^14 + 
        487/2401*T^13 + 5316/2401*T^12 + 5231/2401*T^11 - 118/343*T^10 - 99/49*T^9 -
        3432/2401*T^8 - 1205/2401*T^7 + 398/2401*T^6 + 572/2401*T^5 - 1231/2401*T^4 
        - 255/343*T^3 + 39/49*T^2 + 13/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 2*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 5*X*Y^8 +
        4*X*Y^7 + 2*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 3*X + 3*Y^30 + 6*Y^29 + 5*Y^28 + 
        5*Y^27 + 5*Y^26 + Y^25 + 6*Y^23 + Y^22 + 4*Y^21 + 4*Y^20 + 2*Y^19 + 4*Y^18 +
        3*Y^17 + Y^16 + 4*Y^15 + 3*Y^14 + 6*Y^13 + 3*Y^12 + Y^11 + 6*Y^10 + 3*Y^9 + 
        4*Y^8 + 6*Y^7 + 4*Y^6 + 6*Y^5 + 2*Y^3 + 3*Y^2 + Y + 5,
    T^56 - 12/7*T^55 + 2/49*T^54 + 774/343*T^53 - 2888/2401*T^52 - 4414/2401*T^51 + 
        2509/2401*T^50 + 6392/2401*T^49 - 4833/2401*T^48 - 7220/2401*T^47 + 
        8529/2401*T^46 + 627/343*T^45 - 7234/2401*T^44 - 5986/2401*T^43 + 
        9486/2401*T^42 + 5255/2401*T^41 - 12211/2401*T^40 - 142/343*T^39 + 
        9780/2401*T^38 + 100/343*T^37 - 9154/2401*T^36 - 842/2401*T^35 + 
        10272/2401*T^34 - 398/343*T^33 - 5947/2401*T^32 + 585/2401*T^31 + 
        5340/2401*T^30 + 216/343*T^29 - 8046/2401*T^28 + 216/343*T^27 + 
        5340/2401*T^26 + 585/2401*T^25 - 5947/2401*T^24 - 398/343*T^23 + 
        10272/2401*T^22 - 842/2401*T^21 - 9154/2401*T^20 + 100/343*T^19 + 
        9780/2401*T^18 - 142/343*T^17 - 12211/2401*T^16 + 5255/2401*T^15 + 
        9486/2401*T^14 - 5986/2401*T^13 - 7234/2401*T^12 + 627/343*T^11 + 
        8529/2401*T^10 - 7220/2401*T^9 - 4833/2401*T^8 + 6392/2401*T^7 + 
        2509/2401*T^6 - 4414/2401*T^5 - 2888/2401*T^4 + 774/343*T^3 + 2/49*T^2 - 
        12/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 6*X*Y^12 + 3*X*Y^11 + X*Y^10 + 4*X*Y^9 + 4*X*Y^8 + 
        2*X*Y^7 + 4*X*Y^4 + X*Y^3 + 6*X*Y^2 + 5*X*Y + 6*X + 6*Y^30 + 5*Y^28 + 3*Y^27
        + 3*Y^25 + 5*Y^23 + 5*Y^22 + 2*Y^21 + 5*Y^20 + 6*Y^19 + Y^18 + 6*Y^17 + 
        4*Y^15 + 3*Y^14 + 4*Y^13 + 4*Y^12 + 3*Y^11 + 6*Y^9 + 5*Y^8 + 3*Y^7 + 3*Y^6 +
        3*Y^5 + 2*Y^4 + Y^3 + Y^2 + 4*Y + 6,
    T^56 + 11/7*T^55 + 5/7*T^54 + 26/49*T^53 - 442/2401*T^52 - 347/343*T^51 - 
        2581/2401*T^50 - 2536/2401*T^49 - 58/343*T^48 + 1548/2401*T^47 + 
        261/343*T^46 + 1123/2401*T^45 + 1104/2401*T^44 - 677/2401*T^43 - 
        2059/2401*T^42 - 1467/2401*T^41 - 307/343*T^40 + 547/2401*T^39 + 
        2764/2401*T^38 + 2603/2401*T^37 + 2286/2401*T^36 + 558/2401*T^35 - 
        250/343*T^34 - 4044/2401*T^33 - 3511/2401*T^32 - 320/343*T^31 + 
        810/2401*T^30 + 3047/2401*T^29 + 2178/2401*T^28 + 3047/2401*T^27 + 
        810/2401*T^26 - 320/343*T^25 - 3511/2401*T^24 - 4044/2401*T^23 - 
        250/343*T^22 + 558/2401*T^21 + 2286/2401*T^20 + 2603/2401*T^19 + 
        2764/2401*T^18 + 547/2401*T^17 - 307/343*T^16 - 1467/2401*T^15 - 
        2059/2401*T^14 - 677/2401*T^13 + 1104/2401*T^12 + 1123/2401*T^11 + 
        261/343*T^10 + 1548/2401*T^9 - 58/343*T^8 - 2536/2401*T^7 - 2581/2401*T^6 - 
        347/343*T^5 - 442/2401*T^4 + 26/49*T^3 + 5/7*T^2 + 11/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 4*X*Y^8 
        + 4*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 5*X*Y^2 + X*Y + 5*X + 6*Y^30 + 4*Y^29 + 
        5*Y^28 + 4*Y^26 + 4*Y^25 + 3*Y^24 + Y^22 + 3*Y^21 + 5*Y^20 + 2*Y^18 + 2*Y^16
        + 6*Y^15 + 4*Y^14 + 5*Y^13 + 5*Y^12 + 4*Y^11 + 2*Y^10 + 2*Y^9 + 2*Y^8 + 
        4*Y^7 + 5*Y^6 + 4*Y^5 + 5*Y^4 + 2*Y^3 + 6*Y^2 + 5*Y + 6,
    -T^56 - 18/7*T^55 - 2*T^54 + 60/343*T^53 + 3215/2401*T^52 + 2685/2401*T^51 + 
        391/2401*T^50 - 1320/2401*T^49 - 479/2401*T^48 + 1004/2401*T^47 - 
        509/2401*T^46 - 3602/2401*T^45 - 3103/2401*T^44 + 724/2401*T^43 + 
        4467/2401*T^42 + 6509/2401*T^41 + 11/7*T^40 - 1710/2401*T^39 - 
        3288/2401*T^38 - 1152/2401*T^37 + 205/343*T^36 + 334/343*T^35 + 
        850/2401*T^34 - 586/2401*T^33 - 423/2401*T^32 + 934/2401*T^31 + 
        1685/2401*T^30 + 116/343*T^29 - 116/343*T^27 - 1685/2401*T^26 - 
        934/2401*T^25 + 423/2401*T^24 + 586/2401*T^23 - 850/2401*T^22 - 334/343*T^21
        - 205/343*T^20 + 1152/2401*T^19 + 3288/2401*T^18 + 1710/2401*T^17 - 
        11/7*T^16 - 6509/2401*T^15 - 4467/2401*T^14 - 724/2401*T^13 + 3103/2401*T^12
        + 3602/2401*T^11 + 509/2401*T^10 - 1004/2401*T^9 + 479/2401*T^8 + 
        1320/2401*T^7 - 391/2401*T^6 - 2685/2401*T^5 - 3215/2401*T^4 - 60/343*T^3 + 
        2*T^2 + 18/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + X*Y^10 + 2*X*Y^8 + 
        6*X*Y^7 + X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + X*Y^3 + 4*X*Y^2 + 5*X*Y + 2*X + 6*Y^30
        + Y^29 + Y^28 + 3*Y^27 + Y^26 + 5*Y^25 + 2*Y^24 + 6*Y^23 + Y^22 + 2*Y^21 + 
        2*Y^20 + Y^19 + 5*Y^18 + 3*Y^16 + Y^14 + 4*Y^13 + 2*Y^12 + Y^9 + 2*Y^8 + Y^7
        + 2*Y^5 + 3*Y^4 + 5*Y^3 + 5*Y^2 + 6*Y + 1,
    -T^56 + 6/7*T^55 - 18/49*T^54 - 57/343*T^53 + 1556/2401*T^52 + 192/2401*T^51 - 
        1587/2401*T^50 + 978/2401*T^49 + 291/2401*T^48 + 48/2401*T^47 - 
        431/2401*T^46 + 257/2401*T^45 - 526/2401*T^44 - 264/2401*T^43 + 31/2401*T^42
        + 717/2401*T^41 + 486/2401*T^40 - 774/2401*T^39 + 551/2401*T^38 - 
        187/2401*T^37 + 1249/2401*T^36 - 1273/2401*T^35 + 820/2401*T^34 - 
        226/2401*T^33 - 1718/2401*T^32 + 950/2401*T^31 + 578/2401*T^30 - 
        223/2401*T^29 + 223/2401*T^27 - 578/2401*T^26 - 950/2401*T^25 + 
        1718/2401*T^24 + 226/2401*T^23 - 820/2401*T^22 + 1273/2401*T^21 - 
        1249/2401*T^20 + 187/2401*T^19 - 551/2401*T^18 + 774/2401*T^17 - 
        486/2401*T^16 - 717/2401*T^15 - 31/2401*T^14 + 264/2401*T^13 + 526/2401*T^12
        - 257/2401*T^11 + 431/2401*T^10 - 48/2401*T^9 - 291/2401*T^8 - 978/2401*T^7 
        + 1587/2401*T^6 - 192/2401*T^5 - 1556/2401*T^4 + 57/343*T^3 + 18/49*T^2 - 
        6/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 2*X*Y^13 + X*Y^11 + 2*X*Y^10 + 4*X*Y^8 + 6*X*Y^7 + 5*X*Y^6 + 
        2*X*Y^5 + 6*X*Y^4 + X*Y^2 + X*Y + 5*X + Y^30 + 2*Y^29 + 3*Y^28 + 2*Y^27 + 
        2*Y^26 + 6*Y^25 + 2*Y^24 + 4*Y^23 + 2*Y^22 + Y^21 + 2*Y^20 + 2*Y^19 + 2*Y^17
        + Y^16 + 5*Y^15 + Y^14 + 3*Y^13 + 6*Y^12 + Y^11 + 3*Y^9 + 4*Y^8 + Y^7 + 
        4*Y^6 + 4*Y^5 + Y^4 + Y^3 + Y^2 + 5*Y,
    -T^56 - 6/7*T^55 + 1/7*T^54 + 229/343*T^53 + 1790/2401*T^52 + 391/343*T^51 + 
        2011/2401*T^50 + 275/2401*T^49 - 1446/2401*T^48 - 2459/2401*T^47 - 
        1024/2401*T^46 + 220/2401*T^45 - 414/2401*T^44 - 47/343*T^43 + 
        1206/2401*T^42 + 447/2401*T^41 - 345/2401*T^40 - 566/2401*T^39 - 
        1668/2401*T^38 - 370/2401*T^37 + 1205/2401*T^36 + 1367/2401*T^35 + 
        1621/2401*T^34 + 1308/2401*T^33 - 1182/2401*T^32 - 1334/2401*T^31 - 
        1845/2401*T^30 - 2189/2401*T^29 + 2189/2401*T^27 + 1845/2401*T^26 + 
        1334/2401*T^25 + 1182/2401*T^24 - 1308/2401*T^23 - 1621/2401*T^22 - 
        1367/2401*T^21 - 1205/2401*T^20 + 370/2401*T^19 + 1668/2401*T^18 + 
        566/2401*T^17 + 345/2401*T^16 - 447/2401*T^15 - 1206/2401*T^14 + 47/343*T^13
        + 414/2401*T^12 - 220/2401*T^11 + 1024/2401*T^10 + 2459/2401*T^9 + 
        1446/2401*T^8 - 275/2401*T^7 - 2011/2401*T^6 - 391/343*T^5 - 1790/2401*T^4 -
        229/343*T^3 - 1/7*T^2 + 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + 
        5*X*Y^8 + 6*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + X*Y^3 + 2*X*Y^2 + 5*X*Y + 5*X + 
        5*Y^30 + 5*Y^29 + Y^28 + Y^27 + 6*Y^26 + 5*Y^25 + 2*Y^24 + Y^23 + 3*Y^22 + 
        Y^21 + Y^20 + 2*Y^19 + 2*Y^18 + Y^17 + 6*Y^16 + 6*Y^15 + 4*Y^14 + 2*Y^12 + 
        4*Y^10 + 6*Y^9 + 5*Y^8 + 6*Y^7 + 6*Y^6 + 6*Y^5 + 3*Y^4 + 3*Y^3 + 5*Y^2 + Y +
        4,
    T^56 - 1/7*T^55 - 37/49*T^54 + 102/343*T^53 + 1497/2401*T^52 + 1756/2401*T^51 + 
        377/2401*T^50 - 472/343*T^49 - 9/49*T^48 + 3716/2401*T^47 + 1567/2401*T^46 -
        485/2401*T^45 - 2070/2401*T^44 - 341/343*T^43 + 2414/2401*T^42 + 
        3673/2401*T^41 - 1452/2401*T^40 - 2409/2401*T^39 - 1817/2401*T^38 - 
        195/2401*T^37 + 3620/2401*T^36 + 1622/2401*T^35 - 594/343*T^34 - 
        337/343*T^33 + 114/2401*T^32 + 1434/2401*T^31 + 2300/2401*T^30 - 
        1244/2401*T^29 - 4556/2401*T^28 - 1244/2401*T^27 + 2300/2401*T^26 + 
        1434/2401*T^25 + 114/2401*T^24 - 337/343*T^23 - 594/343*T^22 + 
        1622/2401*T^21 + 3620/2401*T^20 - 195/2401*T^19 - 1817/2401*T^18 - 
        2409/2401*T^17 - 1452/2401*T^16 + 3673/2401*T^15 + 2414/2401*T^14 - 
        341/343*T^13 - 2070/2401*T^12 - 485/2401*T^11 + 1567/2401*T^10 + 
        3716/2401*T^9 - 9/49*T^8 - 472/343*T^7 + 377/2401*T^6 + 1756/2401*T^5 + 
        1497/2401*T^4 + 102/343*T^3 - 37/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 6*X*Y^13 + X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 2*X*Y^8 + 
        4*X*Y^6 + 5*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 3*X*Y + 2*X + 3*Y^30 + 2*Y^29 + Y^28
        + Y^27 + Y^26 + 3*Y^25 + 5*Y^24 + 5*Y^23 + 3*Y^21 + 3*Y^20 + Y^19 + 4*Y^18 +
        Y^17 + 5*Y^16 + 6*Y^15 + 6*Y^14 + 2*Y^13 + 2*Y^12 + 6*Y^11 + 6*Y^10 + 4*Y^9 
        + 3*Y^8 + 5*Y^7 + 6*Y^6 + 6*Y^5 + 2*Y^4 + 6*Y^3 + 5*Y^2 + 3*Y + 4,
    -T^56 + 2/7*T^55 + 66/49*T^54 - 564/343*T^53 + 2295/2401*T^52 + 590/343*T^51 - 
        134/49*T^50 + 3014/2401*T^49 + 3674/2401*T^48 - 6660/2401*T^47 + 
        2181/2401*T^46 + 2346/2401*T^45 - 4258/2401*T^44 + 1128/2401*T^43 + 
        2402/2401*T^42 - 1142/2401*T^41 - 1591/2401*T^40 + 220/343*T^39 + 
        1307/2401*T^38 - 3755/2401*T^37 + 53/343*T^36 + 3462/2401*T^35 - 
        3212/2401*T^34 - 586/2401*T^33 + 4687/2401*T^32 - 220/343*T^31 - 
        2694/2401*T^30 + 3746/2401*T^29 - 3746/2401*T^27 + 2694/2401*T^26 + 
        220/343*T^25 - 4687/2401*T^24 + 586/2401*T^23 + 3212/2401*T^22 - 
        3462/2401*T^21 - 53/343*T^20 + 3755/2401*T^19 - 1307/2401*T^18 - 
        220/343*T^17 + 1591/2401*T^16 + 1142/2401*T^15 - 2402/2401*T^14 - 
        1128/2401*T^13 + 4258/2401*T^12 - 2346/2401*T^11 - 2181/2401*T^10 + 
        6660/2401*T^9 - 3674/2401*T^8 - 3014/2401*T^7 + 134/49*T^6 - 590/343*T^5 - 
        2295/2401*T^4 + 564/343*T^3 - 66/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 6*X*Y^8 
        + 5*X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 5*X*Y + 3*X + Y^30 + 
        2*Y^29 + Y^28 + Y^27 + Y^25 + 5*Y^24 + 3*Y^22 + 4*Y^20 + 5*Y^18 + 6*Y^17 + 
        4*Y^15 + 5*Y^14 + Y^13 + 4*Y^12 + 5*Y^11 + 4*Y^9 + 3*Y^8 + 4*Y^7 + 3*Y^6 + 
        4*Y^5 + 4*Y^4 + 3*Y^3 + 2*Y^2 + 2*Y + 6,
    T^56 + 12/7*T^55 + 107/49*T^54 + 858/343*T^53 + 899/343*T^52 + 6110/2401*T^51 + 
        5877/2401*T^50 + 5485/2401*T^49 + 5583/2401*T^48 + 738/343*T^47 + 
        3807/2401*T^46 + 2647/2401*T^45 + 1257/2401*T^44 + 1397/2401*T^43 + 
        31/343*T^42 - 1254/2401*T^41 - 3404/2401*T^40 - 4386/2401*T^39 - 
        5689/2401*T^38 - 6037/2401*T^37 - 5875/2401*T^36 - 4540/2401*T^35 - 
        3804/2401*T^34 - 4421/2401*T^33 - 4485/2401*T^32 - 4729/2401*T^31 - 
        4784/2401*T^30 - 5500/2401*T^29 - 5105/2401*T^28 - 5500/2401*T^27 - 
        4784/2401*T^26 - 4729/2401*T^25 - 4485/2401*T^24 - 4421/2401*T^23 - 
        3804/2401*T^22 - 4540/2401*T^21 - 5875/2401*T^20 - 6037/2401*T^19 - 
        5689/2401*T^18 - 4386/2401*T^17 - 3404/2401*T^16 - 1254/2401*T^15 + 
        31/343*T^14 + 1397/2401*T^13 + 1257/2401*T^12 + 2647/2401*T^11 + 
        3807/2401*T^10 + 738/343*T^9 + 5583/2401*T^8 + 5485/2401*T^7 + 5877/2401*T^6
        + 6110/2401*T^5 + 899/343*T^4 + 858/343*T^3 + 107/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^12 + X*Y^11 + 4*X*Y^10 + X*Y^9 + X*Y^8 + 6*X*Y^7 + 
        3*X*Y^6 + X*Y^5 + X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 4*X*Y + 5*X + 6*Y^30 + 2*Y^29 
        + 6*Y^28 + Y^27 + 4*Y^26 + 4*Y^25 + 3*Y^24 + 3*Y^23 + 4*Y^22 + 3*Y^21 + Y^20
        + 2*Y^19 + Y^18 + 3*Y^17 + 6*Y^16 + 5*Y^15 + 6*Y^14 + 5*Y^12 + 4*Y^11 + 
        6*Y^10 + 4*Y^9 + 5*Y^8 + 5*Y^7 + 2*Y^6 + 4*Y^5 + 2*Y^3 + 4*Y^2 + 5*Y + 3,
    T^56 + 2/7*T^55 - 45/49*T^54 + 4/343*T^53 + 989/2401*T^52 + 82/2401*T^51 - 
        19/2401*T^50 + 421/2401*T^49 + 64/343*T^48 - 1543/2401*T^47 - 731/2401*T^46 
        + 850/2401*T^45 - 185/2401*T^44 + 125/2401*T^43 + 591/2401*T^42 - 
        538/2401*T^41 - 1506/2401*T^40 + 205/2401*T^39 + 1308/2401*T^38 - 
        186/2401*T^37 - 25/2401*T^36 + 288/2401*T^35 - 639/2401*T^34 - 186/2401*T^33
        + 256/2401*T^32 + 606/2401*T^31 - 228/2401*T^30 - 640/2401*T^29 - 
        345/2401*T^28 - 640/2401*T^27 - 228/2401*T^26 + 606/2401*T^25 + 
        256/2401*T^24 - 186/2401*T^23 - 639/2401*T^22 + 288/2401*T^21 - 25/2401*T^20
        - 186/2401*T^19 + 1308/2401*T^18 + 205/2401*T^17 - 1506/2401*T^16 - 
        538/2401*T^15 + 591/2401*T^14 + 125/2401*T^13 - 185/2401*T^12 + 
        850/2401*T^11 - 731/2401*T^10 - 1543/2401*T^9 + 64/343*T^8 + 421/2401*T^7 - 
        19/2401*T^6 + 82/2401*T^5 + 989/2401*T^4 + 4/343*T^3 - 45/49*T^2 + 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + X*Y^12 + 4*X*Y^11 + X*Y^10 + X*Y^8 + 
        3*X*Y^7 + 6*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 5*X + 3*Y^30 + 5*Y^29 + 
        5*Y^28 + 5*Y^27 + 2*Y^26 + Y^25 + 3*Y^24 + Y^23 + 6*Y^22 + 4*Y^21 + 6*Y^20 +
        2*Y^19 + Y^18 + 5*Y^17 + Y^16 + 3*Y^15 + Y^14 + 5*Y^13 + Y^11 + 3*Y^10 + 
        2*Y^9 + 2*Y^8 + 5*Y^7 + 3*Y^6 + 6*Y^5 + 6*Y^3 + 5*Y^2 + 3*Y + 3,
    -T^56 + T^55 + 32/49*T^54 - 4/343*T^53 - 58/49*T^52 - 2740/2401*T^51 + 
        3909/2401*T^50 + 1629/2401*T^49 - 62/343*T^48 - 1817/2401*T^47 - 
        237/343*T^46 + 163/343*T^45 + 1243/2401*T^44 - 34/2401*T^43 + 860/2401*T^42 
        - 1881/2401*T^41 + 565/2401*T^40 + 299/2401*T^39 + 170/2401*T^38 - 
        354/2401*T^37 - 1667/2401*T^36 + 2489/2401*T^35 + 2091/2401*T^34 - 
        94/343*T^33 - 3772/2401*T^32 - 1839/2401*T^31 + 3433/2401*T^30 + 
        3721/2401*T^29 - 3721/2401*T^27 - 3433/2401*T^26 + 1839/2401*T^25 + 
        3772/2401*T^24 + 94/343*T^23 - 2091/2401*T^22 - 2489/2401*T^21 + 
        1667/2401*T^20 + 354/2401*T^19 - 170/2401*T^18 - 299/2401*T^17 - 
        565/2401*T^16 + 1881/2401*T^15 - 860/2401*T^14 + 34/2401*T^13 - 
        1243/2401*T^12 - 163/343*T^11 + 237/343*T^10 + 1817/2401*T^9 + 62/343*T^8 - 
        1629/2401*T^7 - 3909/2401*T^6 + 2740/2401*T^5 + 58/49*T^4 + 4/343*T^3 - 
        32/49*T^2 - T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + X*Y^10 + 3*X*Y^9 + 
        4*X*Y^8 + 3*X*Y^7 + X*Y^6 + 6*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + X*Y^2 + X + 6*Y^30
        + 2*Y^29 + 4*Y^28 + 6*Y^27 + 6*Y^26 + Y^25 + 5*Y^24 + Y^23 + 6*Y^22 + 4*Y^21
        + 2*Y^20 + 6*Y^19 + 4*Y^18 + 6*Y^17 + 3*Y^16 + 5*Y^15 + 3*Y^14 + Y^12 + Y^11
        + 2*Y^10 + 6*Y^9 + Y^8 + 3*Y^7 + 6*Y^6 + 4*Y^5 + 5*Y^3 + Y^2 + 2*Y + 1,
    -T^56 - 8/7*T^55 + 8/7*T^54 + 48/49*T^53 - T^52 - 30/343*T^51 + 2494/2401*T^50 +
        83/2401*T^49 - 1982/2401*T^48 - 489/2401*T^47 + 1622/2401*T^46 + 
        1784/2401*T^45 + 683/2401*T^44 - 216/343*T^43 - 2726/2401*T^42 - 
        387/2401*T^41 + 45/2401*T^40 - 2479/2401*T^39 + 93/2401*T^38 + 
        2750/2401*T^37 - 610/2401*T^36 - 1387/2401*T^35 + 1509/2401*T^34 + 
        890/2401*T^33 - 411/2401*T^32 + 450/2401*T^31 + 1240/2401*T^30 + 
        1654/2401*T^29 - 1654/2401*T^27 - 1240/2401*T^26 - 450/2401*T^25 + 
        411/2401*T^24 - 890/2401*T^23 - 1509/2401*T^22 + 1387/2401*T^21 + 
        610/2401*T^20 - 2750/2401*T^19 - 93/2401*T^18 + 2479/2401*T^17 - 
        45/2401*T^16 + 387/2401*T^15 + 2726/2401*T^14 + 216/343*T^13 - 683/2401*T^12
        - 1784/2401*T^11 - 1622/2401*T^10 + 489/2401*T^9 + 1982/2401*T^8 - 
        83/2401*T^7 - 2494/2401*T^6 + 30/343*T^5 + T^4 - 48/49*T^3 - 8/7*T^2 + 8/7*T
        + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 6*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 +
        4*X*Y^7 + 6*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 5*X*Y + 3*X + 
        Y^30 + 3*Y^29 + Y^28 + 6*Y^27 + 3*Y^26 + 6*Y^25 + 3*Y^24 + 2*Y^23 + Y^22 + 
        3*Y^21 + 6*Y^20 + Y^19 + Y^18 + Y^17 + 5*Y^16 + Y^15 + 3*Y^14 + Y^13 + Y^12 
        + 5*Y^11 + 4*Y^10 + 4*Y^9 + Y^7 + 2*Y^6 + 3*Y^5 + 4*Y^4 + 2*Y^3 + 2*Y^2 + 6,
    T^56 - T^55 + 29/49*T^54 + 134/343*T^53 - 3800/2401*T^52 + 493/343*T^51 - 
        715/2401*T^50 - 3264/2401*T^49 + 3432/2401*T^48 - 2762/2401*T^47 - 
        737/2401*T^46 + 3450/2401*T^45 - 3050/2401*T^44 + 1359/2401*T^43 + 
        1443/2401*T^42 - 2285/2401*T^41 + 38/49*T^40 + 53/2401*T^39 - 1002/2401*T^38
        + 1072/2401*T^37 - 66/2401*T^36 - 148/2401*T^35 - 81/2401*T^34 - 67/343*T^33
        + 76/2401*T^32 + 391/2401*T^31 - 151/2401*T^30 + 75/343*T^29 - 
        1157/2401*T^28 + 75/343*T^27 - 151/2401*T^26 + 391/2401*T^25 + 76/2401*T^24 
        - 67/343*T^23 - 81/2401*T^22 - 148/2401*T^21 - 66/2401*T^20 + 1072/2401*T^19
        - 1002/2401*T^18 + 53/2401*T^17 + 38/49*T^16 - 2285/2401*T^15 + 
        1443/2401*T^14 + 1359/2401*T^13 - 3050/2401*T^12 + 3450/2401*T^11 - 
        737/2401*T^10 - 2762/2401*T^9 + 3432/2401*T^8 - 3264/2401*T^7 - 715/2401*T^6
        + 493/343*T^5 - 3800/2401*T^4 + 134/343*T^3 + 29/49*T^2 - T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + X*Y^12 + 4*X*Y^11 + 6*X*Y^9 + 5*X*Y^8 + 
        6*X*Y^7 + 4*X*Y^5 + 2*X*Y^3 + 4*X*Y^2 + X*Y + X + 5*Y^30 + 4*Y^29 + 4*Y^28 +
        2*Y^27 + 3*Y^26 + 6*Y^24 + 5*Y^23 + 3*Y^22 + 5*Y^21 + 2*Y^20 + Y^19 + 4*Y^18
        + 6*Y^17 + Y^15 + 2*Y^13 + 5*Y^12 + 4*Y^11 + 6*Y^10 + 5*Y^9 + Y^8 + 3*Y^7 + 
        2*Y^6 + 6*Y^4 + 5*Y^3 + Y^2 + 6*Y + 4,
    T^56 - 2/7*T^55 - 55/49*T^54 - 167/343*T^53 + 583/2401*T^52 + 2732/2401*T^51 + 
        265/2401*T^50 - 1616/2401*T^49 - 2461/2401*T^48 + 1609/2401*T^47 + 
        1171/2401*T^46 + 1139/2401*T^45 + 394/2401*T^44 - 2545/2401*T^43 + 
        570/2401*T^42 - 159/2401*T^41 + 1774/2401*T^40 + 1194/2401*T^39 - 
        1794/2401*T^38 - 1467/2401*T^37 - 1797/2401*T^36 + 1822/2401*T^35 + 
        1117/2401*T^34 + 782/2401*T^33 - 1669/2401*T^32 - 703/2401*T^31 + 
        383/2401*T^30 - 135/343*T^29 + 508/343*T^28 - 135/343*T^27 + 383/2401*T^26 -
        703/2401*T^25 - 1669/2401*T^24 + 782/2401*T^23 + 1117/2401*T^22 + 
        1822/2401*T^21 - 1797/2401*T^20 - 1467/2401*T^19 - 1794/2401*T^18 + 
        1194/2401*T^17 + 1774/2401*T^16 - 159/2401*T^15 + 570/2401*T^14 - 
        2545/2401*T^13 + 394/2401*T^12 + 1139/2401*T^11 + 1171/2401*T^10 + 
        1609/2401*T^9 - 2461/2401*T^8 - 1616/2401*T^7 + 265/2401*T^6 + 2732/2401*T^5
        + 583/2401*T^4 - 167/343*T^3 - 55/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 
        + 3*X*Y^8 + 2*X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + X*Y^3 + X*Y^2 + 5*X*Y + 
        6*X + Y^30 + 4*Y^29 + 5*Y^28 + 6*Y^27 + Y^26 + 5*Y^25 + 4*Y^21 + Y^20 + 
        2*Y^19 + Y^18 + 6*Y^17 + 4*Y^16 + Y^15 + 6*Y^14 + Y^13 + 6*Y^12 + 4*Y^11 + 
        3*Y^10 + 4*Y^9 + 3*Y^8 + 3*Y^7 + 5*Y^5 + 5*Y^4 + Y^3 + 5*Y^2 + Y + 4,
    -T^56 + 46/49*T^54 + 404/343*T^53 + 664/2401*T^52 - 1181/2401*T^51 - 
        718/2401*T^50 - 757/2401*T^49 - 2355/2401*T^48 - 2509/2401*T^47 + 
        1333/2401*T^46 + 2393/2401*T^45 + 293/2401*T^44 + 466/2401*T^43 + 
        1798/2401*T^42 + 1177/2401*T^41 - 1500/2401*T^40 - 3651/2401*T^39 - 
        39/2401*T^38 + 804/2401*T^37 + 1342/2401*T^36 - 677/2401*T^35 + 225/343*T^34
        + 1460/2401*T^33 - 1836/2401*T^32 - 2514/2401*T^31 + 52/2401*T^30 + 
        36/49*T^29 - 36/49*T^27 - 52/2401*T^26 + 2514/2401*T^25 + 1836/2401*T^24 - 
        1460/2401*T^23 - 225/343*T^22 + 677/2401*T^21 - 1342/2401*T^20 - 
        804/2401*T^19 + 39/2401*T^18 + 3651/2401*T^17 + 1500/2401*T^16 - 
        1177/2401*T^15 - 1798/2401*T^14 - 466/2401*T^13 - 293/2401*T^12 - 
        2393/2401*T^11 - 1333/2401*T^10 + 2509/2401*T^9 + 2355/2401*T^8 + 
        757/2401*T^7 + 718/2401*T^6 + 1181/2401*T^5 - 664/2401*T^4 - 404/343*T^3 - 
        46/49*T^2 + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + X*Y^13 + 5*X*Y^12 + X*Y^11 + 6*X*Y^9 + 6*X*Y^8 + 
        X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + X*Y^4 + 6*X*Y^2 + X*Y + 3*X + 4*Y^30 + 5*Y^28 + 
        4*Y^27 + 6*Y^26 + Y^25 + 3*Y^23 + 2*Y^22 + 4*Y^21 + 6*Y^20 + 5*Y^19 + 6*Y^18
        + 5*Y^17 + 5*Y^15 + 2*Y^14 + 3*Y^13 + 2*Y^12 + 6*Y^11 + Y^10 + 5*Y^9 + 5*Y^8
        + 5*Y^7 + 6*Y^6 + 3*Y^5 + 4*Y^4 + 6*Y^3 + 2*Y^2 + 3*Y + 3,
    T^56 + T^55 + 8/49*T^54 - 149/343*T^53 - 24/49*T^52 - 2592/2401*T^51 - 
        3141/2401*T^50 + 747/2401*T^49 + 3483/2401*T^48 + 2253/2401*T^47 + 
        887/2401*T^46 + 421/2401*T^45 - 1703/2401*T^44 - 3589/2401*T^43 - 
        1838/2401*T^42 + 1979/2401*T^41 + 1859/2401*T^40 + 1023/2401*T^39 + 
        188/343*T^38 + 1262/2401*T^37 - 991/2401*T^36 - 1424/2401*T^35 + 
        153/343*T^34 + 176/343*T^33 - 60/343*T^32 - 348/2401*T^31 + 1214/2401*T^30 -
        772/2401*T^29 - 2239/2401*T^28 - 772/2401*T^27 + 1214/2401*T^26 - 
        348/2401*T^25 - 60/343*T^24 + 176/343*T^23 + 153/343*T^22 - 1424/2401*T^21 -
        991/2401*T^20 + 1262/2401*T^19 + 188/343*T^18 + 1023/2401*T^17 + 
        1859/2401*T^16 + 1979/2401*T^15 - 1838/2401*T^14 - 3589/2401*T^13 - 
        1703/2401*T^12 + 421/2401*T^11 + 887/2401*T^10 + 2253/2401*T^9 + 
        3483/2401*T^8 + 747/2401*T^7 - 3141/2401*T^6 - 2592/2401*T^5 - 24/49*T^4 - 
        149/343*T^3 + 8/49*T^2 + T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + X*Y^10 + 5*X*Y^9 + 4*X*Y^8 + 
        X*Y^7 + X*Y^6 + X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + X*Y + 2*X + 6*Y^30 + 
        3*Y^29 + 5*Y^28 + 6*Y^27 + 2*Y^25 + 6*Y^24 + 4*Y^23 + Y^22 + 5*Y^21 + 4*Y^20
        + 6*Y^19 + 3*Y^18 + 6*Y^17 + Y^16 + 5*Y^15 + 6*Y^14 + 4*Y^13 + 6*Y^12 + 
        6*Y^11 + 3*Y^10 + 5*Y^9 + 5*Y^8 + Y^7 + 3*Y^6 + 3*Y^5 + 6*Y^4 + 5*Y^3 + 
        5*Y^2 + 5*Y,
    T^56 + 2/7*T^55 - 22/49*T^54 + 145/343*T^53 - 337/2401*T^52 - 2308/2401*T^51 + 
        818/2401*T^50 + 484/2401*T^49 - 1130/2401*T^48 + 946/2401*T^47 - 
        162/2401*T^46 + 135/2401*T^45 + 450/2401*T^44 - 69/343*T^43 - 192/2401*T^42 
        - 381/2401*T^41 - 480/2401*T^40 + 695/2401*T^39 + 398/2401*T^38 + 
        1024/2401*T^37 + 1313/2401*T^36 - 1401/2401*T^35 + 188/2401*T^34 + 
        458/2401*T^33 - 1696/2401*T^32 + 18/343*T^31 + 710/2401*T^30 - 30/2401*T^29 
        - 113/2401*T^28 - 30/2401*T^27 + 710/2401*T^26 + 18/343*T^25 - 
        1696/2401*T^24 + 458/2401*T^23 + 188/2401*T^22 - 1401/2401*T^21 + 
        1313/2401*T^20 + 1024/2401*T^19 + 398/2401*T^18 + 695/2401*T^17 - 
        480/2401*T^16 - 381/2401*T^15 - 192/2401*T^14 - 69/343*T^13 + 450/2401*T^12 
        + 135/2401*T^11 - 162/2401*T^10 + 946/2401*T^9 - 1130/2401*T^8 + 
        484/2401*T^7 + 818/2401*T^6 - 2308/2401*T^5 - 337/2401*T^4 + 145/343*T^3 - 
        22/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        2*X*Y^8 + 6*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 2*X*Y + 2*X + 
        4*Y^30 + 5*Y^29 + 3*Y^28 + Y^26 + 4*Y^25 + 6*Y^24 + 6*Y^23 + 4*Y^22 + 5*Y^21
        + 6*Y^20 + Y^19 + Y^18 + 5*Y^17 + 5*Y^16 + 6*Y^14 + 2*Y^13 + 4*Y^12 + 4*Y^11
        + 4*Y^10 + 5*Y^9 + 4*Y^8 + Y^7 + 3*Y^6 + Y^5 + Y^4 + 6*Y^3 + 5*Y^2 + 6*Y + 
        1,
    T^56 + T^55 + 48/49*T^54 + 253/343*T^53 + 246/343*T^52 + 950/2401*T^51 + 
        589/2401*T^50 + 619/2401*T^49 - 636/2401*T^48 - 1563/2401*T^47 - 
        1377/2401*T^46 - 1475/2401*T^45 - 299/2401*T^44 + 776/2401*T^43 + 
        625/2401*T^42 + 107/343*T^41 + 1237/2401*T^40 + 1835/2401*T^39 + 50/343*T^38
        + 1494/2401*T^37 + 1749/2401*T^36 + 905/2401*T^35 + 961/2401*T^34 + 
        1282/2401*T^33 + 1129/2401*T^32 + 237/2401*T^31 + 493/2401*T^30 + 
        1485/2401*T^29 + 701/2401*T^28 + 1485/2401*T^27 + 493/2401*T^26 + 
        237/2401*T^25 + 1129/2401*T^24 + 1282/2401*T^23 + 961/2401*T^22 + 
        905/2401*T^21 + 1749/2401*T^20 + 1494/2401*T^19 + 50/343*T^18 + 
        1835/2401*T^17 + 1237/2401*T^16 + 107/343*T^15 + 625/2401*T^14 + 
        776/2401*T^13 - 299/2401*T^12 - 1475/2401*T^11 - 1377/2401*T^10 - 
        1563/2401*T^9 - 636/2401*T^8 + 619/2401*T^7 + 589/2401*T^6 + 950/2401*T^5 + 
        246/343*T^4 + 253/343*T^3 + 48/49*T^2 + T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 
        + 6*X*Y^8 + 4*X*Y^6 + 6*X*Y^2 + 5*X*Y + 6*X + 4*Y^30 + 6*Y^29 + Y^28 + 
        2*Y^27 + 6*Y^26 + 2*Y^25 + Y^24 + 6*Y^22 + Y^20 + 3*Y^19 + Y^18 + 6*Y^17 + 
        4*Y^16 + 5*Y^15 + 2*Y^14 + 6*Y^13 + Y^12 + 2*Y^11 + 5*Y^10 + 2*Y^8 + 5*Y^7 +
        4*Y^6 + 5*Y^5 + 5*Y^4 + 3*Y^3 + 2*Y^2 + 3*Y + 4,
    T^56 + 2*T^55 + 34/49*T^54 - 807/343*T^53 - 9316/2401*T^52 - 3559/2401*T^51 + 
        6926/2401*T^50 + 10140/2401*T^49 + 1782/2401*T^48 - 8420/2401*T^47 - 
        9593/2401*T^46 - 113/343*T^45 + 8770/2401*T^44 + 9329/2401*T^43 + 24/49*T^42
        - 8833/2401*T^41 - 11425/2401*T^40 - 2633/2401*T^39 + 10217/2401*T^38 + 
        14701/2401*T^37 + 5546/2401*T^36 - 9348/2401*T^35 - 16481/2401*T^34 - 
        8471/2401*T^33 + 7507/2401*T^32 + 15867/2401*T^31 + 1192/343*T^30 - 
        1035/343*T^29 - 2117/343*T^28 - 1035/343*T^27 + 1192/343*T^26 + 
        15867/2401*T^25 + 7507/2401*T^24 - 8471/2401*T^23 - 16481/2401*T^22 - 
        9348/2401*T^21 + 5546/2401*T^20 + 14701/2401*T^19 + 10217/2401*T^18 - 
        2633/2401*T^17 - 11425/2401*T^16 - 8833/2401*T^15 + 24/49*T^14 + 
        9329/2401*T^13 + 8770/2401*T^12 - 113/343*T^11 - 9593/2401*T^10 - 
        8420/2401*T^9 + 1782/2401*T^8 + 10140/2401*T^7 + 6926/2401*T^6 - 
        3559/2401*T^5 - 9316/2401*T^4 - 807/343*T^3 + 34/49*T^2 + 2*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 + 
        2*X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + X*Y^4 + 4*X*Y^3 + 6*X*Y + 5*X + Y^30 + 2*Y^29 
        + 6*Y^26 + 4*Y^25 + 3*Y^24 + 4*Y^22 + 2*Y^20 + 5*Y^19 + 5*Y^18 + 2*Y^17 + 
        5*Y^15 + 6*Y^14 + 3*Y^13 + 5*Y^12 + 3*Y^11 + 2*Y^10 + 4*Y^9 + 2*Y^8 + 3*Y^7 
        + Y^6 + 5*Y^5 + 2*Y^4 + 5*Y^3 + 6*Y^2 + 5*Y + 2,
    -T^56 + 5/7*T^54 - 64/343*T^53 + 1717/2401*T^52 - 1968/2401*T^51 - 
        2460/2401*T^50 + 1317/2401*T^49 + 31/2401*T^48 + 1650/2401*T^47 + 
        894/2401*T^46 - 2377/2401*T^45 - 1742/2401*T^44 + 419/2401*T^43 + 
        389/2401*T^42 + 1699/2401*T^41 + 921/2401*T^40 - 366/343*T^39 - 
        821/2401*T^38 + 517/2401*T^37 + 24/343*T^36 + 1287/2401*T^35 + 767/2401*T^34
        - 2510/2401*T^33 - 989/2401*T^32 + 495/2401*T^31 - 731/2401*T^30 + 
        3349/2401*T^29 - 3349/2401*T^27 + 731/2401*T^26 - 495/2401*T^25 + 
        989/2401*T^24 + 2510/2401*T^23 - 767/2401*T^22 - 1287/2401*T^21 - 
        24/343*T^20 - 517/2401*T^19 + 821/2401*T^18 + 366/343*T^17 - 921/2401*T^16 -
        1699/2401*T^15 - 389/2401*T^14 - 419/2401*T^13 + 1742/2401*T^12 + 
        2377/2401*T^11 - 894/2401*T^10 - 1650/2401*T^9 - 31/2401*T^8 - 1317/2401*T^7
        + 2460/2401*T^6 + 1968/2401*T^5 - 1717/2401*T^4 + 64/343*T^3 - 5/7*T^2 + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 5*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 2*X*Y^8 +
        4*X*Y^6 + X*Y^5 + X*Y^4 + X*Y^3 + 2*X*Y^2 + 6*X*Y + 3*X + 3*Y^30 + 3*Y^29 + 
        4*Y^28 + 6*Y^27 + 4*Y^26 + Y^25 + Y^24 + 6*Y^22 + 4*Y^21 + 6*Y^19 + 5*Y^18 +
        6*Y^17 + 5*Y^16 + 6*Y^15 + 2*Y^14 + 4*Y^13 + 4*Y^12 + 4*Y^11 + Y^10 + 3*Y^9 
        + Y^8 + 4*Y^7 + Y^6 + 6*Y^5 + 5*Y^4 + 5*Y^3 + Y,
    -T^56 + 5/7*T^55 + 2*T^54 - 660/343*T^53 - 4236/2401*T^52 + 626/343*T^51 + 
        2221/2401*T^50 - 841/2401*T^49 - 15/343*T^48 - 3608/2401*T^47 - 
        1699/2401*T^46 + 972/343*T^45 + 47/49*T^44 - 6073/2401*T^43 - 2602/2401*T^42
        + 3436/2401*T^41 + 3502/2401*T^40 - 1133/2401*T^39 - 3392/2401*T^38 - 
        803/2401*T^37 + 520/343*T^36 + 1765/2401*T^35 - 4219/2401*T^34 - 
        1803/2401*T^33 + 487/343*T^32 + 53/49*T^31 - 1782/2401*T^30 - 3491/2401*T^29
        + 3491/2401*T^27 + 1782/2401*T^26 - 53/49*T^25 - 487/343*T^24 + 
        1803/2401*T^23 + 4219/2401*T^22 - 1765/2401*T^21 - 520/343*T^20 + 
        803/2401*T^19 + 3392/2401*T^18 + 1133/2401*T^17 - 3502/2401*T^16 - 
        3436/2401*T^15 + 2602/2401*T^14 + 6073/2401*T^13 - 47/49*T^12 - 972/343*T^11
        + 1699/2401*T^10 + 3608/2401*T^9 + 15/343*T^8 + 841/2401*T^7 - 2221/2401*T^6
        - 626/343*T^5 + 4236/2401*T^4 + 660/343*T^3 - 2*T^2 - 5/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + X*Y^9 + 3*X*Y^8 + 4*X*Y^6 + 
        3*X*Y^5 + X*Y^4 + 6*X*Y + 3*X + 5*Y^30 + 2*Y^28 + 6*Y^27 + Y^26 + 6*Y^25 + 
        4*Y^24 + 5*Y^23 + 6*Y^22 + 4*Y^21 + 6*Y^20 + 4*Y^19 + 2*Y^18 + 4*Y^17 + 
        5*Y^16 + 2*Y^15 + 3*Y^14 + 4*Y^12 + Y^11 + Y^9 + Y^8 + 3*Y^6 + Y^5 + 6*Y^4 +
        Y^3 + Y^2 + 4*Y + 3,
    T^56 + 10/7*T^55 + 47/49*T^54 + 316/343*T^53 - 92/2401*T^52 - 645/2401*T^51 - 
        1051/2401*T^50 - 2756/2401*T^49 - 864/2401*T^48 - 348/2401*T^47 + 
        396/2401*T^46 + 2025/2401*T^45 + 1086/2401*T^44 + 2040/2401*T^43 + 
        2419/2401*T^42 + 618/2401*T^41 + 1277/2401*T^40 - 87/343*T^39 - 
        1376/2401*T^38 - 538/2401*T^37 - 3273/2401*T^36 - 1692/2401*T^35 - 
        1802/2401*T^34 - 2787/2401*T^33 - 82/343*T^32 - 1626/2401*T^31 + 
        550/2401*T^30 + 2260/2401*T^29 + 593/2401*T^28 + 2260/2401*T^27 + 
        550/2401*T^26 - 1626/2401*T^25 - 82/343*T^24 - 2787/2401*T^23 - 
        1802/2401*T^22 - 1692/2401*T^21 - 3273/2401*T^20 - 538/2401*T^19 - 
        1376/2401*T^18 - 87/343*T^17 + 1277/2401*T^16 + 618/2401*T^15 + 
        2419/2401*T^14 + 2040/2401*T^13 + 1086/2401*T^12 + 2025/2401*T^11 + 
        396/2401*T^10 - 348/2401*T^9 - 864/2401*T^8 - 2756/2401*T^7 - 1051/2401*T^6 
        - 645/2401*T^5 - 92/2401*T^4 + 316/343*T^3 + 47/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + X*Y^13 + X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 
        6*X*Y^8 + 5*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 6*X*Y 
        + 3*X + 6*Y^30 + 2*Y^29 + 3*Y^28 + 4*Y^27 + 4*Y^26 + 4*Y^25 + 4*Y^24 + 
        5*Y^23 + Y^22 + 4*Y^21 + 6*Y^19 + 3*Y^18 + 4*Y^17 + 4*Y^16 + 3*Y^15 + 6*Y^14
        + 2*Y^13 + 2*Y^12 + 2*Y^11 + 3*Y^9 + 6*Y^7 + 3*Y^6 + 4*Y^5 + 4*Y^4 + Y^2 + 
        4*Y + 1,
    T^56 - 1/7*T^55 + 62/49*T^54 - 30/343*T^53 + 572/2401*T^52 + 1/49*T^51 - 
        1920/2401*T^50 + 79/343*T^49 - 1265/2401*T^48 + 1525/2401*T^47 - 
        821/2401*T^46 + 2973/2401*T^45 - 1803/2401*T^44 + 1454/2401*T^43 - 
        2035/2401*T^42 - 76/343*T^41 + 6/2401*T^40 - 1466/2401*T^39 + 2308/2401*T^38
        - 1114/2401*T^37 + 2094/2401*T^36 - 1602/2401*T^35 - 453/2401*T^34 - 
        2407/2401*T^33 - 1056/2401*T^32 - 725/2401*T^31 - 164/2401*T^30 + 
        2167/2401*T^29 + 361/2401*T^28 + 2167/2401*T^27 - 164/2401*T^26 - 
        725/2401*T^25 - 1056/2401*T^24 - 2407/2401*T^23 - 453/2401*T^22 - 
        1602/2401*T^21 + 2094/2401*T^20 - 1114/2401*T^19 + 2308/2401*T^18 - 
        1466/2401*T^17 + 6/2401*T^16 - 76/343*T^15 - 2035/2401*T^14 + 1454/2401*T^13
        - 1803/2401*T^12 + 2973/2401*T^11 - 821/2401*T^10 + 1525/2401*T^9 - 
        1265/2401*T^8 + 79/343*T^7 - 1920/2401*T^6 + 1/49*T^5 + 572/2401*T^4 - 
        30/343*T^3 + 62/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^13 + X*Y^11 + 5*X*Y^10 + 3*X*Y^8 + 3*X*Y^7 + 6*X*Y^6 + 
        3*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 6*X*Y + 4*Y^30 + 3*Y^28 + 6*Y^27 + 
        4*Y^26 + 4*Y^25 + 3*Y^24 + Y^23 + 4*Y^22 + 4*Y^21 + 6*Y^19 + Y^18 + 6*Y^16 +
        6*Y^15 + 3*Y^14 + Y^13 + 4*Y^11 + 2*Y^10 + 5*Y^9 + 3*Y^8 + 5*Y^7 + 2*Y^6 + 
        6*Y^5 + 3*Y^4 + 2*Y^3 + 3*Y^2 + 4*Y + 3,
    -T^56 + 4/7*T^55 - 41/49*T^54 + 11/49*T^53 - 773/2401*T^52 - 1321/2401*T^51 + 
        463/2401*T^50 - 1290/2401*T^49 - 47/343*T^48 - 727/2401*T^47 + 108/2401*T^46
        - 814/2401*T^45 - 75/343*T^44 + 383/2401*T^43 - 782/2401*T^42 + 
        121/2401*T^41 - 617/2401*T^40 - 834/2401*T^39 - 253/2401*T^38 + 
        586/2401*T^37 - 1560/2401*T^36 + 1060/2401*T^35 - 432/2401*T^34 + 
        228/2401*T^33 + 109/343*T^32 - 233/2401*T^31 - 311/2401*T^30 - 207/2401*T^29
        + 207/2401*T^27 + 311/2401*T^26 + 233/2401*T^25 - 109/343*T^24 - 
        228/2401*T^23 + 432/2401*T^22 - 1060/2401*T^21 + 1560/2401*T^20 - 
        586/2401*T^19 + 253/2401*T^18 + 834/2401*T^17 + 617/2401*T^16 - 
        121/2401*T^15 + 782/2401*T^14 - 383/2401*T^13 + 75/343*T^12 + 814/2401*T^11 
        - 108/2401*T^10 + 727/2401*T^9 + 47/343*T^8 + 1290/2401*T^7 - 463/2401*T^6 +
        1321/2401*T^5 + 773/2401*T^4 - 11/49*T^3 + 41/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 6*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 2*X*Y + 5*X + 
        Y^30 + 4*Y^28 + 5*Y^26 + 4*Y^25 + 6*Y^24 + 4*Y^23 + 6*Y^22 + 3*Y^21 + 6*Y^20
        + 6*Y^19 + 3*Y^18 + Y^17 + 4*Y^16 + 3*Y^15 + 3*Y^14 + Y^13 + 6*Y^12 + 3*Y^11
        + 3*Y^10 + 3*Y^9 + 4*Y^7 + 4*Y^6 + 5*Y^5 + 2*Y^4 + Y^3 + 2,
    -T^56 + 1/7*T^55 + 82/49*T^54 + 33/343*T^53 - 3466/2401*T^52 + 2998/2401*T^51 + 
        1130/2401*T^50 - 4908/2401*T^49 - 698/2401*T^48 + 2909/2401*T^47 - 
        582/2401*T^46 - 1138/2401*T^45 + 1345/2401*T^44 + 1433/2401*T^43 - 
        10/2401*T^42 - 2305/2401*T^41 + 2171/2401*T^40 + 2173/2401*T^39 - 
        803/343*T^38 - 618/2401*T^37 + 5581/2401*T^36 - 2426/2401*T^35 - 
        4000/2401*T^34 + 5926/2401*T^33 + 1005/2401*T^32 - 545/343*T^31 - 
        559/2401*T^30 + 1216/2401*T^29 - 1216/2401*T^27 + 559/2401*T^26 + 
        545/343*T^25 - 1005/2401*T^24 - 5926/2401*T^23 + 4000/2401*T^22 + 
        2426/2401*T^21 - 5581/2401*T^20 + 618/2401*T^19 + 803/343*T^18 - 
        2173/2401*T^17 - 2171/2401*T^16 + 2305/2401*T^15 + 10/2401*T^14 - 
        1433/2401*T^13 - 1345/2401*T^12 + 1138/2401*T^11 + 582/2401*T^10 - 
        2909/2401*T^9 + 698/2401*T^8 + 4908/2401*T^7 - 1130/2401*T^6 - 2998/2401*T^5
        + 3466/2401*T^4 - 33/343*T^3 - 82/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 
        6*X*Y^7 + X*Y^6 + X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 5*X*Y + 2*X + Y^30 +
        4*Y^29 + 4*Y^28 + 5*Y^27 + 6*Y^25 + 3*Y^24 + 6*Y^23 + Y^22 + 5*Y^21 + 3*Y^18
        + Y^17 + 4*Y^16 + 5*Y^14 + Y^13 + Y^11 + 3*Y^10 + Y^9 + 6*Y^8 + 2*Y^7 + 
        6*Y^6 + 5*Y^5 + 5*Y^4 + 6*Y^2 + 5*Y + 4,
    -T^56 + 8/7*T^55 + 58/49*T^54 - 802/343*T^53 - 1328/2401*T^52 + 4029/2401*T^51 +
        652/343*T^50 - 3530/2401*T^49 - 8471/2401*T^48 + 5958/2401*T^47 + 
        1139/343*T^46 - 4407/2401*T^45 - 6315/2401*T^44 - 405/2401*T^43 + 
        7926/2401*T^42 + 73/2401*T^41 - 6130/2401*T^40 + 1780/2401*T^39 - 
        869/2401*T^38 - 6/343*T^37 + 3298/2401*T^36 + 13/2401*T^35 - 1468/2401*T^34 
        - 5959/2401*T^33 + 3155/2401*T^32 + 10243/2401*T^31 - 5106/2401*T^30 - 
        1089/343*T^29 + 1089/343*T^27 + 5106/2401*T^26 - 10243/2401*T^25 - 
        3155/2401*T^24 + 5959/2401*T^23 + 1468/2401*T^22 - 13/2401*T^21 - 
        3298/2401*T^20 + 6/343*T^19 + 869/2401*T^18 - 1780/2401*T^17 + 
        6130/2401*T^16 - 73/2401*T^15 - 7926/2401*T^14 + 405/2401*T^13 + 
        6315/2401*T^12 + 4407/2401*T^11 - 1139/343*T^10 - 5958/2401*T^9 + 
        8471/2401*T^8 + 3530/2401*T^7 - 652/343*T^6 - 4029/2401*T^5 + 1328/2401*T^4 
        + 802/343*T^3 - 58/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + X*Y^11 + 6*X*Y^10 + X*Y^9 + X*Y^8 + X*Y^7
        + 2*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + X*Y^2 + 4*X*Y + 6*X + 3*Y^30 + 4*Y^29 + 
        3*Y^28 + 6*Y^26 + 5*Y^25 + 2*Y^24 + 2*Y^23 + 2*Y^22 + 6*Y^21 + 3*Y^20 + 
        3*Y^19 + 6*Y^18 + 5*Y^16 + 3*Y^15 + 6*Y^14 + 2*Y^13 + 3*Y^12 + 3*Y^11 + 
        6*Y^9 + 3*Y^8 + Y^7 + 4*Y^6 + 6*Y^4 + 2*Y^3 + 4*Y^2 + 4,
    T^56 - 17/7*T^55 + 106/49*T^54 - 38/49*T^53 + 3054/2401*T^52 - 7372/2401*T^51 + 
        579/343*T^50 + 4824/2401*T^49 - 5921/2401*T^48 - 586/2401*T^47 - 
        143/2401*T^46 + 8804/2401*T^45 - 9089/2401*T^44 - 642/2401*T^43 + 
        4635/2401*T^42 + 1334/2401*T^41 - 3078/2401*T^40 - 5928/2401*T^39 + 
        10858/2401*T^38 - 2834/2401*T^37 - 3886/2401*T^36 - 2078/2401*T^35 + 
        7447/2401*T^34 + 1501/2401*T^33 - 10258/2401*T^32 + 4288/2401*T^31 + 
        2201/2401*T^30 + 6319/2401*T^29 - 14806/2401*T^28 + 6319/2401*T^27 + 
        2201/2401*T^26 + 4288/2401*T^25 - 10258/2401*T^24 + 1501/2401*T^23 + 
        7447/2401*T^22 - 2078/2401*T^21 - 3886/2401*T^20 - 2834/2401*T^19 + 
        10858/2401*T^18 - 5928/2401*T^17 - 3078/2401*T^16 + 1334/2401*T^15 + 
        4635/2401*T^14 - 642/2401*T^13 - 9089/2401*T^12 + 8804/2401*T^11 - 
        143/2401*T^10 - 586/2401*T^9 - 5921/2401*T^8 + 4824/2401*T^7 + 579/343*T^6 -
        7372/2401*T^5 + 3054/2401*T^4 - 38/49*T^3 + 106/49*T^2 - 17/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 +
        2*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + X*Y^4 + X*Y^3 + 3*X*Y + 6*X + 5*Y^30 + 4*Y^29 
        + 5*Y^28 + 5*Y^27 + 4*Y^26 + 2*Y^25 + 4*Y^24 + 6*Y^23 + 2*Y^22 + 3*Y^20 + 
        Y^19 + 6*Y^18 + 4*Y^15 + 3*Y^14 + 6*Y^13 + 6*Y^12 + 3*Y^11 + 3*Y^10 + 2*Y^9 
        + 2*Y^8 + 5*Y^7 + 4*Y^6 + 6*Y^5 + 5*Y^4 + 2*Y^3 + 4*Y^2 + 4*Y,
    T^56 + 10/7*T^55 - 17/49*T^54 - 803/343*T^53 - 5449/2401*T^52 - 124/2401*T^51 + 
        4316/2401*T^50 + 5352/2401*T^49 + 3368/2401*T^48 - 544/2401*T^47 - 
        3917/2401*T^46 - 4264/2401*T^45 - 2253/2401*T^44 - 481/2401*T^43 + 
        774/2401*T^42 + 267/343*T^41 + 3183/2401*T^40 + 3110/2401*T^39 + 
        1023/2401*T^38 - 1662/2401*T^37 - 4072/2401*T^36 - 4548/2401*T^35 - 
        1891/2401*T^34 + 2622/2401*T^33 + 5673/2401*T^32 + 4191/2401*T^31 - 
        65/2401*T^30 - 3344/2401*T^29 - 4463/2401*T^28 - 3344/2401*T^27 - 
        65/2401*T^26 + 4191/2401*T^25 + 5673/2401*T^24 + 2622/2401*T^23 - 
        1891/2401*T^22 - 4548/2401*T^21 - 4072/2401*T^20 - 1662/2401*T^19 + 
        1023/2401*T^18 + 3110/2401*T^17 + 3183/2401*T^16 + 267/343*T^15 + 
        774/2401*T^14 - 481/2401*T^13 - 2253/2401*T^12 - 4264/2401*T^11 - 
        3917/2401*T^10 - 544/2401*T^9 + 3368/2401*T^8 + 5352/2401*T^7 + 
        4316/2401*T^6 - 124/2401*T^5 - 5449/2401*T^4 - 803/343*T^3 - 17/49*T^2 + 
        10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 4*X*Y^12 + X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 
        3*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 5*X*Y^3 + 2*X*Y^2 + 5*X*Y + 4*X + Y^30 + 
        3*Y^29 + Y^28 + Y^27 + 2*Y^26 + 3*Y^24 + 5*Y^23 + 4*Y^22 + 6*Y^21 + Y^20 + 
        6*Y^19 + 2*Y^18 + 2*Y^17 + 4*Y^16 + 5*Y^15 + 4*Y^13 + 2*Y^12 + Y^11 + 6*Y^10
        + 5*Y^9 + 5*Y^8 + 2*Y^7 + 5*Y^5 + 2*Y^4 + 2*Y^2 + Y + 4,
    T^56 - T^55 - 13/49*T^54 + 32/49*T^53 - 1219/2401*T^52 - 188/2401*T^51 - 
        667/2401*T^50 + 1910/2401*T^49 + 355/2401*T^48 - 1808/2401*T^47 + 
        334/343*T^46 - 1354/2401*T^45 - 1710/2401*T^44 + 1245/2401*T^43 - 
        311/2401*T^42 + 1086/2401*T^41 - 29/49*T^40 + 977/2401*T^39 + 25/49*T^38 - 
        1816/2401*T^37 + 277/2401*T^36 - 62/2401*T^35 - 115/2401*T^34 + 
        634/2401*T^33 - 8/49*T^32 + 900/2401*T^31 - 467/2401*T^30 - 781/2401*T^29 + 
        947/2401*T^28 - 781/2401*T^27 - 467/2401*T^26 + 900/2401*T^25 - 8/49*T^24 + 
        634/2401*T^23 - 115/2401*T^22 - 62/2401*T^21 + 277/2401*T^20 - 
        1816/2401*T^19 + 25/49*T^18 + 977/2401*T^17 - 29/49*T^16 + 1086/2401*T^15 - 
        311/2401*T^14 + 1245/2401*T^13 - 1710/2401*T^12 - 1354/2401*T^11 + 
        334/343*T^10 - 1808/2401*T^9 + 355/2401*T^8 + 1910/2401*T^7 - 667/2401*T^6 -
        188/2401*T^5 - 1219/2401*T^4 + 32/49*T^3 - 13/49*T^2 - T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + X*Y^10 + X*Y^9 + 5*X*Y^8 + 
        4*X*Y^7 + X*Y^6 + 4*X*Y^5 + 4*X*Y^2 + 3*X*Y + X + 6*Y^30 + 2*Y^29 + 3*Y^28 +
        Y^27 + 3*Y^26 + 5*Y^25 + 2*Y^24 + 3*Y^23 + 3*Y^22 + 4*Y^21 + 6*Y^20 + Y^19 +
        6*Y^18 + 2*Y^16 + 6*Y^15 + 4*Y^13 + 3*Y^12 + 4*Y^11 + 3*Y^10 + 5*Y^9 + 6*Y^8
        + 3*Y^7 + 4*Y^6 + 5*Y^5 + 2*Y^4 + 5*Y^3 + Y^2 + 3*Y + 4,
    -T^56 - 4/7*T^55 + 45/49*T^54 + 146/343*T^53 - 311/2401*T^52 + 863/2401*T^51 - 
        1114/2401*T^50 - 285/343*T^49 + 1137/2401*T^48 + 305/2401*T^47 - 
        1887/2401*T^46 + 526/2401*T^45 + 1076/2401*T^44 - 272/2401*T^43 + 
        582/2401*T^42 + 145/2401*T^41 - 414/2401*T^40 + 556/2401*T^39 + 
        425/2401*T^38 - 969/2401*T^37 - 66/343*T^36 - 387/2401*T^35 - 592/2401*T^34 
        + 171/343*T^33 + 1749/2401*T^32 - 514/2401*T^31 - 821/2401*T^30 + 
        74/343*T^29 - 74/343*T^27 + 821/2401*T^26 + 514/2401*T^25 - 1749/2401*T^24 -
        171/343*T^23 + 592/2401*T^22 + 387/2401*T^21 + 66/343*T^20 + 969/2401*T^19 -
        425/2401*T^18 - 556/2401*T^17 + 414/2401*T^16 - 145/2401*T^15 - 
        582/2401*T^14 + 272/2401*T^13 - 1076/2401*T^12 - 526/2401*T^11 + 
        1887/2401*T^10 - 305/2401*T^9 - 1137/2401*T^8 + 285/343*T^7 + 1114/2401*T^6 
        - 863/2401*T^5 + 311/2401*T^4 - 146/343*T^3 - 45/49*T^2 + 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 + 5*X*Y^7 + 
        2*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + X*Y^3 + 4*X*Y^2 + X*Y + 5*X + 2*Y^30 + 4*Y^29 
        + Y^28 + 3*Y^27 + 2*Y^25 + 4*Y^23 + 3*Y^22 + 6*Y^21 + 3*Y^20 + Y^19 + 4*Y^18
        + 3*Y^17 + Y^16 + 6*Y^15 + 3*Y^14 + 5*Y^13 + 4*Y^12 + 4*Y^11 + 3*Y^10 + 
        2*Y^9 + Y^8 + Y^7 + 6*Y^6 + 6*Y^5 + Y^3 + 3*Y^2 + Y + 4,
    T^56 - 6/7*T^54 + 97/343*T^53 + 1336/2401*T^52 - 1508/2401*T^51 - 1569/2401*T^50
        + 676/2401*T^49 + 1998/2401*T^48 - 681/2401*T^47 + 67/2401*T^46 + 
        235/2401*T^45 + 321/2401*T^44 - 82/2401*T^43 - 870/2401*T^42 - 255/2401*T^41
        + 313/2401*T^40 - 787/2401*T^39 + 727/2401*T^38 + 313/2401*T^37 - 
        1558/2401*T^36 + 317/2401*T^35 + 276/343*T^34 - 1056/2401*T^33 - 
        744/2401*T^32 + 621/2401*T^31 + 156/2401*T^30 - 536/2401*T^29 - 
        751/2401*T^28 - 536/2401*T^27 + 156/2401*T^26 + 621/2401*T^25 - 
        744/2401*T^24 - 1056/2401*T^23 + 276/343*T^22 + 317/2401*T^21 - 
        1558/2401*T^20 + 313/2401*T^19 + 727/2401*T^18 - 787/2401*T^17 + 
        313/2401*T^16 - 255/2401*T^15 - 870/2401*T^14 - 82/2401*T^13 + 321/2401*T^12
        + 235/2401*T^11 + 67/2401*T^10 - 681/2401*T^9 + 1998/2401*T^8 + 676/2401*T^7
        - 1569/2401*T^6 - 1508/2401*T^5 + 1336/2401*T^4 + 97/343*T^3 - 6/7*T^2 + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + X*Y^11 + X*Y^9 + 5*X*Y^8 + 5*X*Y^6 + 
        3*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + X*Y^2 + 3*X*Y + X + 2*Y^30 + 3*Y^28 + 3*Y^27 +
        2*Y^26 + Y^25 + 5*Y^24 + 5*Y^23 + 5*Y^22 + 4*Y^21 + 6*Y^20 + Y^19 + 6*Y^17 +
        3*Y^16 + Y^15 + 4*Y^14 + 6*Y^13 + 4*Y^11 + 4*Y^10 + 6*Y^9 + 2*Y^8 + Y^6 + 
        6*Y^5 + 3*Y^4 + 3*Y^3 + 2*Y^2 + 5*Y + 3,
    -T^56 + 4/7*T^55 - 23/49*T^54 + 229/343*T^53 - 1650/2401*T^52 + 242/2401*T^51 + 
        1787/2401*T^50 + 23/343*T^49 + 1206/2401*T^48 - 1303/2401*T^47 + 
        905/2401*T^46 + 416/2401*T^45 - 984/2401*T^44 - 180/2401*T^43 - 
        2127/2401*T^42 + 635/2401*T^41 - 1088/2401*T^40 + 223/2401*T^39 + 
        83/2401*T^38 - 68/2401*T^37 + 923/2401*T^36 - 177/2401*T^35 + 163/343*T^34 -
        440/2401*T^33 + 662/2401*T^32 - 678/2401*T^31 + 549/2401*T^30 + 73/2401*T^29
        - 73/2401*T^27 - 549/2401*T^26 + 678/2401*T^25 - 662/2401*T^24 + 
        440/2401*T^23 - 163/343*T^22 + 177/2401*T^21 - 923/2401*T^20 + 68/2401*T^19 
        - 83/2401*T^18 - 223/2401*T^17 + 1088/2401*T^16 - 635/2401*T^15 + 
        2127/2401*T^14 + 180/2401*T^13 + 984/2401*T^12 - 416/2401*T^11 - 
        905/2401*T^10 + 1303/2401*T^9 - 1206/2401*T^8 - 23/343*T^7 - 1787/2401*T^6 -
        242/2401*T^5 + 1650/2401*T^4 - 229/343*T^3 + 23/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 
        3*X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + X*Y^5 + X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 2*X*Y + 
        2*X + 2*Y^30 + 6*Y^28 + 5*Y^27 + 2*Y^26 + Y^25 + 5*Y^24 + 4*Y^23 + 2*Y^22 + 
        6*Y^21 + 2*Y^20 + Y^19 + 6*Y^18 + Y^17 + 4*Y^16 + 5*Y^15 + 2*Y^13 + Y^12 + 
        2*Y^11 + 4*Y^10 + Y^9 + 4*Y^8 + 4*Y^7 + 2*Y^6 + 2*Y^4 + 4*Y^3 + 4*Y^2 + 5*Y 
        + 4,
    T^56 - 2*T^55 + 88/49*T^54 - 626/343*T^53 + 1781/2401*T^52 + 338/343*T^51 - 
        2893/2401*T^50 + 4450/2401*T^49 - 5347/2401*T^48 + 2760/2401*T^47 - 
        2432/2401*T^46 + 1872/2401*T^45 + 285/2401*T^44 + 78/343*T^43 - 6/2401*T^42 
        - 2092/2401*T^41 + 246/343*T^40 - 2385/2401*T^39 + 183/343*T^38 + 
        3404/2401*T^37 - 5062/2401*T^36 + 5027/2401*T^35 - 4474/2401*T^34 + 
        307/2401*T^33 + 2376/2401*T^32 - 2097/2401*T^31 + 4756/2401*T^30 - 
        5480/2401*T^29 + 3613/2401*T^28 - 5480/2401*T^27 + 4756/2401*T^26 - 
        2097/2401*T^25 + 2376/2401*T^24 + 307/2401*T^23 - 4474/2401*T^22 + 
        5027/2401*T^21 - 5062/2401*T^20 + 3404/2401*T^19 + 183/343*T^18 - 
        2385/2401*T^17 + 246/343*T^16 - 2092/2401*T^15 - 6/2401*T^14 + 78/343*T^13 +
        285/2401*T^12 + 1872/2401*T^11 - 2432/2401*T^10 + 2760/2401*T^9 - 
        5347/2401*T^8 + 4450/2401*T^7 - 2893/2401*T^6 + 338/343*T^5 + 1781/2401*T^4 
        - 626/343*T^3 + 88/49*T^2 - 2*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 5*X*Y^10 + 6*X*Y^9 + 2*X*Y^8 + 
        4*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + X*Y^3 + 5*X + 3*Y^30 + 5*Y^29 + 
        4*Y^28 + 3*Y^27 + 6*Y^26 + Y^25 + 3*Y^24 + 3*Y^23 + 6*Y^21 + 4*Y^20 + 3*Y^18
        + 4*Y^17 + 5*Y^16 + 6*Y^15 + Y^14 + 4*Y^13 + 5*Y^12 + 2*Y^11 + 2*Y^10 + Y^9 
        + Y^8 + 5*Y^7 + 5*Y^6 + 5*Y^5 + 2*Y^4 + Y + 4,
    -T^56 + 20/7*T^55 - 219/49*T^54 + 1695/343*T^53 - 9928/2401*T^52 + 
        5353/2401*T^51 + 249/2401*T^50 - 4041/2401*T^49 + 794/343*T^48 - 
        5637/2401*T^47 + 4595/2401*T^46 - 3550/2401*T^45 + 3580/2401*T^44 - 
        4947/2401*T^43 + 6386/2401*T^42 - 7359/2401*T^41 + 7569/2401*T^40 - 
        7185/2401*T^39 + 6333/2401*T^38 - 4796/2401*T^37 + 3091/2401*T^36 - 
        597/2401*T^35 - 2264/2401*T^34 + 4035/2401*T^33 - 4320/2401*T^32 + 
        481/343*T^31 - 2211/2401*T^30 + 18/49*T^29 - 18/49*T^27 + 2211/2401*T^26 - 
        481/343*T^25 + 4320/2401*T^24 - 4035/2401*T^23 + 2264/2401*T^22 + 
        597/2401*T^21 - 3091/2401*T^20 + 4796/2401*T^19 - 6333/2401*T^18 + 
        7185/2401*T^17 - 7569/2401*T^16 + 7359/2401*T^15 - 6386/2401*T^14 + 
        4947/2401*T^13 - 3580/2401*T^12 + 3550/2401*T^11 - 4595/2401*T^10 + 
        5637/2401*T^9 - 794/343*T^8 + 4041/2401*T^7 - 249/2401*T^6 - 5353/2401*T^5 +
        9928/2401*T^4 - 1695/343*T^3 + 219/49*T^2 - 20/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + X*Y^10 + 2*X*Y^9 + X*Y^8 + 
        4*X*Y^7 + X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 6*X*Y + 2*X + 4*Y^30 + 
        2*Y^29 + 4*Y^28 + 5*Y^27 + 3*Y^26 + 2*Y^25 + 3*Y^23 + 6*Y^22 + Y^21 + 6*Y^20
        + Y^19 + 3*Y^17 + 4*Y^15 + 6*Y^14 + 5*Y^13 + 5*Y^12 + 3*Y^11 + 4*Y^10 + 
        3*Y^9 + 5*Y^8 + 5*Y^7 + Y^6 + 6*Y^5 + Y^4 + 4*Y^3 + 5*Y + 3,
    T^56 + 10/7*T^55 + 73/49*T^54 + 52/49*T^53 - 1135/2401*T^52 - 1280/2401*T^51 - 
        1892/2401*T^50 - 421/2401*T^49 + 3041/2401*T^48 + 1002/2401*T^47 + 
        34/2401*T^46 - 233/343*T^45 - 2836/2401*T^44 + 1945/2401*T^43 + 
        2921/2401*T^42 + 4737/2401*T^41 + 4926/2401*T^40 - 590/2401*T^39 - 
        2367/2401*T^38 - 4371/2401*T^37 - 4188/2401*T^36 - 1531/2401*T^35 - 
        2559/2401*T^34 - 2263/2401*T^33 - 1843/2401*T^32 - 2752/2401*T^31 - 
        919/2401*T^30 + 1261/2401*T^29 + 1910/2401*T^28 + 1261/2401*T^27 - 
        919/2401*T^26 - 2752/2401*T^25 - 1843/2401*T^24 - 2263/2401*T^23 - 
        2559/2401*T^22 - 1531/2401*T^21 - 4188/2401*T^20 - 4371/2401*T^19 - 
        2367/2401*T^18 - 590/2401*T^17 + 4926/2401*T^16 + 4737/2401*T^15 + 
        2921/2401*T^14 + 1945/2401*T^13 - 2836/2401*T^12 - 233/343*T^11 + 
        34/2401*T^10 + 1002/2401*T^9 + 3041/2401*T^8 - 421/2401*T^7 - 1892/2401*T^6 
        - 1280/2401*T^5 - 1135/2401*T^4 + 52/49*T^3 + 73/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + X*Y^12 + 5*X*Y^10 + 4*X*Y^9 + 4*X*Y^8 + 
        X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 4*X*Y^2 + 2*X*Y + 6*X + 5*Y^30 + Y^29 
        + 6*Y^28 + 2*Y^27 + 3*Y^26 + Y^25 + 2*Y^22 + 6*Y^21 + 5*Y^20 + 3*Y^19 + 
        3*Y^18 + Y^17 + Y^16 + 6*Y^14 + Y^13 + 5*Y^12 + 3*Y^11 + 4*Y^10 + 5*Y^8 + 
        6*Y^6 + 6*Y^5 + 6*Y^4 + 5*Y^3 + 4*Y^2 + 1,
    T^56 - T^55 - 45/49*T^54 + 381/343*T^53 - 1028/2401*T^52 + 554/2401*T^51 - 
        191/2401*T^50 - 33/343*T^49 + 2134/2401*T^48 - 1249/2401*T^47 + 
        320/2401*T^46 - 1339/2401*T^45 - 2045/2401*T^44 + 3608/2401*T^43 - 
        601/2401*T^42 - 1030/2401*T^41 + 1649/2401*T^40 - 1409/2401*T^39 + 
        769/2401*T^38 - 115/2401*T^37 - 1199/2401*T^36 + 149/2401*T^35 + 
        124/2401*T^34 + 1261/2401*T^33 + 351/2401*T^32 - 901/2401*T^31 + 
        559/2401*T^30 + 391/2401*T^29 - 1970/2401*T^28 + 391/2401*T^27 + 
        559/2401*T^26 - 901/2401*T^25 + 351/2401*T^24 + 1261/2401*T^23 + 
        124/2401*T^22 + 149/2401*T^21 - 1199/2401*T^20 - 115/2401*T^19 + 
        769/2401*T^18 - 1409/2401*T^17 + 1649/2401*T^16 - 1030/2401*T^15 - 
        601/2401*T^14 + 3608/2401*T^13 - 2045/2401*T^12 - 1339/2401*T^11 + 
        320/2401*T^10 - 1249/2401*T^9 + 2134/2401*T^8 - 33/343*T^7 - 191/2401*T^6 + 
        554/2401*T^5 - 1028/2401*T^4 + 381/343*T^3 - 45/49*T^2 - T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 
        + 3*X*Y^8 + 5*X*Y^7 + 5*X*Y^5 + X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 2*X*Y + 5*X + 
        2*Y^30 + 4*Y^29 + Y^27 + 2*Y^26 + 3*Y^25 + 2*Y^23 + 4*Y^22 + Y^21 + 6*Y^20 +
        Y^19 + 5*Y^18 + 4*Y^17 + 4*Y^16 + Y^15 + 3*Y^13 + 3*Y^11 + 5*Y^9 + 2*Y^7 + 
        3*Y^6 + Y^5 + 6*Y^3 + 4*Y + 5,
    -T^56 + 3/7*T^55 + 11/49*T^54 + 121/343*T^53 + 1773/2401*T^52 - 1737/2401*T^51 +
        639/2401*T^50 - 1248/2401*T^49 - 1278/2401*T^48 + 818/2401*T^47 + 
        1643/2401*T^46 + 107/343*T^45 - 465/2401*T^44 - 743/2401*T^43 - 
        724/2401*T^42 + 299/2401*T^41 + 809/2401*T^40 - 258/2401*T^39 + 
        1087/2401*T^38 - 447/2401*T^37 - 1830/2401*T^36 + 47/343*T^35 - 
        624/2401*T^34 + 949/2401*T^33 + 794/2401*T^32 - 717/2401*T^31 + 
        338/2401*T^30 - 417/2401*T^29 + 417/2401*T^27 - 338/2401*T^26 + 
        717/2401*T^25 - 794/2401*T^24 - 949/2401*T^23 + 624/2401*T^22 - 47/343*T^21 
        + 1830/2401*T^20 + 447/2401*T^19 - 1087/2401*T^18 + 258/2401*T^17 - 
        809/2401*T^16 - 299/2401*T^15 + 724/2401*T^14 + 743/2401*T^13 + 
        465/2401*T^12 - 107/343*T^11 - 1643/2401*T^10 - 818/2401*T^9 + 1278/2401*T^8
        + 1248/2401*T^7 - 639/2401*T^6 + 1737/2401*T^5 - 1773/2401*T^4 - 121/343*T^3
        - 11/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 
        2*X*Y^7 + 5*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 6*X*Y + 2*X + 6*Y^30 + 
        4*Y^29 + Y^28 + 5*Y^27 + 6*Y^26 + 2*Y^24 + 6*Y^23 + Y^22 + 3*Y^21 + Y^20 + 
        5*Y^19 + 3*Y^18 + 6*Y^17 + 6*Y^16 + 3*Y^15 + 4*Y^13 + 5*Y^12 + Y^11 + Y^10 +
        6*Y^9 + 4*Y^8 + 2*Y^6 + 6*Y^3 + 6*Y^2 + 2*Y + 4,
    T^56 + 20/7*T^55 + 153/49*T^54 + 283/343*T^53 - 4254/2401*T^52 - 955/343*T^51 - 
        4100/2401*T^50 + 3270/2401*T^49 + 9823/2401*T^48 + 7537/2401*T^47 - 
        345/343*T^46 - 8770/2401*T^45 - 5773/2401*T^44 + 93/343*T^43 + 
        4258/2401*T^42 + 3996/2401*T^41 - 348/2401*T^40 - 5252/2401*T^39 - 
        3870/2401*T^38 + 2628/2401*T^37 + 5403/2401*T^36 + 2000/2401*T^35 - 
        2160/2401*T^34 - 3148/2401*T^33 - 1629/2401*T^32 + 862/2401*T^31 + 
        1987/2401*T^30 + 150/2401*T^29 - 1464/2401*T^28 + 150/2401*T^27 + 
        1987/2401*T^26 + 862/2401*T^25 - 1629/2401*T^24 - 3148/2401*T^23 - 
        2160/2401*T^22 + 2000/2401*T^21 + 5403/2401*T^20 + 2628/2401*T^19 - 
        3870/2401*T^18 - 5252/2401*T^17 - 348/2401*T^16 + 3996/2401*T^15 + 
        4258/2401*T^14 + 93/343*T^13 - 5773/2401*T^12 - 8770/2401*T^11 - 
        345/343*T^10 + 7537/2401*T^9 + 9823/2401*T^8 + 3270/2401*T^7 - 4100/2401*T^6
        - 955/343*T^5 - 4254/2401*T^4 + 283/343*T^3 + 153/49*T^2 + 20/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 5*X*Y^8 
        + 5*X*Y^7 + 5*X*Y^6 + 3*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 2*X*Y + 6*X + 4*Y^30 + 
        6*Y^29 + 3*Y^28 + 5*Y^27 + 5*Y^26 + 4*Y^25 + Y^24 + 4*Y^23 + 3*Y^22 + 2*Y^21
        + 2*Y^19 + 3*Y^18 + 6*Y^17 + 2*Y^16 + 5*Y^15 + 6*Y^12 + 6*Y^11 + Y^10 + 
        4*Y^9 + 3*Y^8 + 6*Y^7 + 6*Y^6 + 3*Y^5 + 5*Y^4 + 6*Y^3 + 3*Y + 2,
    -T^56 - 1/7*T^55 + 17/49*T^54 - 32/49*T^53 - 3/49*T^52 + 2775/2401*T^51 - 
        1163/2401*T^50 - 837/2401*T^49 + 3893/2401*T^48 + 1156/2401*T^47 - 
        2155/2401*T^46 + 2005/2401*T^45 + 1957/2401*T^44 - 3414/2401*T^43 + 
        598/2401*T^42 + 3194/2401*T^41 - 2391/2401*T^40 - 275/343*T^39 + 
        2291/2401*T^38 - 1867/2401*T^37 - 2049/2401*T^36 + 1454/2401*T^35 + 
        82/2401*T^34 - 2274/2401*T^33 + 446/2401*T^32 + 356/2401*T^31 - 
        333/2401*T^30 + 621/2401*T^29 - 621/2401*T^27 + 333/2401*T^26 - 
        356/2401*T^25 - 446/2401*T^24 + 2274/2401*T^23 - 82/2401*T^22 - 
        1454/2401*T^21 + 2049/2401*T^20 + 1867/2401*T^19 - 2291/2401*T^18 + 
        275/343*T^17 + 2391/2401*T^16 - 3194/2401*T^15 - 598/2401*T^14 + 
        3414/2401*T^13 - 1957/2401*T^12 - 2005/2401*T^11 + 2155/2401*T^10 - 
        1156/2401*T^9 - 3893/2401*T^8 + 837/2401*T^7 + 1163/2401*T^6 - 2775/2401*T^5
        + 3/49*T^4 + 32/49*T^3 - 17/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + X*Y^11 + 4*X*Y^10 + 5*X*Y^8 + 
        5*X*Y^7 + 4*X*Y^6 + X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 5*X*Y + 2*X + 
        3*Y^30 + 6*Y^29 + Y^27 + 6*Y^26 + 2*Y^25 + 2*Y^23 + 4*Y^22 + Y^20 + 5*Y^18 +
        6*Y^17 + 2*Y^16 + 6*Y^14 + 2*Y^12 + 5*Y^11 + 6*Y^10 + 5*Y^9 + 3*Y^8 + 4*Y^7 
        + 5*Y^6 + 6*Y^5 + 5*Y^4 + 2*Y^3 + 5*Y^2 + 5*Y,
    T^56 - 1/7*T^55 - 48/49*T^54 - 138/343*T^53 - 5/2401*T^52 + 1389/2401*T^51 - 
        765/2401*T^50 + 1231/2401*T^49 - 15/2401*T^48 - 1158/2401*T^47 + 
        108/2401*T^46 + 458/2401*T^45 + 131/2401*T^44 - 211/2401*T^43 + 310/343*T^42
        - 1558/2401*T^41 - 1325/2401*T^40 - 192/2401*T^39 + 772/2401*T^38 + 
        419/2401*T^37 - 1114/2401*T^36 + 1952/2401*T^35 - 26/49*T^34 - 442/2401*T^33
        + 178/343*T^32 + 382/2401*T^31 - 891/2401*T^30 - 982/2401*T^29 + 
        1884/2401*T^28 - 982/2401*T^27 - 891/2401*T^26 + 382/2401*T^25 + 
        178/343*T^24 - 442/2401*T^23 - 26/49*T^22 + 1952/2401*T^21 - 1114/2401*T^20 
        + 419/2401*T^19 + 772/2401*T^18 - 192/2401*T^17 - 1325/2401*T^16 - 
        1558/2401*T^15 + 310/343*T^14 - 211/2401*T^13 + 131/2401*T^12 + 
        458/2401*T^11 + 108/2401*T^10 - 1158/2401*T^9 - 15/2401*T^8 + 1231/2401*T^7 
        - 765/2401*T^6 + 1389/2401*T^5 - 5/2401*T^4 - 138/343*T^3 - 48/49*T^2 - 
        1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 5*X*Y^9 + 3*X*Y^8 + 
        6*X*Y^7 + X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + X*Y + 5*Y^30 + 
        6*Y^28 + 4*Y^27 + 6*Y^26 + 3*Y^24 + 2*Y^23 + 4*Y^21 + 5*Y^20 + 4*Y^19 + 
        4*Y^18 + 4*Y^17 + 4*Y^15 + 3*Y^14 + Y^13 + 4*Y^12 + 2*Y^11 + 5*Y^10 + 4*Y^9 
        + 5*Y^8 + 5*Y^7 + 2*Y^6 + 2*Y^5 + 2*Y^4 + 2*Y^3 + 3*Y^2 + 2*Y + 6,
    T^56 + 3/7*T^55 - 55/49*T^54 - 290/343*T^53 + 768/2401*T^52 + 1392/2401*T^51 - 
        383/2401*T^50 - 2726/2401*T^49 - 964/2401*T^48 + 2395/2401*T^47 + 
        236/343*T^46 + 171/2401*T^45 - 297/2401*T^44 - 633/2401*T^43 - 474/2401*T^42
        + 50/2401*T^41 + 1313/2401*T^40 + 2/343*T^39 - 2327/2401*T^38 - 
        1224/2401*T^37 + 1480/2401*T^36 + 270/343*T^35 - 263/2401*T^34 - 
        1779/2401*T^33 - 295/2401*T^32 + 1711/2401*T^31 + 1445/2401*T^30 - 
        702/2401*T^29 - 251/343*T^28 - 702/2401*T^27 + 1445/2401*T^26 + 
        1711/2401*T^25 - 295/2401*T^24 - 1779/2401*T^23 - 263/2401*T^22 + 
        270/343*T^21 + 1480/2401*T^20 - 1224/2401*T^19 - 2327/2401*T^18 + 2/343*T^17
        + 1313/2401*T^16 + 50/2401*T^15 - 474/2401*T^14 - 633/2401*T^13 - 
        297/2401*T^12 + 171/2401*T^11 + 236/343*T^10 + 2395/2401*T^9 - 964/2401*T^8 
        - 2726/2401*T^7 - 383/2401*T^6 + 1392/2401*T^5 + 768/2401*T^4 - 290/343*T^3 
        - 55/49*T^2 + 3/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 6*X*Y^13 + 5*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + X*Y^8 + 
        6*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + X*Y^3 + 5*X*Y^2 + 4*X*Y + 6*Y^30 + 
        3*Y^29 + 3*Y^28 + 2*Y^25 + 2*Y^24 + 4*Y^23 + Y^22 + 2*Y^21 + 5*Y^20 + Y^19 +
        Y^18 + 4*Y^17 + 3*Y^16 + 4*Y^15 + 5*Y^13 + Y^12 + 5*Y^11 + 5*Y^10 + 6*Y^9 + 
        5*Y^6 + Y^5 + 2*Y^4 + 6*Y^3 + Y^2 + 4*Y + 1,
    T^56 + 1/7*T^55 + 22/49*T^54 - 157/343*T^53 - 351/343*T^52 - 132/343*T^51 - 
        64/2401*T^50 + 1846/2401*T^49 + 3215/2401*T^48 + 556/2401*T^47 - 
        802/2401*T^46 - 2344/2401*T^45 - 2332/2401*T^44 - 297/2401*T^43 + 
        213/343*T^42 + 347/343*T^41 + 276/343*T^40 - 166/2401*T^39 - 2101/2401*T^38 
        - 1721/2401*T^37 - 1410/2401*T^36 + 208/2401*T^35 + 919/2401*T^34 + 
        1073/2401*T^33 - 48/2401*T^32 + 109/2401*T^31 - 694/2401*T^30 - 
        397/2401*T^29 + 16/343*T^28 - 397/2401*T^27 - 694/2401*T^26 + 109/2401*T^25 
        - 48/2401*T^24 + 1073/2401*T^23 + 919/2401*T^22 + 208/2401*T^21 - 
        1410/2401*T^20 - 1721/2401*T^19 - 2101/2401*T^18 - 166/2401*T^17 + 
        276/343*T^16 + 347/343*T^15 + 213/343*T^14 - 297/2401*T^13 - 2332/2401*T^12 
        - 2344/2401*T^11 - 802/2401*T^10 + 556/2401*T^9 + 3215/2401*T^8 + 
        1846/2401*T^7 - 64/2401*T^6 - 132/343*T^5 - 351/343*T^4 - 157/343*T^3 + 
        22/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 4*X*Y^12 + 5*X*Y^11 + 6*X*Y^9 + X*Y^8 + 2*X*Y^5 + 
        4*X*Y^4 + X*Y^3 + X*Y^2 + 6*X*Y + 6*X + 6*Y^30 + 2*Y^29 + 5*Y^28 + 5*Y^27 + 
        6*Y^26 + 4*Y^25 + 4*Y^24 + 3*Y^23 + Y^22 + Y^21 + 5*Y^20 + 2*Y^19 + 2*Y^17 +
        5*Y^16 + Y^15 + 4*Y^14 + 5*Y^13 + 2*Y^12 + 6*Y^11 + 6*Y^9 + 6*Y^8 + Y^7 + 
        3*Y^6 + 4*Y^5 + 6*Y^4 + 6*Y^3 + 6*Y^2 + Y + 5,
    -T^56 - 8/7*T^55 - 55/49*T^54 - 66/343*T^53 + 632/2401*T^52 + 2059/2401*T^51 + 
        94/2401*T^50 + 99/2401*T^49 - 500/2401*T^48 - 365/2401*T^47 - 246/2401*T^46 
        - 319/2401*T^45 - 597/2401*T^44 - 130/2401*T^43 + 1213/2401*T^42 + 
        1558/2401*T^41 + 1854/2401*T^40 + 18/49*T^39 + 332/2401*T^38 + 396/2401*T^37
        + 451/2401*T^36 + 6/49*T^35 - 641/2401*T^34 - 754/2401*T^33 - 437/2401*T^32 
        + 262/343*T^31 + 3135/2401*T^30 + 2748/2401*T^29 - 2748/2401*T^27 - 
        3135/2401*T^26 - 262/343*T^25 + 437/2401*T^24 + 754/2401*T^23 + 
        641/2401*T^22 - 6/49*T^21 - 451/2401*T^20 - 396/2401*T^19 - 332/2401*T^18 - 
        18/49*T^17 - 1854/2401*T^16 - 1558/2401*T^15 - 1213/2401*T^14 + 
        130/2401*T^13 + 597/2401*T^12 + 319/2401*T^11 + 246/2401*T^10 + 365/2401*T^9
        + 500/2401*T^8 - 99/2401*T^7 - 94/2401*T^6 - 2059/2401*T^5 - 632/2401*T^4 + 
        66/343*T^3 + 55/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 4*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 3*X*Y^7 +
        5*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 3*X*Y + 6*X + Y^30 + 2*Y^29 + 2*Y^28
        + 2*Y^27 + 4*Y^26 + 4*Y^25 + Y^24 + 4*Y^23 + 4*Y^22 + 3*Y^20 + 5*Y^19 + 
        6*Y^18 + 5*Y^17 + 5*Y^16 + 2*Y^14 + 5*Y^13 + Y^12 + 5*Y^11 + 5*Y^9 + 3*Y^7 +
        4*Y^6 + 3*Y^5 + 6*Y^4 + 2*Y^3 + 2*Y^2 + 4*Y + 1,
    -T^56 + 15/7*T^55 - 80/49*T^54 - 279/343*T^53 + 6001/2401*T^52 - 3776/2401*T^51 
        - 1732/2401*T^50 + 478/343*T^49 + 1798/2401*T^48 - 7481/2401*T^47 + 
        6183/2401*T^46 + 870/2401*T^45 - 5682/2401*T^44 + 3940/2401*T^43 + 
        1210/2401*T^42 - 3037/2401*T^41 - 622/2401*T^40 + 4555/2401*T^39 - 
        2948/2401*T^38 - 1677/2401*T^37 + 3335/2401*T^36 - 659/2401*T^35 - 
        1699/2401*T^34 + 122/343*T^33 + 1025/2401*T^32 - 209/2401*T^31 - 
        2362/2401*T^30 + 2832/2401*T^29 - 2832/2401*T^27 + 2362/2401*T^26 + 
        209/2401*T^25 - 1025/2401*T^24 - 122/343*T^23 + 1699/2401*T^22 + 
        659/2401*T^21 - 3335/2401*T^20 + 1677/2401*T^19 + 2948/2401*T^18 - 
        4555/2401*T^17 + 622/2401*T^16 + 3037/2401*T^15 - 1210/2401*T^14 - 
        3940/2401*T^13 + 5682/2401*T^12 - 870/2401*T^11 - 6183/2401*T^10 + 
        7481/2401*T^9 - 1798/2401*T^8 - 478/343*T^7 + 1732/2401*T^6 + 3776/2401*T^5 
        - 6001/2401*T^4 + 279/343*T^3 + 80/49*T^2 - 15/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + X*Y^10 + 5*X*Y^9 + X*Y^8 + 
        5*X*Y^7 + 4*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + X*Y^2 + 2*X*Y + 5*X + Y^30
        + 2*Y^29 + 5*Y^28 + 5*Y^26 + 3*Y^25 + 4*Y^24 + 6*Y^23 + 5*Y^22 + 2*Y^21 + 
        Y^19 + 6*Y^18 + 5*Y^17 + 3*Y^16 + 4*Y^15 + 3*Y^14 + Y^13 + 4*Y^12 + 4*Y^11 +
        5*Y^10 + Y^8 + 5*Y^7 + 2*Y^5 + 2*Y^4 + 5*Y^3 + 4*Y^2 + 4*Y + 4,
    T^56 - 83/49*T^54 + 104/343*T^53 + 1987/2401*T^52 + 101/2401*T^51 + 
        135/2401*T^50 - 1595/2401*T^49 - 326/2401*T^48 - 85/2401*T^47 - 44/2401*T^46
        + 1619/2401*T^45 - 136/343*T^44 - 1877/2401*T^43 + 1847/2401*T^42 + 
        38/343*T^41 - 2285/2401*T^40 + 2484/2401*T^39 + 2007/2401*T^38 - 
        2196/2401*T^37 - 611/2401*T^36 + 349/2401*T^35 - 2/343*T^34 + 459/2401*T^33 
        + 1415/2401*T^32 + 304/2401*T^31 - 3854/2401*T^30 - 533/2401*T^29 + 
        682/343*T^28 - 533/2401*T^27 - 3854/2401*T^26 + 304/2401*T^25 + 
        1415/2401*T^24 + 459/2401*T^23 - 2/343*T^22 + 349/2401*T^21 - 611/2401*T^20 
        - 2196/2401*T^19 + 2007/2401*T^18 + 2484/2401*T^17 - 2285/2401*T^16 + 
        38/343*T^15 + 1847/2401*T^14 - 1877/2401*T^13 - 136/343*T^12 + 
        1619/2401*T^11 - 44/2401*T^10 - 85/2401*T^9 - 326/2401*T^8 - 1595/2401*T^7 +
        135/2401*T^6 + 101/2401*T^5 + 1987/2401*T^4 + 104/343*T^3 - 83/49*T^2 + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 
        + 3*X*Y^8 + 5*X*Y^7 + X*Y^6 + X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + X*Y^2 + 4*X*Y + 
        4*X + 5*Y^30 + Y^29 + Y^28 + 6*Y^27 + 3*Y^26 + 2*Y^25 + 2*Y^24 + 2*Y^23 + 
        Y^22 + 5*Y^21 + 2*Y^19 + 3*Y^18 + 6*Y^17 + 3*Y^16 + 4*Y^15 + 4*Y^14 + Y^13 +
        3*Y^12 + 4*Y^11 + Y^10 + 6*Y^9 + 5*Y^8 + 6*Y^7 + Y^6 + 2*Y^5 + Y^4 + 4*Y^3 +
        3*Y^2 + 5*Y + 3,
    T^56 + 8/7*T^55 - 47/49*T^54 - 677/343*T^53 - 3106/2401*T^52 - 4/343*T^51 + 
        4268/2401*T^50 + 4590/2401*T^49 + 1275/2401*T^48 - 673/2401*T^47 - 
        3105/2401*T^46 - 5101/2401*T^45 - 2995/2401*T^44 + 1847/2401*T^43 + 
        5156/2401*T^42 + 4815/2401*T^41 + 1870/2401*T^40 - 2442/2401*T^39 - 
        813/343*T^38 - 4360/2401*T^37 + 15/49*T^36 + 3761/2401*T^35 + 3005/2401*T^34
        + 1901/2401*T^33 - 593/2401*T^32 - 2883/2401*T^31 - 335/2401*T^30 + 
        592/2401*T^29 - 1091/2401*T^28 + 592/2401*T^27 - 335/2401*T^26 - 
        2883/2401*T^25 - 593/2401*T^24 + 1901/2401*T^23 + 3005/2401*T^22 + 
        3761/2401*T^21 + 15/49*T^20 - 4360/2401*T^19 - 813/343*T^18 - 2442/2401*T^17
        + 1870/2401*T^16 + 4815/2401*T^15 + 5156/2401*T^14 + 1847/2401*T^13 - 
        2995/2401*T^12 - 5101/2401*T^11 - 3105/2401*T^10 - 673/2401*T^9 + 
        1275/2401*T^8 + 4590/2401*T^7 + 4268/2401*T^6 - 4/343*T^5 - 3106/2401*T^4 - 
        677/343*T^3 - 47/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 2*X*Y^8 + 4*X*Y^6 +
        X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + 5*X*Y + 3*X + 4*Y^30 + 5*Y^29 + Y^28 +
        6*Y^27 + 4*Y^26 + 6*Y^25 + 2*Y^24 + Y^23 + 6*Y^22 + Y^21 + Y^20 + 4*Y^19 + 
        4*Y^18 + 6*Y^16 + 2*Y^15 + 6*Y^14 + 5*Y^13 + 6*Y^12 + 5*Y^11 + 4*Y^10 + 
        3*Y^9 + 3*Y^8 + Y^7 + Y^6 + Y^4 + 2*Y^3 + 6*Y^2 + 3*Y,
    -T^56 - 3/7*T^55 + 11/7*T^54 + 190/343*T^53 - 2606/2401*T^52 + 1410/2401*T^51 + 
        1782/2401*T^50 - 2236/2401*T^49 - 386/2401*T^48 + 1572/2401*T^47 - 
        2143/2401*T^46 - 40/49*T^45 + 480/343*T^44 + 2850/2401*T^43 - 2552/2401*T^42
        - 1990/2401*T^41 + 1802/2401*T^40 + 25/343*T^39 - 2245/2401*T^38 - 
        5/2401*T^37 + 1657/2401*T^36 - 365/2401*T^35 - 143/2401*T^34 + 239/343*T^33 
        - 599/2401*T^32 - 2098/2401*T^31 + 167/2401*T^30 + 825/2401*T^29 - 
        825/2401*T^27 - 167/2401*T^26 + 2098/2401*T^25 + 599/2401*T^24 - 
        239/343*T^23 + 143/2401*T^22 + 365/2401*T^21 - 1657/2401*T^20 + 5/2401*T^19 
        + 2245/2401*T^18 - 25/343*T^17 - 1802/2401*T^16 + 1990/2401*T^15 + 
        2552/2401*T^14 - 2850/2401*T^13 - 480/343*T^12 + 40/49*T^11 + 2143/2401*T^10
        - 1572/2401*T^9 + 386/2401*T^8 + 2236/2401*T^7 - 1782/2401*T^6 - 
        1410/2401*T^5 + 2606/2401*T^4 - 190/343*T^3 - 11/7*T^2 + 3/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 5*X*Y^11 + 5*X*Y^10 + X*Y^9 + 4*X*Y^8 + 
        2*X*Y^7 + X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 5*Y^30 + 6*Y^29 + 
        2*Y^28 + 2*Y^27 + Y^26 + 3*Y^25 + 2*Y^24 + 5*Y^23 + 4*Y^22 + 4*Y^20 + 5*Y^19
        + 4*Y^16 + 5*Y^15 + 4*Y^14 + Y^13 + 6*Y^12 + 3*Y^11 + 5*Y^10 + 5*Y^9 + Y^8 +
        5*Y^7 + 5*Y^5 + 3*Y^4 + 2*Y^3 + 2*Y^2 + 6*Y + 1,
    -T^56 + 10/7*T^55 - 47/49*T^54 + 452/343*T^53 - 3362/2401*T^52 + 4099/2401*T^51 
        - 5090/2401*T^50 + 3484/2401*T^49 - 2033/2401*T^48 + 3182/2401*T^47 - 
        2886/2401*T^46 + 2201/2401*T^45 - 1697/2401*T^44 - 529/2401*T^43 - 2/49*T^42
        - 78/2401*T^41 + 2731/2401*T^40 - 410/343*T^39 + 3442/2401*T^38 - 
        4864/2401*T^37 + 554/343*T^36 - 4430/2401*T^35 + 5114/2401*T^34 - 
        3551/2401*T^33 + 584/343*T^32 - 3617/2401*T^31 + 194/343*T^30 - 214/343*T^29
        + 214/343*T^27 - 194/343*T^26 + 3617/2401*T^25 - 584/343*T^24 + 
        3551/2401*T^23 - 5114/2401*T^22 + 4430/2401*T^21 - 554/343*T^20 + 
        4864/2401*T^19 - 3442/2401*T^18 + 410/343*T^17 - 2731/2401*T^16 + 
        78/2401*T^15 + 2/49*T^14 + 529/2401*T^13 + 1697/2401*T^12 - 2201/2401*T^11 +
        2886/2401*T^10 - 3182/2401*T^9 + 2033/2401*T^8 - 3484/2401*T^7 + 
        5090/2401*T^6 - 4099/2401*T^5 + 3362/2401*T^4 - 452/343*T^3 + 47/49*T^2 - 
        10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 2*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 3*X*Y^7 +
        3*X*Y^5 + 5*X*Y^4 + 5*X*Y + 6*X + Y^30 + Y^29 + Y^28 + 6*Y^27 + 3*Y^26 + 
        2*Y^25 + 3*Y^24 + Y^23 + 4*Y^22 + 2*Y^21 + Y^20 + 6*Y^19 + 2*Y^18 + 4*Y^17 +
        5*Y^16 + 2*Y^15 + 4*Y^14 + 5*Y^13 + 4*Y^12 + 3*Y^11 + Y^10 + 5*Y^9 + 4*Y^8 +
        5*Y^7 + 2*Y^6 + 5*Y^5 + 6*Y^3 + 4*Y^2 + 4,
    -T^56 - 2/7*T^55 - 27/49*T^54 + 66/343*T^53 + 72/2401*T^52 - 292/2401*T^51 + 
        1126/2401*T^50 - 151/2401*T^49 + 1072/2401*T^48 + 62/2401*T^47 - 
        716/2401*T^46 + 1152/2401*T^45 - 334/2401*T^44 + 866/2401*T^43 + 
        116/2401*T^42 - 227/2401*T^41 + 572/2401*T^40 - 1170/2401*T^39 + 
        115/343*T^38 - 366/2401*T^37 + 857/2401*T^36 + 1065/2401*T^35 + 22/343*T^34 
        + 775/2401*T^33 - 99/2401*T^32 + 443/2401*T^31 - 521/2401*T^30 + 
        18/2401*T^29 - 18/2401*T^27 + 521/2401*T^26 - 443/2401*T^25 + 99/2401*T^24 -
        775/2401*T^23 - 22/343*T^22 - 1065/2401*T^21 - 857/2401*T^20 + 366/2401*T^19
        - 115/343*T^18 + 1170/2401*T^17 - 572/2401*T^16 + 227/2401*T^15 - 
        116/2401*T^14 - 866/2401*T^13 + 334/2401*T^12 - 1152/2401*T^11 + 
        716/2401*T^10 - 62/2401*T^9 - 1072/2401*T^8 + 151/2401*T^7 - 1126/2401*T^6 +
        292/2401*T^5 - 72/2401*T^4 - 66/343*T^3 + 27/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 5*X*Y^13 + 3*X*Y^11 + X*Y^10 + 3*X*Y^9 + 5*X*Y^6 + 3*X*Y^5 + 
        5*X*Y^3 + 5*X*Y^2 + X + 4*Y^30 + 6*Y^29 + 4*Y^28 + 5*Y^27 + 3*Y^26 + 4*Y^25 
        + 5*Y^23 + 2*Y^22 + Y^21 + 5*Y^20 + Y^19 + 2*Y^17 + 5*Y^16 + 5*Y^15 + 4*Y^14
        + 5*Y^13 + 3*Y^12 + 4*Y^9 + 4*Y^8 + 2*Y^7 + 4*Y^6 + Y^5 + Y^4 + 6*Y^3 + 
        5*Y^2 + 3*Y,
    -T^56 - T^55 - 5/49*T^54 + 188/343*T^53 + 2204/2401*T^52 + 2367/2401*T^51 + 
        1147/2401*T^50 + 187/2401*T^49 - 67/2401*T^48 - 2217/2401*T^47 - 
        1563/2401*T^46 - 740/2401*T^45 - 179/2401*T^44 + 737/2401*T^43 + 
        136/343*T^42 + 934/2401*T^41 + 149/2401*T^40 + 580/2401*T^39 + 986/2401*T^38
        + 886/2401*T^37 - 479/2401*T^36 - 1808/2401*T^35 - 316/343*T^34 - 
        220/343*T^33 + 1751/2401*T^32 + 1900/2401*T^31 + 1608/2401*T^30 + 
        813/2401*T^29 - 813/2401*T^27 - 1608/2401*T^26 - 1900/2401*T^25 - 
        1751/2401*T^24 + 220/343*T^23 + 316/343*T^22 + 1808/2401*T^21 + 
        479/2401*T^20 - 886/2401*T^19 - 986/2401*T^18 - 580/2401*T^17 - 
        149/2401*T^16 - 934/2401*T^15 - 136/343*T^14 - 737/2401*T^13 + 179/2401*T^12
        + 740/2401*T^11 + 1563/2401*T^10 + 2217/2401*T^9 + 67/2401*T^8 - 
        187/2401*T^7 - 1147/2401*T^6 - 2367/2401*T^5 - 2204/2401*T^4 - 188/343*T^3 +
        5/49*T^2 + T + 1
*], [*
    X^3 + 2*X*Y^14 + X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 4*X*Y^6 + 
        5*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 5*X*Y + 2*X + 3*Y^30 + 3*Y^29 + 
        6*Y^28 + 2*Y^26 + 3*Y^25 + 6*Y^23 + Y^22 + 6*Y^21 + 6*Y^20 + 2*Y^18 + 2*Y^17
        + Y^15 + 5*Y^14 + 5*Y^13 + Y^11 + 3*Y^10 + Y^9 + 3*Y^8 + 5*Y^7 + 4*Y^6 + 
        6*Y^5 + 6*Y^4 + 6*Y^2 + 4*Y + 6,
    -T^56 + 11/7*T^55 - 11/7*T^54 + 241/343*T^53 + 1209/2401*T^52 - 1824/2401*T^51 +
        216/343*T^50 + 928/2401*T^49 - 2535/2401*T^48 + 2189/2401*T^47 - 
        1223/2401*T^46 + 328/2401*T^45 - 249/2401*T^44 + 1277/2401*T^43 - 
        1713/2401*T^42 + 1513/2401*T^41 + 383/2401*T^40 - 2083/2401*T^39 + 
        1572/2401*T^38 - 470/2401*T^37 - 1672/2401*T^36 + 2196/2401*T^35 - 
        1249/2401*T^34 - 570/2401*T^33 + 236/343*T^32 - 1300/2401*T^31 + 
        53/2401*T^30 + 183/2401*T^29 - 183/2401*T^27 - 53/2401*T^26 + 1300/2401*T^25
        - 236/343*T^24 + 570/2401*T^23 + 1249/2401*T^22 - 2196/2401*T^21 + 
        1672/2401*T^20 + 470/2401*T^19 - 1572/2401*T^18 + 2083/2401*T^17 - 
        383/2401*T^16 - 1513/2401*T^15 + 1713/2401*T^14 - 1277/2401*T^13 + 
        249/2401*T^12 - 328/2401*T^11 + 1223/2401*T^10 - 2189/2401*T^9 + 
        2535/2401*T^8 - 928/2401*T^7 - 216/343*T^6 + 1824/2401*T^5 - 1209/2401*T^4 -
        241/343*T^3 + 11/7*T^2 - 11/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + X*Y^13 + 2*X*Y^12 + 4*X*Y^10 + 5*X*Y^9 + 6*X*Y^7 + 
        5*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 4*X*Y + 2*Y^30 + 4*Y^29 + 
        Y^28 + Y^27 + 6*Y^26 + 6*Y^25 + Y^24 + Y^23 + Y^22 + 6*Y^21 + 2*Y^20 + Y^18 
        + 3*Y^17 + 3*Y^16 + 6*Y^15 + 6*Y^14 + 4*Y^13 + 6*Y^12 + 2*Y^11 + Y^10 + 
        3*Y^9 + Y^7 + 6*Y^6 + Y^5 + 2*Y^4 + 4*Y^3 + 3*Y^2 + 3,
    -T^56 + 34/49*T^54 + 348/343*T^53 - 999/2401*T^52 - 2174/2401*T^51 - 
        943/2401*T^50 + 1182/2401*T^49 + 1157/2401*T^48 - 940/2401*T^47 - 
        149/343*T^46 - 48/343*T^45 + 1194/2401*T^44 - 920/2401*T^43 - 226/2401*T^42 
        - 624/2401*T^41 + 281/2401*T^40 + 765/2401*T^39 + 844/2401*T^38 - 
        598/2401*T^37 - 1002/2401*T^36 - 503/2401*T^35 + 1098/2401*T^34 + 
        499/2401*T^33 - 829/2401*T^32 - 2074/2401*T^31 + 732/2401*T^30 + 
        2472/2401*T^29 - 2472/2401*T^27 - 732/2401*T^26 + 2074/2401*T^25 + 
        829/2401*T^24 - 499/2401*T^23 - 1098/2401*T^22 + 503/2401*T^21 + 
        1002/2401*T^20 + 598/2401*T^19 - 844/2401*T^18 - 765/2401*T^17 - 
        281/2401*T^16 + 624/2401*T^15 + 226/2401*T^14 + 920/2401*T^13 - 
        1194/2401*T^12 + 48/343*T^11 + 149/343*T^10 + 940/2401*T^9 - 1157/2401*T^8 -
        1182/2401*T^7 + 943/2401*T^6 + 2174/2401*T^5 + 999/2401*T^4 - 348/343*T^3 - 
        34/49*T^2 + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 2*X*Y^12 + 3*X*Y^11 + 3*X*Y^9 + 6*X*Y^8 + 5*X*Y^7 + 
        5*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 3*X*Y + X + 5*Y^30 + 2*Y^29 + 2*Y^28
        + 3*Y^27 + 5*Y^26 + Y^25 + 4*Y^24 + 6*Y^23 + Y^22 + 5*Y^20 + 5*Y^19 + Y^18 +
        2*Y^17 + 2*Y^16 + 4*Y^15 + Y^14 + 6*Y^13 + Y^12 + 2*Y^11 + 2*Y^10 + 2*Y^9 + 
        2*Y^8 + Y^7 + 5*Y^6 + 4*Y^5 + 4*Y^4 + 3*Y^2 + 5*Y,
    T^56 - 5/7*T^55 + 37/49*T^54 + 178/343*T^53 - 519/2401*T^52 + 1445/2401*T^51 + 
        1562/2401*T^50 - 115/2401*T^49 + 760/2401*T^48 + 24/49*T^47 - 215/343*T^46 +
        33/49*T^45 - 1692/2401*T^44 + 512/2401*T^43 - 337/2401*T^42 - 2145/2401*T^41
        + 1347/2401*T^40 - 347/343*T^39 - 48/2401*T^38 - 109/2401*T^37 - 
        333/2401*T^36 - 159/343*T^35 + 2042/2401*T^34 - 979/2401*T^33 + 
        843/2401*T^32 + 270/343*T^31 + 132/2401*T^30 + 1879/2401*T^29 + 
        624/2401*T^28 + 1879/2401*T^27 + 132/2401*T^26 + 270/343*T^25 + 
        843/2401*T^24 - 979/2401*T^23 + 2042/2401*T^22 - 159/343*T^21 - 
        333/2401*T^20 - 109/2401*T^19 - 48/2401*T^18 - 347/343*T^17 + 1347/2401*T^16
        - 2145/2401*T^15 - 337/2401*T^14 + 512/2401*T^13 - 1692/2401*T^12 + 
        33/49*T^11 - 215/343*T^10 + 24/49*T^9 + 760/2401*T^8 - 115/2401*T^7 + 
        1562/2401*T^6 + 1445/2401*T^5 - 519/2401*T^4 + 178/343*T^3 + 37/49*T^2 - 
        5/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 3*X*Y^11 + X*Y^10 + X*Y^9 + 5*X*Y^8 + 
        4*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + 3*X*Y + X + Y^30
        + 5*Y^29 + 3*Y^28 + 4*Y^27 + 4*Y^26 + Y^25 + 2*Y^24 + Y^23 + Y^21 + 6*Y^19 +
        Y^18 + 3*Y^17 + 5*Y^15 + 3*Y^14 + 4*Y^13 + Y^11 + 6*Y^10 + 4*Y^8 + 4*Y^7 + 
        2*Y^6 + 4*Y^5 + 6*Y^4 + 6*Y^3 + 2*Y^2 + Y + 3,
    T^56 - 1/7*T^55 + 3/49*T^54 - 232/343*T^53 + 759/2401*T^52 - 1949/2401*T^51 - 
        1494/2401*T^50 - 67/343*T^49 + 18/49*T^48 + 557/2401*T^47 + 179/2401*T^46 + 
        1039/2401*T^45 + 431/2401*T^44 + 226/2401*T^43 - 18/2401*T^42 + 165/343*T^41
        - 649/2401*T^40 - 1300/2401*T^39 - 697/2401*T^38 + 342/2401*T^37 + 
        10/2401*T^36 - 612/2401*T^35 + 621/2401*T^34 + 1635/2401*T^33 + 
        262/2401*T^32 - 131/2401*T^31 - 698/2401*T^30 + 111/2401*T^29 - 
        1222/2401*T^28 + 111/2401*T^27 - 698/2401*T^26 - 131/2401*T^25 + 
        262/2401*T^24 + 1635/2401*T^23 + 621/2401*T^22 - 612/2401*T^21 + 
        10/2401*T^20 + 342/2401*T^19 - 697/2401*T^18 - 1300/2401*T^17 - 
        649/2401*T^16 + 165/343*T^15 - 18/2401*T^14 + 226/2401*T^13 + 431/2401*T^12 
        + 1039/2401*T^11 + 179/2401*T^10 + 557/2401*T^9 + 18/49*T^8 - 67/343*T^7 - 
        1494/2401*T^6 - 1949/2401*T^5 + 759/2401*T^4 - 232/343*T^3 + 3/49*T^2 - 
        1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 
        + 5*X*Y^8 + X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 2*X*Y + 6*X + 
        3*Y^30 + 6*Y^29 + 2*Y^28 + 4*Y^27 + 2*Y^26 + Y^25 + 2*Y^23 + 2*Y^22 + 3*Y^21
        + Y^18 + 4*Y^17 + 6*Y^15 + Y^14 + 4*Y^13 + 4*Y^12 + Y^11 + 2*Y^10 + 5*Y^9 + 
        3*Y^8 + 4*Y^6 + Y^5 + 2*Y^4 + 5*Y^3 + 6*Y^2 + 3*Y,
    T^56 - 6/7*T^55 - 9/49*T^54 + 39/343*T^53 - 176/2401*T^52 + 1723/2401*T^51 - 
        2010/2401*T^50 + 247/2401*T^49 - 201/2401*T^48 + 1263/2401*T^47 - 
        24/2401*T^46 + 1048/2401*T^45 - 1140/2401*T^44 - 1095/2401*T^43 + 
        1839/2401*T^42 - 123/343*T^41 + 725/2401*T^40 - 1514/2401*T^39 - 
        201/2401*T^38 + 1675/2401*T^37 - 443/2401*T^36 + 1103/2401*T^35 - 
        1206/2401*T^34 + 299/2401*T^33 - 129/2401*T^32 + 227/2401*T^31 + 
        1587/2401*T^30 - 1553/2401*T^29 + 648/2401*T^28 - 1553/2401*T^27 + 
        1587/2401*T^26 + 227/2401*T^25 - 129/2401*T^24 + 299/2401*T^23 - 
        1206/2401*T^22 + 1103/2401*T^21 - 443/2401*T^20 + 1675/2401*T^19 - 
        201/2401*T^18 - 1514/2401*T^17 + 725/2401*T^16 - 123/343*T^15 + 
        1839/2401*T^14 - 1095/2401*T^13 - 1140/2401*T^12 + 1048/2401*T^11 - 
        24/2401*T^10 + 1263/2401*T^9 - 201/2401*T^8 + 247/2401*T^7 - 2010/2401*T^6 +
        1723/2401*T^5 - 176/2401*T^4 + 39/343*T^3 - 9/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + X*Y^8 + 
        2*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 5*X*Y + 3*X + 
        3*Y^30 + 4*Y^28 + 2*Y^27 + 2*Y^26 + 2*Y^25 + 6*Y^24 + 2*Y^23 + 4*Y^22 + 
        3*Y^21 + 4*Y^20 + Y^19 + Y^18 + 3*Y^17 + Y^16 + 6*Y^15 + 4*Y^14 + 3*Y^13 + 
        5*Y^11 + Y^10 + 3*Y^9 + 3*Y^8 + 4*Y^7 + 2*Y^5 + Y^3 + 5*Y^2 + 6*Y + 3,
    T^56 - T^55 - 72/49*T^54 + 55/49*T^53 + 1287/2401*T^52 + 101/2401*T^51 + 
        710/2401*T^50 - 1130/2401*T^49 + 573/2401*T^48 + 108/2401*T^47 - 
        2615/2401*T^46 + 457/2401*T^45 + 51/49*T^44 + 236/2401*T^43 - 1818/2401*T^42
        - 656/2401*T^41 + 320/2401*T^40 + 146/343*T^39 + 914/2401*T^38 - 
        1553/2401*T^37 - 261/2401*T^36 + 169/343*T^35 + 683/2401*T^34 - 
        640/2401*T^33 - 2256/2401*T^32 + 1224/2401*T^31 + 551/2401*T^30 - 
        676/2401*T^29 + 163/343*T^28 - 676/2401*T^27 + 551/2401*T^26 + 
        1224/2401*T^25 - 2256/2401*T^24 - 640/2401*T^23 + 683/2401*T^22 + 
        169/343*T^21 - 261/2401*T^20 - 1553/2401*T^19 + 914/2401*T^18 + 146/343*T^17
        + 320/2401*T^16 - 656/2401*T^15 - 1818/2401*T^14 + 236/2401*T^13 + 
        51/49*T^12 + 457/2401*T^11 - 2615/2401*T^10 + 108/2401*T^9 + 573/2401*T^8 - 
        1130/2401*T^7 + 710/2401*T^6 + 101/2401*T^5 + 1287/2401*T^4 + 55/49*T^3 - 
        72/49*T^2 - T + 1
*], [*
    X^3 + 5*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 3*X*Y^8 +
        5*X*Y^7 + 5*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 4*X*Y + 3*X + 5*Y^30 + 4*Y^29 + 
        2*Y^28 + Y^27 + 3*Y^26 + 3*Y^25 + 2*Y^24 + 3*Y^23 + 3*Y^22 + 6*Y^21 + 6*Y^20
        + 4*Y^19 + 3*Y^18 + 5*Y^17 + Y^16 + 2*Y^15 + 6*Y^14 + 3*Y^13 + 6*Y^12 + 
        3*Y^11 + 6*Y^10 + 4*Y^9 + Y^8 + Y^7 + 6*Y^6 + 2*Y^5 + 5*Y^4 + 6*Y^3 + 3*Y^2 
        + 3*Y,
    T^56 - 2/7*T^55 - 26/49*T^54 + 46/49*T^53 - 3638/2401*T^52 - 50/343*T^51 + 
        2005/2401*T^50 - 3914/2401*T^49 + 2705/2401*T^48 + 2392/2401*T^47 - 
        4104/2401*T^46 + 3273/2401*T^45 + 316/2401*T^44 - 4258/2401*T^43 + 
        668/343*T^42 - 1454/2401*T^41 - 1968/2401*T^40 + 103/49*T^39 - 
        3244/2401*T^38 - 851/2401*T^37 + 2456/2401*T^36 - 557/343*T^35 + 52/343*T^34
        + 2101/2401*T^33 - 2459/2401*T^32 + 2556/2401*T^31 + 482/2401*T^30 - 
        2241/2401*T^29 + 375/343*T^28 - 2241/2401*T^27 + 482/2401*T^26 + 
        2556/2401*T^25 - 2459/2401*T^24 + 2101/2401*T^23 + 52/343*T^22 - 
        557/343*T^21 + 2456/2401*T^20 - 851/2401*T^19 - 3244/2401*T^18 + 103/49*T^17
        - 1968/2401*T^16 - 1454/2401*T^15 + 668/343*T^14 - 4258/2401*T^13 + 
        316/2401*T^12 + 3273/2401*T^11 - 4104/2401*T^10 + 2392/2401*T^9 + 
        2705/2401*T^8 - 3914/2401*T^7 + 2005/2401*T^6 - 50/343*T^5 - 3638/2401*T^4 +
        46/49*T^3 - 26/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + X*Y^10 + 4*X*Y^9 + 
        5*X*Y^8 + X*Y^7 + 2*X*Y^6 + 2*X*Y^4 + 4*X*Y^3 + X*Y^2 + X*Y + 6*X + 4*Y^30 +
        4*Y^29 + 3*Y^28 + 5*Y^27 + 5*Y^25 + 6*Y^24 + 5*Y^23 + 3*Y^22 + 5*Y^21 + 
        6*Y^20 + 6*Y^19 + 2*Y^17 + 3*Y^16 + 3*Y^14 + 5*Y^13 + 3*Y^12 + 6*Y^11 + 
        2*Y^10 + 4*Y^9 + 6*Y^8 + 2*Y^7 + 6*Y^6 + 6*Y^5 + 3*Y^2 + 3*Y + 5,
    T^56 + 4/7*T^55 - 43/49*T^54 - 48/343*T^53 + 1371/2401*T^52 - 1538/2401*T^51 - 
        1630/2401*T^50 - 748/2401*T^49 - 776/2401*T^48 + 806/2401*T^47 + 
        957/2401*T^46 - 4/2401*T^45 + 505/2401*T^44 + 2168/2401*T^43 + 
        1083/2401*T^42 - 1693/2401*T^41 - 1616/2401*T^40 - 345/2401*T^39 - 
        271/2401*T^38 - 6/49*T^37 - 299/2401*T^36 + 1/7*T^35 + 1441/2401*T^34 + 
        187/343*T^33 + 1262/2401*T^32 + 335/2401*T^31 - 813/2401*T^30 - 
        1492/2401*T^29 - 1486/2401*T^28 - 1492/2401*T^27 - 813/2401*T^26 + 
        335/2401*T^25 + 1262/2401*T^24 + 187/343*T^23 + 1441/2401*T^22 + 1/7*T^21 - 
        299/2401*T^20 - 6/49*T^19 - 271/2401*T^18 - 345/2401*T^17 - 1616/2401*T^16 -
        1693/2401*T^15 + 1083/2401*T^14 + 2168/2401*T^13 + 505/2401*T^12 - 
        4/2401*T^11 + 957/2401*T^10 + 806/2401*T^9 - 776/2401*T^8 - 748/2401*T^7 - 
        1630/2401*T^6 - 1538/2401*T^5 + 1371/2401*T^4 - 48/343*T^3 - 43/49*T^2 + 
        4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 
        + X*Y^6 + 5*X*Y^5 + X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 5*X*Y + 4*X + 2*Y^30 + 
        2*Y^29 + 5*Y^28 + 2*Y^27 + 6*Y^26 + Y^25 + Y^24 + 2*Y^23 + 4*Y^22 + 5*Y^21 +
        5*Y^20 + 5*Y^19 + 5*Y^17 + 3*Y^16 + 5*Y^15 + Y^14 + 6*Y^13 + 4*Y^12 + 4*Y^11
        + 4*Y^10 + Y^8 + Y^7 + 4*Y^5 + 6*Y^4 + 5*Y^3 + 4*Y^2 + 5*Y + 6,
    T^56 - 1/7*T^55 + 6/49*T^54 + 86/343*T^53 - 2859/2401*T^52 + 2224/2401*T^51 - 
        670/2401*T^50 - 955/2401*T^49 + 2722/2401*T^48 - 3240/2401*T^47 + 
        2577/2401*T^46 + 129/343*T^45 - 74/49*T^44 + 3266/2401*T^43 - 2662/2401*T^42
        - 403/2401*T^41 + 2804/2401*T^40 - 3891/2401*T^39 + 204/343*T^38 + 
        47/343*T^37 - 1772/2401*T^36 + 3373/2401*T^35 - 1359/2401*T^34 - 
        1261/2401*T^33 + 2696/2401*T^32 - 1796/2401*T^31 + 1012/2401*T^30 + 
        1549/2401*T^29 - 3322/2401*T^28 + 1549/2401*T^27 + 1012/2401*T^26 - 
        1796/2401*T^25 + 2696/2401*T^24 - 1261/2401*T^23 - 1359/2401*T^22 + 
        3373/2401*T^21 - 1772/2401*T^20 + 47/343*T^19 + 204/343*T^18 - 
        3891/2401*T^17 + 2804/2401*T^16 - 403/2401*T^15 - 2662/2401*T^14 + 
        3266/2401*T^13 - 74/49*T^12 + 129/343*T^11 + 2577/2401*T^10 - 3240/2401*T^9 
        + 2722/2401*T^8 - 955/2401*T^7 - 670/2401*T^6 + 2224/2401*T^5 - 
        2859/2401*T^4 + 86/343*T^3 + 6/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 4*X*Y^8 +
        4*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + X*Y^2 + 4*X*Y + 6*X + 
        2*Y^30 + 4*Y^29 + 2*Y^28 + 2*Y^27 + Y^26 + 4*Y^25 + 5*Y^23 + 2*Y^22 + 2*Y^21
        + 5*Y^19 + Y^18 + 3*Y^17 + 2*Y^16 + 5*Y^15 + 6*Y^14 + 6*Y^13 + 4*Y^11 + 
        2*Y^10 + 3*Y^9 + 4*Y^8 + Y^7 + 6*Y^6 + 2*Y^5 + 4*Y^4 + Y^2 + 6*Y + 3,
    -T^56 - 18/49*T^54 - 37/49*T^53 + 2/343*T^52 - 898/2401*T^51 + 214/2401*T^50 - 
        1850/2401*T^49 + 230/343*T^48 - 1695/2401*T^47 - 137/2401*T^46 + 
        605/2401*T^45 - 941/2401*T^44 + 2162/2401*T^43 - 1090/2401*T^42 + 
        1831/2401*T^41 - 478/2401*T^40 + 970/2401*T^39 + 45/2401*T^38 + 
        282/2401*T^37 + 1805/2401*T^36 - 677/2401*T^35 + 1968/2401*T^34 + 
        32/2401*T^33 + 498/2401*T^32 - 26/343*T^31 - 178/2401*T^30 + 20/2401*T^29 - 
        20/2401*T^27 + 178/2401*T^26 + 26/343*T^25 - 498/2401*T^24 - 32/2401*T^23 - 
        1968/2401*T^22 + 677/2401*T^21 - 1805/2401*T^20 - 282/2401*T^19 - 
        45/2401*T^18 - 970/2401*T^17 + 478/2401*T^16 - 1831/2401*T^15 + 
        1090/2401*T^14 - 2162/2401*T^13 + 941/2401*T^12 - 605/2401*T^11 + 
        137/2401*T^10 + 1695/2401*T^9 - 230/343*T^8 + 1850/2401*T^7 - 214/2401*T^6 +
        898/2401*T^5 - 2/343*T^4 + 37/49*T^3 + 18/49*T^2 + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + X*Y^13 + 4*X*Y^11 + 3*X*Y^10 + X*Y^9 + 2*X*Y^8 + 
        4*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + X*Y + 3*X + 
        4*Y^30 + Y^29 + 6*Y^28 + 5*Y^27 + 3*Y^26 + Y^25 + 6*Y^24 + 2*Y^23 + 5*Y^20 +
        2*Y^19 + 3*Y^18 + 6*Y^17 + 3*Y^16 + 3*Y^15 + Y^14 + 5*Y^12 + 6*Y^11 + 4*Y^10
        + 5*Y^9 + 3*Y^8 + Y^7 + 2*Y^6 + 4*Y^5 + 4*Y^4 + 2*Y^3 + 3*Y^2 + Y + 4,
    T^56 + 8/7*T^55 + 34/49*T^54 + 164/343*T^53 + 2411/2401*T^52 + 2946/2401*T^51 + 
        2092/2401*T^50 + 324/343*T^49 + 201/343*T^48 + 20/49*T^47 + 3/2401*T^46 - 
        1643/2401*T^45 - 2582/2401*T^44 - 1387/2401*T^43 - 1275/2401*T^42 - 
        2995/2401*T^41 - 3779/2401*T^40 - 401/343*T^39 - 2804/2401*T^38 - 
        2019/2401*T^37 - 187/343*T^36 - 632/2401*T^35 - 130/2401*T^34 + 
        643/2401*T^33 + 59/343*T^32 + 587/2401*T^31 + 2434/2401*T^30 + 
        2417/2401*T^29 + 2629/2401*T^28 + 2417/2401*T^27 + 2434/2401*T^26 + 
        587/2401*T^25 + 59/343*T^24 + 643/2401*T^23 - 130/2401*T^22 - 632/2401*T^21 
        - 187/343*T^20 - 2019/2401*T^19 - 2804/2401*T^18 - 401/343*T^17 - 
        3779/2401*T^16 - 2995/2401*T^15 - 1275/2401*T^14 - 1387/2401*T^13 - 
        2582/2401*T^12 - 1643/2401*T^11 + 3/2401*T^10 + 20/49*T^9 + 201/343*T^8 + 
        324/343*T^7 + 2092/2401*T^6 + 2946/2401*T^5 + 2411/2401*T^4 + 164/343*T^3 + 
        34/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 4*X*Y^8 + 
        X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + X*Y^3 + X*Y^2 + 4*X*Y + 5*X + 4*Y^30 +
        4*Y^29 + 2*Y^28 + 5*Y^27 + 5*Y^26 + 3*Y^25 + 6*Y^24 + 3*Y^23 + 3*Y^22 + 
        3*Y^21 + 5*Y^20 + Y^19 + 4*Y^18 + 2*Y^17 + 3*Y^16 + 3*Y^15 + 6*Y^14 + Y^12 +
        2*Y^11 + 6*Y^10 + 5*Y^8 + 3*Y^5 + 6*Y^4 + 4*Y^2 + 4*Y + 6,
    -T^56 - 9/7*T^55 - 86/49*T^54 - 559/343*T^53 - 804/2401*T^52 + 1318/2401*T^51 + 
        4479/2401*T^50 + 6506/2401*T^49 + 5671/2401*T^48 + 5125/2401*T^47 + 
        2204/2401*T^46 - 1269/2401*T^45 - 3884/2401*T^44 - 6893/2401*T^43 - 
        1076/343*T^42 - 5962/2401*T^41 - 452/343*T^40 + 157/343*T^39 + 
        5956/2401*T^38 + 7710/2401*T^37 + 8219/2401*T^36 + 5636/2401*T^35 + 
        3/49*T^34 - 3476/2401*T^33 - 7026/2401*T^32 - 8773/2401*T^31 - 
        6017/2401*T^30 - 90/49*T^29 + 90/49*T^27 + 6017/2401*T^26 + 8773/2401*T^25 +
        7026/2401*T^24 + 3476/2401*T^23 - 3/49*T^22 - 5636/2401*T^21 - 
        8219/2401*T^20 - 7710/2401*T^19 - 5956/2401*T^18 - 157/343*T^17 + 
        452/343*T^16 + 5962/2401*T^15 + 1076/343*T^14 + 6893/2401*T^13 + 
        3884/2401*T^12 + 1269/2401*T^11 - 2204/2401*T^10 - 5125/2401*T^9 - 
        5671/2401*T^8 - 6506/2401*T^7 - 4479/2401*T^6 - 1318/2401*T^5 + 804/2401*T^4
        + 559/343*T^3 + 86/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + X*Y^11 + X*Y^10 + 5*X*Y^9 + 
        2*X*Y^8 + 3*X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 3*X*Y 
        + 3*X + 4*Y^30 + 5*Y^29 + 5*Y^28 + 5*Y^27 + 2*Y^26 + Y^25 + Y^24 + Y^23 + 
        3*Y^22 + 6*Y^20 + 2*Y^18 + 4*Y^17 + 5*Y^16 + 2*Y^15 + 6*Y^14 + Y^13 + 5*Y^12
        + 3*Y^11 + 3*Y^10 + 6*Y^9 + 6*Y^7 + Y^6 + 6*Y^4 + 2*Y^3 + 6*Y^2 + Y + 3,
    -T^56 - 1/7*T^55 - 1/49*T^54 + 36/343*T^53 + 1283/2401*T^52 - 260/2401*T^51 + 
        607/2401*T^50 + 12/49*T^49 - 187/2401*T^48 - 232/2401*T^47 - 41/2401*T^46 - 
        839/2401*T^45 - 365/2401*T^44 + 74/2401*T^43 + 629/2401*T^42 + 71/2401*T^41 
        + 803/2401*T^40 + 1075/2401*T^39 - 397/2401*T^38 - 515/2401*T^37 - 
        174/343*T^36 - 873/2401*T^35 + 319/2401*T^34 + 2/343*T^33 - 116/2401*T^32 + 
        1732/2401*T^31 + 594/2401*T^30 + 1522/2401*T^29 - 1522/2401*T^27 - 
        594/2401*T^26 - 1732/2401*T^25 + 116/2401*T^24 - 2/343*T^23 - 319/2401*T^22 
        + 873/2401*T^21 + 174/343*T^20 + 515/2401*T^19 + 397/2401*T^18 - 
        1075/2401*T^17 - 803/2401*T^16 - 71/2401*T^15 - 629/2401*T^14 - 74/2401*T^13
        + 365/2401*T^12 + 839/2401*T^11 + 41/2401*T^10 + 232/2401*T^9 + 187/2401*T^8
        - 12/49*T^7 - 607/2401*T^6 + 260/2401*T^5 - 1283/2401*T^4 - 36/343*T^3 + 
        1/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 6*X*Y^13 + X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + X*Y^9 + 3*X*Y^8 + 
        4*X*Y^7 + 3*X*Y^5 + X*Y^4 + X*Y^3 + 5*X*Y + X + Y^30 + 2*Y^29 + 6*Y^27 + 
        2*Y^26 + 6*Y^25 + 2*Y^24 + 5*Y^23 + 2*Y^22 + Y^19 + 4*Y^18 + 2*Y^17 + 2*Y^16
        + Y^15 + 4*Y^14 + 6*Y^13 + 2*Y^12 + 4*Y^11 + 4*Y^10 + 4*Y^9 + 5*Y^8 + 4*Y^6 
        + 2*Y^5 + 3*Y^4 + 2*Y^3 + 6*Y^2 + 5*Y + 6,
    -T^56 + 8/7*T^55 + 20/49*T^54 - 96/49*T^53 + 3460/2401*T^52 + 346/2401*T^51 - 
        3271/2401*T^50 + 2956/2401*T^49 + 682/2401*T^48 - 2102/2401*T^47 + 
        1364/2401*T^46 - 89/2401*T^45 - 1067/2401*T^44 + 365/343*T^43 - 
        902/2401*T^42 - 647/2401*T^41 + 1508/2401*T^40 - 2298/2401*T^39 + 
        86/343*T^38 + 2648/2401*T^37 - 2087/2401*T^36 - 2181/2401*T^35 + 
        2797/2401*T^34 - 593/2401*T^33 - 1870/2401*T^32 + 2451/2401*T^31 - 
        958/2401*T^30 - 835/2401*T^29 + 835/2401*T^27 + 958/2401*T^26 - 
        2451/2401*T^25 + 1870/2401*T^24 + 593/2401*T^23 - 2797/2401*T^22 + 
        2181/2401*T^21 + 2087/2401*T^20 - 2648/2401*T^19 - 86/343*T^18 + 
        2298/2401*T^17 - 1508/2401*T^16 + 647/2401*T^15 + 902/2401*T^14 - 
        365/343*T^13 + 1067/2401*T^12 + 89/2401*T^11 - 1364/2401*T^10 + 
        2102/2401*T^9 - 682/2401*T^8 - 2956/2401*T^7 + 3271/2401*T^6 - 346/2401*T^5 
        - 3460/2401*T^4 + 96/49*T^3 - 20/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 5*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 
        4*X*Y^6 + X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 6*X*Y + X + 2*Y^30 + 6*Y^29 
        + 3*Y^28 + 3*Y^27 + 4*Y^26 + 6*Y^24 + 6*Y^23 + 4*Y^22 + Y^21 + 5*Y^20 + 
        5*Y^19 + 4*Y^18 + 6*Y^17 + 2*Y^16 + 5*Y^15 + 5*Y^14 + 3*Y^13 + 3*Y^11 + Y^10
        + 5*Y^9 + 5*Y^8 + 3*Y^7 + 6*Y^6 + Y^5 + 3*Y^4 + 6*Y^3 + 6*Y^2 + 1,
    T^56 + 1/7*T^55 - 68/49*T^54 - 67/49*T^53 + 2053/2401*T^52 + 5233/2401*T^51 + 
        527/2401*T^50 - 2795/2401*T^49 - 3491/2401*T^48 - 513/2401*T^47 + 
        304/343*T^46 + 2325/2401*T^45 - 376/2401*T^44 - 1185/2401*T^43 - 
        555/2401*T^42 + 97/2401*T^41 - 145/343*T^40 + 838/2401*T^39 + 2148/2401*T^38
        - 199/2401*T^37 - 827/2401*T^36 - 116/343*T^35 - 37/2401*T^34 - 22/343*T^33 
        + 1346/2401*T^32 + 443/2401*T^31 - 1487/2401*T^30 - 296/2401*T^29 + 
        1119/2401*T^28 - 296/2401*T^27 - 1487/2401*T^26 + 443/2401*T^25 + 
        1346/2401*T^24 - 22/343*T^23 - 37/2401*T^22 - 116/343*T^21 - 827/2401*T^20 -
        199/2401*T^19 + 2148/2401*T^18 + 838/2401*T^17 - 145/343*T^16 + 97/2401*T^15
        - 555/2401*T^14 - 1185/2401*T^13 - 376/2401*T^12 + 2325/2401*T^11 + 
        304/343*T^10 - 513/2401*T^9 - 3491/2401*T^8 - 2795/2401*T^7 + 527/2401*T^6 +
        5233/2401*T^5 + 2053/2401*T^4 - 67/49*T^3 - 68/49*T^2 + 1/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 
        2*X*Y^8 + 2*X*Y^6 + 3*X*Y^5 + 6*X*Y^3 + X*Y^2 + 3*X*Y + X + 4*Y^30 + 6*Y^29 
        + 5*Y^28 + 2*Y^27 + Y^26 + 2*Y^24 + Y^23 + 4*Y^22 + 6*Y^21 + 5*Y^20 + 6*Y^19
        + 3*Y^18 + 2*Y^17 + 6*Y^16 + Y^15 + 2*Y^14 + Y^12 + 6*Y^11 + 6*Y^10 + 5*Y^9 
        + 2*Y^8 + 5*Y^7 + 2*Y^6 + Y^5 + 2*Y^3 + Y^2 + 4*Y + 6,
    T^56 - 10/7*T^55 + 24/49*T^54 - 199/343*T^53 + 192/343*T^52 + 900/2401*T^51 - 
        1693/2401*T^50 + 597/2401*T^49 - 1294/2401*T^48 + 1766/2401*T^47 + 
        1153/2401*T^46 - 2131/2401*T^45 + 507/2401*T^44 - 1364/2401*T^43 + 
        1398/2401*T^42 + 32/343*T^41 - 741/2401*T^40 + 44/49*T^39 - 2173/2401*T^38 +
        660/2401*T^37 + 136/343*T^36 - 1328/2401*T^35 + 1797/2401*T^34 - 
        1952/2401*T^33 + 94/2401*T^32 + 551/2401*T^31 - 842/2401*T^30 + 
        2194/2401*T^29 - 3057/2401*T^28 + 2194/2401*T^27 - 842/2401*T^26 + 
        551/2401*T^25 + 94/2401*T^24 - 1952/2401*T^23 + 1797/2401*T^22 - 
        1328/2401*T^21 + 136/343*T^20 + 660/2401*T^19 - 2173/2401*T^18 + 44/49*T^17 
        - 741/2401*T^16 + 32/343*T^15 + 1398/2401*T^14 - 1364/2401*T^13 + 
        507/2401*T^12 - 2131/2401*T^11 + 1153/2401*T^10 + 1766/2401*T^9 - 
        1294/2401*T^8 + 597/2401*T^7 - 1693/2401*T^6 + 900/2401*T^5 + 192/343*T^4 - 
        199/343*T^3 + 24/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 
        2*X*Y^7 + 5*X*Y^6 + 6*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 3*X*Y + 4*Y^30 + 3*Y^29 + 
        Y^28 + 2*Y^27 + 5*Y^26 + 2*Y^25 + 4*Y^24 + 2*Y^23 + 4*Y^22 + 5*Y^21 + 2*Y^20
        + 2*Y^19 + Y^17 + Y^16 + Y^15 + 4*Y^12 + 4*Y^11 + 2*Y^9 + 2*Y^8 + Y^7 + Y^6 
        + 6*Y^4 + Y^3 + 2*Y^2 + 2*Y + 2,
    T^56 + 8/7*T^55 - 1/7*T^54 - 207/343*T^53 + 1342/2401*T^52 + 3380/2401*T^51 + 
        36/49*T^50 + 597/2401*T^49 + 227/343*T^48 + 2582/2401*T^47 + 1278/2401*T^46 
        + 2175/2401*T^45 + 3406/2401*T^44 + 878/2401*T^43 - 820/2401*T^42 + 
        1629/2401*T^41 + 101/49*T^40 + 468/343*T^39 - 416/2401*T^38 - 543/2401*T^37 
        + 251/343*T^36 + 1978/2401*T^35 + 1044/2401*T^34 + 1668/2401*T^33 + 
        1426/2401*T^32 + 359/2401*T^31 + 164/2401*T^30 + 960/2401*T^29 + 
        1675/2401*T^28 + 960/2401*T^27 + 164/2401*T^26 + 359/2401*T^25 + 
        1426/2401*T^24 + 1668/2401*T^23 + 1044/2401*T^22 + 1978/2401*T^21 + 
        251/343*T^20 - 543/2401*T^19 - 416/2401*T^18 + 468/343*T^17 + 101/49*T^16 + 
        1629/2401*T^15 - 820/2401*T^14 + 878/2401*T^13 + 3406/2401*T^12 + 
        2175/2401*T^11 + 1278/2401*T^10 + 2582/2401*T^9 + 227/343*T^8 + 597/2401*T^7
        + 36/49*T^6 + 3380/2401*T^5 + 1342/2401*T^4 - 207/343*T^3 - 1/7*T^2 + 8/7*T 
        + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 5*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 3*X*Y^8 + 
        3*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 5*X*Y^2 + 4*X*Y + 5*Y^30 + 6*Y^29 + Y^28 + 
        4*Y^26 + Y^25 + 2*Y^24 + 4*Y^23 + 3*Y^22 + 3*Y^21 + 2*Y^20 + 5*Y^19 + 2*Y^18
        + 5*Y^17 + 5*Y^16 + 5*Y^15 + 4*Y^14 + 4*Y^13 + Y^12 + 6*Y^11 + 5*Y^10 + 
        2*Y^9 + Y^8 + 4*Y^6 + 5*Y^5 + 3*Y^4 + 6*Y^3 + Y^2 + Y + 3,
    -T^56 + 6/7*T^55 + 22/49*T^54 - 19/49*T^53 - 1866/2401*T^52 - 272/2401*T^51 + 
        2746/2401*T^50 - 221/2401*T^49 - 311/2401*T^48 - 2738/2401*T^47 + 
        1975/2401*T^46 + 1172/2401*T^45 - 956/2401*T^44 - 808/2401*T^43 - 
        317/2401*T^42 + 1570/2401*T^41 - 897/2401*T^40 + 204/2401*T^39 - 
        1562/2401*T^38 + 1509/2401*T^37 + 1147/2401*T^36 - 15/49*T^35 - 
        621/2401*T^34 - 278/343*T^33 + 3499/2401*T^32 - 277/2401*T^31 + 
        132/2401*T^30 - 2722/2401*T^29 + 2722/2401*T^27 - 132/2401*T^26 + 
        277/2401*T^25 - 3499/2401*T^24 + 278/343*T^23 + 621/2401*T^22 + 15/49*T^21 -
        1147/2401*T^20 - 1509/2401*T^19 + 1562/2401*T^18 - 204/2401*T^17 + 
        897/2401*T^16 - 1570/2401*T^15 + 317/2401*T^14 + 808/2401*T^13 + 
        956/2401*T^12 - 1172/2401*T^11 - 1975/2401*T^10 + 2738/2401*T^9 + 
        311/2401*T^8 + 221/2401*T^7 - 2746/2401*T^6 + 272/2401*T^5 + 1866/2401*T^4 +
        19/49*T^3 - 22/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + X*Y^13 + 4*X*Y^12 + 4*X*Y^9 + 2*X*Y^8 + X*Y^7 + 
        2*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + X*Y + 5*X + 3*Y^30 + 2*Y^29 + 6*Y^27
        + 2*Y^26 + 2*Y^24 + Y^23 + 2*Y^22 + Y^21 + 5*Y^20 + 6*Y^19 + 5*Y^18 + 2*Y^17
        + 2*Y^16 + 2*Y^15 + 5*Y^14 + 2*Y^13 + 4*Y^12 + 5*Y^11 + 2*Y^10 + 5*Y^9 + 
        3*Y^8 + 2*Y^7 + Y^6 + 6*Y^5 + 5*Y^4 + 6*Y^3 + 2*Y^2 + 4*Y + 2,
    T^56 - 8/7*T^55 + 31/49*T^54 + 303/343*T^53 - 4471/2401*T^52 + 4615/2401*T^51 - 
        3002/2401*T^50 + 372/2401*T^49 + 1203/2401*T^48 - 4217/2401*T^47 + 
        628/343*T^46 - 3252/2401*T^45 + 48/343*T^44 + 660/2401*T^43 - 1668/2401*T^42
        + 1119/2401*T^41 - 1264/2401*T^40 + 643/2401*T^39 + 121/2401*T^38 - 
        556/2401*T^37 - 1332/2401*T^36 + 2337/2401*T^35 - 1200/2401*T^34 - 
        405/2401*T^33 + 2316/2401*T^32 - 1716/2401*T^31 + 922/2401*T^30 + 
        915/2401*T^29 - 47/343*T^28 + 915/2401*T^27 + 922/2401*T^26 - 1716/2401*T^25
        + 2316/2401*T^24 - 405/2401*T^23 - 1200/2401*T^22 + 2337/2401*T^21 - 
        1332/2401*T^20 - 556/2401*T^19 + 121/2401*T^18 + 643/2401*T^17 - 
        1264/2401*T^16 + 1119/2401*T^15 - 1668/2401*T^14 + 660/2401*T^13 + 
        48/343*T^12 - 3252/2401*T^11 + 628/343*T^10 - 4217/2401*T^9 + 1203/2401*T^8 
        + 372/2401*T^7 - 3002/2401*T^6 + 4615/2401*T^5 - 4471/2401*T^4 + 303/343*T^3
        + 31/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 6*X*Y^11 + 3*X*Y^8 + X*Y^7 + 5*X*Y^6 + 5*X*Y^4 + 
        3*X*Y^3 + 6*X*Y^2 + 3*X*Y + 3*X + 5*Y^30 + Y^29 + 4*Y^28 + 5*Y^26 + Y^25 + 
        Y^23 + 2*Y^22 + 6*Y^20 + 4*Y^19 + 3*Y^18 + 3*Y^17 + 4*Y^16 + 4*Y^15 + 6*Y^14
        + Y^13 + 3*Y^12 + 6*Y^11 + 5*Y^10 + 6*Y^9 + 4*Y^8 + 3*Y^7 + 5*Y^6 + Y^5 + 
        6*Y^4 + Y^3 + Y + 3,
    T^56 + 9/7*T^55 + 26/49*T^54 + 170/343*T^53 + 2775/2401*T^52 + 3609/2401*T^51 + 
        1766/2401*T^50 + 909/2401*T^49 + 2169/2401*T^48 + 1500/2401*T^47 + 
        751/2401*T^46 - 131/2401*T^45 - 289/2401*T^44 - 871/2401*T^43 - 44/49*T^42 -
        1233/2401*T^41 + 1/7*T^40 - 458/2401*T^39 - 2482/2401*T^38 - 1462/2401*T^37 
        + 207/343*T^36 + 515/2401*T^35 - 277/343*T^34 - 1322/2401*T^33 + 
        697/2401*T^32 - 43/2401*T^31 - 1742/2401*T^30 - 940/2401*T^29 + 5/343*T^28 -
        940/2401*T^27 - 1742/2401*T^26 - 43/2401*T^25 + 697/2401*T^24 - 
        1322/2401*T^23 - 277/343*T^22 + 515/2401*T^21 + 207/343*T^20 - 
        1462/2401*T^19 - 2482/2401*T^18 - 458/2401*T^17 + 1/7*T^16 - 1233/2401*T^15 
        - 44/49*T^14 - 871/2401*T^13 - 289/2401*T^12 - 131/2401*T^11 + 751/2401*T^10
        + 1500/2401*T^9 + 2169/2401*T^8 + 909/2401*T^7 + 1766/2401*T^6 + 
        3609/2401*T^5 + 2775/2401*T^4 + 170/343*T^3 + 26/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 4*X*Y^7 + X*Y^6 + 6*X*Y^5 + X*Y^4 + 4*X*Y^3 + X*Y^2 + 5*X*Y + 2*X 
        + 6*Y^30 + 4*Y^29 + 2*Y^28 + 5*Y^27 + 3*Y^26 + 3*Y^25 + 5*Y^24 + Y^23 + 
        3*Y^21 + 6*Y^20 + Y^19 + 3*Y^18 + 2*Y^17 + 4*Y^16 + 3*Y^15 + 3*Y^14 + Y^13 +
        2*Y^11 + 3*Y^10 + 6*Y^9 + 2*Y^8 + 4*Y^6 + 4*Y^4 + 6*Y^3 + 5*Y^2 + 4*Y + 3,
    T^56 + 13/7*T^55 + 113/49*T^54 + 496/343*T^53 + 75/2401*T^52 - 1251/2401*T^51 - 
        1269/2401*T^50 + 177/343*T^49 + 62/2401*T^48 - 2451/2401*T^47 - 578/343*T^46
        - 3286/2401*T^45 + 979/2401*T^44 + 2259/2401*T^43 + 2732/2401*T^42 - 
        129/2401*T^41 - 2216/2401*T^40 - 2236/2401*T^39 - 454/343*T^38 - 
        2833/2401*T^37 - 3316/2401*T^36 - 1209/2401*T^35 + 444/2401*T^34 + 
        750/2401*T^33 + 8/49*T^32 - 13/49*T^31 + 530/2401*T^30 + 359/343*T^29 + 
        3907/2401*T^28 + 359/343*T^27 + 530/2401*T^26 - 13/49*T^25 + 8/49*T^24 + 
        750/2401*T^23 + 444/2401*T^22 - 1209/2401*T^21 - 3316/2401*T^20 - 
        2833/2401*T^19 - 454/343*T^18 - 2236/2401*T^17 - 2216/2401*T^16 - 
        129/2401*T^15 + 2732/2401*T^14 + 2259/2401*T^13 + 979/2401*T^12 - 
        3286/2401*T^11 - 578/343*T^10 - 2451/2401*T^9 + 62/2401*T^8 + 177/343*T^7 - 
        1269/2401*T^6 - 1251/2401*T^5 + 75/2401*T^4 + 496/343*T^3 + 113/49*T^2 + 
        13/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + X*Y^10 + 4*X*Y^9 + X*Y^8 + 
        4*X*Y^7 + X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 6*X*Y + 3*X + 4*Y^30 + 
        6*Y^29 + 5*Y^28 + Y^26 + 4*Y^25 + Y^24 + 6*Y^23 + 3*Y^22 + Y^21 + 5*Y^20 + 
        2*Y^19 + 4*Y^18 + 5*Y^17 + 5*Y^16 + 3*Y^15 + 3*Y^14 + 2*Y^13 + 4*Y^12 + 
        3*Y^11 + 2*Y^10 + 3*Y^9 + 2*Y^8 + 6*Y^7 + Y^5 + 4*Y^4 + 4*Y^3 + 2*Y^2 + Y + 
        6,
    -T^56 - 8/7*T^55 + 3/49*T^54 + 402/343*T^53 + 2760/2401*T^52 - 431/2401*T^51 - 
        1431/2401*T^50 - 960/2401*T^49 + 366/2401*T^48 + 1819/2401*T^47 + 
        1075/2401*T^46 - 76/2401*T^45 - 127/2401*T^44 + 288/2401*T^43 - 
        314/2401*T^42 - 1079/2401*T^41 + 282/2401*T^40 + 1457/2401*T^39 + 
        850/2401*T^38 - 902/2401*T^37 - 1944/2401*T^36 - 925/2401*T^35 + 
        472/2401*T^34 + 1532/2401*T^33 + 536/2401*T^32 - 1525/2401*T^31 - 
        110/343*T^30 - 76/343*T^29 + 76/343*T^27 + 110/343*T^26 + 1525/2401*T^25 - 
        536/2401*T^24 - 1532/2401*T^23 - 472/2401*T^22 + 925/2401*T^21 + 
        1944/2401*T^20 + 902/2401*T^19 - 850/2401*T^18 - 1457/2401*T^17 - 
        282/2401*T^16 + 1079/2401*T^15 + 314/2401*T^14 - 288/2401*T^13 + 
        127/2401*T^12 + 76/2401*T^11 - 1075/2401*T^10 - 1819/2401*T^9 - 366/2401*T^8
        + 960/2401*T^7 + 1431/2401*T^6 + 431/2401*T^5 - 2760/2401*T^4 - 402/343*T^3 
        - 3/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 +
        2*X*Y^7 + 6*X*Y^4 + 6*X*Y^3 + X*Y + X + 6*Y^30 + 2*Y^29 + 3*Y^28 + 3*Y^26 + 
        4*Y^24 + 6*Y^23 + 3*Y^22 + 5*Y^21 + 3*Y^20 + 6*Y^19 + 4*Y^17 + 5*Y^16 + 
        4*Y^15 + Y^14 + 6*Y^13 + 5*Y^12 + 2*Y^11 + 6*Y^8 + 6*Y^7 + 2*Y^6 + Y^5 + 
        2*Y^4 + Y^3 + 5*Y^2 + 5*Y + 6,
    -T^56 - 9/7*T^55 + 4/7*T^54 + 382/343*T^53 - 1307/2401*T^52 - 2824/2401*T^51 - 
        1788/2401*T^50 - 1766/2401*T^49 - 1595/2401*T^48 - 3/343*T^47 + 
        1011/2401*T^46 - 174/343*T^45 - 466/343*T^44 - 1780/2401*T^43 - 24/49*T^42 -
        2369/2401*T^41 - 195/2401*T^40 + 2528/2401*T^39 - 60/343*T^38 - 
        4769/2401*T^37 - 3410/2401*T^36 + 453/2401*T^35 + 1276/2401*T^34 + 
        800/2401*T^33 + 727/2401*T^32 - 688/2401*T^31 - 2496/2401*T^30 - 
        2234/2401*T^29 + 2234/2401*T^27 + 2496/2401*T^26 + 688/2401*T^25 - 
        727/2401*T^24 - 800/2401*T^23 - 1276/2401*T^22 - 453/2401*T^21 + 
        3410/2401*T^20 + 4769/2401*T^19 + 60/343*T^18 - 2528/2401*T^17 + 
        195/2401*T^16 + 2369/2401*T^15 + 24/49*T^14 + 1780/2401*T^13 + 466/343*T^12 
        + 174/343*T^11 - 1011/2401*T^10 + 3/343*T^9 + 1595/2401*T^8 + 1766/2401*T^7 
        + 1788/2401*T^6 + 2824/2401*T^5 + 1307/2401*T^4 - 382/343*T^3 - 4/7*T^2 + 
        9/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + X*Y^12 + X*Y^11 + 2*X*Y^10 + 5*X*Y^8 + 
        X*Y^7 + 5*X*Y^5 + X*Y^4 + 2*X*Y^3 + X*Y + 2*X + 5*Y^30 + 5*Y^29 + 3*Y^27 + 
        4*Y^26 + 3*Y^25 + Y^24 + Y^23 + 6*Y^22 + 2*Y^21 + Y^20 + 2*Y^19 + 3*Y^18 + 
        2*Y^17 + 4*Y^16 + 4*Y^14 + 5*Y^13 + Y^12 + 5*Y^11 + 6*Y^10 + 2*Y^9 + 2*Y^8 +
        6*Y^7 + Y^6 + 4*Y^5 + Y^4 + 6*Y^3 + 2*Y^2 + 4*Y,
    T^56 + 3/7*T^55 + 34/49*T^54 + 211/343*T^53 + 1517/2401*T^52 + 884/2401*T^51 + 
        186/343*T^50 + 786/2401*T^49 - 101/2401*T^48 + 1453/2401*T^47 + 
        878/2401*T^46 + 993/2401*T^45 + 51/343*T^44 + 144/343*T^43 + 489/2401*T^42 +
        1091/2401*T^41 + 843/2401*T^40 + 982/2401*T^39 + 277/2401*T^38 + 
        433/2401*T^37 + 20/49*T^36 + 81/343*T^35 + 253/2401*T^34 + 1041/2401*T^33 + 
        494/2401*T^32 + 120/2401*T^31 + 765/2401*T^30 - 8/2401*T^29 - 430/2401*T^28 
        - 8/2401*T^27 + 765/2401*T^26 + 120/2401*T^25 + 494/2401*T^24 + 
        1041/2401*T^23 + 253/2401*T^22 + 81/343*T^21 + 20/49*T^20 + 433/2401*T^19 + 
        277/2401*T^18 + 982/2401*T^17 + 843/2401*T^16 + 1091/2401*T^15 + 
        489/2401*T^14 + 144/343*T^13 + 51/343*T^12 + 993/2401*T^11 + 878/2401*T^10 +
        1453/2401*T^9 - 101/2401*T^8 + 786/2401*T^7 + 186/343*T^6 + 884/2401*T^5 + 
        1517/2401*T^4 + 211/343*T^3 + 34/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 2*X*Y^9 + X*Y^8 + 
        3*X*Y^7 + 6*X*Y^6 + 2*X*Y^5 + X*Y^4 + X*Y^3 + 2*X*Y^2 + 2*X*Y + 6*X + 2*Y^30
        + 4*Y^29 + 5*Y^27 + Y^26 + 5*Y^25 + 4*Y^24 + 6*Y^23 + 5*Y^22 + 5*Y^21 + Y^20
        + 2*Y^19 + Y^17 + 4*Y^16 + 5*Y^15 + Y^14 + Y^13 + 2*Y^12 + 5*Y^11 + 5*Y^10 +
        4*Y^9 + Y^8 + 3*Y^7 + 2*Y^6 + 5*Y^5 + 6*Y^4 + 3*Y^3 + 6*Y^2 + 6*Y,
    -T^56 + 3/7*T^55 + 52/49*T^54 + 34/49*T^53 - 321/343*T^52 - 249/343*T^51 - 
        1858/2401*T^50 + 1000/2401*T^49 + 2797/2401*T^48 + 1294/2401*T^47 - 
        971/2401*T^46 - 1807/2401*T^45 - 108/2401*T^44 - 275/2401*T^43 + 
        471/2401*T^42 + 1805/2401*T^41 + 99/343*T^40 - 1942/2401*T^39 - 
        1958/2401*T^38 + 538/2401*T^37 + 2322/2401*T^36 + 1352/2401*T^35 - 
        60/343*T^34 - 2932/2401*T^33 - 106/343*T^32 + 615/2401*T^31 + 1986/2401*T^30
        + 891/2401*T^29 - 891/2401*T^27 - 1986/2401*T^26 - 615/2401*T^25 + 
        106/343*T^24 + 2932/2401*T^23 + 60/343*T^22 - 1352/2401*T^21 - 
        2322/2401*T^20 - 538/2401*T^19 + 1958/2401*T^18 + 1942/2401*T^17 - 
        99/343*T^16 - 1805/2401*T^15 - 471/2401*T^14 + 275/2401*T^13 + 108/2401*T^12
        + 1807/2401*T^11 + 971/2401*T^10 - 1294/2401*T^9 - 2797/2401*T^8 - 
        1000/2401*T^7 + 1858/2401*T^6 + 249/343*T^5 + 321/343*T^4 - 34/49*T^3 - 
        52/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 
        + 4*X*Y^8 + 2*X*Y^7 + 4*X*Y^6 + X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 6*X*Y 
        + 4*X + 4*Y^30 + 2*Y^29 + 4*Y^28 + 3*Y^27 + 6*Y^26 + 5*Y^25 + 5*Y^24 + 
        5*Y^22 + 6*Y^20 + 4*Y^19 + Y^16 + Y^14 + 3*Y^13 + 5*Y^12 + 3*Y^11 + 2*Y^10 +
        4*Y^9 + Y^8 + 3*Y^7 + 3*Y^6 + 5*Y^5 + 6*Y^4 + Y^2 + 4*Y + 1,
    -T^56 - 10/7*T^55 - 30/49*T^54 - 27/343*T^53 + 508/2401*T^52 - 20/343*T^51 - 
        204/2401*T^50 + 1171/2401*T^49 + 1290/2401*T^48 + 528/2401*T^47 - 
        487/2401*T^46 - 8/2401*T^45 + 2108/2401*T^44 + 2078/2401*T^43 + 
        1425/2401*T^42 + 1467/2401*T^41 + 983/2401*T^40 + 421/2401*T^39 + 
        822/2401*T^38 - 109/2401*T^37 - 1557/2401*T^36 - 647/2401*T^35 + 
        426/2401*T^34 + 984/2401*T^33 - 326/2401*T^32 - 1417/2401*T^31 - 
        230/2401*T^30 - 335/2401*T^29 + 335/2401*T^27 + 230/2401*T^26 + 
        1417/2401*T^25 + 326/2401*T^24 - 984/2401*T^23 - 426/2401*T^22 + 
        647/2401*T^21 + 1557/2401*T^20 + 109/2401*T^19 - 822/2401*T^18 - 
        421/2401*T^17 - 983/2401*T^16 - 1467/2401*T^15 - 1425/2401*T^14 - 
        2078/2401*T^13 - 2108/2401*T^12 + 8/2401*T^11 + 487/2401*T^10 - 528/2401*T^9
        - 1290/2401*T^8 - 1171/2401*T^7 + 204/2401*T^6 + 20/343*T^5 - 508/2401*T^4 +
        27/343*T^3 + 30/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 
        + 6*X*Y^7 + 4*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 2*X*Y + X + Y^30 + 
        3*Y^29 + 2*Y^28 + Y^27 + 3*Y^26 + 2*Y^25 + Y^24 + 6*Y^23 + 6*Y^22 + 2*Y^20 +
        5*Y^17 + 5*Y^16 + Y^15 + Y^14 + 4*Y^13 + 5*Y^12 + 3*Y^11 + 6*Y^10 + Y^9 + 
        2*Y^8 + 4*Y^7 + Y^5 + 6*Y^3 + 6*Y^2 + 2*Y,
    -T^56 + 4/7*T^55 + 3/49*T^54 - 496/343*T^53 + 2353/2401*T^52 - 1068/2401*T^51 - 
        736/2401*T^50 + 2706/2401*T^49 - 67/49*T^48 + 345/343*T^47 + 1401/2401*T^46 
        - 333/343*T^45 + 2568/2401*T^44 - 816/2401*T^43 + 1873/2401*T^42 + 
        285/2401*T^41 - 1842/2401*T^40 + 3357/2401*T^39 - 1728/2401*T^38 + 
        702/2401*T^37 + 878/2401*T^36 - 2801/2401*T^35 + 3625/2401*T^34 - 
        349/343*T^33 - 472/2401*T^32 + 3177/2401*T^31 - 597/343*T^30 + 
        2780/2401*T^29 - 2780/2401*T^27 + 597/343*T^26 - 3177/2401*T^25 + 
        472/2401*T^24 + 349/343*T^23 - 3625/2401*T^22 + 2801/2401*T^21 - 
        878/2401*T^20 - 702/2401*T^19 + 1728/2401*T^18 - 3357/2401*T^17 + 
        1842/2401*T^16 - 285/2401*T^15 - 1873/2401*T^14 + 816/2401*T^13 - 
        2568/2401*T^12 + 333/343*T^11 - 1401/2401*T^10 - 345/343*T^9 + 67/49*T^8 - 
        2706/2401*T^7 + 736/2401*T^6 + 1068/2401*T^5 - 2353/2401*T^4 + 496/343*T^3 -
        3/49*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 
        6*X*Y^8 + 3*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 6*X*Y + X + 2*Y^30 + Y^29 
        + 3*Y^28 + Y^27 + 6*Y^26 + Y^25 + 4*Y^24 + 3*Y^23 + 5*Y^22 + 4*Y^21 + 6*Y^20
        + 2*Y^19 + 2*Y^18 + Y^17 + 2*Y^16 + 2*Y^15 + 4*Y^14 + Y^13 + 5*Y^12 + 4*Y^11
        + Y^10 + 5*Y^9 + 6*Y^8 + Y^7 + 4*Y^6 + 2*Y^4 + 4*Y^3 + 5*Y + 3,
    -T^56 - 18/7*T^55 - 102/49*T^54 + 526/343*T^53 + 10911/2401*T^52 + 
        7090/2401*T^51 - 3995/2401*T^50 - 8971/2401*T^49 - 4037/2401*T^48 + 
        1159/2401*T^47 + 664/2401*T^46 - 519/2401*T^45 + 1731/2401*T^44 + 
        3565/2401*T^43 + 731/2401*T^42 - 3315/2401*T^41 - 64/49*T^40 - 417/2401*T^39
        - 1006/2401*T^38 - 4523/2401*T^37 - 4664/2401*T^36 + 1404/2401*T^35 + 
        8157/2401*T^34 + 8760/2401*T^33 + 373/343*T^32 - 4759/2401*T^31 - 
        8293/2401*T^30 - 6082/2401*T^29 + 6082/2401*T^27 + 8293/2401*T^26 + 
        4759/2401*T^25 - 373/343*T^24 - 8760/2401*T^23 - 8157/2401*T^22 - 
        1404/2401*T^21 + 4664/2401*T^20 + 4523/2401*T^19 + 1006/2401*T^18 + 
        417/2401*T^17 + 64/49*T^16 + 3315/2401*T^15 - 731/2401*T^14 - 3565/2401*T^13
        - 1731/2401*T^12 + 519/2401*T^11 - 664/2401*T^10 - 1159/2401*T^9 + 
        4037/2401*T^8 + 8971/2401*T^7 + 3995/2401*T^6 - 7090/2401*T^5 - 
        10911/2401*T^4 - 526/343*T^3 + 102/49*T^2 + 18/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^13 + 2*X*Y^11 + 3*X*Y^10 + 3*X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 
        2*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 5*X*Y + 5*Y^30 + Y^29 + 2*Y^27 + 
        5*Y^26 + 5*Y^25 + 6*Y^24 + 2*Y^23 + Y^22 + 3*Y^19 + Y^18 + 6*Y^17 + 6*Y^15 +
        Y^14 + Y^13 + 5*Y^12 + 2*Y^11 + 5*Y^10 + 4*Y^9 + 2*Y^8 + 2*Y^7 + 6*Y^6 + 
        6*Y^5 + 6*Y^4 + 5*Y^3 + 5*Y^2 + Y + 5,
    T^56 + 2/7*T^55 - 54/49*T^54 - 16/343*T^53 + 836/2401*T^52 + 523/2401*T^51 + 
        211/2401*T^50 - 2188/2401*T^49 - 822/2401*T^48 + 1059/2401*T^47 + 
        1461/2401*T^46 + 1056/2401*T^45 - 1567/2401*T^44 - 1041/2401*T^43 + 
        1189/2401*T^42 - 757/2401*T^41 - 242/2401*T^40 + 440/2401*T^39 - 
        1996/2401*T^38 - 117/2401*T^37 + 1046/2401*T^36 - 375/2401*T^35 + 
        1109/2401*T^34 + 961/2401*T^33 - 67/2401*T^32 - 89/2401*T^31 - 706/2401*T^30
        - 424/2401*T^29 + 351/2401*T^28 - 424/2401*T^27 - 706/2401*T^26 - 
        89/2401*T^25 - 67/2401*T^24 + 961/2401*T^23 + 1109/2401*T^22 - 375/2401*T^21
        + 1046/2401*T^20 - 117/2401*T^19 - 1996/2401*T^18 + 440/2401*T^17 - 
        242/2401*T^16 - 757/2401*T^15 + 1189/2401*T^14 - 1041/2401*T^13 - 
        1567/2401*T^12 + 1056/2401*T^11 + 1461/2401*T^10 + 1059/2401*T^9 - 
        822/2401*T^8 - 2188/2401*T^7 + 211/2401*T^6 + 523/2401*T^5 + 836/2401*T^4 - 
        16/343*T^3 - 54/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 5*X*Y^13 + X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 
        3*X*Y^8 + 5*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 5*X*Y 
        + X + 5*Y^30 + 2*Y^28 + 4*Y^27 + 3*Y^26 + 5*Y^25 + Y^24 + 3*Y^23 + 6*Y^22 + 
        2*Y^21 + 4*Y^20 + 6*Y^18 + Y^17 + 4*Y^16 + 4*Y^15 + 5*Y^14 + 5*Y^13 + 3*Y^12
        + 6*Y^10 + 2*Y^9 + 5*Y^8 + 4*Y^7 + 4*Y^6 + 5*Y^5 + Y^4 + 2*Y^3 + 4*Y^2 + Y +
        1,
    -T^56 + T^55 + 81/343*T^53 - 270/343*T^52 + 2917/2401*T^51 - 1487/2401*T^50 - 
        1664/2401*T^49 - 619/2401*T^48 + 4436/2401*T^47 - 3107/2401*T^46 - 
        375/2401*T^45 + 846/2401*T^44 + 3845/2401*T^43 - 5093/2401*T^42 - 5/49*T^41 
        + 2050/2401*T^40 + 23/49*T^39 - 629/343*T^38 + 2190/2401*T^37 + 
        3641/2401*T^36 - 292/343*T^35 - 4588/2401*T^34 + 4072/2401*T^33 + 43/49*T^32
        - 3480/2401*T^31 - 307/343*T^30 + 719/343*T^29 - 719/343*T^27 + 307/343*T^26
        + 3480/2401*T^25 - 43/49*T^24 - 4072/2401*T^23 + 4588/2401*T^22 + 
        292/343*T^21 - 3641/2401*T^20 - 2190/2401*T^19 + 629/343*T^18 - 23/49*T^17 -
        2050/2401*T^16 + 5/49*T^15 + 5093/2401*T^14 - 3845/2401*T^13 - 846/2401*T^12
        + 375/2401*T^11 + 3107/2401*T^10 - 4436/2401*T^9 + 619/2401*T^8 + 
        1664/2401*T^7 + 1487/2401*T^6 - 2917/2401*T^5 + 270/343*T^4 - 81/343*T^3 - T
        + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 5*X*Y^6 
        + X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + X*Y + 5*Y^30 + Y^29 + 3*Y^28 + 
        2*Y^27 + 6*Y^26 + 2*Y^25 + Y^24 + 4*Y^23 + 2*Y^22 + 2*Y^21 + 4*Y^20 + Y^19 +
        6*Y^16 + 2*Y^15 + 2*Y^14 + Y^13 + 2*Y^12 + 4*Y^11 + 5*Y^10 + 3*Y^9 + 5*Y^7 +
        4*Y^6 + 4*Y^5 + 3*Y^4 + 3*Y^3 + 2*Y + 3,
    T^56 - 2/7*T^54 + 73/343*T^53 - 857/2401*T^52 + 767/2401*T^51 - 995/2401*T^50 - 
        279/343*T^49 + 352/2401*T^48 - 66/2401*T^47 - 291/2401*T^46 + 1/343*T^45 + 
        12/2401*T^44 + 1691/2401*T^43 + 531/2401*T^42 - 366/2401*T^41 + 
        601/2401*T^40 + 505/2401*T^39 - 47/343*T^38 + 479/2401*T^37 - 1202/2401*T^36
        + 61/2401*T^35 + 365/2401*T^34 - 1415/2401*T^33 + 1195/2401*T^32 - 
        874/2401*T^31 - 25/2401*T^30 + 1010/2401*T^29 - 202/343*T^28 + 
        1010/2401*T^27 - 25/2401*T^26 - 874/2401*T^25 + 1195/2401*T^24 - 
        1415/2401*T^23 + 365/2401*T^22 + 61/2401*T^21 - 1202/2401*T^20 + 
        479/2401*T^19 - 47/343*T^18 + 505/2401*T^17 + 601/2401*T^16 - 366/2401*T^15 
        + 531/2401*T^14 + 1691/2401*T^13 + 12/2401*T^12 + 1/343*T^11 - 291/2401*T^10
        - 66/2401*T^9 + 352/2401*T^8 - 279/343*T^7 - 995/2401*T^6 + 767/2401*T^5 - 
        857/2401*T^4 + 73/343*T^3 - 2/7*T^2 + 1
*], [*
    X^3 + 4*X*Y^14 + 4*X*Y^12 + 2*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 5*X*Y^7 + X*Y^5 + 
        3*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 2*X*Y + 3*X + 3*Y^30 + 6*Y^29 + Y^28 + 4*Y^27 
        + 2*Y^26 + 4*Y^25 + 6*Y^24 + 2*Y^23 + Y^22 + Y^21 + 5*Y^20 + 6*Y^19 + 5*Y^18
        + 4*Y^17 + 4*Y^16 + 6*Y^15 + Y^14 + 4*Y^13 + Y^12 + 4*Y^11 + Y^9 + Y^8 + Y^7
        + Y^6 + 5*Y^5 + 5*Y^4 + 3*Y^3 + Y^2 + 4*Y + 3,
    T^56 - 4/7*T^55 - 18/49*T^54 - 138/343*T^53 + 22/343*T^52 + 212/343*T^51 - 
        1514/2401*T^50 + 1161/2401*T^49 - 2116/2401*T^48 + 1038/2401*T^47 + 
        73/343*T^46 - 300/2401*T^45 - 150/2401*T^44 - 1076/2401*T^43 + 369/343*T^42 
        - 327/2401*T^41 + 283/2401*T^40 - 762/2401*T^39 + 179/2401*T^38 + 
        1149/2401*T^37 - 613/2401*T^36 - 618/2401*T^35 - 913/2401*T^34 + 
        646/2401*T^33 + 107/2401*T^32 + 206/2401*T^31 + 216/2401*T^30 - 
        578/2401*T^29 + 174/2401*T^28 - 578/2401*T^27 + 216/2401*T^26 + 
        206/2401*T^25 + 107/2401*T^24 + 646/2401*T^23 - 913/2401*T^22 - 
        618/2401*T^21 - 613/2401*T^20 + 1149/2401*T^19 + 179/2401*T^18 - 
        762/2401*T^17 + 283/2401*T^16 - 327/2401*T^15 + 369/343*T^14 - 
        1076/2401*T^13 - 150/2401*T^12 - 300/2401*T^11 + 73/343*T^10 + 1038/2401*T^9
        - 2116/2401*T^8 + 1161/2401*T^7 - 1514/2401*T^6 + 212/343*T^5 + 22/343*T^4 -
        138/343*T^3 - 18/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 
        5*X*Y^8 + 5*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 4*X*Y 
        + 2*X + 5*Y^30 + 4*Y^28 + 5*Y^27 + Y^26 + 3*Y^25 + 2*Y^24 + 2*Y^23 + 2*Y^22 
        + 2*Y^21 + 6*Y^20 + 3*Y^18 + 3*Y^17 + Y^16 + Y^15 + 2*Y^14 + 2*Y^13 + 6*Y^12
        + Y^11 + 4*Y^10 + 5*Y^8 + 5*Y^4 + 2*Y^3 + 2*Y^2 + 4*Y + 3,
    -T^56 - 2/7*T^55 + 55/49*T^54 + 235/343*T^53 + 95/2401*T^52 - 1243/2401*T^51 - 
        803/2401*T^50 - 356/2401*T^49 + 1853/2401*T^48 + 3282/2401*T^47 - 
        1443/2401*T^46 - 2619/2401*T^45 - 1367/2401*T^44 - 86/343*T^43 + 
        1145/2401*T^42 + 389/2401*T^41 + 1047/2401*T^40 - 635/2401*T^39 - 
        759/2401*T^38 + 464/2401*T^37 - 922/2401*T^36 + 1111/2401*T^35 + 12/343*T^34
        + 533/2401*T^33 + 1070/2401*T^32 - 1697/2401*T^31 - 173/2401*T^30 - 
        51/343*T^29 + 51/343*T^27 + 173/2401*T^26 + 1697/2401*T^25 - 1070/2401*T^24 
        - 533/2401*T^23 - 12/343*T^22 - 1111/2401*T^21 + 922/2401*T^20 - 
        464/2401*T^19 + 759/2401*T^18 + 635/2401*T^17 - 1047/2401*T^16 - 
        389/2401*T^15 - 1145/2401*T^14 + 86/343*T^13 + 1367/2401*T^12 + 
        2619/2401*T^11 + 1443/2401*T^10 - 3282/2401*T^9 - 1853/2401*T^8 + 
        356/2401*T^7 + 803/2401*T^6 + 1243/2401*T^5 - 95/2401*T^4 - 235/343*T^3 - 
        55/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 5*X*Y^12 + 5*X*Y^10 + 6*X*Y^9 + 2*X*Y^8 + 5*X*Y^7 + 
        4*X*Y^6 + X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 2*X*Y + 4*X + 5*Y^30 + 5*Y^29 + Y^28 +
        2*Y^27 + 2*Y^26 + Y^24 + Y^23 + 4*Y^22 + 5*Y^21 + 5*Y^19 + 4*Y^18 + 6*Y^17 +
        4*Y^16 + 6*Y^15 + Y^13 + 6*Y^12 + 2*Y^11 + 2*Y^10 + 6*Y^9 + 6*Y^8 + 4*Y^7 + 
        Y^6 + 6*Y^5 + 6*Y^4 + 3*Y^3 + Y^2 + 6*Y + 6,
    T^56 - 1/7*T^55 - 67/49*T^54 - 23/49*T^53 + 1907/2401*T^52 + 1682/2401*T^51 - 
        849/2401*T^50 - 468/2401*T^49 - 726/2401*T^48 + 62/343*T^47 + 1083/2401*T^46
        + 158/2401*T^45 - 44/2401*T^44 + 109/2401*T^43 - 1380/2401*T^42 - 
        1224/2401*T^41 + 985/2401*T^40 + 2635/2401*T^39 + 71/2401*T^38 - 
        1044/2401*T^37 - 1368/2401*T^36 - 1524/2401*T^35 + 1416/2401*T^34 + 
        1926/2401*T^33 - 570/2401*T^32 - 2700/2401*T^31 + 23/2401*T^30 + 
        1480/2401*T^29 + 705/2401*T^28 + 1480/2401*T^27 + 23/2401*T^26 - 
        2700/2401*T^25 - 570/2401*T^24 + 1926/2401*T^23 + 1416/2401*T^22 - 
        1524/2401*T^21 - 1368/2401*T^20 - 1044/2401*T^19 + 71/2401*T^18 + 
        2635/2401*T^17 + 985/2401*T^16 - 1224/2401*T^15 - 1380/2401*T^14 + 
        109/2401*T^13 - 44/2401*T^12 + 158/2401*T^11 + 1083/2401*T^10 + 62/343*T^9 -
        726/2401*T^8 - 468/2401*T^7 - 849/2401*T^6 + 1682/2401*T^5 + 1907/2401*T^4 -
        23/49*T^3 - 67/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + X*Y^13 + 4*X*Y^12 + 5*X*Y^10 + 6*X*Y^9 + 4*X*Y^8 + 
        5*X*Y^7 + X*Y^6 + 3*X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + X*Y + 4*X + Y^30 + Y^28 + 
        5*Y^27 + 4*Y^26 + 3*Y^25 + Y^24 + 6*Y^22 + Y^21 + 6*Y^20 + 2*Y^18 + 3*Y^17 +
        2*Y^16 + 4*Y^15 + 3*Y^14 + 4*Y^13 + 6*Y^11 + Y^10 + 2*Y^9 + 6*Y^8 + 6*Y^7 + 
        3*Y^6 + Y^5 + 6*Y^4 + 2*Y^3 + 2*Y^2 + Y + 4,
    T^56 + 3/7*T^55 - 13/49*T^54 - 188/343*T^53 + 251/343*T^52 + 10/7*T^51 - 
        61/2401*T^50 - 474/2401*T^49 - 601/2401*T^48 + 1486/2401*T^47 + 
        397/2401*T^46 + 157/343*T^45 + 99/2401*T^44 - 2088/2401*T^43 - 512/2401*T^42
        + 495/2401*T^41 + 1592/2401*T^40 - 239/343*T^39 - 1625/2401*T^38 - 
        300/2401*T^37 - 726/2401*T^36 + 544/2401*T^35 - 100/343*T^34 - 480/2401*T^33
        - 1789/2401*T^32 - 517/2401*T^31 + 1245/2401*T^30 - 152/343*T^29 - 
        1238/2401*T^28 - 152/343*T^27 + 1245/2401*T^26 - 517/2401*T^25 - 
        1789/2401*T^24 - 480/2401*T^23 - 100/343*T^22 + 544/2401*T^21 - 
        726/2401*T^20 - 300/2401*T^19 - 1625/2401*T^18 - 239/343*T^17 + 
        1592/2401*T^16 + 495/2401*T^15 - 512/2401*T^14 - 2088/2401*T^13 + 
        99/2401*T^12 + 157/343*T^11 + 397/2401*T^10 + 1486/2401*T^9 - 601/2401*T^8 -
        474/2401*T^7 - 61/2401*T^6 + 10/7*T^5 + 251/343*T^4 - 188/343*T^3 - 
        13/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 5*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 4*X*Y^8 +
        6*X*Y^7 + 4*X*Y^6 + X*Y^5 + X*Y^4 + X*Y^3 + 2*X*Y^2 + 5*X*Y + 4*X + Y^30 + 
        2*Y^29 + 3*Y^28 + 5*Y^27 + 3*Y^26 + 2*Y^25 + Y^22 + 5*Y^21 + 6*Y^20 + 2*Y^19
        + 4*Y^18 + 3*Y^17 + 5*Y^16 + 3*Y^15 + 5*Y^14 + 6*Y^13 + 3*Y^12 + Y^10 + 
        2*Y^9 + 4*Y^8 + 2*Y^7 + 3*Y^6 + 2*Y^5 + 3*Y^4 + 4*Y^3 + 3*Y^2 + 3*Y + 3,
    -T^56 + 2/7*T^55 + 38/49*T^54 - 22/343*T^53 + 799/2401*T^52 - 1417/2401*T^51 + 
        2/49*T^50 + 1934/2401*T^49 - 1978/2401*T^48 - 857/2401*T^47 + 450/2401*T^46 
        + 461/2401*T^45 + 1546/2401*T^44 + 8/343*T^43 - 886/2401*T^42 - 
        493/2401*T^41 + 1410/2401*T^40 - 362/2401*T^39 - 810/2401*T^38 + 
        272/2401*T^37 - 1081/2401*T^36 + 330/2401*T^35 + 927/2401*T^34 - 
        1047/2401*T^33 + 614/2401*T^32 - 508/2401*T^31 - 655/2401*T^30 + 
        1252/2401*T^29 - 1252/2401*T^27 + 655/2401*T^26 + 508/2401*T^25 - 
        614/2401*T^24 + 1047/2401*T^23 - 927/2401*T^22 - 330/2401*T^21 + 
        1081/2401*T^20 - 272/2401*T^19 + 810/2401*T^18 + 362/2401*T^17 - 
        1410/2401*T^16 + 493/2401*T^15 + 886/2401*T^14 - 8/343*T^13 - 1546/2401*T^12
        - 461/2401*T^11 - 450/2401*T^10 + 857/2401*T^9 + 1978/2401*T^8 - 
        1934/2401*T^7 - 2/49*T^6 + 1417/2401*T^5 - 799/2401*T^4 + 22/343*T^3 - 
        38/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 2*X*Y^8 +
        4*X*Y^7 + 4*X*Y^6 + X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 2*X*Y + 3*X + 
        5*Y^30 + 4*Y^29 + 6*Y^28 + 5*Y^27 + 3*Y^26 + 2*Y^25 + 3*Y^24 + 4*Y^22 + 
        6*Y^21 + 3*Y^20 + 6*Y^18 + 5*Y^17 + Y^16 + 3*Y^15 + Y^14 + 5*Y^13 + 4*Y^11 +
        4*Y^10 + 4*Y^8 + 2*Y^7 + Y^6 + 6*Y^5 + 4*Y^4 + 5*Y^3 + 3*Y^2 + 3*Y + 5,
    -T^56 - 5/7*T^55 - 2/49*T^54 + 82/343*T^53 + 561/2401*T^52 + 1231/2401*T^51 - 
        261/2401*T^50 + 102/2401*T^49 + 741/2401*T^48 + 1584/2401*T^47 + 
        275/2401*T^46 - 768/2401*T^45 - 166/2401*T^44 - 649/2401*T^43 - 
        754/2401*T^42 - 484/2401*T^41 + 527/2401*T^40 + 320/2401*T^39 + 
        876/2401*T^38 - 1122/2401*T^37 - 379/2401*T^36 - 122/343*T^35 + 
        390/2401*T^34 + 30/343*T^33 + 642/2401*T^32 - 586/2401*T^31 - 19/2401*T^30 +
        17/343*T^29 - 17/343*T^27 + 19/2401*T^26 + 586/2401*T^25 - 642/2401*T^24 - 
        30/343*T^23 - 390/2401*T^22 + 122/343*T^21 + 379/2401*T^20 + 1122/2401*T^19 
        - 876/2401*T^18 - 320/2401*T^17 - 527/2401*T^16 + 484/2401*T^15 + 
        754/2401*T^14 + 649/2401*T^13 + 166/2401*T^12 + 768/2401*T^11 - 
        275/2401*T^10 - 1584/2401*T^9 - 741/2401*T^8 - 102/2401*T^7 + 261/2401*T^6 -
        1231/2401*T^5 - 561/2401*T^4 - 82/343*T^3 + 2/49*T^2 + 5/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 
        X*Y^8 + 5*X*Y^7 + 3*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + Y^30 + 4*Y^29 + 
        3*Y^28 + 3*Y^27 + 6*Y^26 + 6*Y^25 + 5*Y^24 + 6*Y^23 + 2*Y^22 + 2*Y^21 + Y^20
        + Y^19 + Y^18 + Y^17 + 2*Y^16 + 4*Y^15 + 6*Y^14 + 6*Y^13 + Y^12 + 3*Y^11 + 
        4*Y^10 + 5*Y^9 + 4*Y^8 + Y^6 + 2*Y^5 + 2*Y^3 + 5*Y^2 + 4,
    -T^56 - 4/7*T^55 - 39/49*T^54 - 115/343*T^53 - 590/2401*T^52 - 226/343*T^51 - 
        173/2401*T^50 + 752/2401*T^49 + 1355/2401*T^48 + 1902/2401*T^47 + 
        296/2401*T^46 + 1067/2401*T^45 + 1257/2401*T^44 + 1224/2401*T^43 + 
        1121/2401*T^42 - 44/343*T^41 + 95/2401*T^40 + 615/2401*T^39 - 5/49*T^38 - 
        229/2401*T^37 - 160/343*T^36 - 1079/2401*T^35 - 634/2401*T^34 - 
        1377/2401*T^33 - 1615/2401*T^32 - 866/2401*T^31 - 860/2401*T^30 + 
        51/343*T^29 - 51/343*T^27 + 860/2401*T^26 + 866/2401*T^25 + 1615/2401*T^24 +
        1377/2401*T^23 + 634/2401*T^22 + 1079/2401*T^21 + 160/343*T^20 + 
        229/2401*T^19 + 5/49*T^18 - 615/2401*T^17 - 95/2401*T^16 + 44/343*T^15 - 
        1121/2401*T^14 - 1224/2401*T^13 - 1257/2401*T^12 - 1067/2401*T^11 - 
        296/2401*T^10 - 1902/2401*T^9 - 1355/2401*T^8 - 752/2401*T^7 + 173/2401*T^6 
        + 226/343*T^5 + 590/2401*T^4 + 115/343*T^3 + 39/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 
        6*X*Y^8 + 6*X*Y^6 + X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 2*X*Y + 3*X + 
        6*Y^30 + 6*Y^29 + 5*Y^28 + 5*Y^27 + 4*Y^26 + 5*Y^25 + 5*Y^24 + 6*Y^23 + Y^22
        + 6*Y^21 + 6*Y^20 + 3*Y^19 + 3*Y^18 + 6*Y^17 + 2*Y^16 + 3*Y^15 + 4*Y^14 + 
        Y^13 + Y^10 + 4*Y^9 + 6*Y^8 + Y^6 + 4*Y^5 + Y^4 + 5*Y^3 + 2*Y^2 + 5*Y + 2,
    -T^56 - 8/7*T^55 - 55/49*T^54 - 45/49*T^53 - 1352/2401*T^52 - 862/2401*T^51 - 
        177/2401*T^50 + 163/343*T^49 + 1934/2401*T^48 + 2129/2401*T^47 + 
        1587/2401*T^46 + 531/2401*T^45 - 190/2401*T^44 + 207/2401*T^43 - 15/49*T^42 
        - 1266/2401*T^41 - 533/2401*T^40 + 193/2401*T^39 + 778/2401*T^38 + 
        1052/2401*T^37 + 661/2401*T^36 + 484/2401*T^35 + 11/2401*T^34 - 
        648/2401*T^33 - 179/343*T^32 - 1450/2401*T^31 - 599/2401*T^30 - 60/2401*T^29
        + 60/2401*T^27 + 599/2401*T^26 + 1450/2401*T^25 + 179/343*T^24 + 
        648/2401*T^23 - 11/2401*T^22 - 484/2401*T^21 - 661/2401*T^20 - 
        1052/2401*T^19 - 778/2401*T^18 - 193/2401*T^17 + 533/2401*T^16 + 
        1266/2401*T^15 + 15/49*T^14 - 207/2401*T^13 + 190/2401*T^12 - 531/2401*T^11 
        - 1587/2401*T^10 - 2129/2401*T^9 - 1934/2401*T^8 - 163/343*T^7 + 
        177/2401*T^6 + 862/2401*T^5 + 1352/2401*T^4 + 45/49*T^3 + 55/49*T^2 + 8/7*T 
        + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        6*X*Y^8 + 4*X*Y^6 + 3*X*Y^5 + 3*X*Y^2 + 2*X*Y + 5*Y^30 + 6*Y^29 + Y^28 + 
        2*Y^27 + 4*Y^26 + 2*Y^25 + 4*Y^24 + 6*Y^23 + 6*Y^22 + 5*Y^21 + 2*Y^19 + 
        2*Y^18 + 2*Y^17 + Y^16 + 5*Y^15 + 2*Y^14 + 6*Y^13 + 5*Y^12 + 4*Y^11 + 5*Y^10
        + 2*Y^9 + 4*Y^8 + 3*Y^7 + Y^6 + 3*Y^5 + 4*Y^4 + 2*Y^3 + 4*Y^2 + 5*Y + 6,
    -T^56 + 1/7*T^55 - 4/49*T^54 - 376/343*T^53 - 669/2401*T^52 + 95/343*T^51 - 
        1180/2401*T^50 - 761/2401*T^49 - 96/343*T^48 + 1259/2401*T^47 + 
        471/2401*T^46 - 838/2401*T^45 + 291/343*T^44 + 1341/2401*T^43 + 78/2401*T^42
        + 646/2401*T^41 - 254/2401*T^40 + 2/7*T^39 - 666/2401*T^38 - 1397/2401*T^37 
        + 102/2401*T^36 - 248/2401*T^35 - 295/343*T^34 + 201/2401*T^33 - 83/343*T^32
        - 1193/2401*T^31 - 645/2401*T^30 + 32/343*T^29 - 32/343*T^27 + 645/2401*T^26
        + 1193/2401*T^25 + 83/343*T^24 - 201/2401*T^23 + 295/343*T^22 + 
        248/2401*T^21 - 102/2401*T^20 + 1397/2401*T^19 + 666/2401*T^18 - 2/7*T^17 + 
        254/2401*T^16 - 646/2401*T^15 - 78/2401*T^14 - 1341/2401*T^13 - 291/343*T^12
        + 838/2401*T^11 - 471/2401*T^10 - 1259/2401*T^9 + 96/343*T^8 + 761/2401*T^7 
        + 1180/2401*T^6 - 95/343*T^5 + 669/2401*T^4 + 376/343*T^3 + 4/49*T^2 - 1/7*T
        + 1
*], [*
    X^3 + 5*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 + 5*X*Y^7 + 
        6*X*Y^6 + 4*X*Y^5 + X*Y^4 + X*Y^3 + 5*X*Y^2 + 3*X*Y + 5*Y^30 + 4*Y^29 + 
        2*Y^28 + Y^27 + Y^25 + Y^24 + 4*Y^23 + 6*Y^22 + 2*Y^21 + 2*Y^20 + 3*Y^19 + 
        2*Y^18 + 2*Y^17 + 4*Y^16 + 3*Y^15 + Y^14 + 3*Y^13 + 6*Y^12 + 2*Y^11 + 4*Y^10
        + 6*Y^9 + 6*Y^8 + 6*Y^7 + 6*Y^6 + 6*Y^5 + 5*Y^4 + Y^3 + 3*Y^2 + 3*Y + 3,
    -T^56 - 4/7*T^55 + 66/49*T^54 + 593/343*T^53 - 793/2401*T^52 - 4804/2401*T^51 - 
        1881/2401*T^50 + 5/7*T^49 + 1067/2401*T^48 - 5/2401*T^47 + 2293/2401*T^46 + 
        2965/2401*T^45 - 355/343*T^44 - 5924/2401*T^43 - 1348/2401*T^42 + 
        597/343*T^41 + 3335/2401*T^40 + 155/2401*T^39 - 374/2401*T^38 + 12/2401*T^37
        - 2914/2401*T^36 - 4082/2401*T^35 + 1719/2401*T^34 + 6557/2401*T^33 + 
        2308/2401*T^32 - 4559/2401*T^31 - 2931/2401*T^30 + 723/2401*T^29 - 
        723/2401*T^27 + 2931/2401*T^26 + 4559/2401*T^25 - 2308/2401*T^24 - 
        6557/2401*T^23 - 1719/2401*T^22 + 4082/2401*T^21 + 2914/2401*T^20 - 
        12/2401*T^19 + 374/2401*T^18 - 155/2401*T^17 - 3335/2401*T^16 - 597/343*T^15
        + 1348/2401*T^14 + 5924/2401*T^13 + 355/343*T^12 - 2965/2401*T^11 - 
        2293/2401*T^10 + 5/2401*T^9 - 1067/2401*T^8 - 5/7*T^7 + 1881/2401*T^6 + 
        4804/2401*T^5 + 793/2401*T^4 - 593/343*T^3 - 66/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + X*Y^13 + 4*X*Y^12 + X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 
        3*X*Y^8 + X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + X*Y^4 + 4*X*Y^2 + X + 6*Y^30 + 2*Y^28 
        + Y^27 + 4*Y^26 + Y^25 + 5*Y^24 + Y^23 + Y^22 + Y^21 + 2*Y^20 + 5*Y^19 + 
        5*Y^18 + 6*Y^17 + 4*Y^16 + 5*Y^14 + 6*Y^13 + 2*Y^12 + Y^11 + 4*Y^10 + 4*Y^9 
        + 6*Y^7 + 6*Y^6 + Y^5 + Y^4 + 5*Y^3 + 4*Y^2 + 4,
    -T^56 - 9/7*T^55 + 195/343*T^53 + 439/2401*T^52 + 969/2401*T^51 + 3739/2401*T^50
        + 3666/2401*T^49 + 2718/2401*T^48 + 2467/2401*T^47 + 1158/2401*T^46 - 
        153/2401*T^45 - 2351/2401*T^44 - 5066/2401*T^43 - 6831/2401*T^42 - 
        3672/2401*T^41 - 1093/2401*T^40 - 2369/2401*T^39 - 1380/2401*T^38 + 
        205/343*T^37 + 3127/2401*T^36 + 2840/2401*T^35 + 3352/2401*T^34 + 
        3016/2401*T^33 + 2483/2401*T^32 + 3266/2401*T^31 + 309/2401*T^30 - 
        349/343*T^29 + 349/343*T^27 - 309/2401*T^26 - 3266/2401*T^25 - 
        2483/2401*T^24 - 3016/2401*T^23 - 3352/2401*T^22 - 2840/2401*T^21 - 
        3127/2401*T^20 - 205/343*T^19 + 1380/2401*T^18 + 2369/2401*T^17 + 
        1093/2401*T^16 + 3672/2401*T^15 + 6831/2401*T^14 + 5066/2401*T^13 + 
        2351/2401*T^12 + 153/2401*T^11 - 1158/2401*T^10 - 2467/2401*T^9 - 
        2718/2401*T^8 - 3666/2401*T^7 - 3739/2401*T^6 - 969/2401*T^5 - 439/2401*T^4 
        - 195/343*T^3 + 9/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 5*X*Y^8 
        + 5*X*Y^7 + 5*X*Y^6 + X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 4*X*Y + 2*X + 
        5*Y^30 + 5*Y^29 + 5*Y^28 + 2*Y^27 + 4*Y^26 + 6*Y^25 + 4*Y^24 + Y^23 + 4*Y^21
        + 5*Y^20 + Y^19 + 3*Y^18 + 5*Y^17 + 6*Y^16 + 6*Y^15 + 2*Y^14 + 6*Y^13 + 
        2*Y^12 + 4*Y^11 + 2*Y^10 + 3*Y^9 + Y^8 + 2*Y^7 + 2*Y^6 + 4*Y^5 + 3*Y^4 + 
        3*Y^2 + 6*Y + 4,
    -T^56 - 2/7*T^55 + 18/49*T^54 - 122/343*T^53 + 709/2401*T^52 - 155/2401*T^51 - 
        1087/2401*T^50 + 475/2401*T^49 + 446/2401*T^48 - 429/2401*T^47 + 
        550/2401*T^46 - 404/2401*T^45 - 778/2401*T^44 + 426/2401*T^43 - 
        869/2401*T^42 - 439/2401*T^41 + 382/2401*T^40 - 151/2401*T^39 - 
        110/2401*T^38 + 465/2401*T^37 - 65/2401*T^36 - 3/49*T^35 - 362/2401*T^34 - 
        284/2401*T^33 + 760/2401*T^32 - 817/2401*T^31 + 333/2401*T^30 + 24/343*T^29 
        - 24/343*T^27 - 333/2401*T^26 + 817/2401*T^25 - 760/2401*T^24 + 
        284/2401*T^23 + 362/2401*T^22 + 3/49*T^21 + 65/2401*T^20 - 465/2401*T^19 + 
        110/2401*T^18 + 151/2401*T^17 - 382/2401*T^16 + 439/2401*T^15 + 
        869/2401*T^14 - 426/2401*T^13 + 778/2401*T^12 + 404/2401*T^11 - 
        550/2401*T^10 + 429/2401*T^9 - 446/2401*T^8 - 475/2401*T^7 + 1087/2401*T^6 +
        155/2401*T^5 - 709/2401*T^4 + 122/343*T^3 - 18/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 3*X*Y^13 + 4*X*Y^11 + X*Y^9 + 3*X*Y^8 + 6*X*Y^7 + 
        X*Y^6 + 3*X*Y^5 + X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 4*X*Y + 2*X + 3*Y^30 + 2*Y^29 
        + 6*Y^28 + 4*Y^27 + 6*Y^26 + 3*Y^24 + 2*Y^23 + 6*Y^21 + 4*Y^19 + 3*Y^18 + 
        4*Y^17 + 4*Y^16 + 3*Y^15 + Y^12 + 4*Y^11 + 5*Y^10 + 3*Y^9 + Y^8 + 2*Y^7 + 
        4*Y^6 + 3*Y^5 + 6*Y^4 + 5*Y^2 + 2*Y + 4,
    -T^56 + 12/7*T^55 - 22/49*T^54 - 167/343*T^53 - 1108/2401*T^52 + 384/343*T^51 - 
        356/2401*T^50 - 1959/2401*T^49 + 2390/2401*T^48 - 1597/2401*T^47 + 
        912/2401*T^46 - 185/343*T^45 + 1114/2401*T^44 - 47/2401*T^43 + 461/2401*T^42
        - 1083/2401*T^41 - 1229/2401*T^40 + 480/343*T^39 - 2370/2401*T^38 + 
        122/343*T^37 - 4/2401*T^36 - 1178/2401*T^35 + 187/343*T^34 - 1089/2401*T^33 
        + 1571/2401*T^32 - 246/343*T^31 + 2195/2401*T^30 - 303/343*T^29 + 
        303/343*T^27 - 2195/2401*T^26 + 246/343*T^25 - 1571/2401*T^24 + 
        1089/2401*T^23 - 187/343*T^22 + 1178/2401*T^21 + 4/2401*T^20 - 122/343*T^19 
        + 2370/2401*T^18 - 480/343*T^17 + 1229/2401*T^16 + 1083/2401*T^15 - 
        461/2401*T^14 + 47/2401*T^13 - 1114/2401*T^12 + 185/343*T^11 - 912/2401*T^10
        + 1597/2401*T^9 - 2390/2401*T^8 + 1959/2401*T^7 + 356/2401*T^6 - 384/343*T^5
        + 1108/2401*T^4 + 167/343*T^3 + 22/49*T^2 - 12/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 
        3*X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 4*X*Y^3 + X*Y + 5*X + 4*Y^30 + 
        3*Y^29 + 2*Y^28 + 6*Y^27 + 2*Y^26 + 5*Y^25 + 2*Y^24 + 6*Y^23 + 3*Y^21 + 
        5*Y^20 + 2*Y^19 + 2*Y^18 + 6*Y^17 + 5*Y^16 + 2*Y^13 + 2*Y^12 + Y^11 + Y^10 +
        2*Y^7 + 4*Y^6 + 4*Y^5 + 3*Y^4 + 6*Y^3 + 6*Y^2 + Y + 4,
    -T^56 - 5/7*T^55 - 47/49*T^54 - 410/343*T^53 - 489/343*T^52 - 2446/2401*T^51 - 
        2004/2401*T^50 - 2925/2401*T^49 - 137/343*T^48 + 34/2401*T^47 + 20/49*T^46 +
        9/49*T^45 + 2067/2401*T^44 + 2286/2401*T^43 + 897/2401*T^42 - 274/2401*T^41 
        + 824/2401*T^40 + 144/2401*T^39 - 747/2401*T^38 - 692/2401*T^37 + 
        48/2401*T^36 - 1350/2401*T^35 - 1389/2401*T^34 - 1025/2401*T^33 - 
        1038/2401*T^32 - 648/2401*T^31 - 318/2401*T^30 + 482/2401*T^29 - 
        482/2401*T^27 + 318/2401*T^26 + 648/2401*T^25 + 1038/2401*T^24 + 
        1025/2401*T^23 + 1389/2401*T^22 + 1350/2401*T^21 - 48/2401*T^20 + 
        692/2401*T^19 + 747/2401*T^18 - 144/2401*T^17 - 824/2401*T^16 + 
        274/2401*T^15 - 897/2401*T^14 - 2286/2401*T^13 - 2067/2401*T^12 - 9/49*T^11 
        - 20/49*T^10 - 34/2401*T^9 + 137/343*T^8 + 2925/2401*T^7 + 2004/2401*T^6 + 
        2446/2401*T^5 + 489/343*T^4 + 410/343*T^3 + 47/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + X*Y^10 + 2*X*Y^9 + 6*X*Y^6 + 
        X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 4*X*Y + 6*X + 6*Y^30 + Y^29 + 4*Y^27 +
        Y^26 + Y^25 + 4*Y^24 + 6*Y^23 + 6*Y^21 + 5*Y^20 + 5*Y^18 + 4*Y^17 + Y^16 + 
        4*Y^15 + Y^14 + 2*Y^13 + 2*Y^12 + Y^11 + 3*Y^10 + 3*Y^9 + 3*Y^8 + 6*Y^7 + 
        3*Y^5 + 5*Y^4 + 2*Y^2 + 2*Y + 2,
    -T^56 - 2/7*T^55 + 3/7*T^54 - 123/343*T^53 - 289/2401*T^52 - 472/2401*T^51 + 
        178/343*T^50 - 111/2401*T^49 - 2040/2401*T^48 + 1677/2401*T^47 + 
        881/2401*T^46 - 611/2401*T^45 + 191/2401*T^44 + 905/2401*T^43 + 
        1912/2401*T^42 + 9/2401*T^41 - 648/2401*T^40 + 1397/2401*T^39 + 11/343*T^38 
        - 787/2401*T^37 + 6/49*T^36 - 73/343*T^35 + 643/2401*T^34 - 142/2401*T^33 - 
        663/2401*T^32 + 865/2401*T^31 - 1229/2401*T^30 - 223/2401*T^29 + 
        223/2401*T^27 + 1229/2401*T^26 - 865/2401*T^25 + 663/2401*T^24 + 
        142/2401*T^23 - 643/2401*T^22 + 73/343*T^21 - 6/49*T^20 + 787/2401*T^19 - 
        11/343*T^18 - 1397/2401*T^17 + 648/2401*T^16 - 9/2401*T^15 - 1912/2401*T^14 
        - 905/2401*T^13 - 191/2401*T^12 + 611/2401*T^11 - 881/2401*T^10 - 
        1677/2401*T^9 + 2040/2401*T^8 + 111/2401*T^7 - 178/343*T^6 + 472/2401*T^5 + 
        289/2401*T^4 + 123/343*T^3 - 3/7*T^2 + 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 
        + 3*X*Y^7 + 2*X*Y^5 + X*Y^2 + 4*X + Y^30 + 3*Y^29 + 6*Y^27 + 5*Y^26 + 2*Y^25
        + 4*Y^24 + 2*Y^23 + 5*Y^22 + 5*Y^21 + 6*Y^20 + 5*Y^19 + 3*Y^18 + Y^17 + 
        5*Y^16 + Y^14 + 5*Y^13 + 2*Y^12 + 2*Y^11 + 2*Y^10 + 4*Y^8 + 2*Y^7 + 4*Y^6 + 
        Y^4 + 6*Y^2 + 6*Y,
    T^56 - 4/7*T^55 + 12/49*T^54 - 30/343*T^53 - 1795/2401*T^52 - 184/2401*T^51 + 
        926/2401*T^50 - 975/2401*T^49 + 75/343*T^48 + 162/2401*T^47 - 306/2401*T^46 
        - 19/343*T^45 - 239/2401*T^44 + 534/2401*T^43 - 54/343*T^42 + 1114/2401*T^41
        + 1159/2401*T^40 + 279/2401*T^39 + 36/2401*T^38 - 1194/2401*T^37 - 
        1433/2401*T^36 - 1007/2401*T^35 + 52/343*T^34 + 617/2401*T^33 - 
        397/2401*T^32 + 1507/2401*T^31 - 457/2401*T^30 - 1024/2401*T^29 + 
        1809/2401*T^28 - 1024/2401*T^27 - 457/2401*T^26 + 1507/2401*T^25 - 
        397/2401*T^24 + 617/2401*T^23 + 52/343*T^22 - 1007/2401*T^21 - 
        1433/2401*T^20 - 1194/2401*T^19 + 36/2401*T^18 + 279/2401*T^17 + 
        1159/2401*T^16 + 1114/2401*T^15 - 54/343*T^14 + 534/2401*T^13 - 
        239/2401*T^12 - 19/343*T^11 - 306/2401*T^10 + 162/2401*T^9 + 75/343*T^8 - 
        975/2401*T^7 + 926/2401*T^6 - 184/2401*T^5 - 1795/2401*T^4 - 30/343*T^3 + 
        12/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 
        + 3*X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 4*X + 5*Y^30 +
        6*Y^28 + 2*Y^27 + 3*Y^26 + 2*Y^25 + 6*Y^24 + 4*Y^23 + 5*Y^22 + Y^21 + 5*Y^20
        + 3*Y^19 + Y^18 + 6*Y^16 + 6*Y^15 + 4*Y^14 + 4*Y^13 + 2*Y^12 + 5*Y^11 + 
        5*Y^10 + 3*Y^9 + 3*Y^8 + 4*Y^7 + 2*Y^6 + 2*Y^5 + 4*Y^4 + 2*Y^3 + 6*Y + 3,
    -T^56 - 2/7*T^55 + 27/49*T^54 - 145/343*T^53 - 61/2401*T^52 + 753/2401*T^51 + 
        1221/2401*T^50 + 631/2401*T^49 - 85/343*T^48 + 635/2401*T^47 + 
        1093/2401*T^46 + 272/2401*T^45 - 587/2401*T^44 + 976/2401*T^43 + 
        1552/2401*T^42 - 1019/2401*T^41 - 648/2401*T^40 + 1121/2401*T^39 + 
        40/343*T^38 - 2006/2401*T^37 - 774/2401*T^36 + 673/2401*T^35 + 32/2401*T^34 
        - 1651/2401*T^33 - 1277/2401*T^32 + 743/2401*T^31 - 688/2401*T^30 - 
        1143/2401*T^29 + 1143/2401*T^27 + 688/2401*T^26 - 743/2401*T^25 + 
        1277/2401*T^24 + 1651/2401*T^23 - 32/2401*T^22 - 673/2401*T^21 + 
        774/2401*T^20 + 2006/2401*T^19 - 40/343*T^18 - 1121/2401*T^17 + 
        648/2401*T^16 + 1019/2401*T^15 - 1552/2401*T^14 - 976/2401*T^13 + 
        587/2401*T^12 - 272/2401*T^11 - 1093/2401*T^10 - 635/2401*T^9 + 85/343*T^8 -
        631/2401*T^7 - 1221/2401*T^6 - 753/2401*T^5 + 61/2401*T^4 + 145/343*T^3 - 
        27/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 
        5*X*Y^8 + 2*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + X*Y^4 + 6*X*Y^3 + X*Y^2 + 4*X*Y + 
        4*X + Y^30 + Y^28 + 3*Y^27 + 4*Y^26 + 3*Y^25 + 6*Y^24 + Y^23 + 4*Y^22 + 
        3*Y^21 + 6*Y^20 + Y^19 + 4*Y^17 + 5*Y^16 + 4*Y^15 + 2*Y^14 + 3*Y^13 + 5*Y^12
        + 4*Y^11 + 6*Y^10 + 6*Y^9 + 6*Y^8 + 4*Y^6 + 3*Y^4 + Y^2 + 6*Y + 1,
    T^56 - 3/7*T^55 - 38/49*T^54 + 162/343*T^53 + 653/2401*T^52 - 905/2401*T^51 + 
        1079/2401*T^50 + 877/2401*T^49 - 3177/2401*T^48 + 1189/2401*T^47 + 
        1326/2401*T^46 - 916/2401*T^45 + 121/343*T^44 + 31/343*T^43 - 2358/2401*T^42
        + 23/343*T^41 + 2893/2401*T^40 - 1648/2401*T^39 - 508/2401*T^38 + 
        1317/2401*T^37 - 1677/2401*T^36 - 48/343*T^35 + 2369/2401*T^34 - 
        337/2401*T^33 - 1182/2401*T^32 + 1041/2401*T^31 - 982/2401*T^30 - 
        457/2401*T^29 + 2341/2401*T^28 - 457/2401*T^27 - 982/2401*T^26 + 
        1041/2401*T^25 - 1182/2401*T^24 - 337/2401*T^23 + 2369/2401*T^22 - 
        48/343*T^21 - 1677/2401*T^20 + 1317/2401*T^19 - 508/2401*T^18 - 
        1648/2401*T^17 + 2893/2401*T^16 + 23/343*T^15 - 2358/2401*T^14 + 31/343*T^13
        + 121/343*T^12 - 916/2401*T^11 + 1326/2401*T^10 + 1189/2401*T^9 - 
        3177/2401*T^8 + 877/2401*T^7 + 1079/2401*T^6 - 905/2401*T^5 + 653/2401*T^4 +
        162/343*T^3 - 38/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 
        + 3*X*Y^8 + 2*X*Y^6 + 2*X*Y^5 + X*Y^4 + X*Y^3 + 4*X*Y^2 + X*Y + 6*X + Y^30 +
        5*Y^29 + Y^28 + 3*Y^27 + Y^26 + 5*Y^25 + 4*Y^24 + 5*Y^22 + 2*Y^21 + 5*Y^20 +
        4*Y^19 + 6*Y^18 + 2*Y^17 + 2*Y^16 + 3*Y^15 + 3*Y^14 + Y^13 + 5*Y^11 + 5*Y^10
        + 3*Y^9 + 4*Y^8 + 6*Y^7 + 3*Y^5 + 5*Y^4 + 6*Y^3 + 5*Y^2 + 6*Y + 1,
    -T^56 + 9/7*T^55 + 2/49*T^54 - 235/343*T^53 - 29/343*T^52 + 1772/2401*T^51 - 
        1979/2401*T^50 + 1758/2401*T^49 + 279/2401*T^48 - 958/2401*T^47 - 
        145/343*T^46 + 2633/2401*T^45 - 2775/2401*T^44 + 411/2401*T^43 + 
        1230/2401*T^42 - 541/2401*T^41 - 953/2401*T^40 + 1759/2401*T^39 - 
        2104/2401*T^38 + 942/2401*T^37 + 1513/2401*T^36 - 934/2401*T^35 - 
        1017/2401*T^34 + 1426/2401*T^33 - 727/2401*T^32 - 243/2401*T^31 + 
        390/2401*T^30 - 281/2401*T^29 + 281/2401*T^27 - 390/2401*T^26 + 
        243/2401*T^25 + 727/2401*T^24 - 1426/2401*T^23 + 1017/2401*T^22 + 
        934/2401*T^21 - 1513/2401*T^20 - 942/2401*T^19 + 2104/2401*T^18 - 
        1759/2401*T^17 + 953/2401*T^16 + 541/2401*T^15 - 1230/2401*T^14 - 
        411/2401*T^13 + 2775/2401*T^12 - 2633/2401*T^11 + 145/343*T^10 + 
        958/2401*T^9 - 279/2401*T^8 - 1758/2401*T^7 + 1979/2401*T^6 - 1772/2401*T^5 
        + 29/343*T^4 + 235/343*T^3 - 2/49*T^2 - 9/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 
        + X*Y^8 + 4*X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 2*X*Y + 2*X + 
        2*Y^30 + 4*Y^29 + 4*Y^28 + 3*Y^27 + Y^26 + 4*Y^25 + 2*Y^24 + 5*Y^23 + 5*Y^21
        + 3*Y^20 + 2*Y^19 + 5*Y^18 + 6*Y^17 + 4*Y^16 + 6*Y^15 + 3*Y^14 + 6*Y^12 + 
        6*Y^10 + 6*Y^9 + 2*Y^8 + 3*Y^7 + 5*Y^6 + 2*Y^5 + 6*Y^4 + 5*Y^2 + 4*Y + 6,
    T^56 - 5/7*T^55 - 9/49*T^54 + 16/343*T^53 - 1609/2401*T^52 + 2146/2401*T^51 - 
        1606/2401*T^50 + 1303/2401*T^49 + 138/2401*T^48 - 1226/2401*T^47 + 
        1451/2401*T^46 - 1613/2401*T^45 + 1152/2401*T^44 + 367/2401*T^43 - 
        515/2401*T^42 + 886/2401*T^41 - 141/343*T^40 + 1280/2401*T^39 - 
        1831/2401*T^38 - 447/2401*T^37 + 243/343*T^36 - 1671/2401*T^35 + 
        2194/2401*T^34 - 1856/2401*T^33 + 116/2401*T^32 - 122/2401*T^31 - 
        1005/2401*T^30 + 2472/2401*T^29 - 298/343*T^28 + 2472/2401*T^27 - 
        1005/2401*T^26 - 122/2401*T^25 + 116/2401*T^24 - 1856/2401*T^23 + 
        2194/2401*T^22 - 1671/2401*T^21 + 243/343*T^20 - 447/2401*T^19 - 
        1831/2401*T^18 + 1280/2401*T^17 - 141/343*T^16 + 886/2401*T^15 - 
        515/2401*T^14 + 367/2401*T^13 + 1152/2401*T^12 - 1613/2401*T^11 + 
        1451/2401*T^10 - 1226/2401*T^9 + 138/2401*T^8 + 1303/2401*T^7 - 
        1606/2401*T^6 + 2146/2401*T^5 - 1609/2401*T^4 + 16/343*T^3 - 9/49*T^2 - 
        5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + X*Y^9 + 3*X*Y^8 + 
        6*X*Y^7 + X*Y^6 + 5*X*Y^5 + 6*X*Y^2 + 5*X*Y + 3*X + 4*Y^30 + 2*Y^29 + 6*Y^28
        + 2*Y^27 + 4*Y^26 + 4*Y^25 + 3*Y^24 + 3*Y^22 + 2*Y^21 + 5*Y^20 + 5*Y^19 + 
        4*Y^18 + 2*Y^17 + Y^15 + Y^14 + 4*Y^13 + 4*Y^12 + 6*Y^11 + Y^9 + 5*Y^8 + 
        2*Y^7 + 4*Y^6 + 6*Y^5 + 2*Y^4 + 2*Y + 3,
    T^56 + 11/7*T^55 - 18/49*T^54 - 12/7*T^53 - 779/2401*T^52 + 5/2401*T^51 - 
        306/2401*T^50 + 2108/2401*T^49 - 6/49*T^48 - 3170/2401*T^47 + 108/2401*T^46 
        + 988/2401*T^45 + 821/2401*T^44 + 2809/2401*T^43 - 564/2401*T^42 - 
        3371/2401*T^41 - 704/2401*T^40 - 65/343*T^39 + 234/343*T^38 + 5672/2401*T^37
        + 1410/2401*T^36 - 507/343*T^35 - 1628/2401*T^34 - 681/2401*T^33 + 
        255/2401*T^32 + 2802/2401*T^31 + 920/2401*T^30 - 2095/2401*T^29 - 
        2511/2401*T^28 - 2095/2401*T^27 + 920/2401*T^26 + 2802/2401*T^25 + 
        255/2401*T^24 - 681/2401*T^23 - 1628/2401*T^22 - 507/343*T^21 + 
        1410/2401*T^20 + 5672/2401*T^19 + 234/343*T^18 - 65/343*T^17 - 704/2401*T^16
        - 3371/2401*T^15 - 564/2401*T^14 + 2809/2401*T^13 + 821/2401*T^12 + 
        988/2401*T^11 + 108/2401*T^10 - 3170/2401*T^9 - 6/49*T^8 + 2108/2401*T^7 - 
        306/2401*T^6 + 5/2401*T^5 - 779/2401*T^4 - 12/7*T^3 - 18/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 
        + 4*X*Y^8 + 6*X*Y^7 + X*Y^6 + 4*X*Y^5 + 6*X*Y^3 + 6*X*Y^2 + 6*X*Y + 6*X + 
        5*Y^30 + 2*Y^29 + 4*Y^28 + 5*Y^27 + Y^25 + Y^24 + 5*Y^23 + 4*Y^22 + 5*Y^21 +
        5*Y^20 + 5*Y^18 + 6*Y^17 + Y^16 + 6*Y^15 + 6*Y^13 + 4*Y^12 + 4*Y^10 + 6*Y^8 
        + 6*Y^6 + Y^5 + 2*Y^4 + 4*Y^2 + 5*Y + 6,
    T^56 + 1/7*T^55 - 69/49*T^54 + 79/343*T^53 + 2413/2401*T^52 - 1181/2401*T^51 - 
        411/2401*T^50 - 715/2401*T^49 - 786/2401*T^48 + 3274/2401*T^47 + 
        830/2401*T^46 - 3137/2401*T^45 + 40/343*T^44 - 80/2401*T^43 - 74/2401*T^42 +
        2393/2401*T^41 - 1697/2401*T^40 - 2088/2401*T^39 + 1812/2401*T^38 + 
        10/2401*T^37 + 262/2401*T^36 + 274/2401*T^35 - 3110/2401*T^34 + 
        1726/2401*T^33 + 2605/2401*T^32 - 3323/2401*T^31 + 746/2401*T^30 + 
        1777/2401*T^29 - 2903/2401*T^28 + 1777/2401*T^27 + 746/2401*T^26 - 
        3323/2401*T^25 + 2605/2401*T^24 + 1726/2401*T^23 - 3110/2401*T^22 + 
        274/2401*T^21 + 262/2401*T^20 + 10/2401*T^19 + 1812/2401*T^18 - 
        2088/2401*T^17 - 1697/2401*T^16 + 2393/2401*T^15 - 74/2401*T^14 - 
        80/2401*T^13 + 40/343*T^12 - 3137/2401*T^11 + 830/2401*T^10 + 3274/2401*T^9 
        - 786/2401*T^8 - 715/2401*T^7 - 411/2401*T^6 - 1181/2401*T^5 + 2413/2401*T^4
        + 79/343*T^3 - 69/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 5*X*Y^11 + X*Y^10 + 2*X*Y^9 + X*Y^8 + 6*X*Y^7 + 
        2*X*Y^6 + 6*X*Y^5 + X*Y^4 + X*Y^3 + 5*X*Y^2 + 3*X + 2*Y^30 + 2*Y^29 + Y^28 +
        4*Y^27 + 4*Y^26 + 2*Y^25 + 4*Y^24 + Y^23 + 2*Y^21 + 6*Y^20 + 6*Y^17 + 2*Y^16
        + 6*Y^14 + 3*Y^13 + 5*Y^11 + 6*Y^9 + Y^8 + 3*Y^7 + Y^6 + 5*Y^5 + 4*Y^4 + 
        5*Y^3 + 4*Y^2 + 5*Y + 6,
    T^56 - 8/7*T^55 + 55/49*T^54 - 242/343*T^53 - 195/343*T^52 + 62/49*T^51 - 
        1707/2401*T^50 - 195/2401*T^49 + 1156/2401*T^48 - 234/343*T^47 + 
        638/2401*T^46 + 489/2401*T^45 - 31/343*T^44 - 17/49*T^43 + 836/2401*T^42 - 
        60/343*T^41 + 1013/2401*T^40 - 537/2401*T^39 + 40/343*T^38 + 948/2401*T^37 -
        1079/2401*T^36 + 1563/2401*T^35 - 431/2401*T^34 - 1696/2401*T^33 + 
        41/49*T^32 - 827/2401*T^31 + 723/2401*T^30 + 323/2401*T^29 - 1614/2401*T^28 
        + 323/2401*T^27 + 723/2401*T^26 - 827/2401*T^25 + 41/49*T^24 - 
        1696/2401*T^23 - 431/2401*T^22 + 1563/2401*T^21 - 1079/2401*T^20 + 
        948/2401*T^19 + 40/343*T^18 - 537/2401*T^17 + 1013/2401*T^16 - 60/343*T^15 +
        836/2401*T^14 - 17/49*T^13 - 31/343*T^12 + 489/2401*T^11 + 638/2401*T^10 - 
        234/343*T^9 + 1156/2401*T^8 - 195/2401*T^7 - 1707/2401*T^6 + 62/49*T^5 - 
        195/343*T^4 - 242/343*T^3 + 55/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 6*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 4*X*Y^8 + 3*X*Y^7 + 
        3*X*Y^6 + 2*X*Y^5 + X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 4*X + 4*Y^30 + Y^29 + 5*Y^28
        + 2*Y^26 + 3*Y^24 + Y^23 + 3*Y^22 + 4*Y^21 + 5*Y^20 + 5*Y^18 + 3*Y^17 + Y^16
        + 2*Y^15 + 6*Y^14 + 2*Y^13 + Y^12 + 4*Y^11 + Y^10 + 4*Y^9 + 6*Y^7 + 3*Y^6 + 
        2*Y^5 + 6*Y^4 + 5*Y^3 + Y^2 + 2*Y + 6,
    T^56 - 1/7*T^55 - 6/7*T^54 + 4/49*T^53 - 472/2401*T^52 + 1161/2401*T^51 + 
        377/2401*T^50 - 162/2401*T^49 + 136/343*T^48 - 1826/2401*T^47 - 
        768/2401*T^46 + 1027/2401*T^45 - 1066/2401*T^44 + 1259/2401*T^43 + 
        748/2401*T^42 - 198/343*T^41 - 303/2401*T^40 - 986/2401*T^39 - 62/2401*T^38 
        + 962/2401*T^37 - 941/2401*T^36 + 1279/2401*T^35 + 221/2401*T^34 - 
        1683/2401*T^33 + 2147/2401*T^32 - 37/343*T^31 - 863/2401*T^30 + 
        1013/2401*T^29 - 41/2401*T^28 + 1013/2401*T^27 - 863/2401*T^26 - 37/343*T^25
        + 2147/2401*T^24 - 1683/2401*T^23 + 221/2401*T^22 + 1279/2401*T^21 - 
        941/2401*T^20 + 962/2401*T^19 - 62/2401*T^18 - 986/2401*T^17 - 303/2401*T^16
        - 198/343*T^15 + 748/2401*T^14 + 1259/2401*T^13 - 1066/2401*T^12 + 
        1027/2401*T^11 - 768/2401*T^10 - 1826/2401*T^9 + 136/343*T^8 - 162/2401*T^7 
        + 377/2401*T^6 + 1161/2401*T^5 - 472/2401*T^4 + 4/49*T^3 - 6/7*T^2 - 1/7*T +
        1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^13 + 2*X*Y^12 + X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 2*X*Y^8 + 
        X*Y^7 + 5*X*Y^6 + 6*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + X*Y + 3*X + 5*Y^30 + 4*Y^29 
        + 6*Y^28 + 4*Y^27 + 4*Y^26 + 4*Y^25 + Y^24 + 5*Y^22 + 4*Y^21 + 3*Y^20 + 
        4*Y^19 + 4*Y^17 + Y^16 + 4*Y^15 + 6*Y^14 + 6*Y^13 + 3*Y^12 + Y^11 + 6*Y^10 +
        Y^9 + 4*Y^8 + 4*Y^7 + 2*Y^6 + 5*Y^5 + 5*Y^4 + 3*Y^3 + 4*Y + 6,
    T^56 + 3/7*T^55 - 19/49*T^54 - 34/343*T^53 - 321/2401*T^52 - 491/2401*T^51 + 
        534/2401*T^50 + 670/2401*T^49 - 1885/2401*T^48 - 1333/2401*T^47 + 
        610/2401*T^46 + 102/343*T^45 + 144/2401*T^44 + 645/2401*T^43 - 
        1013/2401*T^42 - 1724/2401*T^41 + 1326/2401*T^40 + 1726/2401*T^39 - 
        297/2401*T^38 - 296/343*T^37 - 968/2401*T^36 - 169/343*T^35 + 727/2401*T^34 
        + 2133/2401*T^33 - 11/49*T^32 - 1671/2401*T^31 - 16/2401*T^30 + 
        1507/2401*T^29 + 24/49*T^28 + 1507/2401*T^27 - 16/2401*T^26 - 1671/2401*T^25
        - 11/49*T^24 + 2133/2401*T^23 + 727/2401*T^22 - 169/343*T^21 - 968/2401*T^20
        - 296/343*T^19 - 297/2401*T^18 + 1726/2401*T^17 + 1326/2401*T^16 - 
        1724/2401*T^15 - 1013/2401*T^14 + 645/2401*T^13 + 144/2401*T^12 + 
        102/343*T^11 + 610/2401*T^10 - 1333/2401*T^9 - 1885/2401*T^8 + 670/2401*T^7 
        + 534/2401*T^6 - 491/2401*T^5 - 321/2401*T^4 - 34/343*T^3 - 19/49*T^2 + 
        3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 6*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 
        3*X*Y^6 + X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 6*X*Y + 5*X + 2*Y^30 + 
        5*Y^29 + 6*Y^28 + 3*Y^27 + Y^26 + Y^25 + 5*Y^24 + Y^23 + 3*Y^22 + 4*Y^21 + 
        3*Y^20 + 3*Y^18 + 2*Y^17 + 5*Y^16 + 3*Y^14 + 4*Y^13 + 4*Y^12 + 6*Y^11 + 
        3*Y^9 + 5*Y^8 + Y^7 + 4*Y^6 + 5*Y^5 + 6*Y^4 + 6*Y^3 + 3*Y^2 + 3*Y + 3,
    -T^56 - 1/7*T^55 + 66/49*T^54 + 148/343*T^53 + 12/2401*T^52 + 295/2401*T^51 - 
        3025/2401*T^50 - 1920/2401*T^49 + 1815/2401*T^48 + 1571/2401*T^47 - 
        10/343*T^46 + 341/2401*T^45 + 148/2401*T^44 - 1534/2401*T^43 + 157/2401*T^42
        + 1157/2401*T^41 - 943/2401*T^40 - 240/2401*T^39 + 468/2401*T^38 + 
        117/2401*T^37 + 972/2401*T^36 + 55/2401*T^35 - 1651/2401*T^34 - 
        438/2401*T^33 + 330/2401*T^32 + 59/343*T^31 + 558/2401*T^30 + 477/2401*T^29 
        - 477/2401*T^27 - 558/2401*T^26 - 59/343*T^25 - 330/2401*T^24 + 
        438/2401*T^23 + 1651/2401*T^22 - 55/2401*T^21 - 972/2401*T^20 - 
        117/2401*T^19 - 468/2401*T^18 + 240/2401*T^17 + 943/2401*T^16 - 
        1157/2401*T^15 - 157/2401*T^14 + 1534/2401*T^13 - 148/2401*T^12 - 
        341/2401*T^11 + 10/343*T^10 - 1571/2401*T^9 - 1815/2401*T^8 + 1920/2401*T^7 
        + 3025/2401*T^6 - 295/2401*T^5 - 12/2401*T^4 - 148/343*T^3 - 66/49*T^2 + 
        1/7*T + 1
*], [*
    X^3 + 5*X*Y^13 + X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 5*X*Y^8 + 5*X*Y^7 + 
        X*Y^5 + 5*X*Y^4 + X*Y^3 + 3*X*Y^2 + 4*X*Y + 2*Y^30 + 3*Y^28 + 4*Y^27 + 
        4*Y^26 + 6*Y^25 + 5*Y^24 + Y^23 + 4*Y^22 + 3*Y^19 + 4*Y^18 + 4*Y^17 + Y^16 +
        6*Y^15 + 4*Y^13 + 2*Y^12 + 6*Y^11 + 5*Y^10 + 5*Y^9 + 5*Y^7 + 5*Y^6 + Y^5 + 
        Y^4 + 2*Y^3 + 3*Y^2 + 5*Y + 5,
    T^56 + 1/7*T^55 + 3/49*T^54 - 60/343*T^53 - 370/2401*T^52 - 955/2401*T^51 - 
        412/2401*T^50 - 135/2401*T^49 - 416/2401*T^48 + 166/2401*T^47 + 
        782/2401*T^46 - 57/343*T^45 + 208/2401*T^44 - 292/2401*T^43 + 817/2401*T^42 
        - 107/2401*T^41 - 386/2401*T^40 - 165/2401*T^39 + 627/2401*T^38 + 
        446/2401*T^37 - 508/2401*T^36 - 186/2401*T^35 - 569/2401*T^34 + 
        538/2401*T^33 + 345/2401*T^32 - 34/2401*T^31 - 76/343*T^30 - 208/2401*T^29 +
        312/2401*T^28 - 208/2401*T^27 - 76/343*T^26 - 34/2401*T^25 + 345/2401*T^24 +
        538/2401*T^23 - 569/2401*T^22 - 186/2401*T^21 - 508/2401*T^20 + 
        446/2401*T^19 + 627/2401*T^18 - 165/2401*T^17 - 386/2401*T^16 - 
        107/2401*T^15 + 817/2401*T^14 - 292/2401*T^13 + 208/2401*T^12 - 57/343*T^11 
        + 782/2401*T^10 + 166/2401*T^9 - 416/2401*T^8 - 135/2401*T^7 - 412/2401*T^6 
        - 955/2401*T^5 - 370/2401*T^4 - 60/343*T^3 + 3/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 5*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 5*X*Y^8 + 6*X*Y^7 + 
        3*X*Y^6 + 2*X*Y^5 + X*Y^4 + 6*X*Y^2 + 5*X*Y + 3*X + 3*Y^30 + 2*Y^29 + 2*Y^28
        + Y^27 + 3*Y^25 + 4*Y^24 + Y^23 + 4*Y^22 + 6*Y^21 + 5*Y^20 + 6*Y^19 + 5*Y^18
        + 2*Y^17 + 4*Y^16 + 3*Y^15 + 6*Y^14 + 4*Y^13 + 4*Y^12 + 2*Y^11 + 6*Y^10 + 
        5*Y^9 + 6*Y^8 + 4*Y^6 + Y^5 + 2*Y^4 + 4*Y^3 + 6*Y^2 + 6*Y + 3,
    -T^56 + 2/7*T^55 + 59/49*T^54 - 181/343*T^53 + 180/343*T^52 + 472/2401*T^51 - 
        4119/2401*T^50 + 942/2401*T^49 + 2104/2401*T^48 - 467/2401*T^47 + 
        1647/2401*T^46 - 288/2401*T^45 - 3335/2401*T^44 - 103/2401*T^43 + 
        1882/2401*T^42 + 988/2401*T^41 + 1770/2401*T^40 - 225/343*T^39 - 
        244/343*T^38 + 17/2401*T^37 - 1273/2401*T^36 + 2355/2401*T^35 + 
        1112/2401*T^34 - 2330/2401*T^33 + 62/343*T^32 - 615/2401*T^31 - 
        375/2401*T^30 + 1787/2401*T^29 - 1787/2401*T^27 + 375/2401*T^26 + 
        615/2401*T^25 - 62/343*T^24 + 2330/2401*T^23 - 1112/2401*T^22 - 
        2355/2401*T^21 + 1273/2401*T^20 - 17/2401*T^19 + 244/343*T^18 + 225/343*T^17
        - 1770/2401*T^16 - 988/2401*T^15 - 1882/2401*T^14 + 103/2401*T^13 + 
        3335/2401*T^12 + 288/2401*T^11 - 1647/2401*T^10 + 467/2401*T^9 - 
        2104/2401*T^8 - 942/2401*T^7 + 4119/2401*T^6 - 472/2401*T^5 - 180/343*T^4 + 
        181/343*T^3 - 59/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 3*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 4*X + 
        2*Y^30 + 6*Y^29 + 6*Y^28 + 3*Y^27 + 4*Y^26 + 3*Y^25 + 2*Y^23 + 2*Y^22 + 
        2*Y^21 + 4*Y^20 + 4*Y^19 + 3*Y^18 + 4*Y^17 + 6*Y^16 + 6*Y^15 + 2*Y^14 + 
        6*Y^13 + 4*Y^11 + 6*Y^10 + 3*Y^9 + 2*Y^8 + 2*Y^7 + 3*Y^6 + 4*Y^5 + 5*Y^4 + 
        5*Y^2 + 4*Y,
    T^56 + 3/7*T^55 - 6/49*T^54 - 114/343*T^53 - 1283/2401*T^52 + 379/2401*T^51 - 
        415/2401*T^50 + 318/2401*T^49 + 30/49*T^48 + 444/2401*T^47 - 1161/2401*T^46 
        + 87/2401*T^45 + 1184/2401*T^44 + 176/2401*T^43 - 1333/2401*T^42 - 
        1513/2401*T^41 + 33/343*T^40 + 1032/2401*T^39 + 803/2401*T^38 + 
        1367/2401*T^37 + 1781/2401*T^36 - 1103/2401*T^35 - 2192/2401*T^34 - 
        830/2401*T^33 + 18/343*T^32 + 671/2401*T^31 - 520/2401*T^30 - 2/49*T^29 + 
        982/2401*T^28 - 2/49*T^27 - 520/2401*T^26 + 671/2401*T^25 + 18/343*T^24 - 
        830/2401*T^23 - 2192/2401*T^22 - 1103/2401*T^21 + 1781/2401*T^20 + 
        1367/2401*T^19 + 803/2401*T^18 + 1032/2401*T^17 + 33/343*T^16 - 
        1513/2401*T^15 - 1333/2401*T^14 + 176/2401*T^13 + 1184/2401*T^12 + 
        87/2401*T^11 - 1161/2401*T^10 + 444/2401*T^9 + 30/49*T^8 + 318/2401*T^7 - 
        415/2401*T^6 + 379/2401*T^5 - 1283/2401*T^4 - 114/343*T^3 - 6/49*T^2 + 3/7*T
        + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 
        + 6*X*Y^8 + X*Y^7 + 4*X*Y^6 + X*Y^4 + X*Y^3 + 6*X*Y^2 + 3*X*Y + 5*X + 4*Y^30
        + 3*Y^29 + 2*Y^27 + 2*Y^26 + 2*Y^25 + 6*Y^24 + 4*Y^23 + 3*Y^22 + 6*Y^21 + 
        Y^20 + 2*Y^19 + 2*Y^18 + 2*Y^17 + 2*Y^15 + 5*Y^14 + Y^13 + 2*Y^11 + 4*Y^10 +
        3*Y^9 + Y^7 + 5*Y^6 + 2*Y^5 + 5*Y^4 + 3*Y^3 + 5*Y^2 + 2*Y + 4,
    -T^56 - 3/7*T^55 + 31/49*T^54 + 333/343*T^53 - 425/2401*T^52 + 408/2401*T^51 + 
        1524/2401*T^50 - 702/2401*T^49 - 3407/2401*T^48 + 232/2401*T^47 + 
        2574/2401*T^46 + 412/2401*T^45 - 233/343*T^44 + 48/2401*T^43 + 599/2401*T^42
        - 2848/2401*T^41 - 1195/2401*T^40 + 2252/2401*T^39 + 3595/2401*T^38 - 
        115/343*T^37 - 936/2401*T^36 + 1044/2401*T^35 + 334/2401*T^34 - 
        3901/2401*T^33 - 796/2401*T^32 + 2502/2401*T^31 + 26/49*T^30 - 
        2524/2401*T^29 + 2524/2401*T^27 - 26/49*T^26 - 2502/2401*T^25 + 
        796/2401*T^24 + 3901/2401*T^23 - 334/2401*T^22 - 1044/2401*T^21 + 
        936/2401*T^20 + 115/343*T^19 - 3595/2401*T^18 - 2252/2401*T^17 + 
        1195/2401*T^16 + 2848/2401*T^15 - 599/2401*T^14 - 48/2401*T^13 + 
        233/343*T^12 - 412/2401*T^11 - 2574/2401*T^10 - 232/2401*T^9 + 3407/2401*T^8
        + 702/2401*T^7 - 1524/2401*T^6 - 408/2401*T^5 + 425/2401*T^4 - 333/343*T^3 -
        31/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + X*Y^10 + 3*X*Y^9 + 2*X*Y^7 + 3*X*Y^6 + 
        3*X*Y^5 + 3*X*Y^4 + 4*X*Y^2 + 6*Y^30 + 2*Y^29 + 4*Y^28 + 4*Y^27 + Y^26 + 
        4*Y^25 + 3*Y^24 + 4*Y^23 + 4*Y^22 + 5*Y^21 + 5*Y^20 + 4*Y^19 + Y^18 + 2*Y^17
        + 4*Y^16 + 4*Y^14 + 5*Y^13 + 2*Y^12 + 2*Y^11 + 6*Y^8 + 6*Y^7 + 2*Y^6 + 5*Y^5
        + 5*Y^3 + 6*Y^2 + 4*Y + 3,
    T^56 - 10/7*T^55 + 22/49*T^54 - 67/343*T^53 + 337/2401*T^52 + 370/2401*T^51 + 
        1639/2401*T^50 - 2724/2401*T^49 + 1852/2401*T^48 - 1614/2401*T^47 - 
        458/2401*T^46 + 1152/2401*T^45 + 460/2401*T^44 - 454/2401*T^43 + 
        879/2401*T^42 - 1894/2401*T^41 + 785/2401*T^40 - 754/2401*T^39 + 
        1412/2401*T^38 - 52/343*T^37 + 428/2401*T^36 - 656/2401*T^35 + 509/2401*T^34
        - 1397/2401*T^33 + 1553/2401*T^32 - 939/2401*T^31 + 144/343*T^30 - 
        95/2401*T^29 - 941/2401*T^28 - 95/2401*T^27 + 144/343*T^26 - 939/2401*T^25 +
        1553/2401*T^24 - 1397/2401*T^23 + 509/2401*T^22 - 656/2401*T^21 + 
        428/2401*T^20 - 52/343*T^19 + 1412/2401*T^18 - 754/2401*T^17 + 785/2401*T^16
        - 1894/2401*T^15 + 879/2401*T^14 - 454/2401*T^13 + 460/2401*T^12 + 
        1152/2401*T^11 - 458/2401*T^10 - 1614/2401*T^9 + 1852/2401*T^8 - 
        2724/2401*T^7 + 1639/2401*T^6 + 370/2401*T^5 + 337/2401*T^4 - 67/343*T^3 + 
        22/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 
        + 5*X*Y^7 + 5*X*Y^6 + 2*X*Y + Y^30 + 3*Y^29 + 4*Y^28 + 2*Y^27 + 6*Y^26 + 
        Y^25 + 4*Y^24 + 4*Y^23 + 3*Y^22 + 5*Y^21 + Y^20 + 5*Y^19 + 2*Y^18 + 5*Y^15 +
        5*Y^13 + 4*Y^12 + Y^11 + 6*Y^10 + Y^9 + 4*Y^8 + 6*Y^7 + 3*Y^6 + Y^5 + 5*Y^4 
        + 3*Y^3 + 3*Y^2 + 2*Y + 6,
    T^56 + 3/7*T^55 + 66/49*T^54 + 243/343*T^53 + 355/343*T^52 + 145/2401*T^51 + 
        2291/2401*T^50 - 974/2401*T^49 - 489/2401*T^48 - 2052/2401*T^47 - 
        2043/2401*T^46 - 1702/2401*T^45 - 621/2401*T^44 + 1418/2401*T^43 + 
        1560/2401*T^42 + 2853/2401*T^41 + 3204/2401*T^40 + 3620/2401*T^39 + 
        1698/2401*T^38 + 1340/2401*T^37 + 173/2401*T^36 - 2020/2401*T^35 - 
        921/2401*T^34 - 2050/2401*T^33 - 470/2401*T^32 - 1735/2401*T^31 + 
        2222/2401*T^30 + 418/2401*T^29 + 3434/2401*T^28 + 418/2401*T^27 + 
        2222/2401*T^26 - 1735/2401*T^25 - 470/2401*T^24 - 2050/2401*T^23 - 
        921/2401*T^22 - 2020/2401*T^21 + 173/2401*T^20 + 1340/2401*T^19 + 
        1698/2401*T^18 + 3620/2401*T^17 + 3204/2401*T^16 + 2853/2401*T^15 + 
        1560/2401*T^14 + 1418/2401*T^13 - 621/2401*T^12 - 1702/2401*T^11 - 
        2043/2401*T^10 - 2052/2401*T^9 - 489/2401*T^8 - 974/2401*T^7 + 2291/2401*T^6
        + 145/2401*T^5 + 355/343*T^4 + 243/343*T^3 + 66/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 3*X*Y^13 + 3*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 5*X*Y^8 + 6*X*Y^7 + 
        5*X*Y^6 + X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 2*X*Y + 6*X + 5*Y^30 + 
        2*Y^29 + 6*Y^28 + 4*Y^27 + 5*Y^26 + 6*Y^25 + Y^24 + 6*Y^22 + Y^21 + 2*Y^20 +
        6*Y^19 + 4*Y^18 + 2*Y^17 + 5*Y^16 + 3*Y^15 + 4*Y^14 + 2*Y^13 + 5*Y^12 + 
        4*Y^11 + 5*Y^9 + 5*Y^8 + 2*Y^7 + 3*Y^6 + Y^5 + 5*Y^4 + 2*Y^3 + 4*Y^2 + 5*Y +
        6,
    T^56 + 10/7*T^55 + 20/49*T^54 - 11/49*T^53 + 908/2401*T^52 + 2276/2401*T^51 + 
        1161/2401*T^50 + 331/2401*T^49 + 272/2401*T^48 - 809/2401*T^47 - 
        2392/2401*T^46 - 1712/2401*T^45 - 911/2401*T^44 - 3056/2401*T^43 - 
        2920/2401*T^42 - 426/2401*T^41 - 1563/2401*T^40 - 4478/2401*T^39 - 
        2722/2401*T^38 + 138/343*T^37 + 221/2401*T^36 - 83/343*T^35 + 1955/2401*T^34
        + 2566/2401*T^33 - 625/2401*T^32 - 415/2401*T^31 + 2952/2401*T^30 + 
        2655/2401*T^29 + 1306/2401*T^28 + 2655/2401*T^27 + 2952/2401*T^26 - 
        415/2401*T^25 - 625/2401*T^24 + 2566/2401*T^23 + 1955/2401*T^22 - 
        83/343*T^21 + 221/2401*T^20 + 138/343*T^19 - 2722/2401*T^18 - 4478/2401*T^17
        - 1563/2401*T^16 - 426/2401*T^15 - 2920/2401*T^14 - 3056/2401*T^13 - 
        911/2401*T^12 - 1712/2401*T^11 - 2392/2401*T^10 - 809/2401*T^9 + 
        272/2401*T^8 + 331/2401*T^7 + 1161/2401*T^6 + 2276/2401*T^5 + 908/2401*T^4 -
        11/49*T^3 + 20/49*T^2 + 10/7*T + 1
*], [*
    X^3 + X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 5*X*Y^9 + 2*X*Y^8 + 4*X*Y^7 + 2*X*Y^5 + 
        6*X*Y^4 + 3*X*Y^2 + 2*X*Y + 3*Y^30 + 4*Y^29 + 5*Y^28 + 5*Y^27 + 5*Y^26 + 
        4*Y^25 + 4*Y^24 + 3*Y^23 + 5*Y^22 + 5*Y^21 + 4*Y^20 + 4*Y^18 + 5*Y^17 + 
        4*Y^16 + Y^15 + 2*Y^12 + 3*Y^10 + 2*Y^9 + 5*Y^7 + 5*Y^6 + 5*Y^5 + 4*Y^4 + 
        3*Y^2 + Y + 1,
    T^56 - 17/7*T^55 + 153/49*T^54 - 935/343*T^53 + 5847/2401*T^52 - 5386/2401*T^51 
        + 3867/2401*T^50 - 530/2401*T^49 - 2468/2401*T^48 + 4372/2401*T^47 - 
        5112/2401*T^46 + 793/343*T^45 - 766/343*T^44 + 5563/2401*T^43 - 
        6932/2401*T^42 + 8672/2401*T^41 - 8787/2401*T^40 + 7892/2401*T^39 - 
        7121/2401*T^38 + 5795/2401*T^37 - 435/343*T^36 - 753/2401*T^35 + 
        3846/2401*T^34 - 5503/2401*T^33 + 6316/2401*T^32 - 7307/2401*T^31 + 
        7961/2401*T^30 - 7485/2401*T^29 + 6938/2401*T^28 - 7485/2401*T^27 + 
        7961/2401*T^26 - 7307/2401*T^25 + 6316/2401*T^24 - 5503/2401*T^23 + 
        3846/2401*T^22 - 753/2401*T^21 - 435/343*T^20 + 5795/2401*T^19 - 
        7121/2401*T^18 + 7892/2401*T^17 - 8787/2401*T^16 + 8672/2401*T^15 - 
        6932/2401*T^14 + 5563/2401*T^13 - 766/343*T^12 + 793/343*T^11 - 
        5112/2401*T^10 + 4372/2401*T^9 - 2468/2401*T^8 - 530/2401*T^7 + 
        3867/2401*T^6 - 5386/2401*T^5 + 5847/2401*T^4 - 935/343*T^3 + 153/49*T^2 - 
        17/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 
        + 5*X*Y^7 + 4*X*Y^5 + X*Y^3 + 6*X*Y^2 + X*Y + 3*X + 5*Y^30 + 3*Y^29 + Y^28 +
        2*Y^27 + 5*Y^25 + Y^24 + 2*Y^23 + 3*Y^22 + Y^21 + 3*Y^20 + Y^19 + Y^18 + 
        3*Y^17 + 2*Y^15 + 2*Y^14 + 4*Y^13 + 2*Y^12 + Y^11 + 6*Y^9 + 2*Y^8 + 6*Y^7 + 
        4*Y^6 + 2*Y^5 + 2*Y^4 + 5*Y^3 + 4*Y^2 + 5*Y,
    -T^56 - 4/7*T^55 + 45/49*T^54 + 113/343*T^53 - 998/2401*T^52 + 31/2401*T^51 + 
        1048/2401*T^50 + 885/2401*T^49 + 12/2401*T^48 - 1482/2401*T^47 - 
        827/2401*T^46 + 2381/2401*T^45 + 125/2401*T^44 - 145/343*T^43 + 
        1268/2401*T^42 - 4/49*T^41 - 274/2401*T^40 - 57/2401*T^39 - 1025/2401*T^38 +
        822/2401*T^37 + 1826/2401*T^36 - 486/2401*T^35 - 414/2401*T^34 + 
        1020/2401*T^33 - 184/343*T^32 - 747/2401*T^31 + 67/343*T^30 - 2273/2401*T^29
        + 2273/2401*T^27 - 67/343*T^26 + 747/2401*T^25 + 184/343*T^24 - 
        1020/2401*T^23 + 414/2401*T^22 + 486/2401*T^21 - 1826/2401*T^20 - 
        822/2401*T^19 + 1025/2401*T^18 + 57/2401*T^17 + 274/2401*T^16 + 4/49*T^15 - 
        1268/2401*T^14 + 145/343*T^13 - 125/2401*T^12 - 2381/2401*T^11 + 
        827/2401*T^10 + 1482/2401*T^9 - 12/2401*T^8 - 885/2401*T^7 - 1048/2401*T^6 -
        31/2401*T^5 + 998/2401*T^4 - 113/343*T^3 - 45/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 
        X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + 4*X*Y^3 + X*Y^2 + 3*X*Y + X + 6*Y^30 +
        3*Y^29 + 2*Y^28 + 5*Y^26 + 6*Y^25 + 6*Y^24 + 5*Y^23 + 3*Y^22 + Y^21 + Y^19 +
        2*Y^18 + 3*Y^17 + 4*Y^16 + Y^15 + 2*Y^14 + 2*Y^13 + 5*Y^12 + 6*Y^11 + 3*Y^10
        + 4*Y^9 + Y^8 + 2*Y^7 + 2*Y^6 + 4*Y^5 + 6*Y^4 + 5*Y^3 + 6*Y^2 + 5*Y + 4,
    T^56 - 3/7*T^55 - 43/49*T^54 + 540/343*T^53 - 299/2401*T^52 - 3333/2401*T^51 + 
        3441/2401*T^50 - 838/2401*T^49 - 2242/2401*T^48 + 3879/2401*T^47 - 
        620/2401*T^46 - 3676/2401*T^45 + 3148/2401*T^44 + 1971/2401*T^43 - 
        3338/2401*T^42 - 146/2401*T^41 + 2263/2401*T^40 - 1154/2401*T^39 - 
        405/2401*T^38 + 1154/2401*T^37 - 1660/2401*T^36 + 393/2401*T^35 + 
        1885/2401*T^34 - 1039/2401*T^33 - 636/2401*T^32 + 116/2401*T^31 + 
        1471/2401*T^30 + 572/2401*T^29 - 2279/2401*T^28 + 572/2401*T^27 + 
        1471/2401*T^26 + 116/2401*T^25 - 636/2401*T^24 - 1039/2401*T^23 + 
        1885/2401*T^22 + 393/2401*T^21 - 1660/2401*T^20 + 1154/2401*T^19 - 
        405/2401*T^18 - 1154/2401*T^17 + 2263/2401*T^16 - 146/2401*T^15 - 
        3338/2401*T^14 + 1971/2401*T^13 + 3148/2401*T^12 - 3676/2401*T^11 - 
        620/2401*T^10 + 3879/2401*T^9 - 2242/2401*T^8 - 838/2401*T^7 + 3441/2401*T^6
        - 3333/2401*T^5 - 299/2401*T^4 + 540/343*T^3 - 43/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 
        X*Y^8 + X*Y^7 + 4*X*Y^6 + 4*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 2*X*Y + 3*X + Y^30 +
        Y^29 + Y^28 + 4*Y^27 + 2*Y^26 + 4*Y^25 + 4*Y^24 + Y^23 + 2*Y^22 + 4*Y^21 + 
        Y^20 + 3*Y^18 + Y^16 + 5*Y^15 + 3*Y^14 + 5*Y^13 + 2*Y^12 + Y^11 + 2*Y^10 + 
        3*Y^9 + 3*Y^8 + Y^7 + 6*Y^6 + 4*Y^5 + 4*Y^4 + 2*Y^3 + Y^2 + 2*Y,
    T^56 - 3/7*T^55 - 45/49*T^54 + 508/343*T^53 - 2161/2401*T^52 - 2538/2401*T^51 + 
        3426/2401*T^50 - 1027/2401*T^49 - 1639/2401*T^48 + 1781/2401*T^47 - 
        106/343*T^46 - 1867/2401*T^45 + 1432/2401*T^44 + 1132/2401*T^43 - 
        2160/2401*T^42 + 1466/2401*T^41 + 2029/2401*T^40 - 3618/2401*T^39 + 
        1304/2401*T^38 + 373/343*T^37 - 2990/2401*T^36 + 1516/2401*T^35 + 
        3547/2401*T^34 - 3442/2401*T^33 - 715/2401*T^32 + 2853/2401*T^31 - 
        3267/2401*T^30 - 206/343*T^29 + 3580/2401*T^28 - 206/343*T^27 - 
        3267/2401*T^26 + 2853/2401*T^25 - 715/2401*T^24 - 3442/2401*T^23 + 
        3547/2401*T^22 + 1516/2401*T^21 - 2990/2401*T^20 + 373/343*T^19 + 
        1304/2401*T^18 - 3618/2401*T^17 + 2029/2401*T^16 + 1466/2401*T^15 - 
        2160/2401*T^14 + 1132/2401*T^13 + 1432/2401*T^12 - 1867/2401*T^11 - 
        106/343*T^10 + 1781/2401*T^9 - 1639/2401*T^8 - 1027/2401*T^7 + 3426/2401*T^6
        - 2538/2401*T^5 - 2161/2401*T^4 + 508/343*T^3 - 45/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + X*Y^13 + X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + X*Y^8 + 
        2*X*Y^7 + 3*X*Y^6 + X*Y^5 + X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 6*X*Y + 3*X + Y^30 +
        2*Y^29 + 5*Y^28 + 5*Y^27 + 3*Y^26 + 5*Y^25 + 2*Y^23 + 5*Y^22 + Y^20 + 2*Y^18
        + 4*Y^17 + 5*Y^16 + Y^15 + 6*Y^14 + 5*Y^13 + 2*Y^12 + 5*Y^11 + 5*Y^10 + 
        4*Y^9 + Y^8 + 5*Y^7 + 6*Y^6 + 2*Y^5 + 3*Y^4 + 5*Y^3 + 4*Y^2 + 2,
    T^56 - 2/7*T^55 - 62/49*T^54 + 80/343*T^53 + 335/343*T^52 - 442/2401*T^51 - 
        1633/2401*T^50 + 159/343*T^49 - 103/343*T^48 + 34/2401*T^47 + 130/343*T^46 +
        15/2401*T^45 - 1994/2401*T^44 + 64/2401*T^43 + 2217/2401*T^42 - 11/49*T^41 -
        1809/2401*T^40 - 144/2401*T^39 + 2076/2401*T^38 - 831/2401*T^37 - 
        1427/2401*T^36 + 1290/2401*T^35 + 1093/2401*T^34 - 150/343*T^33 + 
        155/2401*T^32 + 139/343*T^31 - 319/343*T^30 - 348/2401*T^29 + 3334/2401*T^28
        - 348/2401*T^27 - 319/343*T^26 + 139/343*T^25 + 155/2401*T^24 - 150/343*T^23
        + 1093/2401*T^22 + 1290/2401*T^21 - 1427/2401*T^20 - 831/2401*T^19 + 
        2076/2401*T^18 - 144/2401*T^17 - 1809/2401*T^16 - 11/49*T^15 + 
        2217/2401*T^14 + 64/2401*T^13 - 1994/2401*T^12 + 15/2401*T^11 + 130/343*T^10
        + 34/2401*T^9 - 103/343*T^8 + 159/343*T^7 - 1633/2401*T^6 - 442/2401*T^5 + 
        335/343*T^4 + 80/343*T^3 - 62/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 4*X*Y^9 + 
        3*X*Y^8 + 5*X*Y^7 + 6*X*Y^3 + 4*X*Y^2 + 4*X*Y + 3*X + 4*Y^30 + 4*Y^29 + 
        3*Y^28 + 3*Y^27 + 6*Y^26 + 4*Y^25 + 2*Y^24 + 6*Y^23 + Y^22 + 6*Y^21 + 2*Y^20
        + 2*Y^19 + Y^18 + 6*Y^17 + 5*Y^16 + 6*Y^15 + Y^14 + 4*Y^13 + 4*Y^12 + 4*Y^11
        + 3*Y^10 + 6*Y^9 + Y^8 + Y^7 + 2*Y^6 + 4*Y^4 + 3*Y^3 + 6*Y^2 + 5*Y + 2,
    -T^56 - 1/7*T^55 - 27/49*T^54 - 214/343*T^53 + 1137/2401*T^52 - 10/7*T^51 + 
        320/2401*T^50 - 2103/2401*T^49 - 2788/2401*T^48 + 1525/2401*T^47 - 
        3497/2401*T^46 + 734/2401*T^45 + 179/2401*T^44 - 3210/2401*T^43 + 
        2024/2401*T^42 - 2167/2401*T^41 - 566/2401*T^40 + 53/49*T^39 - 
        2718/2401*T^38 + 2550/2401*T^37 + 317/2401*T^36 - 1237/2401*T^35 + 
        3057/2401*T^34 - 1203/2401*T^33 + 1751/2401*T^32 + 1952/2401*T^31 - 
        2124/2401*T^30 + 1361/2401*T^29 - 1361/2401*T^27 + 2124/2401*T^26 - 
        1952/2401*T^25 - 1751/2401*T^24 + 1203/2401*T^23 - 3057/2401*T^22 + 
        1237/2401*T^21 - 317/2401*T^20 - 2550/2401*T^19 + 2718/2401*T^18 - 
        53/49*T^17 + 566/2401*T^16 + 2167/2401*T^15 - 2024/2401*T^14 + 
        3210/2401*T^13 - 179/2401*T^12 - 734/2401*T^11 + 3497/2401*T^10 - 
        1525/2401*T^9 + 2788/2401*T^8 + 2103/2401*T^7 - 320/2401*T^6 + 10/7*T^5 - 
        1137/2401*T^4 + 214/343*T^3 + 27/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 5*X*Y^13 + X*Y^11 + 2*X*Y^10 + 4*X*Y^9 + X*Y^7 + 
        6*X*Y^6 + 2*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 6*X*Y + 6*X + 3*Y^30 + 4*Y^29 + Y^28
        + 4*Y^27 + Y^26 + 6*Y^25 + 5*Y^24 + 5*Y^23 + 5*Y^22 + 5*Y^21 + 2*Y^20 + 
        3*Y^19 + 4*Y^18 + 2*Y^17 + 3*Y^16 + 6*Y^14 + 6*Y^13 + 2*Y^12 + 2*Y^11 + 
        3*Y^10 + 2*Y^9 + 5*Y^8 + 3*Y^7 + 4*Y^5 + 2*Y^4 + 5*Y^3 + 2*Y^2 + Y + 6,
    T^56 - 5/7*T^55 + 8/49*T^54 - 33/49*T^53 + 1067/2401*T^52 + 708/2401*T^51 + 
        1091/2401*T^50 - 1487/2401*T^49 - 1192/2401*T^48 - 465/2401*T^47 + 
        3076/2401*T^46 - 1719/2401*T^45 + 1408/2401*T^44 - 3618/2401*T^43 + 
        1283/2401*T^42 + 1609/2401*T^41 + 204/343*T^40 - 1815/2401*T^39 - 
        1952/2401*T^38 - 1388/2401*T^37 + 3872/2401*T^36 - 379/2401*T^35 + 
        1432/2401*T^34 - 4964/2401*T^33 + 1333/2401*T^32 + 697/2401*T^31 + 
        2615/2401*T^30 - 731/2401*T^29 - 2676/2401*T^28 - 731/2401*T^27 + 
        2615/2401*T^26 + 697/2401*T^25 + 1333/2401*T^24 - 4964/2401*T^23 + 
        1432/2401*T^22 - 379/2401*T^21 + 3872/2401*T^20 - 1388/2401*T^19 - 
        1952/2401*T^18 - 1815/2401*T^17 + 204/343*T^16 + 1609/2401*T^15 + 
        1283/2401*T^14 - 3618/2401*T^13 + 1408/2401*T^12 - 1719/2401*T^11 + 
        3076/2401*T^10 - 465/2401*T^9 - 1192/2401*T^8 - 1487/2401*T^7 + 
        1091/2401*T^6 + 708/2401*T^5 + 1067/2401*T^4 - 33/49*T^3 + 8/49*T^2 - 5/7*T 
        + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + X*Y^10 + 5*X*Y^9 + 2*X*Y^7 + 
        5*X*Y^6 + 6*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 3*X*Y + Y^30 + 3*Y^29 + 3*Y^28 + 
        5*Y^27 + 2*Y^26 + 4*Y^25 + 2*Y^24 + 3*Y^23 + 2*Y^21 + 5*Y^19 + 2*Y^17 + Y^16
        + 5*Y^15 + 5*Y^14 + 6*Y^13 + 5*Y^12 + 6*Y^10 + 3*Y^9 + 5*Y^8 + 6*Y^7 + Y^5 +
        2*Y^4 + Y^3 + 2*Y^2 + 6*Y + 4,
    T^56 + 4/7*T^54 + 32/343*T^53 - 2319/2401*T^52 + 389/2401*T^51 - 909/2401*T^50 -
        344/2401*T^49 + 537/2401*T^48 + 1114/2401*T^47 - 941/2401*T^46 + 
        2526/2401*T^45 + 24/2401*T^44 - 1079/2401*T^43 + 922/2401*T^42 - 
        2358/2401*T^41 - 695/2401*T^40 + 636/2401*T^39 - 2022/2401*T^38 + 
        520/2401*T^37 + 297/2401*T^36 + 220/2401*T^35 + 1200/2401*T^34 + 
        837/2401*T^33 - 871/2401*T^32 - 565/2401*T^31 + 8/2401*T^30 - 303/343*T^29 +
        1994/2401*T^28 - 303/343*T^27 + 8/2401*T^26 - 565/2401*T^25 - 871/2401*T^24 
        + 837/2401*T^23 + 1200/2401*T^22 + 220/2401*T^21 + 297/2401*T^20 + 
        520/2401*T^19 - 2022/2401*T^18 + 636/2401*T^17 - 695/2401*T^16 - 
        2358/2401*T^15 + 922/2401*T^14 - 1079/2401*T^13 + 24/2401*T^12 + 
        2526/2401*T^11 - 941/2401*T^10 + 1114/2401*T^9 + 537/2401*T^8 - 344/2401*T^7
        - 909/2401*T^6 + 389/2401*T^5 - 2319/2401*T^4 + 32/343*T^3 + 4/7*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 3*X*Y^12 + X*Y^11 + 6*X*Y^10 + X*Y^9 + 6*X*Y^8 + 
        5*X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + X*Y^3 + 4*X*Y^2 + X*Y + 5*Y^30 + 
        Y^28 + 4*Y^27 + 4*Y^26 + 6*Y^25 + 6*Y^24 + 2*Y^23 + 6*Y^21 + Y^20 + 6*Y^19 +
        6*Y^18 + 4*Y^17 + Y^16 + 6*Y^15 + 2*Y^14 + 4*Y^12 + 6*Y^11 + 6*Y^10 + 5*Y^9 
        + 6*Y^8 + 5*Y^7 + 2*Y^6 + Y^5 + Y^2 + 2,
    T^56 + 2/7*T^55 - 20/49*T^54 - 411/343*T^53 - 4379/2401*T^52 + 678/2401*T^51 + 
        4933/2401*T^50 + 5686/2401*T^49 + 850/2401*T^48 - 5185/2401*T^47 - 
        8271/2401*T^46 - 2364/2401*T^45 + 718/343*T^44 + 8496/2401*T^43 + 
        4695/2401*T^42 - 4915/2401*T^41 - 7859/2401*T^40 - 5181/2401*T^39 + 
        3155/2401*T^38 + 8366/2401*T^37 + 4852/2401*T^36 - 3725/2401*T^35 - 
        7943/2401*T^34 - 4533/2401*T^33 + 3457/2401*T^32 + 8758/2401*T^31 + 
        4243/2401*T^30 - 3998/2401*T^29 - 8135/2401*T^28 - 3998/2401*T^27 + 
        4243/2401*T^26 + 8758/2401*T^25 + 3457/2401*T^24 - 4533/2401*T^23 - 
        7943/2401*T^22 - 3725/2401*T^21 + 4852/2401*T^20 + 8366/2401*T^19 + 
        3155/2401*T^18 - 5181/2401*T^17 - 7859/2401*T^16 - 4915/2401*T^15 + 
        4695/2401*T^14 + 8496/2401*T^13 + 718/343*T^12 - 2364/2401*T^11 - 
        8271/2401*T^10 - 5185/2401*T^9 + 850/2401*T^8 + 5686/2401*T^7 + 
        4933/2401*T^6 + 678/2401*T^5 - 4379/2401*T^4 - 411/343*T^3 - 20/49*T^2 + 
        2/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 3*X*Y^7 +
        X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 2*X*Y + 2*X + 2*Y^30 + 
        5*Y^28 + 4*Y^27 + 4*Y^26 + Y^25 + 4*Y^23 + 4*Y^22 + 3*Y^21 + 5*Y^20 + Y^19 +
        3*Y^18 + 4*Y^17 + 3*Y^15 + 5*Y^14 + 6*Y^12 + 3*Y^11 + 5*Y^10 + 4*Y^9 + 6*Y^8
        + 2*Y^7 + 2*Y^6 + 3*Y^5 + 3*Y^4 + 2*Y^3 + 4*Y + 6,
    T^56 - 5/7*T^55 - 4/7*T^54 - 41/343*T^53 + 106/2401*T^52 + 818/2401*T^51 + 
        590/2401*T^50 + 1/343*T^49 - 223/343*T^48 - 125/343*T^47 + 184/343*T^46 + 
        1782/2401*T^45 - 192/2401*T^44 - 1514/2401*T^43 - 436/2401*T^42 + 
        338/2401*T^41 + 929/2401*T^40 + 911/2401*T^39 - 76/2401*T^38 - 789/2401*T^37
        - 1376/2401*T^36 + 855/2401*T^35 + 878/2401*T^34 + 283/2401*T^33 - 
        123/343*T^32 + 164/2401*T^31 - 573/2401*T^30 - 410/2401*T^29 + 
        1410/2401*T^28 - 410/2401*T^27 - 573/2401*T^26 + 164/2401*T^25 - 
        123/343*T^24 + 283/2401*T^23 + 878/2401*T^22 + 855/2401*T^21 - 
        1376/2401*T^20 - 789/2401*T^19 - 76/2401*T^18 + 911/2401*T^17 + 
        929/2401*T^16 + 338/2401*T^15 - 436/2401*T^14 - 1514/2401*T^13 - 
        192/2401*T^12 + 1782/2401*T^11 + 184/343*T^10 - 125/343*T^9 - 223/343*T^8 + 
        1/343*T^7 + 590/2401*T^6 + 818/2401*T^5 + 106/2401*T^4 - 41/343*T^3 - 
        4/7*T^2 - 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^12 + 6*X*Y^11 + X*Y^10 + 4*X*Y^9 + 3*X*Y^7 + 4*X*Y^6 + 
        4*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 2*X*Y + 2*X + 6*Y^30 + 4*Y^29 + 5*Y^28 + 
        4*Y^26 + 4*Y^25 + Y^23 + 3*Y^22 + 2*Y^21 + 4*Y^20 + 5*Y^18 + 2*Y^17 + 3*Y^16
        + 4*Y^15 + Y^14 + Y^13 + 6*Y^11 + 4*Y^10 + 2*Y^8 + Y^7 + Y^6 + 3*Y^5 + 3*Y^4
        + 5*Y^2 + Y + 6,
    T^56 + 3/7*T^55 - 26/49*T^54 + 1/343*T^53 + 89/2401*T^52 - 239/343*T^51 - 
        1934/2401*T^50 + 1629/2401*T^49 + 2007/2401*T^48 - 828/2401*T^47 - 
        649/2401*T^46 + 1077/2401*T^45 + 6/2401*T^44 - 887/2401*T^43 + 408/2401*T^42
        + 277/343*T^41 + 50/2401*T^40 - 1306/2401*T^39 - 1191/2401*T^38 - 
        524/2401*T^37 - 17/343*T^36 - 320/2401*T^35 + 825/2401*T^34 + 1370/2401*T^33
        - 129/2401*T^32 - 915/2401*T^31 + 229/2401*T^30 - 268/2401*T^29 - 
        729/2401*T^28 - 268/2401*T^27 + 229/2401*T^26 - 915/2401*T^25 - 
        129/2401*T^24 + 1370/2401*T^23 + 825/2401*T^22 - 320/2401*T^21 - 17/343*T^20
        - 524/2401*T^19 - 1191/2401*T^18 - 1306/2401*T^17 + 50/2401*T^16 + 
        277/343*T^15 + 408/2401*T^14 - 887/2401*T^13 + 6/2401*T^12 + 1077/2401*T^11 
        - 649/2401*T^10 - 828/2401*T^9 + 2007/2401*T^8 + 1629/2401*T^7 - 
        1934/2401*T^6 - 239/343*T^5 + 89/2401*T^4 + 1/343*T^3 - 26/49*T^2 + 3/7*T + 
        1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 
        + 6*X*Y^8 + X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 6*X + 4*Y^30 + 5*Y^28 + 
        Y^27 + Y^25 + 3*Y^24 + 6*Y^23 + 6*Y^22 + 4*Y^21 + Y^20 + 2*Y^19 + 2*Y^18 + 
        4*Y^17 + 4*Y^16 + 6*Y^15 + Y^14 + 6*Y^12 + 4*Y^11 + 4*Y^9 + 4*Y^8 + Y^7 + 
        Y^6 + 5*Y^5 + 5*Y^4 + 6*Y^3 + 6*Y^2 + 4*Y + 2,
    -T^56 + 8/7*T^55 + 8/49*T^54 - 24/49*T^53 + 1129/2401*T^52 - 2764/2401*T^51 + 
        311/343*T^50 - 148/343*T^49 + 493/2401*T^48 + 750/2401*T^47 - 1454/2401*T^46
        + 2350/2401*T^45 - 411/343*T^44 + 2798/2401*T^43 - 988/2401*T^42 - 
        1930/2401*T^41 + 1718/2401*T^40 - 988/2401*T^39 + 2752/2401*T^38 - 
        1401/2401*T^37 + 488/2401*T^36 - 149/343*T^35 - 157/2401*T^34 + 
        1171/2401*T^33 - 2263/2401*T^32 + 2683/2401*T^31 - 1614/2401*T^30 + 
        1422/2401*T^29 - 1422/2401*T^27 + 1614/2401*T^26 - 2683/2401*T^25 + 
        2263/2401*T^24 - 1171/2401*T^23 + 157/2401*T^22 + 149/343*T^21 - 
        488/2401*T^20 + 1401/2401*T^19 - 2752/2401*T^18 + 988/2401*T^17 - 
        1718/2401*T^16 + 1930/2401*T^15 + 988/2401*T^14 - 2798/2401*T^13 + 
        411/343*T^12 - 2350/2401*T^11 + 1454/2401*T^10 - 750/2401*T^9 - 493/2401*T^8
        + 148/343*T^7 - 311/343*T^6 + 2764/2401*T^5 - 1129/2401*T^4 + 24/49*T^3 - 
        8/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + 4*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 + X*Y^7 + 
        4*X*Y^6 + 2*X*Y^5 + X*Y^4 + X*Y^3 + 5*X*Y^2 + 4*X + 3*Y^30 + 6*Y^27 + 4*Y^26
        + 3*Y^25 + 4*Y^24 + Y^23 + 2*Y^22 + 2*Y^21 + 4*Y^20 + Y^19 + 2*Y^18 + 5*Y^17
        + 3*Y^16 + 3*Y^14 + Y^12 + 3*Y^11 + 5*Y^10 + 5*Y^9 + 6*Y^8 + 4*Y^7 + 5*Y^6 +
        5*Y^5 + 2*Y^4 + 2*Y^3 + Y^2 + 4*Y + 1,
    -T^56 + 8/7*T^55 - 24/49*T^54 - 303/343*T^53 + 2131/2401*T^52 + 809/2401*T^51 - 
        1738/2401*T^50 + 645/2401*T^49 + 1619/2401*T^48 - 1861/2401*T^47 + 
        404/2401*T^46 + 1136/2401*T^45 - 1150/2401*T^44 - 5/2401*T^43 + 
        1690/2401*T^42 - 100/343*T^41 - 87/2401*T^40 + 256/2401*T^39 + 741/2401*T^38
        - 592/2401*T^37 - 27/343*T^36 + 1016/2401*T^35 + 429/2401*T^34 - 12/49*T^33 
        - 153/2401*T^32 + 1585/2401*T^31 - 1698/2401*T^30 + 722/2401*T^29 - 
        722/2401*T^27 + 1698/2401*T^26 - 1585/2401*T^25 + 153/2401*T^24 + 12/49*T^23
        - 429/2401*T^22 - 1016/2401*T^21 + 27/343*T^20 + 592/2401*T^19 - 
        741/2401*T^18 - 256/2401*T^17 + 87/2401*T^16 + 100/343*T^15 - 1690/2401*T^14
        + 5/2401*T^13 + 1150/2401*T^12 - 1136/2401*T^11 - 404/2401*T^10 + 
        1861/2401*T^9 - 1619/2401*T^8 - 645/2401*T^7 + 1738/2401*T^6 - 809/2401*T^5 
        - 2131/2401*T^4 + 303/343*T^3 + 24/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 5*X*Y^13 + 6*X*Y^11 + 5*X*Y^9 + 4*X*Y^7 + 6*X*Y^6 + 
        X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 5*X*Y + 4*X + 2*Y^30 + 6*Y^29 + 2*Y^28 + 4*Y^27 
        + Y^26 + 2*Y^25 + 6*Y^23 + 3*Y^22 + 6*Y^20 + 6*Y^19 + 2*Y^18 + 5*Y^16 + 
        5*Y^15 + Y^14 + 5*Y^13 + 5*Y^12 + 3*Y^11 + Y^10 + Y^6 + 2*Y^5 + 4*Y^4 + Y^3 
        + Y^2 + Y + 6,
    T^56 + 4/7*T^55 + 4/49*T^54 - 1/49*T^53 + 684/2401*T^52 - 1844/2401*T^51 - 
        285/343*T^50 + 2041/2401*T^49 + 600/2401*T^48 - 1861/2401*T^47 - 
        563/2401*T^46 + 1317/2401*T^45 - 3061/2401*T^44 - 2006/2401*T^43 + 
        3536/2401*T^42 + 1539/2401*T^41 - 2434/2401*T^40 + 283/2401*T^39 + 
        1795/2401*T^38 - 3250/2401*T^37 - 2476/2401*T^36 + 510/343*T^35 + 
        618/2401*T^34 - 407/343*T^33 + 1613/2401*T^32 + 2074/2401*T^31 - 
        337/343*T^30 - 466/2401*T^29 + 4748/2401*T^28 - 466/2401*T^27 - 337/343*T^26
        + 2074/2401*T^25 + 1613/2401*T^24 - 407/343*T^23 + 618/2401*T^22 + 
        510/343*T^21 - 2476/2401*T^20 - 3250/2401*T^19 + 1795/2401*T^18 + 
        283/2401*T^17 - 2434/2401*T^16 + 1539/2401*T^15 + 3536/2401*T^14 - 
        2006/2401*T^13 - 3061/2401*T^12 + 1317/2401*T^11 - 563/2401*T^10 - 
        1861/2401*T^9 + 600/2401*T^8 + 2041/2401*T^7 - 285/343*T^6 - 1844/2401*T^5 +
        684/2401*T^4 - 1/49*T^3 + 4/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + X*Y^11 + 5*X*Y^8 + 3*X*Y^7 + 
        5*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 3*X*Y + 6*X + Y^30 + 
        3*Y^29 + 6*Y^28 + 3*Y^27 + 5*Y^26 + 5*Y^23 + 4*Y^22 + 6*Y^21 + 5*Y^20 + 
        4*Y^19 + 6*Y^18 + 3*Y^17 + Y^16 + Y^15 + 2*Y^14 + 2*Y^13 + 2*Y^12 + 5*Y^11 +
        2*Y^10 + 6*Y^9 + 4*Y^8 + 4*Y^7 + 2*Y^6 + 4*Y^5 + Y^4 + Y^3 + 3*Y^2 + Y + 2,
    T^56 - 2/7*T^55 - 1/49*T^54 + 55/343*T^53 - 1686/2401*T^52 + 309/2401*T^51 - 
        3201/2401*T^50 + 1013/2401*T^49 - 545/2401*T^48 + 856/2401*T^47 + 
        1780/2401*T^46 - 374/2401*T^45 + 3837/2401*T^44 - 1180/2401*T^43 + 
        606/2401*T^42 - 1430/2401*T^41 - 820/2401*T^40 - 971/2401*T^39 - 
        1794/2401*T^38 + 876/2401*T^37 - 1119/2401*T^36 + 2151/2401*T^35 - 
        529/2401*T^34 + 1079/2401*T^33 + 732/2401*T^32 - 27/343*T^31 + 19/343*T^30 -
        1599/2401*T^29 + 1184/2401*T^28 - 1599/2401*T^27 + 19/343*T^26 - 27/343*T^25
        + 732/2401*T^24 + 1079/2401*T^23 - 529/2401*T^22 + 2151/2401*T^21 - 
        1119/2401*T^20 + 876/2401*T^19 - 1794/2401*T^18 - 971/2401*T^17 - 
        820/2401*T^16 - 1430/2401*T^15 + 606/2401*T^14 - 1180/2401*T^13 + 
        3837/2401*T^12 - 374/2401*T^11 + 1780/2401*T^10 + 856/2401*T^9 - 
        545/2401*T^8 + 1013/2401*T^7 - 3201/2401*T^6 + 309/2401*T^5 - 1686/2401*T^4 
        + 55/343*T^3 - 1/49*T^2 - 2/7*T + 1
*], [*
    X^3 + X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + X*Y^9 + 4*X*Y^8 + 
        4*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 5*X*Y + X + 
        3*Y^30 + 2*Y^29 + Y^28 + 5*Y^27 + 4*Y^26 + 2*Y^24 + 3*Y^23 + 5*Y^22 + Y^21 +
        3*Y^20 + 3*Y^19 + 5*Y^18 + 3*Y^17 + 6*Y^16 + Y^15 + 5*Y^14 + 4*Y^13 + 3*Y^12
        + 5*Y^10 + 2*Y^9 + 4*Y^7 + 5*Y^6 + Y^5 + 6*Y^4 + 3*Y^3 + 3*Y^2 + Y,
    -T^56 + 3/7*T^55 - 6/49*T^54 + 354/343*T^53 - 139/343*T^52 + 235/2401*T^51 - 
        1331/2401*T^50 - 75/343*T^49 + 446/2401*T^48 - 46/2401*T^47 + 506/2401*T^46 
        + 298/2401*T^45 + 1039/2401*T^44 - 291/2401*T^43 - 1353/2401*T^42 - 
        10/343*T^41 - 479/2401*T^40 + 909/2401*T^39 + 610/2401*T^38 + 1269/2401*T^37
        + 65/2401*T^36 - 1485/2401*T^35 + 20/343*T^34 - 1465/2401*T^33 + 
        1301/2401*T^32 + 421/2401*T^31 + 1389/2401*T^30 - 548/2401*T^29 + 
        548/2401*T^27 - 1389/2401*T^26 - 421/2401*T^25 - 1301/2401*T^24 + 
        1465/2401*T^23 - 20/343*T^22 + 1485/2401*T^21 - 65/2401*T^20 - 
        1269/2401*T^19 - 610/2401*T^18 - 909/2401*T^17 + 479/2401*T^16 + 10/343*T^15
        + 1353/2401*T^14 + 291/2401*T^13 - 1039/2401*T^12 - 298/2401*T^11 - 
        506/2401*T^10 + 46/2401*T^9 - 446/2401*T^8 + 75/343*T^7 + 1331/2401*T^6 - 
        235/2401*T^5 + 139/343*T^4 - 354/343*T^3 + 6/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + X*Y^13 + X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 
        4*X*Y^8 + X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + X*Y + 
        4*X + 5*Y^30 + Y^29 + Y^28 + 3*Y^27 + 5*Y^26 + 5*Y^25 + 4*Y^24 + 3*Y^22 + 
        Y^21 + 5*Y^20 + 3*Y^19 + 6*Y^18 + 5*Y^17 + 5*Y^16 + Y^15 + 2*Y^13 + 4*Y^12 +
        4*Y^11 + 3*Y^10 + 5*Y^8 + 2*Y^7 + 5*Y^5 + 3*Y^4 + Y^3 + 3*Y^2 + 2*Y + 3,
    T^56 - T^55 + 10/49*T^54 + 297/343*T^53 - 1597/2401*T^52 - 1560/2401*T^51 + 
        2956/2401*T^50 - 1681/2401*T^49 - 999/2401*T^48 + 2382/2401*T^47 - 
        95/343*T^46 - 1644/2401*T^45 + 263/343*T^44 - 23/343*T^43 - 216/343*T^42 + 
        1441/2401*T^41 - 162/343*T^40 + 38/343*T^39 + 606/2401*T^38 - 1217/2401*T^37
        + 604/2401*T^36 + 3/7*T^35 - 2729/2401*T^34 + 1819/2401*T^33 + 781/2401*T^32
        - 2535/2401*T^31 + 1592/2401*T^30 + 1607/2401*T^29 - 2822/2401*T^28 + 
        1607/2401*T^27 + 1592/2401*T^26 - 2535/2401*T^25 + 781/2401*T^24 + 
        1819/2401*T^23 - 2729/2401*T^22 + 3/7*T^21 + 604/2401*T^20 - 1217/2401*T^19 
        + 606/2401*T^18 + 38/343*T^17 - 162/343*T^16 + 1441/2401*T^15 - 216/343*T^14
        - 23/343*T^13 + 263/343*T^12 - 1644/2401*T^11 - 95/343*T^10 + 2382/2401*T^9 
        - 999/2401*T^8 - 1681/2401*T^7 + 2956/2401*T^6 - 1560/2401*T^5 - 
        1597/2401*T^4 + 297/343*T^3 + 10/49*T^2 - T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 3*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 3*X*Y^7 +
        4*X*Y^6 + 2*X*Y^5 + X*Y^4 + X*Y^3 + 4*X*Y^2 + 6*X*Y + 5*X + 3*Y^30 + 2*Y^29 
        + 2*Y^28 + 6*Y^27 + 2*Y^26 + 2*Y^25 + 4*Y^23 + 5*Y^21 + 4*Y^20 + 4*Y^19 + 
        2*Y^18 + 5*Y^17 + Y^15 + 6*Y^14 + 3*Y^13 + 2*Y^12 + 3*Y^10 + 3*Y^9 + Y^7 + 
        6*Y^6 + 6*Y^5 + 3*Y^4 + 2*Y^2 + 4,
    T^56 - 9/7*T^55 + 13/49*T^54 + 227/343*T^53 - 2123/2401*T^52 - 139/2401*T^51 + 
        1052/2401*T^50 + 540/2401*T^49 - 1720/2401*T^48 + 318/343*T^47 - 
        440/2401*T^46 - 1609/2401*T^45 + 1914/2401*T^44 - 1261/2401*T^43 - 
        9/343*T^42 + 1755/2401*T^41 - 1299/2401*T^40 + 818/2401*T^39 - 393/2401*T^38
        + 4/2401*T^37 - 13/49*T^36 + 422/2401*T^35 - 34/2401*T^34 - 47/2401*T^33 + 
        1416/2401*T^32 - 1153/2401*T^31 + 716/2401*T^30 + 428/2401*T^29 - 
        1801/2401*T^28 + 428/2401*T^27 + 716/2401*T^26 - 1153/2401*T^25 + 
        1416/2401*T^24 - 47/2401*T^23 - 34/2401*T^22 + 422/2401*T^21 - 13/49*T^20 + 
        4/2401*T^19 - 393/2401*T^18 + 818/2401*T^17 - 1299/2401*T^16 + 
        1755/2401*T^15 - 9/343*T^14 - 1261/2401*T^13 + 1914/2401*T^12 - 
        1609/2401*T^11 - 440/2401*T^10 + 318/343*T^9 - 1720/2401*T^8 + 540/2401*T^7 
        + 1052/2401*T^6 - 139/2401*T^5 - 2123/2401*T^4 + 227/343*T^3 + 13/49*T^2 - 
        9/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 4*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 + 
        4*X*Y^7 + 6*X*Y^6 + X*Y^5 + X*Y^4 + X*Y^3 + 4*X*Y + 4*Y^30 + Y^28 + 4*Y^26 +
        Y^25 + 2*Y^24 + 5*Y^23 + 5*Y^22 + Y^21 + 2*Y^20 + Y^18 + 6*Y^17 + 3*Y^14 + 
        4*Y^13 + 5*Y^12 + 6*Y^11 + 4*Y^10 + 5*Y^9 + Y^8 + 2*Y^6 + 5*Y^5 + 3*Y^4 + 
        2*Y^2 + 2*Y + 6,
    T^56 - 2/7*T^55 - 9/49*T^54 + 1/7*T^53 - 1443/2401*T^52 + 150/343*T^51 - 
        410/2401*T^50 - 900/2401*T^49 + 1551/2401*T^48 - 1767/2401*T^47 + 
        250/2401*T^46 + 1390/2401*T^45 - 3041/2401*T^44 + 1143/2401*T^43 - 
        872/2401*T^42 - 643/2401*T^41 + 566/343*T^40 - 1901/2401*T^39 + 67/343*T^38 
        + 171/343*T^37 - 3067/2401*T^36 + 2441/2401*T^35 - 111/2401*T^34 - 
        1523/2401*T^33 + 3054/2401*T^32 - 1952/2401*T^31 + 96/2401*T^30 + 
        1808/2401*T^29 - 4171/2401*T^28 + 1808/2401*T^27 + 96/2401*T^26 - 
        1952/2401*T^25 + 3054/2401*T^24 - 1523/2401*T^23 - 111/2401*T^22 + 
        2441/2401*T^21 - 3067/2401*T^20 + 171/343*T^19 + 67/343*T^18 - 
        1901/2401*T^17 + 566/343*T^16 - 643/2401*T^15 - 872/2401*T^14 + 
        1143/2401*T^13 - 3041/2401*T^12 + 1390/2401*T^11 + 250/2401*T^10 - 
        1767/2401*T^9 + 1551/2401*T^8 - 900/2401*T^7 - 410/2401*T^6 + 150/343*T^5 - 
        1443/2401*T^4 + 1/7*T^3 - 9/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 
        + 4*X*Y^8 + X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + X*Y^3 + 6*X*Y^2 + 5*X*Y + 
        6*Y^30 + 2*Y^29 + 3*Y^28 + 3*Y^27 + 3*Y^26 + 5*Y^25 + 4*Y^24 + 3*Y^23 + 
        6*Y^21 + 4*Y^20 + 5*Y^19 + 3*Y^18 + 6*Y^17 + 6*Y^16 + 2*Y^15 + 5*Y^13 + 
        3*Y^12 + 6*Y^11 + 5*Y^10 + 6*Y^9 + 2*Y^8 + 3*Y^7 + Y^6 + 5*Y^5 + 3*Y^3 + 
        4*Y^2 + 5*Y + 2,
    -T^56 - 2/7*T^55 - 1/49*T^54 - 22/343*T^53 + 571/343*T^52 + 1088/2401*T^51 + 
        54/343*T^50 + 135/343*T^49 - 3953/2401*T^48 - 3295/2401*T^47 - 
        2004/2401*T^46 - 1796/2401*T^45 + 3707/2401*T^44 + 3926/2401*T^43 + 
        1996/2401*T^42 + 1861/2401*T^41 - 339/343*T^40 - 2278/2401*T^39 - 
        200/343*T^38 - 2970/2401*T^37 + 824/2401*T^36 + 2098/2401*T^35 + 
        137/343*T^34 + 376/343*T^33 - 118/343*T^32 - 2133/2401*T^31 + 129/343*T^30 -
        201/343*T^29 + 201/343*T^27 - 129/343*T^26 + 2133/2401*T^25 + 118/343*T^24 -
        376/343*T^23 - 137/343*T^22 - 2098/2401*T^21 - 824/2401*T^20 + 
        2970/2401*T^19 + 200/343*T^18 + 2278/2401*T^17 + 339/343*T^16 - 
        1861/2401*T^15 - 1996/2401*T^14 - 3926/2401*T^13 - 3707/2401*T^12 + 
        1796/2401*T^11 + 2004/2401*T^10 + 3295/2401*T^9 + 3953/2401*T^8 - 
        135/343*T^7 - 54/343*T^6 - 1088/2401*T^5 - 571/343*T^4 + 22/343*T^3 + 
        1/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 
        + 2*X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + X*Y^4 + 5*X*Y^2 + 2*X*Y + 5*X + 6*Y^30 + 
        3*Y^29 + 3*Y^28 + 6*Y^26 + 3*Y^25 + 6*Y^24 + 2*Y^23 + Y^22 + Y^21 + 3*Y^20 +
        2*Y^19 + 2*Y^18 + 3*Y^17 + 2*Y^15 + 2*Y^14 + 6*Y^12 + 5*Y^11 + 3*Y^10 + 
        5*Y^9 + 5*Y^7 + 2*Y^6 + 2*Y^4 + 6*Y^3 + Y^2 + 3,
    T^56 + 1/7*T^55 - 22/49*T^54 - 145/343*T^53 - 1371/2401*T^52 - 1264/2401*T^51 - 
        1075/2401*T^50 + 82/343*T^49 + 876/2401*T^48 + 1073/2401*T^47 + 
        1769/2401*T^46 + 2341/2401*T^45 - 96/2401*T^44 - 502/2401*T^43 - 
        570/2401*T^42 - 1894/2401*T^41 - 2255/2401*T^40 - 1593/2401*T^39 - 
        926/2401*T^38 + 107/2401*T^37 + 2101/2401*T^36 + 2574/2401*T^35 + 
        1436/2401*T^34 + 1203/2401*T^33 + 508/2401*T^32 + 72/2401*T^31 - 
        1356/2401*T^30 - 2019/2401*T^29 - 664/2401*T^28 - 2019/2401*T^27 - 
        1356/2401*T^26 + 72/2401*T^25 + 508/2401*T^24 + 1203/2401*T^23 + 
        1436/2401*T^22 + 2574/2401*T^21 + 2101/2401*T^20 + 107/2401*T^19 - 
        926/2401*T^18 - 1593/2401*T^17 - 2255/2401*T^16 - 1894/2401*T^15 - 
        570/2401*T^14 - 502/2401*T^13 - 96/2401*T^12 + 2341/2401*T^11 + 
        1769/2401*T^10 + 1073/2401*T^9 + 876/2401*T^8 + 82/343*T^7 - 1075/2401*T^6 -
        1264/2401*T^5 - 1371/2401*T^4 - 145/343*T^3 - 22/49*T^2 + 1/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        6*X*Y^8 + X*Y^7 + 6*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 2*X*Y + 5*X + 
        4*Y^30 + Y^29 + 3*Y^28 + 4*Y^27 + 5*Y^26 + 4*Y^24 + 5*Y^23 + 2*Y^22 + 6*Y^21
        + Y^20 + 6*Y^18 + 4*Y^17 + 2*Y^15 + 4*Y^13 + 2*Y^12 + 5*Y^11 + 2*Y^10 + 
        6*Y^9 + Y^8 + 4*Y^6 + 4*Y^5 + 3*Y^3 + 6*Y^2 + 4*Y + 4,
    T^56 + 1/7*T^55 - 18/49*T^54 + 213/343*T^53 + 888/2401*T^52 - 1256/2401*T^51 - 
        1959/2401*T^50 + 1483/2401*T^49 - 15/343*T^48 - 1669/2401*T^47 - 
        18/2401*T^46 + 624/2401*T^45 + 450/2401*T^44 - 97/343*T^43 + 99/343*T^42 + 
        46/343*T^41 + 75/2401*T^40 + 38/2401*T^39 - 176/2401*T^38 - 612/2401*T^37 - 
        1404/2401*T^36 + 1083/2401*T^35 - 1369/2401*T^34 - 249/343*T^33 + 
        741/2401*T^32 + 1236/2401*T^31 - 855/2401*T^30 - 181/2401*T^29 + 
        4289/2401*T^28 - 181/2401*T^27 - 855/2401*T^26 + 1236/2401*T^25 + 
        741/2401*T^24 - 249/343*T^23 - 1369/2401*T^22 + 1083/2401*T^21 - 
        1404/2401*T^20 - 612/2401*T^19 - 176/2401*T^18 + 38/2401*T^17 + 75/2401*T^16
        + 46/343*T^15 + 99/343*T^14 - 97/343*T^13 + 450/2401*T^12 + 624/2401*T^11 - 
        18/2401*T^10 - 1669/2401*T^9 - 15/343*T^8 + 1483/2401*T^7 - 1959/2401*T^6 - 
        1256/2401*T^5 + 888/2401*T^4 + 213/343*T^3 - 18/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + X*Y^8 + 
        X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + 5*X + 5*Y^30 + 
        2*Y^29 + 3*Y^28 + 6*Y^27 + 4*Y^25 + Y^22 + 3*Y^21 + 2*Y^20 + 3*Y^19 + 6*Y^18
        + 3*Y^17 + 4*Y^16 + 3*Y^15 + Y^14 + 5*Y^13 + Y^12 + 3*Y^11 + 4*Y^10 + 2*Y^9 
        + Y^8 + 5*Y^7 + 6*Y^6 + 4*Y^3 + Y^2 + 4*Y + 3,
    T^56 - 11/7*T^55 - 1/49*T^54 + 608/343*T^53 - 5189/2401*T^52 + 2288/2401*T^51 + 
        244/343*T^50 - 2616/2401*T^49 - 225/2401*T^48 + 569/2401*T^47 + 429/343*T^46
        - 3371/2401*T^45 + 61/343*T^44 + 2588/2401*T^43 - 3308/2401*T^42 + 
        978/2401*T^41 + 664/2401*T^40 - 20/343*T^39 + 10/343*T^38 - 2582/2401*T^37 +
        3771/2401*T^36 - 955/2401*T^35 - 3239/2401*T^34 + 6178/2401*T^33 - 
        2816/2401*T^32 - 2778/2401*T^31 + 3363/2401*T^30 - 733/2401*T^29 - 
        944/2401*T^28 - 733/2401*T^27 + 3363/2401*T^26 - 2778/2401*T^25 - 
        2816/2401*T^24 + 6178/2401*T^23 - 3239/2401*T^22 - 955/2401*T^21 + 
        3771/2401*T^20 - 2582/2401*T^19 + 10/343*T^18 - 20/343*T^17 + 664/2401*T^16 
        + 978/2401*T^15 - 3308/2401*T^14 + 2588/2401*T^13 + 61/343*T^12 - 
        3371/2401*T^11 + 429/343*T^10 + 569/2401*T^9 - 225/2401*T^8 - 2616/2401*T^7 
        + 244/343*T^6 + 2288/2401*T^5 - 5189/2401*T^4 + 608/343*T^3 - 1/49*T^2 - 
        11/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 4*X*Y^9 + 3*X*Y^8 +
        X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 3*X + 3*Y^30 + 
        Y^29 + Y^27 + 2*Y^26 + 4*Y^25 + 4*Y^24 + 3*Y^23 + 6*Y^22 + Y^19 + Y^17 + 
        4*Y^16 + 2*Y^15 + 6*Y^14 + 5*Y^13 + 3*Y^12 + 2*Y^11 + 2*Y^10 + Y^9 + 6*Y^8 +
        2*Y^7 + 6*Y^6 + Y^5 + 5*Y^3 + 4*Y,
    -T^56 - 3/7*T^55 + 65/49*T^54 + 50/49*T^53 - 1606/2401*T^52 - 3170/2401*T^51 - 
        1476/2401*T^50 + 2867/2401*T^49 + 3393/2401*T^48 + 377/2401*T^47 - 
        346/343*T^46 - 2391/2401*T^45 + 745/2401*T^44 + 3672/2401*T^43 + 
        1286/2401*T^42 - 3320/2401*T^41 - 3216/2401*T^40 + 17/343*T^39 + 
        2628/2401*T^38 + 3315/2401*T^37 - 339/2401*T^36 - 4397/2401*T^35 - 
        2728/2401*T^34 + 1570/2401*T^33 + 593/343*T^32 + 1531/2401*T^31 - 
        408/343*T^30 - 2916/2401*T^29 + 2916/2401*T^27 + 408/343*T^26 - 
        1531/2401*T^25 - 593/343*T^24 - 1570/2401*T^23 + 2728/2401*T^22 + 
        4397/2401*T^21 + 339/2401*T^20 - 3315/2401*T^19 - 2628/2401*T^18 - 
        17/343*T^17 + 3216/2401*T^16 + 3320/2401*T^15 - 1286/2401*T^14 - 
        3672/2401*T^13 - 745/2401*T^12 + 2391/2401*T^11 + 346/343*T^10 - 
        377/2401*T^9 - 3393/2401*T^8 - 2867/2401*T^7 + 1476/2401*T^6 + 3170/2401*T^5
        + 1606/2401*T^4 - 50/49*T^3 - 65/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        2*X*Y^8 + 3*X*Y^7 + X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + X*Y + 
        2*X + 6*Y^30 + 5*Y^29 + Y^28 + 2*Y^27 + 6*Y^26 + 4*Y^25 + 5*Y^24 + 6*Y^23 + 
        4*Y^22 + 5*Y^21 + 3*Y^20 + Y^19 + 3*Y^18 + 3*Y^17 + Y^16 + 6*Y^15 + 4*Y^14 +
        Y^13 + 3*Y^12 + 5*Y^11 + 2*Y^10 + 5*Y^9 + 2*Y^7 + 5*Y^6 + 5*Y^5 + 3*Y^4 + 
        6*Y^3 + 3*Y + 3,
    -T^56 - 8/7*T^55 + 20/49*T^54 + 319/343*T^53 + 708/2401*T^52 + 13/343*T^51 + 
        335/2401*T^50 - 47/343*T^49 + 145/343*T^48 + 1434/2401*T^47 - 1283/2401*T^46
        - 2235/2401*T^45 + 883/2401*T^44 + 291/343*T^43 - 6/49*T^42 - 199/2401*T^41 
        + 31/343*T^40 + 69/2401*T^39 + 691/2401*T^38 + 59/2401*T^37 - 3005/2401*T^36
        - 2119/2401*T^35 + 1796/2401*T^34 + 1117/2401*T^33 + 50/2401*T^32 + 
        1371/2401*T^31 + 919/2401*T^30 - 856/2401*T^29 + 856/2401*T^27 - 
        919/2401*T^26 - 1371/2401*T^25 - 50/2401*T^24 - 1117/2401*T^23 - 
        1796/2401*T^22 + 2119/2401*T^21 + 3005/2401*T^20 - 59/2401*T^19 - 
        691/2401*T^18 - 69/2401*T^17 - 31/343*T^16 + 199/2401*T^15 + 6/49*T^14 - 
        291/343*T^13 - 883/2401*T^12 + 2235/2401*T^11 + 1283/2401*T^10 - 
        1434/2401*T^9 - 145/343*T^8 + 47/343*T^7 - 335/2401*T^6 - 13/343*T^5 - 
        708/2401*T^4 - 319/343*T^3 - 20/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 
        X*Y^8 + 3*X*Y^7 + 5*X*Y^5 + 4*X*Y^3 + X*Y + 4*X + 4*Y^30 + Y^29 + 4*Y^28 + 
        6*Y^27 + Y^26 + 6*Y^24 + 2*Y^23 + 3*Y^22 + 5*Y^21 + 2*Y^20 + 6*Y^19 + Y^16 +
        2*Y^15 + 2*Y^12 + 4*Y^11 + Y^10 + Y^9 + 6*Y^8 + 5*Y^7 + 6*Y^6 + 2*Y^4 + 
        5*Y^3 + 3*Y + 3,
    T^56 - 68/49*T^54 - 594/343*T^53 + 2440/2401*T^52 + 7065/2401*T^51 + 47/49*T^50 
        - 704/343*T^49 - 5832/2401*T^48 + 9/2401*T^47 + 3384/2401*T^46 + 
        2714/2401*T^45 + 500/2401*T^44 + 31/2401*T^43 - 2046/2401*T^42 - 
        1635/2401*T^41 - 788/2401*T^40 + 2977/2401*T^39 + 123/343*T^38 - 
        2663/2401*T^37 - 2385/2401*T^36 + 2977/2401*T^35 + 4989/2401*T^34 - 
        1352/2401*T^33 - 5251/2401*T^32 - 2377/2401*T^31 + 3209/2401*T^30 + 
        1142/2401*T^29 - 461/2401*T^28 + 1142/2401*T^27 + 3209/2401*T^26 - 
        2377/2401*T^25 - 5251/2401*T^24 - 1352/2401*T^23 + 4989/2401*T^22 + 
        2977/2401*T^21 - 2385/2401*T^20 - 2663/2401*T^19 + 123/343*T^18 + 
        2977/2401*T^17 - 788/2401*T^16 - 1635/2401*T^15 - 2046/2401*T^14 + 
        31/2401*T^13 + 500/2401*T^12 + 2714/2401*T^11 + 3384/2401*T^10 + 9/2401*T^9 
        - 5832/2401*T^8 - 704/343*T^7 + 47/49*T^6 + 7065/2401*T^5 + 2440/2401*T^4 - 
        594/343*T^3 - 68/49*T^2 + 1
*], [*
    X^3 + 2*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + X*Y^11 + 5*X*Y^10 + X*Y^9 + X*Y^8 + 
        3*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 3*X*Y + 2*X + 5*Y^30 + 
        3*Y^29 + 2*Y^28 + 6*Y^27 + 2*Y^26 + 4*Y^25 + 4*Y^24 + 5*Y^23 + 4*Y^22 + 
        2*Y^21 + 6*Y^20 + 3*Y^19 + 5*Y^18 + 5*Y^17 + 5*Y^16 + 4*Y^15 + 6*Y^13 + 
        5*Y^11 + 2*Y^10 + 4*Y^9 + 6*Y^8 + 5*Y^6 + Y^5 + 3*Y^3 + 6*Y,
    -T^56 - 2*T^55 - 11/49*T^54 + 823/343*T^53 + 3609/2401*T^52 - 3006/2401*T^51 - 
        2579/2401*T^50 + 2539/2401*T^49 + 2556/2401*T^48 - 1392/2401*T^47 - 
        1949/2401*T^46 + 1077/2401*T^45 + 3645/2401*T^44 + 2267/2401*T^43 - 
        3152/2401*T^42 - 849/343*T^41 - 1383/2401*T^40 + 4160/2401*T^39 + 
        2581/2401*T^38 - 2668/2401*T^37 - 3041/2401*T^36 + 716/2401*T^35 + 
        2199/2401*T^34 + 255/2401*T^33 - 1823/2401*T^32 - 965/2401*T^31 + 
        2405/2401*T^30 + 3587/2401*T^29 - 3587/2401*T^27 - 2405/2401*T^26 + 
        965/2401*T^25 + 1823/2401*T^24 - 255/2401*T^23 - 2199/2401*T^22 - 
        716/2401*T^21 + 3041/2401*T^20 + 2668/2401*T^19 - 2581/2401*T^18 - 
        4160/2401*T^17 + 1383/2401*T^16 + 849/343*T^15 + 3152/2401*T^14 - 
        2267/2401*T^13 - 3645/2401*T^12 - 1077/2401*T^11 + 1949/2401*T^10 + 
        1392/2401*T^9 - 2556/2401*T^8 - 2539/2401*T^7 + 2579/2401*T^6 + 
        3006/2401*T^5 - 3609/2401*T^4 - 823/343*T^3 + 11/49*T^2 + 2*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 5*X*Y^8 +
        2*X*Y^7 + X*Y^6 + 5*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 5*X*Y + X + 5*Y^30 + 2*Y^29 
        + Y^28 + 4*Y^27 + 4*Y^26 + 6*Y^25 + 6*Y^24 + 2*Y^23 + 6*Y^22 + 6*Y^21 + 
        6*Y^20 + 6*Y^18 + 5*Y^15 + 3*Y^13 + 2*Y^12 + 4*Y^11 + 3*Y^10 + 4*Y^9 + 4*Y^8
        + Y^7 + Y^6 + Y^3 + 4*Y^2,
    T^56 + 4/7*T^55 - 38/49*T^54 - 55/343*T^53 + 50/49*T^52 + 783/2401*T^51 - 
        1944/2401*T^50 - 74/343*T^49 + 1719/2401*T^48 + 629/2401*T^47 - 
        2236/2401*T^46 - 311/343*T^45 + 1080/2401*T^44 + 1202/2401*T^43 - 
        1515/2401*T^42 - 1389/2401*T^41 + 302/2401*T^40 + 886/2401*T^39 + 
        22/343*T^38 - 620/2401*T^37 - 222/2401*T^36 + 1122/2401*T^35 + 913/2401*T^34
        - 912/2401*T^33 - 1187/2401*T^32 + 653/2401*T^31 + 578/2401*T^30 - 
        514/2401*T^29 - 106/343*T^28 - 514/2401*T^27 + 578/2401*T^26 + 653/2401*T^25
        - 1187/2401*T^24 - 912/2401*T^23 + 913/2401*T^22 + 1122/2401*T^21 - 
        222/2401*T^20 - 620/2401*T^19 + 22/343*T^18 + 886/2401*T^17 + 302/2401*T^16 
        - 1389/2401*T^15 - 1515/2401*T^14 + 1202/2401*T^13 + 1080/2401*T^12 - 
        311/343*T^11 - 2236/2401*T^10 + 629/2401*T^9 + 1719/2401*T^8 - 74/343*T^7 - 
        1944/2401*T^6 + 783/2401*T^5 + 50/49*T^4 - 55/343*T^3 - 38/49*T^2 + 4/7*T + 
        1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^13 + 6*X*Y^12 + X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 2*X*Y^8 + 
        2*X*Y^7 + 3*X*Y^6 + X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 5*X + 5*Y^30 + 
        Y^29 + 5*Y^28 + 4*Y^27 + 2*Y^26 + 2*Y^25 + 4*Y^24 + 2*Y^23 + 4*Y^22 + Y^20 +
        4*Y^19 + 5*Y^18 + 2*Y^17 + 2*Y^15 + 5*Y^14 + 5*Y^12 + 2*Y^11 + 6*Y^10 + 
        6*Y^8 + 5*Y^7 + 4*Y^5 + 2*Y^3 + 3*Y^2 + 4*Y + 3,
    -T^56 + 11/49*T^54 - 128/343*T^53 + 16/2401*T^52 + 1354/2401*T^51 - 
        1634/2401*T^50 + 160/2401*T^49 + 1111/2401*T^48 - 85/343*T^47 - 24/343*T^46 
        - 335/2401*T^45 - 106/2401*T^44 + 583/2401*T^43 - 54/343*T^42 - 
        549/2401*T^41 + 683/2401*T^40 - 1892/2401*T^39 + 381/2401*T^38 + 71/343*T^37
        - 1159/2401*T^36 - 251/2401*T^35 + 627/2401*T^34 - 1061/2401*T^33 + 
        104/343*T^32 + 225/2401*T^31 - 157/343*T^30 + 116/343*T^29 - 116/343*T^27 + 
        157/343*T^26 - 225/2401*T^25 - 104/343*T^24 + 1061/2401*T^23 - 627/2401*T^22
        + 251/2401*T^21 + 1159/2401*T^20 - 71/343*T^19 - 381/2401*T^18 + 
        1892/2401*T^17 - 683/2401*T^16 + 549/2401*T^15 + 54/343*T^14 - 583/2401*T^13
        + 106/2401*T^12 + 335/2401*T^11 + 24/343*T^10 + 85/343*T^9 - 1111/2401*T^8 -
        160/2401*T^7 + 1634/2401*T^6 - 1354/2401*T^5 - 16/2401*T^4 + 128/343*T^3 - 
        11/49*T^2 + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 6*X*Y^13 + X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        2*X*Y^8 + X*Y^7 + X*Y^6 + 3*X*Y^5 + X*Y^4 + 5*X*Y^3 + 6*X*Y + 4*Y^30 + 
        4*Y^29 + 6*Y^28 + 6*Y^27 + Y^25 + 6*Y^24 + 5*Y^23 + 4*Y^21 + 6*Y^19 + 6*Y^18
        + 5*Y^16 + 3*Y^13 + 5*Y^12 + 5*Y^11 + 2*Y^10 + Y^9 + 4*Y^8 + 6*Y^7 + 4*Y^6 +
        5*Y^5 + 2*Y^4 + 4*Y + 2,
    T^56 + T^55 - 4/7*T^54 - 214/343*T^53 - 1031/2401*T^52 - 1549/2401*T^51 + 
        1038/2401*T^50 - 58/2401*T^49 - 2013/2401*T^48 + 236/2401*T^47 - 
        895/2401*T^46 - 1847/2401*T^45 + 1818/2401*T^44 + 1480/2401*T^43 - 
        215/2401*T^42 + 173/343*T^41 + 40/343*T^40 - 40/2401*T^39 + 1751/2401*T^38 +
        104/2401*T^37 - 929/2401*T^36 + 1289/2401*T^35 + 958/2401*T^34 - 
        333/2401*T^33 - 739/2401*T^32 - 173/343*T^31 - 566/2401*T^30 + 55/2401*T^29 
        - 491/2401*T^28 + 55/2401*T^27 - 566/2401*T^26 - 173/343*T^25 - 
        739/2401*T^24 - 333/2401*T^23 + 958/2401*T^22 + 1289/2401*T^21 - 
        929/2401*T^20 + 104/2401*T^19 + 1751/2401*T^18 - 40/2401*T^17 + 40/343*T^16 
        + 173/343*T^15 - 215/2401*T^14 + 1480/2401*T^13 + 1818/2401*T^12 - 
        1847/2401*T^11 - 895/2401*T^10 + 236/2401*T^9 - 2013/2401*T^8 - 58/2401*T^7 
        + 1038/2401*T^6 - 1549/2401*T^5 - 1031/2401*T^4 - 214/343*T^3 - 4/7*T^2 + T 
        + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 
        2*X*Y^7 + 5*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 6*X*Y + 5*Y^30 + 5*Y^28 + 
        Y^27 + 2*Y^26 + 6*Y^25 + Y^24 + 2*Y^23 + 6*Y^22 + 2*Y^21 + 4*Y^20 + 2*Y^18 +
        6*Y^17 + Y^15 + Y^14 + 3*Y^12 + 4*Y^11 + Y^8 + 5*Y^6 + 6*Y^5 + 4*Y^4 + 4*Y^3
        + 6*Y^2 + 4*Y + 6,
    -T^56 - 2/7*T^55 + 30/49*T^54 - 37/343*T^53 - 1097/2401*T^52 - 415/2401*T^51 + 
        1927/2401*T^50 + 30/49*T^49 - 2059/2401*T^48 - 612/2401*T^47 + 
        2855/2401*T^46 + 1863/2401*T^45 - 73/343*T^44 - 943/2401*T^43 + 
        2476/2401*T^42 + 291/343*T^41 - 2440/2401*T^40 - 1997/2401*T^39 + 
        1684/2401*T^38 + 492/2401*T^37 - 1836/2401*T^36 - 2308/2401*T^35 + 
        443/2401*T^34 + 1795/2401*T^33 - 40/49*T^32 - 2874/2401*T^31 + 327/2401*T^30
        + 1942/2401*T^29 - 1942/2401*T^27 - 327/2401*T^26 + 2874/2401*T^25 + 
        40/49*T^24 - 1795/2401*T^23 - 443/2401*T^22 + 2308/2401*T^21 + 
        1836/2401*T^20 - 492/2401*T^19 - 1684/2401*T^18 + 1997/2401*T^17 + 
        2440/2401*T^16 - 291/343*T^15 - 2476/2401*T^14 + 943/2401*T^13 + 73/343*T^12
        - 1863/2401*T^11 - 2855/2401*T^10 + 612/2401*T^9 + 2059/2401*T^8 - 30/49*T^7
        - 1927/2401*T^6 + 415/2401*T^5 + 1097/2401*T^4 + 37/343*T^3 - 30/49*T^2 + 
        2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 2*X*Y^9 + X*Y^8 + 3*X*Y^7 + 
        2*X*Y^6 + 4*X*Y^5 + 5*X*Y^3 + 4*X*Y^2 + 3*X*Y + 3*X + 6*Y^30 + 6*Y^29 + 
        4*Y^28 + 6*Y^27 + 5*Y^26 + 4*Y^25 + 4*Y^24 + 3*Y^23 + 3*Y^22 + 6*Y^21 + 
        6*Y^20 + 6*Y^19 + 2*Y^18 + 5*Y^17 + 5*Y^15 + 6*Y^13 + 5*Y^11 + 2*Y^10 + Y^9 
        + Y^8 + Y^7 + 4*Y^4 + 2*Y^3 + 5*Y + 5,
    -T^56 - 3/7*T^55 + 29/49*T^54 + 79/343*T^53 - 1597/2401*T^52 - 1514/2401*T^51 - 
        1642/2401*T^50 + 892/2401*T^49 + 2330/2401*T^48 - 10/343*T^47 - 
        1951/2401*T^46 - 1060/2401*T^45 + 716/2401*T^44 + 1727/2401*T^43 + 
        939/2401*T^42 - 1014/2401*T^41 - 806/2401*T^40 - 447/2401*T^39 + 
        603/2401*T^38 + 1376/2401*T^37 - 830/2401*T^36 - 218/343*T^35 - 
        111/2401*T^34 + 69/2401*T^33 - 229/2401*T^32 + 314/2401*T^31 - 72/343*T^30 -
        871/2401*T^29 + 871/2401*T^27 + 72/343*T^26 - 314/2401*T^25 + 229/2401*T^24 
        - 69/2401*T^23 + 111/2401*T^22 + 218/343*T^21 + 830/2401*T^20 - 
        1376/2401*T^19 - 603/2401*T^18 + 447/2401*T^17 + 806/2401*T^16 + 
        1014/2401*T^15 - 939/2401*T^14 - 1727/2401*T^13 - 716/2401*T^12 + 
        1060/2401*T^11 + 1951/2401*T^10 + 10/343*T^9 - 2330/2401*T^8 - 892/2401*T^7 
        + 1642/2401*T^6 + 1514/2401*T^5 + 1597/2401*T^4 - 79/343*T^3 - 29/49*T^2 + 
        3/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 
        + 5*X*Y^8 + 4*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + X*Y^3 + 5*X*Y^2 + 5*X*Y 
        + X + 3*Y^30 + 4*Y^29 + 2*Y^28 + 5*Y^27 + Y^26 + 3*Y^25 + Y^24 + 5*Y^22 + 
        4*Y^21 + 4*Y^19 + 5*Y^17 + 6*Y^16 + Y^15 + 3*Y^14 + 3*Y^13 + 4*Y^12 + Y^11 +
        6*Y^10 + 3*Y^9 + 5*Y^8 + 5*Y^7 + 2*Y^6 + 4*Y^5 + 5*Y^4 + 4*Y^3 + 3*Y + 4,
    T^56 - T^55 + 12/49*T^54 + 5/49*T^53 - 705/2401*T^52 - 106/2401*T^51 - 
        725/2401*T^50 + 745/2401*T^49 - 99/2401*T^48 + 1574/2401*T^47 - 
        1717/2401*T^46 + 1066/2401*T^45 - 205/2401*T^44 - 888/2401*T^43 + 
        1263/2401*T^42 - 1950/2401*T^41 + 1830/2401*T^40 - 15/343*T^39 - 
        122/2401*T^38 - 73/2401*T^37 + 129/2401*T^36 + 130/2401*T^35 - 359/2401*T^34
        + 442/2401*T^33 - 1395/2401*T^32 + 1447/2401*T^31 + 96/2401*T^30 - 
        1170/2401*T^29 + 1728/2401*T^28 - 1170/2401*T^27 + 96/2401*T^26 + 
        1447/2401*T^25 - 1395/2401*T^24 + 442/2401*T^23 - 359/2401*T^22 + 
        130/2401*T^21 + 129/2401*T^20 - 73/2401*T^19 - 122/2401*T^18 - 15/343*T^17 +
        1830/2401*T^16 - 1950/2401*T^15 + 1263/2401*T^14 - 888/2401*T^13 - 
        205/2401*T^12 + 1066/2401*T^11 - 1717/2401*T^10 + 1574/2401*T^9 - 
        99/2401*T^8 + 745/2401*T^7 - 725/2401*T^6 - 106/2401*T^5 - 705/2401*T^4 + 
        5/49*T^3 + 12/49*T^2 - T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 +
        6*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + X*Y^3 + 4*X*Y^2 + X*Y + 6*X + 2*Y^30
        + 6*Y^29 + 6*Y^28 + 6*Y^27 + 3*Y^26 + 6*Y^25 + 2*Y^24 + 4*Y^23 + 4*Y^22 + 
        4*Y^21 + Y^20 + 3*Y^17 + 2*Y^16 + 6*Y^14 + 2*Y^13 + Y^12 + 5*Y^10 + 2*Y^9 + 
        3*Y^7 + 2*Y^5 + Y^4 + 6*Y^2 + Y + 1,
    T^56 - 16/7*T^55 + 96/49*T^54 + 11/49*T^53 - 5052/2401*T^52 + 2755/2401*T^51 + 
        390/343*T^50 - 69/49*T^49 - 1444/2401*T^48 + 3881/2401*T^47 - 1060/2401*T^46
        - 2561/2401*T^45 + 2434/2401*T^44 - 774/2401*T^43 + 1576/2401*T^42 - 
        2006/2401*T^41 - 654/2401*T^40 + 2837/2401*T^39 - 873/2401*T^38 - 
        1629/2401*T^37 - 393/2401*T^36 + 4856/2401*T^35 - 4793/2401*T^34 - 
        212/2401*T^33 + 3001/2401*T^32 - 251/2401*T^31 - 2459/2401*T^30 + 
        1427/2401*T^29 - 186/2401*T^28 + 1427/2401*T^27 - 2459/2401*T^26 - 
        251/2401*T^25 + 3001/2401*T^24 - 212/2401*T^23 - 4793/2401*T^22 + 
        4856/2401*T^21 - 393/2401*T^20 - 1629/2401*T^19 - 873/2401*T^18 + 
        2837/2401*T^17 - 654/2401*T^16 - 2006/2401*T^15 + 1576/2401*T^14 - 
        774/2401*T^13 + 2434/2401*T^12 - 2561/2401*T^11 - 1060/2401*T^10 + 
        3881/2401*T^9 - 1444/2401*T^8 - 69/49*T^7 + 390/343*T^6 + 2755/2401*T^5 - 
        5052/2401*T^4 + 11/49*T^3 + 96/49*T^2 - 16/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + X*Y^9 + 2*X*Y^7 + 
        6*X*Y^4 + 6*X*Y^3 + X*Y + X + 5*Y^30 + 3*Y^29 + Y^28 + 3*Y^27 + 5*Y^26 + 
        6*Y^25 + 4*Y^24 + 3*Y^23 + 6*Y^22 + 2*Y^21 + 2*Y^20 + 2*Y^19 + 2*Y^18 + 
        3*Y^17 + 3*Y^16 + 5*Y^15 + 2*Y^14 + 6*Y^13 + Y^11 + 4*Y^10 + 2*Y^9 + 3*Y^8 +
        Y^7 + 4*Y^6 + 5*Y^4 + 3*Y^3 + 3*Y^2 + 6*Y,
    -T^56 + 9/7*T^55 + 5/49*T^54 - 228/343*T^53 + 325/2401*T^52 + 827/2401*T^51 - 
        1195/2401*T^50 + 857/2401*T^49 - 612/2401*T^48 - 611/2401*T^47 + 
        2435/2401*T^46 - 173/343*T^45 - 1441/2401*T^44 + 1359/2401*T^43 - 
        290/2401*T^42 + 166/2401*T^41 + 694/2401*T^40 - 1278/2401*T^39 - 
        577/2401*T^38 + 2104/2401*T^37 - 2386/2401*T^36 + 986/2401*T^35 + 
        1394/2401*T^34 - 1738/2401*T^33 + 605/2401*T^32 + 1117/2401*T^31 - 
        2353/2401*T^30 + 1250/2401*T^29 - 1250/2401*T^27 + 2353/2401*T^26 - 
        1117/2401*T^25 - 605/2401*T^24 + 1738/2401*T^23 - 1394/2401*T^22 - 
        986/2401*T^21 + 2386/2401*T^20 - 2104/2401*T^19 + 577/2401*T^18 + 
        1278/2401*T^17 - 694/2401*T^16 - 166/2401*T^15 + 290/2401*T^14 - 
        1359/2401*T^13 + 1441/2401*T^12 + 173/343*T^11 - 2435/2401*T^10 + 
        611/2401*T^9 + 612/2401*T^8 - 857/2401*T^7 + 1195/2401*T^6 - 827/2401*T^5 - 
        325/2401*T^4 + 228/343*T^3 - 5/49*T^2 - 9/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + X*Y^11 + 6*X*Y^10 + 5*X*Y^8 + 
        5*X*Y^7 + 6*X*Y^6 + X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 2*X*Y + 6*X + Y^30
        + 6*Y^28 + 4*Y^27 + 6*Y^26 + 6*Y^25 + 3*Y^24 + 2*Y^23 + Y^22 + 6*Y^21 + 
        6*Y^20 + 3*Y^19 + 2*Y^18 + 3*Y^17 + 6*Y^16 + 6*Y^15 + Y^14 + 2*Y^13 + 2*Y^12
        + 5*Y^11 + 2*Y^10 + 4*Y^9 + 3*Y^7 + Y^4 + 4*Y^3 + 6*Y^2 + 4*Y + 6,
    -T^56 - 17/49*T^54 - 30/343*T^53 + 192/2401*T^52 - 1093/2401*T^51 + 
        1104/2401*T^50 + 199/2401*T^49 + 758/2401*T^48 - 548/2401*T^47 + 
        1168/2401*T^46 - 260/2401*T^45 + 813/2401*T^44 - 492/2401*T^43 - 45/343*T^42
        + 796/2401*T^41 - 271/2401*T^40 + 284/2401*T^39 - 659/2401*T^38 + 
        776/2401*T^37 - 493/2401*T^36 + 1042/2401*T^35 + 92/2401*T^34 + 
        858/2401*T^33 + 212/2401*T^32 + 55/2401*T^31 - 366/2401*T^30 + 578/2401*T^29
        - 578/2401*T^27 + 366/2401*T^26 - 55/2401*T^25 - 212/2401*T^24 - 
        858/2401*T^23 - 92/2401*T^22 - 1042/2401*T^21 + 493/2401*T^20 - 
        776/2401*T^19 + 659/2401*T^18 - 284/2401*T^17 + 271/2401*T^16 - 
        796/2401*T^15 + 45/343*T^14 + 492/2401*T^13 - 813/2401*T^12 + 260/2401*T^11 
        - 1168/2401*T^10 + 548/2401*T^9 - 758/2401*T^8 - 199/2401*T^7 - 
        1104/2401*T^6 + 1093/2401*T^5 - 192/2401*T^4 + 30/343*T^3 + 17/49*T^2 + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + X*Y^11 + X*Y^10 + X*Y^9 + X*Y^8 
        + X*Y^7 + 5*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + X*Y^2 + 4*X*Y + 2*X + 5*Y^30 + Y^29 
        + 6*Y^28 + 5*Y^27 + 3*Y^26 + 5*Y^25 + 3*Y^24 + 5*Y^23 + Y^22 + 2*Y^21 + 
        4*Y^20 + 3*Y^19 + 2*Y^17 + Y^16 + 5*Y^15 + 2*Y^14 + 4*Y^13 + 3*Y^12 + 5*Y^11
        + 4*Y^10 + 4*Y^9 + 6*Y^8 + 2*Y^7 + 5*Y^6 + 4*Y^5 + 2*Y^4 + 3*Y,
    T^56 - 5/7*T^55 + 12/49*T^54 + 4/343*T^53 - 823/2401*T^52 + 103/343*T^51 - 
        13/49*T^50 + 369/2401*T^49 - 1037/2401*T^48 + 1594/2401*T^47 - 802/2401*T^46
        + 1079/2401*T^45 - 912/2401*T^44 - 25/343*T^43 - 15/343*T^42 - 254/2401*T^41
        + 985/2401*T^40 - 1601/2401*T^39 + 1073/2401*T^38 - 656/2401*T^37 + 
        387/2401*T^36 + 2/49*T^35 - 127/2401*T^34 + 361/2401*T^33 + 69/2401*T^31 - 
        5/343*T^30 + 82/2401*T^29 - 468/2401*T^28 + 82/2401*T^27 - 5/343*T^26 + 
        69/2401*T^25 + 361/2401*T^23 - 127/2401*T^22 + 2/49*T^21 + 387/2401*T^20 - 
        656/2401*T^19 + 1073/2401*T^18 - 1601/2401*T^17 + 985/2401*T^16 - 
        254/2401*T^15 - 15/343*T^14 - 25/343*T^13 - 912/2401*T^12 + 1079/2401*T^11 -
        802/2401*T^10 + 1594/2401*T^9 - 1037/2401*T^8 + 369/2401*T^7 - 13/49*T^6 + 
        103/343*T^5 - 823/2401*T^4 + 4/343*T^3 + 12/49*T^2 - 5/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 
        5*X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + X*Y^4 + 4*X*Y^3 + X*Y + 3*X + 5*Y^30
        + 3*Y^29 + 6*Y^28 + 3*Y^27 + 5*Y^26 + 2*Y^25 + 2*Y^23 + Y^22 + Y^21 + 2*Y^20
        + 4*Y^19 + 3*Y^18 + 6*Y^17 + 4*Y^16 + 6*Y^15 + 4*Y^14 + 6*Y^13 + 4*Y^11 + 
        6*Y^10 + 5*Y^9 + Y^8 + 6*Y^6 + Y^5 + 3*Y^4 + 3*Y^3 + 3*Y^2 + 3*Y + 4,
    -T^56 - 1/7*T^55 + 59/49*T^54 - 23/343*T^53 - 92/2401*T^52 + 390/2401*T^51 - 
        2459/2401*T^50 + 61/343*T^49 + 2134/2401*T^48 - 918/2401*T^47 - 
        540/2401*T^46 + 486/2401*T^45 - 1133/2401*T^44 + 1107/2401*T^43 + 
        1837/2401*T^42 - 321/343*T^41 - 611/2401*T^40 + 1724/2401*T^39 - 
        1602/2401*T^38 + 498/2401*T^37 + 2113/2401*T^36 - 1563/2401*T^35 + 
        270/2401*T^34 + 538/2401*T^33 - 2308/2401*T^32 + 111/2401*T^31 + 
        1191/2401*T^30 + 283/2401*T^29 - 283/2401*T^27 - 1191/2401*T^26 - 
        111/2401*T^25 + 2308/2401*T^24 - 538/2401*T^23 - 270/2401*T^22 + 
        1563/2401*T^21 - 2113/2401*T^20 - 498/2401*T^19 + 1602/2401*T^18 - 
        1724/2401*T^17 + 611/2401*T^16 + 321/343*T^15 - 1837/2401*T^14 - 
        1107/2401*T^13 + 1133/2401*T^12 - 486/2401*T^11 + 540/2401*T^10 + 
        918/2401*T^9 - 2134/2401*T^8 - 61/343*T^7 + 2459/2401*T^6 - 390/2401*T^5 + 
        92/2401*T^4 + 23/343*T^3 - 59/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 
        + 3*X*Y^8 + 3*X*Y^6 + 2*X*Y^4 + 6*X*Y^3 + X*Y^2 + 3*X*Y + 6*X + 6*Y^30 + 
        2*Y^29 + 3*Y^28 + 2*Y^24 + 4*Y^23 + 4*Y^22 + 5*Y^21 + 3*Y^20 + 6*Y^19 + 
        5*Y^18 + 3*Y^16 + 5*Y^15 + 5*Y^14 + 6*Y^12 + Y^11 + 4*Y^10 + 6*Y^9 + 6*Y^8 +
        3*Y^7 + 6*Y^6 + 3*Y^4 + 3*Y^3 + Y^2 + 3*Y + 1,
    -T^56 + 1/7*T^55 + 1/49*T^54 + 32/49*T^53 + 1121/2401*T^52 - 328/2401*T^51 - 
        1447/2401*T^50 - 915/2401*T^49 - 1014/2401*T^48 + 843/2401*T^47 + 
        1728/2401*T^46 + 520/2401*T^45 - 50/343*T^44 - 732/2401*T^43 - 339/2401*T^42
        - 125/2401*T^41 + 1471/2401*T^40 - 166/2401*T^39 + 74/343*T^38 - 
        377/2401*T^37 + 34/2401*T^36 - 12/2401*T^35 + 1451/2401*T^34 - 438/2401*T^33
        + 29/343*T^32 + 83/2401*T^31 - 369/2401*T^30 + 608/2401*T^29 - 608/2401*T^27
        + 369/2401*T^26 - 83/2401*T^25 - 29/343*T^24 + 438/2401*T^23 - 
        1451/2401*T^22 + 12/2401*T^21 - 34/2401*T^20 + 377/2401*T^19 - 74/343*T^18 +
        166/2401*T^17 - 1471/2401*T^16 + 125/2401*T^15 + 339/2401*T^14 + 
        732/2401*T^13 + 50/343*T^12 - 520/2401*T^11 - 1728/2401*T^10 - 843/2401*T^9 
        + 1014/2401*T^8 + 915/2401*T^7 + 1447/2401*T^6 + 328/2401*T^5 - 
        1121/2401*T^4 - 32/49*T^3 - 1/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + X*Y^9 + 6*X*Y^8 + 3*X*Y^7 + 
        X*Y^6 + 4*X*Y^3 + X*Y^2 + X*Y + 5*X + Y^30 + 3*Y^29 + 2*Y^28 + Y^27 + 3*Y^26
        + Y^25 + Y^24 + 6*Y^21 + 2*Y^20 + 3*Y^17 + 6*Y^16 + 2*Y^15 + 2*Y^14 + 3*Y^12
        + 6*Y^11 + 2*Y^10 + 3*Y^9 + 5*Y^7 + 2*Y^6 + 4*Y^5 + 3*Y^3 + 4*Y^2 + 6*Y + 4,
    T^56 - 4/7*T^55 + 19/49*T^54 + 65/343*T^53 - 993/2401*T^52 + 359/343*T^51 - 
        928/2401*T^50 + 1003/2401*T^49 + 359/2401*T^48 - 71/343*T^47 + 
        2204/2401*T^46 - 293/2401*T^45 + 849/2401*T^44 + 411/2401*T^43 - 
        34/2401*T^42 + 1276/2401*T^41 - 419/2401*T^40 + 2078/2401*T^39 - 
        1000/2401*T^38 + 1412/2401*T^37 + 1124/2401*T^36 - 695/2401*T^35 + 
        3000/2401*T^34 - 1957/2401*T^33 + 2379/2401*T^32 + 401/2401*T^31 - 
        397/2401*T^30 + 2524/2401*T^29 - 1070/2401*T^28 + 2524/2401*T^27 - 
        397/2401*T^26 + 401/2401*T^25 + 2379/2401*T^24 - 1957/2401*T^23 + 
        3000/2401*T^22 - 695/2401*T^21 + 1124/2401*T^20 + 1412/2401*T^19 - 
        1000/2401*T^18 + 2078/2401*T^17 - 419/2401*T^16 + 1276/2401*T^15 - 
        34/2401*T^14 + 411/2401*T^13 + 849/2401*T^12 - 293/2401*T^11 + 
        2204/2401*T^10 - 71/343*T^9 + 359/2401*T^8 + 1003/2401*T^7 - 928/2401*T^6 + 
        359/343*T^5 - 993/2401*T^4 + 65/343*T^3 + 19/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 3*X*Y^7 + X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 2*X*Y + 
        5*X + 6*Y^30 + 4*Y^29 + 4*Y^28 + 5*Y^27 + 3*Y^26 + Y^25 + 3*Y^24 + 3*Y^23 + 
        Y^21 + 2*Y^20 + 2*Y^19 + 2*Y^18 + 5*Y^17 + 4*Y^16 + Y^15 + 2*Y^14 + 5*Y^13 +
        Y^12 + 3*Y^10 + 5*Y^9 + 4*Y^8 + 4*Y^7 + Y^6 + 5*Y^4 + Y^3 + 3*Y^2 + 2*Y + 2,
    T^56 + T^55 + 18/49*T^54 + 410/343*T^53 + 330/343*T^52 + 4/7*T^51 + 
        1592/2401*T^50 + 1199/2401*T^49 + 1280/2401*T^48 + 1381/2401*T^47 + 
        1770/2401*T^46 - 335/2401*T^45 - 1020/2401*T^44 - 27/343*T^43 - 
        1278/2401*T^42 - 640/2401*T^41 - 1000/2401*T^40 - 176/343*T^39 + 
        121/2401*T^38 - 57/2401*T^37 - 1495/2401*T^36 - 1140/2401*T^35 - 
        531/2401*T^34 - 270/343*T^33 - 1090/2401*T^32 - 141/343*T^31 - 
        3246/2401*T^30 - 2654/2401*T^29 - 170/343*T^28 - 2654/2401*T^27 - 
        3246/2401*T^26 - 141/343*T^25 - 1090/2401*T^24 - 270/343*T^23 - 
        531/2401*T^22 - 1140/2401*T^21 - 1495/2401*T^20 - 57/2401*T^19 + 
        121/2401*T^18 - 176/343*T^17 - 1000/2401*T^16 - 640/2401*T^15 - 
        1278/2401*T^14 - 27/343*T^13 - 1020/2401*T^12 - 335/2401*T^11 + 
        1770/2401*T^10 + 1381/2401*T^9 + 1280/2401*T^8 + 1199/2401*T^7 + 
        1592/2401*T^6 + 4/7*T^5 + 330/343*T^4 + 410/343*T^3 + 18/49*T^2 + T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 4*X*Y^11 + X*Y^10 + 3*X*Y^6 + 4*X*Y^5 + 
        2*X*Y^4 + 3*X*Y^3 + X*Y + X + 3*Y^30 + 2*Y^29 + Y^28 + 5*Y^27 + Y^26 + 
        5*Y^25 + 2*Y^23 + 3*Y^22 + 2*Y^21 + 3*Y^20 + Y^19 + 3*Y^18 + 6*Y^17 + 5*Y^16
        + 4*Y^15 + 6*Y^14 + 2*Y^13 + 4*Y^12 + 4*Y^11 + 3*Y^10 + 5*Y^9 + Y^7 + 2*Y^6 
        + 4*Y^4 + 3*Y^3 + Y^2 + 4,
    T^56 - 13/7*T^55 + 64/49*T^54 + 152/343*T^53 - 2491/2401*T^52 - 764/2401*T^51 + 
        2911/2401*T^50 + 32/2401*T^49 - 2382/2401*T^48 + 736/2401*T^47 + 
        1075/2401*T^46 - 354/2401*T^45 + 475/2401*T^44 - 3525/2401*T^43 + 
        2825/2401*T^42 + 3202/2401*T^41 - 5183/2401*T^40 + 248/2401*T^39 + 
        2915/2401*T^38 + 939/2401*T^37 - 659/343*T^36 + 4/7*T^35 + 2055/2401*T^34 + 
        24/2401*T^33 - 1867/2401*T^32 - 1254/2401*T^31 + 2986/2401*T^30 + 
        975/2401*T^29 - 4789/2401*T^28 + 975/2401*T^27 + 2986/2401*T^26 - 
        1254/2401*T^25 - 1867/2401*T^24 + 24/2401*T^23 + 2055/2401*T^22 + 4/7*T^21 -
        659/343*T^20 + 939/2401*T^19 + 2915/2401*T^18 + 248/2401*T^17 - 
        5183/2401*T^16 + 3202/2401*T^15 + 2825/2401*T^14 - 3525/2401*T^13 + 
        475/2401*T^12 - 354/2401*T^11 + 1075/2401*T^10 + 736/2401*T^9 - 
        2382/2401*T^8 + 32/2401*T^7 + 2911/2401*T^6 - 764/2401*T^5 - 2491/2401*T^4 +
        152/343*T^3 + 64/49*T^2 - 13/7*T + 1
*], [*
    X^3 + 6*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 3*X*Y^8 + X*Y^7 + 4*X*Y^6 + 
        4*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 5*X*Y + 3*X + 6*Y^30 + 6*Y^29 + 
        6*Y^28 + 4*Y^26 + Y^25 + 3*Y^24 + 4*Y^23 + 6*Y^22 + 4*Y^21 + 5*Y^20 + 5*Y^19
        + 2*Y^18 + 5*Y^17 + 6*Y^16 + Y^15 + 5*Y^14 + 6*Y^13 + 2*Y^12 + 2*Y^11 + 
        2*Y^10 + 3*Y^9 + 5*Y^8 + 6*Y^7 + 5*Y^5 + 2*Y^3 + 5*Y^2 + 3*Y + 1,
    T^56 + T^55 + 10/49*T^54 + 104/343*T^53 - 691/2401*T^52 - 804/2401*T^51 - 
        1060/2401*T^50 - 3179/2401*T^49 - 2350/2401*T^48 - 81/343*T^47 - 
        438/2401*T^46 + 195/2401*T^45 + 760/2401*T^44 + 1166/2401*T^43 + 
        1524/2401*T^42 + 122/2401*T^41 - 1539/2401*T^40 - 1772/2401*T^39 - 
        773/2401*T^38 - 573/2401*T^37 - 405/2401*T^36 + 33/2401*T^35 + 104/343*T^34 
        + 2819/2401*T^33 + 2459/2401*T^32 + 279/2401*T^31 - 543/2401*T^30 - 
        888/2401*T^29 - 1010/2401*T^28 - 888/2401*T^27 - 543/2401*T^26 + 
        279/2401*T^25 + 2459/2401*T^24 + 2819/2401*T^23 + 104/343*T^22 + 
        33/2401*T^21 - 405/2401*T^20 - 573/2401*T^19 - 773/2401*T^18 - 
        1772/2401*T^17 - 1539/2401*T^16 + 122/2401*T^15 + 1524/2401*T^14 + 
        1166/2401*T^13 + 760/2401*T^12 + 195/2401*T^11 - 438/2401*T^10 - 81/343*T^9 
        - 2350/2401*T^8 - 3179/2401*T^7 - 1060/2401*T^6 - 804/2401*T^5 - 
        691/2401*T^4 + 104/343*T^3 + 10/49*T^2 + T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + X*Y^10 + 3*X*Y^9 + 5*X*Y^8 + 
        2*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 4*X*Y + Y^30 + 4*Y^29 + 
        5*Y^28 + Y^27 + Y^26 + 3*Y^25 + Y^24 + 2*Y^23 + 2*Y^22 + 6*Y^21 + 5*Y^20 + 
        5*Y^19 + Y^18 + 5*Y^17 + 5*Y^16 + 5*Y^14 + 2*Y^13 + 4*Y^12 + 2*Y^11 + 2*Y^10
        + 4*Y^9 + 3*Y^7 + 2*Y^6 + 6*Y^5 + 6*Y^3 + 3*Y^2 + 5*Y + 2,
    -T^56 + 10/7*T^55 - 64/49*T^54 + 71/49*T^53 - 325/343*T^52 + 1915/2401*T^51 - 
        1559/2401*T^50 + 538/2401*T^49 - 601/2401*T^48 - 281/2401*T^47 + 
        1259/2401*T^46 - 670/2401*T^45 + 1859/2401*T^44 - 408/343*T^43 + 
        2539/2401*T^42 - 2503/2401*T^41 + 194/343*T^40 - 59/2401*T^39 - 
        876/2401*T^38 + 1248/2401*T^37 - 2126/2401*T^36 + 3396/2401*T^35 - 
        582/343*T^34 + 4180/2401*T^33 - 3503/2401*T^32 + 3540/2401*T^31 - 
        2733/2401*T^30 + 799/2401*T^29 - 799/2401*T^27 + 2733/2401*T^26 - 
        3540/2401*T^25 + 3503/2401*T^24 - 4180/2401*T^23 + 582/343*T^22 - 
        3396/2401*T^21 + 2126/2401*T^20 - 1248/2401*T^19 + 876/2401*T^18 + 
        59/2401*T^17 - 194/343*T^16 + 2503/2401*T^15 - 2539/2401*T^14 + 408/343*T^13
        - 1859/2401*T^12 + 670/2401*T^11 - 1259/2401*T^10 + 281/2401*T^9 + 
        601/2401*T^8 - 538/2401*T^7 + 1559/2401*T^6 - 1915/2401*T^5 + 325/343*T^4 - 
        71/49*T^3 + 64/49*T^2 - 10/7*T + 1
*], [*
    X^3 + X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + X*Y^8 + 
        5*X*Y^7 + X*Y^6 + 5*X*Y^5 + 5*X*Y^2 + 6*X*Y + 3*X + 5*Y^30 + 6*Y^29 + Y^28 +
        Y^26 + 5*Y^25 + Y^24 + 3*Y^23 + 5*Y^22 + 3*Y^21 + 3*Y^20 + 2*Y^19 + 2*Y^18 +
        5*Y^17 + Y^16 + Y^13 + 4*Y^12 + 2*Y^11 + 6*Y^10 + Y^9 + Y^8 + 3*Y^7 + 5*Y^6 
        + 5*Y^5 + 3*Y^4 + 6*Y^3 + 3*Y^2 + 2,
    T^56 + 6/7*T^55 - 127/343*T^53 - 15/343*T^52 - 507/2401*T^51 + 38/2401*T^50 + 
        1115/2401*T^49 + 408/2401*T^48 + 626/2401*T^47 + 2512/2401*T^46 + 
        2042/2401*T^45 + 152/2401*T^44 - 276/2401*T^43 - 2/343*T^42 - 5/49*T^41 - 
        368/2401*T^40 + 555/2401*T^39 + 295/2401*T^38 + 1068/2401*T^37 + 
        1986/2401*T^36 + 872/2401*T^35 - 1371/2401*T^34 - 1357/2401*T^33 - 
        893/2401*T^32 - 150/2401*T^31 + 1195/2401*T^30 + 764/2401*T^29 - 
        720/2401*T^28 + 764/2401*T^27 + 1195/2401*T^26 - 150/2401*T^25 - 
        893/2401*T^24 - 1357/2401*T^23 - 1371/2401*T^22 + 872/2401*T^21 + 
        1986/2401*T^20 + 1068/2401*T^19 + 295/2401*T^18 + 555/2401*T^17 - 
        368/2401*T^16 - 5/49*T^15 - 2/343*T^14 - 276/2401*T^13 + 152/2401*T^12 + 
        2042/2401*T^11 + 2512/2401*T^10 + 626/2401*T^9 + 408/2401*T^8 + 
        1115/2401*T^7 + 38/2401*T^6 - 507/2401*T^5 - 15/343*T^4 - 127/343*T^3 + 
        6/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 3*X*Y^10 + 3*X*Y^9 + X*Y^7 + 
        X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 3*X*Y + 4*X + 4*Y^30 + 2*Y^29 + 2*Y^28
        + 3*Y^25 + 3*Y^23 + 6*Y^22 + 3*Y^21 + 5*Y^19 + 3*Y^16 + 5*Y^15 + 3*Y^14 + 
        6*Y^13 + 4*Y^11 + 2*Y^10 + 3*Y^9 + 2*Y^8 + Y^7 + Y^5 + 2*Y^4 + Y^3 + 6*Y^2 +
        6*Y + 3,
    -T^56 + 66/49*T^54 - 34/343*T^53 - 2741/2401*T^52 + 911/2401*T^51 + 
        915/2401*T^50 + 312/2401*T^49 + 1598/2401*T^48 - 837/2401*T^47 - 
        1280/2401*T^46 + 1790/2401*T^45 + 705/2401*T^44 - 2237/2401*T^43 - 
        1361/2401*T^42 + 519/2401*T^41 + 1444/2401*T^40 - 1186/2401*T^39 - 
        2494/2401*T^38 + 759/2401*T^37 + 1340/2401*T^36 - 184/2401*T^35 + 
        474/2401*T^34 + 289/2401*T^33 - 376/2401*T^32 + 2155/2401*T^31 + 
        803/2401*T^30 - 2095/2401*T^29 + 2095/2401*T^27 - 803/2401*T^26 - 
        2155/2401*T^25 + 376/2401*T^24 - 289/2401*T^23 - 474/2401*T^22 + 
        184/2401*T^21 - 1340/2401*T^20 - 759/2401*T^19 + 2494/2401*T^18 + 
        1186/2401*T^17 - 1444/2401*T^16 - 519/2401*T^15 + 1361/2401*T^14 + 
        2237/2401*T^13 - 705/2401*T^12 - 1790/2401*T^11 + 1280/2401*T^10 + 
        837/2401*T^9 - 1598/2401*T^8 - 312/2401*T^7 - 915/2401*T^6 - 911/2401*T^5 + 
        2741/2401*T^4 + 34/343*T^3 - 66/49*T^2 + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 3*X*Y^8 
        + 2*X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + X + Y^30 + 
        4*Y^28 + 3*Y^27 + 2*Y^26 + 5*Y^25 + Y^24 + 2*Y^23 + 3*Y^22 + 6*Y^21 + 2*Y^20
        + 6*Y^19 + 4*Y^17 + 6*Y^16 + 5*Y^15 + 3*Y^14 + 5*Y^13 + 5*Y^12 + Y^11 + 
        2*Y^10 + 6*Y^9 + 6*Y^8 + 5*Y^7 + 6*Y^5 + 3*Y^4 + 3*Y^3 + 3*Y + 1,
    T^56 + 3/7*T^55 - 2/7*T^54 + 141/343*T^53 - 2190/2401*T^52 - 94/343*T^51 + 
        348/343*T^50 - 635/2401*T^49 + 573/2401*T^48 + 1035/2401*T^47 - 
        2903/2401*T^46 - 1172/2401*T^45 + 1482/2401*T^44 - 143/343*T^43 + 
        1462/2401*T^42 + 272/343*T^41 - 2865/2401*T^40 - 152/2401*T^39 - 
        260/2401*T^38 - 2208/2401*T^37 + 1870/2401*T^36 + 1664/2401*T^35 - 
        393/2401*T^34 + 562/2401*T^33 - 828/2401*T^32 - 2522/2401*T^31 + 
        32/2401*T^30 + 1158/2401*T^29 - 180/2401*T^28 + 1158/2401*T^27 + 
        32/2401*T^26 - 2522/2401*T^25 - 828/2401*T^24 + 562/2401*T^23 - 
        393/2401*T^22 + 1664/2401*T^21 + 1870/2401*T^20 - 2208/2401*T^19 - 
        260/2401*T^18 - 152/2401*T^17 - 2865/2401*T^16 + 272/343*T^15 + 
        1462/2401*T^14 - 143/343*T^13 + 1482/2401*T^12 - 1172/2401*T^11 - 
        2903/2401*T^10 + 1035/2401*T^9 + 573/2401*T^8 - 635/2401*T^7 + 348/343*T^6 -
        94/343*T^5 - 2190/2401*T^4 + 141/343*T^3 - 2/7*T^2 + 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + X*Y^8 + 
        X*Y^6 + X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 6*X*Y + 5*X + 4*Y^30 + 5*Y^29 
        + 2*Y^28 + 2*Y^27 + Y^26 + 2*Y^25 + 3*Y^24 + 3*Y^23 + 6*Y^22 + 5*Y^21 + 
        5*Y^20 + 4*Y^19 + 2*Y^18 + 5*Y^16 + 6*Y^14 + 6*Y^13 + 3*Y^12 + 2*Y^10 + Y^9 
        + 3*Y^8 + 2*Y^7 + 6*Y^6 + Y^5 + 2*Y^4 + 2*Y^3 + 5*Y + 2,
    T^56 - 11/49*T^54 - 197/343*T^53 - 1499/2401*T^52 + 825/2401*T^51 - 
        580/2401*T^50 + 498/2401*T^49 - 753/2401*T^48 - 324/2401*T^47 + 
        1067/2401*T^46 + 1616/2401*T^45 + 1509/2401*T^44 - 684/2401*T^43 - 
        1774/2401*T^42 - 893/2401*T^41 - 654/2401*T^40 + 652/2401*T^39 - 9/49*T^38 -
        319/2401*T^37 - 575/2401*T^36 + 18/2401*T^35 + 407/343*T^34 + 1185/2401*T^33
        + 62/343*T^32 - 1368/2401*T^31 - 1026/2401*T^30 + 281/2401*T^29 - 
        613/2401*T^28 + 281/2401*T^27 - 1026/2401*T^26 - 1368/2401*T^25 + 
        62/343*T^24 + 1185/2401*T^23 + 407/343*T^22 + 18/2401*T^21 - 575/2401*T^20 -
        319/2401*T^19 - 9/49*T^18 + 652/2401*T^17 - 654/2401*T^16 - 893/2401*T^15 - 
        1774/2401*T^14 - 684/2401*T^13 + 1509/2401*T^12 + 1616/2401*T^11 + 
        1067/2401*T^10 - 324/2401*T^9 - 753/2401*T^8 + 498/2401*T^7 - 580/2401*T^6 +
        825/2401*T^5 - 1499/2401*T^4 - 197/343*T^3 - 11/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 
        + X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + 6*X*Y^4 + 6*X*Y^3 + X*Y^2 + X*Y + 5*X + 4*Y^30
        + 2*Y^29 + 6*Y^28 + 6*Y^27 + Y^26 + 2*Y^24 + 2*Y^23 + 2*Y^22 + 3*Y^21 + Y^20
        + 6*Y^19 + 4*Y^18 + 2*Y^17 + Y^16 + 2*Y^15 + 5*Y^14 + Y^13 + 3*Y^12 + 3*Y^11
        + 4*Y^10 + Y^9 + 5*Y^8 + 5*Y^7 + 4*Y^6 + 2*Y^5 + 5*Y^4 + 6*Y^2 + 6*Y + 5,
    T^56 + 3/7*T^55 + 24/49*T^54 + 262/343*T^53 - 2084/2401*T^52 - 64/343*T^51 - 
        869/2401*T^50 - 1481/2401*T^49 + 1453/2401*T^48 - 890/2401*T^47 - 
        1270/2401*T^46 - 3/343*T^45 - 2655/2401*T^44 + 1201/2401*T^43 + 
        1664/2401*T^42 + 359/2401*T^41 + 1763/2401*T^40 - 240/343*T^39 - 
        1600/2401*T^38 - 255/2401*T^37 + 359/2401*T^36 + 376/343*T^35 + 
        1738/2401*T^34 - 87/343*T^33 - 831/2401*T^32 - 2561/2401*T^31 - 
        1345/2401*T^30 + 965/2401*T^29 + 450/2401*T^28 + 965/2401*T^27 - 
        1345/2401*T^26 - 2561/2401*T^25 - 831/2401*T^24 - 87/343*T^23 + 
        1738/2401*T^22 + 376/343*T^21 + 359/2401*T^20 - 255/2401*T^19 - 
        1600/2401*T^18 - 240/343*T^17 + 1763/2401*T^16 + 359/2401*T^15 + 
        1664/2401*T^14 + 1201/2401*T^13 - 2655/2401*T^12 - 3/343*T^11 - 
        1270/2401*T^10 - 890/2401*T^9 + 1453/2401*T^8 - 1481/2401*T^7 - 869/2401*T^6
        - 64/343*T^5 - 2084/2401*T^4 + 262/343*T^3 + 24/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 2*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + X*Y^10 + 6*X*Y^9 + 4*X*Y^8 + 3*X*Y^7 + 
        4*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + X*Y + 5*Y^30 + Y^29 + 
        4*Y^27 + 6*Y^26 + 6*Y^25 + 6*Y^22 + Y^21 + 3*Y^20 + 6*Y^19 + Y^18 + Y^17 + 
        3*Y^16 + 2*Y^15 + 3*Y^14 + 4*Y^13 + 3*Y^12 + 3*Y^11 + 2*Y^10 + 2*Y^9 + 4*Y^8
        + 3*Y^7 + 6*Y^6 + 5*Y^5 + 6*Y^4 + 4*Y^3 + 3*Y + 3,
    -T^56 + 9/7*T^55 - 6/7*T^54 + 261/343*T^53 - 2076/2401*T^52 - 769/2401*T^51 + 
        1531/2401*T^50 + 761/2401*T^49 - 235/2401*T^48 - 1179/2401*T^47 - 
        521/2401*T^46 + 2643/2401*T^45 - 955/2401*T^44 + 66/343*T^43 - 
        1175/2401*T^42 + 363/2401*T^41 + 2262/2401*T^40 - 124/343*T^39 - 
        850/2401*T^38 + 247/2401*T^37 + 88/2401*T^36 + 2043/2401*T^35 - 
        1849/2401*T^34 - 99/2401*T^33 + 533/2401*T^32 + 62/2401*T^31 + 138/343*T^30 
        - 1504/2401*T^29 + 1504/2401*T^27 - 138/343*T^26 - 62/2401*T^25 - 
        533/2401*T^24 + 99/2401*T^23 + 1849/2401*T^22 - 2043/2401*T^21 - 
        88/2401*T^20 - 247/2401*T^19 + 850/2401*T^18 + 124/343*T^17 - 2262/2401*T^16
        - 363/2401*T^15 + 1175/2401*T^14 - 66/343*T^13 + 955/2401*T^12 - 
        2643/2401*T^11 + 521/2401*T^10 + 1179/2401*T^9 + 235/2401*T^8 - 761/2401*T^7
        - 1531/2401*T^6 + 769/2401*T^5 + 2076/2401*T^4 - 261/343*T^3 + 6/7*T^2 - 
        9/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 
        5*X*Y^8 + 2*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 6*X*Y^3 + 6*X*Y^2 + 2*X*Y + 3*Y^30 +
        5*Y^29 + 6*Y^28 + 2*Y^27 + 2*Y^26 + 5*Y^25 + 4*Y^24 + 6*Y^23 + 3*Y^22 + 
        4*Y^21 + 6*Y^19 + 3*Y^18 + 6*Y^17 + 6*Y^16 + 6*Y^15 + 4*Y^14 + 6*Y^13 + Y^12
        + 3*Y^11 + 4*Y^10 + 2*Y^9 + 3*Y^8 + 5*Y^7 + 5*Y^5 + Y^4 + 6*Y^3 + Y^2 + 3*Y 
        + 6,
    T^56 - 3/7*T^55 - 11/49*T^54 - 59/49*T^53 + 40/343*T^52 + 71/343*T^51 + 
        3057/2401*T^50 + 12/2401*T^49 + 470/2401*T^48 - 2311/2401*T^47 - 
        1304/2401*T^46 - 1406/2401*T^45 + 477/2401*T^44 + 244/343*T^43 + 
        312/343*T^42 + 885/2401*T^41 - 1724/2401*T^40 - 1311/2401*T^39 - 
        1737/2401*T^38 - 522/2401*T^37 + 1214/2401*T^36 + 2311/2401*T^35 + 
        2255/2401*T^34 - 641/2401*T^33 - 1893/2401*T^32 - 3138/2401*T^31 - 
        218/2401*T^30 + 789/2401*T^29 + 612/343*T^28 + 789/2401*T^27 - 218/2401*T^26
        - 3138/2401*T^25 - 1893/2401*T^24 - 641/2401*T^23 + 2255/2401*T^22 + 
        2311/2401*T^21 + 1214/2401*T^20 - 522/2401*T^19 - 1737/2401*T^18 - 
        1311/2401*T^17 - 1724/2401*T^16 + 885/2401*T^15 + 312/343*T^14 + 
        244/343*T^13 + 477/2401*T^12 - 1406/2401*T^11 - 1304/2401*T^10 - 
        2311/2401*T^9 + 470/2401*T^8 + 12/2401*T^7 + 3057/2401*T^6 + 71/343*T^5 + 
        40/343*T^4 - 59/49*T^3 - 11/49*T^2 - 3/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + X*Y^10 + 4*X*Y^9 + 
        6*X*Y^7 + 4*X*Y^6 + X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + X*Y^2 + X*Y + X + 5*Y^30 + 
        5*Y^29 + 2*Y^27 + 6*Y^26 + 5*Y^25 + 6*Y^24 + 6*Y^23 + 3*Y^22 + 3*Y^21 + Y^19
        + 5*Y^18 + 2*Y^17 + 5*Y^16 + 6*Y^15 + 3*Y^14 + Y^12 + 6*Y^10 + 4*Y^9 + 4*Y^8
        + 5*Y^7 + 5*Y^6 + 6*Y^5 + 3*Y^4 + 6*Y^3 + 3*Y^2 + 5*Y,
    -T^56 - 5/7*T^55 - 30/49*T^54 - 410/343*T^53 - 1234/2401*T^52 - 143/2401*T^51 - 
        1269/2401*T^50 - 925/2401*T^49 - 131/2401*T^48 - 626/2401*T^47 - 12/343*T^46
        - 517/2401*T^45 - 1170/2401*T^44 - 1574/2401*T^43 - 1336/2401*T^42 - 
        1446/2401*T^41 - 670/2401*T^40 - 326/2401*T^39 - 967/2401*T^38 - 
        1221/2401*T^37 - 99/343*T^36 - 291/2401*T^35 + 360/2401*T^34 + 54/343*T^33 +
        1467/2401*T^32 + 690/2401*T^31 - 142/2401*T^30 + 744/2401*T^29 - 
        744/2401*T^27 + 142/2401*T^26 - 690/2401*T^25 - 1467/2401*T^24 - 54/343*T^23
        - 360/2401*T^22 + 291/2401*T^21 + 99/343*T^20 + 1221/2401*T^19 + 
        967/2401*T^18 + 326/2401*T^17 + 670/2401*T^16 + 1446/2401*T^15 + 
        1336/2401*T^14 + 1574/2401*T^13 + 1170/2401*T^12 + 517/2401*T^11 + 
        12/343*T^10 + 626/2401*T^9 + 131/2401*T^8 + 925/2401*T^7 + 1269/2401*T^6 + 
        143/2401*T^5 + 1234/2401*T^4 + 410/343*T^3 + 30/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 4*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 + 6*X*Y^7 + 
        5*X*Y^6 + 2*X*Y^5 + X*Y^3 + 4*X*Y + 3*X + 4*Y^30 + 6*Y^29 + 5*Y^28 + 6*Y^27 
        + 2*Y^26 + 6*Y^25 + 2*Y^24 + 2*Y^20 + 4*Y^19 + 2*Y^18 + 3*Y^17 + 5*Y^16 + 
        Y^15 + 5*Y^14 + Y^13 + 2*Y^12 + 3*Y^11 + 2*Y^9 + 2*Y^8 + Y^7 + 3*Y^6 + 2*Y^5
        + 4*Y^4 + 6*Y^3 + 4*Y^2 + 3,
    T^56 + 8/7*T^55 + 62/49*T^54 + 255/343*T^53 + 2635/2401*T^52 + 3534/2401*T^51 + 
        3466/2401*T^50 + 2819/2401*T^49 + 2375/2401*T^48 + 2788/2401*T^47 + 
        1952/2401*T^46 + 499/2401*T^45 + 433/2401*T^44 + 482/2401*T^43 + 
        618/2401*T^42 - 248/343*T^41 - 2602/2401*T^40 - 1998/2401*T^39 - 
        738/2401*T^38 - 1026/2401*T^37 - 1949/2401*T^36 - 2113/2401*T^35 - 
        1401/2401*T^34 - 941/2401*T^33 - 377/2401*T^32 + 737/2401*T^31 + 
        995/2401*T^30 + 39/343*T^29 - 522/2401*T^28 + 39/343*T^27 + 995/2401*T^26 + 
        737/2401*T^25 - 377/2401*T^24 - 941/2401*T^23 - 1401/2401*T^22 - 
        2113/2401*T^21 - 1949/2401*T^20 - 1026/2401*T^19 - 738/2401*T^18 - 
        1998/2401*T^17 - 2602/2401*T^16 - 248/343*T^15 + 618/2401*T^14 + 
        482/2401*T^13 + 433/2401*T^12 + 499/2401*T^11 + 1952/2401*T^10 + 
        2788/2401*T^9 + 2375/2401*T^8 + 2819/2401*T^7 + 3466/2401*T^6 + 
        3534/2401*T^5 + 2635/2401*T^4 + 255/343*T^3 + 62/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 
        X*Y^8 + 4*X*Y^7 + 2*X*Y^6 + X*Y^5 + 2*X*Y^2 + 5*X*Y + 4*X + 5*Y^30 + Y^29 + 
        3*Y^27 + 6*Y^26 + 5*Y^25 + 4*Y^23 + 5*Y^22 + Y^20 + 6*Y^19 + 2*Y^18 + 5*Y^17
        + 4*Y^15 + 2*Y^14 + 6*Y^13 + 5*Y^12 + 6*Y^11 + 4*Y^7 + 5*Y^5 + 2*Y^4 + 6*Y^3
        + 3*Y^2 + 2*Y + 4,
    T^56 + 2*T^55 + 50/49*T^54 - 218/343*T^53 - 764/2401*T^52 + 4766/2401*T^51 + 
        5450/2401*T^50 - 47/343*T^49 - 2812/2401*T^48 + 141/2401*T^47 + 
        2060/2401*T^46 - 485/2401*T^45 - 2215/2401*T^44 - 276/2401*T^43 + 
        961/2401*T^42 + 1128/2401*T^41 + 1427/2401*T^40 + 183/2401*T^39 - 
        270/343*T^38 - 1405/2401*T^37 + 2431/2401*T^36 + 3137/2401*T^35 - 
        1346/2401*T^34 - 3771/2401*T^33 - 2385/2401*T^32 - 1446/2401*T^31 - 
        2461/2401*T^30 - 2624/2401*T^29 - 284/343*T^28 - 2624/2401*T^27 - 
        2461/2401*T^26 - 1446/2401*T^25 - 2385/2401*T^24 - 3771/2401*T^23 - 
        1346/2401*T^22 + 3137/2401*T^21 + 2431/2401*T^20 - 1405/2401*T^19 - 
        270/343*T^18 + 183/2401*T^17 + 1427/2401*T^16 + 1128/2401*T^15 + 
        961/2401*T^14 - 276/2401*T^13 - 2215/2401*T^12 - 485/2401*T^11 + 
        2060/2401*T^10 + 141/2401*T^9 - 2812/2401*T^8 - 47/343*T^7 + 5450/2401*T^6 +
        4766/2401*T^5 - 764/2401*T^4 - 218/343*T^3 + 50/49*T^2 + 2*T + 1
*], [*
    X^3 + 2*X*Y^14 + 6*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 3*X*Y^8 + 4*X*Y^7 + 2*X*Y^6 + 
        6*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 4*X*Y + 3*X + 5*Y^30 + Y^29 + 6*Y^28
        + 5*Y^27 + 6*Y^26 + 5*Y^25 + 4*Y^24 + 3*Y^23 + 6*Y^22 + 3*Y^21 + 2*Y^20 + 
        6*Y^19 + 4*Y^18 + Y^17 + 4*Y^16 + Y^15 + 2*Y^14 + 3*Y^13 + Y^12 + Y^11 + 
        3*Y^10 + 5*Y^9 + 3*Y^8 + 5*Y^5 + 5*Y^4 + 4*Y^3 + 4*Y^2 + 6*Y + 1,
    -T^56 + 13/7*T^55 - 33/49*T^54 - 410/343*T^53 + 3930/2401*T^52 - 611/2401*T^51 -
        426/343*T^50 + 2883/2401*T^49 - 817/2401*T^48 + 71/2401*T^47 + 
        1216/2401*T^46 - 2694/2401*T^45 + 2174/2401*T^44 + 233/2401*T^43 - 
        1895/2401*T^42 + 1066/2401*T^41 + 729/2401*T^40 - 316/343*T^39 + 
        2846/2401*T^38 - 3295/2401*T^37 + 2913/2401*T^36 - 699/2401*T^35 - 
        170/343*T^34 + 1451/2401*T^33 - 1236/2401*T^32 - 872/2401*T^31 + 
        432/343*T^30 - 2185/2401*T^29 + 2185/2401*T^27 - 432/343*T^26 + 
        872/2401*T^25 + 1236/2401*T^24 - 1451/2401*T^23 + 170/343*T^22 + 
        699/2401*T^21 - 2913/2401*T^20 + 3295/2401*T^19 - 2846/2401*T^18 + 
        316/343*T^17 - 729/2401*T^16 - 1066/2401*T^15 + 1895/2401*T^14 - 
        233/2401*T^13 - 2174/2401*T^12 + 2694/2401*T^11 - 1216/2401*T^10 - 
        71/2401*T^9 + 817/2401*T^8 - 2883/2401*T^7 + 426/343*T^6 + 611/2401*T^5 - 
        3930/2401*T^4 + 410/343*T^3 + 33/49*T^2 - 13/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 3*X*Y^11 + 2*X*Y^9 + 5*X*Y^8 + X*Y^6 + 4*X*Y^4 + 
        5*X*Y^3 + 2*X*Y^2 + X*Y + 5*X + 4*Y^30 + 3*Y^29 + Y^28 + 6*Y^25 + 5*Y^24 + 
        Y^23 + 3*Y^20 + 4*Y^19 + 4*Y^18 + 6*Y^17 + 2*Y^16 + 4*Y^15 + 2*Y^14 + 5*Y^13
        + 5*Y^12 + 3*Y^11 + 3*Y^10 + 4*Y^9 + 5*Y^8 + 3*Y^7 + 3*Y^6 + 6*Y^5 + 6*Y + 
        1,
    -T^56 + 2/7*T^55 - 2/49*T^54 + 65/343*T^53 + 372/2401*T^52 + 300/2401*T^51 + 
        1892/2401*T^50 - 1398/2401*T^49 + 1063/2401*T^48 - 820/2401*T^47 - 
        164/2401*T^46 + 996/2401*T^45 - 1882/2401*T^44 + 264/343*T^43 - 
        1592/2401*T^42 + 622/2401*T^41 - 410/2401*T^40 - 1466/2401*T^39 + 
        382/343*T^38 - 407/343*T^37 + 1987/2401*T^36 - 1133/2401*T^35 - 
        242/2401*T^34 + 1222/2401*T^33 - 2466/2401*T^32 + 3673/2401*T^31 - 
        1978/2401*T^30 + 1740/2401*T^29 - 1740/2401*T^27 + 1978/2401*T^26 - 
        3673/2401*T^25 + 2466/2401*T^24 - 1222/2401*T^23 + 242/2401*T^22 + 
        1133/2401*T^21 - 1987/2401*T^20 + 407/343*T^19 - 382/343*T^18 + 
        1466/2401*T^17 + 410/2401*T^16 - 622/2401*T^15 + 1592/2401*T^14 - 
        264/343*T^13 + 1882/2401*T^12 - 996/2401*T^11 + 164/2401*T^10 + 820/2401*T^9
        - 1063/2401*T^8 + 1398/2401*T^7 - 1892/2401*T^6 - 300/2401*T^5 - 
        372/2401*T^4 - 65/343*T^3 + 2/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 4*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 +
        2*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 3*X*Y + 4*Y^30 + 
        4*Y^29 + 6*Y^28 + 3*Y^27 + 5*Y^26 + 6*Y^25 + 6*Y^24 + 5*Y^23 + 2*Y^22 + 
        6*Y^21 + 3*Y^20 + Y^19 + 6*Y^18 + 3*Y^16 + Y^15 + Y^14 + 3*Y^13 + 3*Y^12 + 
        Y^11 + 3*Y^10 + 6*Y^9 + Y^8 + 4*Y^7 + 4*Y^6 + 6*Y^5 + 2*Y^4 + 6*Y^3 + 3*Y^2 
        + 3*Y + 2,
    -T^56 - 13/7*T^55 - 85/49*T^54 - T^53 + 1059/2401*T^52 + 1888/2401*T^51 + 
        1971/2401*T^50 + 1602/2401*T^49 + 1138/2401*T^48 + 2118/2401*T^47 + 
        1787/2401*T^46 + 752/2401*T^45 - 1051/2401*T^44 - 2050/2401*T^43 - 
        1577/2401*T^42 + 46/343*T^41 + 1782/2401*T^40 + 278/343*T^39 + 
        1275/2401*T^38 - 64/343*T^37 - 1465/2401*T^36 - 300/343*T^35 - 
        1472/2401*T^34 - 587/2401*T^33 + 43/2401*T^32 + 556/2401*T^31 + 1/2401*T^30 
        - 103/2401*T^29 + 103/2401*T^27 - 1/2401*T^26 - 556/2401*T^25 - 43/2401*T^24
        + 587/2401*T^23 + 1472/2401*T^22 + 300/343*T^21 + 1465/2401*T^20 + 
        64/343*T^19 - 1275/2401*T^18 - 278/343*T^17 - 1782/2401*T^16 - 46/343*T^15 +
        1577/2401*T^14 + 2050/2401*T^13 + 1051/2401*T^12 - 752/2401*T^11 - 
        1787/2401*T^10 - 2118/2401*T^9 - 1138/2401*T^8 - 1602/2401*T^7 - 
        1971/2401*T^6 - 1888/2401*T^5 - 1059/2401*T^4 + T^3 + 85/49*T^2 + 13/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + X*Y^9 + 3*X*Y^8 + 
        5*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + X*Y + 6*X + 
        2*Y^30 + 5*Y^29 + 4*Y^28 + 4*Y^25 + 3*Y^24 + 5*Y^23 + 2*Y^22 + 4*Y^21 + Y^20
        + 4*Y^19 + Y^18 + 5*Y^17 + 6*Y^16 + 5*Y^14 + 3*Y^13 + 4*Y^12 + 3*Y^11 + 
        4*Y^10 + 2*Y^9 + 6*Y^8 + 3*Y^6 + 2*Y^4 + 3*Y^3 + 6*Y^2 + 4*Y + 6,
    T^56 + 16/7*T^55 + 88/49*T^54 + 104/343*T^53 + 327/343*T^52 + 8381/2401*T^51 + 
        201/49*T^50 + 4447/2401*T^49 + 681/2401*T^48 + 4099/2401*T^47 + 
        8626/2401*T^46 + 6026/2401*T^45 + 128/2401*T^44 + 339/2401*T^43 + 
        4745/2401*T^42 + 4204/2401*T^41 - 1107/2401*T^40 - 2746/2401*T^39 + 
        1364/2401*T^38 + 3161/2401*T^37 - 2279/2401*T^36 - 7235/2401*T^35 - 
        11/7*T^34 + 2083/2401*T^33 - 555/2401*T^32 - 8535/2401*T^31 - 
        10169/2401*T^30 - 488/343*T^29 + 1049/2401*T^28 - 488/343*T^27 - 
        10169/2401*T^26 - 8535/2401*T^25 - 555/2401*T^24 + 2083/2401*T^23 - 
        11/7*T^22 - 7235/2401*T^21 - 2279/2401*T^20 + 3161/2401*T^19 + 
        1364/2401*T^18 - 2746/2401*T^17 - 1107/2401*T^16 + 4204/2401*T^15 + 
        4745/2401*T^14 + 339/2401*T^13 + 128/2401*T^12 + 6026/2401*T^11 + 
        8626/2401*T^10 + 4099/2401*T^9 + 681/2401*T^8 + 4447/2401*T^7 + 201/49*T^6 +
        8381/2401*T^5 + 327/343*T^4 + 104/343*T^3 + 88/49*T^2 + 16/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 5*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 3*X*Y^8 + 
        2*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 5*X*Y + 5*X + 4*Y^30 + 6*Y^29 + 
        5*Y^28 + Y^26 + 5*Y^25 + 5*Y^23 + 3*Y^22 + 2*Y^21 + 5*Y^20 + 3*Y^19 + 3*Y^18
        + 4*Y^17 + 4*Y^16 + 5*Y^15 + 2*Y^14 + 2*Y^13 + 3*Y^12 + Y^11 + 5*Y^10 + 
        3*Y^9 + 5*Y^8 + 6*Y^7 + 6*Y^6 + 6*Y^5 + Y^4 + 3*Y^3 + Y + 1,
    -T^56 + 1/7*T^55 - 1/7*T^54 + 16/343*T^53 + 295/2401*T^52 + 1026/2401*T^51 + 
        1690/2401*T^50 - 300/2401*T^49 + 5/2401*T^48 + 15/343*T^47 + 173/2401*T^46 -
        145/2401*T^45 - 2200/2401*T^44 - 19/343*T^43 - 69/2401*T^42 - 1156/2401*T^41
        + 192/2401*T^40 + 1024/2401*T^39 + 589/2401*T^38 + 793/2401*T^37 + 
        73/2401*T^36 - 297/2401*T^35 - 90/2401*T^34 + 225/2401*T^33 - 694/2401*T^32 
        - 86/343*T^31 + 557/2401*T^30 - 59/343*T^29 + 59/343*T^27 - 557/2401*T^26 + 
        86/343*T^25 + 694/2401*T^24 - 225/2401*T^23 + 90/2401*T^22 + 297/2401*T^21 -
        73/2401*T^20 - 793/2401*T^19 - 589/2401*T^18 - 1024/2401*T^17 - 
        192/2401*T^16 + 1156/2401*T^15 + 69/2401*T^14 + 19/343*T^13 + 2200/2401*T^12
        + 145/2401*T^11 - 173/2401*T^10 - 15/343*T^9 - 5/2401*T^8 + 300/2401*T^7 - 
        1690/2401*T^6 - 1026/2401*T^5 - 295/2401*T^4 - 16/343*T^3 + 1/7*T^2 - 1/7*T 
        + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + X*Y^10 + 5*X*Y^9 + 
        6*X*Y^8 + X*Y^7 + 5*X*Y^5 + 3*X*Y^4 + X*Y^3 + 6*X*Y^2 + 4*X*Y + X + 5*Y^30 +
        Y^29 + 3*Y^28 + 6*Y^27 + Y^25 + 2*Y^24 + 2*Y^23 + 2*Y^22 + 3*Y^20 + Y^19 + 
        Y^18 + 4*Y^17 + 4*Y^16 + 4*Y^15 + 4*Y^14 + 6*Y^12 + 3*Y^11 + 2*Y^10 + 6*Y^9 
        + Y^8 + Y^7 + 5*Y^6 + 5*Y^5 + 3*Y^4 + 6*Y^3 + 5*Y^2 + Y + 6,
    -T^56 - T^55 + 9/49*T^54 + 213/343*T^53 + 1031/2401*T^52 - 1471/2401*T^51 - 
        2802/2401*T^50 + 62/2401*T^49 + 2655/2401*T^48 + 134/343*T^47 - 
        1258/2401*T^46 - 732/2401*T^45 + 1636/2401*T^44 + 1779/2401*T^43 - 
        324/2401*T^42 - 2082/2401*T^41 - 592/2401*T^40 + 2670/2401*T^39 + 
        2116/2401*T^38 - 1431/2401*T^37 - 376/343*T^36 - 188/2401*T^35 + 
        1593/2401*T^34 + 940/2401*T^33 - 1920/2401*T^32 - 2517/2401*T^31 - 
        135/2401*T^30 + 1836/2401*T^29 - 1836/2401*T^27 + 135/2401*T^26 + 
        2517/2401*T^25 + 1920/2401*T^24 - 940/2401*T^23 - 1593/2401*T^22 + 
        188/2401*T^21 + 376/343*T^20 + 1431/2401*T^19 - 2116/2401*T^18 - 
        2670/2401*T^17 + 592/2401*T^16 + 2082/2401*T^15 + 324/2401*T^14 - 
        1779/2401*T^13 - 1636/2401*T^12 + 732/2401*T^11 + 1258/2401*T^10 - 
        134/343*T^9 - 2655/2401*T^8 - 62/2401*T^7 + 2802/2401*T^6 + 1471/2401*T^5 - 
        1031/2401*T^4 - 213/343*T^3 - 9/49*T^2 + T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 3*X*Y^9 + 6*X*Y^8 +
        2*X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 4*X*Y + 2*X + 6*Y^30 + 
        4*Y^29 + 2*Y^28 + 3*Y^27 + Y^26 + 5*Y^25 + 6*Y^24 + 5*Y^23 + Y^22 + 3*Y^21 +
        5*Y^19 + 2*Y^18 + 2*Y^17 + 6*Y^16 + Y^15 + Y^14 + 4*Y^13 + 3*Y^12 + 4*Y^11 +
        4*Y^7 + 6*Y^6 + 3*Y^5 + Y^4 + 6*Y^2 + 4*Y + 3,
    -T^56 - 5/7*T^55 - 1/49*T^54 - 36/49*T^53 + 88/343*T^52 + 2385/2401*T^51 + 
        534/2401*T^50 + 2169/2401*T^49 + 2385/2401*T^48 + 1159/2401*T^47 + 
        1577/2401*T^46 - 65/343*T^45 - 864/2401*T^44 - 74/343*T^43 - 325/343*T^42 - 
        1299/2401*T^41 + 198/2401*T^40 - 1280/2401*T^39 + 66/2401*T^38 + 
        1654/2401*T^37 - 199/2401*T^36 + 313/2401*T^35 + 143/343*T^34 - 
        1730/2401*T^33 - 690/2401*T^32 - 66/343*T^31 - 1712/2401*T^30 + 
        270/2401*T^29 - 270/2401*T^27 + 1712/2401*T^26 + 66/343*T^25 + 690/2401*T^24
        + 1730/2401*T^23 - 143/343*T^22 - 313/2401*T^21 + 199/2401*T^20 - 
        1654/2401*T^19 - 66/2401*T^18 + 1280/2401*T^17 - 198/2401*T^16 + 
        1299/2401*T^15 + 325/343*T^14 + 74/343*T^13 + 864/2401*T^12 + 65/343*T^11 - 
        1577/2401*T^10 - 1159/2401*T^9 - 2385/2401*T^8 - 2169/2401*T^7 - 
        534/2401*T^6 - 2385/2401*T^5 - 88/343*T^4 + 36/49*T^3 + 1/49*T^2 + 5/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + X*Y^10 + 3*X*Y^9 + 
        4*X*Y^8 + 3*X*Y^7 + 4*X*Y^4 + 2*X*Y^3 + X*Y^2 + X*Y + 5*X + 6*Y^30 + 2*Y^29 
        + 4*Y^28 + Y^27 + 5*Y^26 + 2*Y^25 + 4*Y^24 + Y^21 + Y^19 + Y^18 + Y^17 + 
        4*Y^16 + 3*Y^14 + 4*Y^13 + 2*Y^12 + 5*Y^11 + Y^10 + 4*Y^9 + 5*Y^7 + 4*Y^6 + 
        5*Y^5 + 3*Y^3 + Y^2 + 4*Y + 1,
    -T^56 - 16/7*T^55 - 20/7*T^54 - 845/343*T^53 - 4411/2401*T^52 - 2227/2401*T^51 +
        620/2401*T^50 + 10/7*T^49 + 4582/2401*T^48 + 4246/2401*T^47 + 445/343*T^46 +
        1104/2401*T^45 - 1230/2401*T^44 - 2027/2401*T^43 - 459/2401*T^42 + 
        2423/2401*T^41 + 3893/2401*T^40 + 631/343*T^39 + 5594/2401*T^38 + 
        7001/2401*T^37 + 5667/2401*T^36 + 3032/2401*T^35 + 143/343*T^34 - 
        816/2401*T^33 - 3592/2401*T^32 - 759/343*T^31 - 4285/2401*T^30 - 
        1861/2401*T^29 + 1861/2401*T^27 + 4285/2401*T^26 + 759/343*T^25 + 
        3592/2401*T^24 + 816/2401*T^23 - 143/343*T^22 - 3032/2401*T^21 - 
        5667/2401*T^20 - 7001/2401*T^19 - 5594/2401*T^18 - 631/343*T^17 - 
        3893/2401*T^16 - 2423/2401*T^15 + 459/2401*T^14 + 2027/2401*T^13 + 
        1230/2401*T^12 - 1104/2401*T^11 - 445/343*T^10 - 4246/2401*T^9 - 
        4582/2401*T^8 - 10/7*T^7 - 620/2401*T^6 + 2227/2401*T^5 + 4411/2401*T^4 + 
        845/343*T^3 + 20/7*T^2 + 16/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 
        + 6*X*Y^8 + X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + X*Y^2 + 5*X*Y + 
        4*X + 6*Y^30 + Y^29 + 2*Y^28 + 5*Y^26 + 4*Y^25 + 6*Y^24 + 6*Y^23 + 6*Y^22 + 
        5*Y^21 + 3*Y^20 + 6*Y^19 + 2*Y^18 + 2*Y^17 + 2*Y^16 + 4*Y^15 + 4*Y^14 + 
        6*Y^13 + 3*Y^12 + 4*Y^11 + 3*Y^10 + 3*Y^9 + 2*Y^8 + 5*Y^7 + 3*Y^6 + 3*Y^5 + 
        6*Y^4 + 6*Y^3 + 2*Y^2 + 1,
    T^56 + T^55 + 3/7*T^54 + 52/343*T^53 - 325/2401*T^52 + 83/343*T^51 + 
        1317/2401*T^50 + 601/2401*T^49 - 1408/2401*T^48 - 1527/2401*T^47 - 
        625/2401*T^46 - 921/2401*T^45 - 689/2401*T^44 - 1747/2401*T^43 - 
        2090/2401*T^42 - 102/2401*T^41 + 1296/2401*T^40 - 298/2401*T^39 - 
        293/2401*T^38 + 1077/2401*T^37 + 1777/2401*T^36 + 1954/2401*T^35 + 
        171/2401*T^34 - 1811/2401*T^33 - 502/2401*T^32 + 1511/2401*T^31 + 
        254/2401*T^30 - 2083/2401*T^29 - 2690/2401*T^28 - 2083/2401*T^27 + 
        254/2401*T^26 + 1511/2401*T^25 - 502/2401*T^24 - 1811/2401*T^23 + 
        171/2401*T^22 + 1954/2401*T^21 + 1777/2401*T^20 + 1077/2401*T^19 - 
        293/2401*T^18 - 298/2401*T^17 + 1296/2401*T^16 - 102/2401*T^15 - 
        2090/2401*T^14 - 1747/2401*T^13 - 689/2401*T^12 - 921/2401*T^11 - 
        625/2401*T^10 - 1527/2401*T^9 - 1408/2401*T^8 + 601/2401*T^7 + 1317/2401*T^6
        + 83/343*T^5 - 325/2401*T^4 + 52/343*T^3 + 3/7*T^2 + T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^13 + 4*X*Y^11 + X*Y^10 + 6*X*Y^9 + 3*X*Y^7 + 4*X*Y^6 + 
        5*X*Y^5 + 5*X*Y^4 + X*Y^3 + 3*X*Y^2 + X*Y + 4*X + 3*Y^30 + 5*Y^28 + 4*Y^27 +
        2*Y^26 + 4*Y^25 + 4*Y^24 + 3*Y^23 + Y^21 + 5*Y^20 + Y^19 + 6*Y^18 + 6*Y^17 +
        3*Y^16 + 2*Y^14 + Y^13 + 4*Y^12 + 3*Y^11 + 5*Y^10 + 5*Y^9 + Y^8 + 2*Y^6 + 
        5*Y^4 + 5*Y^3 + 4*Y^2 + 2*Y + 1,
    -T^56 - 1/7*T^55 + 50/49*T^54 - 104/343*T^53 + 67/343*T^52 + 55/2401*T^51 - 
        2032/2401*T^50 + 55/343*T^49 + 358/2401*T^48 + 163/343*T^47 - 43/343*T^46 - 
        1216/2401*T^45 + 64/2401*T^44 - 1237/2401*T^43 + 207/343*T^42 + 
        1111/2401*T^41 - 649/2401*T^40 - 353/2401*T^39 - 1408/2401*T^38 + 
        552/2401*T^37 + 727/2401*T^36 + 186/2401*T^35 + 225/2401*T^34 - 
        1061/2401*T^33 - 834/2401*T^32 + 389/2401*T^31 + 1833/2401*T^30 + 
        29/343*T^29 - 29/343*T^27 - 1833/2401*T^26 - 389/2401*T^25 + 834/2401*T^24 +
        1061/2401*T^23 - 225/2401*T^22 - 186/2401*T^21 - 727/2401*T^20 - 
        552/2401*T^19 + 1408/2401*T^18 + 353/2401*T^17 + 649/2401*T^16 - 
        1111/2401*T^15 - 207/343*T^14 + 1237/2401*T^13 - 64/2401*T^12 + 
        1216/2401*T^11 + 43/343*T^10 - 163/343*T^9 - 358/2401*T^8 - 55/343*T^7 + 
        2032/2401*T^6 - 55/2401*T^5 - 67/343*T^4 + 104/343*T^3 - 50/49*T^2 + 1/7*T +
        1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + X*Y^10 + 6*X*Y^9 + 
        X*Y^8 + 3*X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 5*X*Y + 5*X + 
        2*Y^30 + 4*Y^29 + 3*Y^28 + 4*Y^26 + 5*Y^25 + 4*Y^24 + 5*Y^23 + Y^22 + 4*Y^21
        + 6*Y^20 + 4*Y^19 + 6*Y^18 + 3*Y^17 + 3*Y^16 + 4*Y^15 + 2*Y^14 + 2*Y^13 + 
        2*Y^12 + 3*Y^11 + 4*Y^10 + 5*Y^9 + 5*Y^8 + 4*Y^7 + 4*Y^6 + 2*Y^5 + 2*Y^4 + 
        2*Y^3 + Y^2 + 1,
    -T^56 + 6/7*T^55 + 11/49*T^54 - 199/343*T^53 - 281/2401*T^52 + 2481/2401*T^51 - 
        1683/2401*T^50 - 73/2401*T^49 + 669/2401*T^48 - 316/2401*T^47 + 61/2401*T^46
        - 330/2401*T^45 + 642/2401*T^44 + 1030/2401*T^43 - 822/2401*T^42 - 
        684/2401*T^41 + 1342/2401*T^40 - 872/2401*T^39 - 1405/2401*T^38 + 
        1837/2401*T^37 - 1317/2401*T^36 + 681/2401*T^35 + 456/2401*T^34 - 
        78/2401*T^33 - 828/2401*T^32 + 1131/2401*T^31 - 1137/2401*T^30 + 
        269/2401*T^29 - 269/2401*T^27 + 1137/2401*T^26 - 1131/2401*T^25 + 
        828/2401*T^24 + 78/2401*T^23 - 456/2401*T^22 - 681/2401*T^21 + 
        1317/2401*T^20 - 1837/2401*T^19 + 1405/2401*T^18 + 872/2401*T^17 - 
        1342/2401*T^16 + 684/2401*T^15 + 822/2401*T^14 - 1030/2401*T^13 - 
        642/2401*T^12 + 330/2401*T^11 - 61/2401*T^10 + 316/2401*T^9 - 669/2401*T^8 +
        73/2401*T^7 + 1683/2401*T^6 - 2481/2401*T^5 + 281/2401*T^4 + 199/343*T^3 - 
        11/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 6*X*Y^13 + 2*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + X*Y^8 + 
        X*Y^7 + 2*X*Y^6 + X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 5*X*Y + 2*Y^30 + 
        5*Y^29 + 6*Y^28 + Y^27 + 5*Y^26 + 2*Y^25 + 4*Y^24 + 3*Y^22 + 5*Y^21 + 3*Y^20
        + 6*Y^18 + 6*Y^17 + 2*Y^16 + 4*Y^15 + 6*Y^14 + 2*Y^12 + 2*Y^11 + 6*Y^9 + 
        4*Y^8 + 6*Y^7 + 6*Y^6 + Y^5 + 3*Y^4 + 2*Y^2 + 6*Y + 3,
    T^56 - 5/7*T^55 - 48/49*T^54 + 246/343*T^53 + 1101/2401*T^52 - 1272/2401*T^51 - 
        328/343*T^50 + 3618/2401*T^49 + 789/2401*T^48 - 1898/2401*T^47 - 
        1055/2401*T^46 + 52/2401*T^45 + 1343/2401*T^44 - 541/2401*T^43 - 
        851/2401*T^42 + 360/2401*T^41 + 2137/2401*T^40 + 858/2401*T^39 - 
        2946/2401*T^38 - 736/2401*T^37 + 2469/2401*T^36 - 509/2401*T^35 - 
        2221/2401*T^34 - 62/2401*T^33 + 3307/2401*T^32 + 503/2401*T^31 - 
        2829/2401*T^30 - 348/2401*T^29 + 298/343*T^28 - 348/2401*T^27 - 
        2829/2401*T^26 + 503/2401*T^25 + 3307/2401*T^24 - 62/2401*T^23 - 
        2221/2401*T^22 - 509/2401*T^21 + 2469/2401*T^20 - 736/2401*T^19 - 
        2946/2401*T^18 + 858/2401*T^17 + 2137/2401*T^16 + 360/2401*T^15 - 
        851/2401*T^14 - 541/2401*T^13 + 1343/2401*T^12 + 52/2401*T^11 - 
        1055/2401*T^10 - 1898/2401*T^9 + 789/2401*T^8 + 3618/2401*T^7 - 328/343*T^6 
        - 1272/2401*T^5 + 1101/2401*T^4 + 246/343*T^3 - 48/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + X*Y^10 + 5*X*Y^9 + 
        4*X*Y^8 + 6*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 3*X*Y + 
        6*X + 4*Y^30 + 3*Y^29 + 4*Y^28 + Y^27 + 3*Y^26 + 6*Y^25 + 5*Y^24 + 5*Y^23 + 
        6*Y^22 + Y^21 + 6*Y^20 + 4*Y^19 + 3*Y^18 + 2*Y^17 + 5*Y^16 + 2*Y^15 + 6*Y^14
        + 2*Y^13 + Y^12 + 3*Y^11 + 5*Y^10 + 6*Y^9 + 2*Y^8 + 4*Y^7 + 2*Y^6 + 2*Y^5 + 
        5*Y^4 + Y^3 + 6*Y^2 + Y + 4,
    T^56 + 9/7*T^55 - 24/49*T^54 - 235/343*T^53 + 3048/2401*T^52 + 3754/2401*T^51 - 
        58/343*T^50 - 919/2401*T^49 + 682/2401*T^48 - 148/2401*T^47 + 220/2401*T^46 
        + 1412/2401*T^45 + 33/2401*T^44 - 1959/2401*T^43 - 92/2401*T^42 + 
        1943/2401*T^41 - 355/2401*T^40 - 2042/2401*T^39 + 1150/2401*T^38 + 
        2736/2401*T^37 - 1742/2401*T^36 - 2949/2401*T^35 + 1404/2401*T^34 + 
        1746/2401*T^33 - 250/343*T^32 - 2167/2401*T^31 - 506/2401*T^30 - 
        411/2401*T^29 - 897/2401*T^28 - 411/2401*T^27 - 506/2401*T^26 - 
        2167/2401*T^25 - 250/343*T^24 + 1746/2401*T^23 + 1404/2401*T^22 - 
        2949/2401*T^21 - 1742/2401*T^20 + 2736/2401*T^19 + 1150/2401*T^18 - 
        2042/2401*T^17 - 355/2401*T^16 + 1943/2401*T^15 - 92/2401*T^14 - 
        1959/2401*T^13 + 33/2401*T^12 + 1412/2401*T^11 + 220/2401*T^10 - 
        148/2401*T^9 + 682/2401*T^8 - 919/2401*T^7 - 58/343*T^6 + 3754/2401*T^5 + 
        3048/2401*T^4 - 235/343*T^3 - 24/49*T^2 + 9/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 6*X*Y^8 + 
        2*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 6*X*Y^2 + 2*Y^30 + Y^29 + 2*Y^28 + 
        2*Y^27 + 5*Y^26 + 5*Y^25 + 3*Y^24 + 5*Y^23 + 6*Y^22 + 2*Y^21 + 3*Y^20 + 
        5*Y^19 + 6*Y^18 + Y^17 + 6*Y^16 + 6*Y^15 + 6*Y^14 + 3*Y^13 + Y^12 + 4*Y^11 +
        6*Y^9 + 3*Y^8 + 4*Y^7 + 6*Y^6 + 2*Y^5 + 5*Y^4 + 4*Y^3 + 6*Y^2 + 6*Y + 4,
    -T^56 - 1/7*T^55 + 39/49*T^54 - 156/343*T^53 + 24/49*T^52 + 759/2401*T^51 - 
        2721/2401*T^50 + 960/2401*T^49 + 649/2401*T^48 - 1334/2401*T^47 + 
        1264/2401*T^46 - 837/2401*T^45 - 485/2401*T^44 + 2298/2401*T^43 - 
        600/2401*T^42 + 1/343*T^41 + 298/343*T^40 - 2080/2401*T^39 - 188/343*T^38 + 
        1511/2401*T^37 - 2/7*T^36 + 298/2401*T^35 + 1233/2401*T^34 - 1272/2401*T^33 
        + 54/343*T^32 + 422/2401*T^31 - 1671/2401*T^30 + 614/2401*T^29 - 
        614/2401*T^27 + 1671/2401*T^26 - 422/2401*T^25 - 54/343*T^24 + 
        1272/2401*T^23 - 1233/2401*T^22 - 298/2401*T^21 + 2/7*T^20 - 1511/2401*T^19 
        + 188/343*T^18 + 2080/2401*T^17 - 298/343*T^16 - 1/343*T^15 + 600/2401*T^14 
        - 2298/2401*T^13 + 485/2401*T^12 + 837/2401*T^11 - 1264/2401*T^10 + 
        1334/2401*T^9 - 649/2401*T^8 - 960/2401*T^7 + 2721/2401*T^6 - 759/2401*T^5 -
        24/49*T^4 + 156/343*T^3 - 39/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        2*X*Y^8 + 3*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + X*Y^3 + 3*X*Y + 5*X + 2*Y^30 + 
        6*Y^29 + 3*Y^28 + Y^27 + Y^26 + 4*Y^25 + 3*Y^24 + Y^22 + 2*Y^21 + 2*Y^20 + 
        5*Y^19 + 3*Y^18 + 6*Y^17 + Y^16 + 6*Y^15 + 3*Y^14 + 3*Y^13 + 3*Y^12 + 2*Y^10
        + 2*Y^9 + 4*Y^8 + 5*Y^7 + 5*Y^6 + 2*Y^3 + Y^2 + 4*Y + 4,
    -T^56 + 31/49*T^54 + 199/343*T^53 + 25/2401*T^52 - 703/2401*T^51 - 
        1230/2401*T^50 - 1321/2401*T^49 + 227/2401*T^48 + 800/2401*T^47 + 
        2421/2401*T^46 - 249/2401*T^45 - 1469/2401*T^44 - 2297/2401*T^43 - 
        1448/2401*T^42 + 1415/2401*T^41 + 2299/2401*T^40 + 1384/2401*T^39 - 
        1695/2401*T^38 - 176/343*T^37 - 1045/2401*T^36 - 614/2401*T^35 + 
        1128/2401*T^34 + 666/2401*T^33 + 289/343*T^32 - 1111/2401*T^31 - 
        1711/2401*T^30 - 743/2401*T^29 + 743/2401*T^27 + 1711/2401*T^26 + 
        1111/2401*T^25 - 289/343*T^24 - 666/2401*T^23 - 1128/2401*T^22 + 
        614/2401*T^21 + 1045/2401*T^20 + 176/343*T^19 + 1695/2401*T^18 - 
        1384/2401*T^17 - 2299/2401*T^16 - 1415/2401*T^15 + 1448/2401*T^14 + 
        2297/2401*T^13 + 1469/2401*T^12 + 249/2401*T^11 - 2421/2401*T^10 - 
        800/2401*T^9 - 227/2401*T^8 + 1321/2401*T^7 + 1230/2401*T^6 + 703/2401*T^5 -
        25/2401*T^4 - 199/343*T^3 - 31/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^13 + 5*X*Y^12 + X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 4*X*Y^8 + 
        3*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 5*X*Y^3 + 4*X*Y^2 + 5*X*Y + 2*X + 5*Y^30 + 
        4*Y^29 + 5*Y^28 + 3*Y^27 + 3*Y^26 + Y^24 + 2*Y^23 + 3*Y^22 + 2*Y^19 + Y^18 +
        4*Y^17 + 6*Y^16 + 5*Y^15 + Y^14 + 2*Y^12 + 4*Y^11 + 2*Y^10 + 6*Y^9 + 5*Y^8 +
        6*Y^7 + 5*Y^6 + 5*Y^5 + 3*Y^3 + 3*Y^2,
    T^56 + 8/7*T^55 + 39/49*T^54 + 15/343*T^53 + 1020/2401*T^52 + 218/2401*T^51 + 
        275/2401*T^50 + 498/2401*T^49 + 1301/2401*T^48 + 823/2401*T^47 - 
        489/2401*T^46 + 281/2401*T^45 + 717/2401*T^44 + 1948/2401*T^43 + 94/343*T^42
        + 832/2401*T^41 - 746/2401*T^40 + 690/2401*T^39 + 41/2401*T^38 - 
        367/2401*T^37 - 1437/2401*T^36 - 1070/2401*T^35 - 1170/2401*T^34 - 
        1508/2401*T^33 + 83/2401*T^32 + 439/2401*T^31 + 961/2401*T^30 - 146/343*T^29
        - 674/2401*T^28 - 146/343*T^27 + 961/2401*T^26 + 439/2401*T^25 + 
        83/2401*T^24 - 1508/2401*T^23 - 1170/2401*T^22 - 1070/2401*T^21 - 
        1437/2401*T^20 - 367/2401*T^19 + 41/2401*T^18 + 690/2401*T^17 - 
        746/2401*T^16 + 832/2401*T^15 + 94/343*T^14 + 1948/2401*T^13 + 717/2401*T^12
        + 281/2401*T^11 - 489/2401*T^10 + 823/2401*T^9 + 1301/2401*T^8 + 
        498/2401*T^7 + 275/2401*T^6 + 218/2401*T^5 + 1020/2401*T^4 + 15/343*T^3 + 
        39/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 2*X*Y^13 + 3*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 5*X*Y^8 + 6*X*Y^7 + 
        6*X*Y^5 + X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 4*X*Y + 6*X + 5*Y^30 + 2*Y^29 + Y^28 +
        2*Y^27 + 5*Y^26 + 2*Y^25 + 5*Y^24 + 6*Y^23 + 2*Y^21 + 6*Y^20 + 2*Y^18 + Y^17
        + 6*Y^16 + 2*Y^15 + 2*Y^14 + 4*Y^13 + 6*Y^12 + 4*Y^10 + 6*Y^9 + 3*Y^8 + 
        5*Y^7 + Y^6 + 5*Y^5 + 6*Y^3 + 3*Y^2 + 5*Y + 5,
    -T^56 + 62/49*T^54 + 141/343*T^53 - 4861/2401*T^52 - 760/2401*T^51 + 
        5227/2401*T^50 + 2349/2401*T^49 - 4652/2401*T^48 - 30/49*T^47 + 
        2970/2401*T^46 + 3406/2401*T^45 - 1711/2401*T^44 - 2374/2401*T^43 - 
        362/2401*T^42 + 2112/2401*T^41 + 242/2401*T^40 - 691/2401*T^39 - 
        2564/2401*T^38 - 894/2401*T^37 + 1937/2401*T^36 + 3049/2401*T^35 - 
        2988/2401*T^34 - 3674/2401*T^33 + 363/343*T^32 + 4306/2401*T^31 - 
        1419/2401*T^30 - 4114/2401*T^29 + 4114/2401*T^27 + 1419/2401*T^26 - 
        4306/2401*T^25 - 363/343*T^24 + 3674/2401*T^23 + 2988/2401*T^22 - 
        3049/2401*T^21 - 1937/2401*T^20 + 894/2401*T^19 + 2564/2401*T^18 + 
        691/2401*T^17 - 242/2401*T^16 - 2112/2401*T^15 + 362/2401*T^14 + 
        2374/2401*T^13 + 1711/2401*T^12 - 3406/2401*T^11 - 2970/2401*T^10 + 
        30/49*T^9 + 4652/2401*T^8 - 2349/2401*T^7 - 5227/2401*T^6 + 760/2401*T^5 + 
        4861/2401*T^4 - 141/343*T^3 - 62/49*T^2 + 1
*], [*
    X^3 + 4*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 5*X*Y^8 +
        2*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + X*Y^2 + X*Y + 3*X + 6*Y^30
        + 5*Y^29 + 6*Y^28 + 3*Y^27 + 4*Y^26 + 5*Y^25 + 3*Y^24 + 3*Y^23 + 2*Y^22 + 
        4*Y^21 + 4*Y^19 + Y^18 + 4*Y^17 + 3*Y^16 + 5*Y^15 + 3*Y^14 + 5*Y^13 + 3*Y^12
        + 2*Y^9 + 6*Y^8 + 6*Y^7 + 6*Y^6 + 2*Y^4 + Y^3 + 3*Y^2 + 4,
    T^56 - 4/7*T^55 + 33/49*T^54 - 51/343*T^53 + 1978/2401*T^52 - 470/2401*T^51 - 
        727/2401*T^50 + 262/343*T^49 - 898/2401*T^48 + 488/2401*T^47 - 481/2401*T^46
        + 407/2401*T^45 - 635/2401*T^44 - 79/2401*T^43 + 456/2401*T^42 - 
        44/2401*T^41 - 447/2401*T^40 + 195/343*T^39 + 64/2401*T^38 - 93/2401*T^37 + 
        11/343*T^36 + 1000/2401*T^35 - 138/2401*T^34 - 433/2401*T^33 + 837/2401*T^32
        + 256/2401*T^31 - 356/2401*T^30 - 478/2401*T^29 + 1452/2401*T^28 - 
        478/2401*T^27 - 356/2401*T^26 + 256/2401*T^25 + 837/2401*T^24 - 
        433/2401*T^23 - 138/2401*T^22 + 1000/2401*T^21 + 11/343*T^20 - 93/2401*T^19 
        + 64/2401*T^18 + 195/343*T^17 - 447/2401*T^16 - 44/2401*T^15 + 456/2401*T^14
        - 79/2401*T^13 - 635/2401*T^12 + 407/2401*T^11 - 481/2401*T^10 + 
        488/2401*T^9 - 898/2401*T^8 + 262/343*T^7 - 727/2401*T^6 - 470/2401*T^5 + 
        1978/2401*T^4 - 51/343*T^3 + 33/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 
        4*X*Y^8 + X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 5*X*Y + 
        X + 3*Y^30 + 4*Y^29 + 2*Y^28 + 2*Y^27 + 5*Y^26 + 3*Y^24 + 4*Y^23 + 4*Y^22 + 
        5*Y^21 + 4*Y^20 + Y^19 + Y^18 + 3*Y^17 + 5*Y^16 + 6*Y^15 + 4*Y^14 + Y^13 + 
        2*Y^12 + 5*Y^11 + 3*Y^10 + 5*Y^9 + 6*Y^8 + 3*Y^7 + 3*Y^6 + 6*Y^5 + Y^4 + 
        3*Y^3 + 4*Y^2,
    T^56 - 6/7*T^55 - 4/7*T^54 + 9/49*T^53 - 27/2401*T^52 + 2222/2401*T^51 - 
        1546/2401*T^50 - 1336/2401*T^49 + 2698/2401*T^48 + 367/2401*T^47 - 
        1100/2401*T^46 - 68/343*T^45 - 1594/2401*T^44 + 198/343*T^43 + 
        1614/2401*T^42 - 1943/2401*T^41 + 246/2401*T^40 + 690/2401*T^39 + 
        319/2401*T^38 + 633/2401*T^37 - 1798/2401*T^36 - 851/2401*T^35 + 
        1318/2401*T^34 + 457/2401*T^33 + 275/2401*T^32 - 9/343*T^31 - 300/2401*T^30 
        + 15/2401*T^29 - 275/2401*T^28 + 15/2401*T^27 - 300/2401*T^26 - 9/343*T^25 +
        275/2401*T^24 + 457/2401*T^23 + 1318/2401*T^22 - 851/2401*T^21 - 
        1798/2401*T^20 + 633/2401*T^19 + 319/2401*T^18 + 690/2401*T^17 + 
        246/2401*T^16 - 1943/2401*T^15 + 1614/2401*T^14 + 198/343*T^13 - 
        1594/2401*T^12 - 68/343*T^11 - 1100/2401*T^10 + 367/2401*T^9 + 2698/2401*T^8
        - 1336/2401*T^7 - 1546/2401*T^6 + 2222/2401*T^5 - 27/2401*T^4 + 9/49*T^3 - 
        4/7*T^2 - 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 5*X*Y^13 + X*Y^12 + 4*X*Y^11 + X*Y^10 + 3*X*Y^9 + 
        2*X*Y^8 + X*Y^7 + X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + X*Y^2 + X*Y + 3*X + 
        4*Y^30 + 4*Y^29 + 6*Y^28 + 4*Y^27 + 5*Y^26 + 5*Y^24 + 6*Y^23 + 2*Y^22 + 
        6*Y^20 + Y^19 + 4*Y^18 + 6*Y^17 + 6*Y^16 + 4*Y^14 + 2*Y^13 + Y^12 + 3*Y^11 +
        2*Y^9 + Y^8 + 6*Y^7 + 6*Y^6 + 6*Y^5 + 2*Y^4 + 4*Y^3 + 3*Y^2 + 4*Y + 1,
    T^56 + 1/7*T^55 + 1/49*T^54 - 117/343*T^53 + 34/2401*T^52 + 705/2401*T^51 + 
        432/2401*T^50 - 283/2401*T^49 - 2454/2401*T^48 - 44/49*T^47 - 906/2401*T^46 
        + 50/343*T^45 - 253/2401*T^44 + 73/2401*T^43 - 2081/2401*T^42 + 
        436/2401*T^41 + 1187/2401*T^40 + 2676/2401*T^39 + 1042/2401*T^38 + 
        267/2401*T^37 - 262/2401*T^36 + 738/2401*T^35 + 1527/2401*T^34 + 
        933/2401*T^33 - 410/2401*T^32 - 1997/2401*T^31 - 528/2401*T^30 - 
        1194/2401*T^29 + 16/49*T^28 - 1194/2401*T^27 - 528/2401*T^26 - 
        1997/2401*T^25 - 410/2401*T^24 + 933/2401*T^23 + 1527/2401*T^22 + 
        738/2401*T^21 - 262/2401*T^20 + 267/2401*T^19 + 1042/2401*T^18 + 
        2676/2401*T^17 + 1187/2401*T^16 + 436/2401*T^15 - 2081/2401*T^14 + 
        73/2401*T^13 - 253/2401*T^12 + 50/343*T^11 - 906/2401*T^10 - 44/49*T^9 - 
        2454/2401*T^8 - 283/2401*T^7 + 432/2401*T^6 + 705/2401*T^5 + 34/2401*T^4 - 
        117/343*T^3 + 1/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 5*X*Y^12 + 6*X*Y^11 + X*Y^10 + 5*X*Y^9 + 5*X*Y^8 + X*Y^7 + 
        2*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + X*Y + X + 5*Y^30 + 3*Y^29 + 4*Y^28 +
        2*Y^27 + 5*Y^26 + 2*Y^25 + 6*Y^24 + 2*Y^23 + 5*Y^22 + 6*Y^21 + 6*Y^19 + 
        2*Y^18 + 4*Y^17 + 2*Y^16 + 4*Y^14 + 5*Y^13 + Y^12 + 5*Y^11 + 4*Y^10 + 3*Y^8 
        + 2*Y^7 + Y^6 + 5*Y^5 + 4*Y^4 + 4*Y^3 + 4*Y^2 + 3*Y + 1,
    -T^56 + 9/7*T^55 - 16/49*T^54 + 276/343*T^53 - 81/49*T^52 + 1441/2401*T^51 + 
        1845/2401*T^50 + 1591/2401*T^49 - 2617/2401*T^48 - 2676/2401*T^47 + 
        2747/2401*T^46 + 703/2401*T^45 + 1579/2401*T^44 - 639/343*T^43 + 
        634/2401*T^42 + 1621/2401*T^41 + 508/2401*T^40 + 73/2401*T^39 - 
        1809/2401*T^38 + 197/343*T^37 - 159/343*T^36 + 991/2401*T^35 - 13/49*T^34 + 
        1744/2401*T^33 - 1588/2401*T^32 - 1663/2401*T^31 + 1278/2401*T^30 + 
        1630/2401*T^29 - 1630/2401*T^27 - 1278/2401*T^26 + 1663/2401*T^25 + 
        1588/2401*T^24 - 1744/2401*T^23 + 13/49*T^22 - 991/2401*T^21 + 159/343*T^20 
        - 197/343*T^19 + 1809/2401*T^18 - 73/2401*T^17 - 508/2401*T^16 - 
        1621/2401*T^15 - 634/2401*T^14 + 639/343*T^13 - 1579/2401*T^12 - 
        703/2401*T^11 - 2747/2401*T^10 + 2676/2401*T^9 + 2617/2401*T^8 - 
        1591/2401*T^7 - 1845/2401*T^6 - 1441/2401*T^5 + 81/49*T^4 - 276/343*T^3 + 
        16/49*T^2 - 9/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 4*X*Y^12 + 5*X*Y^11 + X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 
        3*X*Y^7 + 6*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + X*Y^2 + 3*X*Y + 4*X + Y^30 + Y^29 + 
        4*Y^28 + 6*Y^27 + 4*Y^26 + 2*Y^25 + 6*Y^24 + 3*Y^23 + 3*Y^22 + 3*Y^20 + Y^18
        + 3*Y^17 + 6*Y^16 + 5*Y^15 + 2*Y^14 + 3*Y^13 + 2*Y^12 + Y^11 + 5*Y^10 + 
        4*Y^9 + Y^8 + 3*Y^7 + 3*Y^6 + Y^5 + Y^3 + 4*Y^2 + Y + 3,
    T^56 + 6/7*T^55 + 31/49*T^54 + 15/49*T^53 + 877/2401*T^52 + 898/2401*T^51 + 
        1270/2401*T^50 + 219/343*T^49 + 157/343*T^48 - 115/2401*T^47 - 549/2401*T^46
        + 323/2401*T^45 + 223/2401*T^44 + 320/2401*T^43 + 605/2401*T^42 + 
        131/2401*T^41 - 654/2401*T^40 - 531/2401*T^39 - 1061/2401*T^38 - 
        1002/2401*T^37 - 681/2401*T^36 + 72/2401*T^35 - 190/2401*T^34 - 3/343*T^33 +
        87/2401*T^32 + 332/2401*T^31 - 15/343*T^30 + 811/2401*T^29 + 1730/2401*T^28 
        + 811/2401*T^27 - 15/343*T^26 + 332/2401*T^25 + 87/2401*T^24 - 3/343*T^23 - 
        190/2401*T^22 + 72/2401*T^21 - 681/2401*T^20 - 1002/2401*T^19 - 
        1061/2401*T^18 - 531/2401*T^17 - 654/2401*T^16 + 131/2401*T^15 + 
        605/2401*T^14 + 320/2401*T^13 + 223/2401*T^12 + 323/2401*T^11 - 
        549/2401*T^10 - 115/2401*T^9 + 157/343*T^8 + 219/343*T^7 + 1270/2401*T^6 + 
        898/2401*T^5 + 877/2401*T^4 + 15/49*T^3 + 31/49*T^2 + 6/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 
        5*X*Y^8 + 6*X*Y^7 + 5*X*Y^6 + 4*X*Y^5 + 4*X*Y^3 + 2*X*Y^2 + 3*X + Y^30 + 
        4*Y^28 + 3*Y^27 + Y^26 + 3*Y^24 + 3*Y^23 + 4*Y^22 + 3*Y^19 + 4*Y^18 + 3*Y^17
        + 5*Y^16 + 6*Y^15 + 4*Y^14 + 6*Y^13 + 3*Y^12 + 3*Y^10 + 3*Y^8 + 3*Y^7 + 
        6*Y^6 + 6*Y^5 + 5*Y^2 + 5*Y + 5,
    -T^56 - 1/7*T^55 - 3/49*T^54 - 188/343*T^53 - 1574/2401*T^52 + 134/343*T^51 - 
        1010/2401*T^50 + 1340/2401*T^49 + 212/2401*T^48 + 1230/2401*T^47 + 
        93/343*T^46 + 5/7*T^45 + 87/2401*T^44 + 946/2401*T^43 - 424/2401*T^42 + 
        429/2401*T^41 - 188/343*T^40 + 180/2401*T^39 - 172/2401*T^38 - 746/2401*T^37
        + 173/2401*T^36 + 841/2401*T^35 - 355/2401*T^34 + 74/343*T^33 + 
        860/2401*T^32 + 306/2401*T^31 + 373/2401*T^30 + 4/2401*T^29 - 4/2401*T^27 - 
        373/2401*T^26 - 306/2401*T^25 - 860/2401*T^24 - 74/343*T^23 + 355/2401*T^22 
        - 841/2401*T^21 - 173/2401*T^20 + 746/2401*T^19 + 172/2401*T^18 - 
        180/2401*T^17 + 188/343*T^16 - 429/2401*T^15 + 424/2401*T^14 - 946/2401*T^13
        - 87/2401*T^12 - 5/7*T^11 - 93/343*T^10 - 1230/2401*T^9 - 212/2401*T^8 - 
        1340/2401*T^7 + 1010/2401*T^6 - 134/343*T^5 + 1574/2401*T^4 + 188/343*T^3 + 
        3/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 3*X*Y^9 + 
        5*X*Y^8 + 6*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + X*Y^4 + X*Y^3 + 5*X*Y^2 + 4*X*Y + X 
        + 3*Y^30 + 5*Y^29 + Y^28 + 2*Y^27 + 3*Y^26 + 2*Y^25 + 5*Y^24 + 4*Y^22 + 
        5*Y^20 + 5*Y^19 + 4*Y^18 + Y^17 + 4*Y^16 + 4*Y^15 + 4*Y^14 + 4*Y^13 + Y^12 +
        5*Y^10 + 3*Y^9 + 6*Y^8 + 4*Y^7 + 3*Y^5 + Y^4 + 2*Y^3 + 4*Y^2 + 5*Y + 3,
    T^56 + 5/7*T^55 - 4/49*T^54 + 170/343*T^53 + 1906/2401*T^52 + 562/2401*T^51 + 
        968/2401*T^50 + 1832/2401*T^49 + 54/343*T^48 - 172/2401*T^47 + 186/2401*T^46
        + 61/2401*T^45 + 641/2401*T^44 + 184/2401*T^43 - 1544/2401*T^42 - 
        1710/2401*T^41 - 557/2401*T^40 - 1317/2401*T^39 - 1962/2401*T^38 - 
        383/2401*T^37 - 395/2401*T^36 - 1480/2401*T^35 - 1300/2401*T^34 - 
        570/2401*T^33 + 18/343*T^32 + 101/2401*T^31 - 362/2401*T^30 - 15/343*T^29 - 
        5/343*T^28 - 15/343*T^27 - 362/2401*T^26 + 101/2401*T^25 + 18/343*T^24 - 
        570/2401*T^23 - 1300/2401*T^22 - 1480/2401*T^21 - 395/2401*T^20 - 
        383/2401*T^19 - 1962/2401*T^18 - 1317/2401*T^17 - 557/2401*T^16 - 
        1710/2401*T^15 - 1544/2401*T^14 + 184/2401*T^13 + 641/2401*T^12 + 
        61/2401*T^11 + 186/2401*T^10 - 172/2401*T^9 + 54/343*T^8 + 1832/2401*T^7 + 
        968/2401*T^6 + 562/2401*T^5 + 1906/2401*T^4 + 170/343*T^3 - 4/49*T^2 + 5/7*T
        + 1
*], [*
    X^3 + 4*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + X*Y^10 + 2*X*Y^9 + 3*X*Y^8 + 
        2*X*Y^7 + 5*X*Y^6 + 6*X*Y^4 + 4*X*Y^3 + X*Y + 5*Y^30 + 4*Y^29 + 3*Y^27 + 
        2*Y^26 + 6*Y^25 + 5*Y^24 + 2*Y^23 + 2*Y^22 + Y^21 + 3*Y^20 + 6*Y^19 + 2*Y^18
        + 6*Y^17 + 4*Y^16 + 2*Y^15 + 6*Y^14 + 5*Y^13 + 6*Y^12 + 3*Y^11 + 3*Y^10 + 
        3*Y^8 + 5*Y^6 + 5*Y^5 + 4*Y^4 + 2*Y^3 + 6*Y^2 + 2*Y + 5,
    T^56 + 9/7*T^55 - 3/7*T^54 - 563/343*T^53 - 4478/2401*T^52 - 2560/2401*T^51 + 
        2409/2401*T^50 + 4061/2401*T^49 + 696/2401*T^48 - 143/343*T^47 - 
        1097/2401*T^46 - 618/2401*T^45 + 1032/2401*T^44 + 1486/2401*T^43 + 
        85/343*T^42 + 223/2401*T^41 + 179/2401*T^40 - 986/2401*T^39 - 1226/2401*T^38
        + 829/2401*T^37 + 2116/2401*T^36 + 1598/2401*T^35 + 880/2401*T^34 - 
        2115/2401*T^33 - 4220/2401*T^32 - 2069/2401*T^31 - 181/2401*T^30 + 
        2006/2401*T^29 + 3910/2401*T^28 + 2006/2401*T^27 - 181/2401*T^26 - 
        2069/2401*T^25 - 4220/2401*T^24 - 2115/2401*T^23 + 880/2401*T^22 + 
        1598/2401*T^21 + 2116/2401*T^20 + 829/2401*T^19 - 1226/2401*T^18 - 
        986/2401*T^17 + 179/2401*T^16 + 223/2401*T^15 + 85/343*T^14 + 1486/2401*T^13
        + 1032/2401*T^12 - 618/2401*T^11 - 1097/2401*T^10 - 143/343*T^9 + 
        696/2401*T^8 + 4061/2401*T^7 + 2409/2401*T^6 - 2560/2401*T^5 - 4478/2401*T^4
        - 563/343*T^3 - 3/7*T^2 + 9/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 
        + 4*X*Y^7 + 3*X*Y^6 + 2*X*Y^4 + 4*X*Y^2 + 2*X*Y + X + 6*Y^30 + 5*Y^29 + 
        3*Y^28 + Y^27 + 6*Y^26 + 3*Y^25 + 4*Y^24 + Y^23 + 3*Y^22 + Y^19 + 5*Y^18 + 
        2*Y^17 + 6*Y^16 + 4*Y^14 + Y^13 + 6*Y^12 + Y^10 + 5*Y^9 + 2*Y^8 + Y^7 + Y^6 
        + 5*Y^5 + 3*Y^2 + 5*Y + 4,
    -T^56 + 6/7*T^55 - 4/49*T^54 - 149/343*T^53 + 92/2401*T^52 + 327/2401*T^51 + 
        198/2401*T^50 + 269/2401*T^49 - 61/343*T^48 + 736/2401*T^47 + 396/2401*T^46 
        + 65/2401*T^45 - 24/343*T^44 + 1032/2401*T^43 - 570/2401*T^42 - 
        101/2401*T^41 - 65/2401*T^40 + 1123/2401*T^39 - 1352/2401*T^38 + 
        46/2401*T^37 - 240/2401*T^36 - 59/2401*T^35 + 73/2401*T^34 - 1450/2401*T^33 
        + 954/2401*T^32 + 167/2401*T^31 - 722/2401*T^30 + 144/2401*T^29 - 
        144/2401*T^27 + 722/2401*T^26 - 167/2401*T^25 - 954/2401*T^24 + 
        1450/2401*T^23 - 73/2401*T^22 + 59/2401*T^21 + 240/2401*T^20 - 46/2401*T^19 
        + 1352/2401*T^18 - 1123/2401*T^17 + 65/2401*T^16 + 101/2401*T^15 + 
        570/2401*T^14 - 1032/2401*T^13 + 24/343*T^12 - 65/2401*T^11 - 396/2401*T^10 
        - 736/2401*T^9 + 61/343*T^8 - 269/2401*T^7 - 198/2401*T^6 - 327/2401*T^5 - 
        92/2401*T^4 + 149/343*T^3 + 4/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 6*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 4*X*Y^8 +
        X*Y^7 + X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 5*X*Y + 4*X + 3*Y^30
        + 6*Y^29 + 4*Y^28 + 3*Y^27 + 5*Y^26 + Y^25 + 4*Y^24 + 3*Y^23 + 5*Y^22 + 
        4*Y^21 + 4*Y^20 + 3*Y^18 + 4*Y^17 + 6*Y^16 + 5*Y^14 + 2*Y^12 + 3*Y^11 + 
        5*Y^10 + 4*Y^8 + 5*Y^7 + 5*Y^6 + 3*Y^5 + Y^4 + Y^2 + 4*Y + 4,
    -T^56 + 2*T^55 - 104/49*T^54 + 547/343*T^53 - 1245/2401*T^52 - 2662/2401*T^51 + 
        4583/2401*T^50 - 2936/2401*T^49 - 362/2401*T^48 + 2021/2401*T^47 - 
        2201/2401*T^46 + 611/2401*T^45 + 2295/2401*T^44 - 4009/2401*T^43 + 
        2909/2401*T^42 - 1126/2401*T^41 + 106/343*T^40 - 1110/2401*T^39 + 
        2414/2401*T^38 - 4898/2401*T^37 + 873/343*T^36 - 4339/2401*T^35 + 
        1594/2401*T^34 + 242/2401*T^33 - 1100/2401*T^32 + 807/2401*T^31 + 
        353/2401*T^30 - 694/2401*T^29 + 694/2401*T^27 - 353/2401*T^26 - 
        807/2401*T^25 + 1100/2401*T^24 - 242/2401*T^23 - 1594/2401*T^22 + 
        4339/2401*T^21 - 873/343*T^20 + 4898/2401*T^19 - 2414/2401*T^18 + 
        1110/2401*T^17 - 106/343*T^16 + 1126/2401*T^15 - 2909/2401*T^14 + 
        4009/2401*T^13 - 2295/2401*T^12 - 611/2401*T^11 + 2201/2401*T^10 - 
        2021/2401*T^9 + 362/2401*T^8 + 2936/2401*T^7 - 4583/2401*T^6 + 2662/2401*T^5
        + 1245/2401*T^4 - 547/343*T^3 + 104/49*T^2 - 2*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + X*Y^10 + X*Y^7 + 
        4*X*Y^6 + 6*X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 2*X*Y + 5*X + 2*Y^30 + 
        Y^28 + Y^26 + Y^25 + 2*Y^24 + 4*Y^23 + Y^22 + 4*Y^21 + 5*Y^20 + 4*Y^19 + 
        5*Y^18 + 3*Y^17 + 3*Y^16 + 5*Y^15 + Y^14 + Y^13 + 5*Y^12 + 5*Y^11 + Y^10 + 
        5*Y^9 + Y^6 + 2*Y^5 + 4*Y^4 + 3*Y^3 + 5*Y^2 + 2*Y + 1,
    -T^56 - 3/7*T^55 + 13/49*T^54 + 131/343*T^53 + 2108/2401*T^52 + 779/2401*T^51 - 
        1264/2401*T^50 - 2288/2401*T^49 - 1749/2401*T^48 + 1023/2401*T^47 + 
        2876/2401*T^46 + 1438/2401*T^45 + 778/2401*T^44 - 2388/2401*T^43 - 
        3204/2401*T^42 - 612/2401*T^41 + 1070/2401*T^40 + 2496/2401*T^39 + 
        1214/2401*T^38 - 1558/2401*T^37 - 2600/2401*T^36 - 1045/2401*T^35 + 
        2008/2401*T^34 + 2621/2401*T^33 + 1755/2401*T^32 - 298/2401*T^31 - 
        2410/2401*T^30 - 2516/2401*T^29 + 2516/2401*T^27 + 2410/2401*T^26 + 
        298/2401*T^25 - 1755/2401*T^24 - 2621/2401*T^23 - 2008/2401*T^22 + 
        1045/2401*T^21 + 2600/2401*T^20 + 1558/2401*T^19 - 1214/2401*T^18 - 
        2496/2401*T^17 - 1070/2401*T^16 + 612/2401*T^15 + 3204/2401*T^14 + 
        2388/2401*T^13 - 778/2401*T^12 - 1438/2401*T^11 - 2876/2401*T^10 - 
        1023/2401*T^9 + 1749/2401*T^8 + 2288/2401*T^7 + 1264/2401*T^6 - 779/2401*T^5
        - 2108/2401*T^4 - 131/343*T^3 - 13/49*T^2 + 3/7*T + 1
*], [*
    X^3 + X*Y^14 + X*Y^13 + 5*X*Y^11 + 2*X*Y^10 + 4*X*Y^9 + 2*X*Y^8 + 4*X*Y^7 + 
        3*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + X*Y^2 + X*Y + 2*X + 6*Y^30 + 6*Y^29 
        + 5*Y^28 + 3*Y^27 + 4*Y^24 + Y^23 + 3*Y^22 + 6*Y^20 + 6*Y^19 + Y^18 + 3*Y^17
        + 5*Y^15 + Y^14 + 5*Y^12 + 2*Y^11 + 2*Y^10 + 3*Y^9 + 6*Y^8 + 6*Y^7 + 6*Y^6 +
        6*Y^5 + 2*Y^4 + 6*Y^3 + 4*Y^2 + Y + 4,
    T^56 - 6/7*T^55 - 18/49*T^54 + 334/343*T^53 + 382/2401*T^52 - 1501/2401*T^51 - 
        58/343*T^50 + 241/343*T^49 - 1378/2401*T^48 + 44/2401*T^47 + 1194/2401*T^46 
        - 2606/2401*T^45 + 1268/2401*T^44 + 1026/2401*T^43 - 1430/2401*T^42 - 
        48/2401*T^41 + 739/2401*T^40 - 193/2401*T^39 - 757/2401*T^38 + 
        1156/2401*T^37 - 1301/2401*T^36 - 352/2401*T^35 + 771/2401*T^34 - 
        687/2401*T^33 + 41/2401*T^32 + 212/343*T^31 - 1429/2401*T^30 - 180/2401*T^29
        + 2083/2401*T^28 - 180/2401*T^27 - 1429/2401*T^26 + 212/343*T^25 + 
        41/2401*T^24 - 687/2401*T^23 + 771/2401*T^22 - 352/2401*T^21 - 
        1301/2401*T^20 + 1156/2401*T^19 - 757/2401*T^18 - 193/2401*T^17 + 
        739/2401*T^16 - 48/2401*T^15 - 1430/2401*T^14 + 1026/2401*T^13 + 
        1268/2401*T^12 - 2606/2401*T^11 + 1194/2401*T^10 + 44/2401*T^9 - 
        1378/2401*T^8 + 241/343*T^7 - 58/343*T^6 - 1501/2401*T^5 + 382/2401*T^4 + 
        334/343*T^3 - 18/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 
        X*Y^8 + X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + X*Y^2 + 3*X*Y + 3*X + 3*Y^30 +
        6*Y^29 + 2*Y^28 + Y^27 + 5*Y^26 + 6*Y^25 + 5*Y^24 + 3*Y^23 + 4*Y^22 + 3*Y^20
        + Y^19 + 4*Y^18 + 3*Y^17 + Y^16 + Y^15 + 3*Y^14 + 6*Y^13 + 3*Y^12 + 6*Y^11 +
        6*Y^10 + 3*Y^9 + 3*Y^8 + 4*Y^7 + 3*Y^6 + 2*Y^5 + Y^4 + Y^3 + 6*Y^2 + 2*Y + 
        3,
    T^56 + 4/7*T^55 + 12/49*T^54 + 193/343*T^53 + 111/2401*T^52 - 907/2401*T^51 - 
        172/2401*T^50 + 1146/2401*T^49 - 669/2401*T^48 - 171/2401*T^47 + 
        108/343*T^46 - 513/2401*T^45 - 1285/2401*T^44 - 800/2401*T^43 - 
        2256/2401*T^42 - 58/49*T^41 - 916/2401*T^40 - 639/2401*T^39 - 999/2401*T^38 
        - 585/2401*T^37 + 206/2401*T^36 - 51/343*T^35 + 107/2401*T^34 + 
        1014/2401*T^33 + 24/343*T^32 + 1/7*T^31 + 201/343*T^30 + 2106/2401*T^29 + 
        2671/2401*T^28 + 2106/2401*T^27 + 201/343*T^26 + 1/7*T^25 + 24/343*T^24 + 
        1014/2401*T^23 + 107/2401*T^22 - 51/343*T^21 + 206/2401*T^20 - 585/2401*T^19
        - 999/2401*T^18 - 639/2401*T^17 - 916/2401*T^16 - 58/49*T^15 - 
        2256/2401*T^14 - 800/2401*T^13 - 1285/2401*T^12 - 513/2401*T^11 + 
        108/343*T^10 - 171/2401*T^9 - 669/2401*T^8 + 1146/2401*T^7 - 172/2401*T^6 - 
        907/2401*T^5 + 111/2401*T^4 + 193/343*T^3 + 12/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + 5*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 2*X*Y^7 +
        3*X*Y^6 + 4*X*Y^5 + 6*X*Y^3 + 4*X*Y^2 + 5*X*Y + 6*X + 2*Y^30 + Y^29 + 2*Y^27
        + 3*Y^26 + 6*Y^24 + 5*Y^23 + 5*Y^22 + 2*Y^21 + 5*Y^20 + 3*Y^18 + 6*Y^17 + 
        6*Y^16 + Y^15 + Y^14 + 5*Y^12 + 4*Y^11 + Y^10 + 5*Y^8 + 6*Y^5 + 2*Y^4 + 
        6*Y^3 + 4*Y^2 + Y + 6,
    -T^56 + 29/49*T^54 + 44/343*T^53 - 764/2401*T^52 + 1655/2401*T^51 + 
        853/2401*T^50 - 1187/2401*T^49 - 1238/2401*T^48 + 468/2401*T^47 + 
        818/2401*T^46 - 706/2401*T^45 - 830/2401*T^44 + 929/2401*T^43 + 
        425/2401*T^42 - 1551/2401*T^41 - 576/2401*T^40 + 1013/2401*T^39 + 
        115/2401*T^38 - 697/2401*T^37 + 177/2401*T^36 + 228/343*T^35 - 408/2401*T^34
        - 932/2401*T^33 + 1/343*T^32 + 856/2401*T^31 - 305/2401*T^30 - 558/2401*T^29
        + 558/2401*T^27 + 305/2401*T^26 - 856/2401*T^25 - 1/343*T^24 + 932/2401*T^23
        + 408/2401*T^22 - 228/343*T^21 - 177/2401*T^20 + 697/2401*T^19 - 
        115/2401*T^18 - 1013/2401*T^17 + 576/2401*T^16 + 1551/2401*T^15 - 
        425/2401*T^14 - 929/2401*T^13 + 830/2401*T^12 + 706/2401*T^11 - 
        818/2401*T^10 - 468/2401*T^9 + 1238/2401*T^8 + 1187/2401*T^7 - 853/2401*T^6 
        - 1655/2401*T^5 + 764/2401*T^4 - 44/343*T^3 - 29/49*T^2 + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^9 + 4*X*Y^8 + 2*X*Y^7 + 
        2*X*Y^6 + X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + 6*X*Y + 2*Y^30 + 3*Y^29 + Y^27 + Y^26 
        + 4*Y^25 + 6*Y^24 + 4*Y^23 + 3*Y^22 + 3*Y^21 + 6*Y^20 + 5*Y^18 + 3*Y^17 + 
        Y^16 + 5*Y^15 + 5*Y^14 + 2*Y^13 + 4*Y^12 + 2*Y^11 + 5*Y^10 + 5*Y^9 + 6*Y^8 +
        Y^7 + 5*Y^5 + 3*Y^4 + 6*Y^2 + 5*Y + 2,
    -T^56 - 4/7*T^55 + 19/49*T^54 - 4/343*T^53 - 1520/2401*T^52 - 832/2401*T^51 + 
        786/2401*T^50 + 1591/2401*T^49 + 759/2401*T^48 - 610/2401*T^47 + 
        669/2401*T^46 + 1401/2401*T^45 + 358/2401*T^44 - 94/343*T^43 - 288/343*T^42 
        + 247/2401*T^41 + 885/2401*T^40 - 739/2401*T^39 - 2090/2401*T^38 + 9/49*T^37
        + 2841/2401*T^36 + 180/343*T^35 - 1630/2401*T^34 - 683/2401*T^33 + 
        2899/2401*T^32 + 1710/2401*T^31 - 341/2401*T^30 - 1182/2401*T^29 + 
        1182/2401*T^27 + 341/2401*T^26 - 1710/2401*T^25 - 2899/2401*T^24 + 
        683/2401*T^23 + 1630/2401*T^22 - 180/343*T^21 - 2841/2401*T^20 - 9/49*T^19 +
        2090/2401*T^18 + 739/2401*T^17 - 885/2401*T^16 - 247/2401*T^15 + 
        288/343*T^14 + 94/343*T^13 - 358/2401*T^12 - 1401/2401*T^11 - 669/2401*T^10 
        + 610/2401*T^9 - 759/2401*T^8 - 1591/2401*T^7 - 786/2401*T^6 + 832/2401*T^5 
        + 1520/2401*T^4 + 4/343*T^3 - 19/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 3*X*Y^10 + 6*X*Y^9 + X*Y^8 + 5*X*Y^7 + 
        3*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 2*X*Y + 5*X + 5*Y^30 + 
        5*Y^29 + 5*Y^28 + 5*Y^27 + 5*Y^25 + 6*Y^24 + Y^23 + 3*Y^22 + 6*Y^21 + 5*Y^20
        + 5*Y^19 + Y^18 + 2*Y^17 + 4*Y^16 + 5*Y^15 + 5*Y^14 + 3*Y^13 + 4*Y^11 + 
        5*Y^10 + 3*Y^9 + 3*Y^8 + 3*Y^7 + 4*Y^6 + 5*Y^5 + 6*Y^4 + 5*Y^3 + 6*Y^2 + 4*Y
        + 2,
    T^56 + 2/7*T^55 - 27/49*T^54 - 160/343*T^53 - 258/343*T^52 - 1882/2401*T^51 - 
        583/2401*T^50 + 1972/2401*T^49 + 1370/2401*T^48 + 82/343*T^47 + 
        1070/2401*T^46 + 233/2401*T^45 - 130/343*T^44 - 468/2401*T^43 + 
        991/2401*T^42 + 663/2401*T^41 - 503/2401*T^40 - 1248/2401*T^39 - 
        1818/2401*T^38 - 752/2401*T^37 + 81/2401*T^36 + 1933/2401*T^35 + 
        2094/2401*T^34 + 1121/2401*T^33 - 907/2401*T^31 - 97/2401*T^30 - 
        710/2401*T^29 - 1548/2401*T^28 - 710/2401*T^27 - 97/2401*T^26 - 
        907/2401*T^25 + 1121/2401*T^23 + 2094/2401*T^22 + 1933/2401*T^21 + 
        81/2401*T^20 - 752/2401*T^19 - 1818/2401*T^18 - 1248/2401*T^17 - 
        503/2401*T^16 + 663/2401*T^15 + 991/2401*T^14 - 468/2401*T^13 - 130/343*T^12
        + 233/2401*T^11 + 1070/2401*T^10 + 82/343*T^9 + 1370/2401*T^8 + 
        1972/2401*T^7 - 583/2401*T^6 - 1882/2401*T^5 - 258/343*T^4 - 160/343*T^3 - 
        27/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 +
        2*X*Y^7 + 4*X*Y^6 + 6*X*Y^3 + 2*X*Y^2 + X + 6*Y^30 + 4*Y^29 + 5*Y^28 + 
        5*Y^27 + 4*Y^26 + 3*Y^25 + 6*Y^24 + 5*Y^23 + 3*Y^22 + 5*Y^21 + 2*Y^20 + 
        3*Y^19 + 2*Y^18 + 4*Y^17 + Y^16 + 6*Y^15 + 2*Y^14 + 3*Y^13 + 5*Y^12 + 3*Y^11
        + 4*Y^10 + 3*Y^9 + 5*Y^8 + 6*Y^7 + 6*Y^6 + 5*Y^5 + 3*Y^4 + 2*Y^3 + 5*Y^2 + 
        2*Y + 3,
    T^56 + 6/7*T^55 - 9/49*T^54 - 69/343*T^53 + 258/2401*T^52 - 2512/2401*T^51 - 
        2243/2401*T^50 + 122/343*T^49 + 638/2401*T^48 - 1557/2401*T^47 - 
        724/2401*T^46 - 52/2401*T^45 - 488/2401*T^44 + 340/2401*T^43 + 
        1531/2401*T^42 + 1448/2401*T^41 + 677/2401*T^40 - 521/2401*T^39 - 
        597/2401*T^38 + 1009/2401*T^37 + 347/2401*T^36 - 115/2401*T^35 + 33/49*T^34 
        + 1483/2401*T^33 - 355/343*T^32 - 1700/2401*T^31 + 988/2401*T^30 - 
        324/2401*T^29 - 2778/2401*T^28 - 324/2401*T^27 + 988/2401*T^26 - 
        1700/2401*T^25 - 355/343*T^24 + 1483/2401*T^23 + 33/49*T^22 - 115/2401*T^21 
        + 347/2401*T^20 + 1009/2401*T^19 - 597/2401*T^18 - 521/2401*T^17 + 
        677/2401*T^16 + 1448/2401*T^15 + 1531/2401*T^14 + 340/2401*T^13 - 
        488/2401*T^12 - 52/2401*T^11 - 724/2401*T^10 - 1557/2401*T^9 + 638/2401*T^8 
        + 122/343*T^7 - 2243/2401*T^6 - 2512/2401*T^5 + 258/2401*T^4 - 69/343*T^3 - 
        9/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 5*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + X*Y^8 + 
        3*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + X*Y^4 + 4*X*Y^3 + 5*X*Y + 6*X + 3*Y^30 + 
        4*Y^29 + 4*Y^28 + 5*Y^27 + 2*Y^26 + 5*Y^25 + Y^23 + 2*Y^22 + 3*Y^20 + 5*Y^19
        + 5*Y^18 + 2*Y^17 + 5*Y^16 + Y^15 + 3*Y^14 + 2*Y^12 + 5*Y^11 + Y^10 + 6*Y^8 
        + 5*Y^7 + 6*Y^6 + 2*Y^5 + 3*Y^4 + 3*Y^2 + 3*Y + 4,
    -T^56 - 3/7*T^55 + 9/49*T^54 + 396/343*T^53 + 2020/2401*T^52 - 3144/2401*T^51 - 
        2061/2401*T^50 + 142/2401*T^49 + 4706/2401*T^48 + 2797/2401*T^47 - 
        2770/2401*T^46 - 4684/2401*T^45 - 2834/2401*T^44 + 524/343*T^43 + 
        3474/2401*T^42 + 495/2401*T^41 - 3575/2401*T^40 - 72/49*T^39 + 
        1326/2401*T^38 + 2466/2401*T^37 + 2012/2401*T^36 - 1637/2401*T^35 - 
        1933/2401*T^34 - 36/2401*T^33 + 817/2401*T^32 + 1867/2401*T^31 - 
        174/2401*T^30 + 365/2401*T^29 - 365/2401*T^27 + 174/2401*T^26 - 
        1867/2401*T^25 - 817/2401*T^24 + 36/2401*T^23 + 1933/2401*T^22 + 
        1637/2401*T^21 - 2012/2401*T^20 - 2466/2401*T^19 - 1326/2401*T^18 + 
        72/49*T^17 + 3575/2401*T^16 - 495/2401*T^15 - 3474/2401*T^14 - 524/343*T^13 
        + 2834/2401*T^12 + 4684/2401*T^11 + 2770/2401*T^10 - 2797/2401*T^9 - 
        4706/2401*T^8 - 142/2401*T^7 + 2061/2401*T^6 + 3144/2401*T^5 - 2020/2401*T^4
        - 396/343*T^3 - 9/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 6*X*Y^13 + X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 4*X*Y^9 + 
        5*X*Y^8 + 5*X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 6*X*Y 
        + 3*Y^30 + 2*Y^29 + 2*Y^28 + 5*Y^27 + 2*Y^26 + 6*Y^25 + Y^24 + 6*Y^23 + 
        2*Y^22 + 6*Y^21 + 2*Y^20 + 3*Y^19 + 4*Y^17 + 2*Y^16 + 2*Y^15 + 5*Y^14 + 
        6*Y^12 + 6*Y^11 + 5*Y^10 + 2*Y^9 + 3*Y^8 + 6*Y^7 + 2*Y^6 + Y^5 + 2*Y^4 + 
        3*Y^3 + 5*Y^2 + 4*Y + 5,
    T^56 + 8/7*T^55 + 10/49*T^54 - 219/343*T^53 - 1619/2401*T^52 - 894/2401*T^51 - 
        1228/2401*T^50 - 1585/2401*T^49 - 405/2401*T^48 + 675/2401*T^47 + 
        529/2401*T^46 + 762/2401*T^45 - 292/2401*T^44 - 499/2401*T^43 - 61/2401*T^42
        + 1367/2401*T^41 + 1370/2401*T^40 + 281/2401*T^39 - 128/343*T^38 - 
        1405/2401*T^37 - 253/343*T^36 - 1107/2401*T^35 + 493/2401*T^34 + 
        1202/2401*T^33 + 200/343*T^32 + 1178/2401*T^31 + 120/343*T^30 - 
        808/2401*T^29 - 1737/2401*T^28 - 808/2401*T^27 + 120/343*T^26 + 
        1178/2401*T^25 + 200/343*T^24 + 1202/2401*T^23 + 493/2401*T^22 - 
        1107/2401*T^21 - 253/343*T^20 - 1405/2401*T^19 - 128/343*T^18 + 
        281/2401*T^17 + 1370/2401*T^16 + 1367/2401*T^15 - 61/2401*T^14 - 
        499/2401*T^13 - 292/2401*T^12 + 762/2401*T^11 + 529/2401*T^10 + 675/2401*T^9
        - 405/2401*T^8 - 1585/2401*T^7 - 1228/2401*T^6 - 894/2401*T^5 - 
        1619/2401*T^4 - 219/343*T^3 + 10/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + X*Y^12 + X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 
        4*X*Y^8 + 4*X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 2*X*Y + X + 
        2*Y^30 + 5*Y^29 + 3*Y^28 + Y^27 + Y^26 + Y^25 + 2*Y^24 + 3*Y^23 + 4*Y^22 + 
        6*Y^21 + 6*Y^20 + 6*Y^19 + 4*Y^18 + 5*Y^17 + 6*Y^16 + 4*Y^15 + 3*Y^14 + 
        3*Y^13 + 6*Y^12 + 4*Y^10 + 4*Y^9 + 2*Y^8 + 4*Y^7 + 4*Y^6 + 2*Y^5 + 2*Y^4 + 
        6*Y,
    -T^56 - 1/7*T^55 + 38/49*T^54 + 122/343*T^53 + 214/343*T^52 - 1977/2401*T^51 - 
        1598/2401*T^50 + 299/343*T^49 + 654/2401*T^48 + 992/2401*T^47 - 
        283/2401*T^46 - 1522/2401*T^45 + 696/2401*T^44 + 30/2401*T^43 - 
        346/2401*T^42 + 169/2401*T^41 - 150/2401*T^40 + 155/2401*T^39 - 
        1275/2401*T^38 - 415/2401*T^37 + 181/343*T^36 + 775/2401*T^35 + 
        446/2401*T^34 - 1788/2401*T^33 - 1870/2401*T^32 + 290/2401*T^31 + 
        1364/2401*T^30 + 2054/2401*T^29 - 2054/2401*T^27 - 1364/2401*T^26 - 
        290/2401*T^25 + 1870/2401*T^24 + 1788/2401*T^23 - 446/2401*T^22 - 
        775/2401*T^21 - 181/343*T^20 + 415/2401*T^19 + 1275/2401*T^18 - 
        155/2401*T^17 + 150/2401*T^16 - 169/2401*T^15 + 346/2401*T^14 - 30/2401*T^13
        - 696/2401*T^12 + 1522/2401*T^11 + 283/2401*T^10 - 992/2401*T^9 - 
        654/2401*T^8 - 299/343*T^7 + 1598/2401*T^6 + 1977/2401*T^5 - 214/343*T^4 - 
        122/343*T^3 - 38/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        6*X*Y^8 + 3*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 6*X + 
        4*Y^30 + Y^29 + 3*Y^28 + 5*Y^27 + Y^26 + 5*Y^25 + Y^24 + 2*Y^23 + 3*Y^22 + 
        5*Y^21 + 3*Y^20 + 6*Y^19 + 6*Y^18 + 3*Y^16 + 4*Y^15 + 5*Y^14 + 5*Y^13 + 
        4*Y^12 + Y^10 + 3*Y^9 + 4*Y^7 + 6*Y^6 + 5*Y^5 + 2*Y^4 + Y^2 + 2*Y + 6,
    T^56 + 12/7*T^55 + 87/49*T^54 + 60/49*T^53 + 3216/2401*T^52 + 2909/2401*T^51 + 
        775/2401*T^50 - 41/49*T^49 - 1838/2401*T^48 - 918/2401*T^47 - 1086/2401*T^46
        - 2490/2401*T^45 - 1758/2401*T^44 + 142/2401*T^43 - 576/2401*T^42 - 
        2116/2401*T^41 - 50/49*T^40 - 907/2401*T^39 - 1684/2401*T^38 - 
        3688/2401*T^37 - 599/343*T^36 - 1517/2401*T^35 + 51/2401*T^34 - 
        234/2401*T^33 - 319/2401*T^32 + 2438/2401*T^31 + 4012/2401*T^30 + 
        2966/2401*T^29 + 1832/2401*T^28 + 2966/2401*T^27 + 4012/2401*T^26 + 
        2438/2401*T^25 - 319/2401*T^24 - 234/2401*T^23 + 51/2401*T^22 - 
        1517/2401*T^21 - 599/343*T^20 - 3688/2401*T^19 - 1684/2401*T^18 - 
        907/2401*T^17 - 50/49*T^16 - 2116/2401*T^15 - 576/2401*T^14 + 142/2401*T^13 
        - 1758/2401*T^12 - 2490/2401*T^11 - 1086/2401*T^10 - 918/2401*T^9 - 
        1838/2401*T^8 - 41/49*T^7 + 775/2401*T^6 + 2909/2401*T^5 + 3216/2401*T^4 + 
        60/49*T^3 + 87/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + X*Y^11 + 2*X*Y^10 + 4*X*Y^9 + 6*X*Y^8 + 
        5*X*Y^7 + 2*X*Y^6 + 5*X*Y^4 + X*Y^3 + 5*X*Y^2 + 6*X*Y + X + 3*Y^30 + 5*Y^28 
        + 2*Y^27 + 6*Y^26 + 2*Y^25 + 5*Y^24 + Y^22 + 3*Y^21 + 6*Y^20 + Y^19 + 6*Y^18
        + 5*Y^17 + 2*Y^16 + 5*Y^15 + Y^14 + 3*Y^13 + 2*Y^11 + 3*Y^10 + 6*Y^9 + 5*Y^8
        + 6*Y^7 + 2*Y^6 + 4*Y^4 + 5*Y^3 + 5*Y^2 + 5*Y,
    T^56 - 4/7*T^55 + 46/49*T^54 - 177/343*T^53 + 710/2401*T^52 + 229/2401*T^51 - 
        2993/2401*T^50 + 2281/2401*T^49 - 3669/2401*T^48 + 2008/2401*T^47 - 
        1681/2401*T^46 + 1261/2401*T^45 + 1073/2401*T^44 + 138/343*T^43 + 
        2146/2401*T^42 - 193/2401*T^41 + 1699/2401*T^40 - 1503/2401*T^39 + 
        824/2401*T^38 - 1628/2401*T^37 - 877/2401*T^36 - 510/2401*T^35 - 
        909/2401*T^34 + 32/343*T^33 - 656/2401*T^32 + 475/2401*T^31 + 1175/2401*T^30
        + 358/2401*T^29 + 1016/2401*T^28 + 358/2401*T^27 + 1175/2401*T^26 + 
        475/2401*T^25 - 656/2401*T^24 + 32/343*T^23 - 909/2401*T^22 - 510/2401*T^21 
        - 877/2401*T^20 - 1628/2401*T^19 + 824/2401*T^18 - 1503/2401*T^17 + 
        1699/2401*T^16 - 193/2401*T^15 + 2146/2401*T^14 + 138/343*T^13 + 
        1073/2401*T^12 + 1261/2401*T^11 - 1681/2401*T^10 + 2008/2401*T^9 - 
        3669/2401*T^8 + 2281/2401*T^7 - 2993/2401*T^6 + 229/2401*T^5 + 710/2401*T^4 
        - 177/343*T^3 + 46/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 2*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 3*X*Y^9 + 3*X*Y^8 + 
        6*X*Y^7 + X*Y^6 + 2*X*Y^5 + 4*X*Y^2 + 3*X + Y^30 + 4*Y^29 + 4*Y^28 + 6*Y^27 
        + 6*Y^26 + 6*Y^25 + 6*Y^24 + 5*Y^22 + 2*Y^21 + 5*Y^20 + Y^19 + 4*Y^18 + 
        2*Y^17 + 4*Y^16 + 5*Y^15 + 4*Y^14 + 3*Y^11 + Y^10 + 2*Y^9 + 3*Y^8 + Y^7 + 
        Y^6 + 3*Y^5 + Y^4 + 6*Y^3 + 2*Y^2 + 6*Y + 5,
    -T^56 + 5/7*T^55 + 8/7*T^54 - 71/49*T^53 - 106/2401*T^52 + 250/343*T^51 + 
        649/2401*T^50 - 1675/2401*T^49 - 1131/2401*T^48 + 2991/2401*T^47 - 
        453/2401*T^46 - 2239/2401*T^45 + 1151/2401*T^44 + 1744/2401*T^43 - 
        663/2401*T^42 - 1312/2401*T^41 + 809/2401*T^40 + 1740/2401*T^39 - 
        1636/2401*T^38 - 195/343*T^37 + 2304/2401*T^36 - 382/2401*T^35 - 
        1641/2401*T^34 + 762/2401*T^33 + 1054/2401*T^32 - 960/2401*T^31 - 
        142/343*T^30 + 1763/2401*T^29 - 1763/2401*T^27 + 142/343*T^26 + 
        960/2401*T^25 - 1054/2401*T^24 - 762/2401*T^23 + 1641/2401*T^22 + 
        382/2401*T^21 - 2304/2401*T^20 + 195/343*T^19 + 1636/2401*T^18 - 
        1740/2401*T^17 - 809/2401*T^16 + 1312/2401*T^15 + 663/2401*T^14 - 
        1744/2401*T^13 - 1151/2401*T^12 + 2239/2401*T^11 + 453/2401*T^10 - 
        2991/2401*T^9 + 1131/2401*T^8 + 1675/2401*T^7 - 649/2401*T^6 - 250/343*T^5 +
        106/2401*T^4 + 71/49*T^3 - 8/7*T^2 - 5/7*T + 1
*], [*
    X^3 + 6*X*Y^13 + 2*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + X*Y^8 + 5*X*Y^7 + 5*X*Y^6 + 
        3*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 6*X*Y + 6*X + 4*Y^30 + 4*Y^28 + Y^27 + 5*Y^26 
        + 3*Y^25 + 5*Y^24 + Y^23 + Y^22 + 4*Y^21 + 2*Y^19 + Y^18 + 5*Y^17 + 3*Y^16 +
        4*Y^15 + Y^14 + 6*Y^13 + 2*Y^12 + 5*Y^11 + 4*Y^10 + 4*Y^9 + 3*Y^8 + Y^7 + 
        5*Y^6 + 5*Y^5 + Y^4 + 5*Y^3 + 6*Y^2 + 2*Y + 4,
    -T^56 + 4/7*T^55 + 18/49*T^54 + 82/343*T^53 - 2320/2401*T^52 + 1626/2401*T^51 + 
        341/2401*T^50 + 2049/2401*T^49 - 1887/2401*T^48 + 2/343*T^47 - 576/2401*T^46
        + 2033/2401*T^45 - 853/2401*T^44 - 489/2401*T^43 - 1431/2401*T^42 + 
        1405/2401*T^41 + 464/2401*T^40 - 81/343*T^39 - 1821/2401*T^38 + 
        1006/2401*T^37 + 1023/2401*T^36 + 473/2401*T^35 - 1499/2401*T^34 - 
        568/2401*T^33 + 129/343*T^32 + 1719/2401*T^31 - 134/343*T^30 - 
        1451/2401*T^29 + 1451/2401*T^27 + 134/343*T^26 - 1719/2401*T^25 - 
        129/343*T^24 + 568/2401*T^23 + 1499/2401*T^22 - 473/2401*T^21 - 
        1023/2401*T^20 - 1006/2401*T^19 + 1821/2401*T^18 + 81/343*T^17 - 
        464/2401*T^16 - 1405/2401*T^15 + 1431/2401*T^14 + 489/2401*T^13 + 
        853/2401*T^12 - 2033/2401*T^11 + 576/2401*T^10 - 2/343*T^9 + 1887/2401*T^8 -
        2049/2401*T^7 - 341/2401*T^6 - 1626/2401*T^5 + 2320/2401*T^4 - 82/343*T^3 - 
        18/49*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 
        6*X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 2*X*Y 
        + X + 5*Y^30 + 3*Y^29 + 4*Y^28 + 5*Y^27 + 2*Y^25 + Y^24 + 5*Y^23 + 6*Y^21 + 
        6*Y^19 + 2*Y^18 + 2*Y^17 + 6*Y^14 + 4*Y^13 + 5*Y^12 + 2*Y^11 + 6*Y^10 + 
        2*Y^9 + 6*Y^8 + 2*Y^7 + 4*Y^6 + 3*Y^5 + 5*Y^4 + 2*Y^3 + 4,
    -T^56 + 1/7*T^55 + 48/49*T^54 + 65/343*T^53 - 611/2401*T^52 - 467/2401*T^51 - 
        768/2401*T^50 - 90/2401*T^49 + 1513/2401*T^48 + 29/49*T^47 - 1265/2401*T^46 
        - 1574/2401*T^45 + 2176/2401*T^44 - 181/2401*T^43 - 26/49*T^42 + 
        137/343*T^41 - 465/2401*T^40 - 2038/2401*T^39 + 1123/2401*T^38 + 
        1576/2401*T^37 - 1095/2401*T^36 - 1184/2401*T^35 + 162/343*T^34 + 
        915/2401*T^33 - 898/2401*T^32 + 1410/2401*T^31 + 503/2401*T^30 - 
        3196/2401*T^29 + 3196/2401*T^27 - 503/2401*T^26 - 1410/2401*T^25 + 
        898/2401*T^24 - 915/2401*T^23 - 162/343*T^22 + 1184/2401*T^21 + 
        1095/2401*T^20 - 1576/2401*T^19 - 1123/2401*T^18 + 2038/2401*T^17 + 
        465/2401*T^16 - 137/343*T^15 + 26/49*T^14 + 181/2401*T^13 - 2176/2401*T^12 +
        1574/2401*T^11 + 1265/2401*T^10 - 29/49*T^9 - 1513/2401*T^8 + 90/2401*T^7 + 
        768/2401*T^6 + 467/2401*T^5 + 611/2401*T^4 - 65/343*T^3 - 48/49*T^2 - 1/7*T 
        + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 2*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 3*X*Y^8 + X*Y^6 + 
        4*X*Y^4 + 5*X*Y^3 + X*Y^2 + 6*X*Y + 5*X + 5*Y^30 + Y^29 + 5*Y^28 + Y^27 + 
        2*Y^26 + 4*Y^25 + 4*Y^24 + 3*Y^23 + 6*Y^22 + 3*Y^20 + 5*Y^19 + 3*Y^18 + 
        2*Y^17 + 4*Y^15 + Y^14 + 3*Y^13 + 2*Y^12 + 5*Y^11 + 5*Y^10 + 4*Y^9 + 5*Y^8 +
        3*Y^6 + Y^5 + 3*Y^4 + Y^3 + 5*Y^2 + 4*Y + 2,
    -T^56 + 8/7*T^55 + 6/49*T^54 - 173/343*T^53 + 1368/2401*T^52 - 249/2401*T^51 - 
        691/2401*T^50 - 453/2401*T^49 + 2038/2401*T^48 - 3853/2401*T^47 + 
        3281/2401*T^46 - 1000/2401*T^45 - 156/343*T^44 + 1779/2401*T^43 - 
        386/2401*T^42 - 32/2401*T^41 - 123/343*T^40 + 1978/2401*T^39 - 
        2402/2401*T^38 + 1831/2401*T^37 - 264/343*T^36 + 1152/2401*T^35 + 
        681/2401*T^34 - 1622/2401*T^33 + 1362/2401*T^32 - 940/2401*T^31 - 
        170/2401*T^30 + 1290/2401*T^29 - 1290/2401*T^27 + 170/2401*T^26 + 
        940/2401*T^25 - 1362/2401*T^24 + 1622/2401*T^23 - 681/2401*T^22 - 
        1152/2401*T^21 + 264/343*T^20 - 1831/2401*T^19 + 2402/2401*T^18 - 
        1978/2401*T^17 + 123/343*T^16 + 32/2401*T^15 + 386/2401*T^14 - 
        1779/2401*T^13 + 156/343*T^12 + 1000/2401*T^11 - 3281/2401*T^10 + 
        3853/2401*T^9 - 2038/2401*T^8 + 453/2401*T^7 + 691/2401*T^6 + 249/2401*T^5 -
        1368/2401*T^4 + 173/343*T^3 - 6/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + X*Y^11 + 3*X*Y^9 + 5*X*Y^8 + 5*X*Y^7 + 
        3*X*Y^6 + 6*X*Y^5 + X*Y^3 + 6*X*Y^2 + X*Y + 5*Y^30 + 6*Y^28 + Y^27 + Y^26 + 
        4*Y^25 + 3*Y^24 + 5*Y^23 + 4*Y^22 + Y^21 + 5*Y^20 + 6*Y^19 + 6*Y^17 + 5*Y^15
        + Y^14 + Y^13 + 2*Y^12 + 5*Y^11 + 5*Y^10 + 3*Y^9 + Y^8 + Y^6 + 6*Y^5 + 6*Y^4
        + 6*Y^2 + 5*Y + 6,
    -T^56 + 4/7*T^55 + 3/7*T^54 - 302/343*T^53 + 1/2401*T^52 + 316/2401*T^51 + 
        2218/2401*T^50 - 1471/2401*T^49 - 1262/2401*T^48 + 1745/2401*T^47 + 
        17/2401*T^46 + 39/2401*T^45 - 1349/2401*T^44 + 1509/2401*T^43 - 
        612/2401*T^42 + 1016/2401*T^41 + 1374/2401*T^40 - 2235/2401*T^39 + 
        1699/2401*T^38 - 386/2401*T^37 + 992/2401*T^36 - 2367/2401*T^35 - 
        969/2401*T^34 + 3141/2401*T^33 - 240/343*T^32 - 24/2401*T^31 - 
        1256/2401*T^30 + 2675/2401*T^29 - 2675/2401*T^27 + 1256/2401*T^26 + 
        24/2401*T^25 + 240/343*T^24 - 3141/2401*T^23 + 969/2401*T^22 + 
        2367/2401*T^21 - 992/2401*T^20 + 386/2401*T^19 - 1699/2401*T^18 + 
        2235/2401*T^17 - 1374/2401*T^16 - 1016/2401*T^15 + 612/2401*T^14 - 
        1509/2401*T^13 + 1349/2401*T^12 - 39/2401*T^11 - 17/2401*T^10 - 
        1745/2401*T^9 + 1262/2401*T^8 + 1471/2401*T^7 - 2218/2401*T^6 - 316/2401*T^5
        - 1/2401*T^4 + 302/343*T^3 - 3/7*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 
        + 3*X*Y^5 + 5*X*Y^2 + 5*X*Y + 5*X + 2*Y^30 + Y^29 + 6*Y^28 + 6*Y^27 + 4*Y^26
        + Y^25 + 2*Y^24 + 2*Y^23 + 2*Y^21 + 6*Y^20 + 2*Y^19 + 6*Y^18 + 3*Y^17 + 
        6*Y^16 + 2*Y^15 + 4*Y^14 + 6*Y^12 + 5*Y^11 + 4*Y^10 + Y^9 + 2*Y^8 + Y^6 + 
        6*Y^5 + 3*Y^4 + 3*Y^3 + Y^2 + 6*Y + 2,
    T^56 - 3/7*T^55 - 31/49*T^54 + 122/343*T^53 + 1341/2401*T^52 - 675/2401*T^51 - 
        90/343*T^50 + 257/2401*T^49 + 104/343*T^48 - 1374/2401*T^47 - 86/2401*T^46 -
        857/2401*T^45 + 1163/2401*T^44 + 600/2401*T^43 - 796/2401*T^42 - 51/343*T^41
        + 701/2401*T^40 + 503/2401*T^39 - 1102/2401*T^38 + 761/2401*T^37 + 
        1397/2401*T^36 - 40/343*T^35 - 709/2401*T^34 + 120/2401*T^33 + 2/343*T^32 - 
        142/2401*T^31 - 57/343*T^30 + 669/2401*T^29 - 2147/2401*T^28 + 669/2401*T^27
        - 57/343*T^26 - 142/2401*T^25 + 2/343*T^24 + 120/2401*T^23 - 709/2401*T^22 -
        40/343*T^21 + 1397/2401*T^20 + 761/2401*T^19 - 1102/2401*T^18 + 
        503/2401*T^17 + 701/2401*T^16 - 51/343*T^15 - 796/2401*T^14 + 600/2401*T^13 
        + 1163/2401*T^12 - 857/2401*T^11 - 86/2401*T^10 - 1374/2401*T^9 + 
        104/343*T^8 + 257/2401*T^7 - 90/343*T^6 - 675/2401*T^5 + 1341/2401*T^4 + 
        122/343*T^3 - 31/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^13 + X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + X*Y^8 + 3*X*Y^7 + 
        3*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 4*X + 5*Y^30 + 6*Y^29 + 2*Y^28 + 2*Y^27 + 
        6*Y^26 + Y^25 + 2*Y^24 + 6*Y^23 + 4*Y^22 + 2*Y^21 + 6*Y^20 + 5*Y^18 + 6*Y^17
        + 3*Y^16 + 3*Y^15 + 5*Y^14 + 5*Y^13 + 2*Y^12 + 2*Y^11 + 6*Y^10 + 6*Y^9 + 
        4*Y^8 + 5*Y^6 + 4*Y^5 + 6*Y^4 + 2*Y^3 + 3*Y^2 + 4*Y + 4,
    T^56 - 45/49*T^54 - 66/343*T^53 + 496/2401*T^52 - 408/2401*T^51 - 51/343*T^50 + 
        1416/2401*T^49 + 1301/2401*T^48 + 501/2401*T^47 - 1213/2401*T^46 - 
        19/343*T^45 - 92/343*T^44 - 478/2401*T^43 + 68/2401*T^42 + 101/2401*T^41 + 
        277/2401*T^40 + 72/2401*T^39 + 269/2401*T^38 + 667/2401*T^37 + 505/2401*T^36
        - 27/343*T^35 + 361/2401*T^34 - 544/2401*T^33 - 2139/2401*T^32 - 
        1405/2401*T^31 + 991/2401*T^30 + 1115/2401*T^29 + 428/2401*T^28 + 
        1115/2401*T^27 + 991/2401*T^26 - 1405/2401*T^25 - 2139/2401*T^24 - 
        544/2401*T^23 + 361/2401*T^22 - 27/343*T^21 + 505/2401*T^20 + 667/2401*T^19 
        + 269/2401*T^18 + 72/2401*T^17 + 277/2401*T^16 + 101/2401*T^15 + 
        68/2401*T^14 - 478/2401*T^13 - 92/343*T^12 - 19/343*T^11 - 1213/2401*T^10 + 
        501/2401*T^9 + 1301/2401*T^8 + 1416/2401*T^7 - 51/343*T^6 - 408/2401*T^5 + 
        496/2401*T^4 - 66/343*T^3 - 45/49*T^2 + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 4*X*Y + 
        6*X + 6*Y^30 + 3*Y^29 + 4*Y^28 + 5*Y^27 + 2*Y^26 + 2*Y^25 + 6*Y^24 + Y^23 + 
        6*Y^21 + Y^20 + 5*Y^19 + 4*Y^18 + 4*Y^17 + 5*Y^16 + 4*Y^15 + Y^13 + 6*Y^11 +
        4*Y^10 + 4*Y^8 + 4*Y^7 + Y^5 + 5*Y^4 + 6*Y + 5,
    T^56 + 5/7*T^55 - 4/7*T^54 - 104/343*T^53 - 221/343*T^52 - 2694/2401*T^51 - 
        192/2401*T^50 + 1445/2401*T^49 + 731/2401*T^48 + 1718/2401*T^47 + 
        103/2401*T^46 - 2027/2401*T^45 - 1574/2401*T^44 - 796/2401*T^43 + 
        1604/2401*T^42 + 1935/2401*T^41 + 824/2401*T^40 + 94/2401*T^39 - 
        123/343*T^38 - 1268/2401*T^37 - 15/2401*T^36 + 31/343*T^35 + 674/2401*T^34 +
        2868/2401*T^33 + 860/2401*T^32 - 1737/2401*T^31 - 247/2401*T^30 - 
        96/343*T^29 - 2629/2401*T^28 - 96/343*T^27 - 247/2401*T^26 - 1737/2401*T^25 
        + 860/2401*T^24 + 2868/2401*T^23 + 674/2401*T^22 + 31/343*T^21 - 
        15/2401*T^20 - 1268/2401*T^19 - 123/343*T^18 + 94/2401*T^17 + 824/2401*T^16 
        + 1935/2401*T^15 + 1604/2401*T^14 - 796/2401*T^13 - 1574/2401*T^12 - 
        2027/2401*T^11 + 103/2401*T^10 + 1718/2401*T^9 + 731/2401*T^8 + 
        1445/2401*T^7 - 192/2401*T^6 - 2694/2401*T^5 - 221/343*T^4 - 104/343*T^3 - 
        4/7*T^2 + 5/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + 
        5*X*Y^8 + 2*X*Y^7 + X*Y^6 + X*Y^3 + 5*X*Y^2 + 4*X + 4*Y^30 + 4*Y^29 + 6*Y^28
        + 6*Y^27 + 5*Y^26 + 3*Y^24 + 2*Y^23 + 5*Y^22 + Y^21 + 2*Y^20 + 5*Y^19 + 
        5*Y^18 + 3*Y^17 + 3*Y^16 + 4*Y^15 + 6*Y^13 + 2*Y^12 + 2*Y^11 + Y^10 + Y^9 + 
        Y^8 + 3*Y^7 + 2*Y^6 + 5*Y^5 + 4*Y^4 + Y^2 + 3*Y + 4,
    -T^56 + 1/7*T^55 - 17/49*T^54 - 230/343*T^53 + 1261/2401*T^52 - 2594/2401*T^51 +
        453/2401*T^50 - 1494/2401*T^49 - 1745/2401*T^48 + 376/2401*T^47 - 
        1874/2401*T^46 + 631/2401*T^45 - 157/343*T^44 + 29/343*T^43 - 2109/2401*T^42
        - 948/2401*T^41 - 96/2401*T^40 - 2235/2401*T^39 + 1714/2401*T^38 - 
        2022/2401*T^37 + 1033/2401*T^36 - 102/343*T^35 - 1709/2401*T^34 + 
        1313/2401*T^33 - 2151/2401*T^32 + 1290/2401*T^31 - 544/2401*T^30 + 
        613/2401*T^29 - 613/2401*T^27 + 544/2401*T^26 - 1290/2401*T^25 + 
        2151/2401*T^24 - 1313/2401*T^23 + 1709/2401*T^22 + 102/343*T^21 - 
        1033/2401*T^20 + 2022/2401*T^19 - 1714/2401*T^18 + 2235/2401*T^17 + 
        96/2401*T^16 + 948/2401*T^15 + 2109/2401*T^14 - 29/343*T^13 + 157/343*T^12 -
        631/2401*T^11 + 1874/2401*T^10 - 376/2401*T^9 + 1745/2401*T^8 + 
        1494/2401*T^7 - 453/2401*T^6 + 2594/2401*T^5 - 1261/2401*T^4 + 230/343*T^3 +
        17/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + X*Y^12 + X*Y^11 + X*Y^10 + 3*X*Y^9 + 
        5*X*Y^8 + 3*X*Y^7 + 4*X*Y^6 + X*Y^5 + X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 5*X*Y + 
        2*Y^30 + Y^28 + 3*Y^27 + 5*Y^26 + 6*Y^25 + Y^24 + Y^23 + 4*Y^22 + 3*Y^21 + 
        2*Y^18 + 5*Y^17 + 2*Y^14 + 2*Y^13 + 2*Y^12 + 4*Y^11 + 2*Y^10 + 5*Y^9 + 2*Y^8
        + 5*Y^7 + 2*Y^6 + 2*Y^5 + 4*Y^4 + 2*Y^3 + 4*Y^2 + 6*Y + 3,
    -T^56 + T^55 - 55/49*T^54 - 86/343*T^53 + 213/343*T^52 - 2329/2401*T^51 + 
        1188/2401*T^50 + 43/343*T^49 + 188/2401*T^48 + 731/2401*T^47 - 115/2401*T^46
        + 961/2401*T^45 + 73/2401*T^44 - 213/2401*T^43 + 369/2401*T^42 - 
        115/2401*T^41 - 9/49*T^40 + 23/343*T^39 + 97/343*T^38 - 2048/2401*T^37 + 
        1590/2401*T^36 - 1395/2401*T^35 - 688/2401*T^34 - 538/2401*T^33 - 
        470/2401*T^32 - 310/2401*T^31 - 1825/2401*T^30 + 1170/2401*T^29 - 
        1170/2401*T^27 + 1825/2401*T^26 + 310/2401*T^25 + 470/2401*T^24 + 
        538/2401*T^23 + 688/2401*T^22 + 1395/2401*T^21 - 1590/2401*T^20 + 
        2048/2401*T^19 - 97/343*T^18 - 23/343*T^17 + 9/49*T^16 + 115/2401*T^15 - 
        369/2401*T^14 + 213/2401*T^13 - 73/2401*T^12 - 961/2401*T^11 + 115/2401*T^10
        - 731/2401*T^9 - 188/2401*T^8 - 43/343*T^7 - 1188/2401*T^6 + 2329/2401*T^5 -
        213/343*T^4 + 86/343*T^3 + 55/49*T^2 - T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 
        + 2*X*Y^8 + 2*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 5*X 
        + 6*Y^30 + 3*Y^29 + Y^28 + 4*Y^27 + 6*Y^26 + 2*Y^25 + 2*Y^23 + 2*Y^20 + 
        4*Y^19 + 3*Y^18 + Y^17 + 5*Y^16 + 4*Y^15 + 5*Y^14 + 4*Y^13 + 6*Y^12 + 4*Y^11
        + 4*Y^10 + Y^8 + 3*Y^7 + 4*Y^6 + 2*Y^5 + 3*Y^3 + 2*Y^2 + 3*Y,
    -T^56 + 4/7*T^55 + 9/49*T^54 - 30/343*T^53 + 1266/2401*T^52 - 1553/2401*T^51 - 
        787/2401*T^50 + 2144/2401*T^49 - 734/2401*T^48 + 345/2401*T^47 + 
        331/2401*T^46 - 748/2401*T^45 + 789/2401*T^44 + 1517/2401*T^43 - 
        1154/2401*T^42 - 76/343*T^41 + 638/2401*T^40 - 732/2401*T^39 + 215/2401*T^38
        + 1802/2401*T^37 - 2238/2401*T^36 - 302/2401*T^35 + 1028/2401*T^34 - 
        1784/2401*T^33 + 1266/2401*T^32 + 880/2401*T^31 - 2245/2401*T^30 + 
        1842/2401*T^29 - 1842/2401*T^27 + 2245/2401*T^26 - 880/2401*T^25 - 
        1266/2401*T^24 + 1784/2401*T^23 - 1028/2401*T^22 + 302/2401*T^21 + 
        2238/2401*T^20 - 1802/2401*T^19 - 215/2401*T^18 + 732/2401*T^17 - 
        638/2401*T^16 + 76/343*T^15 + 1154/2401*T^14 - 1517/2401*T^13 - 
        789/2401*T^12 + 748/2401*T^11 - 331/2401*T^10 - 345/2401*T^9 + 734/2401*T^8 
        - 2144/2401*T^7 + 787/2401*T^6 + 1553/2401*T^5 - 1266/2401*T^4 + 30/343*T^3 
        - 9/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 4*X*Y^9 + 3*X*Y^8 + 
        3*X*Y^7 + 2*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 2*X*Y + X + 2*Y^30 + 
        5*Y^29 + 6*Y^28 + 6*Y^27 + 6*Y^26 + 4*Y^25 + 6*Y^24 + 5*Y^23 + 2*Y^22 + Y^21
        + Y^20 + 5*Y^19 + 6*Y^18 + 3*Y^17 + 2*Y^16 + 4*Y^15 + 4*Y^14 + 2*Y^13 + Y^12
        + 5*Y^11 + 3*Y^10 + 4*Y^9 + 5*Y^8 + 2*Y^6 + 6*Y^5 + 3*Y^4 + 5*Y^3 + Y^2 + 
        3*Y + 4,
    T^56 + 4/7*T^55 - 52/49*T^54 - 346/343*T^53 + 23/343*T^52 + 1244/2401*T^51 + 
        1516/2401*T^50 + 1219/2401*T^49 - 732/2401*T^48 - 1643/2401*T^47 - 
        1332/2401*T^46 - 117/2401*T^45 + 2572/2401*T^44 + 2207/2401*T^43 - 
        401/2401*T^42 - 1004/2401*T^41 - 2353/2401*T^40 - 512/2401*T^39 + 
        1609/2401*T^38 + 1376/2401*T^37 + 115/343*T^36 - 45/2401*T^35 - 
        2097/2401*T^34 - 1727/2401*T^33 + 1853/2401*T^32 + 1774/2401*T^31 + 
        369/2401*T^30 - 723/2401*T^29 - 1548/2401*T^28 - 723/2401*T^27 + 
        369/2401*T^26 + 1774/2401*T^25 + 1853/2401*T^24 - 1727/2401*T^23 - 
        2097/2401*T^22 - 45/2401*T^21 + 115/343*T^20 + 1376/2401*T^19 + 
        1609/2401*T^18 - 512/2401*T^17 - 2353/2401*T^16 - 1004/2401*T^15 - 
        401/2401*T^14 + 2207/2401*T^13 + 2572/2401*T^12 - 117/2401*T^11 - 
        1332/2401*T^10 - 1643/2401*T^9 - 732/2401*T^8 + 1219/2401*T^7 + 
        1516/2401*T^6 + 1244/2401*T^5 + 23/343*T^4 - 346/343*T^3 - 52/49*T^2 + 4/7*T
        + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^13 + 4*X*Y^12 + 3*X*Y^10 + 2*X*Y^9 + 5*X*Y^8 + 5*X*Y^7 + 
        3*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + X*Y^2 + 4*X*Y + X + 2*Y^30 + 3*Y^29 
        + 2*Y^28 + 3*Y^27 + 3*Y^26 + 3*Y^24 + 3*Y^23 + 2*Y^22 + Y^21 + 4*Y^20 + 
        4*Y^19 + 5*Y^17 + 3*Y^16 + 2*Y^15 + Y^14 + 5*Y^13 + 4*Y^12 + 5*Y^11 + 5*Y^10
        + 5*Y^6 + 4*Y^5 + Y^4 + 5*Y^3 + 4*Y^2 + 5*Y + 3,
    -T^56 + 1/7*T^55 + 68/49*T^54 + 61/343*T^53 - 1973/2401*T^52 - 1467/2401*T^51 + 
        1032/2401*T^50 + 765/2401*T^49 - 1443/2401*T^48 + 393/2401*T^47 + 
        544/2401*T^46 + 619/2401*T^45 + 1186/2401*T^44 - 748/2401*T^43 - 
        2085/2401*T^42 - 2/7*T^41 + 2064/2401*T^40 + 1297/2401*T^39 - 1075/2401*T^38
        - 888/2401*T^37 + 118/2401*T^36 - 299/2401*T^35 + 653/2401*T^34 + 
        610/2401*T^33 - 8/49*T^32 - 1234/2401*T^31 - 46/343*T^30 + 257/343*T^29 - 
        257/343*T^27 + 46/343*T^26 + 1234/2401*T^25 + 8/49*T^24 - 610/2401*T^23 - 
        653/2401*T^22 + 299/2401*T^21 - 118/2401*T^20 + 888/2401*T^19 + 
        1075/2401*T^18 - 1297/2401*T^17 - 2064/2401*T^16 + 2/7*T^15 + 2085/2401*T^14
        + 748/2401*T^13 - 1186/2401*T^12 - 619/2401*T^11 - 544/2401*T^10 - 
        393/2401*T^9 + 1443/2401*T^8 - 765/2401*T^7 - 1032/2401*T^6 + 1467/2401*T^5 
        + 1973/2401*T^4 - 61/343*T^3 - 68/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 2*X*Y^12 + 6*X*Y^10 + 3*X*Y^9 + 2*X*Y^7 + 3*X*Y^6 + 
        3*X*Y^4 + X*Y^2 + 4*X*Y + 5*X + 5*Y^30 + 6*Y^28 + 2*Y^27 + 3*Y^26 + 6*Y^25 +
        3*Y^24 + 3*Y^23 + 6*Y^22 + 5*Y^21 + 6*Y^20 + 4*Y^19 + 3*Y^18 + 4*Y^17 + Y^16
        + 6*Y^15 + 5*Y^14 + 3*Y^13 + 4*Y^12 + 6*Y^11 + 2*Y^10 + 3*Y^9 + 3*Y^8 + 
        6*Y^7 + 5*Y^6 + Y^5 + 3*Y^4 + 6*Y^3 + 2*Y^2 + 5*Y + 2,
    -T^56 + 3/7*T^55 + 29/49*T^54 - 5/49*T^53 - 1394/2401*T^52 + 222/2401*T^51 + 
        2445/2401*T^50 - 866/2401*T^49 - 1818/2401*T^48 - 198/2401*T^47 + 
        2251/2401*T^46 - 90/2401*T^45 - 208/343*T^44 - 608/2401*T^43 + 
        1507/2401*T^42 - 79/2401*T^41 - 1178/2401*T^40 + 913/2401*T^39 + 
        314/2401*T^38 - 961/2401*T^37 - 373/2401*T^36 + 137/343*T^35 + 996/2401*T^34
        - 1588/2401*T^33 + 430/2401*T^32 + 642/2401*T^31 - 23/2401*T^30 - 
        2322/2401*T^29 + 2322/2401*T^27 + 23/2401*T^26 - 642/2401*T^25 - 
        430/2401*T^24 + 1588/2401*T^23 - 996/2401*T^22 - 137/343*T^21 + 
        373/2401*T^20 + 961/2401*T^19 - 314/2401*T^18 - 913/2401*T^17 + 
        1178/2401*T^16 + 79/2401*T^15 - 1507/2401*T^14 + 608/2401*T^13 + 
        208/343*T^12 + 90/2401*T^11 - 2251/2401*T^10 + 198/2401*T^9 + 1818/2401*T^8 
        + 866/2401*T^7 - 2445/2401*T^6 - 222/2401*T^5 + 1394/2401*T^4 + 5/49*T^3 - 
        29/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^13 + 2*X*Y^12 + X*Y^10 + 2*X*Y^9 + 3*X*Y^8 + 6*X*Y^6 + 
        2*X*Y^3 + 3*X*Y^2 + X*Y + 4*X + 5*Y^30 + 5*Y^29 + 6*Y^28 + 5*Y^27 + 4*Y^26 +
        2*Y^25 + 5*Y^23 + 4*Y^22 + 6*Y^20 + 5*Y^19 + 5*Y^18 + 2*Y^17 + 2*Y^15 + 
        2*Y^14 + 2*Y^13 + 2*Y^12 + 5*Y^10 + 5*Y^9 + 5*Y^8 + 5*Y^7 + 6*Y^6 + 4*Y^5 + 
        6*Y^4 + 5*Y^3 + 3*Y^2 + 4*Y + 3,
    T^56 + 3/7*T^55 - 33/49*T^54 - 116/343*T^53 + 773/2401*T^52 + 471/2401*T^51 - 
        517/2401*T^50 - 838/2401*T^49 + 10/2401*T^48 - 16/49*T^47 - 519/2401*T^46 + 
        601/2401*T^45 + 1686/2401*T^44 - 914/2401*T^43 - 2607/2401*T^42 + 
        383/2401*T^41 + 1976/2401*T^40 + 384/2401*T^39 - 1138/2401*T^38 - 
        435/2401*T^37 + 8/343*T^36 + 65/2401*T^35 + 1207/2401*T^34 + 215/343*T^33 + 
        183/2401*T^32 - 916/2401*T^31 - 1451/2401*T^30 + 261/2401*T^29 + 
        878/2401*T^28 + 261/2401*T^27 - 1451/2401*T^26 - 916/2401*T^25 + 
        183/2401*T^24 + 215/343*T^23 + 1207/2401*T^22 + 65/2401*T^21 + 8/343*T^20 - 
        435/2401*T^19 - 1138/2401*T^18 + 384/2401*T^17 + 1976/2401*T^16 + 
        383/2401*T^15 - 2607/2401*T^14 - 914/2401*T^13 + 1686/2401*T^12 + 
        601/2401*T^11 - 519/2401*T^10 - 16/49*T^9 + 10/2401*T^8 - 838/2401*T^7 - 
        517/2401*T^6 + 471/2401*T^5 + 773/2401*T^4 - 116/343*T^3 - 33/49*T^2 + 3/7*T
        + 1
*], [*
    X^3 + 6*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 4*X*Y^7 +
        4*X*Y^6 + 5*X*Y^5 + 4*X*Y + 6*X + 4*Y^30 + Y^29 + 5*Y^28 + 6*Y^27 + 4*Y^26 +
        4*Y^25 + 3*Y^24 + 6*Y^23 + 4*Y^22 + 4*Y^21 + 2*Y^20 + 5*Y^19 + 5*Y^18 + Y^17
        + 3*Y^16 + 4*Y^15 + 4*Y^14 + 2*Y^13 + 3*Y^11 + 6*Y^9 + 2*Y^8 + 5*Y^7 + Y^6 +
        3*Y^5 + Y^4 + 2*Y^3 + 3*Y^2 + 4*Y + 4,
    -T^56 - 1/7*T^55 - 31/49*T^54 - 34/343*T^53 + 543/2401*T^52 - 484/2401*T^51 - 
        883/2401*T^50 - 710/2401*T^49 - 124/343*T^48 - 744/2401*T^47 + 437/2401*T^46
        - 159/2401*T^45 - 298/2401*T^44 + 738/2401*T^43 + 166/2401*T^42 + 
        362/2401*T^41 + 368/2401*T^40 + 295/2401*T^39 - 505/2401*T^38 + 
        200/2401*T^37 + 844/2401*T^36 - 115/343*T^35 - 109/2401*T^34 - 633/2401*T^33
        - 622/2401*T^32 + 229/2401*T^31 + 1242/2401*T^30 + 74/2401*T^29 - 
        74/2401*T^27 - 1242/2401*T^26 - 229/2401*T^25 + 622/2401*T^24 + 
        633/2401*T^23 + 109/2401*T^22 + 115/343*T^21 - 844/2401*T^20 - 200/2401*T^19
        + 505/2401*T^18 - 295/2401*T^17 - 368/2401*T^16 - 362/2401*T^15 - 
        166/2401*T^14 - 738/2401*T^13 + 298/2401*T^12 + 159/2401*T^11 - 
        437/2401*T^10 + 744/2401*T^9 + 124/343*T^8 + 710/2401*T^7 + 883/2401*T^6 + 
        484/2401*T^5 - 543/2401*T^4 + 34/343*T^3 + 31/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        6*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + X*Y^3 + 4*X*Y^2 + 6*X*Y + 5*X + 
        5*Y^30 + 2*Y^28 + 3*Y^26 + 4*Y^25 + 2*Y^24 + 3*Y^23 + 2*Y^22 + Y^21 + 6*Y^20
        + 4*Y^19 + 6*Y^18 + Y^17 + 5*Y^16 + 4*Y^15 + 3*Y^13 + Y^11 + 6*Y^9 + 2*Y^8 +
        2*Y^7 + Y^6 + 2*Y^5 + 4*Y^4 + 4*Y^2 + 4*Y + 5,
    T^56 + 1/7*T^55 - 36/49*T^54 - 247/343*T^53 - 121/2401*T^52 + 2519/2401*T^51 + 
        897/2401*T^50 - 2013/2401*T^49 - 2087/2401*T^48 - 765/2401*T^47 + 
        3162/2401*T^46 + 286/2401*T^45 - 430/343*T^44 - 759/2401*T^43 + 
        1213/2401*T^42 + 3288/2401*T^41 + 43/2401*T^40 - 2297/2401*T^39 + 
        85/2401*T^38 + 184/343*T^37 + 1751/2401*T^36 - 787/2401*T^35 - 
        2094/2401*T^34 + 304/2401*T^33 + 160/343*T^32 + 773/2401*T^31 - 
        684/2401*T^30 - 1350/2401*T^29 - 22/2401*T^28 - 1350/2401*T^27 - 
        684/2401*T^26 + 773/2401*T^25 + 160/343*T^24 + 304/2401*T^23 - 
        2094/2401*T^22 - 787/2401*T^21 + 1751/2401*T^20 + 184/343*T^19 + 
        85/2401*T^18 - 2297/2401*T^17 + 43/2401*T^16 + 3288/2401*T^15 + 
        1213/2401*T^14 - 759/2401*T^13 - 430/343*T^12 + 286/2401*T^11 + 
        3162/2401*T^10 - 765/2401*T^9 - 2087/2401*T^8 - 2013/2401*T^7 + 897/2401*T^6
        + 2519/2401*T^5 - 121/2401*T^4 - 247/343*T^3 - 36/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 6*X*Y^12 + 3*X*Y^11 + 3*X*Y^9 + 2*X*Y^8 + 3*X*Y^7 + 
        X*Y^6 + 6*X*Y^5 + 2*X*Y^3 + 5*X*Y^2 + 4*X*Y + 2*X + 4*Y^30 + Y^29 + 6*Y^28 +
        6*Y^27 + 5*Y^25 + 6*Y^24 + 6*Y^23 + 5*Y^22 + 5*Y^21 + Y^20 + 3*Y^19 + 6*Y^18
        + 4*Y^16 + 5*Y^15 + 5*Y^13 + 6*Y^12 + 4*Y^11 + 3*Y^10 + 4*Y^9 + 4*Y^8 + 
        4*Y^7 + Y^6 + 6*Y^5 + Y^4 + Y^3 + 5*Y^2 + 2*Y + 4,
    -T^56 - 6/7*T^55 - 5/7*T^54 - 3/49*T^53 + 226/343*T^52 + 716/2401*T^51 + 
        2404/2401*T^50 + 850/2401*T^49 + 1896/2401*T^48 + 1271/2401*T^47 - 
        66/2401*T^46 + 1201/2401*T^45 + 369/2401*T^44 + 296/2401*T^43 - 
        1053/2401*T^42 - 2533/2401*T^41 - 2115/2401*T^40 - 2287/2401*T^39 - 
        1654/2401*T^38 - 139/2401*T^37 - 509/2401*T^36 + 2067/2401*T^35 + 
        2094/2401*T^34 + 2482/2401*T^33 + 3124/2401*T^32 + 690/2401*T^31 + 
        1598/2401*T^30 - 1/7*T^29 + 1/7*T^27 - 1598/2401*T^26 - 690/2401*T^25 - 
        3124/2401*T^24 - 2482/2401*T^23 - 2094/2401*T^22 - 2067/2401*T^21 + 
        509/2401*T^20 + 139/2401*T^19 + 1654/2401*T^18 + 2287/2401*T^17 + 
        2115/2401*T^16 + 2533/2401*T^15 + 1053/2401*T^14 - 296/2401*T^13 - 
        369/2401*T^12 - 1201/2401*T^11 + 66/2401*T^10 - 1271/2401*T^9 - 
        1896/2401*T^8 - 850/2401*T^7 - 2404/2401*T^6 - 716/2401*T^5 - 226/343*T^4 + 
        3/49*T^3 + 5/7*T^2 + 6/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 
        3*X*Y^8 + X*Y^6 + 4*X*Y^5 + X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 5*X*Y + Y^30 + 
        4*Y^28 + 5*Y^27 + 6*Y^26 + Y^25 + 4*Y^24 + 5*Y^22 + 3*Y^21 + 6*Y^19 + 5*Y^18
        + Y^17 + Y^16 + 4*Y^15 + 5*Y^14 + 2*Y^13 + Y^12 + 2*Y^11 + Y^10 + Y^9 + 
        3*Y^8 + Y^7 + 6*Y^6 + Y^5 + Y^4 + 5,
    -T^56 + 6/7*T^55 + 60/49*T^54 - 744/343*T^53 + 1865/2401*T^52 + 4654/2401*T^51 -
        5372/2401*T^50 - 1370/2401*T^49 + 6151/2401*T^48 - 2286/2401*T^47 - 
        5652/2401*T^46 + 6777/2401*T^45 - 6/49*T^44 - 982/343*T^43 + 5664/2401*T^42 
        + 1455/2401*T^41 - 4835/2401*T^40 + 2309/2401*T^39 + 3676/2401*T^38 - 
        3935/2401*T^37 - 1826/2401*T^36 + 5321/2401*T^35 - 422/343*T^34 - 
        2227/2401*T^33 + 4889/2401*T^32 - 2299/2401*T^31 - 386/343*T^30 + 
        3228/2401*T^29 - 3228/2401*T^27 + 386/343*T^26 + 2299/2401*T^25 - 
        4889/2401*T^24 + 2227/2401*T^23 + 422/343*T^22 - 5321/2401*T^21 + 
        1826/2401*T^20 + 3935/2401*T^19 - 3676/2401*T^18 - 2309/2401*T^17 + 
        4835/2401*T^16 - 1455/2401*T^15 - 5664/2401*T^14 + 982/343*T^13 + 6/49*T^12 
        - 6777/2401*T^11 + 5652/2401*T^10 + 2286/2401*T^9 - 6151/2401*T^8 + 
        1370/2401*T^7 + 5372/2401*T^6 - 4654/2401*T^5 - 1865/2401*T^4 + 744/343*T^3 
        - 60/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 6*X*Y^9 + 3*X*Y^7 +
        2*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 6*X*Y + 3*X + Y^30 + 
        5*Y^29 + 3*Y^28 + 2*Y^27 + 6*Y^26 + 2*Y^25 + 4*Y^24 + 6*Y^23 + 6*Y^22 + 
        3*Y^21 + Y^20 + 6*Y^19 + 2*Y^18 + 5*Y^17 + 6*Y^16 + 4*Y^15 + 5*Y^14 + 4*Y^13
        + 2*Y^12 + 2*Y^11 + 6*Y^9 + 5*Y^8 + 5*Y^7 + Y^6 + 6*Y^5 + 3*Y^4 + 3*Y^3 + 
        3*Y,
    -T^56 + 6/7*T^55 + 26/49*T^54 - 432/343*T^53 + 215/343*T^52 - 136/343*T^51 - 
        1794/2401*T^50 + 537/343*T^49 - 303/2401*T^48 - 473/343*T^47 + 123/2401*T^46
        + 316/343*T^45 + 920/2401*T^44 - 1347/2401*T^43 + 64/343*T^42 - 
        1446/2401*T^41 - 244/2401*T^40 + 4210/2401*T^39 - 1592/2401*T^38 - 
        2384/2401*T^37 + 796/2401*T^36 + 914/2401*T^35 + 920/2401*T^34 - 
        620/2401*T^33 - 710/2401*T^32 - 606/2401*T^31 - 44/343*T^30 + 2397/2401*T^29
        - 2397/2401*T^27 + 44/343*T^26 + 606/2401*T^25 + 710/2401*T^24 + 
        620/2401*T^23 - 920/2401*T^22 - 914/2401*T^21 - 796/2401*T^20 + 
        2384/2401*T^19 + 1592/2401*T^18 - 4210/2401*T^17 + 244/2401*T^16 + 
        1446/2401*T^15 - 64/343*T^14 + 1347/2401*T^13 - 920/2401*T^12 - 316/343*T^11
        - 123/2401*T^10 + 473/343*T^9 + 303/2401*T^8 - 537/343*T^7 + 1794/2401*T^6 +
        136/343*T^5 - 215/343*T^4 + 432/343*T^3 - 26/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 
        + 2*X*Y^8 + 5*X*Y^7 + X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + X*Y^2 + 2*X + 
        2*Y^30 + 4*Y^28 + 3*Y^27 + Y^26 + 6*Y^25 + 5*Y^24 + Y^23 + 6*Y^22 + 2*Y^21 +
        6*Y^20 + 2*Y^19 + Y^18 + 3*Y^17 + 4*Y^16 + 5*Y^15 + 4*Y^14 + Y^13 + Y^12 + 
        5*Y^11 + 5*Y^10 + 5*Y^6 + Y^4 + 3*Y^3 + 5*Y^2 + 6*Y,
    T^56 - 1/7*T^55 + 3/49*T^54 - 25/49*T^53 - 1864/2401*T^52 - 200/2401*T^51 + 
        1297/2401*T^50 + 298/2401*T^49 + 515/2401*T^48 + 443/2401*T^47 - 
        1882/2401*T^46 + 1129/2401*T^45 - 977/2401*T^44 + 821/2401*T^43 - 
        489/2401*T^42 + 2/49*T^41 - 157/2401*T^40 - 793/2401*T^39 + 271/2401*T^38 + 
        59/2401*T^37 + 358/2401*T^36 + 634/2401*T^35 + 10/49*T^34 - 923/2401*T^33 + 
        500/2401*T^32 - 1068/2401*T^31 - 242/2401*T^30 + 1195/2401*T^29 - 
        86/2401*T^28 + 1195/2401*T^27 - 242/2401*T^26 - 1068/2401*T^25 + 
        500/2401*T^24 - 923/2401*T^23 + 10/49*T^22 + 634/2401*T^21 + 358/2401*T^20 +
        59/2401*T^19 + 271/2401*T^18 - 793/2401*T^17 - 157/2401*T^16 + 2/49*T^15 - 
        489/2401*T^14 + 821/2401*T^13 - 977/2401*T^12 + 1129/2401*T^11 - 
        1882/2401*T^10 + 443/2401*T^9 + 515/2401*T^8 + 298/2401*T^7 + 1297/2401*T^6 
        - 200/2401*T^5 - 1864/2401*T^4 - 25/49*T^3 + 3/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 5*X*Y^13 + X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 + 
        X*Y^7 + 3*X*Y^6 + X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + X*Y + X + 5*Y^30 + 
        4*Y^29 + 6*Y^28 + 4*Y^27 + 2*Y^25 + 3*Y^23 + 4*Y^21 + 2*Y^20 + 2*Y^18 + 
        5*Y^17 + 4*Y^16 + 5*Y^15 + 5*Y^13 + 4*Y^12 + 4*Y^11 + 2*Y^10 + 6*Y^9 + Y^8 +
        Y^7 + 3*Y^6 + 4*Y^5 + 5*Y^4 + Y^3 + Y^2 + 3*Y + 6,
    -T^56 - 1/7*T^55 + 64/49*T^54 + 80/343*T^53 - 403/2401*T^52 + 1630/2401*T^51 - 
        80/2401*T^50 - 267/343*T^49 - 923/2401*T^48 - 958/2401*T^47 - 806/2401*T^46 
        + 625/2401*T^45 + 1458/2401*T^44 + 873/2401*T^43 + 1150/2401*T^42 + 
        3/2401*T^41 - 1290/2401*T^40 + 62/2401*T^39 + 1/7*T^38 - 229/343*T^37 - 
        1555/2401*T^36 + 1661/2401*T^35 + 1445/2401*T^34 - 275/2401*T^33 - 
        184/2401*T^32 + 473/2401*T^31 - 66/2401*T^30 - 767/2401*T^29 + 767/2401*T^27
        + 66/2401*T^26 - 473/2401*T^25 + 184/2401*T^24 + 275/2401*T^23 - 
        1445/2401*T^22 - 1661/2401*T^21 + 1555/2401*T^20 + 229/343*T^19 - 1/7*T^18 -
        62/2401*T^17 + 1290/2401*T^16 - 3/2401*T^15 - 1150/2401*T^14 - 873/2401*T^13
        - 1458/2401*T^12 - 625/2401*T^11 + 806/2401*T^10 + 958/2401*T^9 + 
        923/2401*T^8 + 267/343*T^7 + 80/2401*T^6 - 1630/2401*T^5 + 403/2401*T^4 - 
        80/343*T^3 - 64/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + X*Y^13 + 5*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 + 2*X*Y^7 + 
        3*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + X*Y^3 + 5*X*Y + 4*X + 5*Y^30 + 4*Y^28 + 4*Y^27
        + 6*Y^26 + 5*Y^25 + 2*Y^24 + 3*Y^23 + Y^22 + 2*Y^21 + 2*Y^20 + Y^19 + 6*Y^18
        + Y^17 + 4*Y^16 + 5*Y^15 + 3*Y^14 + 3*Y^13 + 2*Y^12 + 3*Y^11 + 5*Y^10 + Y^9 
        + 3*Y^8 + 2*Y^7 + Y^6 + 2*Y^4 + 4*Y^3 + 2*Y^2 + 6*Y,
    -T^56 - 2/7*T^55 + 33/49*T^54 + 164/343*T^53 + 39/343*T^52 - 410/2401*T^51 + 
        1229/2401*T^50 - 669/2401*T^49 - 2529/2401*T^48 - 585/2401*T^47 + 
        1720/2401*T^46 + 1419/2401*T^45 - 1082/2401*T^44 - 230/2401*T^43 + 
        13/2401*T^42 - 547/2401*T^41 - 724/2401*T^40 - 19/2401*T^39 + 1858/2401*T^38
        + 446/2401*T^37 - 85/2401*T^36 - 1020/2401*T^35 - 359/2401*T^34 + 
        926/2401*T^33 - 87/343*T^32 - 76/343*T^31 - 54/2401*T^30 + 1031/2401*T^29 - 
        1031/2401*T^27 + 54/2401*T^26 + 76/343*T^25 + 87/343*T^24 - 926/2401*T^23 + 
        359/2401*T^22 + 1020/2401*T^21 + 85/2401*T^20 - 446/2401*T^19 - 
        1858/2401*T^18 + 19/2401*T^17 + 724/2401*T^16 + 547/2401*T^15 - 13/2401*T^14
        + 230/2401*T^13 + 1082/2401*T^12 - 1419/2401*T^11 - 1720/2401*T^10 + 
        585/2401*T^9 + 2529/2401*T^8 + 669/2401*T^7 - 1229/2401*T^6 + 410/2401*T^5 -
        39/343*T^4 - 164/343*T^3 - 33/49*T^2 + 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + X*Y^11 + X*Y^10 + X*Y^9 + X*Y^8 
        + 6*X*Y^6 + 6*X*Y^5 + X*Y^3 + X*Y^2 + 3*X*Y + 4*X + 5*Y^30 + Y^29 + 6*Y^28 +
        4*Y^27 + Y^26 + 3*Y^25 + 3*Y^23 + 4*Y^22 + Y^21 + 3*Y^20 + 6*Y^17 + 6*Y^16 +
        5*Y^15 + 2*Y^14 + 2*Y^12 + Y^11 + 2*Y^10 + Y^9 + 3*Y^8 + Y^7 + 6*Y^6 + 6*Y^5
        + 3*Y^3 + Y,
    T^56 + 4/7*T^55 - 19/49*T^54 - 326/343*T^53 - 1093/2401*T^52 - 768/2401*T^51 + 
        1095/2401*T^50 + 2358/2401*T^49 + 165/343*T^48 - 600/2401*T^47 - 
        457/2401*T^46 - 2803/2401*T^45 - 1987/2401*T^44 - 439/2401*T^43 + 
        1514/2401*T^42 + 551/2401*T^41 + 897/2401*T^40 - 498/2401*T^39 - 
        216/343*T^38 - 1150/2401*T^37 + 283/2401*T^36 - 559/2401*T^35 + 
        837/2401*T^34 + 961/2401*T^33 + 1138/2401*T^32 - 109/2401*T^31 + 
        685/2401*T^30 + 138/2401*T^29 - 330/2401*T^28 + 138/2401*T^27 + 
        685/2401*T^26 - 109/2401*T^25 + 1138/2401*T^24 + 961/2401*T^23 + 
        837/2401*T^22 - 559/2401*T^21 + 283/2401*T^20 - 1150/2401*T^19 - 
        216/343*T^18 - 498/2401*T^17 + 897/2401*T^16 + 551/2401*T^15 + 
        1514/2401*T^14 - 439/2401*T^13 - 1987/2401*T^12 - 2803/2401*T^11 - 
        457/2401*T^10 - 600/2401*T^9 + 165/343*T^8 + 2358/2401*T^7 + 1095/2401*T^6 -
        768/2401*T^5 - 1093/2401*T^4 - 326/343*T^3 - 19/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 4*X*Y^7 + X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + X*Y^2 + 6*X*Y + 
        3*X + 4*Y^30 + Y^29 + 4*Y^28 + 5*Y^27 + 3*Y^26 + 3*Y^25 + Y^24 + Y^23 + 
        5*Y^21 + 3*Y^20 + Y^19 + 3*Y^18 + 4*Y^17 + 3*Y^16 + 3*Y^15 + 3*Y^14 + 3*Y^13
        + 5*Y^12 + 5*Y^11 + 2*Y^9 + 6*Y^8 + 5*Y^7 + 2*Y^6 + 4*Y^5 + 3*Y^4 + 3*Y^3 + 
        Y^2 + Y + 1,
    T^56 + 2/7*T^55 - 17/49*T^54 - 297/343*T^53 + 575/2401*T^52 + 2061/2401*T^51 - 
        148/2401*T^50 - 1027/2401*T^49 - 1553/2401*T^48 + 1944/2401*T^47 - 
        377/2401*T^46 - 836/2401*T^45 - 165/2401*T^44 + 1788/2401*T^43 + 68/343*T^42
        - 2256/2401*T^41 - 16/343*T^40 + 123/343*T^39 + 1328/2401*T^38 - 
        2605/2401*T^37 - 544/2401*T^36 + 1669/2401*T^35 + 320/343*T^34 - 
        1187/2401*T^33 - 2360/2401*T^32 + 911/2401*T^31 + 1399/2401*T^30 + 
        190/2401*T^29 - 435/343*T^28 + 190/2401*T^27 + 1399/2401*T^26 + 
        911/2401*T^25 - 2360/2401*T^24 - 1187/2401*T^23 + 320/343*T^22 + 
        1669/2401*T^21 - 544/2401*T^20 - 2605/2401*T^19 + 1328/2401*T^18 + 
        123/343*T^17 - 16/343*T^16 - 2256/2401*T^15 + 68/343*T^14 + 1788/2401*T^13 -
        165/2401*T^12 - 836/2401*T^11 - 377/2401*T^10 + 1944/2401*T^9 - 
        1553/2401*T^8 - 1027/2401*T^7 - 148/2401*T^6 + 2061/2401*T^5 + 575/2401*T^4 
        - 297/343*T^3 - 17/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 4*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 +
        4*X*Y^7 + 3*X*Y^5 + X*Y^4 + 5*X*Y^2 + 2*X*Y + 3*X + Y^30 + 2*Y^29 + 2*Y^28 +
        Y^27 + 2*Y^26 + 6*Y^25 + Y^24 + 5*Y^23 + 3*Y^22 + 3*Y^20 + Y^19 + 2*Y^18 + 
        4*Y^17 + 5*Y^16 + Y^15 + 4*Y^13 + 6*Y^12 + Y^10 + 5*Y^9 + 6*Y^8 + 6*Y^7 + 
        6*Y^6 + 6*Y^4 + 3*Y^3 + 3*Y^2 + 6*Y + 3,
    T^56 + 4/7*T^55 + 5/49*T^54 - 211/343*T^53 - 50/2401*T^52 - 120/2401*T^51 - 
        1807/2401*T^50 - 1520/2401*T^49 - 744/2401*T^48 + 176/2401*T^47 - 12/49*T^46
        - 134/2401*T^45 + 121/2401*T^44 + 23/343*T^43 + 1031/2401*T^42 + 
        1475/2401*T^41 + 1612/2401*T^40 + 374/2401*T^39 + 173/2401*T^38 + 
        97/343*T^37 - 102/343*T^36 - 1084/2401*T^35 - 1693/2401*T^34 + 108/2401*T^33
        + 244/2401*T^32 + 120/2401*T^31 + 51/2401*T^30 - 66/2401*T^29 + 
        464/2401*T^28 - 66/2401*T^27 + 51/2401*T^26 + 120/2401*T^25 + 244/2401*T^24 
        + 108/2401*T^23 - 1693/2401*T^22 - 1084/2401*T^21 - 102/343*T^20 + 
        97/343*T^19 + 173/2401*T^18 + 374/2401*T^17 + 1612/2401*T^16 + 
        1475/2401*T^15 + 1031/2401*T^14 + 23/343*T^13 + 121/2401*T^12 - 
        134/2401*T^11 - 12/49*T^10 + 176/2401*T^9 - 744/2401*T^8 - 1520/2401*T^7 - 
        1807/2401*T^6 - 120/2401*T^5 - 50/2401*T^4 - 211/343*T^3 + 5/49*T^2 + 4/7*T 
        + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 2*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 +
        2*X*Y^7 + X*Y^6 + 4*X*Y^5 + 5*X*Y^3 + 5*X*Y^2 + 3*X + 5*Y^30 + 6*Y^29 + 
        4*Y^28 + 4*Y^26 + 3*Y^25 + 3*Y^24 + 2*Y^23 + 2*Y^22 + Y^21 + 2*Y^20 + 6*Y^19
        + 3*Y^18 + 2*Y^17 + 5*Y^16 + 3*Y^15 + 4*Y^14 + 4*Y^13 + 4*Y^12 + 2*Y^10 + 
        4*Y^9 + 2*Y^8 + Y^7 + Y^6 + 5*Y^5 + 5*Y^4 + 3*Y^3 + 2*Y^2 + 6*Y + 6,
    T^56 + 9/7*T^55 - 23/49*T^54 - 514/343*T^53 - 1193/2401*T^52 + 1979/2401*T^51 - 
        41/2401*T^50 - 2763/2401*T^49 + 186/2401*T^48 + 3848/2401*T^47 + 
        1772/2401*T^46 - 432/343*T^45 - 2150/2401*T^44 + 1271/2401*T^43 + 
        893/2401*T^42 - 1376/2401*T^41 - 328/343*T^40 + 814/2401*T^39 + 
        2991/2401*T^38 + 1271/2401*T^37 - 1129/2401*T^36 - 1511/2401*T^35 + 
        494/2401*T^34 + 892/2401*T^33 - 138/2401*T^32 - 825/2401*T^31 - 90/2401*T^30
        + 139/2401*T^29 - 713/2401*T^28 + 139/2401*T^27 - 90/2401*T^26 - 
        825/2401*T^25 - 138/2401*T^24 + 892/2401*T^23 + 494/2401*T^22 - 
        1511/2401*T^21 - 1129/2401*T^20 + 1271/2401*T^19 + 2991/2401*T^18 + 
        814/2401*T^17 - 328/343*T^16 - 1376/2401*T^15 + 893/2401*T^14 + 
        1271/2401*T^13 - 2150/2401*T^12 - 432/343*T^11 + 1772/2401*T^10 + 
        3848/2401*T^9 + 186/2401*T^8 - 2763/2401*T^7 - 41/2401*T^6 + 1979/2401*T^5 -
        1193/2401*T^4 - 514/343*T^3 - 23/49*T^2 + 9/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 3*X*Y^12 + X*Y^9 + X*Y^8 + 3*X*Y^7 + 3*X*Y^6 + 4*X*Y^5 +
        6*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 3*X*Y + 3*X + 5*Y^30 + 5*Y^29 + Y^28 + 4*Y^27 
        + 6*Y^26 + Y^25 + 2*Y^23 + Y^22 + 4*Y^21 + 5*Y^20 + 6*Y^19 + Y^18 + 5*Y^16 +
        Y^15 + 5*Y^13 + 5*Y^12 + Y^11 + 4*Y^9 + 2*Y^8 + 4*Y^5 + 2*Y^4 + 4*Y^3 + 
        3*Y^2 + 4,
    T^56 - 11/7*T^55 + 32/49*T^54 + 194/343*T^53 - 3817/2401*T^52 + 538/343*T^51 - 
        123/343*T^50 - 2038/2401*T^49 + 1662/2401*T^48 + 422/2401*T^47 + 
        69/2401*T^46 - 414/2401*T^45 - 92/343*T^44 + 1077/2401*T^43 - 541/2401*T^42 
        - 617/2401*T^41 + 2917/2401*T^40 - 3958/2401*T^39 + 122/343*T^38 + 
        2461/2401*T^37 - 3355/2401*T^36 + 2844/2401*T^35 - 1518/2401*T^34 - 
        230/2401*T^33 + 1914/2401*T^32 - 1889/2401*T^31 + 1244/2401*T^30 - 
        59/343*T^29 - 353/2401*T^28 - 59/343*T^27 + 1244/2401*T^26 - 1889/2401*T^25 
        + 1914/2401*T^24 - 230/2401*T^23 - 1518/2401*T^22 + 2844/2401*T^21 - 
        3355/2401*T^20 + 2461/2401*T^19 + 122/343*T^18 - 3958/2401*T^17 + 
        2917/2401*T^16 - 617/2401*T^15 - 541/2401*T^14 + 1077/2401*T^13 - 
        92/343*T^12 - 414/2401*T^11 + 69/2401*T^10 + 422/2401*T^9 + 1662/2401*T^8 - 
        2038/2401*T^7 - 123/343*T^6 + 538/343*T^5 - 3817/2401*T^4 + 194/343*T^3 + 
        32/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^13 + X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 
        6*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + X*Y^2 + 6*X*Y + 6*X + 3*Y^30 + Y^29 + 4*Y^28 +
        5*Y^27 + Y^26 + 4*Y^25 + Y^24 + 3*Y^23 + 2*Y^21 + 5*Y^20 + 4*Y^19 + Y^18 + 
        3*Y^16 + 3*Y^15 + Y^14 + 5*Y^13 + Y^12 + 5*Y^11 + Y^10 + 2*Y^9 + 5*Y^8 + 
        3*Y^6 + 5*Y^5 + 4*Y^4 + 2*Y^3,
    -T^56 - 3/7*T^55 - 12/49*T^54 + 24/49*T^53 - 501/2401*T^52 + 1299/2401*T^51 + 
        898/2401*T^50 + 207/343*T^49 + 1086/2401*T^48 + 155/2401*T^47 - 
        359/2401*T^46 - 6/2401*T^45 + 1020/2401*T^44 - 171/2401*T^43 - 433/2401*T^42
        - 797/2401*T^41 + 263/2401*T^40 - 108/343*T^39 + 198/2401*T^38 - 
        1201/2401*T^37 + 685/2401*T^36 - 1202/2401*T^35 - 13/2401*T^34 - 
        1461/2401*T^33 + 803/2401*T^32 + 54/343*T^31 + 587/2401*T^30 - 450/2401*T^29
        + 450/2401*T^27 - 587/2401*T^26 - 54/343*T^25 - 803/2401*T^24 + 
        1461/2401*T^23 + 13/2401*T^22 + 1202/2401*T^21 - 685/2401*T^20 + 
        1201/2401*T^19 - 198/2401*T^18 + 108/343*T^17 - 263/2401*T^16 + 
        797/2401*T^15 + 433/2401*T^14 + 171/2401*T^13 - 1020/2401*T^12 + 6/2401*T^11
        + 359/2401*T^10 - 155/2401*T^9 - 1086/2401*T^8 - 207/343*T^7 - 898/2401*T^6 
        - 1299/2401*T^5 + 501/2401*T^4 - 24/49*T^3 + 12/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^10 + 6*X*Y^9 + 4*X*Y^8 +
        6*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 5*X*Y + 6*X + 
        5*Y^30 + Y^29 + Y^28 + 3*Y^27 + 6*Y^26 + 5*Y^25 + 4*Y^24 + 3*Y^23 + 2*Y^22 +
        3*Y^21 + 2*Y^20 + 2*Y^19 + 2*Y^17 + 6*Y^16 + 3*Y^15 + 5*Y^14 + 2*Y^13 + 
        2*Y^12 + 6*Y^11 + 5*Y^10 + 4*Y^9 + 3*Y^8 + 6*Y^7 + 5*Y^6 + 4*Y^5 + 4*Y^4 + 
        4*Y^3 + Y^2 + Y + 1,
    -T^56 + 5/7*T^55 - 3/7*T^54 + 97/343*T^53 + 20/49*T^52 - 486/2401*T^51 + 
        4121/2401*T^50 - 3089/2401*T^49 + 2789/2401*T^48 - 204/343*T^47 - 
        622/2401*T^46 - 226/2401*T^45 - 1370/2401*T^44 + 524/2401*T^43 - 
        1902/2401*T^42 + 904/2401*T^41 - 1243/2401*T^40 + 1599/2401*T^39 - 
        1584/2401*T^38 + 1928/2401*T^37 - 251/2401*T^36 + 492/2401*T^35 + 
        1508/2401*T^34 - 1462/2401*T^33 + 173/343*T^32 - 1538/2401*T^31 + 
        446/2401*T^30 - 1245/2401*T^29 + 1245/2401*T^27 - 446/2401*T^26 + 
        1538/2401*T^25 - 173/343*T^24 + 1462/2401*T^23 - 1508/2401*T^22 - 
        492/2401*T^21 + 251/2401*T^20 - 1928/2401*T^19 + 1584/2401*T^18 - 
        1599/2401*T^17 + 1243/2401*T^16 - 904/2401*T^15 + 1902/2401*T^14 - 
        524/2401*T^13 + 1370/2401*T^12 + 226/2401*T^11 + 622/2401*T^10 + 204/343*T^9
        - 2789/2401*T^8 + 3089/2401*T^7 - 4121/2401*T^6 + 486/2401*T^5 - 20/49*T^4 -
        97/343*T^3 + 3/7*T^2 - 5/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 5*X*Y^8 + X*Y^7 + 
        2*X*Y^5 + 2*X*Y^4 + X*Y^3 + 4*X*Y^2 + 6*X + 5*Y^30 + 3*Y^29 + Y^28 + 3*Y^27 
        + 6*Y^25 + Y^24 + 6*Y^22 + 2*Y^21 + 5*Y^20 + 3*Y^19 + 3*Y^18 + Y^17 + Y^16 +
        6*Y^15 + 2*Y^14 + 2*Y^13 + 5*Y^12 + 5*Y^11 + Y^10 + Y^9 + Y^8 + Y^7 + 2*Y^6 
        + 5*Y^4 + 6*Y^3 + 2*Y^2 + 4*Y,
    T^56 + 2/7*T^55 - 67/49*T^54 - 39/49*T^53 + 457/343*T^52 + 1465/2401*T^51 - 
        2208/2401*T^50 - 1114/2401*T^49 + 1264/2401*T^48 - 37/343*T^47 - 
        1658/2401*T^46 + 711/2401*T^45 + 2465/2401*T^44 - 2409/2401*T^43 - 
        64/49*T^42 + 2252/2401*T^41 + 3441/2401*T^40 - 2616/2401*T^39 - 
        1621/2401*T^38 + 1936/2401*T^37 + 642/2401*T^36 - 1404/2401*T^35 + 
        926/2401*T^34 + 62/343*T^33 - 1606/2401*T^32 - 166/2401*T^31 + 
        2718/2401*T^30 - 101/2401*T^29 - 2080/2401*T^28 - 101/2401*T^27 + 
        2718/2401*T^26 - 166/2401*T^25 - 1606/2401*T^24 + 62/343*T^23 + 
        926/2401*T^22 - 1404/2401*T^21 + 642/2401*T^20 + 1936/2401*T^19 - 
        1621/2401*T^18 - 2616/2401*T^17 + 3441/2401*T^16 + 2252/2401*T^15 - 
        64/49*T^14 - 2409/2401*T^13 + 2465/2401*T^12 + 711/2401*T^11 - 
        1658/2401*T^10 - 37/343*T^9 + 1264/2401*T^8 - 1114/2401*T^7 - 2208/2401*T^6 
        + 1465/2401*T^5 + 457/343*T^4 - 39/49*T^3 - 67/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 6*X*Y^8 + 
        3*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 5*X + 2*Y^30 + 
        4*Y^29 + 3*Y^27 + 5*Y^26 + 3*Y^25 + 6*Y^24 + Y^23 + 3*Y^21 + 6*Y^19 + 3*Y^18
        + Y^16 + 2*Y^15 + 3*Y^14 + 4*Y^13 + 4*Y^12 + 6*Y^11 + Y^10 + 3*Y^9 + Y^8 + 
        2*Y^7 + Y^6 + 3*Y^2 + 5*Y + 3,
    T^56 + T^55 - 25/49*T^54 - 310/343*T^53 - 641/2401*T^52 + 608/2401*T^51 - 
        324/2401*T^50 - 314/343*T^49 - 327/343*T^48 + 1072/2401*T^47 + 
        2693/2401*T^46 + 164/2401*T^45 - 1231/2401*T^44 + 1194/2401*T^43 + 
        2872/2401*T^42 - 20/2401*T^41 - 258/343*T^40 - 786/2401*T^39 - 69/2401*T^38 
        + 926/2401*T^37 + 25/343*T^36 - 363/343*T^35 - 670/2401*T^34 + 
        2385/2401*T^33 + 99/343*T^32 - 1123/2401*T^31 - 859/2401*T^30 + 95/2401*T^29
        + 610/2401*T^28 + 95/2401*T^27 - 859/2401*T^26 - 1123/2401*T^25 + 
        99/343*T^24 + 2385/2401*T^23 - 670/2401*T^22 - 363/343*T^21 + 25/343*T^20 + 
        926/2401*T^19 - 69/2401*T^18 - 786/2401*T^17 - 258/343*T^16 - 20/2401*T^15 +
        2872/2401*T^14 + 1194/2401*T^13 - 1231/2401*T^12 + 164/2401*T^11 + 
        2693/2401*T^10 + 1072/2401*T^9 - 327/343*T^8 - 314/343*T^7 - 324/2401*T^6 + 
        608/2401*T^5 - 641/2401*T^4 - 310/343*T^3 - 25/49*T^2 + T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^13 + X*Y^12 + X*Y^11 + 2*X*Y^10 + 3*X*Y^9 + 6*X*Y^7 + 
        5*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 3*X*Y + X + Y^30 + Y^29 + Y^27 + 
        3*Y^26 + 6*Y^25 + 3*Y^24 + Y^20 + 5*Y^19 + 2*Y^18 + Y^17 + 5*Y^16 + 3*Y^15 +
        4*Y^14 + 4*Y^13 + 5*Y^12 + 3*Y^11 + Y^8 + 4*Y^7 + 6*Y^5 + 2*Y^4 + 5*Y^2 + 
        3*Y + 1,
    T^56 + 5/7*T^55 + 3/49*T^54 - 11/49*T^53 - 403/343*T^52 - 2201/2401*T^51 - 
        1108/2401*T^50 - 255/2401*T^49 + 1101/2401*T^48 + 1784/2401*T^47 + 
        365/343*T^46 + 1614/2401*T^45 + 892/2401*T^44 - 8/2401*T^43 - 1513/2401*T^42
        - 993/2401*T^41 - 1521/2401*T^40 - 1853/2401*T^39 - 1269/2401*T^38 - 
        1375/2401*T^37 + 972/2401*T^36 + 2019/2401*T^35 + 1636/2401*T^34 + 
        2809/2401*T^33 + 1948/2401*T^32 + 152/343*T^31 - 584/2401*T^30 - 
        3418/2401*T^29 - 4462/2401*T^28 - 3418/2401*T^27 - 584/2401*T^26 + 
        152/343*T^25 + 1948/2401*T^24 + 2809/2401*T^23 + 1636/2401*T^22 + 
        2019/2401*T^21 + 972/2401*T^20 - 1375/2401*T^19 - 1269/2401*T^18 - 
        1853/2401*T^17 - 1521/2401*T^16 - 993/2401*T^15 - 1513/2401*T^14 - 
        8/2401*T^13 + 892/2401*T^12 + 1614/2401*T^11 + 365/343*T^10 + 1784/2401*T^9 
        + 1101/2401*T^8 - 255/2401*T^7 - 1108/2401*T^6 - 2201/2401*T^5 - 403/343*T^4
        - 11/49*T^3 + 3/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 4*X*Y^10 + 3*X*Y^9 + X*Y^8 + 
        4*X*Y^7 + 4*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 4*X*Y + 5*X + 5*Y^30 + 
        6*Y^29 + 6*Y^28 + 2*Y^26 + 4*Y^24 + 4*Y^23 + 4*Y^22 + 2*Y^21 + 2*Y^20 + 
        4*Y^19 + 5*Y^18 + 3*Y^17 + 3*Y^16 + 5*Y^15 + 6*Y^14 + Y^13 + 2*Y^12 + 2*Y^11
        + 3*Y^10 + 5*Y^9 + 4*Y^8 + 6*Y^7 + 6*Y^6 + 2*Y^5 + 5*Y^3 + Y^2 + 1,
    T^56 - 9/7*T^55 + 29/49*T^54 - 62/343*T^53 - 1072/2401*T^52 + 2047/2401*T^51 - 
        54/343*T^50 - 323/2401*T^49 + 279/2401*T^48 - 1588/2401*T^47 + 211/2401*T^46
        + 2232/2401*T^45 - 2855/2401*T^44 + 2054/2401*T^43 - 1305/2401*T^42 - 
        277/2401*T^41 + 772/2401*T^40 - 64/343*T^39 + 457/2401*T^38 - 61/343*T^37 - 
        303/343*T^36 + 2267/2401*T^35 + 6/343*T^34 - 443/2401*T^33 + 1927/2401*T^32 
        - 415/343*T^31 + 565/2401*T^30 + 90/343*T^29 + 717/2401*T^28 + 90/343*T^27 +
        565/2401*T^26 - 415/343*T^25 + 1927/2401*T^24 - 443/2401*T^23 + 6/343*T^22 +
        2267/2401*T^21 - 303/343*T^20 - 61/343*T^19 + 457/2401*T^18 - 64/343*T^17 + 
        772/2401*T^16 - 277/2401*T^15 - 1305/2401*T^14 + 2054/2401*T^13 - 
        2855/2401*T^12 + 2232/2401*T^11 + 211/2401*T^10 - 1588/2401*T^9 + 
        279/2401*T^8 - 323/2401*T^7 - 54/343*T^6 + 2047/2401*T^5 - 1072/2401*T^4 - 
        62/343*T^3 + 29/49*T^2 - 9/7*T + 1
*], [*
    X^3 + X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + X*Y^9 + 2*X*Y^7 + 
        4*X*Y^6 + 6*X*Y^5 + X*Y^4 + 3*X*Y^3 + 3*X*Y + 6*X + 5*Y^30 + 4*Y^29 + Y^27 +
        2*Y^26 + 5*Y^25 + 2*Y^24 + 3*Y^23 + Y^22 + 6*Y^21 + 5*Y^20 + 6*Y^18 + 2*Y^17
        + Y^16 + 6*Y^14 + 4*Y^13 + 6*Y^11 + 2*Y^10 + 6*Y^9 + 6*Y^7 + 3*Y^6 + 3*Y^4 +
        Y^3 + 4*Y^2 + Y + 3,
    -T^56 - 2/7*T^55 + 23/49*T^54 + 493/343*T^53 + 264/343*T^52 - 724/2401*T^51 - 
        3728/2401*T^50 - 1971/2401*T^49 + 508/2401*T^48 + 1297/2401*T^47 + 
        2669/2401*T^46 - 172/2401*T^45 - 1588/2401*T^44 - 2570/2401*T^43 - 
        519/2401*T^42 + 2082/2401*T^41 + 724/343*T^40 + 1754/2401*T^39 - 
        2202/2401*T^38 - 4035/2401*T^37 - 3853/2401*T^36 - 321/2401*T^35 + 
        2109/2401*T^34 + 3127/2401*T^33 + 2609/2401*T^32 + 411/2401*T^31 - 
        407/343*T^30 - 1985/2401*T^29 + 1985/2401*T^27 + 407/343*T^26 - 
        411/2401*T^25 - 2609/2401*T^24 - 3127/2401*T^23 - 2109/2401*T^22 + 
        321/2401*T^21 + 3853/2401*T^20 + 4035/2401*T^19 + 2202/2401*T^18 - 
        1754/2401*T^17 - 724/343*T^16 - 2082/2401*T^15 + 519/2401*T^14 + 
        2570/2401*T^13 + 1588/2401*T^12 + 172/2401*T^11 - 2669/2401*T^10 - 
        1297/2401*T^9 - 508/2401*T^8 + 1971/2401*T^7 + 3728/2401*T^6 + 724/2401*T^5 
        - 264/343*T^4 - 493/343*T^3 - 23/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 4*X*Y^9 + 6*X*Y^7 + 
        2*X*Y^6 + 2*X*Y^5 + X*Y^4 + 6*X*Y^3 + 2*X*Y + X + 5*Y^30 + 5*Y^28 + 6*Y^27 +
        3*Y^26 + 6*Y^25 + 6*Y^24 + Y^23 + 5*Y^22 + 2*Y^21 + 2*Y^20 + 6*Y^19 + 5*Y^18
        + 6*Y^17 + 6*Y^16 + 3*Y^15 + 6*Y^14 + 5*Y^13 + 5*Y^12 + 6*Y^10 + 4*Y^9 + 
        5*Y^8 + 2*Y^6 + 4*Y^5 + 4*Y^4 + 5*Y^3 + 6*Y^2 + 4*Y,
    -T^56 - 2/7*T^55 - 10/49*T^54 + 33/343*T^53 + 1333/2401*T^52 + 1023/2401*T^51 - 
        985/2401*T^50 - 85/2401*T^49 - 1077/2401*T^48 + 261/343*T^47 + 
        3229/2401*T^46 + 291/343*T^45 + 1755/2401*T^44 - 845/2401*T^43 - 
        1752/2401*T^42 + 391/2401*T^41 + 1553/2401*T^40 + 1697/2401*T^39 + 
        127/343*T^38 - 3757/2401*T^37 - 3739/2401*T^36 - 452/343*T^35 - 
        400/2401*T^34 + 267/343*T^33 + 873/2401*T^32 - 2112/2401*T^31 - 
        3238/2401*T^30 - 3509/2401*T^29 + 3509/2401*T^27 + 3238/2401*T^26 + 
        2112/2401*T^25 - 873/2401*T^24 - 267/343*T^23 + 400/2401*T^22 + 452/343*T^21
        + 3739/2401*T^20 + 3757/2401*T^19 - 127/343*T^18 - 1697/2401*T^17 - 
        1553/2401*T^16 - 391/2401*T^15 + 1752/2401*T^14 + 845/2401*T^13 - 
        1755/2401*T^12 - 291/343*T^11 - 3229/2401*T^10 - 261/343*T^9 + 1077/2401*T^8
        + 85/2401*T^7 + 985/2401*T^6 - 1023/2401*T^5 - 1333/2401*T^4 - 33/343*T^3 + 
        10/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^13 + X*Y^12 + 5*X*Y^11 + 6*X*Y^9 + X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + 
        2*X*Y^5 + X*Y^3 + 3*X*Y^2 + X*Y + 5*X + 4*Y^30 + 2*Y^28 + 4*Y^25 + Y^24 + 
        4*Y^23 + 4*Y^22 + Y^21 + 5*Y^20 + 2*Y^19 + 5*Y^18 + 3*Y^17 + 3*Y^16 + 3*Y^15
        + Y^13 + Y^11 + 5*Y^10 + 6*Y^9 + 2*Y^8 + 3*Y^7 + 3*Y^6 + Y^5 + 2*Y^4 + 5*Y^3
        + Y^2 + Y + 1,
    -T^56 - 1/7*T^55 - 17/49*T^54 + 260/343*T^53 + 2721/2401*T^52 + 508/343*T^51 + 
        1/2401*T^50 - 691/2401*T^49 - 4525/2401*T^48 - 2714/2401*T^47 - 
        2409/2401*T^46 + 2508/2401*T^45 + 2766/2401*T^44 + 4899/2401*T^43 + 
        884/2401*T^42 - 233/343*T^41 - 3905/2401*T^40 - 4008/2401*T^39 - 
        1821/2401*T^38 + 44/49*T^37 + 2825/2401*T^36 + 4115/2401*T^35 + 
        1842/2401*T^34 - 774/2401*T^33 - 1466/2401*T^32 - 2721/2401*T^31 - 
        2069/2401*T^30 - 636/2401*T^29 + 636/2401*T^27 + 2069/2401*T^26 + 
        2721/2401*T^25 + 1466/2401*T^24 + 774/2401*T^23 - 1842/2401*T^22 - 
        4115/2401*T^21 - 2825/2401*T^20 - 44/49*T^19 + 1821/2401*T^18 + 
        4008/2401*T^17 + 3905/2401*T^16 + 233/343*T^15 - 884/2401*T^14 - 
        4899/2401*T^13 - 2766/2401*T^12 - 2508/2401*T^11 + 2409/2401*T^10 + 
        2714/2401*T^9 + 4525/2401*T^8 + 691/2401*T^7 - 1/2401*T^6 - 508/343*T^5 - 
        2721/2401*T^4 - 260/343*T^3 + 17/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 5*X*Y^9 + 2*X*Y^8 + 
        5*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + X + 3*Y^30 + 
        4*Y^29 + 3*Y^28 + 6*Y^27 + 5*Y^26 + 5*Y^25 + 3*Y^24 + 4*Y^23 + 5*Y^22 + 
        4*Y^21 + 3*Y^20 + 4*Y^19 + 6*Y^18 + 4*Y^16 + Y^15 + 4*Y^14 + Y^13 + 5*Y^12 +
        Y^11 + Y^10 + 4*Y^9 + 4*Y^8 + 5*Y^7 + 3*Y^6 + 4*Y^4 + 4*Y^3 + 3*Y + 3,
    T^56 - 2/7*T^55 + 57/49*T^54 - 601/343*T^53 + 319/343*T^52 - 4899/2401*T^51 + 
        4045/2401*T^50 - 2237/2401*T^49 + 3600/2401*T^48 - 580/2401*T^47 + 
        971/2401*T^46 + 74/2401*T^45 - 2801/2401*T^44 + 37/2401*T^43 - 
        2019/2401*T^42 + 2323/2401*T^41 + 1413/2401*T^40 + 1783/2401*T^39 + 
        849/2401*T^38 - 2300/2401*T^37 + 423/2401*T^36 - 2262/2401*T^35 + 
        978/2401*T^34 + 358/2401*T^33 + 88/2401*T^32 + 2606/2401*T^31 - 
        2616/2401*T^30 + 2508/2401*T^29 - 673/343*T^28 + 2508/2401*T^27 - 
        2616/2401*T^26 + 2606/2401*T^25 + 88/2401*T^24 + 358/2401*T^23 + 
        978/2401*T^22 - 2262/2401*T^21 + 423/2401*T^20 - 2300/2401*T^19 + 
        849/2401*T^18 + 1783/2401*T^17 + 1413/2401*T^16 + 2323/2401*T^15 - 
        2019/2401*T^14 + 37/2401*T^13 - 2801/2401*T^12 + 74/2401*T^11 + 
        971/2401*T^10 - 580/2401*T^9 + 3600/2401*T^8 - 2237/2401*T^7 + 4045/2401*T^6
        - 4899/2401*T^5 + 319/343*T^4 - 601/343*T^3 + 57/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 5*X*Y^13 + X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 5*X*Y^7 + 
        6*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 3*X*Y + 4*X + 6*Y^30 + 
        6*Y^29 + 6*Y^28 + 6*Y^27 + 3*Y^26 + Y^23 + Y^22 + 6*Y^21 + 3*Y^20 + 3*Y^19 +
        2*Y^18 + 4*Y^17 + 4*Y^16 + 2*Y^15 + 4*Y^13 + 6*Y^12 + Y^11 + 6*Y^10 + 6*Y^9 
        + Y^8 + 5*Y^7 + 2*Y^6 + 6*Y^5 + 4*Y^4 + 6*Y^3 + Y^2 + 4*Y + 6,
    T^56 + 12/7*T^55 + 31/49*T^54 - 13/49*T^53 + 185/2401*T^52 + 874/2401*T^51 - 
        137/2401*T^50 - 289/2401*T^49 + 702/2401*T^48 + 538/2401*T^47 - 283/343*T^46
        - 3176/2401*T^45 - 771/2401*T^44 + 950/2401*T^43 - 122/2401*T^42 - 
        121/343*T^41 + 972/2401*T^40 + 2223/2401*T^39 + 102/2401*T^38 - 3/7*T^37 + 
        1538/2401*T^36 + 2525/2401*T^35 + 394/2401*T^34 - 177/343*T^33 - 
        310/343*T^32 - 3089/2401*T^31 - 2538/2401*T^30 - 912/2401*T^29 - 
        123/2401*T^28 - 912/2401*T^27 - 2538/2401*T^26 - 3089/2401*T^25 - 
        310/343*T^24 - 177/343*T^23 + 394/2401*T^22 + 2525/2401*T^21 + 
        1538/2401*T^20 - 3/7*T^19 + 102/2401*T^18 + 2223/2401*T^17 + 972/2401*T^16 -
        121/343*T^15 - 122/2401*T^14 + 950/2401*T^13 - 771/2401*T^12 - 
        3176/2401*T^11 - 283/343*T^10 + 538/2401*T^9 + 702/2401*T^8 - 289/2401*T^7 -
        137/2401*T^6 + 874/2401*T^5 + 185/2401*T^4 - 13/49*T^3 + 31/49*T^2 + 12/7*T 
        + 1
*], [*
    X^3 + X*Y^15 + X*Y^13 + 5*X*Y^12 + 5*X*Y^9 + 4*X*Y^8 + 3*X*Y^7 + X*Y^6 + X*Y^5 +
        4*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 6*X*Y + 5*X + 6*Y^30 + Y^29 + 4*Y^28 + 5*Y^27 
        + Y^26 + 5*Y^25 + Y^24 + Y^22 + 3*Y^21 + 3*Y^19 + 3*Y^18 + 4*Y^17 + Y^16 + 
        4*Y^15 + 3*Y^14 + 3*Y^13 + 2*Y^12 + Y^11 + Y^10 + 2*Y^8 + 2*Y^7 + 3*Y^5 + 
        Y^4 + 5*Y^3 + 5*Y^2 + Y + 2,
    -T^56 - 10/7*T^55 - 39/49*T^54 - 24/343*T^53 + 1108/2401*T^52 + 2260/2401*T^51 +
        1943/2401*T^50 + 355/343*T^49 + 2890/2401*T^48 + 541/2401*T^47 - 
        1748/2401*T^46 - 1615/2401*T^45 - 305/2401*T^44 + 1433/2401*T^43 + 
        120/343*T^42 - 971/2401*T^41 - 37/49*T^40 - 237/343*T^39 - 43/49*T^38 - 
        2358/2401*T^37 - 230/343*T^36 + 773/2401*T^35 + 2960/2401*T^34 + 
        3009/2401*T^33 + 2165/2401*T^32 + 192/343*T^31 + 1222/2401*T^30 + 25/49*T^29
        - 25/49*T^27 - 1222/2401*T^26 - 192/343*T^25 - 2165/2401*T^24 - 
        3009/2401*T^23 - 2960/2401*T^22 - 773/2401*T^21 + 230/343*T^20 + 
        2358/2401*T^19 + 43/49*T^18 + 237/343*T^17 + 37/49*T^16 + 971/2401*T^15 - 
        120/343*T^14 - 1433/2401*T^13 + 305/2401*T^12 + 1615/2401*T^11 + 
        1748/2401*T^10 - 541/2401*T^9 - 2890/2401*T^8 - 355/343*T^7 - 1943/2401*T^6 
        - 2260/2401*T^5 - 1108/2401*T^4 + 24/343*T^3 + 39/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 
        + 4*X*Y^8 + 6*X*Y^7 + 6*X*Y^3 + 5*X*Y + 3*X + 3*Y^30 + 5*Y^28 + Y^26 + 
        6*Y^25 + Y^24 + 2*Y^23 + 6*Y^22 + 6*Y^21 + Y^20 + 5*Y^19 + 4*Y^18 + Y^16 + 
        3*Y^14 + 4*Y^13 + 4*Y^12 + 5*Y^11 + 2*Y^10 + 3*Y^9 + 3*Y^7 + 4*Y^6 + 5*Y^5 +
        5*Y^4 + 2*Y^3 + 2*Y^2 + 4,
    -T^56 - 3/7*T^55 + 40/49*T^54 + 327/343*T^53 + 862/2401*T^52 - 2438/2401*T^51 - 
        3230/2401*T^50 + 429/2401*T^49 + 704/343*T^48 + 330/343*T^47 - 
        1279/2401*T^46 - 683/343*T^45 - 2778/2401*T^44 + 2944/2401*T^43 + 
        556/343*T^42 + 125/343*T^41 - 2894/2401*T^40 - 3463/2401*T^39 - 
        508/2401*T^38 + 3959/2401*T^37 + 332/343*T^36 - 94/2401*T^35 - 
        2374/2401*T^34 - 1947/2401*T^33 + 1371/2401*T^32 + 1217/2401*T^31 - 
        719/2401*T^30 - 445/2401*T^29 + 445/2401*T^27 + 719/2401*T^26 - 
        1217/2401*T^25 - 1371/2401*T^24 + 1947/2401*T^23 + 2374/2401*T^22 + 
        94/2401*T^21 - 332/343*T^20 - 3959/2401*T^19 + 508/2401*T^18 + 
        3463/2401*T^17 + 2894/2401*T^16 - 125/343*T^15 - 556/343*T^14 - 
        2944/2401*T^13 + 2778/2401*T^12 + 683/343*T^11 + 1279/2401*T^10 - 
        330/343*T^9 - 704/343*T^8 - 429/2401*T^7 + 3230/2401*T^6 + 2438/2401*T^5 - 
        862/2401*T^4 - 327/343*T^3 - 40/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 
        6*X*Y^8 + 5*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 3*X*Y + 3*X + 
        6*Y^30 + 5*Y^29 + 5*Y^28 + Y^27 + 6*Y^26 + 6*Y^25 + 6*Y^24 + 5*Y^23 + Y^21 +
        5*Y^20 + Y^17 + 2*Y^15 + 5*Y^14 + 2*Y^13 + Y^12 + 3*Y^11 + 6*Y^10 + 5*Y^9 + 
        4*Y^8 + 3*Y^6 + 6*Y^3 + 4*Y^2 + 2*Y,
    T^56 - 2/7*T^55 - 5/7*T^54 + 297/343*T^53 + 510/2401*T^52 + 925/2401*T^51 - 
        976/2401*T^50 - 1083/2401*T^49 + 2767/2401*T^48 + 277/2401*T^47 - 
        1167/2401*T^46 - 856/2401*T^45 + 1060/2401*T^44 + 2461/2401*T^43 - 
        1226/2401*T^42 - 874/2401*T^41 + 125/2401*T^40 + 318/2401*T^39 + 
        1941/2401*T^38 - 1676/2401*T^37 - 1668/2401*T^36 + 86/343*T^35 + 
        373/2401*T^34 + 2/2401*T^33 - 3272/2401*T^32 + 99/343*T^31 + 1924/2401*T^30 
        - 1804/2401*T^29 - 1229/2401*T^28 - 1804/2401*T^27 + 1924/2401*T^26 + 
        99/343*T^25 - 3272/2401*T^24 + 2/2401*T^23 + 373/2401*T^22 + 86/343*T^21 - 
        1668/2401*T^20 - 1676/2401*T^19 + 1941/2401*T^18 + 318/2401*T^17 + 
        125/2401*T^16 - 874/2401*T^15 - 1226/2401*T^14 + 2461/2401*T^13 + 
        1060/2401*T^12 - 856/2401*T^11 - 1167/2401*T^10 + 277/2401*T^9 + 
        2767/2401*T^8 - 1083/2401*T^7 - 976/2401*T^6 + 925/2401*T^5 + 510/2401*T^4 +
        297/343*T^3 - 5/7*T^2 - 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 
        + 3*X*Y^8 + 6*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + X*Y^4 + 3*X*Y^3 + X*Y^2 + 4*X*Y + 
        5*X + 5*Y^30 + 6*Y^29 + 2*Y^28 + Y^27 + 2*Y^26 + 2*Y^25 + 6*Y^24 + 4*Y^23 + 
        Y^22 + 6*Y^21 + 3*Y^20 + Y^18 + 3*Y^17 + 3*Y^16 + 4*Y^15 + 5*Y^14 + 2*Y^13 +
        Y^12 + 4*Y^11 + 6*Y^9 + Y^8 + 2*Y^7 + 6*Y^5 + 5*Y^4 + 4*Y^3 + 3*Y^2 + 5*Y + 
        1,
    -T^56 - 4/7*T^55 - 36/49*T^54 + 109/343*T^53 + 1685/2401*T^52 + 3079/2401*T^51 +
        318/343*T^50 - 699/2401*T^49 - 2248/2401*T^48 - 2717/2401*T^47 - 
        596/2401*T^46 - 94/2401*T^45 + 1846/2401*T^44 + 1367/2401*T^43 - 
        262/2401*T^42 - 1308/2401*T^41 - 828/2401*T^40 - 79/2401*T^39 - 31/2401*T^38
        + 601/2401*T^37 + 492/2401*T^36 + 193/2401*T^35 - 649/2401*T^34 + 
        295/2401*T^33 - 227/2401*T^32 - 1/2401*T^31 - 970/2401*T^30 + 159/2401*T^29 
        - 159/2401*T^27 + 970/2401*T^26 + 1/2401*T^25 + 227/2401*T^24 - 
        295/2401*T^23 + 649/2401*T^22 - 193/2401*T^21 - 492/2401*T^20 - 
        601/2401*T^19 + 31/2401*T^18 + 79/2401*T^17 + 828/2401*T^16 + 1308/2401*T^15
        + 262/2401*T^14 - 1367/2401*T^13 - 1846/2401*T^12 + 94/2401*T^11 + 
        596/2401*T^10 + 2717/2401*T^9 + 2248/2401*T^8 + 699/2401*T^7 - 318/343*T^6 -
        3079/2401*T^5 - 1685/2401*T^4 - 109/343*T^3 + 36/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 5*X*Y^8 + 
        2*X*Y^7 + 4*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + 6*X*Y + 6*X + 
        2*Y^30 + 5*Y^29 + Y^28 + 3*Y^26 + 3*Y^25 + 4*Y^24 + 4*Y^22 + 6*Y^21 + 2*Y^19
        + 4*Y^18 + 2*Y^16 + 2*Y^15 + 6*Y^14 + Y^13 + 4*Y^11 + 5*Y^9 + 2*Y^8 + 6*Y^7 
        + 3*Y^6 + Y^5 + 5*Y^4 + 5*Y^2 + 3*Y + 4,
    T^56 + 2/7*T^55 - 71/49*T^54 - 202/343*T^53 + 2442/2401*T^52 + 1863/2401*T^51 - 
        1742/2401*T^50 - 2852/2401*T^49 + 1305/2401*T^48 + 3133/2401*T^47 - 
        1420/2401*T^46 - 2053/2401*T^45 + 25/49*T^44 + 359/343*T^43 + 54/2401*T^42 -
        2942/2401*T^41 - 139/343*T^40 + 3527/2401*T^39 + 1402/2401*T^38 - 
        3834/2401*T^37 - 1350/2401*T^36 + 3046/2401*T^35 + 2090/2401*T^34 - 
        229/343*T^33 - 2103/2401*T^32 + 940/2401*T^31 + 1601/2401*T^30 - 
        306/2401*T^29 - 1398/2401*T^28 - 306/2401*T^27 + 1601/2401*T^26 + 
        940/2401*T^25 - 2103/2401*T^24 - 229/343*T^23 + 2090/2401*T^22 + 
        3046/2401*T^21 - 1350/2401*T^20 - 3834/2401*T^19 + 1402/2401*T^18 + 
        3527/2401*T^17 - 139/343*T^16 - 2942/2401*T^15 + 54/2401*T^14 + 359/343*T^13
        + 25/49*T^12 - 2053/2401*T^11 - 1420/2401*T^10 + 3133/2401*T^9 + 
        1305/2401*T^8 - 2852/2401*T^7 - 1742/2401*T^6 + 1863/2401*T^5 + 
        2442/2401*T^4 - 202/343*T^3 - 71/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + X*Y^9 + 2*X*Y^8 + 6*X*Y^7 + 3*X*Y^6 + 
        5*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 2*X*Y + 6*X + 4*Y^30 + 4*Y^29 + 5*Y^28 + 
        5*Y^27 + 3*Y^25 + Y^24 + 3*Y^23 + 5*Y^22 + 3*Y^21 + 6*Y^20 + 3*Y^19 + Y^18 +
        6*Y^17 + 2*Y^16 + 4*Y^15 + 5*Y^14 + 2*Y^13 + 2*Y^11 + 6*Y^10 + 5*Y^9 + 3*Y^8
        + 2*Y^7 + 3*Y^5 + 2*Y^4 + 3*Y^3 + 6*Y,
    T^56 + 15/7*T^55 + 17/7*T^54 + 254/343*T^53 - 2738/2401*T^52 - 5450/2401*T^51 - 
        2677/2401*T^50 + 1681/2401*T^49 + 4737/2401*T^48 + 1994/2401*T^47 - 
        3070/2401*T^46 - 7114/2401*T^45 - 5769/2401*T^44 - 1003/2401*T^43 + 
        446/343*T^42 + 3414/2401*T^41 + 1119/2401*T^40 - 939/2401*T^39 - 
        111/2401*T^38 + 2353/2401*T^37 + 3959/2401*T^36 + 6/7*T^35 - 25/343*T^34 - 
        1399/2401*T^33 + 738/2401*T^32 + 1138/2401*T^31 + 107/2401*T^30 - 
        4432/2401*T^29 - 5475/2401*T^28 - 4432/2401*T^27 + 107/2401*T^26 + 
        1138/2401*T^25 + 738/2401*T^24 - 1399/2401*T^23 - 25/343*T^22 + 6/7*T^21 + 
        3959/2401*T^20 + 2353/2401*T^19 - 111/2401*T^18 - 939/2401*T^17 + 
        1119/2401*T^16 + 3414/2401*T^15 + 446/343*T^14 - 1003/2401*T^13 - 
        5769/2401*T^12 - 7114/2401*T^11 - 3070/2401*T^10 + 1994/2401*T^9 + 
        4737/2401*T^8 + 1681/2401*T^7 - 2677/2401*T^6 - 5450/2401*T^5 - 
        2738/2401*T^4 + 254/343*T^3 + 17/7*T^2 + 15/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 
        5*X*Y^8 + 4*X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + X*Y^3 + 5*X*Y^2 + 2*X + 
        4*Y^30 + 3*Y^29 + 6*Y^28 + 3*Y^27 + 5*Y^26 + 5*Y^23 + 3*Y^22 + 4*Y^21 + 
        4*Y^20 + Y^19 + Y^18 + 2*Y^17 + Y^16 + 2*Y^15 + 3*Y^14 + 6*Y^13 + 4*Y^12 + 
        5*Y^10 + 4*Y^9 + 2*Y^6 + 2*Y^5 + 6*Y^4 + 2*Y^3 + Y^2 + 3*Y + 6,
    -T^56 + T^55 - 34/49*T^54 + 1/343*T^53 + 1735/2401*T^52 - 3846/2401*T^51 + 
        2806/2401*T^50 + 6/343*T^49 - 383/343*T^48 + 4538/2401*T^47 - 3853/2401*T^46
        + 2211/2401*T^45 + 1017/2401*T^44 - 2480/2401*T^43 + 2376/2401*T^42 - 
        1220/2401*T^41 + 1300/2401*T^40 + 236/2401*T^39 - 1002/2401*T^38 + 
        1889/2401*T^37 - 278/343*T^36 + 2617/2401*T^35 - 1446/2401*T^34 - 
        408/2401*T^33 + 209/343*T^32 - 1766/2401*T^31 + 291/343*T^30 - 
        1457/2401*T^29 + 1457/2401*T^27 - 291/343*T^26 + 1766/2401*T^25 - 
        209/343*T^24 + 408/2401*T^23 + 1446/2401*T^22 - 2617/2401*T^21 + 
        278/343*T^20 - 1889/2401*T^19 + 1002/2401*T^18 - 236/2401*T^17 - 
        1300/2401*T^16 + 1220/2401*T^15 - 2376/2401*T^14 + 2480/2401*T^13 - 
        1017/2401*T^12 - 2211/2401*T^11 + 3853/2401*T^10 - 4538/2401*T^9 + 
        383/343*T^8 - 6/343*T^7 - 2806/2401*T^6 + 3846/2401*T^5 - 1735/2401*T^4 - 
        1/343*T^3 + 34/49*T^2 - T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 2*X*Y^11 + X*Y^9 + 4*X*Y^8 + 4*X*Y^7 + 
        X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 2*X + Y^30 + 2*Y^29 + 6*Y^28
        + 3*Y^27 + Y^26 + 4*Y^25 + 2*Y^24 + 3*Y^23 + 5*Y^22 + 4*Y^21 + 2*Y^20 + 
        5*Y^19 + 2*Y^17 + 6*Y^16 + 2*Y^15 + 2*Y^14 + 3*Y^13 + 2*Y^12 + 2*Y^11 + 
        4*Y^10 + 4*Y^9 + 4*Y^8 + 4*Y^7 + 3*Y^6 + 2*Y^4 + 4*Y^3 + 2*Y^2 + Y,
    -T^56 + 9/49*T^54 + 170/343*T^53 + 1052/2401*T^52 - 2137/2401*T^51 + 
        1371/2401*T^50 + 536/2401*T^49 + 20/343*T^48 - 1420/2401*T^47 - 
        2189/2401*T^46 + 1077/2401*T^45 + 251/343*T^44 + 159/2401*T^43 + 
        425/2401*T^42 + 541/2401*T^41 + 942/2401*T^40 + 543/2401*T^39 - 
        2284/2401*T^38 - 96/2401*T^37 - 498/2401*T^36 + 71/343*T^35 + 888/2401*T^34 
        - 883/2401*T^33 + 789/2401*T^32 - 30/343*T^31 + 415/2401*T^30 + 52/2401*T^29
        - 52/2401*T^27 - 415/2401*T^26 + 30/343*T^25 - 789/2401*T^24 + 883/2401*T^23
        - 888/2401*T^22 - 71/343*T^21 + 498/2401*T^20 + 96/2401*T^19 + 
        2284/2401*T^18 - 543/2401*T^17 - 942/2401*T^16 - 541/2401*T^15 - 
        425/2401*T^14 - 159/2401*T^13 - 251/343*T^12 - 1077/2401*T^11 + 
        2189/2401*T^10 + 1420/2401*T^9 - 20/343*T^8 - 536/2401*T^7 - 1371/2401*T^6 +
        2137/2401*T^5 - 1052/2401*T^4 - 170/343*T^3 - 9/49*T^2 + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + 5*X*Y^9 + 3*X*Y^8 + 
        4*X*Y^7 + 3*X*Y^4 + 4*X*Y^3 + 3*X*Y + 5*X + 3*Y^30 + 2*Y^29 + 3*Y^28 + 
        4*Y^26 + 6*Y^24 + 4*Y^23 + 6*Y^22 + 2*Y^21 + 5*Y^20 + 3*Y^19 + 5*Y^18 + 
        6*Y^16 + 4*Y^15 + 2*Y^13 + 5*Y^12 + 3*Y^11 + 3*Y^10 + Y^9 + Y^8 + 6*Y^6 + 
        Y^4 + Y^3 + 4*Y + 1,
    -T^56 + 10/7*T^55 - 51/49*T^54 - 99/343*T^53 + 1700/2401*T^52 - 2150/2401*T^51 +
        3061/2401*T^50 - 2131/2401*T^49 + 127/2401*T^48 + 1646/2401*T^47 + 
        170/2401*T^46 - 48/49*T^45 + 359/343*T^44 - 300/2401*T^43 - 1248/2401*T^42 +
        2521/2401*T^41 - 4052/2401*T^40 + 5002/2401*T^39 - 3098/2401*T^38 - 
        484/2401*T^37 + 1823/2401*T^36 - 307/343*T^35 + 1494/2401*T^34 - 
        2382/2401*T^33 + 1782/2401*T^32 - 1342/2401*T^31 + 1154/2401*T^30 - 
        1153/2401*T^29 + 1153/2401*T^27 - 1154/2401*T^26 + 1342/2401*T^25 - 
        1782/2401*T^24 + 2382/2401*T^23 - 1494/2401*T^22 + 307/343*T^21 - 
        1823/2401*T^20 + 484/2401*T^19 + 3098/2401*T^18 - 5002/2401*T^17 + 
        4052/2401*T^16 - 2521/2401*T^15 + 1248/2401*T^14 + 300/2401*T^13 - 
        359/343*T^12 + 48/49*T^11 - 170/2401*T^10 - 1646/2401*T^9 - 127/2401*T^8 + 
        2131/2401*T^7 - 3061/2401*T^6 + 2150/2401*T^5 - 1700/2401*T^4 + 99/343*T^3 +
        51/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 3*X*Y^9 + 
        X*Y^8 + X*Y^7 + 5*X*Y^5 + 6*X*Y^4 + X*Y^3 + 5*X*Y^2 + 6*X + 4*Y^30 + 4*Y^29 
        + 5*Y^28 + 4*Y^27 + 5*Y^26 + Y^24 + 4*Y^22 + 5*Y^21 + 5*Y^19 + 2*Y^18 + 
        3*Y^17 + 6*Y^16 + 5*Y^15 + 4*Y^14 + 4*Y^13 + 2*Y^12 + 4*Y^11 + Y^10 + 6*Y^9 
        + Y^7 + 4*Y^6 + 4*Y^5 + 3*Y^4 + 2*Y^3 + 3*Y^2 + 4*Y + 6,
    -T^56 - 8/7*T^55 - 2/7*T^54 - 241/343*T^53 - 631/2401*T^52 + 2068/2401*T^51 + 
        996/2401*T^50 + 778/2401*T^49 + 272/343*T^48 - 236/2401*T^47 - 746/2401*T^46
        + 911/2401*T^45 - 127/343*T^44 - 1543/2401*T^43 + 442/2401*T^42 - 
        346/2401*T^41 - 597/2401*T^40 + 1464/2401*T^39 + 817/2401*T^38 + 
        1830/2401*T^37 + 3552/2401*T^36 + 1079/2401*T^35 + 580/2401*T^34 + 
        55/343*T^33 - 2015/2401*T^32 - 1319/2401*T^31 - 134/2401*T^30 - 
        1363/2401*T^29 + 1363/2401*T^27 + 134/2401*T^26 + 1319/2401*T^25 + 
        2015/2401*T^24 - 55/343*T^23 - 580/2401*T^22 - 1079/2401*T^21 - 
        3552/2401*T^20 - 1830/2401*T^19 - 817/2401*T^18 - 1464/2401*T^17 + 
        597/2401*T^16 + 346/2401*T^15 - 442/2401*T^14 + 1543/2401*T^13 + 
        127/343*T^12 - 911/2401*T^11 + 746/2401*T^10 + 236/2401*T^9 - 272/343*T^8 - 
        778/2401*T^7 - 996/2401*T^6 - 2068/2401*T^5 + 631/2401*T^4 + 241/343*T^3 + 
        2/7*T^2 + 8/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^13 + 3*X*Y^12 + 3*X*Y^10 + 4*X*Y^9 + 5*X*Y^7 + 3*X*Y^6 + 
        X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 4*X*Y + 5*X + 3*Y^30 + 3*Y^28 + 4*Y^27
        + 5*Y^26 + Y^25 + Y^24 + Y^23 + Y^22 + Y^20 + 2*Y^19 + Y^18 + 6*Y^17 + Y^15 
        + 6*Y^14 + Y^12 + Y^11 + 6*Y^9 + 5*Y^8 + 5*Y^7 + 2*Y^6 + Y^5 + 5*Y^4 + Y^3 +
        4*Y + 3,
    -T^56 + 8/7*T^55 - 5/49*T^54 - 103/343*T^53 - 699/2401*T^52 + 1215/2401*T^51 - 
        2077/2401*T^50 + 2346/2401*T^49 - 1525/2401*T^48 + 783/2401*T^47 - 
        1564/2401*T^46 + 1812/2401*T^45 - 1/2401*T^44 - 37/2401*T^43 - 
        1207/2401*T^42 + 937/2401*T^41 - 435/2401*T^40 + 1040/2401*T^39 - 
        312/2401*T^38 + 277/2401*T^37 - 367/2401*T^36 - 565/2401*T^35 + 
        1511/2401*T^34 - 1124/2401*T^33 - 587/2401*T^32 + 1151/2401*T^31 - 
        186/2401*T^30 + 48/2401*T^29 - 48/2401*T^27 + 186/2401*T^26 - 1151/2401*T^25
        + 587/2401*T^24 + 1124/2401*T^23 - 1511/2401*T^22 + 565/2401*T^21 + 
        367/2401*T^20 - 277/2401*T^19 + 312/2401*T^18 - 1040/2401*T^17 + 
        435/2401*T^16 - 937/2401*T^15 + 1207/2401*T^14 + 37/2401*T^13 + 1/2401*T^12 
        - 1812/2401*T^11 + 1564/2401*T^10 - 783/2401*T^9 + 1525/2401*T^8 - 
        2346/2401*T^7 + 2077/2401*T^6 - 1215/2401*T^5 + 699/2401*T^4 + 103/343*T^3 +
        5/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + X*Y^12 + 5*X*Y^10 + 5*X*Y^9 + 5*X*Y^8 + 
        3*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 3*X*Y + 3*X + Y^30
        + 5*Y^29 + 6*Y^28 + Y^27 + 3*Y^26 + 5*Y^25 + 3*Y^24 + 3*Y^23 + 2*Y^22 + 
        2*Y^21 + 2*Y^20 + 3*Y^19 + 3*Y^16 + 4*Y^15 + 5*Y^14 + 5*Y^13 + 3*Y^12 + 
        6*Y^11 + 2*Y^10 + 6*Y^8 + 6*Y^7 + 3*Y^5 + 5*Y^3 + 5*Y^2 + 5*Y + 4,
    -T^56 + 4/7*T^55 + 1/7*T^54 + 15/343*T^53 - 255/2401*T^52 + 792/2401*T^51 + 
        498/2401*T^50 - 370/2401*T^49 + 790/2401*T^48 - 81/2401*T^47 + 516/2401*T^46
        + 610/2401*T^45 - 1496/2401*T^44 + 139/2401*T^43 - 155/2401*T^42 - 
        1245/2401*T^41 + 45/343*T^40 - 774/2401*T^39 - 339/2401*T^38 - 208/2401*T^37
        + 1128/2401*T^36 - 559/2401*T^35 - 172/2401*T^34 + 1363/2401*T^33 + 
        68/343*T^32 + 234/2401*T^31 + 32/343*T^30 + 214/2401*T^29 - 214/2401*T^27 - 
        32/343*T^26 - 234/2401*T^25 - 68/343*T^24 - 1363/2401*T^23 + 172/2401*T^22 +
        559/2401*T^21 - 1128/2401*T^20 + 208/2401*T^19 + 339/2401*T^18 + 
        774/2401*T^17 - 45/343*T^16 + 1245/2401*T^15 + 155/2401*T^14 - 139/2401*T^13
        + 1496/2401*T^12 - 610/2401*T^11 - 516/2401*T^10 + 81/2401*T^9 - 
        790/2401*T^8 + 370/2401*T^7 - 498/2401*T^6 - 792/2401*T^5 + 255/2401*T^4 - 
        15/343*T^3 - 1/7*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 
        + 3*X*Y^8 + 6*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 
        5*X*Y + X + 2*Y^30 + 5*Y^29 + 4*Y^28 + 3*Y^27 + 6*Y^26 + 5*Y^25 + 6*Y^23 + 
        6*Y^21 + 5*Y^20 + 6*Y^19 + 2*Y^18 + 3*Y^17 + 4*Y^16 + 6*Y^15 + 3*Y^14 + Y^13
        + 4*Y^12 + 5*Y^10 + 4*Y^9 + Y^8 + Y^7 + 6*Y^5 + 4*Y^4 + 5*Y^3 + 5*Y^2 + Y + 
        1,
    -T^56 - 10/7*T^55 + 23/49*T^54 + 743/343*T^53 + 1332/2401*T^52 - 5564/2401*T^51 
        - 5420/2401*T^50 + 2283/2401*T^49 + 8305/2401*T^48 + 6037/2401*T^47 - 
        2696/2401*T^46 - 8702/2401*T^45 - 4302/2401*T^44 + 6179/2401*T^43 + 
        9559/2401*T^42 + 17/49*T^41 - 9203/2401*T^40 - 8469/2401*T^39 + 
        1726/2401*T^38 + 9217/2401*T^37 + 5102/2401*T^36 - 4521/2401*T^35 - 
        6539/2401*T^34 + 787/2401*T^33 + 6810/2401*T^32 + 4317/2401*T^31 - 
        2098/2401*T^30 - 3945/2401*T^29 + 3945/2401*T^27 + 2098/2401*T^26 - 
        4317/2401*T^25 - 6810/2401*T^24 - 787/2401*T^23 + 6539/2401*T^22 + 
        4521/2401*T^21 - 5102/2401*T^20 - 9217/2401*T^19 - 1726/2401*T^18 + 
        8469/2401*T^17 + 9203/2401*T^16 - 17/49*T^15 - 9559/2401*T^14 - 
        6179/2401*T^13 + 4302/2401*T^12 + 8702/2401*T^11 + 2696/2401*T^10 - 
        6037/2401*T^9 - 8305/2401*T^8 - 2283/2401*T^7 + 5420/2401*T^6 + 
        5564/2401*T^5 - 1332/2401*T^4 - 743/343*T^3 - 23/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 2*X*Y^9 + 2*X*Y^7 + 3*X*Y^6 + 
        X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 2*X*Y + 2*Y^30 + 6*Y^27 + 4*Y^26 + 5*Y^25 + 
        5*Y^23 + 3*Y^22 + 6*Y^20 + 4*Y^19 + 2*Y^17 + 2*Y^13 + 4*Y^12 + Y^11 + 6*Y^10
        + 4*Y^9 + 3*Y^7 + 5*Y^6 + Y^5 + Y^4 + 3*Y^3 + 3*Y^2 + 6*Y + 2,
    -T^56 + 6/7*T^55 - 10/49*T^54 + 22/343*T^53 + 1018/2401*T^52 - 744/2401*T^51 - 
        802/2401*T^50 + 530/2401*T^49 + 165/343*T^48 - 250/2401*T^47 + 787/2401*T^46
        + 187/2401*T^45 - 2689/2401*T^44 + 276/343*T^43 - 1342/2401*T^42 + 
        752/2401*T^41 + 997/2401*T^40 - 1098/2401*T^39 - 1084/2401*T^38 + 
        51/2401*T^37 + 906/2401*T^36 + 410/2401*T^35 + 439/2401*T^34 - 527/2401*T^33
        - 634/2401*T^32 + 437/2401*T^31 - 18/2401*T^30 + 1142/2401*T^29 - 
        1142/2401*T^27 + 18/2401*T^26 - 437/2401*T^25 + 634/2401*T^24 + 
        527/2401*T^23 - 439/2401*T^22 - 410/2401*T^21 - 906/2401*T^20 - 51/2401*T^19
        + 1084/2401*T^18 + 1098/2401*T^17 - 997/2401*T^16 - 752/2401*T^15 + 
        1342/2401*T^14 - 276/343*T^13 + 2689/2401*T^12 - 187/2401*T^11 - 
        787/2401*T^10 + 250/2401*T^9 - 165/343*T^8 - 530/2401*T^7 + 802/2401*T^6 + 
        744/2401*T^5 - 1018/2401*T^4 - 22/343*T^3 + 10/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 3*X*Y^10 + X*Y^8 + 6*X*Y^7 + 4*X*Y^6 + 
        4*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 5*X*Y + X + Y^30 + 3*Y^29 + 4*Y^28 +
        Y^27 + 2*Y^26 + 2*Y^25 + 2*Y^24 + 3*Y^22 + 3*Y^19 + 2*Y^18 + 5*Y^17 + 3*Y^16
        + 4*Y^15 + Y^14 + 3*Y^13 + 5*Y^12 + 6*Y^11 + 5*Y^10 + 2*Y^9 + Y^8 + 3*Y^6 + 
        4*Y^5 + 6*Y^4 + 2*Y^3 + 6*Y + 4,
    -T^56 + 15/7*T^55 - 138/49*T^54 + 999/343*T^53 - 4793/2401*T^52 + 2287/2401*T^51
        + 995/2401*T^50 - 3992/2401*T^49 + 6290/2401*T^48 - 894/343*T^47 + 
        3870/2401*T^46 - 2202/2401*T^45 + 871/2401*T^44 - 541/2401*T^43 + 
        1476/2401*T^42 - 429/343*T^41 + 4097/2401*T^40 - 3862/2401*T^39 + 
        1440/2401*T^38 + 2120/2401*T^37 - 4619/2401*T^36 + 5765/2401*T^35 - 
        5470/2401*T^34 + 4047/2401*T^33 - 1166/2401*T^32 - 1017/2401*T^31 + 
        2110/2401*T^30 - 1849/2401*T^29 + 1849/2401*T^27 - 2110/2401*T^26 + 
        1017/2401*T^25 + 1166/2401*T^24 - 4047/2401*T^23 + 5470/2401*T^22 - 
        5765/2401*T^21 + 4619/2401*T^20 - 2120/2401*T^19 - 1440/2401*T^18 + 
        3862/2401*T^17 - 4097/2401*T^16 + 429/343*T^15 - 1476/2401*T^14 + 
        541/2401*T^13 - 871/2401*T^12 + 2202/2401*T^11 - 3870/2401*T^10 + 
        894/343*T^9 - 6290/2401*T^8 + 3992/2401*T^7 - 995/2401*T^6 - 2287/2401*T^5 +
        4793/2401*T^4 - 999/343*T^3 + 138/49*T^2 - 15/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^13 + 2*X*Y^12 + X*Y^10 + 3*X*Y^9 + 3*X*Y^8 + 3*X*Y^7 + 
        X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + X + 3*Y^30 + 3*Y^29 + 2*Y^28
        + 3*Y^26 + 6*Y^25 + 3*Y^24 + 3*Y^22 + 2*Y^21 + 3*Y^19 + Y^17 + 2*Y^16 + Y^15
        + 3*Y^14 + 2*Y^13 + Y^12 + 5*Y^11 + 6*Y^10 + 2*Y^9 + 5*Y^8 + 6*Y^6 + 3*Y^3 +
        Y^2 + 6*Y + 6,
    -T^56 + 2/7*T^55 - 4/49*T^54 + 46/49*T^53 + 132/2401*T^52 - 256/2401*T^51 - 
        993/2401*T^50 + 1268/2401*T^49 - 944/2401*T^48 + 167/2401*T^47 - 
        1712/2401*T^46 - 65/2401*T^45 + 1739/2401*T^44 + 927/2401*T^43 + 
        858/2401*T^42 - 2291/2401*T^41 - 719/2401*T^40 - 181/2401*T^39 + 
        120/2401*T^38 - 48/343*T^37 + 492/2401*T^36 - 155/2401*T^35 + 2469/2401*T^34
        + 19/2401*T^33 - 109/2401*T^32 - 682/2401*T^31 - 1465/2401*T^30 - 
        228/2401*T^29 + 228/2401*T^27 + 1465/2401*T^26 + 682/2401*T^25 + 
        109/2401*T^24 - 19/2401*T^23 - 2469/2401*T^22 + 155/2401*T^21 - 
        492/2401*T^20 + 48/343*T^19 - 120/2401*T^18 + 181/2401*T^17 + 719/2401*T^16 
        + 2291/2401*T^15 - 858/2401*T^14 - 927/2401*T^13 - 1739/2401*T^12 + 
        65/2401*T^11 + 1712/2401*T^10 - 167/2401*T^9 + 944/2401*T^8 - 1268/2401*T^7 
        + 993/2401*T^6 + 256/2401*T^5 - 132/2401*T^4 - 46/49*T^3 + 4/49*T^2 - 2/7*T 
        + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + X*Y^13 + X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 2*X*Y^8 + 
        3*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + X*Y^3 + 3*X*Y^2 + 3*X*Y + 4*X + 
        6*Y^30 + 2*Y^29 + 5*Y^28 + 5*Y^27 + 2*Y^26 + Y^25 + 6*Y^24 + 6*Y^23 + Y^22 +
        5*Y^21 + 2*Y^20 + 3*Y^19 + 5*Y^18 + 5*Y^17 + 4*Y^16 + 3*Y^15 + 5*Y^14 + Y^13
        + 6*Y^12 + 6*Y^11 + 2*Y^10 + 5*Y^8 + 5*Y^7 + 3*Y^6 + 6*Y^5 + 5*Y^4 + 2*Y^3 +
        6*Y^2 + 2*Y + 4,
    T^56 + 3/7*T^55 - 43/49*T^54 - 106/343*T^53 + 139/343*T^52 + 67/343*T^51 - 
        253/2401*T^50 + 962/2401*T^49 + 965/2401*T^48 - 734/2401*T^47 - 
        412/2401*T^46 + 788/2401*T^45 - 545/2401*T^44 - 503/2401*T^43 + 
        726/2401*T^42 - 352/2401*T^41 - 365/2401*T^40 + 1415/2401*T^39 + 
        965/2401*T^38 - 1406/2401*T^37 - 1782/2401*T^36 + 671/2401*T^35 + 
        405/2401*T^34 - 480/2401*T^33 + 57/343*T^32 - 237/2401*T^31 - 984/2401*T^30 
        - 288/2401*T^29 + 853/2401*T^28 - 288/2401*T^27 - 984/2401*T^26 - 
        237/2401*T^25 + 57/343*T^24 - 480/2401*T^23 + 405/2401*T^22 + 671/2401*T^21 
        - 1782/2401*T^20 - 1406/2401*T^19 + 965/2401*T^18 + 1415/2401*T^17 - 
        365/2401*T^16 - 352/2401*T^15 + 726/2401*T^14 - 503/2401*T^13 - 
        545/2401*T^12 + 788/2401*T^11 - 412/2401*T^10 - 734/2401*T^9 + 965/2401*T^8 
        + 962/2401*T^7 - 253/2401*T^6 + 67/343*T^5 + 139/343*T^4 - 106/343*T^3 - 
        43/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 5*X*Y^12 + 4*X*Y^10 + 6*X*Y^9 + 3*X*Y^8 + 2*X*Y^7 + 
        4*X*Y^6 + 4*X*Y^5 + 3*X*Y^3 + 4*X*Y^2 + 6*X*Y + X + Y^30 + 5*Y^29 + 4*Y^28 +
        3*Y^27 + 5*Y^25 + Y^24 + 6*Y^23 + 6*Y^22 + Y^21 + 2*Y^20 + 3*Y^19 + 3*Y^18 +
        3*Y^17 + 4*Y^16 + Y^15 + 5*Y^14 + 4*Y^13 + 3*Y^12 + 6*Y^11 + 6*Y^9 + Y^8 + 
        6*Y^7 + 6*Y^6 + 6*Y^5 + Y^4 + Y^3 + 3*Y + 1,
    -T^56 + 4/7*T^55 - 4/49*T^54 - 120/343*T^53 + 1592/2401*T^52 - 1518/2401*T^51 + 
        1098/2401*T^50 + 209/343*T^49 - 1074/2401*T^48 - 158/2401*T^47 + 
        299/2401*T^46 - 1093/2401*T^45 + 838/2401*T^44 - 2/7*T^43 - 1381/2401*T^42 +
        1950/2401*T^41 - 920/2401*T^40 + 769/2401*T^39 + 300/2401*T^38 - 
        902/2401*T^37 + 1795/2401*T^36 + 88/2401*T^35 - 1026/2401*T^34 + 
        185/2401*T^33 + 200/2401*T^32 - 734/2401*T^31 + 27/49*T^30 - 207/343*T^29 + 
        207/343*T^27 - 27/49*T^26 + 734/2401*T^25 - 200/2401*T^24 - 185/2401*T^23 + 
        1026/2401*T^22 - 88/2401*T^21 - 1795/2401*T^20 + 902/2401*T^19 - 
        300/2401*T^18 - 769/2401*T^17 + 920/2401*T^16 - 1950/2401*T^15 + 
        1381/2401*T^14 + 2/7*T^13 - 838/2401*T^12 + 1093/2401*T^11 - 299/2401*T^10 +
        158/2401*T^9 + 1074/2401*T^8 - 209/343*T^7 - 1098/2401*T^6 + 1518/2401*T^5 -
        1592/2401*T^4 + 120/343*T^3 + 4/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 2*X*Y^8 + X*Y^7 + 
        X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 3*X*Y + 2*X + 4*Y^30 + Y^29 + 2*Y^26 +
        3*Y^24 + 6*Y^23 + 5*Y^22 + 4*Y^21 + 4*Y^20 + Y^19 + 6*Y^18 + 5*Y^16 + 5*Y^15
        + 6*Y^14 + Y^13 + 3*Y^12 + 3*Y^11 + 2*Y^10 + 4*Y^9 + 5*Y^8 + 3*Y^7 + 4*Y^6 +
        4*Y^5 + 4*Y^3 + 2*Y^2 + 3*Y + 4,
    T^56 + 8/7*T^55 + 45/49*T^54 + 214/343*T^53 - 2410/2401*T^52 - 521/343*T^51 - 
        2850/2401*T^50 - 1655/2401*T^49 - 125/2401*T^48 + 1912/2401*T^47 + 
        1938/2401*T^46 + 1257/2401*T^45 + 2083/2401*T^44 + 1248/2401*T^43 + 
        297/2401*T^42 + 326/2401*T^41 - 993/2401*T^40 - 2685/2401*T^39 - 
        2703/2401*T^38 - 2337/2401*T^37 - 1087/2401*T^36 + 1200/2401*T^35 + 
        2091/2401*T^34 + 2192/2401*T^33 + 1521/2401*T^32 + 5/49*T^31 - 
        1121/2401*T^30 - 2298/2401*T^29 - 2493/2401*T^28 - 2298/2401*T^27 - 
        1121/2401*T^26 + 5/49*T^25 + 1521/2401*T^24 + 2192/2401*T^23 + 
        2091/2401*T^22 + 1200/2401*T^21 - 1087/2401*T^20 - 2337/2401*T^19 - 
        2703/2401*T^18 - 2685/2401*T^17 - 993/2401*T^16 + 326/2401*T^15 + 
        297/2401*T^14 + 1248/2401*T^13 + 2083/2401*T^12 + 1257/2401*T^11 + 
        1938/2401*T^10 + 1912/2401*T^9 - 125/2401*T^8 - 1655/2401*T^7 - 
        2850/2401*T^6 - 521/343*T^5 - 2410/2401*T^4 + 214/343*T^3 + 45/49*T^2 + 
        8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 2*X*Y^13 + X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 6*X*Y^8 + 
        3*X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + X*Y^4 + X*Y^3 + X*Y^2 + 3*X*Y + X + 4*Y^30 + 
        6*Y^29 + 3*Y^28 + 3*Y^27 + 2*Y^26 + 6*Y^25 + 5*Y^24 + 5*Y^23 + 3*Y^22 + 
        4*Y^21 + 3*Y^20 + 2*Y^17 + 5*Y^16 + 5*Y^15 + 3*Y^14 + 3*Y^13 + 4*Y^12 + 
        6*Y^11 + 2*Y^10 + 2*Y^9 + 4*Y^8 + 4*Y^7 + 6*Y^6 + 3*Y^5 + 2*Y^4 + 6*Y^3 + 
        6*Y^2 + 2*Y + 3,
    T^56 + 4/7*T^55 - 48/49*T^54 - 97/343*T^53 + 2048/2401*T^52 - 2181/2401*T^51 - 
        1843/2401*T^50 + 982/2401*T^49 - 1167/2401*T^48 - 169/343*T^47 + 
        2246/2401*T^46 + 1083/2401*T^45 - 41/343*T^44 + 1208/2401*T^43 + 
        1599/2401*T^42 + 737/2401*T^41 + 281/2401*T^40 - 69/2401*T^39 - 
        505/2401*T^38 - 1143/2401*T^37 - 1307/2401*T^36 - 706/2401*T^35 - 
        971/2401*T^34 - 2246/2401*T^33 + 118/2401*T^32 + 1914/2401*T^31 + 
        240/2401*T^30 + 596/2401*T^29 + 2992/2401*T^28 + 596/2401*T^27 + 
        240/2401*T^26 + 1914/2401*T^25 + 118/2401*T^24 - 2246/2401*T^23 - 
        971/2401*T^22 - 706/2401*T^21 - 1307/2401*T^20 - 1143/2401*T^19 - 
        505/2401*T^18 - 69/2401*T^17 + 281/2401*T^16 + 737/2401*T^15 + 
        1599/2401*T^14 + 1208/2401*T^13 - 41/343*T^12 + 1083/2401*T^11 + 
        2246/2401*T^10 - 169/343*T^9 - 1167/2401*T^8 + 982/2401*T^7 - 1843/2401*T^6 
        - 2181/2401*T^5 + 2048/2401*T^4 - 97/343*T^3 - 48/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 3*X*Y^8 
        + 6*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 6*X*Y^2 + 2*X*Y + 6*X + 3*Y^30 + 
        2*Y^29 + 5*Y^28 + 2*Y^27 + 3*Y^26 + 3*Y^24 + Y^22 + 2*Y^20 + 3*Y^19 + 5*Y^18
        + 5*Y^17 + Y^16 + 6*Y^15 + 2*Y^14 + 3*Y^12 + 4*Y^11 + 5*Y^10 + 3*Y^9 + 3*Y^8
        + 5*Y^7 + Y^6 + 5*Y^5 + 5*Y^4 + Y^3 + 4*Y^2 + 3*Y + 6,
    -T^56 - 6/7*T^55 - 71/49*T^54 - 13/49*T^53 - 48/2401*T^52 + 1011/2401*T^51 + 
        1269/2401*T^50 + 375/2401*T^49 + 24/2401*T^48 - 367/2401*T^47 - 1/2401*T^46 
        + 786/2401*T^45 + 1287/2401*T^44 - 669/2401*T^43 - 709/2401*T^42 - 
        2047/2401*T^41 + 244/2401*T^40 + 1320/2401*T^39 + 2803/2401*T^38 + 
        4752/2401*T^37 + 3760/2401*T^36 + 2631/2401*T^35 - 1347/2401*T^34 - 
        2561/2401*T^33 - 2493/2401*T^32 - 305/2401*T^31 + 393/2401*T^30 + 
        697/2401*T^29 - 697/2401*T^27 - 393/2401*T^26 + 305/2401*T^25 + 
        2493/2401*T^24 + 2561/2401*T^23 + 1347/2401*T^22 - 2631/2401*T^21 - 
        3760/2401*T^20 - 4752/2401*T^19 - 2803/2401*T^18 - 1320/2401*T^17 - 
        244/2401*T^16 + 2047/2401*T^15 + 709/2401*T^14 + 669/2401*T^13 - 
        1287/2401*T^12 - 786/2401*T^11 + 1/2401*T^10 + 367/2401*T^9 - 24/2401*T^8 - 
        375/2401*T^7 - 1269/2401*T^6 - 1011/2401*T^5 + 48/2401*T^4 + 13/49*T^3 + 
        71/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^13 + 3*X*Y^12 + X*Y^10 + 2*X*Y^9 + 2*X*Y^7 + 3*X*Y^6 + 
        6*X*Y^5 + X*Y^4 + 3*X*Y^3 + X*Y^2 + 5*X*Y + 6*X + 6*Y^30 + 5*Y^29 + 2*Y^28 +
        4*Y^27 + Y^26 + 6*Y^24 + 4*Y^23 + 6*Y^22 + 4*Y^21 + 2*Y^20 + 5*Y^19 + 2*Y^18
        + 5*Y^17 + 4*Y^15 + 2*Y^14 + 4*Y^13 + 6*Y^12 + Y^11 + Y^10 + 3*Y^8 + Y^7 + 
        Y^6 + 3*Y^4 + Y^3 + 4*Y^2 + 6*Y + 4,
    T^56 + 4/7*T^55 + 4/49*T^54 - 18/49*T^53 - 130/343*T^52 - 58/343*T^51 - 
        117/343*T^50 - 1353/2401*T^49 + 190/2401*T^48 - 123/2401*T^47 - 34/2401*T^46
        - 741/2401*T^45 + 87/2401*T^44 + 578/2401*T^43 + 1472/2401*T^42 + 
        2046/2401*T^41 + 606/2401*T^40 - 316/2401*T^39 + 489/2401*T^38 - 
        751/2401*T^37 - 1682/2401*T^36 - 3090/2401*T^35 - 1544/2401*T^34 + 
        52/2401*T^33 + 120/343*T^32 + 89/2401*T^31 + 1312/2401*T^30 + 475/2401*T^29 
        + 1013/2401*T^28 + 475/2401*T^27 + 1312/2401*T^26 + 89/2401*T^25 + 
        120/343*T^24 + 52/2401*T^23 - 1544/2401*T^22 - 3090/2401*T^21 - 
        1682/2401*T^20 - 751/2401*T^19 + 489/2401*T^18 - 316/2401*T^17 + 
        606/2401*T^16 + 2046/2401*T^15 + 1472/2401*T^14 + 578/2401*T^13 + 
        87/2401*T^12 - 741/2401*T^11 - 34/2401*T^10 - 123/2401*T^9 + 190/2401*T^8 - 
        1353/2401*T^7 - 117/343*T^6 - 58/343*T^5 - 130/343*T^4 - 18/49*T^3 + 
        4/49*T^2 + 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 
        X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + X*Y^3 + 5*X*Y^2 + 6*X*Y + 4*X + 3*Y^30
        + Y^29 + 6*Y^28 + 2*Y^27 + 3*Y^26 + 2*Y^25 + 6*Y^24 + 3*Y^23 + 4*Y^22 + 
        2*Y^21 + Y^20 + Y^19 + 3*Y^18 + 5*Y^17 + 3*Y^15 + 3*Y^14 + 4*Y^12 + 3*Y^10 +
        2*Y^9 + 2*Y^8 + 3*Y^7 + 4*Y^6 + Y^5 + Y^4 + 2*Y^2 + 6*Y + 3,
    T^56 - 2/7*T^55 - 3/49*T^54 + 108/343*T^53 - 1310/2401*T^52 - 204/2401*T^51 - 
        1077/2401*T^50 + 817/2401*T^49 + 673/2401*T^48 - 99/2401*T^47 + 
        740/2401*T^46 - 359/2401*T^45 - 1475/2401*T^44 + 24/2401*T^43 - 
        407/2401*T^42 + 354/2401*T^41 + 1271/2401*T^40 + 456/2401*T^39 - 
        589/2401*T^38 - 391/2401*T^37 - 1256/2401*T^36 - 941/2401*T^35 + 
        72/2401*T^34 + 88/343*T^33 + 1975/2401*T^32 - 176/2401*T^31 + 15/49*T^30 + 
        25/2401*T^29 - 2572/2401*T^28 + 25/2401*T^27 + 15/49*T^26 - 176/2401*T^25 + 
        1975/2401*T^24 + 88/343*T^23 + 72/2401*T^22 - 941/2401*T^21 - 1256/2401*T^20
        - 391/2401*T^19 - 589/2401*T^18 + 456/2401*T^17 + 1271/2401*T^16 + 
        354/2401*T^15 - 407/2401*T^14 + 24/2401*T^13 - 1475/2401*T^12 - 
        359/2401*T^11 + 740/2401*T^10 - 99/2401*T^9 + 673/2401*T^8 + 817/2401*T^7 - 
        1077/2401*T^6 - 204/2401*T^5 - 1310/2401*T^4 + 108/343*T^3 - 3/49*T^2 - 
        2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 6*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 +
        6*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + X*Y^3 + 4*X*Y^2 + X*Y + 6*X + 4*Y^30
        + Y^29 + 4*Y^27 + 4*Y^26 + 5*Y^25 + 3*Y^24 + 6*Y^23 + 6*Y^22 + 4*Y^20 + 
        6*Y^18 + 3*Y^17 + 4*Y^16 + 6*Y^15 + 3*Y^13 + 4*Y^11 + 5*Y^10 + 4*Y^9 + 6*Y^8
        + 4*Y^7 + 5*Y^6 + 5*Y^5 + 3*Y^4 + 3*Y^3 + 6*Y^2 + Y + 1,
    -T^56 + T^55 - 13/49*T^54 - 52/343*T^53 - 1854/2401*T^52 + 1438/2401*T^51 + 
        1426/2401*T^50 - 293/343*T^49 + 163/343*T^48 - 1315/2401*T^47 + 
        3735/2401*T^46 - 2013/2401*T^45 - 190/2401*T^44 + 1123/2401*T^43 + 
        375/2401*T^42 + 256/2401*T^41 - 2936/2401*T^40 + 4570/2401*T^39 - 
        1759/2401*T^38 - 103/343*T^37 - 190/343*T^36 + 172/343*T^35 + 2237/2401*T^34
        - 4125/2401*T^33 + 1728/2401*T^32 - 929/2401*T^31 + 2552/2401*T^30 - 
        3215/2401*T^29 + 3215/2401*T^27 - 2552/2401*T^26 + 929/2401*T^25 - 
        1728/2401*T^24 + 4125/2401*T^23 - 2237/2401*T^22 - 172/343*T^21 + 
        190/343*T^20 + 103/343*T^19 + 1759/2401*T^18 - 4570/2401*T^17 + 
        2936/2401*T^16 - 256/2401*T^15 - 375/2401*T^14 - 1123/2401*T^13 + 
        190/2401*T^12 + 2013/2401*T^11 - 3735/2401*T^10 + 1315/2401*T^9 - 
        163/343*T^8 + 293/343*T^7 - 1426/2401*T^6 - 1438/2401*T^5 + 1854/2401*T^4 + 
        52/343*T^3 + 13/49*T^2 - T + 1
*], [*
    X^3 + 5*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + X*Y^11 + 6*X*Y^9 + X*Y^8 + 2*X*Y^7 + 
        5*X*Y^6 + 6*X*Y^5 + X*Y^4 + 5*X*Y^3 + X*Y^2 + 2*X*Y + 5*X + Y^30 + 3*Y^29 + 
        4*Y^28 + 3*Y^26 + Y^25 + 5*Y^24 + 2*Y^23 + 4*Y^22 + 4*Y^21 + Y^20 + Y^17 + 
        2*Y^16 + 2*Y^14 + 2*Y^13 + 2*Y^12 + 3*Y^10 + 6*Y^9 + 4*Y^7 + 6*Y^6 + 4*Y^4 +
        5*Y^3 + Y^2 + 6*Y + 2,
    -T^56 - 3/7*T^55 - 6/49*T^54 - 117/343*T^53 - 1147/2401*T^52 - 159/2401*T^51 - 
        1710/2401*T^50 + 984/2401*T^49 - 403/2401*T^48 + 747/2401*T^47 - 
        141/2401*T^46 + 149/343*T^45 - 69/343*T^44 + 25/2401*T^43 - 1591/2401*T^42 +
        1392/2401*T^41 - 510/2401*T^40 + 281/2401*T^39 - 1830/2401*T^38 + 
        165/2401*T^37 - 265/2401*T^36 + 227/2401*T^35 - 1453/2401*T^34 - 
        1020/2401*T^33 - 1501/2401*T^32 + 282/2401*T^31 - 142/343*T^30 - 
        183/343*T^29 + 183/343*T^27 + 142/343*T^26 - 282/2401*T^25 + 1501/2401*T^24 
        + 1020/2401*T^23 + 1453/2401*T^22 - 227/2401*T^21 + 265/2401*T^20 - 
        165/2401*T^19 + 1830/2401*T^18 - 281/2401*T^17 + 510/2401*T^16 - 
        1392/2401*T^15 + 1591/2401*T^14 - 25/2401*T^13 + 69/343*T^12 - 149/343*T^11 
        + 141/2401*T^10 - 747/2401*T^9 + 403/2401*T^8 - 984/2401*T^7 + 1710/2401*T^6
        + 159/2401*T^5 + 1147/2401*T^4 + 117/343*T^3 + 6/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + X*Y^11 + X*Y^10 + 2*X*Y^8 + 
        2*X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 2*X*Y + 6*X + 
        3*Y^30 + 2*Y^28 + 4*Y^27 + 4*Y^26 + Y^25 + 6*Y^24 + 4*Y^23 + 4*Y^22 + 2*Y^21
        + 3*Y^20 + 6*Y^17 + 2*Y^16 + 5*Y^15 + 5*Y^14 + 4*Y^13 + 4*Y^12 + 4*Y^10 + 
        6*Y^8 + 6*Y^7 + Y^6 + 3*Y^4 + 2*Y^3 + 6*Y^2 + Y + 2,
    -T^56 - 2/7*T^55 - 11/49*T^54 - 120/343*T^53 - 1756/2401*T^52 - 9/49*T^51 - 
        421/2401*T^50 - 842/2401*T^49 - 128/2401*T^48 - 69/343*T^47 + 599/2401*T^46 
        + 801/2401*T^45 + 129/2401*T^44 + 109/2401*T^43 + 27/343*T^42 + 
        1402/2401*T^41 + 129/2401*T^40 + 1646/2401*T^39 + 48/2401*T^38 + 
        837/2401*T^37 + 101/2401*T^36 - 229/2401*T^35 + 379/2401*T^34 - 
        523/2401*T^33 + 398/2401*T^32 - 992/2401*T^31 - 400/2401*T^30 - 127/343*T^29
        + 127/343*T^27 + 400/2401*T^26 + 992/2401*T^25 - 398/2401*T^24 + 
        523/2401*T^23 - 379/2401*T^22 + 229/2401*T^21 - 101/2401*T^20 - 
        837/2401*T^19 - 48/2401*T^18 - 1646/2401*T^17 - 129/2401*T^16 - 
        1402/2401*T^15 - 27/343*T^14 - 109/2401*T^13 - 129/2401*T^12 - 801/2401*T^11
        - 599/2401*T^10 + 69/343*T^9 + 128/2401*T^8 + 842/2401*T^7 + 421/2401*T^6 + 
        9/49*T^5 + 1756/2401*T^4 + 120/343*T^3 + 11/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 
        + 3*X*Y^8 + 5*X*Y^7 + X*Y^6 + X*Y^5 + X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + X*Y + Y^30
        + 5*Y^29 + 6*Y^27 + 6*Y^26 + Y^25 + 5*Y^24 + 6*Y^23 + 5*Y^22 + Y^21 + 2*Y^20
        + Y^19 + 2*Y^18 + Y^17 + 2*Y^16 + 6*Y^15 + 4*Y^14 + 6*Y^13 + 2*Y^12 + 3*Y^11
        + 5*Y^10 + 3*Y^9 + 3*Y^8 + 6*Y^7 + Y^6 + 6*Y^5 + 2*Y^4 + Y^3 + 5*Y^2 + 5*Y +
        2,
    -T^56 + 2/7*T^55 + 31/49*T^54 - 1/49*T^53 - 2606/2401*T^52 + 762/2401*T^51 + 
        211/343*T^50 + 500/2401*T^49 - 1259/2401*T^48 - 493/2401*T^47 + 
        757/2401*T^46 + 593/2401*T^45 - 232/2401*T^44 + 961/2401*T^43 + 
        141/2401*T^42 - 360/2401*T^41 - 52/2401*T^40 + 60/2401*T^39 + 575/2401*T^38 
        - 748/2401*T^37 - 886/2401*T^36 - 542/2401*T^35 + 1454/2401*T^34 - 
        949/2401*T^33 - 858/2401*T^32 - 13/343*T^31 + 34/2401*T^30 - 95/343*T^29 + 
        95/343*T^27 - 34/2401*T^26 + 13/343*T^25 + 858/2401*T^24 + 949/2401*T^23 - 
        1454/2401*T^22 + 542/2401*T^21 + 886/2401*T^20 + 748/2401*T^19 - 
        575/2401*T^18 - 60/2401*T^17 + 52/2401*T^16 + 360/2401*T^15 - 141/2401*T^14 
        - 961/2401*T^13 + 232/2401*T^12 - 593/2401*T^11 - 757/2401*T^10 + 
        493/2401*T^9 + 1259/2401*T^8 - 500/2401*T^7 - 211/343*T^6 - 762/2401*T^5 + 
        2606/2401*T^4 + 1/49*T^3 - 31/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 3*X*Y^13 + X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 
        6*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + X*Y^2 + X*Y + X + 2*Y^30 +
        Y^28 + 4*Y^27 + 3*Y^26 + 6*Y^25 + 5*Y^24 + Y^23 + 6*Y^22 + 6*Y^21 + 2*Y^20 +
        3*Y^19 + 2*Y^18 + 2*Y^16 + 3*Y^15 + 6*Y^14 + 5*Y^13 + 5*Y^12 + 4*Y^11 + 
        5*Y^10 + 4*Y^9 + 2*Y^8 + 3*Y^7 + 2*Y^4 + 3*Y^3 + 6*Y^2 + 5*Y + 3,
    -T^56 - 6/7*T^55 + 24/49*T^54 - 170/343*T^53 - 2218/2401*T^52 + 30/49*T^51 + 
        69/343*T^50 - 704/2401*T^49 + 1496/2401*T^48 - 67/2401*T^47 - 566/2401*T^46 
        + 642/2401*T^45 - 573/2401*T^44 + 106/2401*T^43 - 20/343*T^42 - 
        489/2401*T^41 + 185/343*T^40 + 2/49*T^39 + 41/343*T^38 + 1923/2401*T^37 - 
        355/2401*T^36 - 444/2401*T^35 + 246/2401*T^34 - 1311/2401*T^33 - 
        24/2401*T^32 - 1314/2401*T^31 - 2061/2401*T^30 + 2214/2401*T^29 - 
        2214/2401*T^27 + 2061/2401*T^26 + 1314/2401*T^25 + 24/2401*T^24 + 
        1311/2401*T^23 - 246/2401*T^22 + 444/2401*T^21 + 355/2401*T^20 - 
        1923/2401*T^19 - 41/343*T^18 - 2/49*T^17 - 185/343*T^16 + 489/2401*T^15 + 
        20/343*T^14 - 106/2401*T^13 + 573/2401*T^12 - 642/2401*T^11 + 566/2401*T^10 
        + 67/2401*T^9 - 1496/2401*T^8 + 704/2401*T^7 - 69/343*T^6 - 30/49*T^5 + 
        2218/2401*T^4 + 170/343*T^3 - 24/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 4*X*Y^12 + X*Y^11 + X*Y^10 + 6*X*Y^9 + 4*X*Y^7 + 
        2*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 4*X*Y + 5*X + Y^30 + 4*Y^29 + 6*Y^28
        + 6*Y^27 + Y^26 + 2*Y^25 + 4*Y^24 + 3*Y^23 + 6*Y^22 + 6*Y^21 + 4*Y^20 + 
        5*Y^19 + Y^18 + 3*Y^17 + 4*Y^16 + 6*Y^15 + Y^14 + Y^13 + 6*Y^12 + 3*Y^10 + 
        5*Y^9 + 3*Y^8 + 6*Y^7 + 2*Y^6 + 6*Y^5 + Y^4 + 2*Y^3 + 5*Y + 4,
    T^56 - 11/7*T^55 + 50/49*T^54 + 256/343*T^53 - 5041/2401*T^52 + 3181/2401*T^51 +
        367/2401*T^50 - 2182/2401*T^49 + 2693/2401*T^48 - 1324/2401*T^47 + 
        2148/2401*T^46 - 365/2401*T^45 - 30/49*T^44 + 1963/2401*T^43 - 351/343*T^42 
        + 2012/2401*T^41 - 2403/2401*T^40 + 169/343*T^39 + 3224/2401*T^38 - 
        3530/2401*T^37 + 2227/2401*T^36 + 1579/2401*T^35 - 2718/2401*T^34 + 
        590/2401*T^33 - 1427/2401*T^32 + 1910/2401*T^31 - 895/2401*T^30 - 
        1902/2401*T^29 + 737/343*T^28 - 1902/2401*T^27 - 895/2401*T^26 + 
        1910/2401*T^25 - 1427/2401*T^24 + 590/2401*T^23 - 2718/2401*T^22 + 
        1579/2401*T^21 + 2227/2401*T^20 - 3530/2401*T^19 + 3224/2401*T^18 + 
        169/343*T^17 - 2403/2401*T^16 + 2012/2401*T^15 - 351/343*T^14 + 
        1963/2401*T^13 - 30/49*T^12 - 365/2401*T^11 + 2148/2401*T^10 - 1324/2401*T^9
        + 2693/2401*T^8 - 2182/2401*T^7 + 367/2401*T^6 + 3181/2401*T^5 - 
        5041/2401*T^4 + 256/343*T^3 + 50/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 4*X*Y^13 + X*Y^12 + X*Y^11 + 2*X*Y^10 + 3*X*Y^9 + 4*X*Y^8 + 4*X*Y^7 + 
        2*X*Y^6 + X*Y^5 + 5*X*Y^2 + 6*X + 3*Y^30 + 4*Y^29 + Y^28 + 4*Y^27 + 5*Y^26 +
        4*Y^25 + Y^24 + 3*Y^22 + 3*Y^21 + 4*Y^20 + 5*Y^19 + 3*Y^17 + 5*Y^16 + 6*Y^15
        + 3*Y^14 + 2*Y^13 + 4*Y^12 + 2*Y^11 + 6*Y^10 + 2*Y^9 + Y^8 + 2*Y^7 + 3*Y^6 +
        2*Y^5 + 2*Y^3 + 3*Y^2 + 5*Y + 6,
    T^56 + 4/7*T^55 - 55/49*T^54 - 4/49*T^53 + 3322/2401*T^52 + 1660/2401*T^51 - 
        1066/2401*T^50 - 2012/2401*T^49 + 639/2401*T^48 + 1810/2401*T^47 - 
        1270/2401*T^46 - 1725/2401*T^45 + 1216/2401*T^44 + 992/2401*T^43 - 
        271/343*T^42 - 2426/2401*T^41 + 860/2401*T^40 + 2176/2401*T^39 - 
        822/2401*T^38 - 2612/2401*T^37 - 898/2401*T^36 + 1564/2401*T^35 + 
        1144/2401*T^34 - 1367/2401*T^33 - 1114/2401*T^32 + 1994/2401*T^31 + 
        1920/2401*T^30 + 174/2401*T^29 - 47/2401*T^28 + 174/2401*T^27 + 
        1920/2401*T^26 + 1994/2401*T^25 - 1114/2401*T^24 - 1367/2401*T^23 + 
        1144/2401*T^22 + 1564/2401*T^21 - 898/2401*T^20 - 2612/2401*T^19 - 
        822/2401*T^18 + 2176/2401*T^17 + 860/2401*T^16 - 2426/2401*T^15 - 
        271/343*T^14 + 992/2401*T^13 + 1216/2401*T^12 - 1725/2401*T^11 - 
        1270/2401*T^10 + 1810/2401*T^9 + 639/2401*T^8 - 2012/2401*T^7 - 
        1066/2401*T^6 + 1660/2401*T^5 + 3322/2401*T^4 - 4/49*T^3 - 55/49*T^2 + 4/7*T
        + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 
        5*X*Y^7 + 4*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 4*X*Y + 3*X + 
        3*Y^30 + 4*Y^29 + 2*Y^28 + Y^27 + 2*Y^26 + 5*Y^25 + 4*Y^24 + 4*Y^23 + Y^22 +
        6*Y^21 + 6*Y^20 + 3*Y^19 + Y^18 + 4*Y^17 + 4*Y^16 + 2*Y^15 + 3*Y^14 + Y^13 +
        2*Y^12 + Y^10 + Y^8 + 5*Y^7 + 6*Y^5 + 5*Y^4 + Y^3 + 4*Y + 4,
    -T^56 + T^55 + 41/49*T^54 - 667/343*T^53 + 181/343*T^52 + 2795/2401*T^51 - 
        2392/2401*T^50 + 1083/2401*T^49 + 1069/2401*T^48 - 3256/2401*T^47 + 
        2453/2401*T^46 + 1710/2401*T^45 - 3779/2401*T^44 + 1451/2401*T^43 + 
        1815/2401*T^42 - 3380/2401*T^41 + 124/343*T^40 + 2524/2401*T^39 - 
        3160/2401*T^38 - 265/2401*T^37 + 2416/2401*T^36 - 1803/2401*T^35 + 
        52/2401*T^34 + 2332/2401*T^33 - 1955/2401*T^32 - 2/7*T^31 + 2942/2401*T^30 -
        1922/2401*T^29 + 1922/2401*T^27 - 2942/2401*T^26 + 2/7*T^25 + 1955/2401*T^24
        - 2332/2401*T^23 - 52/2401*T^22 + 1803/2401*T^21 - 2416/2401*T^20 + 
        265/2401*T^19 + 3160/2401*T^18 - 2524/2401*T^17 - 124/343*T^16 + 
        3380/2401*T^15 - 1815/2401*T^14 - 1451/2401*T^13 + 3779/2401*T^12 - 
        1710/2401*T^11 - 2453/2401*T^10 + 3256/2401*T^9 - 1069/2401*T^8 - 
        1083/2401*T^7 + 2392/2401*T^6 - 2795/2401*T^5 - 181/343*T^4 + 667/343*T^3 - 
        41/49*T^2 - T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 6*X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + X*Y^8 + 3*X*Y^7 + 
        4*X*Y^6 + 3*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 2*X*Y + 2*X + 3*Y^30 + 6*Y^29 + Y^28
        + 5*Y^27 + 2*Y^26 + 5*Y^25 + Y^24 + 5*Y^23 + 5*Y^22 + 2*Y^20 + 3*Y^19 + 
        6*Y^18 + 5*Y^17 + 6*Y^15 + Y^14 + 2*Y^12 + 5*Y^11 + 4*Y^10 + 3*Y^9 + 3*Y^8 +
        4*Y^6 + Y^5 + 3*Y^4 + 2*Y^3 + 5*Y^2,
    T^56 - 11/7*T^55 + 26/49*T^54 + 141/343*T^53 - 1497/2401*T^52 - 541/2401*T^51 + 
        3089/2401*T^50 - 2445/2401*T^49 - 358/2401*T^48 + 2474/2401*T^47 - 
        2706/2401*T^46 + 1084/2401*T^45 + 1208/2401*T^44 - 328/2401*T^43 - 
        2588/2401*T^42 + 2386/2401*T^41 - 1252/2401*T^40 + 124/2401*T^39 + 
        473/2401*T^38 + 1464/2401*T^37 - 351/343*T^36 + 1270/2401*T^35 + 
        627/2401*T^34 - 2010/2401*T^33 + 1202/2401*T^32 + 730/2401*T^31 - 
        379/2401*T^30 - 1507/2401*T^29 + 320/343*T^28 - 1507/2401*T^27 - 
        379/2401*T^26 + 730/2401*T^25 + 1202/2401*T^24 - 2010/2401*T^23 + 
        627/2401*T^22 + 1270/2401*T^21 - 351/343*T^20 + 1464/2401*T^19 + 
        473/2401*T^18 + 124/2401*T^17 - 1252/2401*T^16 + 2386/2401*T^15 - 
        2588/2401*T^14 - 328/2401*T^13 + 1208/2401*T^12 + 1084/2401*T^11 - 
        2706/2401*T^10 + 2474/2401*T^9 - 358/2401*T^8 - 2445/2401*T^7 + 
        3089/2401*T^6 - 541/2401*T^5 - 1497/2401*T^4 + 141/343*T^3 + 26/49*T^2 - 
        11/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 4*X*Y^7 + 
        6*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 6*X*Y + 2*X + 5*Y^30 + 6*Y^29 + 6*Y^28 + 
        2*Y^27 + 3*Y^26 + Y^25 + Y^24 + 4*Y^23 + Y^22 + 5*Y^21 + 4*Y^19 + 2*Y^18 + 
        5*Y^17 + Y^16 + 5*Y^15 + 2*Y^13 + 6*Y^12 + 4*Y^11 + 4*Y^10 + Y^9 + 2*Y^8 + 
        3*Y^7 + 5*Y^6 + 4*Y^5 + 2*Y^3 + 6*Y^2 + Y + 1,
    T^56 + 2*T^55 + 47/49*T^54 - 374/343*T^53 - 843/343*T^52 - 4656/2401*T^51 + 
        2175/2401*T^50 + 1112/343*T^49 + 5281/2401*T^48 - 3686/2401*T^47 - 
        9453/2401*T^46 - 4775/2401*T^45 + 5881/2401*T^44 + 12123/2401*T^43 + 
        6642/2401*T^42 - 6129/2401*T^41 - 13575/2401*T^40 - 7120/2401*T^39 + 
        7488/2401*T^38 + 13753/2401*T^37 + 5149/2401*T^36 - 192/49*T^35 - 
        16297/2401*T^34 - 7360/2401*T^33 + 9047/2401*T^32 + 16064/2401*T^31 + 
        7583/2401*T^30 - 8682/2401*T^29 - 16903/2401*T^28 - 8682/2401*T^27 + 
        7583/2401*T^26 + 16064/2401*T^25 + 9047/2401*T^24 - 7360/2401*T^23 - 
        16297/2401*T^22 - 192/49*T^21 + 5149/2401*T^20 + 13753/2401*T^19 + 
        7488/2401*T^18 - 7120/2401*T^17 - 13575/2401*T^16 - 6129/2401*T^15 + 
        6642/2401*T^14 + 12123/2401*T^13 + 5881/2401*T^12 - 4775/2401*T^11 - 
        9453/2401*T^10 - 3686/2401*T^9 + 5281/2401*T^8 + 1112/343*T^7 + 
        2175/2401*T^6 - 4656/2401*T^5 - 843/343*T^4 - 374/343*T^3 + 47/49*T^2 + 2*T 
        + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 
        6*X*Y^8 + 3*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + X*Y^3 + X*Y + 5*X + 6*Y^30
        + 5*Y^29 + 4*Y^27 + 4*Y^26 + 5*Y^24 + 2*Y^23 + 3*Y^21 + 2*Y^20 + 3*Y^19 + 
        2*Y^17 + Y^15 + 2*Y^14 + 5*Y^11 + 2*Y^10 + Y^9 + 3*Y^8 + 2*Y^7 + 3*Y^5 + 
        4*Y^4 + 6*Y^3 + 4*Y,
    -T^56 - 6/7*T^55 + 5/49*T^54 - 186/343*T^53 + 1754/2401*T^52 + 64/343*T^51 - 
        1853/2401*T^50 + 2095/2401*T^49 - 1193/2401*T^48 + 961/2401*T^47 + 
        3104/2401*T^46 - 1350/2401*T^45 + 1348/2401*T^44 - 82/2401*T^43 - 
        1593/2401*T^42 + 1091/2401*T^41 - 1651/2401*T^40 + 498/2401*T^39 + 
        215/343*T^38 - 1703/2401*T^37 + 1192/2401*T^36 + 297/2401*T^35 + 
        954/2401*T^34 + 3646/2401*T^33 + 114/343*T^32 + 890/2401*T^31 + 26/2401*T^30
        - 1906/2401*T^29 + 1906/2401*T^27 - 26/2401*T^26 - 890/2401*T^25 - 
        114/343*T^24 - 3646/2401*T^23 - 954/2401*T^22 - 297/2401*T^21 - 
        1192/2401*T^20 + 1703/2401*T^19 - 215/343*T^18 - 498/2401*T^17 + 
        1651/2401*T^16 - 1091/2401*T^15 + 1593/2401*T^14 + 82/2401*T^13 - 
        1348/2401*T^12 + 1350/2401*T^11 - 3104/2401*T^10 - 961/2401*T^9 + 
        1193/2401*T^8 - 2095/2401*T^7 + 1853/2401*T^6 - 64/343*T^5 - 1754/2401*T^4 +
        186/343*T^3 - 5/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 2*X*Y^12 + 5*X*Y^11 + X*Y^10 + 2*X*Y^9 + 6*X*Y^7 + 
        2*X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + X*Y^2 + 3*X*Y + 5*X + Y^30 + 5*Y^27 
        + Y^26 + 2*Y^23 + 2*Y^22 + Y^21 + 6*Y^19 + Y^18 + 5*Y^17 + 5*Y^16 + 4*Y^15 +
        Y^14 + 2*Y^13 + 5*Y^12 + 4*Y^11 + 3*Y^8 + 5*Y^7 + 3*Y^6 + 5*Y^5 + 3*Y^4 + 
        5*Y^3 + 6*Y^2 + 5*Y + 3,
    T^56 - 6/7*T^55 + 26/49*T^54 - 307/343*T^53 + 2953/2401*T^52 - 935/2401*T^51 - 
        549/2401*T^50 - 1341/2401*T^49 - 608/2401*T^48 + 2897/2401*T^47 - 
        2545/2401*T^46 + 2231/2401*T^45 - 4072/2401*T^44 + 5266/2401*T^43 - 
        1542/2401*T^42 + 600/2401*T^41 - 906/2401*T^40 - 325/2401*T^39 + 
        2960/2401*T^38 - 3183/2401*T^37 + 23/49*T^36 - 2995/2401*T^35 + 
        2630/2401*T^34 - 1773/2401*T^33 + 513/2401*T^32 - 255/2401*T^31 - 
        53/343*T^30 + 2160/2401*T^29 - 1786/2401*T^28 + 2160/2401*T^27 - 53/343*T^26
        - 255/2401*T^25 + 513/2401*T^24 - 1773/2401*T^23 + 2630/2401*T^22 - 
        2995/2401*T^21 + 23/49*T^20 - 3183/2401*T^19 + 2960/2401*T^18 - 
        325/2401*T^17 - 906/2401*T^16 + 600/2401*T^15 - 1542/2401*T^14 + 
        5266/2401*T^13 - 4072/2401*T^12 + 2231/2401*T^11 - 2545/2401*T^10 + 
        2897/2401*T^9 - 608/2401*T^8 - 1341/2401*T^7 - 549/2401*T^6 - 935/2401*T^5 +
        2953/2401*T^4 - 307/343*T^3 + 26/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 
        5*X*Y^8 + 2*X*Y^7 + 4*X*Y^6 + X*Y^5 + X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 3*X*Y + 
        2*X + Y^30 + 3*Y^29 + Y^28 + 5*Y^26 + 4*Y^25 + 3*Y^24 + 4*Y^23 + Y^22 + 
        6*Y^20 + Y^19 + 6*Y^18 + 2*Y^17 + 5*Y^15 + 4*Y^14 + 2*Y^13 + 2*Y^12 + Y^11 +
        4*Y^10 + 4*Y^9 + 3*Y^8 + 5*Y^7 + 2*Y^6 + 2*Y^5 + 2*Y^4 + 5*Y^3 + 6*Y + 4,
    -T^56 + 18/7*T^55 - 173/49*T^54 + 1093/343*T^53 - 803/343*T^52 + 4104/2401*T^51 
        - 2935/2401*T^50 + 2930/2401*T^49 - 2827/2401*T^48 + 1105/2401*T^47 + 
        325/343*T^46 - 5130/2401*T^45 + 6376/2401*T^44 - 6647/2401*T^43 + 
        5969/2401*T^42 - 5399/2401*T^41 + 6514/2401*T^40 - 7806/2401*T^39 + 
        6649/2401*T^38 - 4044/2401*T^37 + 323/343*T^36 - 2067/2401*T^35 + 
        2462/2401*T^34 - 408/343*T^33 + 23/49*T^32 + 2251/2401*T^31 - 4269/2401*T^30
        + 3182/2401*T^29 - 3182/2401*T^27 + 4269/2401*T^26 - 2251/2401*T^25 - 
        23/49*T^24 + 408/343*T^23 - 2462/2401*T^22 + 2067/2401*T^21 - 323/343*T^20 +
        4044/2401*T^19 - 6649/2401*T^18 + 7806/2401*T^17 - 6514/2401*T^16 + 
        5399/2401*T^15 - 5969/2401*T^14 + 6647/2401*T^13 - 6376/2401*T^12 + 
        5130/2401*T^11 - 325/343*T^10 - 1105/2401*T^9 + 2827/2401*T^8 - 
        2930/2401*T^7 + 2935/2401*T^6 - 4104/2401*T^5 + 803/343*T^4 - 1093/343*T^3 +
        173/49*T^2 - 18/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 
        + 3*X*Y^8 + 4*X*Y^7 + 6*X*Y^6 + 6*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 6*X*Y + X + 
        3*Y^30 + 4*Y^29 + Y^28 + 5*Y^27 + Y^25 + 3*Y^24 + 6*Y^23 + 2*Y^22 + 4*Y^21 +
        6*Y^20 + 5*Y^18 + 2*Y^17 + 4*Y^16 + 3*Y^15 + 4*Y^14 + 3*Y^13 + 4*Y^12 + 
        3*Y^11 + Y^10 + Y^9 + Y^8 + 4*Y^7 + Y^6 + 6*Y^5 + 3*Y^4 + Y^3 + 3*Y^2 + 4*Y 
        + 3,
    T^56 - 11/7*T^55 + 39/49*T^54 - 107/343*T^53 + 2353/2401*T^52 - 2764/2401*T^51 -
        435/2401*T^50 + 1686/2401*T^49 - 1682/2401*T^48 + 178/343*T^47 - 
        2288/2401*T^46 + 550/343*T^45 - 4069/2401*T^44 + 358/343*T^43 - 31/49*T^42 +
        2634/2401*T^41 - 1656/2401*T^40 + 229/2401*T^39 + 1382/2401*T^38 - 
        134/343*T^37 + 578/2401*T^36 - 1733/2401*T^35 + 2521/2401*T^34 - 
        1091/2401*T^33 - 283/2401*T^32 - 1258/2401*T^31 + 237/343*T^30 + 
        64/2401*T^29 - 1528/2401*T^28 + 64/2401*T^27 + 237/343*T^26 - 1258/2401*T^25
        - 283/2401*T^24 - 1091/2401*T^23 + 2521/2401*T^22 - 1733/2401*T^21 + 
        578/2401*T^20 - 134/343*T^19 + 1382/2401*T^18 + 229/2401*T^17 - 
        1656/2401*T^16 + 2634/2401*T^15 - 31/49*T^14 + 358/343*T^13 - 4069/2401*T^12
        + 550/343*T^11 - 2288/2401*T^10 + 178/343*T^9 - 1682/2401*T^8 + 
        1686/2401*T^7 - 435/2401*T^6 - 2764/2401*T^5 + 2353/2401*T^4 - 107/343*T^3 +
        39/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + X*Y^12 + 5*X*Y^11 + X*Y^10 + X*Y^8 + 
        X*Y^7 + X*Y^6 + 3*X*Y^4 + 4*X*Y^3 + X*Y^2 + X*Y + 6*Y^30 + 3*Y^29 + 3*Y^28 +
        2*Y^27 + 5*Y^26 + 5*Y^25 + Y^23 + Y^22 + 4*Y^21 + 2*Y^20 + 3*Y^19 + 2*Y^18 +
        Y^16 + 3*Y^14 + 3*Y^13 + Y^12 + 3*Y^11 + 5*Y^10 + 2*Y^9 + 3*Y^8 + 5*Y^7 + 
        6*Y^6 + 2*Y^5 + 2*Y^4 + 5*Y^3 + 3*Y^2 + 6,
    -T^56 - 1/7*T^55 + 19/49*T^54 + 80/343*T^53 + 1580/2401*T^52 - 251/2401*T^51 - 
        1273/2401*T^50 - 296/2401*T^49 - 316/2401*T^48 + 698/2401*T^47 + 
        3128/2401*T^46 - 146/2401*T^45 - 2126/2401*T^44 - 90/343*T^43 - 
        2455/2401*T^42 + 675/2401*T^41 + 3583/2401*T^40 + 398/2401*T^39 + 
        351/2401*T^38 - 137/343*T^37 - 3575/2401*T^36 - 482/2401*T^35 + 
        2411/2401*T^34 + 480/2401*T^33 + 2384/2401*T^32 - 264/2401*T^31 - 
        4486/2401*T^30 - 390/2401*T^29 + 390/2401*T^27 + 4486/2401*T^26 + 
        264/2401*T^25 - 2384/2401*T^24 - 480/2401*T^23 - 2411/2401*T^22 + 
        482/2401*T^21 + 3575/2401*T^20 + 137/343*T^19 - 351/2401*T^18 - 
        398/2401*T^17 - 3583/2401*T^16 - 675/2401*T^15 + 2455/2401*T^14 + 
        90/343*T^13 + 2126/2401*T^12 + 146/2401*T^11 - 3128/2401*T^10 - 698/2401*T^9
        + 316/2401*T^8 + 296/2401*T^7 + 1273/2401*T^6 + 251/2401*T^5 - 1580/2401*T^4
        - 80/343*T^3 - 19/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 6*X*Y^10 + X*Y^9 + 3*X*Y^7 + 
        3*X*Y^6 + 3*X*Y^5 + 4*X*Y^3 + 2*X*Y + 2*Y^30 + 3*Y^29 + Y^28 + 2*Y^27 + 
        5*Y^26 + 2*Y^25 + 4*Y^24 + 5*Y^23 + 6*Y^22 + Y^21 + 6*Y^20 + 2*Y^19 + 5*Y^18
        + Y^17 + 6*Y^16 + 4*Y^15 + Y^14 + 5*Y^13 + 3*Y^12 + 4*Y^11 + 3*Y^10 + 6*Y^9 
        + Y^8 + 4*Y^7 + 2*Y^6 + Y^5 + 6*Y^4 + Y^3 + 4*Y^2 + Y + 6,
    -T^56 + 22/49*T^54 - 10/343*T^53 + 312/343*T^52 - 78/2401*T^51 - 341/343*T^50 - 
        527/2401*T^49 - 923/2401*T^48 + 54/343*T^47 + 765/2401*T^46 + 53/2401*T^45 +
        1049/2401*T^44 - 8/49*T^43 - 712/2401*T^42 + 263/2401*T^41 - 201/343*T^40 - 
        67/343*T^39 + 230/343*T^38 + 1019/2401*T^37 + 769/2401*T^36 + 51/2401*T^35 -
        1738/2401*T^34 - 344/2401*T^33 - 1005/2401*T^32 + 374/2401*T^31 + 
        430/343*T^30 - 121/2401*T^29 + 121/2401*T^27 - 430/343*T^26 - 374/2401*T^25 
        + 1005/2401*T^24 + 344/2401*T^23 + 1738/2401*T^22 - 51/2401*T^21 - 
        769/2401*T^20 - 1019/2401*T^19 - 230/343*T^18 + 67/343*T^17 + 201/343*T^16 -
        263/2401*T^15 + 712/2401*T^14 + 8/49*T^13 - 1049/2401*T^12 - 53/2401*T^11 - 
        765/2401*T^10 - 54/343*T^9 + 923/2401*T^8 + 527/2401*T^7 + 341/343*T^6 + 
        78/2401*T^5 - 312/343*T^4 + 10/343*T^3 - 22/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 
        + X*Y^8 + X*Y^7 + 6*X*Y^6 + 5*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 2*X*Y + X + 5*Y^30
        + 3*Y^29 + 5*Y^28 + 6*Y^27 + 3*Y^25 + 4*Y^24 + 6*Y^23 + 2*Y^20 + 6*Y^19 + 
        Y^17 + 6*Y^16 + 4*Y^15 + 6*Y^14 + 2*Y^13 + 6*Y^12 + 4*Y^11 + 4*Y^10 + Y^9 + 
        Y^7 + 6*Y^6 + 2*Y^5 + 3*Y^4 + 2*Y^3 + 6*Y^2 + 3*Y + 4,
    T^56 + 1/7*T^55 - 1/7*T^54 + 125/343*T^53 + 202/343*T^52 - 624/2401*T^51 + 
        17/2401*T^50 + 822/2401*T^49 + 88/343*T^48 + 647/2401*T^47 - 129/343*T^46 + 
        489/2401*T^45 + 1033/2401*T^44 - 176/2401*T^43 - 87/343*T^42 + 
        1651/2401*T^41 + 606/2401*T^40 - 3/343*T^39 - 929/2401*T^38 - 94/2401*T^37 +
        20/2401*T^36 - 120/343*T^35 - 799/2401*T^34 - 551/2401*T^33 + 558/2401*T^32 
        - 190/2401*T^31 - 768/2401*T^30 - 113/343*T^29 + 108/343*T^28 - 113/343*T^27
        - 768/2401*T^26 - 190/2401*T^25 + 558/2401*T^24 - 551/2401*T^23 - 
        799/2401*T^22 - 120/343*T^21 + 20/2401*T^20 - 94/2401*T^19 - 929/2401*T^18 -
        3/343*T^17 + 606/2401*T^16 + 1651/2401*T^15 - 87/343*T^14 - 176/2401*T^13 + 
        1033/2401*T^12 + 489/2401*T^11 - 129/343*T^10 + 647/2401*T^9 + 88/343*T^8 + 
        822/2401*T^7 + 17/2401*T^6 - 624/2401*T^5 + 202/343*T^4 + 125/343*T^3 - 
        1/7*T^2 + 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + X*Y^8 + 
        X*Y^7 + X*Y^6 + 5*X*Y^5 + X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 4*X*Y + 4*Y^30 + 
        2*Y^29 + 3*Y^28 + 4*Y^27 + 6*Y^26 + Y^25 + 4*Y^24 + Y^23 + 4*Y^22 + 4*Y^20 +
        3*Y^19 + 5*Y^18 + 3*Y^17 + 4*Y^16 + 2*Y^15 + 5*Y^14 + 6*Y^13 + Y^12 + 2*Y^11
        + 4*Y^10 + 6*Y^9 + 6*Y^8 + 4*Y^7 + 4*Y^6 + Y^5 + 6*Y^4 + 3*Y^3 + 3*Y^2 + Y +
        4,
    T^56 + T^55 + 23/49*T^54 + 116/343*T^53 + 433/2401*T^52 + 169/343*T^51 - 
        443/2401*T^50 - 2165/2401*T^49 - 2911/2401*T^48 - 2789/2401*T^47 - 
        2249/2401*T^46 - 1956/2401*T^45 - 2246/2401*T^44 - 1831/2401*T^43 - 
        439/2401*T^42 + 1170/2401*T^41 + 2482/2401*T^40 + 2854/2401*T^39 + 
        3790/2401*T^38 + 4460/2401*T^37 + 4240/2401*T^36 + 3210/2401*T^35 + 
        1709/2401*T^34 + 269/2401*T^33 - 544/2401*T^32 - 2904/2401*T^31 - 
        4538/2401*T^30 - 4168/2401*T^29 - 4507/2401*T^28 - 4168/2401*T^27 - 
        4538/2401*T^26 - 2904/2401*T^25 - 544/2401*T^24 + 269/2401*T^23 + 
        1709/2401*T^22 + 3210/2401*T^21 + 4240/2401*T^20 + 4460/2401*T^19 + 
        3790/2401*T^18 + 2854/2401*T^17 + 2482/2401*T^16 + 1170/2401*T^15 - 
        439/2401*T^14 - 1831/2401*T^13 - 2246/2401*T^12 - 1956/2401*T^11 - 
        2249/2401*T^10 - 2789/2401*T^9 - 2911/2401*T^8 - 2165/2401*T^7 - 
        443/2401*T^6 + 169/343*T^5 + 433/2401*T^4 + 116/343*T^3 + 23/49*T^2 + T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + 5*X*Y^9 + 6*X*Y^8 + 4*X*Y^7 + 
        3*X*Y^5 + X*Y^3 + 6*X*Y^2 + 5*X*Y + 4*X + Y^30 + 3*Y^29 + 2*Y^28 + 4*Y^27 + 
        5*Y^26 + 5*Y^25 + 3*Y^24 + 6*Y^22 + 4*Y^21 + 4*Y^20 + 3*Y^19 + Y^18 + 2*Y^17
        + 2*Y^16 + Y^15 + 6*Y^14 + 3*Y^13 + 2*Y^12 + 3*Y^11 + 2*Y^10 + 5*Y^9 + Y^8 +
        4*Y^7 + 2*Y^6 + 4*Y^4 + 2*Y^2 + 5*Y + 4,
    -T^56 - 4/7*T^55 + 9/49*T^54 + 39/343*T^53 + 1220/2401*T^52 + 1226/2401*T^51 + 
        304/2401*T^50 + 776/2401*T^49 - 120/2401*T^48 - 54/343*T^47 + 346/2401*T^46 
        - 312/2401*T^45 - 97/2401*T^44 + 81/2401*T^43 + 64/343*T^42 + 361/2401*T^41 
        + 82/2401*T^40 + 155/343*T^39 - 74/2401*T^38 - 103/343*T^37 - 799/2401*T^36 
        - 1306/2401*T^35 + 181/2401*T^34 + 554/2401*T^33 - 215/2401*T^32 - 
        24/2401*T^31 - 310/2401*T^30 - 296/2401*T^29 + 296/2401*T^27 + 310/2401*T^26
        + 24/2401*T^25 + 215/2401*T^24 - 554/2401*T^23 - 181/2401*T^22 + 
        1306/2401*T^21 + 799/2401*T^20 + 103/343*T^19 + 74/2401*T^18 - 155/343*T^17 
        - 82/2401*T^16 - 361/2401*T^15 - 64/343*T^14 - 81/2401*T^13 + 97/2401*T^12 +
        312/2401*T^11 - 346/2401*T^10 + 54/343*T^9 + 120/2401*T^8 - 776/2401*T^7 - 
        304/2401*T^6 - 1226/2401*T^5 - 1220/2401*T^4 - 39/343*T^3 - 9/49*T^2 + 4/7*T
        + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + X*Y^8 + 6*X*Y^6 + 
        X*Y^5 + 2*X*Y^4 + X*Y^3 + X*Y^2 + 6*X + 5*Y^30 + 5*Y^29 + 2*Y^28 + Y^27 + 
        6*Y^26 + 3*Y^25 + 3*Y^24 + 3*Y^23 + Y^21 + 6*Y^20 + Y^19 + 3*Y^18 + 5*Y^17 +
        5*Y^16 + 6*Y^15 + 6*Y^14 + 4*Y^13 + 5*Y^11 + Y^9 + 3*Y^7 + Y^5 + 6*Y^4 + 
        5*Y^3 + 3*Y^2 + 6*Y + 3,
    T^56 - 4/7*T^55 + 3/7*T^54 - 12/343*T^53 - 316/343*T^52 + 1889/2401*T^51 - 
        1672/2401*T^50 - 310/2401*T^49 + 1780/2401*T^48 - 2906/2401*T^47 + 
        1437/2401*T^46 - 141/343*T^45 - 2174/2401*T^44 + 3572/2401*T^43 - 
        1248/2401*T^42 + 81/2401*T^41 + 2217/2401*T^40 - 365/343*T^39 + 
        1467/2401*T^38 - 111/2401*T^37 - 2001/2401*T^36 + 2481/2401*T^35 - 
        1098/2401*T^34 - 170/2401*T^33 + 922/2401*T^32 - 1509/2401*T^31 + 
        689/2401*T^30 + 135/343*T^29 - 921/2401*T^28 + 135/343*T^27 + 689/2401*T^26 
        - 1509/2401*T^25 + 922/2401*T^24 - 170/2401*T^23 - 1098/2401*T^22 + 
        2481/2401*T^21 - 2001/2401*T^20 - 111/2401*T^19 + 1467/2401*T^18 - 
        365/343*T^17 + 2217/2401*T^16 + 81/2401*T^15 - 1248/2401*T^14 + 
        3572/2401*T^13 - 2174/2401*T^12 - 141/343*T^11 + 1437/2401*T^10 - 
        2906/2401*T^9 + 1780/2401*T^8 - 310/2401*T^7 - 1672/2401*T^6 + 1889/2401*T^5
        - 316/343*T^4 - 12/343*T^3 + 3/7*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^13 + 6*X*Y^12 + 5*X*Y^10 + X*Y^9 + 2*X*Y^8 + 3*X*Y^5 + X*Y^4 
        + 4*X*Y^3 + 6*X*Y + 6*X + 4*Y^30 + 4*Y^29 + 2*Y^28 + 2*Y^26 + 2*Y^24 + 
        5*Y^23 + 5*Y^22 + 5*Y^21 + 3*Y^20 + 2*Y^19 + Y^18 + 4*Y^17 + 5*Y^16 + Y^15 +
        4*Y^14 + 5*Y^13 + 6*Y^12 + 3*Y^11 + 4*Y^9 + Y^8 + 5*Y^7 + 6*Y^6 + 6*Y^5 + 
        3*Y^4 + 4*Y^3 + 2*Y^2 + 6,
    T^56 + 4/7*T^55 + 9/49*T^54 + 9/49*T^53 - 1901/2401*T^52 - 2307/2401*T^51 - 
        3690/2401*T^50 - 1900/2401*T^49 + 704/2401*T^48 + 1490/2401*T^47 + 
        3477/2401*T^46 + 2351/2401*T^45 - 135/2401*T^44 - 213/2401*T^43 - 
        1070/2401*T^42 - 1853/2401*T^41 - 58/2401*T^40 + 127/343*T^39 + 
        1664/2401*T^38 + 472/2401*T^37 - 1583/2401*T^36 - 835/2401*T^35 - 
        327/343*T^34 - 1515/2401*T^33 + 201/2401*T^32 + 370/2401*T^31 + 163/343*T^30
        + 1282/2401*T^29 + 1882/2401*T^28 + 1282/2401*T^27 + 163/343*T^26 + 
        370/2401*T^25 + 201/2401*T^24 - 1515/2401*T^23 - 327/343*T^22 - 
        835/2401*T^21 - 1583/2401*T^20 + 472/2401*T^19 + 1664/2401*T^18 + 
        127/343*T^17 - 58/2401*T^16 - 1853/2401*T^15 - 1070/2401*T^14 - 
        213/2401*T^13 - 135/2401*T^12 + 2351/2401*T^11 + 3477/2401*T^10 + 
        1490/2401*T^9 + 704/2401*T^8 - 1900/2401*T^7 - 3690/2401*T^6 - 2307/2401*T^5
        - 1901/2401*T^4 + 9/49*T^3 + 9/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + X*Y^13 + X*Y^12 + X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 
        4*X*Y^8 + X*Y^7 + 5*X*Y^6 + X*Y^5 + 3*X*Y^4 + X*Y^3 + 2*X*Y + 3*Y^30 + 
        5*Y^29 + 2*Y^27 + 5*Y^26 + Y^25 + 6*Y^24 + 2*Y^23 + Y^22 + 3*Y^21 + 3*Y^19 +
        3*Y^18 + 2*Y^17 + 3*Y^16 + 3*Y^15 + 5*Y^13 + Y^11 + 5*Y^10 + 4*Y^9 + 2*Y^8 +
        6*Y^7 + 5*Y^6 + 6*Y^5 + Y^4 + Y^3 + 5*Y^2 + 3*Y + 4,
    -T^56 - T^55 - 30/49*T^54 + 41/343*T^53 + 1/7*T^52 + 575/2401*T^51 - 
        107/2401*T^50 + 59/2401*T^49 + 561/2401*T^48 + 723/2401*T^47 + 723/2401*T^46
        + 106/343*T^45 + 383/2401*T^44 - 745/2401*T^43 - 1156/2401*T^42 - 
        1457/2401*T^41 - 342/2401*T^40 - 199/2401*T^39 + 832/2401*T^38 + 
        328/2401*T^37 + 127/2401*T^36 - 817/2401*T^35 + 750/2401*T^34 + 
        998/2401*T^33 + 1339/2401*T^32 + 619/2401*T^31 + 1111/2401*T^30 + 
        240/2401*T^29 - 240/2401*T^27 - 1111/2401*T^26 - 619/2401*T^25 - 
        1339/2401*T^24 - 998/2401*T^23 - 750/2401*T^22 + 817/2401*T^21 - 
        127/2401*T^20 - 328/2401*T^19 - 832/2401*T^18 + 199/2401*T^17 + 
        342/2401*T^16 + 1457/2401*T^15 + 1156/2401*T^14 + 745/2401*T^13 - 
        383/2401*T^12 - 106/343*T^11 - 723/2401*T^10 - 723/2401*T^9 - 561/2401*T^8 -
        59/2401*T^7 + 107/2401*T^6 - 575/2401*T^5 - 1/7*T^4 - 41/343*T^3 + 30/49*T^2
        + T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 
        + 2*X*Y^7 + 2*X*Y^6 + X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 2*X*Y + 4*X + 
        Y^30 + 5*Y^29 + 2*Y^28 + 2*Y^27 + 3*Y^25 + 3*Y^23 + 5*Y^21 + Y^20 + 4*Y^19 +
        2*Y^18 + 4*Y^17 + 3*Y^15 + 6*Y^14 + Y^13 + 2*Y^12 + 4*Y^10 + 3*Y^9 + 6*Y^8 +
        5*Y^7 + 3*Y^6 + 5*Y^5 + 5*Y^3 + 2*Y^2 + 2*Y,
    -T^56 + 57/49*T^54 + 107/343*T^53 - 1889/2401*T^52 - 1392/2401*T^51 + 
        2426/2401*T^50 + 27/343*T^49 - 2970/2401*T^48 + 260/2401*T^47 + 
        3368/2401*T^46 + 62/2401*T^45 - 2354/2401*T^44 - 57/343*T^43 + 296/343*T^42 
        - 771/2401*T^41 - 331/343*T^40 + 243/343*T^39 + 2011/2401*T^38 - 
        1314/2401*T^37 - 2154/2401*T^36 + 1716/2401*T^35 + 1896/2401*T^34 - 
        3055/2401*T^33 - 1668/2401*T^32 + 3338/2401*T^31 + 39/343*T^30 - 
        3032/2401*T^29 + 3032/2401*T^27 - 39/343*T^26 - 3338/2401*T^25 + 
        1668/2401*T^24 + 3055/2401*T^23 - 1896/2401*T^22 - 1716/2401*T^21 + 
        2154/2401*T^20 + 1314/2401*T^19 - 2011/2401*T^18 - 243/343*T^17 + 
        331/343*T^16 + 771/2401*T^15 - 296/343*T^14 + 57/343*T^13 + 2354/2401*T^12 -
        62/2401*T^11 - 3368/2401*T^10 - 260/2401*T^9 + 2970/2401*T^8 - 27/343*T^7 - 
        2426/2401*T^6 + 1392/2401*T^5 + 1889/2401*T^4 - 107/343*T^3 - 57/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^14 + 6*X*Y^13 + X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 
        2*X*Y^7 + X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + X*Y + 3*X + 3*Y^30 + Y^29 + 
        2*Y^28 + 6*Y^26 + 6*Y^24 + 2*Y^23 + 4*Y^21 + 6*Y^20 + 2*Y^19 + Y^18 + 5*Y^17
        + 2*Y^16 + Y^15 + 6*Y^14 + 6*Y^13 + 2*Y^12 + 5*Y^11 + 3*Y^10 + 4*Y^9 + 3*Y^8
        + 6*Y^7 + 5*Y^5 + 3*Y^4 + 5*Y^3 + 3*Y^2 + 2*Y + 4,
    -T^56 + 13/7*T^55 - 6/7*T^54 - 334/343*T^53 + 4028/2401*T^52 - 2634/2401*T^51 + 
        2297/2401*T^50 - 2445/2401*T^49 + 26/49*T^48 + 1216/2401*T^47 - 
        2553/2401*T^46 + 802/2401*T^45 + 2371/2401*T^44 - 439/343*T^43 + 
        356/2401*T^42 + 1775/2401*T^41 - 2921/2401*T^40 + 596/343*T^39 - 
        4992/2401*T^38 + 2074/2401*T^37 + 2392/2401*T^36 - 3799/2401*T^35 + 
        2290/2401*T^34 - 823/2401*T^33 + 1016/2401*T^32 + 412/2401*T^31 - 
        2575/2401*T^30 + 3011/2401*T^29 - 3011/2401*T^27 + 2575/2401*T^26 - 
        412/2401*T^25 - 1016/2401*T^24 + 823/2401*T^23 - 2290/2401*T^22 + 
        3799/2401*T^21 - 2392/2401*T^20 - 2074/2401*T^19 + 4992/2401*T^18 - 
        596/343*T^17 + 2921/2401*T^16 - 1775/2401*T^15 - 356/2401*T^14 + 
        439/343*T^13 - 2371/2401*T^12 - 802/2401*T^11 + 2553/2401*T^10 - 
        1216/2401*T^9 - 26/49*T^8 + 2445/2401*T^7 - 2297/2401*T^6 + 2634/2401*T^5 - 
        4028/2401*T^4 + 334/343*T^3 + 6/7*T^2 - 13/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 
        + 3*X*Y^8 + X*Y^7 + X*Y^6 + X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + X + 2*Y^30 + 6*Y^29 
        + 5*Y^27 + 3*Y^26 + Y^25 + 3*Y^24 + Y^23 + 2*Y^22 + 3*Y^20 + 5*Y^19 + Y^18 +
        2*Y^16 + 4*Y^15 + 4*Y^14 + 6*Y^13 + 2*Y^12 + 3*Y^11 + 6*Y^10 + 4*Y^9 + 5*Y^8
        + 6*Y^7 + 6*Y^6 + Y^5 + 3*Y^4 + 3*Y^3 + 5*Y^2 + 2*Y + 4,
    -T^56 + 8/7*T^55 + 18/49*T^54 - 80/343*T^53 - 3137/2401*T^52 + 96/343*T^51 + 
        48/49*T^50 + 1046/2401*T^49 - 2055/2401*T^48 - 1508/2401*T^47 + 
        618/2401*T^46 + 2262/2401*T^45 - 645/2401*T^44 - 506/2401*T^43 - 
        752/2401*T^42 - 114/2401*T^41 + 1331/2401*T^40 - 523/2401*T^39 + 
        1031/2401*T^38 - 632/2401*T^37 - 1/2401*T^36 - 1144/2401*T^35 + 
        1469/2401*T^34 + 1236/2401*T^33 - 1126/2401*T^32 - 1681/2401*T^31 + 
        446/2401*T^30 + T^29 - T^27 - 446/2401*T^26 + 1681/2401*T^25 + 
        1126/2401*T^24 - 1236/2401*T^23 - 1469/2401*T^22 + 1144/2401*T^21 + 
        1/2401*T^20 + 632/2401*T^19 - 1031/2401*T^18 + 523/2401*T^17 - 
        1331/2401*T^16 + 114/2401*T^15 + 752/2401*T^14 + 506/2401*T^13 + 
        645/2401*T^12 - 2262/2401*T^11 - 618/2401*T^10 + 1508/2401*T^9 + 
        2055/2401*T^8 - 1046/2401*T^7 - 48/49*T^6 - 96/343*T^5 + 3137/2401*T^4 + 
        80/343*T^3 - 18/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 4*X*Y^13 + 5*X*Y^11 + 4*X*Y^10 + X*Y^9 + 4*X*Y^8 + 
        5*X*Y^7 + 6*X*Y^6 + X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 5*X*Y + X + 4*Y^30
        + 4*Y^29 + 5*Y^28 + 4*Y^26 + 4*Y^24 + 5*Y^23 + 2*Y^21 + 5*Y^20 + 6*Y^19 + 
        4*Y^18 + 4*Y^17 + 5*Y^16 + 3*Y^15 + 5*Y^14 + 3*Y^13 + Y^12 + 2*Y^11 + 3*Y^10
        + 3*Y^9 + Y^8 + 4*Y^7 + 2*Y^6 + 4*Y^4 + 2*Y^3 + 4*Y^2 + 5*Y + 6,
    -T^56 + 12/7*T^55 - 45/49*T^54 - 228/343*T^53 + 3090/2401*T^52 - 171/2401*T^51 -
        2964/2401*T^50 + 1206/2401*T^49 + 4426/2401*T^48 - 7765/2401*T^47 + 
        898/343*T^46 - 1678/2401*T^45 - 2409/2401*T^44 + 3109/2401*T^43 - 
        156/343*T^42 - 1291/2401*T^41 - 277/2401*T^40 + 718/343*T^39 - 
        8063/2401*T^38 + 5247/2401*T^37 + 204/2401*T^36 - 3368/2401*T^35 + 
        2909/2401*T^34 - 202/343*T^33 + 2717/2401*T^32 - 4027/2401*T^31 + 
        3643/2401*T^30 - 1766/2401*T^29 + 1766/2401*T^27 - 3643/2401*T^26 + 
        4027/2401*T^25 - 2717/2401*T^24 + 202/343*T^23 - 2909/2401*T^22 + 
        3368/2401*T^21 - 204/2401*T^20 - 5247/2401*T^19 + 8063/2401*T^18 - 
        718/343*T^17 + 277/2401*T^16 + 1291/2401*T^15 + 156/343*T^14 - 
        3109/2401*T^13 + 2409/2401*T^12 + 1678/2401*T^11 - 898/343*T^10 + 
        7765/2401*T^9 - 4426/2401*T^8 - 1206/2401*T^7 + 2964/2401*T^6 + 171/2401*T^5
        - 3090/2401*T^4 + 228/343*T^3 + 45/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + X*Y^13 + 3*X*Y^11 + 4*X*Y^10 + 2*X*Y^8 + 4*X*Y^7 + 2*X*Y^6 + 
        4*X*Y^4 + 4*X*Y^3 + 4*X*Y + 5*X + 3*Y^30 + 3*Y^29 + 5*Y^28 + 3*Y^27 + 4*Y^26
        + 3*Y^25 + 2*Y^24 + 6*Y^23 + 6*Y^22 + Y^21 + 2*Y^20 + Y^19 + 6*Y^18 + 5*Y^17
        + 6*Y^16 + 3*Y^15 + 3*Y^14 + 3*Y^13 + 3*Y^12 + 4*Y^11 + 4*Y^10 + 4*Y^9 + Y^8
        + 5*Y^7 + 6*Y^6 + 2*Y^5 + 2*Y^4 + Y^3 + 6*Y^2 + 1,
    T^56 - 16/7*T^55 + 164/49*T^54 - 1388/343*T^53 + 9518/2401*T^52 - 
        10303/2401*T^51 + 9045/2401*T^50 - 887/343*T^49 + 5073/2401*T^48 - 
        4283/2401*T^47 + 5165/2401*T^46 - 5379/2401*T^45 + 4941/2401*T^44 - 
        7076/2401*T^43 + 1182/343*T^42 - 8146/2401*T^41 + 6735/2401*T^40 - 
        4621/2401*T^39 + 4412/2401*T^38 - 4134/2401*T^37 + 3706/2401*T^36 - 
        3974/2401*T^35 + 4846/2401*T^34 - 6057/2401*T^33 + 6128/2401*T^32 - 
        4862/2401*T^31 + 554/343*T^30 - 548/343*T^29 + 3916/2401*T^28 - 548/343*T^27
        + 554/343*T^26 - 4862/2401*T^25 + 6128/2401*T^24 - 6057/2401*T^23 + 
        4846/2401*T^22 - 3974/2401*T^21 + 3706/2401*T^20 - 4134/2401*T^19 + 
        4412/2401*T^18 - 4621/2401*T^17 + 6735/2401*T^16 - 8146/2401*T^15 + 
        1182/343*T^14 - 7076/2401*T^13 + 4941/2401*T^12 - 5379/2401*T^11 + 
        5165/2401*T^10 - 4283/2401*T^9 + 5073/2401*T^8 - 887/343*T^7 + 9045/2401*T^6
        - 10303/2401*T^5 + 9518/2401*T^4 - 1388/343*T^3 + 164/49*T^2 - 16/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + X*Y^8 + 
        5*X*Y^7 + 4*X*Y^6 + X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + X*Y^2 + 6*X + 2*Y^30 + 
        2*Y^29 + 2*Y^28 + 5*Y^27 + 5*Y^26 + 4*Y^25 + 3*Y^24 + 3*Y^23 + 3*Y^22 + 
        2*Y^21 + 5*Y^20 + 3*Y^19 + 5*Y^18 + 2*Y^17 + 2*Y^16 + 4*Y^14 + 3*Y^13 + 
        6*Y^12 + 5*Y^11 + 5*Y^10 + Y^9 + 4*Y^8 + 2*Y^7 + 5*Y^6 + Y^5 + Y^3 + 3*Y^2 +
        4*Y + 3,
    -T^56 + 8/7*T^55 - 3/7*T^54 + 6/49*T^53 - 803/2401*T^52 + 2614/2401*T^51 - 
        2143/2401*T^50 + 96/343*T^49 + 198/2401*T^48 + 363/2401*T^47 - 
        1469/2401*T^46 + 1397/2401*T^45 - 648/2401*T^44 - 190/2401*T^43 - 
        862/2401*T^42 + 204/343*T^41 - 659/2401*T^40 + 306/2401*T^39 - 148/343*T^38 
        + 2333/2401*T^37 - 1654/2401*T^36 + 291/2401*T^35 + 51/343*T^34 + 
        750/2401*T^33 - 2465/2401*T^32 + 1581/2401*T^31 + 129/343*T^30 - 
        1501/2401*T^29 + 1501/2401*T^27 - 129/343*T^26 - 1581/2401*T^25 + 
        2465/2401*T^24 - 750/2401*T^23 - 51/343*T^22 - 291/2401*T^21 + 
        1654/2401*T^20 - 2333/2401*T^19 + 148/343*T^18 - 306/2401*T^17 + 
        659/2401*T^16 - 204/343*T^15 + 862/2401*T^14 + 190/2401*T^13 + 648/2401*T^12
        - 1397/2401*T^11 + 1469/2401*T^10 - 363/2401*T^9 - 198/2401*T^8 - 96/343*T^7
        + 2143/2401*T^6 - 2614/2401*T^5 + 803/2401*T^4 - 6/49*T^3 + 3/7*T^2 - 8/7*T 
        + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        6*X*Y^8 + 2*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 2*X*Y 
        + 6*X + 4*Y^30 + 5*Y^29 + 4*Y^28 + 2*Y^27 + 5*Y^26 + Y^25 + 5*Y^24 + 3*Y^23 
        + 4*Y^22 + 3*Y^21 + 6*Y^20 + 3*Y^19 + Y^18 + 6*Y^16 + Y^15 + 5*Y^14 + 4*Y^13
        + 6*Y^12 + 6*Y^11 + 2*Y^10 + 2*Y^9 + 5*Y^8 + 6*Y^7 + 3*Y^6 + Y^5 + 5*Y^4 + 
        2*Y^2 + 5*Y + 4,
    -T^56 - 4/7*T^55 - 30/49*T^54 + 181/343*T^53 + 2300/2401*T^52 + 893/2401*T^51 + 
        530/2401*T^50 - 2780/2401*T^49 - 192/2401*T^48 + 141/2401*T^47 + 
        1506/2401*T^46 + 1373/2401*T^45 - 166/2401*T^44 + 1030/2401*T^43 - 
        212/2401*T^42 + 11/2401*T^41 - 1384/2401*T^40 - 1937/2401*T^39 + 
        173/2401*T^38 + 50/343*T^37 + 1755/2401*T^36 - 4/343*T^35 - 797/2401*T^34 - 
        80/343*T^33 - 1038/2401*T^32 + 1196/2401*T^31 - 647/2401*T^30 + 
        216/2401*T^29 - 216/2401*T^27 + 647/2401*T^26 - 1196/2401*T^25 + 
        1038/2401*T^24 + 80/343*T^23 + 797/2401*T^22 + 4/343*T^21 - 1755/2401*T^20 -
        50/343*T^19 - 173/2401*T^18 + 1937/2401*T^17 + 1384/2401*T^16 - 11/2401*T^15
        + 212/2401*T^14 - 1030/2401*T^13 + 166/2401*T^12 - 1373/2401*T^11 - 
        1506/2401*T^10 - 141/2401*T^9 + 192/2401*T^8 + 2780/2401*T^7 - 530/2401*T^6 
        - 893/2401*T^5 - 2300/2401*T^4 - 181/343*T^3 + 30/49*T^2 + 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 
        2*X*Y^8 + 3*X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + X*Y + 
        X + 3*Y^30 + Y^28 + 3*Y^27 + Y^26 + 3*Y^25 + 5*Y^24 + Y^22 + Y^21 + 2*Y^20 +
        3*Y^19 + Y^18 + 5*Y^17 + 3*Y^16 + 6*Y^15 + 3*Y^14 + 4*Y^13 + 2*Y^12 + 5*Y^11
        + 3*Y^10 + 6*Y^9 + 5*Y^8 + 4*Y^7 + Y^6 + Y^5 + 5*Y^4 + 3*Y^3 + 3*Y^2 + 6*Y +
        6,
    T^56 - 13/7*T^55 + 43/49*T^54 - 48/343*T^53 + 4077/2401*T^52 - 5727/2401*T^51 + 
        209/343*T^50 - 529/2401*T^49 + 4399/2401*T^48 - 3727/2401*T^47 - 
        660/2401*T^46 + 191/2401*T^45 + 1548/2401*T^44 + 191/343*T^43 - 
        2833/2401*T^42 + 125/2401*T^41 - 104/343*T^40 + 3420/2401*T^39 - 
        1222/2401*T^38 - 114/343*T^37 - 3484/2401*T^36 + 5195/2401*T^35 + 
        312/2401*T^34 - 1427/2401*T^33 - 4275/2401*T^32 + 3863/2401*T^31 + 
        1130/2401*T^30 + 1472/2401*T^29 - 5645/2401*T^28 + 1472/2401*T^27 + 
        1130/2401*T^26 + 3863/2401*T^25 - 4275/2401*T^24 - 1427/2401*T^23 + 
        312/2401*T^22 + 5195/2401*T^21 - 3484/2401*T^20 - 114/343*T^19 - 
        1222/2401*T^18 + 3420/2401*T^17 - 104/343*T^16 + 125/2401*T^15 - 
        2833/2401*T^14 + 191/343*T^13 + 1548/2401*T^12 + 191/2401*T^11 - 
        660/2401*T^10 - 3727/2401*T^9 + 4399/2401*T^8 - 529/2401*T^7 + 209/343*T^6 -
        5727/2401*T^5 + 4077/2401*T^4 - 48/343*T^3 + 43/49*T^2 - 13/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 4*X*Y^7 + 
        5*X*Y^6 + X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 6*X*Y + 4*X + Y^30 + 3*Y^29 
        + 3*Y^27 + 3*Y^25 + 3*Y^24 + 4*Y^23 + 6*Y^22 + 3*Y^21 + 5*Y^20 + 3*Y^19 + 
        Y^18 + 3*Y^15 + 5*Y^13 + 2*Y^12 + 4*Y^10 + Y^9 + 4*Y^7 + 2*Y^6 + 3*Y^5 + 
        6*Y^4 + 4*Y^2 + Y + 1,
    -T^56 - 4/7*T^55 - 5/49*T^54 + 153/343*T^53 + 68/343*T^52 - 1899/2401*T^51 - 
        2648/2401*T^50 - 302/343*T^49 + 703/2401*T^48 + 1814/2401*T^47 + 
        1871/2401*T^46 + 305/2401*T^45 - 1642/2401*T^44 - 841/2401*T^43 - 
        24/2401*T^42 + 1858/2401*T^41 + 3025/2401*T^40 + 2337/2401*T^39 + 
        389/2401*T^38 - 146/343*T^37 - 1341/2401*T^36 + 867/2401*T^35 + 
        2550/2401*T^34 + 2391/2401*T^33 + 1180/2401*T^32 - 762/2401*T^31 - 
        1133/2401*T^30 - 655/2401*T^29 + 655/2401*T^27 + 1133/2401*T^26 + 
        762/2401*T^25 - 1180/2401*T^24 - 2391/2401*T^23 - 2550/2401*T^22 - 
        867/2401*T^21 + 1341/2401*T^20 + 146/343*T^19 - 389/2401*T^18 - 
        2337/2401*T^17 - 3025/2401*T^16 - 1858/2401*T^15 + 24/2401*T^14 + 
        841/2401*T^13 + 1642/2401*T^12 - 305/2401*T^11 - 1871/2401*T^10 - 
        1814/2401*T^9 - 703/2401*T^8 + 302/343*T^7 + 2648/2401*T^6 + 1899/2401*T^5 -
        68/343*T^4 - 153/343*T^3 + 5/49*T^2 + 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        3*X*Y^8 + 3*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 2*X*Y 
        + 2*X + 4*Y^30 + 6*Y^29 + 2*Y^28 + 6*Y^27 + 5*Y^26 + 4*Y^25 + Y^24 + Y^23 + 
        Y^21 + 4*Y^20 + 4*Y^19 + 3*Y^17 + 4*Y^16 + 4*Y^14 + 2*Y^13 + 5*Y^12 + 3*Y^11
        + 6*Y^10 + 6*Y^9 + Y^6 + 2*Y^4 + Y^2 + 4*Y,
    T^56 + 2*T^55 + 101/49*T^54 + 633/343*T^53 + 3800/2401*T^52 + 3930/2401*T^51 + 
        977/2401*T^50 - 1045/2401*T^49 + 1384/2401*T^48 + 2301/2401*T^47 + 
        2568/2401*T^46 + 2124/2401*T^45 + 3285/2401*T^44 + 3687/2401*T^43 + 
        1455/2401*T^42 + 2361/2401*T^41 + 1958/2401*T^40 + 1049/2401*T^39 + 
        768/2401*T^38 + 564/2401*T^37 - 233/2401*T^36 - 3169/2401*T^35 - 
        3027/2401*T^34 - 2262/2401*T^33 - 2470/2401*T^32 - 1695/2401*T^31 - 
        2/2401*T^30 + 1548/2401*T^29 + 1651/2401*T^28 + 1548/2401*T^27 - 2/2401*T^26
        - 1695/2401*T^25 - 2470/2401*T^24 - 2262/2401*T^23 - 3027/2401*T^22 - 
        3169/2401*T^21 - 233/2401*T^20 + 564/2401*T^19 + 768/2401*T^18 + 
        1049/2401*T^17 + 1958/2401*T^16 + 2361/2401*T^15 + 1455/2401*T^14 + 
        3687/2401*T^13 + 3285/2401*T^12 + 2124/2401*T^11 + 2568/2401*T^10 + 
        2301/2401*T^9 + 1384/2401*T^8 - 1045/2401*T^7 + 977/2401*T^6 + 3930/2401*T^5
        + 3800/2401*T^4 + 633/343*T^3 + 101/49*T^2 + 2*T + 1
*], [*
    X^3 + 2*X*Y^14 + X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + X*Y^9 + 2*X*Y^8 + 
        4*X*Y^7 + X*Y^6 + 5*X*Y^5 + X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + X*Y + 3*X + Y^30 + 
        Y^29 + 6*Y^28 + 2*Y^27 + 6*Y^25 + 4*Y^24 + 4*Y^22 + Y^20 + Y^19 + 3*Y^18 + 
        6*Y^17 + Y^16 + 6*Y^15 + 2*Y^14 + Y^13 + 4*Y^12 + 5*Y^11 + 3*Y^10 + 5*Y^9 + 
        6*Y^8 + 3*Y^7 + 2*Y^6 + 2*Y^5 + 5*Y^4 + 4*Y^3 + 3*Y^2 + Y + 2,
    T^56 - 4/7*T^55 - 30/49*T^54 + 335/343*T^53 - 2327/2401*T^52 + 431/2401*T^51 + 
        1975/2401*T^50 - 1396/2401*T^49 - 363/2401*T^48 + 1325/2401*T^47 - 
        879/2401*T^46 - 470/2401*T^45 + 1486/2401*T^44 - 2038/2401*T^43 + 6/49*T^42 
        + 170/343*T^41 - 1581/2401*T^40 - 27/2401*T^39 + 228/2401*T^38 - 38/343*T^37
        + 143/2401*T^36 + 449/2401*T^35 + 195/2401*T^34 - 149/343*T^33 + 
        773/2401*T^32 - 204/2401*T^31 - 24/343*T^30 + 156/343*T^29 - 1382/2401*T^28 
        + 156/343*T^27 - 24/343*T^26 - 204/2401*T^25 + 773/2401*T^24 - 149/343*T^23 
        + 195/2401*T^22 + 449/2401*T^21 + 143/2401*T^20 - 38/343*T^19 + 
        228/2401*T^18 - 27/2401*T^17 - 1581/2401*T^16 + 170/343*T^15 + 6/49*T^14 - 
        2038/2401*T^13 + 1486/2401*T^12 - 470/2401*T^11 - 879/2401*T^10 + 
        1325/2401*T^9 - 363/2401*T^8 - 1396/2401*T^7 + 1975/2401*T^6 + 431/2401*T^5 
        - 2327/2401*T^4 + 335/343*T^3 - 30/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 6*X*Y^8 + 
        5*X*Y^7 + X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + Y^30 + 2*Y^29 + 
        4*Y^28 + 4*Y^27 + 4*Y^25 + 4*Y^24 + 5*Y^23 + 6*Y^22 + Y^21 + 3*Y^19 + 5*Y^18
        + 5*Y^17 + 4*Y^16 + 5*Y^15 + 2*Y^14 + Y^13 + 4*Y^12 + 4*Y^11 + 4*Y^10 + 
        5*Y^9 + 6*Y^8 + Y^7 + 3*Y^6 + 6*Y^5 + 5*Y^4 + 2*Y^3 + 4*Y + 3,
    T^56 + 1/7*T^55 + 1/7*T^54 + 73/343*T^53 - 914/2401*T^52 + 89/2401*T^51 + 
        207/2401*T^50 + 366/2401*T^49 + 93/2401*T^48 - 90/343*T^47 - 83/2401*T^46 - 
        943/2401*T^45 + 124/2401*T^44 + 710/2401*T^43 + 45/343*T^42 + 830/2401*T^41 
        - 3/49*T^40 + 145/2401*T^39 - 873/2401*T^38 + 27/343*T^37 - 52/2401*T^36 + 
        558/2401*T^35 + 1021/2401*T^34 - 318/2401*T^33 + 60/343*T^32 - 80/343*T^31 +
        178/2401*T^30 + 1591/2401*T^29 + 272/2401*T^28 + 1591/2401*T^27 + 
        178/2401*T^26 - 80/343*T^25 + 60/343*T^24 - 318/2401*T^23 + 1021/2401*T^22 +
        558/2401*T^21 - 52/2401*T^20 + 27/343*T^19 - 873/2401*T^18 + 145/2401*T^17 -
        3/49*T^16 + 830/2401*T^15 + 45/343*T^14 + 710/2401*T^13 + 124/2401*T^12 - 
        943/2401*T^11 - 83/2401*T^10 - 90/343*T^9 + 93/2401*T^8 + 366/2401*T^7 + 
        207/2401*T^6 + 89/2401*T^5 - 914/2401*T^4 + 73/343*T^3 + 1/7*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        6*X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 3*X*Y 
        + X + 3*Y^30 + Y^29 + 3*Y^28 + 4*Y^27 + 3*Y^26 + 3*Y^25 + 6*Y^23 + 2*Y^22 + 
        6*Y^21 + Y^19 + 4*Y^18 + Y^17 + Y^16 + 3*Y^15 + 6*Y^14 + 6*Y^13 + Y^12 + 
        5*Y^11 + 5*Y^10 + 3*Y^9 + 5*Y^8 + Y^6 + 4*Y^5 + 5*Y^4 + 6*Y^3 + 6*Y^2 + 2*Y 
        + 3,
    T^56 - 4/7*T^55 + 9/49*T^54 - 275/343*T^53 + 659/2401*T^52 - 1879/2401*T^51 + 
        1874/2401*T^50 + 134/2401*T^49 + 226/2401*T^48 + 260/2401*T^47 + 43/343*T^46
        - 1483/2401*T^45 - 1084/2401*T^44 + 488/2401*T^43 - 265/2401*T^42 + 
        76/343*T^41 + 1788/2401*T^40 + 859/2401*T^39 - 790/2401*T^38 - 
        1637/2401*T^37 - 225/2401*T^36 - 1319/2401*T^35 + 179/2401*T^34 + 
        2136/2401*T^33 + 131/343*T^32 + 256/2401*T^31 + 317/2401*T^30 - 
        264/2401*T^29 - 2881/2401*T^28 - 264/2401*T^27 + 317/2401*T^26 + 
        256/2401*T^25 + 131/343*T^24 + 2136/2401*T^23 + 179/2401*T^22 - 
        1319/2401*T^21 - 225/2401*T^20 - 1637/2401*T^19 - 790/2401*T^18 + 
        859/2401*T^17 + 1788/2401*T^16 + 76/343*T^15 - 265/2401*T^14 + 488/2401*T^13
        - 1084/2401*T^12 - 1483/2401*T^11 + 43/343*T^10 + 260/2401*T^9 + 
        226/2401*T^8 + 134/2401*T^7 + 1874/2401*T^6 - 1879/2401*T^5 + 659/2401*T^4 -
        275/343*T^3 + 9/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + X*Y^10 + 3*X*Y^8 + 3*X*Y^7 + 
        3*X*Y^6 + X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 6*X*Y + 3*X + 3*Y^30 + 
        5*Y^29 + 5*Y^27 + 4*Y^26 + 5*Y^25 + 4*Y^24 + 6*Y^21 + 6*Y^20 + 2*Y^19 + 
        4*Y^18 + 3*Y^17 + 2*Y^16 + 6*Y^15 + Y^14 + 4*Y^13 + 6*Y^12 + Y^11 + Y^10 + 
        5*Y^9 + 2*Y^8 + 6*Y^7 + 5*Y^6 + 3*Y^5 + 6*Y^4 + 3*Y,
    -T^56 + 1/7*T^55 - 4/49*T^54 - 312/343*T^53 + 463/2401*T^52 + 696/2401*T^51 - 
        348/2401*T^50 - 475/2401*T^49 + 2311/2401*T^48 - 796/2401*T^47 - 46/343*T^46
        + 874/2401*T^45 - 32/2401*T^44 - 111/343*T^43 + 271/2401*T^42 + 122/343*T^41
        - 1762/2401*T^40 + 1119/2401*T^39 + 900/2401*T^38 + 451/2401*T^37 + 
        30/2401*T^36 + 333/2401*T^35 + 172/2401*T^34 - 1312/2401*T^33 - 
        460/2401*T^32 - 1383/2401*T^31 - 117/2401*T^30 - 1429/2401*T^29 + 
        1429/2401*T^27 + 117/2401*T^26 + 1383/2401*T^25 + 460/2401*T^24 + 
        1312/2401*T^23 - 172/2401*T^22 - 333/2401*T^21 - 30/2401*T^20 - 
        451/2401*T^19 - 900/2401*T^18 - 1119/2401*T^17 + 1762/2401*T^16 - 
        122/343*T^15 - 271/2401*T^14 + 111/343*T^13 + 32/2401*T^12 - 874/2401*T^11 +
        46/343*T^10 + 796/2401*T^9 - 2311/2401*T^8 + 475/2401*T^7 + 348/2401*T^6 - 
        696/2401*T^5 - 463/2401*T^4 + 312/343*T^3 + 4/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 2*X*Y^9 + 5*X*Y^8 +
        X*Y^7 + 3*X*Y^6 + 6*X*Y^4 + X*Y + 4*X + 3*Y^30 + 3*Y^29 + Y^28 + 4*Y^27 + 
        4*Y^26 + Y^25 + 6*Y^23 + 5*Y^22 + Y^21 + 5*Y^20 + 2*Y^19 + 3*Y^18 + 5*Y^17 +
        5*Y^16 + 4*Y^15 + 3*Y^13 + 5*Y^12 + 2*Y^11 + Y^9 + 2*Y^8 + Y^7 + 6*Y^6 + 
        3*Y^5 + Y^4 + Y^2 + 6*Y + 1,
    -T^56 + 32/49*T^54 + 288/343*T^53 - 1060/2401*T^52 - 1434/2401*T^51 - 
        657/2401*T^50 + 1642/2401*T^49 + 1332/2401*T^48 + 16/343*T^47 - 
        1535/2401*T^46 - 927/2401*T^45 + 13/2401*T^44 - 485/2401*T^43 + 
        622/2401*T^42 + 638/2401*T^41 - 613/2401*T^40 - 1595/2401*T^39 + 
        1914/2401*T^38 + 923/2401*T^37 + 870/2401*T^36 - 1481/2401*T^35 - 
        23/343*T^34 + 74/2401*T^33 + 64/343*T^32 - 912/2401*T^31 - 209/2401*T^30 + 
        2/49*T^29 - 2/49*T^27 + 209/2401*T^26 + 912/2401*T^25 - 64/343*T^24 - 
        74/2401*T^23 + 23/343*T^22 + 1481/2401*T^21 - 870/2401*T^20 - 923/2401*T^19 
        - 1914/2401*T^18 + 1595/2401*T^17 + 613/2401*T^16 - 638/2401*T^15 - 
        622/2401*T^14 + 485/2401*T^13 - 13/2401*T^12 + 927/2401*T^11 + 
        1535/2401*T^10 - 16/343*T^9 - 1332/2401*T^8 - 1642/2401*T^7 + 657/2401*T^6 +
        1434/2401*T^5 + 1060/2401*T^4 - 288/343*T^3 - 32/49*T^2 + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 6*X*Y^7 + 4*X*Y^6 + X*Y^5 + X*Y^3 + 6*X*Y^2 + 4*X*Y + 2*X + 5*Y^30
        + 5*Y^29 + 5*Y^28 + 4*Y^26 + 3*Y^25 + 6*Y^21 + 6*Y^20 + 3*Y^19 + 6*Y^18 + 
        Y^17 + 3*Y^16 + 2*Y^15 + 5*Y^14 + 4*Y^13 + 4*Y^12 + 6*Y^11 + 3*Y^9 + 2*Y^8 +
        4*Y^7 + 5*Y^4 + 4*Y^3 + 3*Y^2 + Y + 3,
    -T^56 + 2/7*T^55 - 16/49*T^54 + 409/343*T^53 - 2064/2401*T^52 - 314/2401*T^51 - 
        1856/2401*T^50 + 974/2401*T^49 + 332/2401*T^48 + 436/2401*T^47 + 8/343*T^46 
        - 320/2401*T^45 - 355/2401*T^44 + 57/2401*T^43 + 296/2401*T^42 + 
        628/2401*T^41 - 391/2401*T^40 + 352/2401*T^39 - 1188/2401*T^38 + 
        1425/2401*T^37 - 1634/2401*T^36 + 1098/2401*T^35 - 1240/2401*T^34 + 
        1132/2401*T^33 - 153/2401*T^32 - 92/2401*T^31 - 557/2401*T^30 - 
        380/2401*T^29 + 380/2401*T^27 + 557/2401*T^26 + 92/2401*T^25 + 153/2401*T^24
        - 1132/2401*T^23 + 1240/2401*T^22 - 1098/2401*T^21 + 1634/2401*T^20 - 
        1425/2401*T^19 + 1188/2401*T^18 - 352/2401*T^17 + 391/2401*T^16 - 
        628/2401*T^15 - 296/2401*T^14 - 57/2401*T^13 + 355/2401*T^12 + 320/2401*T^11
        - 8/343*T^10 - 436/2401*T^9 - 332/2401*T^8 - 974/2401*T^7 + 1856/2401*T^6 + 
        314/2401*T^5 + 2064/2401*T^4 - 409/343*T^3 + 16/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 5*X*Y^13 + X*Y^12 + 4*X*Y^9 + 6*X*Y^8 + 6*X*Y^7 + 5*X*Y^6 + 
        X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + X*Y + 4*X + 5*Y^30 + 4*Y^29 + 3*Y^28 +
        Y^27 + 6*Y^26 + 6*Y^25 + 4*Y^24 + Y^23 + 2*Y^22 + Y^21 + 4*Y^20 + 4*Y^19 + 
        3*Y^18 + 2*Y^17 + 4*Y^16 + 3*Y^15 + Y^14 + 6*Y^13 + 2*Y^12 + 6*Y^11 + 6*Y^10
        + 2*Y^9 + 5*Y^8 + 4*Y^7 + 5*Y^6 + 4*Y^5 + 5*Y^4 + 6*Y^3 + 3*Y^2 + 1,
    T^56 - T^55 + 24/49*T^54 + 368/343*T^53 - 3837/2401*T^52 + 2222/2401*T^51 + 
        247/343*T^50 - 3482/2401*T^49 + 2656/2401*T^48 + 9/2401*T^47 - 
        2580/2401*T^46 + 2780/2401*T^45 - 1084/2401*T^44 - 17/49*T^43 + 
        1251/2401*T^42 - 1069/2401*T^41 + 520/2401*T^40 - 68/343*T^39 - 
        197/2401*T^38 + 1359/2401*T^37 - 1110/2401*T^36 - 585/2401*T^35 + 
        1658/2401*T^34 - 1629/2401*T^33 - 787/2401*T^32 + 2280/2401*T^31 - 
        2216/2401*T^30 - 695/2401*T^29 + 953/2401*T^28 - 695/2401*T^27 - 
        2216/2401*T^26 + 2280/2401*T^25 - 787/2401*T^24 - 1629/2401*T^23 + 
        1658/2401*T^22 - 585/2401*T^21 - 1110/2401*T^20 + 1359/2401*T^19 - 
        197/2401*T^18 - 68/343*T^17 + 520/2401*T^16 - 1069/2401*T^15 + 
        1251/2401*T^14 - 17/49*T^13 - 1084/2401*T^12 + 2780/2401*T^11 - 
        2580/2401*T^10 + 9/2401*T^9 + 2656/2401*T^8 - 3482/2401*T^7 + 247/343*T^6 + 
        2222/2401*T^5 - 3837/2401*T^4 + 368/343*T^3 + 24/49*T^2 - T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 
        + 3*X*Y^8 + 3*X*Y^7 + 6*X*Y^6 + 4*X*Y^4 + 5*X*Y^2 + 4*X*Y + 4*X + 3*Y^30 + 
        3*Y^29 + Y^28 + 4*Y^27 + 5*Y^26 + Y^25 + 3*Y^24 + Y^23 + Y^22 + 5*Y^20 + 
        6*Y^19 + 4*Y^16 + 4*Y^15 + 4*Y^14 + 6*Y^13 + 3*Y^12 + 5*Y^11 + Y^9 + 3*Y^8 +
        3*Y^6 + 2*Y^5 + 4*Y^3 + 3*Y^2 + 2*Y + 6,
    -T^56 + 6/7*T^55 - 22/49*T^54 + 488/343*T^53 - 389/343*T^52 + 2663/2401*T^51 - 
        2299/2401*T^50 + 632/2401*T^49 - 1178/2401*T^48 + 732/2401*T^47 - 
        880/2401*T^46 - 837/2401*T^45 + 1166/2401*T^44 - 389/2401*T^43 + 
        216/343*T^42 - 1290/2401*T^41 + 486/343*T^40 - 340/343*T^39 + 272/343*T^38 -
        3581/2401*T^37 + 1646/2401*T^36 - 3630/2401*T^35 + 3194/2401*T^34 - 
        381/343*T^33 + 3525/2401*T^32 - 2117/2401*T^31 + 2887/2401*T^30 - 
        128/343*T^29 + 128/343*T^27 - 2887/2401*T^26 + 2117/2401*T^25 - 
        3525/2401*T^24 + 381/343*T^23 - 3194/2401*T^22 + 3630/2401*T^21 - 
        1646/2401*T^20 + 3581/2401*T^19 - 272/343*T^18 + 340/343*T^17 - 486/343*T^16
        + 1290/2401*T^15 - 216/343*T^14 + 389/2401*T^13 - 1166/2401*T^12 + 
        837/2401*T^11 + 880/2401*T^10 - 732/2401*T^9 + 1178/2401*T^8 - 632/2401*T^7 
        + 2299/2401*T^6 - 2663/2401*T^5 + 389/343*T^4 - 488/343*T^3 + 22/49*T^2 - 
        6/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 +
        3*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 6*X*Y + X + 
        3*Y^30 + 2*Y^29 + 6*Y^28 + 6*Y^27 + 2*Y^26 + 2*Y^25 + 3*Y^24 + 6*Y^23 + 
        2*Y^22 + 3*Y^20 + Y^19 + 6*Y^18 + 4*Y^17 + 4*Y^16 + Y^15 + 2*Y^14 + 2*Y^13 +
        3*Y^12 + Y^11 + 6*Y^9 + 5*Y^8 + Y^7 + 4*Y^4 + 2*Y^3 + Y + 1,
    -T^56 + 8/7*T^55 - 45/49*T^54 + 59/49*T^53 - 386/343*T^52 + 6/7*T^51 - 
        1468/2401*T^50 + 1465/2401*T^49 - 1677/2401*T^48 + 951/2401*T^47 - 
        2822/2401*T^46 + 2883/2401*T^45 - 1958/2401*T^44 + 3816/2401*T^43 - 
        3712/2401*T^42 + 2330/2401*T^41 - 282/343*T^40 + 1061/2401*T^39 - 
        500/2401*T^38 - 857/2401*T^37 + 412/2401*T^36 - 138/2401*T^35 + 
        1182/2401*T^34 + 24/49*T^33 - 52/49*T^32 + 1333/2401*T^31 - 293/343*T^30 + 
        1534/2401*T^29 - 1534/2401*T^27 + 293/343*T^26 - 1333/2401*T^25 + 52/49*T^24
        - 24/49*T^23 - 1182/2401*T^22 + 138/2401*T^21 - 412/2401*T^20 + 
        857/2401*T^19 + 500/2401*T^18 - 1061/2401*T^17 + 282/343*T^16 - 
        2330/2401*T^15 + 3712/2401*T^14 - 3816/2401*T^13 + 1958/2401*T^12 - 
        2883/2401*T^11 + 2822/2401*T^10 - 951/2401*T^9 + 1677/2401*T^8 - 
        1465/2401*T^7 + 1468/2401*T^6 - 6/7*T^5 + 386/343*T^4 - 59/49*T^3 + 
        45/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 3*X*Y^10 + 6*X*Y^8 + 2*X*Y^6 +
        3*X*Y^5 + 6*X*Y^4 + X*Y^3 + X*Y^2 + 6*X*Y + 5*X + 4*Y^30 + Y^29 + 5*Y^28 + 
        Y^27 + 4*Y^26 + 2*Y^25 + 5*Y^24 + 4*Y^23 + 6*Y^22 + Y^21 + 4*Y^19 + 3*Y^17 +
        Y^16 + 2*Y^15 + 2*Y^14 + 2*Y^11 + 3*Y^10 + 4*Y^9 + 3*Y^8 + 3*Y^7 + 3*Y^6 + 
        4*Y^5 + Y^2 + 3*Y + 6,
    T^56 + 11/7*T^55 + 62/49*T^54 + 194/343*T^53 + 78/343*T^52 + 164/343*T^51 + 
        1579/2401*T^50 + 1538/2401*T^49 - 471/2401*T^48 - 960/2401*T^47 + 
        489/2401*T^46 + 944/2401*T^45 + 282/2401*T^44 - 1002/2401*T^43 - 
        743/2401*T^42 + 128/343*T^41 + 1941/2401*T^40 + 1208/2401*T^39 + 
        270/2401*T^38 + 1378/2401*T^37 + 2539/2401*T^36 + 2862/2401*T^35 + 
        2341/2401*T^34 + 37/49*T^33 + 1634/2401*T^32 + 1857/2401*T^31 + 
        1317/2401*T^30 - 720/2401*T^29 - 1996/2401*T^28 - 720/2401*T^27 + 
        1317/2401*T^26 + 1857/2401*T^25 + 1634/2401*T^24 + 37/49*T^23 + 
        2341/2401*T^22 + 2862/2401*T^21 + 2539/2401*T^20 + 1378/2401*T^19 + 
        270/2401*T^18 + 1208/2401*T^17 + 1941/2401*T^16 + 128/343*T^15 - 
        743/2401*T^14 - 1002/2401*T^13 + 282/2401*T^12 + 944/2401*T^11 + 
        489/2401*T^10 - 960/2401*T^9 - 471/2401*T^8 + 1538/2401*T^7 + 1579/2401*T^6 
        + 164/343*T^5 + 78/343*T^4 + 194/343*T^3 + 62/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        X*Y^8 + 3*X*Y^7 + X*Y^6 + 5*X*Y^5 + X*Y^4 + X*Y^3 + 3*X*Y^2 + 3*X*Y + 5*X + 
        5*Y^30 + 4*Y^29 + 3*Y^28 + 5*Y^27 + 6*Y^26 + 6*Y^25 + 2*Y^24 + 2*Y^23 + 
        5*Y^22 + 2*Y^21 + 3*Y^20 + 2*Y^18 + 5*Y^17 + 3*Y^15 + Y^14 + 4*Y^13 + 4*Y^11
        + 2*Y^10 + 5*Y^9 + Y^8 + Y^7 + 4*Y^6 + 2*Y^5 + Y^4 + 4*Y^2 + 2*Y + 1,
    -T^56 + 3/7*T^55 + 31/49*T^54 - 185/343*T^53 + 1532/2401*T^52 - 957/2401*T^51 - 
        975/2401*T^50 + 1587/2401*T^49 - 351/2401*T^48 - 1256/2401*T^47 + 
        1935/2401*T^46 - 346/2401*T^45 - 1182/2401*T^44 + 1053/2401*T^43 - 
        31/49*T^42 + 769/2401*T^41 + 194/2401*T^40 - 716/2401*T^39 + 1105/2401*T^38 
        + 190/2401*T^37 - 1534/2401*T^36 + 538/2401*T^35 + 254/2401*T^34 - 
        125/343*T^33 + 1927/2401*T^32 - 1240/2401*T^31 - 492/2401*T^30 + 
        1143/2401*T^29 - 1143/2401*T^27 + 492/2401*T^26 + 1240/2401*T^25 - 
        1927/2401*T^24 + 125/343*T^23 - 254/2401*T^22 - 538/2401*T^21 + 
        1534/2401*T^20 - 190/2401*T^19 - 1105/2401*T^18 + 716/2401*T^17 - 
        194/2401*T^16 - 769/2401*T^15 + 31/49*T^14 - 1053/2401*T^13 + 1182/2401*T^12
        + 346/2401*T^11 - 1935/2401*T^10 + 1256/2401*T^9 + 351/2401*T^8 - 
        1587/2401*T^7 + 975/2401*T^6 + 957/2401*T^5 - 1532/2401*T^4 + 185/343*T^3 - 
        31/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + X*Y^2 + X*Y + 6*Y^30 + 
        2*Y^29 + 4*Y^28 + 6*Y^27 + 3*Y^24 + 2*Y^23 + Y^22 + 5*Y^21 + Y^19 + 4*Y^18 +
        Y^17 + 4*Y^15 + 3*Y^14 + 6*Y^13 + 4*Y^12 + 4*Y^11 + 6*Y^10 + 5*Y^9 + 2*Y^8 +
        Y^7 + Y^6 + 4*Y^5 + 4*Y^4 + 6*Y^3 + 4*Y^2 + 6*Y + 6,
    T^56 - 1/7*T^55 - 47/49*T^54 - 339/343*T^53 - 846/2401*T^52 + 4135/2401*T^51 + 
        831/2401*T^50 - 865/2401*T^49 - 1858/2401*T^48 - 962/2401*T^47 + 
        3414/2401*T^46 + 815/2401*T^45 - 163/2401*T^44 - 898/2401*T^43 - 
        601/2401*T^42 + 1138/2401*T^41 - 2411/2401*T^40 - 2725/2401*T^39 + 
        810/2401*T^38 + 2482/2401*T^37 + 2719/2401*T^36 - 1776/2401*T^35 - 
        2361/2401*T^34 + 183/343*T^33 + 186/343*T^32 + 321/343*T^31 - 15/343*T^30 - 
        2384/2401*T^29 - 1153/2401*T^28 - 2384/2401*T^27 - 15/343*T^26 + 
        321/343*T^25 + 186/343*T^24 + 183/343*T^23 - 2361/2401*T^22 - 1776/2401*T^21
        + 2719/2401*T^20 + 2482/2401*T^19 + 810/2401*T^18 - 2725/2401*T^17 - 
        2411/2401*T^16 + 1138/2401*T^15 - 601/2401*T^14 - 898/2401*T^13 - 
        163/2401*T^12 + 815/2401*T^11 + 3414/2401*T^10 - 962/2401*T^9 - 
        1858/2401*T^8 - 865/2401*T^7 + 831/2401*T^6 + 4135/2401*T^5 - 846/2401*T^4 -
        339/343*T^3 - 47/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + X*Y^11 + X*Y^10 + 2*X*Y^9 + 4*X*Y^8 + 
        6*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + X*Y^2 + 2*X*Y + 6*X + 5*Y^30 + 
        4*Y^29 + 3*Y^28 + 5*Y^27 + 2*Y^25 + 4*Y^24 + 3*Y^23 + 3*Y^21 + 3*Y^20 + 
        2*Y^19 + Y^18 + 2*Y^17 + 4*Y^15 + 3*Y^14 + 2*Y^13 + 6*Y^11 + Y^10 + 4*Y^9 + 
        5*Y^7 + 6*Y^6 + 6*Y^5 + 2*Y^4 + 2*Y^3 + 3*Y^2 + 6*Y,
    T^56 - 12/7*T^55 + 50/49*T^54 + 136/343*T^53 - 3912/2401*T^52 + 4815/2401*T^51 -
        3698/2401*T^50 + 544/2401*T^49 + 2020/2401*T^48 - 2078/2401*T^47 + 
        257/2401*T^46 + 1601/2401*T^45 - 1058/2401*T^44 - 723/2401*T^43 + 
        3167/2401*T^42 - 4320/2401*T^41 + 3725/2401*T^40 - 933/2401*T^39 - 
        2334/2401*T^38 + 4049/2401*T^37 - 4233/2401*T^36 + 2609/2401*T^35 - 
        1080/2401*T^34 + 580/2401*T^33 - 792/2401*T^32 + 529/2401*T^31 + 
        1625/2401*T^30 - 3277/2401*T^29 + 547/343*T^28 - 3277/2401*T^27 + 
        1625/2401*T^26 + 529/2401*T^25 - 792/2401*T^24 + 580/2401*T^23 - 
        1080/2401*T^22 + 2609/2401*T^21 - 4233/2401*T^20 + 4049/2401*T^19 - 
        2334/2401*T^18 - 933/2401*T^17 + 3725/2401*T^16 - 4320/2401*T^15 + 
        3167/2401*T^14 - 723/2401*T^13 - 1058/2401*T^12 + 1601/2401*T^11 + 
        257/2401*T^10 - 2078/2401*T^9 + 2020/2401*T^8 + 544/2401*T^7 - 3698/2401*T^6
        + 4815/2401*T^5 - 3912/2401*T^4 + 136/343*T^3 + 50/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 
        + 4*X*Y^8 + 3*X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 
        2*Y^30 + 2*Y^28 + 4*Y^27 + 4*Y^26 + Y^25 + Y^24 + 3*Y^22 + 5*Y^20 + 6*Y^19 +
        3*Y^18 + 4*Y^17 + 5*Y^16 + 2*Y^15 + 4*Y^14 + 5*Y^13 + Y^12 + 2*Y^11 + 2*Y^10
        + 2*Y^9 + Y^8 + 4*Y^6 + 4*Y^5 + Y^4 + 3*Y^3 + 6*Y^2 + 4*Y + 1,
    T^56 - 6/7*T^55 + 44/49*T^54 - 174/343*T^53 + 675/2401*T^52 + 122/343*T^51 - 
        486/2401*T^50 + 1095/2401*T^49 - 410/2401*T^48 - 645/2401*T^47 + 
        1081/2401*T^46 - 173/343*T^45 - 580/2401*T^44 + 943/2401*T^43 - 268/343*T^42
        + 1620/2401*T^41 - 2217/2401*T^40 + 587/2401*T^39 + 9/2401*T^38 - 
        1095/2401*T^37 + 1387/2401*T^36 - 884/2401*T^35 - 318/2401*T^34 + 
        768/2401*T^33 - 13/2401*T^32 + 739/2401*T^31 + 781/2401*T^30 - 935/2401*T^29
        + 1544/2401*T^28 - 935/2401*T^27 + 781/2401*T^26 + 739/2401*T^25 - 
        13/2401*T^24 + 768/2401*T^23 - 318/2401*T^22 - 884/2401*T^21 + 
        1387/2401*T^20 - 1095/2401*T^19 + 9/2401*T^18 + 587/2401*T^17 - 
        2217/2401*T^16 + 1620/2401*T^15 - 268/343*T^14 + 943/2401*T^13 - 
        580/2401*T^12 - 173/343*T^11 + 1081/2401*T^10 - 645/2401*T^9 - 410/2401*T^8 
        + 1095/2401*T^7 - 486/2401*T^6 + 122/343*T^5 + 675/2401*T^4 - 174/343*T^3 + 
        44/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 
        + X*Y^8 + 2*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + X*Y^2 + 5*X*Y + 6*X + 
        3*Y^30 + 3*Y^29 + 6*Y^27 + 6*Y^26 + Y^24 + Y^23 + Y^22 + 6*Y^21 + 2*Y^20 + 
        2*Y^19 + 5*Y^18 + 3*Y^17 + Y^16 + 6*Y^14 + 3*Y^13 + Y^12 + Y^11 + Y^10 + 
        5*Y^9 + 5*Y^8 + 6*Y^7 + 3*Y^5 + 2*Y^4 + 6*Y^3 + Y^2 + 6*Y + 1,
    T^56 - 2*T^55 + 104/49*T^54 - 667/343*T^53 + 4525/2401*T^52 - 89/49*T^51 + 
        3288/2401*T^50 - 2910/2401*T^49 + 3209/2401*T^48 - 3403/2401*T^47 + 
        1625/2401*T^46 + 585/2401*T^45 - 22/49*T^44 - 34/343*T^43 + 605/2401*T^42 - 
        15/2401*T^41 - 241/2401*T^40 + 293/2401*T^39 - 716/2401*T^38 + 
        2298/2401*T^37 - 323/343*T^36 + 484/2401*T^35 + 813/2401*T^34 + 31/343*T^33 
        - 1235/2401*T^32 - 20/2401*T^31 + 157/343*T^30 - 229/2401*T^29 - 
        719/2401*T^28 - 229/2401*T^27 + 157/343*T^26 - 20/2401*T^25 - 1235/2401*T^24
        + 31/343*T^23 + 813/2401*T^22 + 484/2401*T^21 - 323/343*T^20 + 
        2298/2401*T^19 - 716/2401*T^18 + 293/2401*T^17 - 241/2401*T^16 - 
        15/2401*T^15 + 605/2401*T^14 - 34/343*T^13 - 22/49*T^12 + 585/2401*T^11 + 
        1625/2401*T^10 - 3403/2401*T^9 + 3209/2401*T^8 - 2910/2401*T^7 + 
        3288/2401*T^6 - 89/49*T^5 + 4525/2401*T^4 - 667/343*T^3 + 104/49*T^2 - 2*T +
        1
*], [*
    X^3 + 5*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 3*X*Y^8 +
        3*X*Y^7 + 5*X*Y^5 + 6*X*Y^4 + X*Y^3 + 2*X*Y^2 + 5*X*Y + 3*X + 4*Y^30 + 
        2*Y^29 + 3*Y^28 + 5*Y^27 + 2*Y^26 + 4*Y^24 + 6*Y^23 + 2*Y^22 + 4*Y^21 + 
        3*Y^20 + 2*Y^19 + Y^18 + 6*Y^17 + 6*Y^16 + 3*Y^15 + 3*Y^12 + 3*Y^11 + 2*Y^10
        + 4*Y^8 + Y^6 + 4*Y^5 + 2*Y^4 + 2*Y^3 + 3*Y^2 + 6*Y + 2,
    -T^56 + 6/7*T^55 - 9/49*T^54 - 55/343*T^53 + 36/49*T^52 - 1207/2401*T^51 + 
        512/2401*T^50 - 225/2401*T^49 - 88/343*T^48 + 1055/2401*T^47 - 379/2401*T^46
        - 27/2401*T^45 + 186/2401*T^44 - 59/2401*T^43 + 90/2401*T^42 - 351/2401*T^41
        + 708/2401*T^40 - 764/2401*T^39 + 1688/2401*T^38 - 1458/2401*T^37 + 
        474/2401*T^36 - 184/2401*T^35 - 1056/2401*T^34 + 463/2401*T^33 + 
        179/2401*T^32 - 212/2401*T^31 - 55/2401*T^30 + 13/2401*T^29 - 13/2401*T^27 +
        55/2401*T^26 + 212/2401*T^25 - 179/2401*T^24 - 463/2401*T^23 + 
        1056/2401*T^22 + 184/2401*T^21 - 474/2401*T^20 + 1458/2401*T^19 - 
        1688/2401*T^18 + 764/2401*T^17 - 708/2401*T^16 + 351/2401*T^15 - 
        90/2401*T^14 + 59/2401*T^13 - 186/2401*T^12 + 27/2401*T^11 + 379/2401*T^10 -
        1055/2401*T^9 + 88/343*T^8 + 225/2401*T^7 - 512/2401*T^6 + 1207/2401*T^5 - 
        36/49*T^4 + 55/343*T^3 + 9/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 2*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + X*Y^9 + 2*X*Y^8 + 3*X*Y^7 + 
        5*X*Y^6 + X*Y^5 + 6*X*Y^3 + 2*X*Y + 6*X + Y^30 + 2*Y^29 + 4*Y^28 + 2*Y^27 + 
        6*Y^25 + 5*Y^24 + 5*Y^23 + 4*Y^20 + 2*Y^19 + 2*Y^17 + 6*Y^16 + 3*Y^15 + 
        5*Y^14 + 6*Y^12 + 3*Y^11 + 2*Y^10 + 5*Y^8 + 3*Y^7 + 2*Y^6 + 2*Y^5 + 4*Y^4 + 
        5*Y^3 + Y^2 + 5*Y + 6,
    T^56 - 4/7*T^55 - 12/49*T^54 - 94/343*T^53 + 83/2401*T^52 + 661/2401*T^51 - 
        2206/2401*T^50 - 264/2401*T^49 + 226/343*T^48 + 852/2401*T^47 - 
        100/2401*T^46 - 1282/2401*T^45 + 1665/2401*T^44 + 1121/2401*T^43 - 
        1047/2401*T^42 - 1338/2401*T^41 - 9/343*T^40 + 207/343*T^39 + 8/2401*T^38 - 
        1152/2401*T^37 + 53/343*T^36 + 65/343*T^35 + 177/2401*T^34 - 1417/2401*T^33 
        - 2/2401*T^32 + 15/2401*T^31 + 40/2401*T^30 + 1145/2401*T^29 - 816/2401*T^28
        + 1145/2401*T^27 + 40/2401*T^26 + 15/2401*T^25 - 2/2401*T^24 - 
        1417/2401*T^23 + 177/2401*T^22 + 65/343*T^21 + 53/343*T^20 - 1152/2401*T^19 
        + 8/2401*T^18 + 207/343*T^17 - 9/343*T^16 - 1338/2401*T^15 - 1047/2401*T^14 
        + 1121/2401*T^13 + 1665/2401*T^12 - 1282/2401*T^11 - 100/2401*T^10 + 
        852/2401*T^9 + 226/343*T^8 - 264/2401*T^7 - 2206/2401*T^6 + 661/2401*T^5 + 
        83/2401*T^4 - 94/343*T^3 - 12/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 
        X*Y^7 + 5*X*Y^6 + 6*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + X*Y + 5*X + 5*Y^30 + Y^29 + 
        Y^28 + 3*Y^27 + Y^26 + 4*Y^25 + 4*Y^24 + 3*Y^23 + 2*Y^22 + 6*Y^21 + Y^20 + 
        3*Y^19 + 2*Y^18 + 5*Y^15 + 2*Y^14 + 3*Y^12 + 6*Y^11 + 4*Y^10 + 5*Y^9 + 6*Y^8
        + 6*Y^6 + 3*Y^5 + 2*Y^4 + 4*Y^3 + 4*Y^2 + 3*Y + 2,
    T^56 + 11/7*T^55 + 18/49*T^54 - 254/343*T^53 - 4045/2401*T^52 - 4777/2401*T^51 -
        1980/2401*T^50 - 915/2401*T^49 - 62/2401*T^48 + 2588/2401*T^47 + 
        2983/2401*T^46 + 2714/2401*T^45 + 2369/2401*T^44 + 101/343*T^43 - 
        29/2401*T^42 - 687/2401*T^41 - 1747/2401*T^40 - 2154/2401*T^39 - 
        2909/2401*T^38 - 2201/2401*T^37 - 872/2401*T^36 + 223/2401*T^35 + 
        401/343*T^34 + 484/343*T^33 + 1842/2401*T^32 + 625/2401*T^31 - 
        1334/2401*T^30 - 223/343*T^29 - 466/2401*T^28 - 223/343*T^27 - 
        1334/2401*T^26 + 625/2401*T^25 + 1842/2401*T^24 + 484/343*T^23 + 
        401/343*T^22 + 223/2401*T^21 - 872/2401*T^20 - 2201/2401*T^19 - 
        2909/2401*T^18 - 2154/2401*T^17 - 1747/2401*T^16 - 687/2401*T^15 - 
        29/2401*T^14 + 101/343*T^13 + 2369/2401*T^12 + 2714/2401*T^11 + 
        2983/2401*T^10 + 2588/2401*T^9 - 62/2401*T^8 - 915/2401*T^7 - 1980/2401*T^6 
        - 4777/2401*T^5 - 4045/2401*T^4 - 254/343*T^3 + 18/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 6*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + X*Y^8 + 2*X*Y^7 + 
        2*X*Y^6 + 5*X*Y^5 + X*Y^2 + 3*X*Y + 3*X + 3*Y^30 + 2*Y^28 + 5*Y^27 + Y^24 + 
        4*Y^23 + 3*Y^22 + 5*Y^19 + 5*Y^18 + 6*Y^17 + 6*Y^15 + 5*Y^14 + 5*Y^13 + 
        2*Y^12 + 3*Y^11 + 2*Y^10 + 6*Y^9 + 6*Y^8 + 2*Y^7 + 4*Y^6 + 6*Y^5 + Y^4 + Y^3
        + 5*Y^2 + 3*Y + 5,
    -T^56 + 1/7*T^55 + 16/49*T^54 - 43/343*T^53 + 125/343*T^52 - 1233/2401*T^51 - 
        94/343*T^50 - 47/2401*T^49 + 1076/2401*T^48 - 93/2401*T^47 - 340/2401*T^46 -
        116/343*T^45 - 92/343*T^44 + 5/49*T^43 + 122/2401*T^42 + 505/2401*T^41 - 
        291/2401*T^40 - 115/2401*T^39 + 352/2401*T^38 + 1052/2401*T^37 - 
        18/2401*T^36 - 17/2401*T^35 - 569/2401*T^34 - 41/2401*T^33 + 25/49*T^32 - 
        43/2401*T^31 - 96/343*T^30 - 600/2401*T^29 + 600/2401*T^27 + 96/343*T^26 + 
        43/2401*T^25 - 25/49*T^24 + 41/2401*T^23 + 569/2401*T^22 + 17/2401*T^21 + 
        18/2401*T^20 - 1052/2401*T^19 - 352/2401*T^18 + 115/2401*T^17 + 
        291/2401*T^16 - 505/2401*T^15 - 122/2401*T^14 - 5/49*T^13 + 92/343*T^12 + 
        116/343*T^11 + 340/2401*T^10 + 93/2401*T^9 - 1076/2401*T^8 + 47/2401*T^7 + 
        94/343*T^6 + 1233/2401*T^5 - 125/343*T^4 + 43/343*T^3 - 16/49*T^2 - 1/7*T + 
        1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 6*X*Y^11 + 6*X*Y^10 + 2*X*Y^9 + 4*X*Y^8 +
        5*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 6*X*Y + X + 
        5*Y^30 + 2*Y^29 + 6*Y^28 + 6*Y^27 + Y^26 + 2*Y^25 + 6*Y^24 + 2*Y^21 + 5*Y^20
        + 2*Y^19 + Y^13 + 2*Y^12 + 2*Y^10 + 3*Y^9 + 5*Y^8 + 2*Y^7 + 3*Y^6 + 3*Y^5 + 
        6*Y^4 + 5*Y^3 + 2*Y^2 + 6*Y + 3,
    T^56 + 2/7*T^55 - 30/49*T^54 + 61/343*T^53 + 81/2401*T^52 - 297/2401*T^51 + 
        419/2401*T^50 - 122/2401*T^49 + 55/2401*T^48 - 121/2401*T^47 - 73/2401*T^46 
        + 1688/2401*T^45 + 44/343*T^44 - 130/343*T^43 + 6/343*T^42 - 396/2401*T^41 +
        10/343*T^40 + 150/2401*T^39 - 76/343*T^38 - 584/2401*T^37 - 430/2401*T^36 + 
        1014/2401*T^35 + 146/343*T^34 - 338/2401*T^33 + 58/2401*T^32 - 586/2401*T^31
        - 135/343*T^30 + 257/2401*T^29 - 267/2401*T^28 + 257/2401*T^27 - 
        135/343*T^26 - 586/2401*T^25 + 58/2401*T^24 - 338/2401*T^23 + 146/343*T^22 +
        1014/2401*T^21 - 430/2401*T^20 - 584/2401*T^19 - 76/343*T^18 + 150/2401*T^17
        + 10/343*T^16 - 396/2401*T^15 + 6/343*T^14 - 130/343*T^13 + 44/343*T^12 + 
        1688/2401*T^11 - 73/2401*T^10 - 121/2401*T^9 + 55/2401*T^8 - 122/2401*T^7 + 
        419/2401*T^6 - 297/2401*T^5 + 81/2401*T^4 + 61/343*T^3 - 30/49*T^2 + 2/7*T +
        1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 4*X*Y^9 + 2*X*Y^8 +
        5*X*Y^7 + 6*X*Y^6 + X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + X*Y^2 + 4*X*Y + 3*X + Y^30 +
        3*Y^29 + 3*Y^28 + 6*Y^27 + Y^26 + 6*Y^25 + Y^23 + 5*Y^22 + 6*Y^21 + 2*Y^20 +
        5*Y^19 + Y^18 + 2*Y^17 + 5*Y^16 + 4*Y^15 + 3*Y^14 + Y^13 + 5*Y^12 + 4*Y^11 +
        6*Y^10 + 5*Y^9 + 3*Y^8 + 5*Y^7 + 3*Y^6 + 4*Y^5 + Y^4 + 6*Y^3 + 3*Y^2 + 2*Y +
        3,
    -T^56 - 8/7*T^55 + 16/49*T^54 + 174/343*T^53 - 2409/2401*T^52 - 3098/2401*T^51 -
        734/2401*T^50 + 2207/2401*T^49 + 255/343*T^48 - 3893/2401*T^47 - 
        3818/2401*T^46 + 2985/2401*T^45 + 2915/2401*T^44 - 36/49*T^43 - 
        2278/2401*T^42 - 1360/2401*T^41 + 2659/2401*T^40 + 3564/2401*T^39 - 
        2754/2401*T^38 - 2372/2401*T^37 + 388/343*T^36 + 1847/2401*T^35 + 
        1299/2401*T^34 + 1662/2401*T^33 - 1979/2401*T^32 + 324/2401*T^31 + 
        3092/2401*T^30 - 65/343*T^29 + 65/343*T^27 - 3092/2401*T^26 - 324/2401*T^25 
        + 1979/2401*T^24 - 1662/2401*T^23 - 1299/2401*T^22 - 1847/2401*T^21 - 
        388/343*T^20 + 2372/2401*T^19 + 2754/2401*T^18 - 3564/2401*T^17 - 
        2659/2401*T^16 + 1360/2401*T^15 + 2278/2401*T^14 + 36/49*T^13 - 
        2915/2401*T^12 - 2985/2401*T^11 + 3818/2401*T^10 + 3893/2401*T^9 - 
        255/343*T^8 - 2207/2401*T^7 + 734/2401*T^6 + 3098/2401*T^5 + 2409/2401*T^4 -
        174/343*T^3 - 16/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 6*X*Y^8 +
        6*X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + X*Y^3 + 5*X*Y^2 + 5*X + 6*Y^30 + 
        2*Y^29 + 3*Y^28 + Y^27 + Y^26 + 3*Y^25 + 6*Y^23 + 6*Y^22 + Y^21 + 6*Y^20 + 
        Y^19 + Y^17 + 4*Y^16 + 3*Y^15 + 2*Y^14 + 5*Y^13 + 4*Y^12 + 3*Y^11 + 6*Y^10 +
        2*Y^9 + 6*Y^8 + 2*Y^7 + 5*Y^6 + 3*Y^5 + 6*Y^4 + 2*Y^3 + 2*Y^2 + 3*Y + 3,
    T^56 - 6/7*T^55 - 6/49*T^54 - 25/49*T^53 - 423/2401*T^52 - 274/2401*T^51 + 
        263/2401*T^50 + 1683/2401*T^49 + 2694/2401*T^48 + 1045/2401*T^47 - 
        2306/2401*T^46 - 684/2401*T^45 - 2572/2401*T^44 - 51/2401*T^43 - 
        1475/2401*T^42 + 1012/2401*T^41 + 398/343*T^40 + 2067/2401*T^39 - 
        503/2401*T^38 - 583/2401*T^37 - 232/2401*T^36 - 1770/2401*T^35 - 
        1020/2401*T^34 + 117/2401*T^33 + 773/2401*T^32 + 23/49*T^31 - 309/2401*T^30 
        - 394/2401*T^29 + 459/2401*T^28 - 394/2401*T^27 - 309/2401*T^26 + 23/49*T^25
        + 773/2401*T^24 + 117/2401*T^23 - 1020/2401*T^22 - 1770/2401*T^21 - 
        232/2401*T^20 - 583/2401*T^19 - 503/2401*T^18 + 2067/2401*T^17 + 
        398/343*T^16 + 1012/2401*T^15 - 1475/2401*T^14 - 51/2401*T^13 - 
        2572/2401*T^12 - 684/2401*T^11 - 2306/2401*T^10 + 1045/2401*T^9 + 
        2694/2401*T^8 + 1683/2401*T^7 + 263/2401*T^6 - 274/2401*T^5 - 423/2401*T^4 -
        25/49*T^3 - 6/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + 5*X*Y^8 + 
        2*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + X*Y^2 + 5*X + Y^30 + 
        4*Y^29 + 3*Y^28 + 2*Y^27 + 3*Y^26 + 4*Y^24 + Y^23 + Y^22 + 6*Y^21 + 5*Y^20 +
        6*Y^19 + 6*Y^18 + Y^17 + 6*Y^16 + Y^15 + 3*Y^14 + Y^13 + Y^12 + 6*Y^11 + 
        2*Y^10 + 6*Y^9 + 6*Y^8 + 3*Y^7 + Y^6 + 3*Y^5 + 5*Y^4 + 6*Y^3 + Y^2 + 3*Y + 
        6,
    -T^56 + 1/7*T^55 + 11/49*T^54 + 29/343*T^53 - 1287/2401*T^52 - 76/2401*T^51 + 
        15/49*T^50 + 100/2401*T^49 + 295/2401*T^48 - 156/2401*T^47 + 103/2401*T^46 +
        681/2401*T^45 + 554/2401*T^44 + 78/343*T^43 + 40/343*T^42 - 99/2401*T^41 + 
        90/2401*T^40 + 9/49*T^39 + 38/343*T^38 - 977/2401*T^37 - 675/2401*T^36 + 
        110/2401*T^35 - 607/2401*T^34 - 534/2401*T^33 - 75/343*T^32 - 514/2401*T^31 
        - 790/2401*T^30 + 1021/2401*T^29 - 1021/2401*T^27 + 790/2401*T^26 + 
        514/2401*T^25 + 75/343*T^24 + 534/2401*T^23 + 607/2401*T^22 - 110/2401*T^21 
        + 675/2401*T^20 + 977/2401*T^19 - 38/343*T^18 - 9/49*T^17 - 90/2401*T^16 + 
        99/2401*T^15 - 40/343*T^14 - 78/343*T^13 - 554/2401*T^12 - 681/2401*T^11 - 
        103/2401*T^10 + 156/2401*T^9 - 295/2401*T^8 - 100/2401*T^7 - 15/49*T^6 + 
        76/2401*T^5 + 1287/2401*T^4 - 29/343*T^3 - 11/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 6*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + X*Y^9 + 6*X*Y^8 + 
        2*X*Y^7 + X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 6*X*Y + 2*X + 2*Y^30 + Y^29 
        + 6*Y^28 + 3*Y^27 + 4*Y^26 + 6*Y^25 + 6*Y^24 + Y^23 + 6*Y^22 + 5*Y^21 + 
        3*Y^20 + 6*Y^19 + Y^18 + Y^17 + 2*Y^16 + 4*Y^14 + 4*Y^13 + 3*Y^10 + 4*Y^9 + 
        6*Y^8 + 4*Y^7 + 4*Y^6 + Y^5 + 4*Y^4 + 2*Y^3 + Y^2 + Y + 6,
    -T^56 + 5/7*T^55 - 9/49*T^54 + 307/343*T^53 - 13/2401*T^52 - 71/343*T^51 - 
        1303/2401*T^50 - 53/2401*T^49 - 457/2401*T^48 + 1622/2401*T^47 - 
        537/2401*T^46 + 1145/2401*T^45 - 1017/2401*T^44 - 416/2401*T^43 - 
        23/2401*T^42 + 734/2401*T^41 - 241/2401*T^40 + 461/2401*T^39 - 549/2401*T^38
        - 1017/2401*T^37 + 468/2401*T^36 + 13/49*T^35 + 236/2401*T^34 + 
        417/2401*T^33 - 794/2401*T^32 + 289/2401*T^31 - 930/2401*T^30 + 87/343*T^29 
        - 87/343*T^27 + 930/2401*T^26 - 289/2401*T^25 + 794/2401*T^24 - 
        417/2401*T^23 - 236/2401*T^22 - 13/49*T^21 - 468/2401*T^20 + 1017/2401*T^19 
        + 549/2401*T^18 - 461/2401*T^17 + 241/2401*T^16 - 734/2401*T^15 + 
        23/2401*T^14 + 416/2401*T^13 + 1017/2401*T^12 - 1145/2401*T^11 + 
        537/2401*T^10 - 1622/2401*T^9 + 457/2401*T^8 + 53/2401*T^7 + 1303/2401*T^6 +
        71/343*T^5 + 13/2401*T^4 - 307/343*T^3 + 9/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 3*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 5*X*Y^8 + 
        3*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + X*Y^2 + X*Y + 6*X + 4*Y^30
        + 5*Y^29 + 6*Y^28 + 2*Y^27 + 4*Y^26 + 5*Y^25 + Y^24 + 3*Y^23 + 5*Y^22 + Y^20
        + 4*Y^19 + Y^18 + 4*Y^17 + Y^16 + 2*Y^15 + 3*Y^14 + 2*Y^13 + 4*Y^12 + 5*Y^11
        + 2*Y^9 + 3*Y^8 + 4*Y^7 + 6*Y^6 + 2*Y^5 + 4*Y^4 + 5*Y^3 + Y^2 + Y + 5,
    T^56 + 13/7*T^55 + 9/49*T^54 - 456/343*T^53 + 1622/2401*T^52 + 801/343*T^51 - 
        275/2401*T^50 - 4398/2401*T^49 + 48/49*T^48 + 6450/2401*T^47 - 206/2401*T^46
        - 3627/2401*T^45 + 1413/2401*T^44 + 2251/2401*T^43 - 2383/2401*T^42 - 
        2094/2401*T^41 + 2438/2401*T^40 + 1055/2401*T^39 - 547/343*T^38 - 
        1103/2401*T^37 + 4516/2401*T^36 + 849/2401*T^35 - 6056/2401*T^34 - 
        3792/2401*T^33 + 1517/2401*T^32 - 1304/2401*T^31 - 5680/2401*T^30 - 
        1245/2401*T^29 + 3690/2401*T^28 - 1245/2401*T^27 - 5680/2401*T^26 - 
        1304/2401*T^25 + 1517/2401*T^24 - 3792/2401*T^23 - 6056/2401*T^22 + 
        849/2401*T^21 + 4516/2401*T^20 - 1103/2401*T^19 - 547/343*T^18 + 
        1055/2401*T^17 + 2438/2401*T^16 - 2094/2401*T^15 - 2383/2401*T^14 + 
        2251/2401*T^13 + 1413/2401*T^12 - 3627/2401*T^11 - 206/2401*T^10 + 
        6450/2401*T^9 + 48/49*T^8 - 4398/2401*T^7 - 275/2401*T^6 + 801/343*T^5 + 
        1622/2401*T^4 - 456/343*T^3 + 9/49*T^2 + 13/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 6*X*Y^9 + 5*X*Y^8 + 2*X*Y^7 + 
        2*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 6*X*Y + 3*X + 2*Y^30 + 4*Y^29 + 
        2*Y^27 + 3*Y^26 + Y^25 + 2*Y^23 + 4*Y^19 + Y^18 + 4*Y^17 + 4*Y^15 + Y^14 + 
        5*Y^13 + 2*Y^12 + 6*Y^11 + Y^9 + 3*Y^8 + 3*Y^7 + 2*Y^6 + Y^5 + 6*Y^3 + 5*Y^2
        + 5*Y + 5,
    -T^56 + 8/7*T^55 - 17/49*T^54 - 138/343*T^53 + 3928/2401*T^52 - 2350/2401*T^51 +
        1196/2401*T^50 - 4/343*T^49 - 2696/2401*T^48 + 1570/2401*T^47 - 
        1458/2401*T^46 - 999/2401*T^45 + 2664/2401*T^44 - 1703/2401*T^43 + 
        1905/2401*T^42 + 27/49*T^41 - 2641/2401*T^40 + 3058/2401*T^39 - 
        3639/2401*T^38 + 24/343*T^37 + 2474/2401*T^36 - 4024/2401*T^35 + 
        3317/2401*T^34 - 87/2401*T^33 - 1299/2401*T^32 + 1664/2401*T^31 - 
        1744/2401*T^30 + 176/343*T^29 - 176/343*T^27 + 1744/2401*T^26 - 
        1664/2401*T^25 + 1299/2401*T^24 + 87/2401*T^23 - 3317/2401*T^22 + 
        4024/2401*T^21 - 2474/2401*T^20 - 24/343*T^19 + 3639/2401*T^18 - 
        3058/2401*T^17 + 2641/2401*T^16 - 27/49*T^15 - 1905/2401*T^14 + 
        1703/2401*T^13 - 2664/2401*T^12 + 999/2401*T^11 + 1458/2401*T^10 - 
        1570/2401*T^9 + 2696/2401*T^8 + 4/343*T^7 - 1196/2401*T^6 + 2350/2401*T^5 - 
        3928/2401*T^4 + 138/343*T^3 + 17/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        3*X*Y^8 + 4*X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 6*X*Y 
        + 6*Y^30 + 5*Y^29 + 5*Y^28 + 2*Y^27 + 3*Y^26 + 4*Y^24 + Y^23 + 5*Y^22 + Y^21
        + Y^19 + 4*Y^18 + 3*Y^17 + 2*Y^16 + 6*Y^15 + Y^14 + 2*Y^13 + 4*Y^12 + Y^11 +
        6*Y^10 + 5*Y^9 + Y^8 + 3*Y^7 + Y^5 + 5*Y^4 + 3*Y^3 + 3*Y^2 + Y + 5,
    -T^56 - 6/7*T^55 - 5/7*T^54 + 4/343*T^53 + 1434/2401*T^52 + 2235/2401*T^51 + 
        2853/2401*T^50 + 225/343*T^49 - 673/2401*T^48 - 2739/2401*T^47 - 
        2546/2401*T^46 - 2344/2401*T^45 + 456/2401*T^44 + 1466/2401*T^43 + 
        3470/2401*T^42 + 3137/2401*T^41 + 477/2401*T^40 - 185/343*T^39 - 
        436/343*T^38 - 2252/2401*T^37 - 1032/2401*T^36 + 32/2401*T^35 + 
        1749/2401*T^34 + 2026/2401*T^33 + 765/2401*T^32 - 1461/2401*T^31 - 
        2144/2401*T^30 - 22/49*T^29 + 22/49*T^27 + 2144/2401*T^26 + 1461/2401*T^25 -
        765/2401*T^24 - 2026/2401*T^23 - 1749/2401*T^22 - 32/2401*T^21 + 
        1032/2401*T^20 + 2252/2401*T^19 + 436/343*T^18 + 185/343*T^17 - 
        477/2401*T^16 - 3137/2401*T^15 - 3470/2401*T^14 - 1466/2401*T^13 - 
        456/2401*T^12 + 2344/2401*T^11 + 2546/2401*T^10 + 2739/2401*T^9 + 
        673/2401*T^8 - 225/343*T^7 - 2853/2401*T^6 - 2235/2401*T^5 - 1434/2401*T^4 -
        4/343*T^3 + 5/7*T^2 + 6/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 +
        X*Y^7 + 3*X*Y^6 + X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + X*Y + 6*Y^30 + 2*Y^29 + Y^28 +
        2*Y^27 + 6*Y^26 + 3*Y^25 + Y^24 + 3*Y^23 + 3*Y^21 + 6*Y^20 + Y^19 + 6*Y^18 +
        4*Y^17 + 3*Y^16 + 2*Y^15 + 4*Y^14 + 2*Y^12 + 6*Y^11 + 3*Y^10 + 3*Y^9 + 5*Y^8
        + 6*Y^7 + 4*Y^6 + 6*Y^4 + 3*Y^3 + 3*Y^2 + 6*Y + 5,
    T^56 + 17/7*T^55 + 145/49*T^54 + 101/49*T^53 - 22/49*T^52 - 8028/2401*T^51 - 
        14053/2401*T^50 - 332/49*T^49 - 12351/2401*T^48 - 3617/2401*T^47 + 
        1033/343*T^46 + 15874/2401*T^45 + 18911/2401*T^44 + 14991/2401*T^43 + 
        6812/2401*T^42 - 1849/2401*T^41 - 9386/2401*T^40 - 12763/2401*T^39 - 
        11608/2401*T^38 - 885/343*T^37 + 23/49*T^36 + 6301/2401*T^35 + 1157/343*T^34
        + 6749/2401*T^33 + 4090/2401*T^32 + 351/2401*T^31 - 3284/2401*T^30 - 
        5746/2401*T^29 - 6791/2401*T^28 - 5746/2401*T^27 - 3284/2401*T^26 + 
        351/2401*T^25 + 4090/2401*T^24 + 6749/2401*T^23 + 1157/343*T^22 + 
        6301/2401*T^21 + 23/49*T^20 - 885/343*T^19 - 11608/2401*T^18 - 
        12763/2401*T^17 - 9386/2401*T^16 - 1849/2401*T^15 + 6812/2401*T^14 + 
        14991/2401*T^13 + 18911/2401*T^12 + 15874/2401*T^11 + 1033/343*T^10 - 
        3617/2401*T^9 - 12351/2401*T^8 - 332/49*T^7 - 14053/2401*T^6 - 8028/2401*T^5
        - 22/49*T^4 + 101/49*T^3 + 145/49*T^2 + 17/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 
        6*X*Y^6 + 3*X*Y^5 + X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 6*X*Y + 2*X + 4*Y^30 + 
        2*Y^29 + 5*Y^28 + 4*Y^27 + 3*Y^24 + Y^23 + 5*Y^22 + 4*Y^21 + Y^20 + 6*Y^19 +
        Y^17 + 3*Y^15 + 4*Y^14 + 2*Y^13 + 5*Y^12 + 3*Y^10 + 3*Y^9 + 5*Y^8 + 4*Y^7 + 
        Y^6 + 2*Y^5 + 4*Y^4 + 6*Y^3 + 4*Y^2 + 6*Y + 1,
    -T^56 - 8/7*T^55 - 24/49*T^54 - 156/343*T^53 - 64/2401*T^52 - 925/2401*T^51 - 
        1531/2401*T^50 - 1887/2401*T^49 - 1807/2401*T^48 - 1795/2401*T^47 - 
        276/343*T^46 + 610/2401*T^45 + 37/2401*T^44 - 1227/2401*T^43 - 
        1350/2401*T^42 - 1714/2401*T^41 - 129/343*T^40 + 697/2401*T^39 + 
        1844/2401*T^38 + 44/2401*T^37 + 373/2401*T^36 + 577/2401*T^35 - 
        520/2401*T^34 - 34/343*T^33 + 265/2401*T^32 + 690/2401*T^31 - 220/2401*T^30 
        + 26/49*T^29 - 26/49*T^27 + 220/2401*T^26 - 690/2401*T^25 - 265/2401*T^24 + 
        34/343*T^23 + 520/2401*T^22 - 577/2401*T^21 - 373/2401*T^20 - 44/2401*T^19 -
        1844/2401*T^18 - 697/2401*T^17 + 129/343*T^16 + 1714/2401*T^15 + 
        1350/2401*T^14 + 1227/2401*T^13 - 37/2401*T^12 - 610/2401*T^11 + 
        276/343*T^10 + 1795/2401*T^9 + 1807/2401*T^8 + 1887/2401*T^7 + 1531/2401*T^6
        + 925/2401*T^5 + 64/2401*T^4 + 156/343*T^3 + 24/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 4*X*Y^13 + 2*X*Y^12 + 6*X*Y^10 + 5*X*Y^8 + 3*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 
        3*X*Y^3 + X*Y^2 + 2*X*Y + 5*X + 6*Y^30 + 3*Y^29 + 6*Y^28 + 5*Y^27 + 2*Y^26 +
        4*Y^25 + 5*Y^24 + Y^23 + 5*Y^22 + 3*Y^21 + Y^20 + 3*Y^19 + 5*Y^18 + 2*Y^17 +
        6*Y^14 + 2*Y^13 + 5*Y^12 + 6*Y^11 + 2*Y^10 + 5*Y^8 + 6*Y^7 + 4*Y^6 + 2*Y^5 +
        Y^4 + Y^3 + 5*Y^2 + 2*Y + 2,
    -T^56 - 13/7*T^55 - 71/49*T^54 - 453/343*T^53 - 4415/2401*T^52 - 2090/2401*T^51 
        + 1754/2401*T^50 + 2269/2401*T^49 + 2236/2401*T^48 + 634/343*T^47 + 
        5421/2401*T^46 + 3118/2401*T^45 + 1397/2401*T^44 + 1725/2401*T^43 + 
        51/2401*T^42 - 3342/2401*T^41 - 2713/2401*T^40 - 2453/2401*T^39 - 
        5123/2401*T^38 - 3261/2401*T^37 + 1689/2401*T^36 + 6/7*T^35 + 1850/2401*T^34
        + 5196/2401*T^33 + 5414/2401*T^32 + 298/343*T^31 + 1705/2401*T^30 + 
        2494/2401*T^29 - 2494/2401*T^27 - 1705/2401*T^26 - 298/343*T^25 - 
        5414/2401*T^24 - 5196/2401*T^23 - 1850/2401*T^22 - 6/7*T^21 - 1689/2401*T^20
        + 3261/2401*T^19 + 5123/2401*T^18 + 2453/2401*T^17 + 2713/2401*T^16 + 
        3342/2401*T^15 - 51/2401*T^14 - 1725/2401*T^13 - 1397/2401*T^12 - 
        3118/2401*T^11 - 5421/2401*T^10 - 634/343*T^9 - 2236/2401*T^8 - 
        2269/2401*T^7 - 1754/2401*T^6 + 2090/2401*T^5 + 4415/2401*T^4 + 453/343*T^3 
        + 71/49*T^2 + 13/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 3*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 2*X*Y^8 +
        5*X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + 6*X*Y^3 + 4*X*Y^2 + 4*X*Y + 4*X + 2*Y^30 + 
        5*Y^29 + 3*Y^28 + 6*Y^27 + 2*Y^26 + 3*Y^25 + 3*Y^24 + 2*Y^23 + 4*Y^22 + 
        4*Y^21 + 2*Y^20 + 2*Y^19 + 5*Y^17 + Y^16 + 4*Y^15 + Y^14 + 6*Y^13 + 4*Y^11 +
        2*Y^10 + 5*Y^9 + 4*Y^8 + 6*Y^7 + Y^6 + 4*Y^5 + 3*Y^4 + Y^2 + Y + 4,
    -T^56 - 2/7*T^55 + 24/49*T^54 + 296/343*T^53 + 2588/2401*T^52 - 29/49*T^51 - 
        2378/2401*T^50 - 109/2401*T^49 + 2493/2401*T^48 + 3209/2401*T^47 - 
        225/2401*T^46 - 3123/2401*T^45 - 1812/2401*T^44 + 1224/2401*T^43 + 
        1923/2401*T^42 - 1697/2401*T^41 - 3742/2401*T^40 - 1740/2401*T^39 + 
        2320/2401*T^38 + 540/343*T^37 + 152/2401*T^36 - 3644/2401*T^35 - 
        2699/2401*T^34 + 2428/2401*T^33 + 666/343*T^32 + 2001/2401*T^31 - 
        2596/2401*T^30 - 4071/2401*T^29 + 4071/2401*T^27 + 2596/2401*T^26 - 
        2001/2401*T^25 - 666/343*T^24 - 2428/2401*T^23 + 2699/2401*T^22 + 
        3644/2401*T^21 - 152/2401*T^20 - 540/343*T^19 - 2320/2401*T^18 + 
        1740/2401*T^17 + 3742/2401*T^16 + 1697/2401*T^15 - 1923/2401*T^14 - 
        1224/2401*T^13 + 1812/2401*T^12 + 3123/2401*T^11 + 225/2401*T^10 - 
        3209/2401*T^9 - 2493/2401*T^8 + 109/2401*T^7 + 2378/2401*T^6 + 29/49*T^5 - 
        2588/2401*T^4 - 296/343*T^3 - 24/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 3*X*Y^12 + 3*X*Y^11 + X*Y^10 + X*Y^9 + 5*X*Y^7 + 
        5*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + X*Y^2 + 3*X*Y + 5*X + 2*Y^30 + 
        6*Y^28 + 5*Y^27 + Y^26 + 2*Y^25 + 6*Y^24 + 6*Y^23 + 6*Y^22 + 6*Y^21 + Y^20 +
        4*Y^19 + 3*Y^18 + Y^17 + 5*Y^16 + 6*Y^15 + 4*Y^14 + Y^13 + 3*Y^12 + 2*Y^11 +
        2*Y^9 + 2*Y^8 + 6*Y^7 + 2*Y^6 + 5*Y^5 + 6*Y^2 + 2*Y + 3,
    -T^56 - T^55 + 4/49*T^54 + 75/343*T^53 - 1038/2401*T^52 + 536/2401*T^51 + 
        216/2401*T^50 + 1075/2401*T^49 + 1966/2401*T^48 - 309/2401*T^47 - 
        1436/2401*T^46 + 972/2401*T^45 - 323/2401*T^44 - 1004/2401*T^43 - 
        1/2401*T^42 + 138/2401*T^41 + 159/343*T^40 + 2315/2401*T^39 + 930/2401*T^38 
        + 717/2401*T^37 + 433/2401*T^36 + 170/2401*T^35 + 1037/2401*T^34 + 
        26/49*T^33 + 26/2401*T^32 + 2/49*T^31 + 535/2401*T^30 + 394/2401*T^29 - 
        394/2401*T^27 - 535/2401*T^26 - 2/49*T^25 - 26/2401*T^24 - 26/49*T^23 - 
        1037/2401*T^22 - 170/2401*T^21 - 433/2401*T^20 - 717/2401*T^19 - 
        930/2401*T^18 - 2315/2401*T^17 - 159/343*T^16 - 138/2401*T^15 + 1/2401*T^14 
        + 1004/2401*T^13 + 323/2401*T^12 - 972/2401*T^11 + 1436/2401*T^10 + 
        309/2401*T^9 - 1966/2401*T^8 - 1075/2401*T^7 - 216/2401*T^6 - 536/2401*T^5 +
        1038/2401*T^4 - 75/343*T^3 - 4/49*T^2 + T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 3*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 4*X*Y^8 +
        5*X*Y^7 + 2*X*Y^6 + 2*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 5*X*Y + 2*X + Y^30 + 
        5*Y^29 + Y^28 + 3*Y^27 + Y^26 + Y^25 + 5*Y^24 + 5*Y^23 + Y^22 + 6*Y^21 + 
        2*Y^19 + 3*Y^18 + 6*Y^17 + 4*Y^16 + 3*Y^15 + 6*Y^14 + Y^12 + 6*Y^11 + 6*Y^10
        + 4*Y^9 + 5*Y^7 + 5*Y^6 + 2*Y^5 + 5*Y^4 + 5*Y^3 + 6*Y^2 + 6*Y,
    -T^56 + 68/49*T^54 + 184/343*T^53 - 354/343*T^52 - 1524/2401*T^51 + 
        425/2401*T^50 + 3/2401*T^49 + 162/2401*T^48 + 2642/2401*T^47 + 769/2401*T^46
        - 2981/2401*T^45 - 2773/2401*T^44 + 1448/2401*T^43 + 321/343*T^42 + 
        1087/2401*T^41 + 82/2401*T^40 - 794/2401*T^39 - 2899/2401*T^38 - 
        1343/2401*T^37 + 2328/2401*T^36 + 3536/2401*T^35 - 302/2401*T^34 - 
        3007/2401*T^33 - 1417/2401*T^32 + 32/343*T^31 + 1835/2401*T^30 + 
        1891/2401*T^29 - 1891/2401*T^27 - 1835/2401*T^26 - 32/343*T^25 + 
        1417/2401*T^24 + 3007/2401*T^23 + 302/2401*T^22 - 3536/2401*T^21 - 
        2328/2401*T^20 + 1343/2401*T^19 + 2899/2401*T^18 + 794/2401*T^17 - 
        82/2401*T^16 - 1087/2401*T^15 - 321/343*T^14 - 1448/2401*T^13 + 
        2773/2401*T^12 + 2981/2401*T^11 - 769/2401*T^10 - 2642/2401*T^9 - 
        162/2401*T^8 - 3/2401*T^7 - 425/2401*T^6 + 1524/2401*T^5 + 354/343*T^4 - 
        184/343*T^3 - 68/49*T^2 + 1
*], [*
    X^3 + 2*X*Y^14 + 6*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + X*Y^8 + 4*X*Y^7 + 
        6*X*Y^5 + 6*X*Y^3 + 5*X*Y^2 + 2*X*Y + 3*X + 5*Y^30 + 2*Y^29 + Y^28 + 4*Y^27 
        + 4*Y^26 + Y^25 + Y^24 + 4*Y^23 + 6*Y^22 + Y^21 + Y^20 + 3*Y^18 + 5*Y^17 + 
        Y^16 + 4*Y^15 + 5*Y^14 + 2*Y^13 + 6*Y^12 + 5*Y^10 + 2*Y^9 + 3*Y^8 + Y^7 + 
        5*Y^6 + 2*Y^5 + Y^4 + 3*Y^3 + 4*Y^2 + 5*Y + 6,
    -T^56 - 11/7*T^55 - 11/7*T^54 - 363/343*T^53 - 1165/2401*T^52 - 674/2401*T^51 - 
        138/343*T^50 - 972/2401*T^49 - 3/343*T^48 + 1178/2401*T^47 + 2963/2401*T^46 
        + 2447/2401*T^45 + 957/2401*T^44 - 941/2401*T^43 - 1437/2401*T^42 - 
        447/2401*T^41 + 852/2401*T^40 + 109/343*T^39 - 116/2401*T^38 - 531/2401*T^37
        - 50/343*T^36 + 127/2401*T^35 + 52/343*T^34 - 24/2401*T^33 - 37/343*T^32 - 
        193/343*T^31 - 1497/2401*T^30 - 108/343*T^29 + 108/343*T^27 + 1497/2401*T^26
        + 193/343*T^25 + 37/343*T^24 + 24/2401*T^23 - 52/343*T^22 - 127/2401*T^21 + 
        50/343*T^20 + 531/2401*T^19 + 116/2401*T^18 - 109/343*T^17 - 852/2401*T^16 +
        447/2401*T^15 + 1437/2401*T^14 + 941/2401*T^13 - 957/2401*T^12 - 
        2447/2401*T^11 - 2963/2401*T^10 - 1178/2401*T^9 + 3/343*T^8 + 972/2401*T^7 +
        138/343*T^6 + 674/2401*T^5 + 1165/2401*T^4 + 363/343*T^3 + 11/7*T^2 + 11/7*T
        + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^13 + 4*X*Y^12 + X*Y^11 + 4*X*Y^9 + 3*X*Y^8 + X*Y^7 + 
        2*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + X*Y^3 + X*Y^2 + 2*X*Y + Y^30 + Y^29 + 6*Y^28 +
        2*Y^27 + 4*Y^26 + 2*Y^25 + 4*Y^24 + 4*Y^23 + 3*Y^22 + 2*Y^21 + 6*Y^20 + 
        5*Y^19 + 5*Y^18 + 3*Y^17 + 3*Y^14 + 3*Y^13 + Y^12 + 3*Y^11 + 4*Y^10 + 5*Y^9 
        + 6*Y^8 + Y^7 + 6*Y^6 + 2*Y^5 + Y^3 + 5*Y^2 + 5*Y + 6,
    -T^56 + 6/7*T^55 - 4/49*T^54 + 81/343*T^53 + 46/2401*T^52 - 445/2401*T^51 + 
        439/2401*T^50 - 1690/2401*T^49 + 1290/2401*T^48 + 167/2401*T^47 - 
        227/2401*T^46 + 45/2401*T^45 + 914/2401*T^44 - 767/2401*T^43 - 
        1167/2401*T^42 + 292/343*T^41 - 1259/2401*T^40 + 61/343*T^39 - 797/2401*T^38
        + 246/343*T^37 - 825/2401*T^36 - 1144/2401*T^35 + 1695/2401*T^34 - 
        1200/2401*T^33 + 16/49*T^32 - 570/2401*T^31 + 1905/2401*T^30 - 
        1762/2401*T^29 + 1762/2401*T^27 - 1905/2401*T^26 + 570/2401*T^25 - 
        16/49*T^24 + 1200/2401*T^23 - 1695/2401*T^22 + 1144/2401*T^21 + 
        825/2401*T^20 - 246/343*T^19 + 797/2401*T^18 - 61/343*T^17 + 1259/2401*T^16 
        - 292/343*T^15 + 1167/2401*T^14 + 767/2401*T^13 - 914/2401*T^12 - 
        45/2401*T^11 + 227/2401*T^10 - 167/2401*T^9 - 1290/2401*T^8 + 1690/2401*T^7 
        - 439/2401*T^6 + 445/2401*T^5 - 46/2401*T^4 - 81/343*T^3 + 4/49*T^2 - 6/7*T 
        + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + X*Y^12 + 2*X*Y^10 + X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 
        X*Y^2 + X*Y + X + 3*Y^30 + Y^29 + 4*Y^28 + Y^27 + 4*Y^26 + 2*Y^25 + 5*Y^24 +
        6*Y^23 + 4*Y^22 + 6*Y^21 + 6*Y^20 + 2*Y^19 + 5*Y^18 + Y^17 + 4*Y^16 + 3*Y^15
        + 3*Y^14 + 5*Y^13 + Y^11 + 2*Y^10 + 3*Y^9 + 2*Y^8 + 6*Y^7 + Y^6 + Y^5 + 
        2*Y^4 + Y,
    T^56 - 12/7*T^55 + 68/49*T^54 - 31/49*T^53 + 642/2401*T^52 - 732/2401*T^51 + 
        2110/2401*T^50 - 309/343*T^49 - 149/2401*T^48 + 2110/2401*T^47 - 
        2349/2401*T^46 + 1973/2401*T^45 - 2652/2401*T^44 + 3803/2401*T^43 - 
        5211/2401*T^42 + 4474/2401*T^41 - 2763/2401*T^40 + 1871/2401*T^39 - 
        2806/2401*T^38 + 2911/2401*T^37 - 2295/2401*T^36 + 415/2401*T^35 + 
        2542/2401*T^34 - 479/343*T^33 + 2095/2401*T^32 - 222/343*T^31 + 
        2720/2401*T^30 - 4267/2401*T^29 + 5256/2401*T^28 - 4267/2401*T^27 + 
        2720/2401*T^26 - 222/343*T^25 + 2095/2401*T^24 - 479/343*T^23 + 
        2542/2401*T^22 + 415/2401*T^21 - 2295/2401*T^20 + 2911/2401*T^19 - 
        2806/2401*T^18 + 1871/2401*T^17 - 2763/2401*T^16 + 4474/2401*T^15 - 
        5211/2401*T^14 + 3803/2401*T^13 - 2652/2401*T^12 + 1973/2401*T^11 - 
        2349/2401*T^10 + 2110/2401*T^9 - 149/2401*T^8 - 309/343*T^7 + 2110/2401*T^6 
        - 732/2401*T^5 + 642/2401*T^4 - 31/49*T^3 + 68/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 
        + 5*X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + X*Y^4 + X*Y^3 + 2*X*Y + X + 5*Y^30
        + Y^29 + 5*Y^28 + Y^27 + 2*Y^26 + 5*Y^25 + 3*Y^24 + Y^23 + 4*Y^22 + 3*Y^21 +
        Y^20 + 4*Y^18 + 6*Y^16 + 3*Y^15 + 3*Y^14 + 4*Y^13 + 2*Y^12 + 5*Y^11 + 4*Y^10
        + 5*Y^9 + 4*Y^8 + Y^7 + 6*Y^6 + 2*Y^4 + 6*Y^3 + 6*Y^2 + 5*Y,
    T^56 - 10/7*T^55 - 19/49*T^54 + 587/343*T^53 - 1651/2401*T^52 - 435/343*T^51 + 
        3615/2401*T^50 + 165/2401*T^49 - 3029/2401*T^48 + 1653/2401*T^47 + 
        1318/2401*T^46 - 1324/2401*T^45 - 1739/2401*T^44 + 2045/2401*T^43 + 
        2412/2401*T^42 - 4776/2401*T^41 + 1096/2401*T^40 + 584/343*T^39 - 
        4000/2401*T^38 + 143/2401*T^37 + 3413/2401*T^36 - 3349/2401*T^35 - 
        718/2401*T^34 + 3236/2401*T^33 - 1503/2401*T^32 - 103/2401*T^31 + 
        377/2401*T^30 - 120/343*T^29 + 114/343*T^28 - 120/343*T^27 + 377/2401*T^26 -
        103/2401*T^25 - 1503/2401*T^24 + 3236/2401*T^23 - 718/2401*T^22 - 
        3349/2401*T^21 + 3413/2401*T^20 + 143/2401*T^19 - 4000/2401*T^18 + 
        584/343*T^17 + 1096/2401*T^16 - 4776/2401*T^15 + 2412/2401*T^14 + 
        2045/2401*T^13 - 1739/2401*T^12 - 1324/2401*T^11 + 1318/2401*T^10 + 
        1653/2401*T^9 - 3029/2401*T^8 + 165/2401*T^7 + 3615/2401*T^6 - 435/343*T^5 -
        1651/2401*T^4 + 587/343*T^3 - 19/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 +
        3*X*Y^7 + 2*X*Y^6 + 3*X*Y^4 + X*Y^3 + 5*X*Y^2 + 6*X*Y + 5*Y^30 + 5*Y^29 + 
        4*Y^27 + 4*Y^26 + Y^25 + Y^24 + 2*Y^23 + 4*Y^22 + Y^19 + 3*Y^18 + 5*Y^17 + 
        3*Y^16 + 3*Y^15 + 3*Y^14 + 6*Y^13 + 2*Y^12 + 5*Y^11 + 2*Y^10 + 4*Y^9 + 3*Y^8
        + 3*Y^7 + 3*Y^6 + 3*Y^5 + Y^4 + 2*Y^3 + 5*Y^2 + 4*Y + 1,
    -T^56 + 6/7*T^55 - 26/49*T^54 + 50/343*T^53 + 1641/2401*T^52 - 675/2401*T^51 + 
        2/343*T^50 - 422/2401*T^49 - 118/2401*T^48 - 682/2401*T^47 + 1241/2401*T^46 
        - 577/2401*T^45 + 925/2401*T^44 - 1244/2401*T^43 + 758/2401*T^42 - 
        800/2401*T^41 - 540/2401*T^40 + 1560/2401*T^39 - 1581/2401*T^38 + 
        386/2401*T^37 + 825/2401*T^36 - 220/343*T^35 + 229/343*T^34 + 54/2401*T^33 -
        94/343*T^32 + 170/2401*T^31 - 55/2401*T^30 - 114/343*T^29 + 114/343*T^27 + 
        55/2401*T^26 - 170/2401*T^25 + 94/343*T^24 - 54/2401*T^23 - 229/343*T^22 + 
        220/343*T^21 - 825/2401*T^20 - 386/2401*T^19 + 1581/2401*T^18 - 
        1560/2401*T^17 + 540/2401*T^16 + 800/2401*T^15 - 758/2401*T^14 + 
        1244/2401*T^13 - 925/2401*T^12 + 577/2401*T^11 - 1241/2401*T^10 + 
        682/2401*T^9 + 118/2401*T^8 + 422/2401*T^7 - 2/343*T^6 + 675/2401*T^5 - 
        1641/2401*T^4 - 50/343*T^3 + 26/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 
        5*X*Y^8 + X*Y^7 + X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + X*Y^3 + X*Y^2 + 6*X*Y + X + 
        2*Y^30 + 6*Y^29 + 3*Y^28 + 3*Y^27 + 5*Y^26 + 2*Y^25 + 6*Y^24 + 2*Y^23 + Y^22
        + 6*Y^21 + Y^20 + 4*Y^19 + 4*Y^18 + 5*Y^17 + 2*Y^16 + 5*Y^15 + 2*Y^14 + 
        3*Y^13 + 2*Y^12 + 5*Y^11 + 2*Y^10 + 5*Y^9 + Y^7 + 3*Y^6 + 4*Y^5 + 5*Y^3 + 
        6*Y^2 + 3*Y + 4,
    -T^56 + 10/7*T^55 - 33/49*T^54 + 74/343*T^53 - 8/343*T^52 - 142/2401*T^51 - 
        354/2401*T^50 + 443/2401*T^49 - 795/2401*T^48 + 2028/2401*T^47 - 
        134/343*T^46 - 548/2401*T^45 + 1388/2401*T^44 - 1833/2401*T^43 + 
        521/2401*T^42 - 370/2401*T^41 + 1219/2401*T^40 + 215/2401*T^39 - 
        254/2401*T^38 - 785/2401*T^37 - 778/2401*T^36 + 1325/2401*T^35 - 
        852/2401*T^34 + 2111/2401*T^33 - 640/2401*T^32 - 2/7*T^31 + 711/2401*T^30 - 
        1342/2401*T^29 + 1342/2401*T^27 - 711/2401*T^26 + 2/7*T^25 + 640/2401*T^24 -
        2111/2401*T^23 + 852/2401*T^22 - 1325/2401*T^21 + 778/2401*T^20 + 
        785/2401*T^19 + 254/2401*T^18 - 215/2401*T^17 - 1219/2401*T^16 + 
        370/2401*T^15 - 521/2401*T^14 + 1833/2401*T^13 - 1388/2401*T^12 + 
        548/2401*T^11 + 134/343*T^10 - 2028/2401*T^9 + 795/2401*T^8 - 443/2401*T^7 +
        354/2401*T^6 + 142/2401*T^5 + 8/343*T^4 - 74/343*T^3 + 33/49*T^2 - 10/7*T + 
        1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 5*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 6*X*Y^7 + 
        2*X*Y^5 + 3*X*Y^3 + 6*X*Y^2 + 2*X*Y + 3*X + 5*Y^30 + Y^29 + Y^28 + 4*Y^26 + 
        3*Y^25 + 6*Y^24 + 4*Y^23 + 2*Y^22 + 5*Y^21 + 4*Y^20 + 2*Y^17 + 6*Y^16 + Y^15
        + 6*Y^13 + 2*Y^12 + Y^11 + 4*Y^10 + 2*Y^8 + 2*Y^7 + 4*Y^6 + 2*Y^5 + 5*Y^4 + 
        2*Y^2 + 4*Y + 6,
    T^56 + 13/7*T^55 + 106/49*T^54 + 789/343*T^53 + 3613/2401*T^52 + 495/2401*T^51 -
        594/2401*T^50 - 185/343*T^49 - 1072/2401*T^48 + 650/2401*T^47 + 
        968/2401*T^46 + 1007/2401*T^45 + 1527/2401*T^44 + 1536/2401*T^43 + 
        1209/2401*T^42 + 1815/2401*T^41 + 2300/2401*T^40 + 1359/2401*T^39 + 
        164/2401*T^38 - 1746/2401*T^37 - 601/343*T^36 - 5458/2401*T^35 - 
        5161/2401*T^34 - 5188/2401*T^33 - 3853/2401*T^32 - 1289/2401*T^31 - 
        445/2401*T^30 + 1352/2401*T^29 + 2928/2401*T^28 + 1352/2401*T^27 - 
        445/2401*T^26 - 1289/2401*T^25 - 3853/2401*T^24 - 5188/2401*T^23 - 
        5161/2401*T^22 - 5458/2401*T^21 - 601/343*T^20 - 1746/2401*T^19 + 
        164/2401*T^18 + 1359/2401*T^17 + 2300/2401*T^16 + 1815/2401*T^15 + 
        1209/2401*T^14 + 1536/2401*T^13 + 1527/2401*T^12 + 1007/2401*T^11 + 
        968/2401*T^10 + 650/2401*T^9 - 1072/2401*T^8 - 185/343*T^7 - 594/2401*T^6 + 
        495/2401*T^5 + 3613/2401*T^4 + 789/343*T^3 + 106/49*T^2 + 13/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 3*X*Y^12 + 4*X*Y^10 + 3*X*Y^9 + X*Y^7 + 6*X*Y^6 + 
        6*X*Y^5 + 5*X*Y^3 + 6*X*Y^2 + 3*X*Y + 5*X + 4*Y^30 + 2*Y^29 + 2*Y^28 + 
        4*Y^27 + 4*Y^26 + 5*Y^25 + 4*Y^24 + 4*Y^22 + 5*Y^19 + 4*Y^18 + 5*Y^17 + 
        5*Y^16 + 4*Y^15 + 5*Y^14 + 5*Y^13 + 2*Y^12 + 4*Y^11 + 5*Y^10 + Y^9 + 6*Y^8 +
        2*Y^7 + 6*Y^6 + Y^5 + 6*Y^4 + 5*Y^3 + Y^2 + Y + 2,
    -T^56 - 1/7*T^55 + 31/49*T^54 + 263/343*T^53 + 139/2401*T^52 - 71/2401*T^51 + 
        67/343*T^50 - 23/2401*T^49 - 206/2401*T^48 + 600/2401*T^47 + 253/2401*T^46 -
        1513/2401*T^45 - 577/2401*T^44 + 513/2401*T^43 - 482/2401*T^42 - 
        1458/2401*T^41 - 351/2401*T^40 + 137/2401*T^39 + 185/343*T^38 - 
        653/2401*T^37 + 1049/2401*T^36 - 45/343*T^35 - 12/2401*T^34 + 242/2401*T^33 
        + 564/2401*T^32 + 382/2401*T^31 + 1249/2401*T^30 + 107/343*T^29 - 
        107/343*T^27 - 1249/2401*T^26 - 382/2401*T^25 - 564/2401*T^24 - 
        242/2401*T^23 + 12/2401*T^22 + 45/343*T^21 - 1049/2401*T^20 + 653/2401*T^19 
        - 185/343*T^18 - 137/2401*T^17 + 351/2401*T^16 + 1458/2401*T^15 + 
        482/2401*T^14 - 513/2401*T^13 + 577/2401*T^12 + 1513/2401*T^11 - 
        253/2401*T^10 - 600/2401*T^9 + 206/2401*T^8 + 23/2401*T^7 - 67/343*T^6 + 
        71/2401*T^5 - 139/2401*T^4 - 263/343*T^3 - 31/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^13 + X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + X*Y^8 + 
        2*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 2*X*Y + 4*X + 
        5*Y^30 + Y^29 + 3*Y^28 + 5*Y^26 + 6*Y^25 + 2*Y^24 + 3*Y^23 + 3*Y^22 + 2*Y^21
        + 6*Y^19 + 2*Y^18 + 4*Y^17 + 5*Y^16 + 6*Y^15 + 3*Y^14 + 4*Y^13 + 6*Y^12 + 
        2*Y^11 + Y^10 + 5*Y^9 + Y^8 + 4*Y^7 + 4*Y^6 + Y^5 + Y^4 + 4*Y^3 + 4*Y + 6,
    -T^56 - 4/49*T^54 + 40/49*T^53 + 1663/2401*T^52 + 1879/2401*T^51 - 
        1144/2401*T^50 + 559/2401*T^49 - 284/343*T^48 - 585/2401*T^47 - 
        2378/2401*T^46 - 698/2401*T^45 - 80/343*T^44 + 122/343*T^43 + 2358/2401*T^42
        + 3251/2401*T^41 + 1167/2401*T^40 - 193/2401*T^39 - 1523/2401*T^38 - 
        3260/2401*T^37 - 1107/2401*T^36 - 48/343*T^35 - 772/2401*T^34 - 
        276/2401*T^33 + 1324/2401*T^32 + 1560/2401*T^31 + 2833/2401*T^30 + 
        1793/2401*T^29 - 1793/2401*T^27 - 2833/2401*T^26 - 1560/2401*T^25 - 
        1324/2401*T^24 + 276/2401*T^23 + 772/2401*T^22 + 48/343*T^21 + 
        1107/2401*T^20 + 3260/2401*T^19 + 1523/2401*T^18 + 193/2401*T^17 - 
        1167/2401*T^16 - 3251/2401*T^15 - 2358/2401*T^14 - 122/343*T^13 + 
        80/343*T^12 + 698/2401*T^11 + 2378/2401*T^10 + 585/2401*T^9 + 284/343*T^8 - 
        559/2401*T^7 + 1144/2401*T^6 - 1879/2401*T^5 - 1663/2401*T^4 - 40/49*T^3 + 
        4/49*T^2 + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 3*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 5*X*Y^8 + 3*X*Y^7 + 
        2*X*Y^6 + 3*X*Y^5 + X*Y^4 + X*Y + X + Y^30 + 6*Y^29 + 3*Y^28 + 6*Y^27 + 
        2*Y^26 + 6*Y^25 + Y^23 + 2*Y^22 + 2*Y^21 + 3*Y^20 + 6*Y^19 + 2*Y^18 + 5*Y^17
        + 4*Y^16 + 3*Y^15 + 4*Y^13 + 5*Y^12 + 3*Y^11 + 5*Y^7 + 4*Y^6 + 2*Y^4 + Y^3 +
        6*Y + 3,
    T^56 + 2/7*T^55 - 44/49*T^54 - 2/7*T^53 + 1014/2401*T^52 - 688/2401*T^51 - 
        306/2401*T^50 + 1007/2401*T^49 + 460/2401*T^48 - 663/2401*T^47 + 
        487/2401*T^46 + 2059/2401*T^45 + 930/2401*T^44 - 327/343*T^43 - 
        1598/2401*T^42 + 130/2401*T^41 + 61/2401*T^40 - 11/2401*T^39 + 
        1066/2401*T^38 + 624/2401*T^37 - 837/2401*T^36 - 747/2401*T^35 + 
        841/2401*T^34 + 867/2401*T^33 - 1466/2401*T^32 - 1619/2401*T^31 + 
        127/2401*T^30 + 431/2401*T^29 - 246/2401*T^28 + 431/2401*T^27 + 
        127/2401*T^26 - 1619/2401*T^25 - 1466/2401*T^24 + 867/2401*T^23 + 
        841/2401*T^22 - 747/2401*T^21 - 837/2401*T^20 + 624/2401*T^19 + 
        1066/2401*T^18 - 11/2401*T^17 + 61/2401*T^16 + 130/2401*T^15 - 
        1598/2401*T^14 - 327/343*T^13 + 930/2401*T^12 + 2059/2401*T^11 + 
        487/2401*T^10 - 663/2401*T^9 + 460/2401*T^8 + 1007/2401*T^7 - 306/2401*T^6 -
        688/2401*T^5 + 1014/2401*T^4 - 2/7*T^3 - 44/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 6*X*Y^9 + 5*X*Y^7 + 6*X*Y^6 + 
        6*X*Y^5 + X*Y^4 + 2*X*Y^3 + X*Y + 4*X + 3*Y^30 + 5*Y^29 + 4*Y^28 + 2*Y^27 + 
        2*Y^26 + 3*Y^25 + 2*Y^24 + 6*Y^23 + 2*Y^22 + 4*Y^21 + 2*Y^20 + 2*Y^19 + 
        4*Y^18 + 2*Y^16 + 4*Y^12 + 5*Y^11 + 3*Y^10 + Y^9 + 2*Y^8 + Y^7 + 3*Y^6 + 
        3*Y^5 + 3*Y^4 + 2*Y^3 + 3*Y,
    T^56 + 3/7*T^55 - 47/49*T^54 - 248/343*T^53 - 376/2401*T^52 + 970/2401*T^51 + 
        1929/2401*T^50 + 171/343*T^49 - 2231/2401*T^48 - 2280/2401*T^47 + 
        1023/2401*T^46 + 1994/2401*T^45 - 106/2401*T^44 - 1009/2401*T^43 - 
        269/2401*T^42 - 25/343*T^41 + 219/343*T^40 + 612/2401*T^39 - 339/343*T^38 - 
        1307/2401*T^37 + 2650/2401*T^36 + 1367/2401*T^35 - 1038/2401*T^34 - 
        202/343*T^33 - 1184/2401*T^32 + 247/2401*T^31 + 1912/2401*T^30 + 
        233/2401*T^29 - 2591/2401*T^28 + 233/2401*T^27 + 1912/2401*T^26 + 
        247/2401*T^25 - 1184/2401*T^24 - 202/343*T^23 - 1038/2401*T^22 + 
        1367/2401*T^21 + 2650/2401*T^20 - 1307/2401*T^19 - 339/343*T^18 + 
        612/2401*T^17 + 219/343*T^16 - 25/343*T^15 - 269/2401*T^14 - 1009/2401*T^13 
        - 106/2401*T^12 + 1994/2401*T^11 + 1023/2401*T^10 - 2280/2401*T^9 - 
        2231/2401*T^8 + 171/343*T^7 + 1929/2401*T^6 + 970/2401*T^5 - 376/2401*T^4 - 
        248/343*T^3 - 47/49*T^2 + 3/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + X*Y^12 + 6*X*Y^9 + 2*X*Y^8 + 4*X*Y^7 + 
        3*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 6*X*Y + X + 2*Y^30 + 
        4*Y^28 + 2*Y^27 + 6*Y^26 + 3*Y^25 + 4*Y^24 + 2*Y^23 + Y^21 + Y^20 + Y^19 + 
        4*Y^18 + 4*Y^16 + 5*Y^14 + 5*Y^13 + 3*Y^12 + 6*Y^11 + 3*Y^10 + 5*Y^9 + 2*Y^8
        + 6*Y^7 + 4*Y^6 + 2*Y^5 + 5*Y^4 + 4*Y^3 + 5*Y^2 + 5*Y + 1,
    -T^56 + 3/7*T^55 + 3/49*T^54 + 4/7*T^53 - 230/343*T^52 + 1460/2401*T^51 - 
        218/2401*T^50 + 463/2401*T^49 - 73/343*T^48 - 124/343*T^47 + 879/2401*T^46 +
        34/2401*T^45 + 1314/2401*T^44 - 437/343*T^43 + 1346/2401*T^42 - 
        1331/2401*T^41 + 1039/2401*T^40 - 1732/2401*T^39 + 1752/2401*T^38 + 
        4/2401*T^37 - 192/2401*T^36 + 243/2401*T^35 - 883/2401*T^34 + 1234/2401*T^33
        - 542/2401*T^32 + 274/2401*T^31 - 12/49*T^30 + 1857/2401*T^29 - 
        1857/2401*T^27 + 12/49*T^26 - 274/2401*T^25 + 542/2401*T^24 - 1234/2401*T^23
        + 883/2401*T^22 - 243/2401*T^21 + 192/2401*T^20 - 4/2401*T^19 - 
        1752/2401*T^18 + 1732/2401*T^17 - 1039/2401*T^16 + 1331/2401*T^15 - 
        1346/2401*T^14 + 437/343*T^13 - 1314/2401*T^12 - 34/2401*T^11 - 
        879/2401*T^10 + 124/343*T^9 + 73/343*T^8 - 463/2401*T^7 + 218/2401*T^6 - 
        1460/2401*T^5 + 230/343*T^4 - 4/7*T^3 - 3/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + X*Y^13 + 5*X*Y^12 + X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 
        3*X*Y^8 + 4*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 4*X*Y 
        + 4*X + 6*Y^30 + 5*Y^28 + 3*Y^27 + 6*Y^25 + 2*Y^24 + 2*Y^23 + 6*Y^22 + 
        4*Y^20 + 3*Y^19 + 4*Y^17 + Y^16 + 5*Y^15 + 4*Y^14 + Y^13 + 2*Y^11 + 2*Y^10 +
        Y^9 + 3*Y^8 + 5*Y^7 + 4*Y^6 + 5*Y^5 + 6*Y^4 + 2*Y^3 + 4*Y^2 + 5*Y + 4,
    -T^56 - 3/7*T^55 + 65/49*T^54 + 282/343*T^53 + 208/2401*T^52 - 160/343*T^51 - 
        306/2401*T^50 + 4/343*T^49 - 1986/2401*T^48 - 247/343*T^47 + 1018/2401*T^46 
        + 3265/2401*T^45 + 1081/2401*T^44 - 1598/2401*T^43 + 86/2401*T^42 + 
        41/49*T^41 - 103/343*T^40 - 3000/2401*T^39 - 1059/2401*T^38 + 198/343*T^37 -
        143/2401*T^36 - 1123/2401*T^35 + 2273/2401*T^34 + 2977/2401*T^33 - 
        416/2401*T^32 - 3292/2401*T^31 - 2255/2401*T^30 + 530/2401*T^29 - 
        530/2401*T^27 + 2255/2401*T^26 + 3292/2401*T^25 + 416/2401*T^24 - 
        2977/2401*T^23 - 2273/2401*T^22 + 1123/2401*T^21 + 143/2401*T^20 - 
        198/343*T^19 + 1059/2401*T^18 + 3000/2401*T^17 + 103/343*T^16 - 41/49*T^15 -
        86/2401*T^14 + 1598/2401*T^13 - 1081/2401*T^12 - 3265/2401*T^11 - 
        1018/2401*T^10 + 247/343*T^9 + 1986/2401*T^8 - 4/343*T^7 + 306/2401*T^6 + 
        160/343*T^5 - 208/2401*T^4 - 282/343*T^3 - 65/49*T^2 + 3/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + X*Y^11 + 5*X*Y^10 + X*Y^9 + 5*X*Y^8 + X*Y^7
        + 5*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + X*Y + 4*X + 5*Y^30 + 5*Y^29 + 
        4*Y^28 + 4*Y^27 + 4*Y^26 + 2*Y^25 + 6*Y^24 + 6*Y^23 + Y^22 + 4*Y^19 + 2*Y^18
        + Y^17 + 2*Y^16 + 5*Y^15 + Y^13 + 6*Y^11 + 4*Y^10 + 6*Y^9 + 5*Y^8 + 4*Y^7 + 
        Y^6 + 4*Y^5 + 4*Y^4 + Y^3 + 1,
    T^56 + 15/7*T^55 + 115/49*T^54 + 316/343*T^53 - 1196/2401*T^52 - 2374/2401*T^51 
        - 778/2401*T^50 + 1301/2401*T^49 + 2337/2401*T^48 + 694/2401*T^47 - 
        2962/2401*T^46 - 804/343*T^45 - 3487/2401*T^44 + 935/2401*T^43 + 
        484/343*T^42 + 1814/2401*T^41 - 320/2401*T^40 - 1963/2401*T^39 - 
        1957/2401*T^38 - 1021/2401*T^37 + 72/2401*T^36 + 183/2401*T^35 - 
        765/2401*T^34 - 946/2401*T^33 - 194/2401*T^32 + 501/2401*T^31 + 
        458/2401*T^30 + 591/2401*T^29 + 873/2401*T^28 + 591/2401*T^27 + 
        458/2401*T^26 + 501/2401*T^25 - 194/2401*T^24 - 946/2401*T^23 - 
        765/2401*T^22 + 183/2401*T^21 + 72/2401*T^20 - 1021/2401*T^19 - 
        1957/2401*T^18 - 1963/2401*T^17 - 320/2401*T^16 + 1814/2401*T^15 + 
        484/343*T^14 + 935/2401*T^13 - 3487/2401*T^12 - 804/343*T^11 - 
        2962/2401*T^10 + 694/2401*T^9 + 2337/2401*T^8 + 1301/2401*T^7 - 778/2401*T^6
        - 2374/2401*T^5 - 1196/2401*T^4 + 316/343*T^3 + 115/49*T^2 + 15/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + X*Y^10 + 3*X*Y^9 + 5*X*Y^7 + 
        4*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + X*Y^3 + 4*X*Y^2 + 4*X*Y + 6*Y^30 + Y^29 + 
        2*Y^27 + 6*Y^26 + 4*Y^25 + 5*Y^24 + 6*Y^23 + 3*Y^22 + 5*Y^20 + 6*Y^19 + 
        2*Y^18 + 2*Y^17 + 4*Y^16 + 6*Y^15 + 6*Y^13 + 5*Y^12 + 2*Y^11 + 2*Y^10 + 
        4*Y^9 + 5*Y^8 + 4*Y^6 + Y^5 + Y^4 + 5*Y^3 + Y^2 + 6,
    T^56 + 1/7*T^55 - 53/49*T^54 - 100/343*T^53 + 1747/2401*T^52 + 1443/2401*T^51 - 
        792/2401*T^50 - 1423/2401*T^49 + 1233/2401*T^48 + 1075/2401*T^47 - 
        2700/2401*T^46 - 1761/2401*T^45 + 209/343*T^44 + 1541/2401*T^43 + 
        20/2401*T^42 - 978/2401*T^41 - 89/2401*T^40 + 221/2401*T^39 - 432/2401*T^38 
        - 156/2401*T^37 + 1842/2401*T^36 + 507/2401*T^35 - 902/2401*T^34 + 
        456/2401*T^33 + 656/2401*T^32 - 803/2401*T^31 - 1654/2401*T^30 + 
        339/2401*T^29 + 2316/2401*T^28 + 339/2401*T^27 - 1654/2401*T^26 - 
        803/2401*T^25 + 656/2401*T^24 + 456/2401*T^23 - 902/2401*T^22 + 
        507/2401*T^21 + 1842/2401*T^20 - 156/2401*T^19 - 432/2401*T^18 + 
        221/2401*T^17 - 89/2401*T^16 - 978/2401*T^15 + 20/2401*T^14 + 1541/2401*T^13
        + 209/343*T^12 - 1761/2401*T^11 - 2700/2401*T^10 + 1075/2401*T^9 + 
        1233/2401*T^8 - 1423/2401*T^7 - 792/2401*T^6 + 1443/2401*T^5 + 1747/2401*T^4
        - 100/343*T^3 - 53/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + X*Y^10 + 5*X*Y^9 + 
        4*X*Y^8 + 2*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 2*X + 
        6*Y^30 + Y^29 + 6*Y^27 + Y^26 + 4*Y^25 + 3*Y^24 + 5*Y^22 + Y^21 + 4*Y^20 + 
        4*Y^19 + 2*Y^17 + 6*Y^16 + Y^15 + 4*Y^14 + 6*Y^12 + 3*Y^11 + Y^10 + 4*Y^9 + 
        6*Y^7 + 6*Y^5 + 6*Y^4 + 2*Y^3 + 5*Y^2 + 5*Y + 4,
    -T^56 - 15/7*T^55 - 125/49*T^54 - 625/343*T^53 - 405/2401*T^52 + 1462/2401*T^51 
        + 1088/2401*T^50 - 1098/2401*T^49 - 486/343*T^48 - 2827/2401*T^47 + 
        1172/2401*T^46 + 6351/2401*T^45 + 9263/2401*T^44 + 997/343*T^43 + 
        1196/2401*T^42 - 3753/2401*T^41 - 4931/2401*T^40 - 989/2401*T^39 + 
        5094/2401*T^38 + 8996/2401*T^37 + 7965/2401*T^36 + 37/49*T^35 - 
        4283/2401*T^34 - 5310/2401*T^33 - 243/2401*T^32 + 7348/2401*T^31 + 
        11559/2401*T^30 + 8599/2401*T^29 - 8599/2401*T^27 - 11559/2401*T^26 - 
        7348/2401*T^25 + 243/2401*T^24 + 5310/2401*T^23 + 4283/2401*T^22 - 
        37/49*T^21 - 7965/2401*T^20 - 8996/2401*T^19 - 5094/2401*T^18 + 
        989/2401*T^17 + 4931/2401*T^16 + 3753/2401*T^15 - 1196/2401*T^14 - 
        997/343*T^13 - 9263/2401*T^12 - 6351/2401*T^11 - 1172/2401*T^10 + 
        2827/2401*T^9 + 486/343*T^8 + 1098/2401*T^7 - 1088/2401*T^6 - 1462/2401*T^5 
        + 405/2401*T^4 + 625/343*T^3 + 125/49*T^2 + 15/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 + 
        5*X*Y^7 + X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 5*X*Y + 4*X + 4*Y^30 + Y^29 + 5*Y^28 +
        Y^27 + Y^26 + Y^25 + 6*Y^24 + 4*Y^23 + 4*Y^22 + Y^21 + Y^20 + Y^19 + 2*Y^18 
        + Y^17 + 5*Y^16 + 2*Y^15 + 3*Y^13 + 2*Y^12 + 5*Y^11 + 4*Y^10 + 2*Y^9 + 3*Y^8
        + 3*Y^7 + 6*Y^5 + 3*Y^4 + 3*Y^3 + 5*Y^2 + 5*Y + 1,
    T^56 - 2/7*T^55 - 5/49*T^54 + 668/343*T^53 - 346/2401*T^52 + 415/2401*T^51 + 
        6078/2401*T^50 - 2060/2401*T^49 + 23/2401*T^48 + 6866/2401*T^47 - 
        2706/2401*T^46 - 2560/2401*T^45 + 4952/2401*T^44 - 517/343*T^43 - 
        3499/2401*T^42 + 3823/2401*T^41 - 4527/2401*T^40 - 5573/2401*T^39 + 
        3688/2401*T^38 - 47/49*T^37 - 766/343*T^36 + 2131/2401*T^35 - 1011/2401*T^34
        - 2990/2401*T^33 + 352/343*T^32 + 148/2401*T^31 - 1850/2401*T^30 + 
        804/2401*T^29 + 1745/2401*T^28 + 804/2401*T^27 - 1850/2401*T^26 + 
        148/2401*T^25 + 352/343*T^24 - 2990/2401*T^23 - 1011/2401*T^22 + 
        2131/2401*T^21 - 766/343*T^20 - 47/49*T^19 + 3688/2401*T^18 - 5573/2401*T^17
        - 4527/2401*T^16 + 3823/2401*T^15 - 3499/2401*T^14 - 517/343*T^13 + 
        4952/2401*T^12 - 2560/2401*T^11 - 2706/2401*T^10 + 6866/2401*T^9 + 
        23/2401*T^8 - 2060/2401*T^7 + 6078/2401*T^6 + 415/2401*T^5 - 346/2401*T^4 + 
        668/343*T^3 - 5/49*T^2 - 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^13 + 6*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + X*Y^8 + X*Y^7 + 
        3*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 6*X*Y + 3*Y^30 + 5*Y^29 + 4*Y^28 + 
        2*Y^27 + 2*Y^26 + 2*Y^25 + 5*Y^24 + 4*Y^23 + 5*Y^20 + 3*Y^19 + 6*Y^18 + 
        6*Y^17 + 5*Y^16 + 4*Y^15 + 2*Y^14 + Y^12 + 6*Y^11 + 3*Y^10 + Y^8 + Y^3 + 4*Y
        + 1,
    -T^56 + 1/7*T^55 + 22/49*T^54 + 260/343*T^53 + 1161/2401*T^52 - 1415/2401*T^51 -
        872/2401*T^50 - 1489/2401*T^49 + 1712/2401*T^48 + 493/2401*T^47 - 
        246/2401*T^46 - 810/2401*T^45 - 213/343*T^44 + 1574/2401*T^43 + 
        708/2401*T^42 + 857/2401*T^41 - 1153/2401*T^40 - 314/2401*T^39 + 
        747/2401*T^38 - 507/2401*T^37 + 160/2401*T^36 - 565/2401*T^35 + 37/2401*T^34
        + 417/2401*T^33 + 408/2401*T^32 + 100/343*T^31 - 80/343*T^30 - 472/2401*T^29
        + 472/2401*T^27 + 80/343*T^26 - 100/343*T^25 - 408/2401*T^24 - 417/2401*T^23
        - 37/2401*T^22 + 565/2401*T^21 - 160/2401*T^20 + 507/2401*T^19 - 
        747/2401*T^18 + 314/2401*T^17 + 1153/2401*T^16 - 857/2401*T^15 - 
        708/2401*T^14 - 1574/2401*T^13 + 213/343*T^12 + 810/2401*T^11 + 
        246/2401*T^10 - 493/2401*T^9 - 1712/2401*T^8 + 1489/2401*T^7 + 872/2401*T^6 
        + 1415/2401*T^5 - 1161/2401*T^4 - 260/343*T^3 - 22/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 4*X*Y^9 + 5*X*Y^8 +
        2*X*Y^6 + 6*X*Y^5 + 4*X*Y^3 + 4*X*Y^2 + X*Y + 6*X + 4*Y^30 + 4*Y^29 + 4*Y^28
        + 2*Y^27 + 4*Y^26 + 4*Y^24 + Y^23 + 2*Y^21 + 2*Y^20 + 6*Y^19 + 4*Y^18 + 
        4*Y^17 + 3*Y^16 + 3*Y^15 + 4*Y^14 + 6*Y^13 + 6*Y^12 + 2*Y^11 + 6*Y^10 + 
        6*Y^9 + Y^8 + Y^7 + 3*Y^6 + 2*Y^5 + 4*Y^3 + 5*Y^2 + Y + 4,
    -T^56 - 5/7*T^55 - 9/49*T^54 - 440/343*T^53 - 3085/2401*T^52 - 1665/2401*T^51 - 
        3000/2401*T^50 - 1821/2401*T^49 - 1355/2401*T^48 - 1971/2401*T^47 - 
        276/2401*T^46 - 673/2401*T^45 + 393/2401*T^44 + 52/343*T^43 - 1214/2401*T^42
        + 225/2401*T^41 + 124/2401*T^40 - 1592/2401*T^39 + 205/2401*T^38 - 
        459/2401*T^37 - 1150/2401*T^36 - 337/2401*T^35 - 502/2401*T^34 - 4/343*T^33 
        - 108/2401*T^32 - 374/2401*T^31 + 548/2401*T^30 + 176/2401*T^29 - 
        176/2401*T^27 - 548/2401*T^26 + 374/2401*T^25 + 108/2401*T^24 + 4/343*T^23 +
        502/2401*T^22 + 337/2401*T^21 + 1150/2401*T^20 + 459/2401*T^19 - 
        205/2401*T^18 + 1592/2401*T^17 - 124/2401*T^16 - 225/2401*T^15 + 
        1214/2401*T^14 - 52/343*T^13 - 393/2401*T^12 + 673/2401*T^11 + 276/2401*T^10
        + 1971/2401*T^9 + 1355/2401*T^8 + 1821/2401*T^7 + 3000/2401*T^6 + 
        1665/2401*T^5 + 3085/2401*T^4 + 440/343*T^3 + 9/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 2*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 4*X*Y^8 +
        5*X*Y^7 + 5*X*Y^6 + X*Y^5 + 3*X*Y^4 + 4*X*Y^2 + 2*X*Y + 2*X + 2*Y^30 + 
        6*Y^29 + 4*Y^28 + 6*Y^26 + Y^25 + 4*Y^24 + 6*Y^23 + 6*Y^22 + 5*Y^21 + 4*Y^20
        + 3*Y^19 + Y^18 + 4*Y^16 + 2*Y^15 + Y^14 + 5*Y^13 + 6*Y^12 + 2*Y^11 + 4*Y^10
        + 4*Y^9 + 6*Y^8 + Y^7 + 5*Y^6 + 3*Y^5 + 6*Y^4 + 3*Y^3 + 3*Y^2 + 2*Y + 6,
    -T^56 - 1/7*T^55 + 23/49*T^54 + 2/49*T^53 + 279/2401*T^52 + 506/2401*T^51 + 
        1097/2401*T^50 + 187/2401*T^49 + 221/2401*T^48 + 167/343*T^47 + 
        954/2401*T^46 - 970/2401*T^45 - 1480/2401*T^44 - 1903/2401*T^43 + 3/49*T^42 
        - 3/2401*T^41 - 590/2401*T^40 + 922/2401*T^39 + 263/2401*T^38 + 82/343*T^37 
        + 997/2401*T^36 + 139/343*T^35 + 677/2401*T^34 - 1028/2401*T^33 - 
        1796/2401*T^32 - 17/2401*T^31 - 313/2401*T^30 - 467/2401*T^29 + 
        467/2401*T^27 + 313/2401*T^26 + 17/2401*T^25 + 1796/2401*T^24 + 
        1028/2401*T^23 - 677/2401*T^22 - 139/343*T^21 - 997/2401*T^20 - 82/343*T^19 
        - 263/2401*T^18 - 922/2401*T^17 + 590/2401*T^16 + 3/2401*T^15 - 3/49*T^14 + 
        1903/2401*T^13 + 1480/2401*T^12 + 970/2401*T^11 - 954/2401*T^10 - 
        167/343*T^9 - 221/2401*T^8 - 187/2401*T^7 - 1097/2401*T^6 - 506/2401*T^5 - 
        279/2401*T^4 - 2/49*T^3 - 23/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + X*Y^12 + X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 
        4*X*Y^8 + 2*X*Y^6 + 3*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 3*X*Y + 5*Y^30 + Y^29 + 
        4*Y^28 + 6*Y^27 + 2*Y^26 + 5*Y^25 + 5*Y^24 + 2*Y^21 + 6*Y^19 + Y^18 + Y^17 +
        6*Y^16 + 3*Y^14 + Y^13 + 3*Y^12 + 3*Y^11 + 6*Y^10 + 4*Y^9 + 2*Y^7 + 5*Y^6 + 
        2*Y^4 + Y^3 + 4*Y^2 + 2*Y + 1,
    T^56 - 37/49*T^54 - 310/343*T^53 - 720/2401*T^52 + 165/343*T^51 + 964/2401*T^50 
        + 1686/2401*T^49 + 398/2401*T^48 - 239/2401*T^47 - 1425/2401*T^46 - 
        964/2401*T^45 + 102/2401*T^44 - 68/2401*T^43 + 278/2401*T^42 + 488/2401*T^41
        + 1307/2401*T^40 + 415/2401*T^39 - 422/2401*T^38 - 1346/2401*T^37 - 
        1794/2401*T^36 - 118/2401*T^35 + 1626/2401*T^34 + 1322/2401*T^33 + 
        20/2401*T^32 + 114/2401*T^31 + 18/343*T^30 - 785/2401*T^29 - 715/2401*T^28 -
        785/2401*T^27 + 18/343*T^26 + 114/2401*T^25 + 20/2401*T^24 + 1322/2401*T^23 
        + 1626/2401*T^22 - 118/2401*T^21 - 1794/2401*T^20 - 1346/2401*T^19 - 
        422/2401*T^18 + 415/2401*T^17 + 1307/2401*T^16 + 488/2401*T^15 + 
        278/2401*T^14 - 68/2401*T^13 + 102/2401*T^12 - 964/2401*T^11 - 
        1425/2401*T^10 - 239/2401*T^9 + 398/2401*T^8 + 1686/2401*T^7 + 964/2401*T^6 
        + 165/343*T^5 - 720/2401*T^4 - 310/343*T^3 - 37/49*T^2 + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 5*X*Y^13 + 3*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 + 
        2*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 6*X*Y + X + 6*Y^30 + 
        3*Y^29 + 4*Y^28 + Y^27 + 4*Y^26 + 2*Y^25 + Y^24 + 6*Y^23 + Y^22 + 6*Y^21 + 
        2*Y^20 + 6*Y^19 + 6*Y^18 + 4*Y^17 + 6*Y^16 + 2*Y^15 + 5*Y^14 + 4*Y^13 + 
        6*Y^12 + 3*Y^10 + 5*Y^9 + 6*Y^8 + 3*Y^7 + Y^6 + 3*Y^5 + 3*Y + 1,
    T^56 + 2*T^55 + 93/49*T^54 + 157/343*T^53 - 2677/2401*T^52 - 4572/2401*T^51 - 
        4050/2401*T^50 - 2265/2401*T^49 - 447/2401*T^48 - 579/2401*T^47 - 
        1109/2401*T^46 - 117/343*T^45 - 32/2401*T^44 + 80/343*T^43 + 1045/2401*T^42 
        + 1828/2401*T^41 + 460/343*T^40 + 3456/2401*T^39 + 1381/2401*T^38 - 
        2370/2401*T^37 - 768/343*T^36 - 5244/2401*T^35 - 2785/2401*T^34 + 
        622/2401*T^33 + 2228/2401*T^32 + 254/343*T^31 + 828/2401*T^30 + 
        1576/2401*T^29 + 1952/2401*T^28 + 1576/2401*T^27 + 828/2401*T^26 + 
        254/343*T^25 + 2228/2401*T^24 + 622/2401*T^23 - 2785/2401*T^22 - 
        5244/2401*T^21 - 768/343*T^20 - 2370/2401*T^19 + 1381/2401*T^18 + 
        3456/2401*T^17 + 460/343*T^16 + 1828/2401*T^15 + 1045/2401*T^14 + 
        80/343*T^13 - 32/2401*T^12 - 117/343*T^11 - 1109/2401*T^10 - 579/2401*T^9 - 
        447/2401*T^8 - 2265/2401*T^7 - 4050/2401*T^6 - 4572/2401*T^5 - 2677/2401*T^4
        + 157/343*T^3 + 93/49*T^2 + 2*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 
        + 4*X*Y^8 + X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + 3*X*Y^3 + 5*X*Y^2 + 2*X*Y + X + Y^30
        + 4*Y^29 + 4*Y^28 + 6*Y^27 + 4*Y^26 + 4*Y^25 + 3*Y^23 + 5*Y^22 + 5*Y^21 + 
        2*Y^20 + 3*Y^19 + 4*Y^18 + Y^17 + Y^16 + 4*Y^14 + 2*Y^13 + 6*Y^12 + 5*Y^10 +
        3*Y^9 + Y^8 + 6*Y^7 + Y^6 + 2*Y^5 + 3*Y^3 + 6*Y^2 + 2*Y + 1,
    T^56 + 9/7*T^55 + 53/49*T^54 + 78/343*T^53 - 2628/2401*T^52 - 2941/2401*T^51 - 
        486/343*T^50 - 264/343*T^49 - 407/2401*T^48 + 243/2401*T^47 + 1661/2401*T^46
        + 4/2401*T^45 - 890/2401*T^44 - 419/2401*T^43 + 68/2401*T^42 + 
        2062/2401*T^41 + 1074/2401*T^40 + 641/2401*T^39 - 367/2401*T^38 - 
        1961/2401*T^37 - 2327/2401*T^36 - 3175/2401*T^35 - 1404/2401*T^34 + 
        1956/2401*T^33 + 2985/2401*T^32 + 377/343*T^31 + 1117/2401*T^30 - 
        613/2401*T^29 - 498/2401*T^28 - 613/2401*T^27 + 1117/2401*T^26 + 
        377/343*T^25 + 2985/2401*T^24 + 1956/2401*T^23 - 1404/2401*T^22 - 
        3175/2401*T^21 - 2327/2401*T^20 - 1961/2401*T^19 - 367/2401*T^18 + 
        641/2401*T^17 + 1074/2401*T^16 + 2062/2401*T^15 + 68/2401*T^14 - 
        419/2401*T^13 - 890/2401*T^12 + 4/2401*T^11 + 1661/2401*T^10 + 243/2401*T^9 
        - 407/2401*T^8 - 264/343*T^7 - 486/343*T^6 - 2941/2401*T^5 - 2628/2401*T^4 +
        78/343*T^3 + 53/49*T^2 + 9/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + X*Y^10 + 2*X*Y^9 + 4*X*Y^8 + 
        5*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 5*X*Y^2 + 2*X*Y + 4*X + 3*Y^30 + 3*Y^29 + 
        6*Y^26 + 5*Y^25 + Y^24 + 3*Y^23 + Y^22 + 5*Y^21 + Y^20 + Y^19 + 3*Y^18 + 
        6*Y^17 + 3*Y^16 + 2*Y^15 + 5*Y^14 + 2*Y^13 + 6*Y^12 + 5*Y^11 + 5*Y^10 + 
        6*Y^9 + 6*Y^8 + 4*Y^7 + 2*Y^6 + 6*Y^5 + 2*Y^4 + 2*Y^3 + 4*Y^2 + Y,
    T^56 - 8/7*T^55 + 41/49*T^54 - 339/343*T^53 - 705/2401*T^52 + 384/2401*T^51 + 
        69/2401*T^50 + 324/343*T^49 - 320/2401*T^48 - 136/2401*T^47 - 1124/2401*T^46
        - 191/2401*T^45 - 1163/2401*T^44 + 976/2401*T^43 + 2253/2401*T^42 - 
        432/2401*T^41 + 4/343*T^40 - 149/2401*T^39 - 2344/2401*T^38 + 86/343*T^37 - 
        302/2401*T^36 + 185/343*T^35 + 1128/2401*T^34 - 171/343*T^33 - 102/343*T^32 
        - 479/2401*T^31 - 13/49*T^30 + 622/2401*T^29 + 1975/2401*T^28 + 
        622/2401*T^27 - 13/49*T^26 - 479/2401*T^25 - 102/343*T^24 - 171/343*T^23 + 
        1128/2401*T^22 + 185/343*T^21 - 302/2401*T^20 + 86/343*T^19 - 2344/2401*T^18
        - 149/2401*T^17 + 4/343*T^16 - 432/2401*T^15 + 2253/2401*T^14 + 
        976/2401*T^13 - 1163/2401*T^12 - 191/2401*T^11 - 1124/2401*T^10 - 
        136/2401*T^9 - 320/2401*T^8 + 324/343*T^7 + 69/2401*T^6 + 384/2401*T^5 - 
        705/2401*T^4 - 339/343*T^3 + 41/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 3*X*Y^11 + 3*X*Y^9 + 2*X*Y^8 + 5*X*Y^7 + 
        3*X*Y^5 + 5*X*Y^4 + 2*X*Y^2 + 2*X*Y + 6*X + 5*Y^30 + 4*Y^29 + 2*Y^28 + 
        3*Y^27 + 3*Y^26 + 6*Y^25 + 6*Y^24 + 5*Y^21 + 3*Y^20 + 4*Y^19 + 4*Y^18 + 
        2*Y^17 + Y^15 + 4*Y^14 + 2*Y^12 + 2*Y^11 + Y^10 + 2*Y^9 + Y^8 + 6*Y^6 + 
        2*Y^4 + 5*Y^3 + Y^2 + 6,
    -T^56 - 16/7*T^55 - 109/49*T^54 - 111/343*T^53 + 5722/2401*T^52 + 9104/2401*T^51
        + 7515/2401*T^50 + 2621/2401*T^49 - 218/343*T^48 - 4575/2401*T^47 - 
        5811/2401*T^46 - 4530/2401*T^45 - 564/2401*T^44 + 4709/2401*T^43 + 
        1130/343*T^42 + 7907/2401*T^41 + 523/343*T^40 - 1819/2401*T^39 - 
        6107/2401*T^38 - 150/49*T^37 - 6243/2401*T^36 - 4435/2401*T^35 - 
        1413/2401*T^34 + 1712/2401*T^33 + 3274/2401*T^32 + 1413/2401*T^31 - 
        1861/2401*T^30 - 3126/2401*T^29 + 3126/2401*T^27 + 1861/2401*T^26 - 
        1413/2401*T^25 - 3274/2401*T^24 - 1712/2401*T^23 + 1413/2401*T^22 + 
        4435/2401*T^21 + 6243/2401*T^20 + 150/49*T^19 + 6107/2401*T^18 + 
        1819/2401*T^17 - 523/343*T^16 - 7907/2401*T^15 - 1130/343*T^14 - 
        4709/2401*T^13 + 564/2401*T^12 + 4530/2401*T^11 + 5811/2401*T^10 + 
        4575/2401*T^9 + 218/343*T^8 - 2621/2401*T^7 - 7515/2401*T^6 - 9104/2401*T^5 
        - 5722/2401*T^4 + 111/343*T^3 + 109/49*T^2 + 16/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + X*Y^7 + 
        6*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 3*X*Y + 5*X + Y^30 + 
        4*Y^29 + 2*Y^27 + 5*Y^26 + 3*Y^25 + 2*Y^24 + 5*Y^21 + 3*Y^20 + 6*Y^19 + 
        5*Y^17 + 2*Y^16 + 5*Y^14 + 5*Y^13 + 4*Y^12 + 2*Y^11 + 4*Y^10 + 5*Y^9 + Y^6 +
        6*Y^5 + Y^4 + 3*Y^3 + 3*Y^2 + 1,
    T^56 + 38/49*T^54 + 46/343*T^53 + 325/343*T^52 + 1304/2401*T^51 + 514/2401*T^50 
        + 1436/2401*T^49 + 726/2401*T^48 + 1163/2401*T^47 - 193/2401*T^46 + 
        391/2401*T^45 + 269/2401*T^44 + 496/2401*T^43 - 299/2401*T^42 - 
        1380/2401*T^41 + 711/2401*T^40 - 340/343*T^39 + 37/343*T^38 - 2059/2401*T^37
        + 144/2401*T^36 - 2158/2401*T^35 - 208/343*T^34 - 136/343*T^33 - 36/343*T^32
        - 499/2401*T^31 - 1234/2401*T^30 + 188/2401*T^29 - 389/2401*T^28 + 
        188/2401*T^27 - 1234/2401*T^26 - 499/2401*T^25 - 36/343*T^24 - 136/343*T^23 
        - 208/343*T^22 - 2158/2401*T^21 + 144/2401*T^20 - 2059/2401*T^19 + 
        37/343*T^18 - 340/343*T^17 + 711/2401*T^16 - 1380/2401*T^15 - 299/2401*T^14 
        + 496/2401*T^13 + 269/2401*T^12 + 391/2401*T^11 - 193/2401*T^10 + 
        1163/2401*T^9 + 726/2401*T^8 + 1436/2401*T^7 + 514/2401*T^6 + 1304/2401*T^5 
        + 325/343*T^4 + 46/343*T^3 + 38/49*T^2 + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + X*Y^13 + 4*X*Y^10 + 4*X*Y^9 + 3*X*Y^7 + 3*X*Y^6 + 
        6*X*Y^5 + 2*X*Y^3 + 3*X*Y^2 + 3*X*Y + X + 4*Y^30 + 4*Y^28 + 2*Y^27 + 4*Y^26 
        + 3*Y^25 + Y^24 + 3*Y^23 + 3*Y^22 + Y^21 + 4*Y^20 + 5*Y^19 + 5*Y^18 + Y^17 +
        3*Y^16 + 3*Y^15 + 6*Y^14 + 3*Y^12 + 2*Y^11 + 6*Y^10 + 3*Y^9 + 5*Y^8 + 3*Y^7 
        + Y^6 + 3*Y^5 + 6*Y^4 + 2*Y^3 + 3*Y^2 + Y + 6,
    -T^56 - 12/7*T^55 - 74/49*T^54 - 404/343*T^53 - 1382/2401*T^52 + 327/2401*T^51 +
        3182/2401*T^50 + 4033/2401*T^49 + 4108/2401*T^48 + 4075/2401*T^47 + 
        2823/2401*T^46 + 1534/2401*T^45 - 605/2401*T^44 - 2522/2401*T^43 - 
        515/343*T^42 - 393/343*T^41 - 1037/2401*T^40 - 25/2401*T^39 + 1109/2401*T^38
        + 2185/2401*T^37 + 2186/2401*T^36 + 1091/2401*T^35 - 850/2401*T^34 - 
        2896/2401*T^33 - 608/343*T^32 - 5185/2401*T^31 - 4717/2401*T^30 - 
        3226/2401*T^29 + 3226/2401*T^27 + 4717/2401*T^26 + 5185/2401*T^25 + 
        608/343*T^24 + 2896/2401*T^23 + 850/2401*T^22 - 1091/2401*T^21 - 
        2186/2401*T^20 - 2185/2401*T^19 - 1109/2401*T^18 + 25/2401*T^17 + 
        1037/2401*T^16 + 393/343*T^15 + 515/343*T^14 + 2522/2401*T^13 + 
        605/2401*T^12 - 1534/2401*T^11 - 2823/2401*T^10 - 4075/2401*T^9 - 
        4108/2401*T^8 - 4033/2401*T^7 - 3182/2401*T^6 - 327/2401*T^5 + 1382/2401*T^4
        + 404/343*T^3 + 74/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 2*X*Y^13 + X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 2*X*Y^7 + 
        X*Y^5 + X*Y^3 + 3*X*Y^2 + 3*X*Y + 6*X + Y^30 + Y^29 + 4*Y^28 + 4*Y^27 + 
        6*Y^26 + 5*Y^25 + 4*Y^24 + 4*Y^23 + 6*Y^22 + 4*Y^21 + 5*Y^20 + 6*Y^18 + 
        2*Y^17 + 5*Y^16 + 5*Y^15 + 5*Y^14 + 5*Y^12 + 3*Y^9 + 4*Y^8 + 6*Y^7 + 2*Y^6 +
        3*Y^4 + 5*Y^3 + 6*Y^2 + 6*Y + 1,
    -T^56 + 9/7*T^55 - 104/49*T^54 + 638/343*T^53 - 4798/2401*T^52 + 4867/2401*T^51 
        - 4077/2401*T^50 + 2908/2401*T^49 - 2057/2401*T^48 + 1824/2401*T^47 - 
        3062/2401*T^46 + 3474/2401*T^45 - 3974/2401*T^44 + 660/343*T^43 - 
        3797/2401*T^42 + 4331/2401*T^41 - 1749/2401*T^40 + 191/343*T^39 + 
        1329/2401*T^38 - 1405/2401*T^37 + 2001/2401*T^36 - 592/2401*T^35 + 
        60/343*T^34 + 1797/2401*T^33 - 1857/2401*T^32 + 3363/2401*T^31 - 
        2111/2401*T^30 + 1332/2401*T^29 - 1332/2401*T^27 + 2111/2401*T^26 - 
        3363/2401*T^25 + 1857/2401*T^24 - 1797/2401*T^23 - 60/343*T^22 + 
        592/2401*T^21 - 2001/2401*T^20 + 1405/2401*T^19 - 1329/2401*T^18 - 
        191/343*T^17 + 1749/2401*T^16 - 4331/2401*T^15 + 3797/2401*T^14 - 
        660/343*T^13 + 3974/2401*T^12 - 3474/2401*T^11 + 3062/2401*T^10 - 
        1824/2401*T^9 + 2057/2401*T^8 - 2908/2401*T^7 + 4077/2401*T^6 - 
        4867/2401*T^5 + 4798/2401*T^4 - 638/343*T^3 + 104/49*T^2 - 9/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + X*Y^13 + X*Y^11 + X*Y^10 + X*Y^9 + 2*X*Y^8 + X*Y^7 + 5*X*Y^6 + 
        3*X*Y^4 + 6*X*Y^3 + X*Y^2 + 6*X*Y + X + 2*Y^30 + 2*Y^29 + 2*Y^28 + 3*Y^27 + 
        6*Y^26 + 5*Y^25 + 2*Y^21 + 3*Y^20 + 3*Y^19 + 6*Y^18 + 2*Y^17 + 5*Y^16 + 
        2*Y^15 + 3*Y^14 + 6*Y^13 + 5*Y^11 + 6*Y^10 + 3*Y^9 + 5*Y^8 + Y^7 + 5*Y^6 + 
        6*Y^5 + 3*Y^4 + Y^3 + 2*Y^2 + 3*Y,
    T^56 - 12/7*T^55 + 31/49*T^54 + 17/343*T^53 + 1487/2401*T^52 - 3072/2401*T^51 + 
        1539/2401*T^50 + 408/2401*T^49 + 1824/2401*T^48 - 3359/2401*T^47 + 
        1343/2401*T^46 + 1340/2401*T^45 - 1257/2401*T^44 - 827/2401*T^43 + 
        1264/2401*T^42 - 461/2401*T^41 - 71/343*T^40 + 57/343*T^39 + 636/2401*T^38 -
        1090/2401*T^37 + 1511/2401*T^36 - 1636/2401*T^35 + 2344/2401*T^34 - 
        1338/2401*T^33 - 1020/2401*T^32 - 115/2401*T^31 + 319/343*T^30 - 
        2467/2401*T^29 + 2452/2401*T^28 - 2467/2401*T^27 + 319/343*T^26 - 
        115/2401*T^25 - 1020/2401*T^24 - 1338/2401*T^23 + 2344/2401*T^22 - 
        1636/2401*T^21 + 1511/2401*T^20 - 1090/2401*T^19 + 636/2401*T^18 + 
        57/343*T^17 - 71/343*T^16 - 461/2401*T^15 + 1264/2401*T^14 - 827/2401*T^13 -
        1257/2401*T^12 + 1340/2401*T^11 + 1343/2401*T^10 - 3359/2401*T^9 + 
        1824/2401*T^8 + 408/2401*T^7 + 1539/2401*T^6 - 3072/2401*T^5 + 1487/2401*T^4
        + 17/343*T^3 + 31/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 
        5*X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 3*X*Y + 6*X + 
        4*Y^30 + 5*Y^29 + 2*Y^28 + 6*Y^27 + Y^25 + 5*Y^24 + 3*Y^23 + Y^21 + 4*Y^20 +
        Y^19 + 6*Y^18 + 4*Y^17 + 2*Y^15 + 5*Y^13 + 3*Y^12 + 3*Y^11 + Y^10 + 6*Y^9 + 
        Y^8 + 5*Y^7 + 4*Y^6 + 6*Y^5 + 6*Y^4 + 4*Y^3 + 6*Y^2 + Y + 5,
    -T^56 - 2/7*T^55 - 19/49*T^54 + 152/343*T^53 + 2914/2401*T^52 + 2019/2401*T^51 +
        2376/2401*T^50 - 2/7*T^49 - 1839/2401*T^48 - 3240/2401*T^47 - 2571/2401*T^46
        - 1215/2401*T^45 - 734/2401*T^44 + 1898/2401*T^43 + 1024/2401*T^42 + 
        2785/2401*T^41 + 1321/2401*T^40 + 278/2401*T^39 + 883/2401*T^38 - 
        332/343*T^37 - 533/2401*T^36 - 2160/2401*T^35 - 214/343*T^34 - 87/2401*T^33 
        + 82/2401*T^32 + 2543/2401*T^31 + 1528/2401*T^30 + 205/343*T^29 - 
        205/343*T^27 - 1528/2401*T^26 - 2543/2401*T^25 - 82/2401*T^24 + 87/2401*T^23
        + 214/343*T^22 + 2160/2401*T^21 + 533/2401*T^20 + 332/343*T^19 - 
        883/2401*T^18 - 278/2401*T^17 - 1321/2401*T^16 - 2785/2401*T^15 - 
        1024/2401*T^14 - 1898/2401*T^13 + 734/2401*T^12 + 1215/2401*T^11 + 
        2571/2401*T^10 + 3240/2401*T^9 + 1839/2401*T^8 + 2/7*T^7 - 2376/2401*T^6 - 
        2019/2401*T^5 - 2914/2401*T^4 - 152/343*T^3 + 19/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + X*Y^10 + 4*X*Y^9 + 
        2*X*Y^8 + 2*X*Y^7 + X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 2*X*Y^2 + 5*X*Y + X + 2*Y^30
        + 2*Y^29 + 6*Y^28 + 6*Y^27 + 5*Y^26 + Y^25 + 4*Y^24 + Y^23 + 5*Y^22 + 6*Y^21
        + Y^20 + 4*Y^19 + 2*Y^18 + 5*Y^17 + 4*Y^16 + Y^15 + Y^14 + 4*Y^13 + 3*Y^12 +
        6*Y^11 + 6*Y^10 + 3*Y^9 + 6*Y^8 + 4*Y^7 + 3*Y^6 + 3*Y^4 + 2*Y^3 + 4*Y^2 + 1,
    -T^56 + 1/7*T^55 + 10/7*T^54 - 503/343*T^53 - 1056/2401*T^52 + 4377/2401*T^51 - 
        3260/2401*T^50 - 2834/2401*T^49 + 368/343*T^48 - 440/2401*T^47 - 
        2269/2401*T^46 - 232/2401*T^45 + 1458/2401*T^44 - 3/2401*T^43 - 
        2419/2401*T^42 - 951/2401*T^41 + 1230/2401*T^40 - 996/2401*T^39 - 
        363/343*T^38 + 1207/2401*T^37 + 1348/2401*T^36 - 1775/2401*T^35 - 
        821/2401*T^34 - 5/2401*T^33 + 244/343*T^32 - 1485/2401*T^31 - 3488/2401*T^30
        + 4418/2401*T^29 - 4418/2401*T^27 + 3488/2401*T^26 + 1485/2401*T^25 - 
        244/343*T^24 + 5/2401*T^23 + 821/2401*T^22 + 1775/2401*T^21 - 1348/2401*T^20
        - 1207/2401*T^19 + 363/343*T^18 + 996/2401*T^17 - 1230/2401*T^16 + 
        951/2401*T^15 + 2419/2401*T^14 + 3/2401*T^13 - 1458/2401*T^12 + 
        232/2401*T^11 + 2269/2401*T^10 + 440/2401*T^9 - 368/343*T^8 + 2834/2401*T^7 
        + 3260/2401*T^6 - 4377/2401*T^5 + 1056/2401*T^4 + 503/343*T^3 - 10/7*T^2 - 
        1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^13 + 3*X*Y^12 + 5*X*Y^10 + 6*X*Y^9 + 2*X*Y^7 + 6*X*Y^6 + 
        3*X*Y^5 + 4*X*Y^3 + 5*X*Y^2 + 3*X*Y + 6*X + Y^30 + 3*Y^29 + 5*Y^28 + 4*Y^27 
        + 5*Y^26 + 3*Y^24 + 2*Y^23 + 5*Y^22 + 3*Y^21 + 6*Y^20 + 2*Y^19 + Y^18 + 
        6*Y^16 + 4*Y^15 + 3*Y^14 + 3*Y^13 + 2*Y^12 + Y^11 + Y^9 + 5*Y^8 + 5*Y^7 + 
        2*Y^6 + 5*Y^5 + 6*Y^3 + 6*Y^2 + 4*Y + 5,
    T^56 - 3/7*T^55 + 20/49*T^54 - 120/343*T^53 + 436/2401*T^52 + 457/2401*T^51 + 
        200/2401*T^50 - 520/2401*T^49 - 33/2401*T^48 + 568/2401*T^47 - 485/2401*T^46
        - 12/343*T^45 + 508/2401*T^44 - 369/2401*T^43 + 92/343*T^42 - 445/2401*T^41 
        - 299/2401*T^40 - 66/2401*T^39 + 258/2401*T^38 - 690/2401*T^37 - 
        592/2401*T^36 + 628/2401*T^35 - 1063/2401*T^34 + 832/2401*T^33 - 31/343*T^32
        - 668/2401*T^31 - 624/2401*T^30 + 1060/2401*T^29 - 935/2401*T^28 + 
        1060/2401*T^27 - 624/2401*T^26 - 668/2401*T^25 - 31/343*T^24 + 832/2401*T^23
        - 1063/2401*T^22 + 628/2401*T^21 - 592/2401*T^20 - 690/2401*T^19 + 
        258/2401*T^18 - 66/2401*T^17 - 299/2401*T^16 - 445/2401*T^15 + 92/343*T^14 -
        369/2401*T^13 + 508/2401*T^12 - 12/343*T^11 - 485/2401*T^10 + 568/2401*T^9 -
        33/2401*T^8 - 520/2401*T^7 + 200/2401*T^6 + 457/2401*T^5 + 436/2401*T^4 - 
        120/343*T^3 + 20/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + X*Y^10 + 4*X*Y^9 + X*Y^7 + 
        6*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 3*X*Y + X + 6*Y^30 + 4*Y^28 + 4*Y^27
        + Y^26 + 3*Y^24 + 2*Y^23 + 5*Y^22 + 2*Y^21 + Y^20 + 2*Y^19 + 5*Y^18 + Y^17 +
        3*Y^16 + 3*Y^15 + 6*Y^14 + 5*Y^13 + 2*Y^12 + 6*Y^11 + 2*Y^10 + 5*Y^9 + 2*Y^8
        + 6*Y^7 + 3*Y^6 + 4*Y^5 + 2*Y^4 + 4*Y^3 + 4*Y^2 + 4*Y + 1,
    -T^56 - 3/7*T^55 + 3/49*T^54 + 263/343*T^53 + 3215/2401*T^52 - 73/2401*T^51 - 
        983/2401*T^50 - 2001/2401*T^49 - 759/2401*T^48 + 146/2401*T^47 - 4/343*T^46 
        + 1612/2401*T^45 + 1010/2401*T^44 + 226/343*T^43 - 274/2401*T^42 - 
        2372/2401*T^41 - 562/2401*T^40 + 31/2401*T^39 + 242/343*T^38 + 
        2182/2401*T^37 - 409/2401*T^36 - 1280/2401*T^35 - 3072/2401*T^34 - 
        2750/2401*T^33 - 78/2401*T^32 + 1279/2401*T^31 + 4591/2401*T^30 + 
        2181/2401*T^29 - 2181/2401*T^27 - 4591/2401*T^26 - 1279/2401*T^25 + 
        78/2401*T^24 + 2750/2401*T^23 + 3072/2401*T^22 + 1280/2401*T^21 + 
        409/2401*T^20 - 2182/2401*T^19 - 242/343*T^18 - 31/2401*T^17 + 562/2401*T^16
        + 2372/2401*T^15 + 274/2401*T^14 - 226/343*T^13 - 1010/2401*T^12 - 
        1612/2401*T^11 + 4/343*T^10 - 146/2401*T^9 + 759/2401*T^8 + 2001/2401*T^7 + 
        983/2401*T^6 + 73/2401*T^5 - 3215/2401*T^4 - 263/343*T^3 - 3/49*T^2 + 3/7*T 
        + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + X*Y^10 + 4*X*Y^8 + 2*X*Y^7 + 
        X*Y^6 + X*Y^5 + 2*X*Y^4 + 4*X*Y + 5*X + 2*Y^30 + 5*Y^29 + 4*Y^27 + 3*Y^26 + 
        6*Y^24 + 4*Y^22 + 2*Y^21 + 5*Y^20 + 6*Y^19 + 2*Y^18 + 6*Y^17 + 4*Y^16 + 
        4*Y^15 + 6*Y^14 + 2*Y^13 + 5*Y^12 + 5*Y^11 + Y^9 + 4*Y^8 + 5*Y^7 + 6*Y^5 + 
        4*Y^4 + Y^3 + Y^2 + 6*Y + 2,
    T^56 + 3/7*T^55 - 2/7*T^54 - 249/343*T^53 - 194/343*T^52 + 8/2401*T^51 + 
        1207/2401*T^50 + 940/2401*T^49 + 673/2401*T^48 - 1000/2401*T^47 - 
        1690/2401*T^46 + 260/2401*T^45 - 380/2401*T^44 - 142/2401*T^43 - 
        314/2401*T^42 - 6/2401*T^41 + 254/2401*T^40 + 310/2401*T^39 + 5/343*T^38 + 
        850/2401*T^37 - 814/2401*T^36 - 1415/2401*T^35 - 486/2401*T^34 + 
        404/2401*T^33 + 1452/2401*T^32 + 1342/2401*T^31 + 1280/2401*T^30 - 
        1404/2401*T^29 - 1978/2401*T^28 - 1404/2401*T^27 + 1280/2401*T^26 + 
        1342/2401*T^25 + 1452/2401*T^24 + 404/2401*T^23 - 486/2401*T^22 - 
        1415/2401*T^21 - 814/2401*T^20 + 850/2401*T^19 + 5/343*T^18 + 310/2401*T^17 
        + 254/2401*T^16 - 6/2401*T^15 - 314/2401*T^14 - 142/2401*T^13 - 
        380/2401*T^12 + 260/2401*T^11 - 1690/2401*T^10 - 1000/2401*T^9 + 
        673/2401*T^8 + 940/2401*T^7 + 1207/2401*T^6 + 8/2401*T^5 - 194/343*T^4 - 
        249/343*T^3 - 2/7*T^2 + 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 4*X*Y^9 + 3*X*Y^7 + 
        5*X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 6*X*Y + X + 3*Y^30 + 
        5*Y^29 + 5*Y^27 + 3*Y^26 + 2*Y^25 + Y^24 + 3*Y^23 + Y^21 + 5*Y^19 + 6*Y^18 +
        3*Y^17 + Y^16 + 4*Y^15 + Y^14 + 3*Y^13 + 2*Y^12 + 2*Y^11 + Y^10 + 5*Y^9 + 
        Y^7 + 5*Y^6 + 2*Y^5 + 6*Y^4 + 4*Y^3 + 6*Y^2 + 2*Y + 6,
    T^56 - 2*T^55 + 138/49*T^54 - 951/343*T^53 + 643/343*T^52 - 1986/2401*T^51 + 
        1219/2401*T^50 - 659/2401*T^49 - 276/2401*T^48 + 1842/2401*T^47 - 
        4136/2401*T^46 + 3837/2401*T^45 - 2545/2401*T^44 + 2046/2401*T^43 - 
        461/343*T^42 + 6219/2401*T^41 - 8783/2401*T^40 + 9104/2401*T^39 - 
        7218/2401*T^38 + 751/343*T^37 - 471/343*T^36 + 1443/2401*T^35 + 
        1296/2401*T^34 - 4474/2401*T^33 + 7157/2401*T^32 - 7244/2401*T^31 + 
        6056/2401*T^30 - 4036/2401*T^29 + 3209/2401*T^28 - 4036/2401*T^27 + 
        6056/2401*T^26 - 7244/2401*T^25 + 7157/2401*T^24 - 4474/2401*T^23 + 
        1296/2401*T^22 + 1443/2401*T^21 - 471/343*T^20 + 751/343*T^19 - 
        7218/2401*T^18 + 9104/2401*T^17 - 8783/2401*T^16 + 6219/2401*T^15 - 
        461/343*T^14 + 2046/2401*T^13 - 2545/2401*T^12 + 3837/2401*T^11 - 
        4136/2401*T^10 + 1842/2401*T^9 - 276/2401*T^8 - 659/2401*T^7 + 1219/2401*T^6
        - 1986/2401*T^5 + 643/343*T^4 - 951/343*T^3 + 138/49*T^2 - 2*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 3*X*Y^13 + 4*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 3*X*Y^8 + 
        X*Y^7 + X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 3*X*Y^2 + 6*X*Y + X + 4*Y^30 + 5*Y^29 + 
        5*Y^28 + 4*Y^27 + 5*Y^26 + 4*Y^25 + 2*Y^24 + 3*Y^22 + Y^21 + 3*Y^20 + 2*Y^19
        + 2*Y^18 + 5*Y^17 + Y^16 + 5*Y^15 + 3*Y^14 + 2*Y^13 + 2*Y^12 + Y^11 + 2*Y^10
        + 3*Y^8 + 6*Y^7 + 5*Y^5 + 4*Y^4 + 3*Y^2 + Y + 4,
    T^56 + 3/7*T^55 + 3/7*T^54 - 1/343*T^53 + 39/2401*T^52 - 716/2401*T^51 - 
        450/2401*T^50 - 862/2401*T^49 - 220/2401*T^48 - 46/2401*T^47 - 332/2401*T^46
        + 545/2401*T^45 + 489/2401*T^44 + 2652/2401*T^43 + 922/2401*T^42 + 
        1250/2401*T^41 - 508/2401*T^40 - 64/343*T^39 - 1234/2401*T^38 - 
        114/2401*T^37 - 488/2401*T^36 + 213/2401*T^35 + 491/2401*T^34 + 
        502/2401*T^33 + 936/2401*T^32 - 73/2401*T^31 + 699/2401*T^30 - 25/2401*T^29 
        + 148/343*T^28 - 25/2401*T^27 + 699/2401*T^26 - 73/2401*T^25 + 936/2401*T^24
        + 502/2401*T^23 + 491/2401*T^22 + 213/2401*T^21 - 488/2401*T^20 - 
        114/2401*T^19 - 1234/2401*T^18 - 64/343*T^17 - 508/2401*T^16 + 
        1250/2401*T^15 + 922/2401*T^14 + 2652/2401*T^13 + 489/2401*T^12 + 
        545/2401*T^11 - 332/2401*T^10 - 46/2401*T^9 - 220/2401*T^8 - 862/2401*T^7 - 
        450/2401*T^6 - 716/2401*T^5 + 39/2401*T^4 - 1/343*T^3 + 3/7*T^2 + 3/7*T + 1
*], [*
    X^3 + 6*X*Y^13 + X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 2*X*Y^8 + 5*X*Y^7 + 
        X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 2*X*Y + 6*X + Y^30 + 5*Y^29 
        + Y^28 + 3*Y^27 + Y^26 + 5*Y^25 + 4*Y^24 + 3*Y^23 + 3*Y^22 + 5*Y^21 + Y^20 +
        5*Y^19 + 6*Y^18 + 5*Y^17 + 4*Y^16 + 4*Y^15 + 6*Y^14 + 5*Y^13 + 4*Y^12 + 
        4*Y^11 + Y^10 + 3*Y^9 + 6*Y^7 + 4*Y^6 + 4*Y^5 + 3*Y^2 + Y,
    T^56 - 5/7*T^55 + 24/49*T^54 + 170/343*T^53 - 2333/2401*T^52 + 306/343*T^51 - 
        212/343*T^50 - 1391/2401*T^49 + 767/2401*T^48 - 661/2401*T^47 - 
        1065/2401*T^46 + 617/2401*T^45 - 87/343*T^44 - 1216/2401*T^43 + 
        1415/2401*T^42 + 530/2401*T^41 - 1439/2401*T^40 + 1664/2401*T^39 + 
        241/2401*T^38 - 1565/2401*T^37 + 1143/2401*T^36 + 244/2401*T^35 - 
        2343/2401*T^34 + 2222/2401*T^33 - 859/2401*T^32 - 249/2401*T^31 + 
        1929/2401*T^30 - 271/343*T^29 + 2434/2401*T^28 - 271/343*T^27 + 
        1929/2401*T^26 - 249/2401*T^25 - 859/2401*T^24 + 2222/2401*T^23 - 
        2343/2401*T^22 + 244/2401*T^21 + 1143/2401*T^20 - 1565/2401*T^19 + 
        241/2401*T^18 + 1664/2401*T^17 - 1439/2401*T^16 + 530/2401*T^15 + 
        1415/2401*T^14 - 1216/2401*T^13 - 87/343*T^12 + 617/2401*T^11 - 
        1065/2401*T^10 - 661/2401*T^9 + 767/2401*T^8 - 1391/2401*T^7 - 212/343*T^6 +
        306/343*T^5 - 2333/2401*T^4 + 170/343*T^3 + 24/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 5*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + X*Y^8 + 
        5*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + 2*X*Y^3 + 6*X*Y^2 + 5*X*Y + 2*Y^30 + 4*Y^29 + 
        Y^28 + 4*Y^27 + Y^26 + 2*Y^25 + 2*Y^24 + Y^23 + 3*Y^22 + 3*Y^21 + 4*Y^20 + 
        2*Y^19 + 3*Y^18 + 6*Y^17 + 4*Y^16 + Y^15 + 5*Y^14 + 5*Y^13 + 3*Y^12 + Y^11 +
        2*Y^9 + 3*Y^8 + 2*Y^7 + 3*Y^6 + Y^5 + Y^4 + Y^3 + Y^2 + 5*Y + 2,
    T^56 + 2/7*T^55 - 69/49*T^54 - 111/343*T^53 + 1378/2401*T^52 + 892/2401*T^51 - 
        807/2401*T^50 - 1503/2401*T^49 + 1263/2401*T^48 + 1053/2401*T^47 - 
        199/343*T^46 + 76/2401*T^45 - 347/2401*T^44 - 1366/2401*T^43 + 158/343*T^42 
        + 1842/2401*T^41 - 405/2401*T^40 - 48/49*T^39 - 12/2401*T^38 + 424/343*T^37 
        + 255/2401*T^36 - 1851/2401*T^35 + 75/2401*T^34 + 1114/2401*T^33 - 
        193/2401*T^32 - 1185/2401*T^31 + 471/2401*T^30 + 402/2401*T^29 - 
        820/2401*T^28 + 402/2401*T^27 + 471/2401*T^26 - 1185/2401*T^25 - 
        193/2401*T^24 + 1114/2401*T^23 + 75/2401*T^22 - 1851/2401*T^21 + 
        255/2401*T^20 + 424/343*T^19 - 12/2401*T^18 - 48/49*T^17 - 405/2401*T^16 + 
        1842/2401*T^15 + 158/343*T^14 - 1366/2401*T^13 - 347/2401*T^12 + 
        76/2401*T^11 - 199/343*T^10 + 1053/2401*T^9 + 1263/2401*T^8 - 1503/2401*T^7 
        - 807/2401*T^6 + 892/2401*T^5 + 1378/2401*T^4 - 111/343*T^3 - 69/49*T^2 + 
        2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 3*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 3*X*Y^8 +
        6*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + X*Y^4 + 2*X*Y^2 + X*Y + 5*X + 2*Y^30 + 4*Y^29 
        + 4*Y^28 + 6*Y^27 + 3*Y^26 + 6*Y^25 + 4*Y^24 + 6*Y^23 + 3*Y^22 + 5*Y^21 + 
        6*Y^20 + 2*Y^19 + 2*Y^18 + 5*Y^16 + 6*Y^15 + 3*Y^14 + 4*Y^13 + 4*Y^12 + 
        3*Y^11 + 4*Y^10 + Y^9 + 6*Y^7 + Y^6 + 5*Y^5 + 3*Y^4 + 4*Y^3 + 2*Y^2 + 5*Y,
    -T^56 - 2/7*T^55 + 27/49*T^54 + 104/343*T^53 + 496/2401*T^52 + 1284/2401*T^51 - 
        1058/2401*T^50 - 1394/2401*T^49 + 188/343*T^48 + 419/2401*T^47 + 
        114/343*T^46 + 131/343*T^45 - 886/2401*T^44 - 744/2401*T^43 + 611/2401*T^42 
        + 440/2401*T^41 + 109/2401*T^40 + 680/2401*T^39 - 439/2401*T^38 + 
        110/2401*T^37 - 328/2401*T^36 - 2031/2401*T^35 + 449/2401*T^34 + 
        283/2401*T^33 - 978/2401*T^32 - 128/2401*T^31 + 1354/2401*T^30 - 
        1665/2401*T^29 + 1665/2401*T^27 - 1354/2401*T^26 + 128/2401*T^25 + 
        978/2401*T^24 - 283/2401*T^23 - 449/2401*T^22 + 2031/2401*T^21 + 
        328/2401*T^20 - 110/2401*T^19 + 439/2401*T^18 - 680/2401*T^17 - 
        109/2401*T^16 - 440/2401*T^15 - 611/2401*T^14 + 744/2401*T^13 + 
        886/2401*T^12 - 131/343*T^11 - 114/343*T^10 - 419/2401*T^9 - 188/343*T^8 + 
        1394/2401*T^7 + 1058/2401*T^6 - 1284/2401*T^5 - 496/2401*T^4 - 104/343*T^3 -
        27/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 5*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 3*X*Y + 
        3*X + 2*Y^30 + Y^29 + 4*Y^28 + 3*Y^27 + 2*Y^26 + 5*Y^25 + Y^24 + 4*Y^23 + 
        4*Y^22 + 4*Y^21 + 4*Y^20 + 3*Y^19 + Y^18 + 4*Y^17 + 4*Y^16 + 2*Y^15 + Y^14 +
        6*Y^12 + 4*Y^10 + 3*Y^9 + 3*Y^8 + 2*Y^7 + 5*Y^6 + 6*Y^4 + 3*Y^3 + 3*Y^2 + Y 
        + 3,
    T^56 + 3/7*T^55 + 5/49*T^54 + 128/343*T^53 + 130/2401*T^52 + 212/343*T^51 + 
        109/343*T^50 - 242/2401*T^49 + 44/343*T^48 + 1494/2401*T^47 - 485/2401*T^46 
        + 233/2401*T^45 - 24/343*T^44 - 249/2401*T^43 + 398/2401*T^42 - 50/343*T^41 
        - 1115/2401*T^40 - 405/2401*T^39 + 501/2401*T^38 - 716/2401*T^37 + 
        552/2401*T^36 - 1489/2401*T^35 - 908/2401*T^34 - 167/2401*T^33 - 
        132/343*T^32 - 100/343*T^31 - 26/49*T^30 - 110/343*T^29 - 748/2401*T^28 - 
        110/343*T^27 - 26/49*T^26 - 100/343*T^25 - 132/343*T^24 - 167/2401*T^23 - 
        908/2401*T^22 - 1489/2401*T^21 + 552/2401*T^20 - 716/2401*T^19 + 
        501/2401*T^18 - 405/2401*T^17 - 1115/2401*T^16 - 50/343*T^15 + 398/2401*T^14
        - 249/2401*T^13 - 24/343*T^12 + 233/2401*T^11 - 485/2401*T^10 + 
        1494/2401*T^9 + 44/343*T^8 - 242/2401*T^7 + 109/343*T^6 + 212/343*T^5 + 
        130/2401*T^4 + 128/343*T^3 + 5/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 +
        4*X*Y^7 + 4*X*Y^6 + X*Y^5 + X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 6*X*Y + X + 4*Y^30 +
        3*Y^29 + 2*Y^28 + Y^27 + 3*Y^26 + Y^25 + 5*Y^24 + 5*Y^23 + 2*Y^22 + 6*Y^21 +
        3*Y^20 + 2*Y^18 + 6*Y^17 + 4*Y^16 + 6*Y^15 + 2*Y^14 + 6*Y^13 + 2*Y^12 + 
        6*Y^11 + Y^9 + 6*Y^8 + 2*Y^7 + 4*Y^6 + 3*Y^5 + 6*Y^4 + 6*Y^3 + 2*Y^2 + 5*Y +
        6,
    -T^56 + 4/7*T^55 - 17/49*T^54 + 33/343*T^53 + 695/2401*T^52 - 488/2401*T^51 + 
        2238/2401*T^50 - 734/2401*T^49 + 558/2401*T^48 + 1208/2401*T^47 - 
        236/343*T^46 + 1/343*T^45 + 468/2401*T^44 - 1578/2401*T^43 + 1263/2401*T^42 
        - 879/2401*T^41 - 2/2401*T^40 + 218/343*T^39 - 213/343*T^38 + 169/343*T^37 -
        290/2401*T^36 - 1594/2401*T^35 + 1983/2401*T^34 - 1814/2401*T^33 + 
        536/2401*T^32 + 96/2401*T^31 - 912/2401*T^30 + 496/2401*T^29 - 496/2401*T^27
        + 912/2401*T^26 - 96/2401*T^25 - 536/2401*T^24 + 1814/2401*T^23 - 
        1983/2401*T^22 + 1594/2401*T^21 + 290/2401*T^20 - 169/343*T^19 + 
        213/343*T^18 - 218/343*T^17 + 2/2401*T^16 + 879/2401*T^15 - 1263/2401*T^14 +
        1578/2401*T^13 - 468/2401*T^12 - 1/343*T^11 + 236/343*T^10 - 1208/2401*T^9 -
        558/2401*T^8 + 734/2401*T^7 - 2238/2401*T^6 + 488/2401*T^5 - 695/2401*T^4 - 
        33/343*T^3 + 17/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + X*Y^10 + 3*X*Y^9 + 3*X*Y^8 + 
        4*X*Y^7 + 6*X*Y^6 + X*Y^4 + X*Y + 2*X + 2*Y^30 + 6*Y^29 + 4*Y^27 + 2*Y^26 + 
        3*Y^25 + 3*Y^24 + 3*Y^23 + 6*Y^22 + Y^21 + 3*Y^19 + 3*Y^18 + 2*Y^17 + 2*Y^16
        + 5*Y^14 + 3*Y^13 + 4*Y^12 + 3*Y^11 + Y^10 + Y^5 + 6*Y^4 + 6*Y^3 + 3*Y^2 + 
        6*Y + 3,
    T^56 - 9/7*T^55 + 20/49*T^54 + 257/343*T^53 - 516/343*T^52 + 3156/2401*T^51 - 
        334/2401*T^50 - 2558/2401*T^49 + 426/343*T^48 - 2054/2401*T^47 + 48/343*T^46
        + 215/343*T^45 - 3435/2401*T^44 + 1593/2401*T^43 + 1552/2401*T^42 - 
        1828/2401*T^41 + 384/2401*T^40 + 124/2401*T^39 - 463/2401*T^38 - 
        281/2401*T^37 + 725/2401*T^36 + 124/2401*T^35 - 18/49*T^34 + 192/343*T^33 - 
        5/7*T^32 + 344/343*T^31 - 869/2401*T^30 - 2293/2401*T^29 + 85/49*T^28 - 
        2293/2401*T^27 - 869/2401*T^26 + 344/343*T^25 - 5/7*T^24 + 192/343*T^23 - 
        18/49*T^22 + 124/2401*T^21 + 725/2401*T^20 - 281/2401*T^19 - 463/2401*T^18 +
        124/2401*T^17 + 384/2401*T^16 - 1828/2401*T^15 + 1552/2401*T^14 + 
        1593/2401*T^13 - 3435/2401*T^12 + 215/343*T^11 + 48/343*T^10 - 2054/2401*T^9
        + 426/343*T^8 - 2558/2401*T^7 - 334/2401*T^6 + 3156/2401*T^5 - 516/343*T^4 +
        257/343*T^3 + 20/49*T^2 - 9/7*T + 1
*], [*
    X^3 + X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + X*Y^8 + 
        2*X*Y^7 + 4*X*Y^6 + X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 5*X*Y + 6*X + 5*Y^30 + 
        6*Y^29 + 6*Y^28 + Y^27 + 3*Y^26 + 3*Y^23 + 5*Y^21 + Y^20 + 3*Y^19 + 6*Y^17 +
        6*Y^16 + 6*Y^15 + 6*Y^14 + 5*Y^13 + 5*Y^12 + 4*Y^11 + 5*Y^10 + 4*Y^9 + 4*Y^8
        + 3*Y^7 + 5*Y^6 + 3*Y^4 + 2*Y^3 + 5*Y^2 + 2*Y,
    -T^56 - 12/7*T^55 - 11/7*T^54 - 691/343*T^53 - 5221/2401*T^52 - 473/343*T^51 - 
        2313/2401*T^50 + 534/2401*T^49 + 4409/2401*T^48 + 643/343*T^47 + 
        6112/2401*T^46 + 7226/2401*T^45 + 4831/2401*T^44 + 4323/2401*T^43 + 
        3419/2401*T^42 - 447/2401*T^41 - 1357/2401*T^40 - 1767/2401*T^39 - 
        3525/2401*T^38 - 2805/2401*T^37 - 2859/2401*T^36 - 3735/2401*T^35 - 
        2190/2401*T^34 - 1348/2401*T^33 - 2022/2401*T^32 - 1019/2401*T^31 - 
        624/2401*T^30 - 180/343*T^29 + 180/343*T^27 + 624/2401*T^26 + 1019/2401*T^25
        + 2022/2401*T^24 + 1348/2401*T^23 + 2190/2401*T^22 + 3735/2401*T^21 + 
        2859/2401*T^20 + 2805/2401*T^19 + 3525/2401*T^18 + 1767/2401*T^17 + 
        1357/2401*T^16 + 447/2401*T^15 - 3419/2401*T^14 - 4323/2401*T^13 - 
        4831/2401*T^12 - 7226/2401*T^11 - 6112/2401*T^10 - 643/343*T^9 - 
        4409/2401*T^8 - 534/2401*T^7 + 2313/2401*T^6 + 473/343*T^5 + 5221/2401*T^4 +
        691/343*T^3 + 11/7*T^2 + 12/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 3*X*Y^8 +
        6*X*Y^7 + 4*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 2*X*Y + 2*Y^30 + Y^29 + 
        4*Y^27 + Y^26 + Y^24 + 4*Y^23 + Y^22 + 5*Y^21 + 4*Y^20 + 6*Y^19 + 3*Y^18 + 
        Y^17 + 4*Y^16 + Y^15 + 2*Y^14 + Y^13 + 3*Y^10 + 5*Y^9 + 3*Y^8 + Y^7 + Y^5 + 
        3*Y^4 + 6*Y^3 + 6*Y + 6,
    -T^56 - 9/7*T^55 + 11/49*T^54 + T^53 + 498/2401*T^52 - 620/2401*T^51 + 
        1809/2401*T^50 + 500/343*T^49 + 1210/2401*T^48 - 628/2401*T^47 + 
        285/2401*T^46 + 220/343*T^45 + 153/343*T^44 - 2207/2401*T^43 - 
        4274/2401*T^42 - 316/343*T^41 + 302/2401*T^40 - 1587/2401*T^39 - 
        4857/2401*T^38 - 1168/2401*T^37 + 4719/2401*T^36 + 463/343*T^35 - 
        1074/2401*T^34 - 93/343*T^33 + 4220/2401*T^32 + 4801/2401*T^31 + 
        344/2401*T^30 - 1543/2401*T^29 + 1543/2401*T^27 - 344/2401*T^26 - 
        4801/2401*T^25 - 4220/2401*T^24 + 93/343*T^23 + 1074/2401*T^22 - 
        463/343*T^21 - 4719/2401*T^20 + 1168/2401*T^19 + 4857/2401*T^18 + 
        1587/2401*T^17 - 302/2401*T^16 + 316/343*T^15 + 4274/2401*T^14 + 
        2207/2401*T^13 - 153/343*T^12 - 220/343*T^11 - 285/2401*T^10 + 628/2401*T^9 
        - 1210/2401*T^8 - 500/343*T^7 - 1809/2401*T^6 + 620/2401*T^5 - 498/2401*T^4 
        - T^3 - 11/49*T^2 + 9/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 4*X*Y^7 + 
        4*X*Y^6 + 2*X*Y^5 + X*Y^4 + 4*X*Y^2 + 5*X*Y + 6*X + 2*Y^30 + 4*Y^29 + 2*Y^28
        + 2*Y^27 + 2*Y^26 + 3*Y^25 + 3*Y^24 + 4*Y^23 + 5*Y^20 + 3*Y^19 + 4*Y^18 + 
        5*Y^17 + 3*Y^15 + Y^14 + Y^13 + 5*Y^12 + 4*Y^11 + 2*Y^10 + 6*Y^8 + 2*Y^7 + 
        2*Y^6 + 2*Y^5 + 2*Y^4 + 2*Y^3 + Y^2 + 2*Y + 3,
    T^56 - 78/49*T^54 + 162/343*T^53 + 533/343*T^52 - 492/2401*T^51 - 4342/2401*T^50
        - 405/2401*T^49 + 6488/2401*T^48 + 1035/2401*T^47 - 6821/2401*T^46 - 
        103/2401*T^45 + 6472/2401*T^44 + 39/343*T^43 - 6226/2401*T^42 - 223/343*T^41
        + 6417/2401*T^40 + 2211/2401*T^39 - 6392/2401*T^38 - 2048/2401*T^37 + 
        5815/2401*T^36 + 1810/2401*T^35 - 5720/2401*T^34 - 2173/2401*T^33 + 
        6075/2401*T^32 + 993/2401*T^31 - 6201/2401*T^30 - 32/343*T^29 + 
        5375/2401*T^28 - 32/343*T^27 - 6201/2401*T^26 + 993/2401*T^25 + 
        6075/2401*T^24 - 2173/2401*T^23 - 5720/2401*T^22 + 1810/2401*T^21 + 
        5815/2401*T^20 - 2048/2401*T^19 - 6392/2401*T^18 + 2211/2401*T^17 + 
        6417/2401*T^16 - 223/343*T^15 - 6226/2401*T^14 + 39/343*T^13 + 
        6472/2401*T^12 - 103/2401*T^11 - 6821/2401*T^10 + 1035/2401*T^9 + 
        6488/2401*T^8 - 405/2401*T^7 - 4342/2401*T^6 - 492/2401*T^5 + 533/343*T^4 + 
        162/343*T^3 - 78/49*T^2 + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + X*Y^13 + 4*X*Y^12 + 3*X*Y^10 + 5*X*Y^9 + 5*X*Y^8 + 
        6*X*Y^6 + 5*X*Y^5 + X*Y^3 + 6*X*Y^2 + 5*X*Y + 6*X + 6*Y^30 + Y^27 + 5*Y^26 +
        3*Y^25 + 2*Y^24 + 4*Y^23 + 4*Y^22 + Y^21 + 5*Y^19 + 5*Y^18 + 6*Y^17 + 2*Y^16
        + 5*Y^15 + 4*Y^14 + Y^12 + 4*Y^11 + 6*Y^10 + 6*Y^9 + 3*Y^8 + 2*Y^7 + 5*Y^6 +
        6*Y^5 + 3*Y^4 + 3*Y^3 + Y,
    -T^56 - 10/7*T^55 - 5/7*T^54 - 143/343*T^53 - 1298/2401*T^52 - 832/2401*T^51 - 
        1/2401*T^50 + 530/2401*T^49 + 2/7*T^48 - 285/2401*T^47 - 174/2401*T^46 - 
        1/2401*T^45 - 159/2401*T^44 - 292/2401*T^43 - 1210/2401*T^42 - 
        1816/2401*T^41 - 1062/2401*T^40 - 985/2401*T^39 - 1531/2401*T^38 - 
        458/2401*T^37 + 176/2401*T^36 + 30/343*T^35 + 117/343*T^34 + 1503/2401*T^33 
        + 1700/2401*T^32 + 1030/2401*T^31 + 933/2401*T^30 + 1010/2401*T^29 - 
        1010/2401*T^27 - 933/2401*T^26 - 1030/2401*T^25 - 1700/2401*T^24 - 
        1503/2401*T^23 - 117/343*T^22 - 30/343*T^21 - 176/2401*T^20 + 458/2401*T^19 
        + 1531/2401*T^18 + 985/2401*T^17 + 1062/2401*T^16 + 1816/2401*T^15 + 
        1210/2401*T^14 + 292/2401*T^13 + 159/2401*T^12 + 1/2401*T^11 + 174/2401*T^10
        + 285/2401*T^9 - 2/7*T^8 - 530/2401*T^7 + 1/2401*T^6 + 832/2401*T^5 + 
        1298/2401*T^4 + 143/343*T^3 + 5/7*T^2 + 10/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^13 + 6*X*Y^12 + X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 2*X*Y^6 + 
        3*X*Y^5 + X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + X*Y + 5*X + Y^30 + 4*Y^28 + 3*Y^27 + 
        5*Y^25 + 4*Y^24 + 5*Y^23 + Y^22 + 5*Y^21 + 6*Y^20 + 2*Y^19 + 2*Y^18 + 5*Y^17
        + 4*Y^15 + 2*Y^14 + 3*Y^13 + 4*Y^12 + 6*Y^10 + 2*Y^9 + 6*Y^7 + 2*Y^4 + 5*Y^2
        + 6*Y + 2,
    T^56 - 2/7*T^55 - 17/49*T^54 + 141/343*T^53 + 855/2401*T^52 - 806/2401*T^51 - 
        389/2401*T^50 + 4/343*T^49 - 524/2401*T^48 - 176/2401*T^47 - 138/2401*T^46 +
        752/2401*T^45 - 375/2401*T^44 - 1217/2401*T^43 - 19/2401*T^42 + 
        391/2401*T^41 - 1107/2401*T^40 - 597/2401*T^39 - 972/2401*T^38 + 
        688/2401*T^37 - 268/2401*T^36 - 432/2401*T^35 + 1440/2401*T^34 + 
        1191/2401*T^33 - 114/343*T^32 - 12/343*T^31 + 1453/2401*T^30 - 8/343*T^29 - 
        166/343*T^28 - 8/343*T^27 + 1453/2401*T^26 - 12/343*T^25 - 114/343*T^24 + 
        1191/2401*T^23 + 1440/2401*T^22 - 432/2401*T^21 - 268/2401*T^20 + 
        688/2401*T^19 - 972/2401*T^18 - 597/2401*T^17 - 1107/2401*T^16 + 
        391/2401*T^15 - 19/2401*T^14 - 1217/2401*T^13 - 375/2401*T^12 + 
        752/2401*T^11 - 138/2401*T^10 - 176/2401*T^9 - 524/2401*T^8 + 4/343*T^7 - 
        389/2401*T^6 - 806/2401*T^5 + 855/2401*T^4 + 141/343*T^3 - 17/49*T^2 - 2/7*T
        + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 6*X*Y^8 + 5*X*Y^7 +
        5*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + X*Y^3 + 2*X*Y^2 + 3*X*Y + 5*X + 2*Y^30 + 
        4*Y^29 + 3*Y^28 + 2*Y^27 + 4*Y^26 + 4*Y^25 + 2*Y^24 + 4*Y^22 + Y^21 + 4*Y^20
        + 2*Y^19 + 4*Y^18 + 2*Y^17 + 4*Y^16 + Y^14 + 5*Y^13 + 5*Y^12 + 2*Y^11 + 
        3*Y^10 + 3*Y^9 + 2*Y^5 + 5*Y^4 + 3*Y^3 + 3*Y^2 + 2*Y,
    -T^56 + 5/7*T^55 + 44/49*T^54 - 209/343*T^53 + 1153/2401*T^52 - 1926/2401*T^51 -
        129/2401*T^50 + 2452/2401*T^49 - 947/2401*T^48 + 604/2401*T^47 - 
        921/2401*T^46 - 1685/2401*T^45 + 1644/2401*T^44 + 598/2401*T^43 - 
        356/2401*T^42 - 675/2401*T^41 - 727/2401*T^40 - 591/2401*T^39 + 209/343*T^38
        + 90/2401*T^37 - 838/2401*T^36 + 250/343*T^35 - 2407/2401*T^34 + 
        471/2401*T^33 + 2078/2401*T^32 - 1245/2401*T^31 + 1700/2401*T^30 - 
        246/343*T^29 + 246/343*T^27 - 1700/2401*T^26 + 1245/2401*T^25 - 
        2078/2401*T^24 - 471/2401*T^23 + 2407/2401*T^22 - 250/343*T^21 + 
        838/2401*T^20 - 90/2401*T^19 - 209/343*T^18 + 591/2401*T^17 + 727/2401*T^16 
        + 675/2401*T^15 + 356/2401*T^14 - 598/2401*T^13 - 1644/2401*T^12 + 
        1685/2401*T^11 + 921/2401*T^10 - 604/2401*T^9 + 947/2401*T^8 - 2452/2401*T^7
        + 129/2401*T^6 + 1926/2401*T^5 - 1153/2401*T^4 + 209/343*T^3 - 44/49*T^2 - 
        5/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + X*Y^10 + X*Y^9 + 
        X*Y^8 + X*Y^7 + 6*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + X*Y^3 + X*Y^2 + 5*X*Y + 2*X + 
        5*Y^30 + 2*Y^29 + 6*Y^28 + Y^27 + Y^26 + 4*Y^25 + 6*Y^24 + 3*Y^23 + 3*Y^22 +
        5*Y^19 + 2*Y^18 + 3*Y^16 + Y^15 + 2*Y^14 + Y^13 + 5*Y^12 + 2*Y^11 + 2*Y^10 +
        2*Y^9 + 4*Y^8 + 4*Y^6 + 4*Y^4 + 2*Y^3 + 3*Y,
    -T^56 - 12/7*T^55 - 54/49*T^54 + 195/343*T^53 + 4120/2401*T^52 + 3397/2401*T^51 
        - 170/2401*T^50 - 2911/2401*T^49 - 3873/2401*T^48 - 2468/2401*T^47 + 
        433/2401*T^46 + 1356/2401*T^45 - 979/2401*T^44 - 386/343*T^43 - 
        765/2401*T^42 + 1565/2401*T^41 + 1654/2401*T^40 - 324/2401*T^39 - 
        2031/2401*T^38 - 1686/2401*T^37 - 145/343*T^36 - 621/2401*T^35 - 67/343*T^34
        - 153/343*T^33 - 1290/2401*T^32 + 866/2401*T^31 + 3568/2401*T^30 + 
        3552/2401*T^29 - 3552/2401*T^27 - 3568/2401*T^26 - 866/2401*T^25 + 
        1290/2401*T^24 + 153/343*T^23 + 67/343*T^22 + 621/2401*T^21 + 145/343*T^20 +
        1686/2401*T^19 + 2031/2401*T^18 + 324/2401*T^17 - 1654/2401*T^16 - 
        1565/2401*T^15 + 765/2401*T^14 + 386/343*T^13 + 979/2401*T^12 - 
        1356/2401*T^11 - 433/2401*T^10 + 2468/2401*T^9 + 3873/2401*T^8 + 
        2911/2401*T^7 + 170/2401*T^6 - 3397/2401*T^5 - 4120/2401*T^4 - 195/343*T^3 +
        54/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 
        + 6*X*Y^8 + 6*X*Y^7 + X*Y^6 + 5*X*Y^5 + 3*X*Y^3 + 2*X*Y^2 + 3*X*Y + 5*X + 
        3*Y^30 + 6*Y^29 + 3*Y^28 + Y^26 + 6*Y^24 + 4*Y^23 + 3*Y^22 + Y^20 + 2*Y^19 +
        Y^18 + 6*Y^17 + Y^16 + 2*Y^15 + Y^14 + 3*Y^13 + 3*Y^12 + 5*Y^11 + 2*Y^10 + 
        4*Y^9 + 5*Y^8 + 4*Y^7 + 6*Y^6 + 4*Y^5 + 3*Y^4 + 4*Y^3 + 6*Y^2 + 6*Y + 2,
    T^56 + 1/7*T^55 - 55/49*T^54 - 237/343*T^53 + 380/2401*T^52 + 2155/2401*T^51 + 
        841/2401*T^50 - 2074/2401*T^49 + 414/2401*T^48 + 1763/2401*T^47 - 
        33/2401*T^46 + 76/2401*T^45 - 1275/2401*T^44 - 1663/2401*T^43 + 
        663/2401*T^42 + 1723/2401*T^41 + 2102/2401*T^40 - 257/343*T^39 - 
        4154/2401*T^38 - 2/2401*T^37 + 4166/2401*T^36 + 2553/2401*T^35 - 
        2060/2401*T^34 - 3681/2401*T^33 + 74/2401*T^32 + 39/49*T^31 + 1406/2401*T^30
        - 90/343*T^29 - 2203/2401*T^28 - 90/343*T^27 + 1406/2401*T^26 + 39/49*T^25 +
        74/2401*T^24 - 3681/2401*T^23 - 2060/2401*T^22 + 2553/2401*T^21 + 
        4166/2401*T^20 - 2/2401*T^19 - 4154/2401*T^18 - 257/343*T^17 + 
        2102/2401*T^16 + 1723/2401*T^15 + 663/2401*T^14 - 1663/2401*T^13 - 
        1275/2401*T^12 + 76/2401*T^11 - 33/2401*T^10 + 1763/2401*T^9 + 414/2401*T^8 
        - 2074/2401*T^7 + 841/2401*T^6 + 2155/2401*T^5 + 380/2401*T^4 - 237/343*T^3 
        - 55/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + X*Y^10 + 6*X*Y^9 + X*Y^8 + 
        5*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 5*X*Y + 5*X + Y^30 + 
        4*Y^29 + 3*Y^27 + 5*Y^26 + Y^25 + 3*Y^24 + 3*Y^23 + 6*Y^22 + 3*Y^21 + 5*Y^20
        + Y^19 + 4*Y^18 + 4*Y^17 + 5*Y^16 + Y^15 + 6*Y^14 + 4*Y^13 + 6*Y^12 + 6*Y^10
        + 5*Y^9 + 6*Y^7 + 4*Y^6 + 3*Y^5 + 5*Y^4 + 6*Y^3 + 2*Y^2 + 5*Y + 5,
    -T^56 + 2/7*T^55 + 64/49*T^54 + 135/343*T^53 - 2403/2401*T^52 - 2942/2401*T^51 +
        219/343*T^50 + 2060/2401*T^49 - 242/2401*T^48 - 691/2401*T^47 - 59/343*T^46 
        + 482/2401*T^45 - 1157/2401*T^44 + 457/2401*T^43 + 1375/2401*T^42 - 
        631/2401*T^41 - 36/49*T^40 + 529/2401*T^39 + 1809/2401*T^38 + 233/2401*T^37 
        - 1712/2401*T^36 - 797/2401*T^35 + 1389/2401*T^34 + 50/343*T^33 - 
        596/2401*T^32 + 367/2401*T^31 - 211/2401*T^30 - 593/2401*T^29 + 
        593/2401*T^27 + 211/2401*T^26 - 367/2401*T^25 + 596/2401*T^24 - 50/343*T^23 
        - 1389/2401*T^22 + 797/2401*T^21 + 1712/2401*T^20 - 233/2401*T^19 - 
        1809/2401*T^18 - 529/2401*T^17 + 36/49*T^16 + 631/2401*T^15 - 1375/2401*T^14
        - 457/2401*T^13 + 1157/2401*T^12 - 482/2401*T^11 + 59/343*T^10 + 
        691/2401*T^9 + 242/2401*T^8 - 2060/2401*T^7 - 219/343*T^6 + 2942/2401*T^5 + 
        2403/2401*T^4 - 135/343*T^3 - 64/49*T^2 - 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        2*X*Y^8 + 2*X*Y^7 + 2*X*Y^5 + 5*X*Y^3 + X*Y^2 + X*Y + 5*X + 6*Y^30 + 2*Y^29 
        + 6*Y^28 + Y^27 + 2*Y^26 + Y^25 + 5*Y^23 + 6*Y^22 + 5*Y^21 + 5*Y^20 + 4*Y^19
        + 5*Y^18 + 4*Y^17 + 6*Y^16 + 5*Y^15 + 5*Y^14 + 4*Y^13 + 6*Y^12 + 5*Y^11 + 
        5*Y^10 + 2*Y^7 + 6*Y^6 + 4*Y^5 + 5*Y^4 + 2*Y^3 + 5*Y^2 + 6,
    T^56 + 12/7*T^55 + 73/49*T^54 + 236/343*T^53 - 1093/2401*T^52 - 1982/2401*T^51 -
        2021/2401*T^50 - 116/343*T^49 + 1251/2401*T^48 + 200/343*T^47 + 
        319/2401*T^46 - 2094/2401*T^45 - 530/343*T^44 - 2778/2401*T^43 - 
        73/2401*T^42 + 2220/2401*T^41 + 2944/2401*T^40 + 3170/2401*T^39 + 
        1549/2401*T^38 - 538/2401*T^37 - 1581/2401*T^36 - 345/2401*T^35 + 
        173/343*T^34 + 1319/2401*T^33 + 341/343*T^32 + 225/343*T^31 - 149/2401*T^30 
        - 251/343*T^29 - 3291/2401*T^28 - 251/343*T^27 - 149/2401*T^26 + 
        225/343*T^25 + 341/343*T^24 + 1319/2401*T^23 + 173/343*T^22 - 345/2401*T^21 
        - 1581/2401*T^20 - 538/2401*T^19 + 1549/2401*T^18 + 3170/2401*T^17 + 
        2944/2401*T^16 + 2220/2401*T^15 - 73/2401*T^14 - 2778/2401*T^13 - 
        530/343*T^12 - 2094/2401*T^11 + 319/2401*T^10 + 200/343*T^9 + 1251/2401*T^8 
        - 116/343*T^7 - 2021/2401*T^6 - 1982/2401*T^5 - 1093/2401*T^4 + 236/343*T^3 
        + 73/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 2*X*Y^13 + X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 2*X*Y^8 + 
        5*X*Y^7 + 5*X*Y^6 + 4*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 4*X*Y + 5*X + 4*Y^30 + 
        3*Y^29 + Y^28 + 2*Y^27 + Y^26 + 2*Y^25 + 2*Y^24 + 3*Y^23 + 6*Y^22 + 3*Y^21 +
        2*Y^20 + 6*Y^19 + 5*Y^18 + 4*Y^16 + 6*Y^15 + Y^14 + 3*Y^13 + 3*Y^12 + 2*Y^11
        + 5*Y^10 + 6*Y^8 + Y^7 + 4*Y^6 + 4*Y^5 + 2*Y^4 + 5*Y^3 + 2*Y^2 + 6*Y,
    -T^56 + 5/7*T^54 - 152/343*T^53 - 111/343*T^52 + 2307/2401*T^51 - 1167/2401*T^50
        - 562/2401*T^49 + 1151/2401*T^48 + 484/2401*T^47 - 192/343*T^46 - 
        58/2401*T^45 - 18/343*T^44 + 611/2401*T^43 + 298/2401*T^42 - 533/2401*T^41 -
        792/2401*T^40 + 1587/2401*T^39 + 8/2401*T^38 - 54/343*T^37 + 604/2401*T^36 -
        43/343*T^35 - 1422/2401*T^34 + 137/2401*T^33 + 131/2401*T^32 + 187/2401*T^31
        + 34/2401*T^30 - 346/2401*T^29 + 346/2401*T^27 - 34/2401*T^26 - 
        187/2401*T^25 - 131/2401*T^24 - 137/2401*T^23 + 1422/2401*T^22 + 43/343*T^21
        - 604/2401*T^20 + 54/343*T^19 - 8/2401*T^18 - 1587/2401*T^17 + 792/2401*T^16
        + 533/2401*T^15 - 298/2401*T^14 - 611/2401*T^13 + 18/343*T^12 + 58/2401*T^11
        + 192/343*T^10 - 484/2401*T^9 - 1151/2401*T^8 + 562/2401*T^7 + 1167/2401*T^6
        - 2307/2401*T^5 + 111/343*T^4 + 152/343*T^3 - 5/7*T^2 + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 2*X*Y^13 + X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 
        3*X*Y^8 + 3*X*Y^7 + 6*X*Y^4 + X*Y^3 + 6*X*Y^2 + 4*X*Y + 5*X + 6*Y^30 + 
        4*Y^29 + 2*Y^28 + Y^27 + 5*Y^26 + 3*Y^25 + 6*Y^24 + 4*Y^23 + 4*Y^22 + 4*Y^21
        + Y^20 + Y^18 + 4*Y^17 + 6*Y^16 + Y^15 + 4*Y^13 + 2*Y^12 + 3*Y^10 + 6*Y^8 + 
        Y^6 + Y^4 + 4*Y^3 + 2*Y + 4,
    T^56 + 12/7*T^55 + 64/49*T^54 - 37/49*T^53 - 641/343*T^52 - 2378/2401*T^51 + 
        698/2401*T^50 + 30/2401*T^49 - 3233/2401*T^48 - 2341/2401*T^47 + 
        293/343*T^46 + 3629/2401*T^45 + 565/2401*T^44 - 1103/2401*T^43 + 
        1578/2401*T^42 + 4471/2401*T^41 + 2091/2401*T^40 - 185/343*T^39 - 
        1860/2401*T^38 + 6/343*T^37 - 921/2401*T^36 - 81/49*T^35 - 3531/2401*T^34 + 
        291/2401*T^33 + 3172/2401*T^32 + 2059/2401*T^31 + 60/343*T^30 + 
        762/2401*T^29 + 1242/2401*T^28 + 762/2401*T^27 + 60/343*T^26 + 
        2059/2401*T^25 + 3172/2401*T^24 + 291/2401*T^23 - 3531/2401*T^22 - 
        81/49*T^21 - 921/2401*T^20 + 6/343*T^19 - 1860/2401*T^18 - 185/343*T^17 + 
        2091/2401*T^16 + 4471/2401*T^15 + 1578/2401*T^14 - 1103/2401*T^13 + 
        565/2401*T^12 + 3629/2401*T^11 + 293/343*T^10 - 2341/2401*T^9 - 
        3233/2401*T^8 + 30/2401*T^7 + 698/2401*T^6 - 2378/2401*T^5 - 641/343*T^4 - 
        37/49*T^3 + 64/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 
        + 2*X*Y^8 + 5*X*Y^7 + X*Y^6 + X*Y^5 + X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + X*Y + 2*X 
        + 6*Y^30 + 5*Y^29 + 5*Y^28 + 5*Y^27 + 2*Y^26 + 3*Y^23 + Y^22 + 3*Y^19 + 
        4*Y^18 + 3*Y^17 + 2*Y^16 + 3*Y^15 + 2*Y^14 + Y^13 + 6*Y^12 + 3*Y^11 + 3*Y^10
        + 2*Y^9 + 5*Y^8 + 3*Y^7 + Y^6 + 6*Y^5 + 4*Y^3 + 4*Y^2 + Y,
    T^56 + 2/7*T^55 - 6/7*T^54 - 319/343*T^53 + 2092/2401*T^52 + 2160/2401*T^51 - 
        408/2401*T^50 - 2127/2401*T^49 - 1101/2401*T^48 + 274/343*T^47 + 
        1937/2401*T^46 - 976/2401*T^45 - 2700/2401*T^44 - 374/2401*T^43 + 
        1132/2401*T^42 + 1384/2401*T^41 - 743/2401*T^40 - 286/343*T^39 - 
        821/2401*T^38 + 1885/2401*T^37 + 1045/2401*T^36 - 74/343*T^35 - 
        1331/2401*T^34 - 687/2401*T^33 + 516/2401*T^32 + 1574/2401*T^31 + 
        876/2401*T^30 - 242/2401*T^29 - 454/2401*T^28 - 242/2401*T^27 + 
        876/2401*T^26 + 1574/2401*T^25 + 516/2401*T^24 - 687/2401*T^23 - 
        1331/2401*T^22 - 74/343*T^21 + 1045/2401*T^20 + 1885/2401*T^19 - 
        821/2401*T^18 - 286/343*T^17 - 743/2401*T^16 + 1384/2401*T^15 + 
        1132/2401*T^14 - 374/2401*T^13 - 2700/2401*T^12 - 976/2401*T^11 + 
        1937/2401*T^10 + 274/343*T^9 - 1101/2401*T^8 - 2127/2401*T^7 - 408/2401*T^6 
        + 2160/2401*T^5 + 2092/2401*T^4 - 319/343*T^3 - 6/7*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + X*Y^12 + X*Y^11 + X*Y^10 + 6*X*Y^9 + 
        3*X*Y^8 + 3*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + X*Y^3 + 5*X*Y + 5*Y^30 + 
        2*Y^29 + 2*Y^27 + Y^26 + 5*Y^24 + 3*Y^22 + 2*Y^21 + 2*Y^20 + 5*Y^19 + 4*Y^18
        + 5*Y^17 + 5*Y^16 + Y^14 + 5*Y^13 + Y^11 + 6*Y^10 + 2*Y^9 + 3*Y^8 + 3*Y^7 + 
        5*Y^6 + 3*Y^5 + Y^4 + 3*Y^3 + 5*Y^2 + 5*Y + 1,
    -T^56 + T^55 + 8/49*T^54 + 34/343*T^53 - 2099/2401*T^52 + 1378/2401*T^51 + 
        94/2401*T^50 + 444/2401*T^49 - 1516/2401*T^48 + 1012/2401*T^47 + 
        243/2401*T^46 - 1042/2401*T^45 + 236/2401*T^44 - 31/2401*T^43 + 
        1940/2401*T^42 - 1978/2401*T^41 + 282/2401*T^40 - 1325/2401*T^39 + 
        2309/2401*T^38 - 86/343*T^37 - 802/2401*T^36 - 356/2401*T^35 + 
        1252/2401*T^34 - 757/2401*T^33 - 30/2401*T^32 + 813/2401*T^31 - 69/2401*T^30
        - 1212/2401*T^29 + 1212/2401*T^27 + 69/2401*T^26 - 813/2401*T^25 + 
        30/2401*T^24 + 757/2401*T^23 - 1252/2401*T^22 + 356/2401*T^21 + 
        802/2401*T^20 + 86/343*T^19 - 2309/2401*T^18 + 1325/2401*T^17 - 
        282/2401*T^16 + 1978/2401*T^15 - 1940/2401*T^14 + 31/2401*T^13 - 
        236/2401*T^12 + 1042/2401*T^11 - 243/2401*T^10 - 1012/2401*T^9 + 
        1516/2401*T^8 - 444/2401*T^7 - 94/2401*T^6 - 1378/2401*T^5 + 2099/2401*T^4 -
        34/343*T^3 - 8/49*T^2 - T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 
        5*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 4*X*Y + 2*X + 
        Y^30 + 2*Y^29 + 4*Y^28 + 4*Y^27 + 3*Y^26 + 3*Y^25 + 2*Y^24 + Y^23 + 4*Y^22 +
        4*Y^21 + 2*Y^20 + 5*Y^19 + 4*Y^18 + 2*Y^16 + 5*Y^15 + 4*Y^14 + 5*Y^13 + 
        4*Y^12 + 6*Y^11 + 5*Y^10 + 5*Y^9 + Y^8 + 4*Y^7 + 3*Y^5 + 3*Y^4 + 6*Y^3 + 
        4*Y^2 + 4*Y + 3,
    -T^56 + 2/7*T^55 + 60/49*T^54 + 146/343*T^53 - 194/343*T^52 - 1289/2401*T^51 - 
        598/2401*T^50 - 275/343*T^49 + 149/343*T^48 + 3945/2401*T^47 + 
        1475/2401*T^46 - 3446/2401*T^45 - 2105/2401*T^44 + 1507/2401*T^43 + 
        1108/2401*T^42 - 173/343*T^41 + 681/2401*T^40 + 778/2401*T^39 - 
        880/2401*T^38 - 794/2401*T^37 + 1289/2401*T^36 + 460/2401*T^35 - 
        215/343*T^34 - 313/2401*T^33 + 1266/2401*T^32 + 324/2401*T^31 - 
        941/2401*T^30 - 402/2401*T^29 + 402/2401*T^27 + 941/2401*T^26 - 
        324/2401*T^25 - 1266/2401*T^24 + 313/2401*T^23 + 215/343*T^22 - 
        460/2401*T^21 - 1289/2401*T^20 + 794/2401*T^19 + 880/2401*T^18 - 
        778/2401*T^17 - 681/2401*T^16 + 173/343*T^15 - 1108/2401*T^14 - 
        1507/2401*T^13 + 2105/2401*T^12 + 3446/2401*T^11 - 1475/2401*T^10 - 
        3945/2401*T^9 - 149/343*T^8 + 275/343*T^7 + 598/2401*T^6 + 1289/2401*T^5 + 
        194/343*T^4 - 146/343*T^3 - 60/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + X*Y^11 + 3*X*Y^9 + 5*X*Y^8 + 
        4*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 3*X*Y^2 + 6*X*Y + 6*X + 3*Y^30 + 
        5*Y^29 + 6*Y^27 + 4*Y^26 + 2*Y^25 + 6*Y^24 + 5*Y^23 + Y^22 + Y^20 + 4*Y^19 +
        5*Y^18 + 6*Y^17 + 2*Y^16 + Y^15 + 2*Y^13 + 6*Y^10 + Y^9 + Y^8 + 4*Y^6 + 
        5*Y^5 + 3*Y^4 + 3*Y^3 + 3*Y^2 + 6*Y + 2,
    T^56 - 3/7*T^55 - 1/7*T^54 + 29/49*T^53 - 89/343*T^52 - 421/343*T^51 + 
        246/2401*T^50 + 248/343*T^49 - 2397/2401*T^48 + 1461/2401*T^47 + 
        713/2401*T^46 - 62/2401*T^45 + 339/2401*T^44 + 104/343*T^43 - 803/2401*T^42 
        + 13/343*T^41 + 1559/2401*T^40 - 2728/2401*T^39 + 313/2401*T^38 + 
        872/2401*T^37 - 109/2401*T^36 - 421/2401*T^35 + 1118/2401*T^34 - 
        78/2401*T^33 - 694/2401*T^32 + 109/2401*T^31 - 648/2401*T^30 + 271/2401*T^29
        + 304/2401*T^28 + 271/2401*T^27 - 648/2401*T^26 + 109/2401*T^25 - 
        694/2401*T^24 - 78/2401*T^23 + 1118/2401*T^22 - 421/2401*T^21 - 
        109/2401*T^20 + 872/2401*T^19 + 313/2401*T^18 - 2728/2401*T^17 + 
        1559/2401*T^16 + 13/343*T^15 - 803/2401*T^14 + 104/343*T^13 + 339/2401*T^12 
        - 62/2401*T^11 + 713/2401*T^10 + 1461/2401*T^9 - 2397/2401*T^8 + 248/343*T^7
        + 246/2401*T^6 - 421/343*T^5 - 89/343*T^4 + 29/49*T^3 - 1/7*T^2 - 3/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 3*X*Y^8 + 4*X*Y^7 +
        6*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 5*X*Y + 6*X + 3*Y^30 + 
        2*Y^29 + 2*Y^28 + 5*Y^27 + 4*Y^26 + 3*Y^23 + 4*Y^22 + 6*Y^20 + 2*Y^19 + 
        3*Y^18 + 3*Y^17 + 2*Y^16 + 3*Y^15 + 6*Y^14 + Y^13 + 3*Y^12 + 5*Y^11 + 3*Y^9 
        + Y^8 + 2*Y^7 + 5*Y^6 + 5*Y + 6,
    -T^56 + 5/7*T^55 - 16/49*T^54 - 132/343*T^53 + 928/2401*T^52 - 4119/2401*T^51 + 
        2598/2401*T^50 - 1020/2401*T^49 - 908/2401*T^48 + 926/2401*T^47 - 
        2638/2401*T^46 + 241/343*T^45 - 324/2401*T^44 - 146/2401*T^43 - 
        905/2401*T^42 + 474/2401*T^41 + 171/2401*T^40 - 4/2401*T^39 + 1203/2401*T^38
        - 1985/2401*T^37 + 1906/2401*T^36 - 162/343*T^35 + 1373/2401*T^34 + 
        912/2401*T^33 - 2526/2401*T^32 + 3062/2401*T^31 - 2595/2401*T^30 + 
        2248/2401*T^29 - 2248/2401*T^27 + 2595/2401*T^26 - 3062/2401*T^25 + 
        2526/2401*T^24 - 912/2401*T^23 - 1373/2401*T^22 + 162/343*T^21 - 
        1906/2401*T^20 + 1985/2401*T^19 - 1203/2401*T^18 + 4/2401*T^17 - 
        171/2401*T^16 - 474/2401*T^15 + 905/2401*T^14 + 146/2401*T^13 + 
        324/2401*T^12 - 241/343*T^11 + 2638/2401*T^10 - 926/2401*T^9 + 908/2401*T^8 
        + 1020/2401*T^7 - 2598/2401*T^6 + 4119/2401*T^5 - 928/2401*T^4 + 132/343*T^3
        + 16/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + X*Y^10 + 6*X*Y^9 + 
        2*X*Y^8 + 3*X*Y^6 + 3*X*Y^5 + X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + X + 4*Y^30 + 
        6*Y^29 + 2*Y^28 + 6*Y^27 + 2*Y^26 + Y^24 + 6*Y^22 + 4*Y^21 + 2*Y^20 + 2*Y^19
        + 2*Y^18 + Y^17 + 2*Y^16 + 2*Y^15 + 2*Y^14 + 3*Y^13 + 5*Y^12 + Y^11 + 2*Y^10
        + 2*Y^9 + 2*Y^8 + 4*Y^7 + 6*Y^6 + Y^5 + Y^4 + 6*Y^3 + 4*Y^2 + 4*Y,
    -T^56 - T^55 + 13/49*T^54 + 45/343*T^53 - 43/343*T^52 + 666/2401*T^51 - 
        282/2401*T^50 - 961/2401*T^49 + 724/2401*T^48 + 304/2401*T^47 - 137/343*T^46
        + 195/2401*T^45 + 939/2401*T^44 + 142/343*T^43 + 834/2401*T^42 + 
        216/2401*T^41 + 302/2401*T^40 + 493/2401*T^39 - 67/2401*T^38 - 912/2401*T^37
        + 22/343*T^36 - 107/2401*T^35 + 705/2401*T^34 + 1564/2401*T^33 - 
        115/343*T^32 - 94/343*T^31 + 270/2401*T^30 - 699/2401*T^29 + 699/2401*T^27 -
        270/2401*T^26 + 94/343*T^25 + 115/343*T^24 - 1564/2401*T^23 - 705/2401*T^22 
        + 107/2401*T^21 - 22/343*T^20 + 912/2401*T^19 + 67/2401*T^18 - 493/2401*T^17
        - 302/2401*T^16 - 216/2401*T^15 - 834/2401*T^14 - 142/343*T^13 - 
        939/2401*T^12 - 195/2401*T^11 + 137/343*T^10 - 304/2401*T^9 - 724/2401*T^8 +
        961/2401*T^7 + 282/2401*T^6 - 666/2401*T^5 + 43/343*T^4 - 45/343*T^3 - 
        13/49*T^2 + T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 3*X*Y^12 + 2*X*Y^11 + X*Y^9 + 2*X*Y^7 + 4*X*Y^6 + 
        4*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 5*X*Y + X + 6*Y^30 + 3*Y^27 + Y^25 + 4*Y^23 + 
        3*Y^20 + 2*Y^19 + 6*Y^18 + Y^17 + 6*Y^16 + 5*Y^15 + 5*Y^14 + 5*Y^13 + 4*Y^12
        + 2*Y^10 + 3*Y^9 + Y^7 + 6*Y^6 + Y^5 + Y^4 + 3*Y^3 + 4*Y^2 + Y + 4,
    -T^56 - 15/7*T^55 - 69/49*T^54 - 20/343*T^53 + 107/343*T^52 + 1889/2401*T^51 + 
        66/49*T^50 + 1651/2401*T^49 - 1348/2401*T^48 - 1884/2401*T^47 - 40/343*T^46 
        + 1350/2401*T^45 + 2249/2401*T^44 + 1488/2401*T^43 + 635/2401*T^42 + 
        276/2401*T^41 - 942/2401*T^40 - 118/2401*T^39 + 2399/2401*T^38 + 
        2165/2401*T^37 + 886/2401*T^36 - 646/2401*T^35 - 2855/2401*T^34 - 
        2629/2401*T^33 - 1308/2401*T^32 - 1685/2401*T^31 - 432/2401*T^30 + 
        1614/2401*T^29 - 1614/2401*T^27 + 432/2401*T^26 + 1685/2401*T^25 + 
        1308/2401*T^24 + 2629/2401*T^23 + 2855/2401*T^22 + 646/2401*T^21 - 
        886/2401*T^20 - 2165/2401*T^19 - 2399/2401*T^18 + 118/2401*T^17 + 
        942/2401*T^16 - 276/2401*T^15 - 635/2401*T^14 - 1488/2401*T^13 - 
        2249/2401*T^12 - 1350/2401*T^11 + 40/343*T^10 + 1884/2401*T^9 + 
        1348/2401*T^8 - 1651/2401*T^7 - 66/49*T^6 - 1889/2401*T^5 - 107/343*T^4 + 
        20/343*T^3 + 69/49*T^2 + 15/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 4*X*Y^10 + X*Y^9 + 3*X*Y^8 + 
        6*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 4*X*Y + 2*X + 
        3*Y^30 + 2*Y^29 + 5*Y^28 + 3*Y^27 + 2*Y^26 + 4*Y^25 + 2*Y^24 + 6*Y^23 + 
        2*Y^22 + 5*Y^21 + 5*Y^20 + 2*Y^19 + 3*Y^18 + 6*Y^17 + 3*Y^16 + Y^15 + 3*Y^14
        + 2*Y^13 + 4*Y^11 + 4*Y^10 + 3*Y^9 + 5*Y^8 + Y^5 + 5*Y^4 + Y^3 + 5*Y^2 + 6*Y
        + 3,
    -T^56 + 1/7*T^55 + 65/49*T^54 + 52/343*T^53 - 1314/2401*T^52 - 2820/2401*T^51 - 
        474/2401*T^50 + 2592/2401*T^49 + 4308/2401*T^48 - 1450/2401*T^47 - 
        4727/2401*T^46 - 528/2401*T^45 + 1494/2401*T^44 + 3722/2401*T^43 + 
        321/2401*T^42 - 2988/2401*T^41 - 2952/2401*T^40 + 1592/2401*T^39 + 
        3687/2401*T^38 + 372/2401*T^37 - 289/2401*T^36 - 3365/2401*T^35 - 
        1875/2401*T^34 + 2722/2401*T^33 + 3385/2401*T^32 + 640/2401*T^31 - 
        478/343*T^30 - 2844/2401*T^29 + 2844/2401*T^27 + 478/343*T^26 - 
        640/2401*T^25 - 3385/2401*T^24 - 2722/2401*T^23 + 1875/2401*T^22 + 
        3365/2401*T^21 + 289/2401*T^20 - 372/2401*T^19 - 3687/2401*T^18 - 
        1592/2401*T^17 + 2952/2401*T^16 + 2988/2401*T^15 - 321/2401*T^14 - 
        3722/2401*T^13 - 1494/2401*T^12 + 528/2401*T^11 + 4727/2401*T^10 + 
        1450/2401*T^9 - 4308/2401*T^8 - 2592/2401*T^7 + 474/2401*T^6 + 2820/2401*T^5
        + 1314/2401*T^4 - 52/343*T^3 - 65/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + X*Y^11 + 2*X*Y^9 + 2*X*Y^8 + 
        5*X*Y^7 + X*Y^6 + 6*X*Y^4 + 3*X*Y^2 + 3*X*Y + 2*X + 2*Y^30 + 4*Y^29 + Y^28 +
        4*Y^26 + 3*Y^24 + 2*Y^23 + 5*Y^22 + 2*Y^21 + 3*Y^20 + 2*Y^19 + 4*Y^18 + 
        5*Y^17 + Y^15 + Y^13 + 3*Y^12 + 5*Y^11 + 3*Y^10 + Y^9 + 3*Y^8 + 5*Y^6 + Y^5 
        + 5*Y^4 + Y^3 + 6*Y^2 + 6*Y,
    -T^56 + 10/7*T^55 - 48/49*T^54 + 95/343*T^53 - 204/2401*T^52 + 824/2401*T^51 + 
        272/2401*T^50 - 1271/2401*T^49 + 2796/2401*T^48 - 1856/2401*T^47 + 
        50/343*T^46 - 862/2401*T^45 + 1914/2401*T^44 - 1336/2401*T^43 - 
        579/2401*T^42 + 864/2401*T^41 - 759/2401*T^40 + 1951/2401*T^39 - 
        2357/2401*T^38 + 1128/2401*T^37 + 776/2401*T^36 - 1949/2401*T^35 + 
        1832/2401*T^34 - 226/343*T^33 + 2549/2401*T^32 - 3056/2401*T^31 + 
        1384/2401*T^30 + 366/2401*T^29 - 366/2401*T^27 - 1384/2401*T^26 + 
        3056/2401*T^25 - 2549/2401*T^24 + 226/343*T^23 - 1832/2401*T^22 + 
        1949/2401*T^21 - 776/2401*T^20 - 1128/2401*T^19 + 2357/2401*T^18 - 
        1951/2401*T^17 + 759/2401*T^16 - 864/2401*T^15 + 579/2401*T^14 + 
        1336/2401*T^13 - 1914/2401*T^12 + 862/2401*T^11 - 50/343*T^10 + 
        1856/2401*T^9 - 2796/2401*T^8 + 1271/2401*T^7 - 272/2401*T^6 - 824/2401*T^5 
        + 204/2401*T^4 - 95/343*T^3 + 48/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 6*X*Y^10 + X*Y^7 + 2*X*Y^6 + 
        5*X*Y^5 + X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 5*X*Y + 5*X + 3*Y^30 + 6*Y^29 + Y^28 +
        3*Y^27 + 6*Y^26 + 4*Y^25 + 6*Y^24 + 2*Y^23 + 6*Y^22 + 3*Y^21 + 3*Y^20 + 
        5*Y^19 + 4*Y^18 + 6*Y^17 + 2*Y^16 + 4*Y^15 + 4*Y^14 + Y^13 + 2*Y^12 + Y^11 +
        4*Y^10 + 4*Y^9 + 6*Y^8 + 5*Y^7 + 2*Y^6 + 3*Y^5 + 3*Y^4 + 5*Y^3 + 5*Y^2 + 4*Y
        + 5,
    T^56 - T^55 + 32/49*T^54 + 47/343*T^53 - 30/2401*T^52 - 537/2401*T^51 - 
        1276/2401*T^50 + 258/343*T^49 - 2742/2401*T^48 + 698/2401*T^47 - 
        268/2401*T^46 + 186/2401*T^45 + 358/2401*T^44 - 863/2401*T^43 + 
        1614/2401*T^42 - 1006/2401*T^41 + 88/343*T^40 - 667/2401*T^39 + 
        171/2401*T^38 + 130/2401*T^37 - 1724/2401*T^36 + 1010/2401*T^35 - 
        363/2401*T^34 + 277/2401*T^33 - 606/2401*T^32 + 709/2401*T^31 + 
        367/2401*T^30 - 87/2401*T^29 + 760/2401*T^28 - 87/2401*T^27 + 367/2401*T^26 
        + 709/2401*T^25 - 606/2401*T^24 + 277/2401*T^23 - 363/2401*T^22 + 
        1010/2401*T^21 - 1724/2401*T^20 + 130/2401*T^19 + 171/2401*T^18 - 
        667/2401*T^17 + 88/343*T^16 - 1006/2401*T^15 + 1614/2401*T^14 - 
        863/2401*T^13 + 358/2401*T^12 + 186/2401*T^11 - 268/2401*T^10 + 698/2401*T^9
        - 2742/2401*T^8 + 258/343*T^7 - 1276/2401*T^6 - 537/2401*T^5 - 30/2401*T^4 +
        47/343*T^3 + 32/49*T^2 - T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 3*X*Y^13 + 3*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 6*X*Y^7 + 
        2*X*Y^6 + X*Y^5 + X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 3*X*Y + X + 3*Y^30 + 4*Y^29 + 
        4*Y^28 + 2*Y^27 + Y^26 + 3*Y^25 + 2*Y^22 + 4*Y^20 + 2*Y^19 + 2*Y^18 + 4*Y^17
        + 3*Y^16 + 4*Y^14 + Y^13 + 6*Y^11 + 2*Y^10 + Y^9 + 6*Y^8 + 2*Y^6 + 3*Y^5 + 
        2*Y^4 + 4*Y^2 + 2*Y,
    T^56 - 12/7*T^55 + 74/49*T^54 - 496/343*T^53 + 6012/2401*T^52 - 1182/343*T^51 + 
        7491/2401*T^50 - 811/343*T^49 + 5681/2401*T^48 - 7587/2401*T^47 + 
        7832/2401*T^46 - 5014/2401*T^45 + 263/343*T^44 - 2458/2401*T^43 + 
        4705/2401*T^42 - 3310/2401*T^41 - 1132/2401*T^40 + 44/49*T^39 + 31/2401*T^38
        - 1343/2401*T^37 - 276/343*T^36 + 5437/2401*T^35 - 4274/2401*T^34 + 
        550/2401*T^33 - 26/343*T^32 + 3872/2401*T^31 - 5235/2401*T^30 + 
        1689/2401*T^29 + 200/343*T^28 + 1689/2401*T^27 - 5235/2401*T^26 + 
        3872/2401*T^25 - 26/343*T^24 + 550/2401*T^23 - 4274/2401*T^22 + 
        5437/2401*T^21 - 276/343*T^20 - 1343/2401*T^19 + 31/2401*T^18 + 44/49*T^17 -
        1132/2401*T^16 - 3310/2401*T^15 + 4705/2401*T^14 - 2458/2401*T^13 + 
        263/343*T^12 - 5014/2401*T^11 + 7832/2401*T^10 - 7587/2401*T^9 + 
        5681/2401*T^8 - 811/343*T^7 + 7491/2401*T^6 - 1182/343*T^5 + 6012/2401*T^4 -
        496/343*T^3 + 74/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 
        + 5*X*Y^8 + 4*X*Y^7 + 6*X*Y^6 + X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 2*X*Y 
        + 6*X + 4*Y^30 + 2*Y^28 + 3*Y^27 + Y^26 + Y^25 + 3*Y^24 + 5*Y^23 + 4*Y^22 + 
        6*Y^21 + 6*Y^20 + 2*Y^19 + 2*Y^18 + 4*Y^16 + 5*Y^15 + 3*Y^14 + 5*Y^13 + 
        4*Y^12 + 2*Y^11 + Y^10 + 6*Y^9 + 4*Y^8 + 4*Y^7 + 2*Y^6 + Y^5 + 2*Y^4 + 5*Y^3
        + 5*Y^2 + 4,
    T^56 + 2/7*T^55 - 5/7*T^54 - 230/343*T^53 - 1812/2401*T^52 + 688/2401*T^51 + 
        1893/2401*T^50 + 2474/2401*T^49 + 272/2401*T^48 - 2370/2401*T^47 - 
        311/343*T^46 - 404/2401*T^45 + 1994/2401*T^44 + 1853/2401*T^43 + 
        195/2401*T^42 - 1352/2401*T^41 - 1867/2401*T^40 - 835/2401*T^39 + 
        208/343*T^38 + 867/2401*T^37 + 663/2401*T^36 - 284/2401*T^35 - 
        1882/2401*T^34 - 37/2401*T^33 + 949/2401*T^32 + 215/343*T^31 + 177/2401*T^30
        - 857/2401*T^29 - 221/2401*T^28 - 857/2401*T^27 + 177/2401*T^26 + 
        215/343*T^25 + 949/2401*T^24 - 37/2401*T^23 - 1882/2401*T^22 - 284/2401*T^21
        + 663/2401*T^20 + 867/2401*T^19 + 208/343*T^18 - 835/2401*T^17 - 
        1867/2401*T^16 - 1352/2401*T^15 + 195/2401*T^14 + 1853/2401*T^13 + 
        1994/2401*T^12 - 404/2401*T^11 - 311/343*T^10 - 2370/2401*T^9 + 272/2401*T^8
        + 2474/2401*T^7 + 1893/2401*T^6 + 688/2401*T^5 - 1812/2401*T^4 - 230/343*T^3
        - 5/7*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 4*X*Y^9 + 2*X*Y^8 +
        X*Y^7 + X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 5*X*Y + 5*X + 2*Y^30
        + Y^29 + 4*Y^28 + 6*Y^27 + 5*Y^26 + 2*Y^25 + 5*Y^24 + 6*Y^23 + 6*Y^21 + Y^20
        + 5*Y^19 + Y^18 + 4*Y^16 + 6*Y^14 + 6*Y^13 + Y^12 + 5*Y^11 + 6*Y^10 + 2*Y^9 
        + 3*Y^7 + 4*Y^6 + 5*Y^5 + 6*Y^4 + 2*Y^3 + 3*Y^2 + 2*Y,
    T^56 - 5/7*T^55 - 9/49*T^54 - 36/343*T^53 + 1522/2401*T^52 - 1264/2401*T^51 + 
        54/2401*T^50 + 1335/2401*T^49 - 1895/2401*T^48 - 1430/2401*T^47 + 
        1418/2401*T^46 + 2047/2401*T^45 - 2560/2401*T^44 - 102/343*T^43 + 
        2172/2401*T^42 + 499/2401*T^41 - 2526/2401*T^40 + 2825/2401*T^39 + 
        1173/2401*T^38 - 2670/2401*T^37 - 617/2401*T^36 + 3485/2401*T^35 - 
        431/2401*T^34 - 3267/2401*T^33 + 2046/2401*T^32 + 1808/2401*T^31 - 
        3025/2401*T^30 - 323/2401*T^29 + 2290/2401*T^28 - 323/2401*T^27 - 
        3025/2401*T^26 + 1808/2401*T^25 + 2046/2401*T^24 - 3267/2401*T^23 - 
        431/2401*T^22 + 3485/2401*T^21 - 617/2401*T^20 - 2670/2401*T^19 + 
        1173/2401*T^18 + 2825/2401*T^17 - 2526/2401*T^16 + 499/2401*T^15 + 
        2172/2401*T^14 - 102/343*T^13 - 2560/2401*T^12 + 2047/2401*T^11 + 
        1418/2401*T^10 - 1430/2401*T^9 - 1895/2401*T^8 + 1335/2401*T^7 + 54/2401*T^6
        - 1264/2401*T^5 + 1522/2401*T^4 - 36/343*T^3 - 9/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 
        X*Y^6 + X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 3*X*Y + 5*X + 2*Y^30 + 6*Y^29 
        + 3*Y^28 + 2*Y^27 + Y^26 + 4*Y^25 + 4*Y^24 + Y^23 + 2*Y^22 + 4*Y^20 + 4*Y^19
        + 5*Y^18 + 6*Y^17 + 2*Y^16 + 5*Y^15 + 6*Y^14 + Y^13 + Y^12 + 3*Y^11 + 4*Y^10
        + Y^9 + 3*Y^8 + Y^7 + 4*Y^6 + 6*Y^5 + 4*Y^4 + Y^3 + 2*Y^2 + 6*Y + 3,
    T^56 - 18/49*T^54 + 24/49*T^53 + 270/2401*T^52 + 594/2401*T^51 - 746/2401*T^50 -
        611/2401*T^49 + 769/2401*T^48 + 260/2401*T^47 - 1430/2401*T^46 + 
        160/2401*T^45 - 27/343*T^44 - 251/2401*T^43 - 513/2401*T^42 - 110/2401*T^41 
        + 1065/2401*T^40 - 702/2401*T^39 - 346/2401*T^38 - 73/2401*T^37 + 
        25/343*T^36 + 404/2401*T^35 - 1115/2401*T^34 - 148/2401*T^33 + 
        1432/2401*T^32 - 1/343*T^31 + 912/2401*T^30 + 1056/2401*T^29 - 46/2401*T^28 
        + 1056/2401*T^27 + 912/2401*T^26 - 1/343*T^25 + 1432/2401*T^24 - 
        148/2401*T^23 - 1115/2401*T^22 + 404/2401*T^21 + 25/343*T^20 - 73/2401*T^19 
        - 346/2401*T^18 - 702/2401*T^17 + 1065/2401*T^16 - 110/2401*T^15 - 
        513/2401*T^14 - 251/2401*T^13 - 27/343*T^12 + 160/2401*T^11 - 1430/2401*T^10
        + 260/2401*T^9 + 769/2401*T^8 - 611/2401*T^7 - 746/2401*T^6 + 594/2401*T^5 +
        270/2401*T^4 + 24/49*T^3 - 18/49*T^2 + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 
        + 2*X*Y^8 + X*Y^7 + 2*X*Y^6 + X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 2*X*Y + 
        4*X + 4*Y^30 + 5*Y^29 + 4*Y^28 + 4*Y^26 + Y^25 + 4*Y^24 + 2*Y^23 + 2*Y^22 + 
        5*Y^20 + 5*Y^19 + Y^18 + 6*Y^16 + 5*Y^15 + 2*Y^14 + Y^13 + 2*Y^12 + 4*Y^11 +
        Y^10 + 6*Y^7 + 4*Y^6 + 2*Y^5 + 3*Y^4 + 4*Y^3 + 3*Y^2,
    -T^56 - 2/7*T^55 - 23/49*T^54 - 6/343*T^53 + 969/2401*T^52 - 113/343*T^51 + 
        1353/2401*T^50 - 650/2401*T^49 - 132/343*T^48 + 653/2401*T^47 - 
        530/2401*T^46 + 1021/2401*T^45 + 635/2401*T^44 + 437/2401*T^43 + 
        1573/2401*T^42 - 799/2401*T^41 + 668/2401*T^40 + 396/2401*T^39 - 
        150/2401*T^38 - 869/2401*T^37 - 1284/2401*T^36 + 1047/2401*T^35 + 
        957/2401*T^34 + 507/2401*T^33 + 884/2401*T^32 - 1080/2401*T^31 + 
        148/2401*T^30 - 1635/2401*T^29 + 1635/2401*T^27 - 148/2401*T^26 + 
        1080/2401*T^25 - 884/2401*T^24 - 507/2401*T^23 - 957/2401*T^22 - 
        1047/2401*T^21 + 1284/2401*T^20 + 869/2401*T^19 + 150/2401*T^18 - 
        396/2401*T^17 - 668/2401*T^16 + 799/2401*T^15 - 1573/2401*T^14 - 
        437/2401*T^13 - 635/2401*T^12 - 1021/2401*T^11 + 530/2401*T^10 - 
        653/2401*T^9 + 132/343*T^8 + 650/2401*T^7 - 1353/2401*T^6 + 113/343*T^5 - 
        969/2401*T^4 + 6/343*T^3 + 23/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 3*X*Y^13 + X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 
        2*X*Y^8 + 4*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + X*Y^3 + 4*X + Y^30 + 3*Y^29 + Y^28 +
        2*Y^27 + 6*Y^26 + 3*Y^25 + 2*Y^24 + 2*Y^23 + 4*Y^21 + Y^20 + 6*Y^18 + 2*Y^17
        + Y^16 + 2*Y^15 + 2*Y^14 + 5*Y^13 + 5*Y^12 + 4*Y^11 + 3*Y^10 + Y^9 + 3*Y^8 +
        Y^7 + 5*Y^6 + 4*Y^5 + 2*Y^4 + 5*Y^3 + 5*Y^2 + 2*Y,
    T^56 - 12/7*T^55 + 59/49*T^54 - 66/343*T^53 - 2543/2401*T^52 + 736/343*T^51 - 
        5142/2401*T^50 + 480/343*T^49 + 647/2401*T^48 - 4581/2401*T^47 + 
        4598/2401*T^46 - 3686/2401*T^45 + 3287/2401*T^44 - 365/343*T^43 + 
        228/343*T^42 + 268/343*T^41 - 5890/2401*T^40 + 6918/2401*T^39 - 
        6564/2401*T^38 + 4586/2401*T^37 + 1264/2401*T^36 - 6835/2401*T^35 + 
        1322/343*T^34 - 7444/2401*T^33 + 3452/2401*T^32 - 26/2401*T^31 - 
        3733/2401*T^30 + 6733/2401*T^29 - 7720/2401*T^28 + 6733/2401*T^27 - 
        3733/2401*T^26 - 26/2401*T^25 + 3452/2401*T^24 - 7444/2401*T^23 + 
        1322/343*T^22 - 6835/2401*T^21 + 1264/2401*T^20 + 4586/2401*T^19 - 
        6564/2401*T^18 + 6918/2401*T^17 - 5890/2401*T^16 + 268/343*T^15 + 
        228/343*T^14 - 365/343*T^13 + 3287/2401*T^12 - 3686/2401*T^11 + 
        4598/2401*T^10 - 4581/2401*T^9 + 647/2401*T^8 + 480/343*T^7 - 5142/2401*T^6 
        + 736/343*T^5 - 2543/2401*T^4 - 66/343*T^3 + 59/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 6*X*Y^11 + 2*X*Y^10 + 6*X*Y^8 + 4*X*Y^7 +
        6*X*Y^6 + X*Y^5 + 5*X*Y^4 + X*Y^3 + X*Y^2 + 4*X + 3*Y^30 + 2*Y^29 + 4*Y^28 +
        3*Y^27 + 5*Y^25 + 2*Y^24 + 2*Y^23 + 4*Y^22 + 5*Y^21 + 3*Y^20 + 2*Y^19 + 
        2*Y^17 + 5*Y^15 + 2*Y^14 + Y^13 + 2*Y^11 + 6*Y^10 + Y^7 + 4*Y^6 + 2*Y^4 + 
        2*Y^3 + 6*Y^2 + 2*Y + 6,
    T^56 - 11/7*T^55 + 62/49*T^54 - 201/343*T^53 - 1508/2401*T^52 + 3392/2401*T^51 -
        1409/2401*T^50 - 1123/2401*T^49 + 234/343*T^48 - 1464/2401*T^47 + 
        1055/2401*T^46 + 341/2401*T^45 - 225/2401*T^44 + 589/2401*T^43 - 
        2698/2401*T^42 + 3154/2401*T^41 - 2003/2401*T^40 + 200/2401*T^39 + 
        1474/2401*T^38 - 1922/2401*T^37 - 200/2401*T^36 + 1115/2401*T^35 - 
        596/2401*T^34 + 1321/2401*T^33 - 1102/2401*T^32 + 82/343*T^31 - 120/343*T^30
        - 122/343*T^29 + 320/343*T^28 - 122/343*T^27 - 120/343*T^26 + 82/343*T^25 - 
        1102/2401*T^24 + 1321/2401*T^23 - 596/2401*T^22 + 1115/2401*T^21 - 
        200/2401*T^20 - 1922/2401*T^19 + 1474/2401*T^18 + 200/2401*T^17 - 
        2003/2401*T^16 + 3154/2401*T^15 - 2698/2401*T^14 + 589/2401*T^13 - 
        225/2401*T^12 + 341/2401*T^11 + 1055/2401*T^10 - 1464/2401*T^9 + 234/343*T^8
        - 1123/2401*T^7 - 1409/2401*T^6 + 3392/2401*T^5 - 1508/2401*T^4 - 
        201/343*T^3 + 62/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 3*X*Y^13 + 2*X*Y^11 + 6*X*Y^10 + 5*X*Y^8 + 3*X*Y^7 + 
        2*X*Y^6 + 6*X*Y^5 + 3*X*Y^4 + 5*X*Y + 4*X + 6*Y^30 + 2*Y^29 + 3*Y^28 + 
        2*Y^27 + Y^26 + 2*Y^25 + 4*Y^24 + 2*Y^23 + Y^22 + 6*Y^21 + 6*Y^20 + 2*Y^19 +
        6*Y^18 + Y^17 + 4*Y^15 + 3*Y^14 + 5*Y^13 + 3*Y^12 + 6*Y^11 + 2*Y^10 + Y^9 + 
        3*Y^8 + 3*Y^7 + 6*Y^5 + 5*Y^4 + 3*Y^3 + Y^2 + 3*Y + 3,
    -T^56 - 10/7*T^55 - 6/7*T^54 + 32/343*T^53 + 1695/2401*T^52 + 2106/2401*T^51 + 
        24/49*T^50 - 946/2401*T^49 - 1504/2401*T^48 - 710/2401*T^47 + 267/343*T^46 +
        3137/2401*T^45 + 2554/2401*T^44 + 299/2401*T^43 - 494/2401*T^42 - 
        1/2401*T^41 + 178/343*T^40 + 2038/2401*T^39 + 1219/2401*T^38 - 
        1599/2401*T^37 - 3747/2401*T^36 - 2277/2401*T^35 - 663/2401*T^34 + 
        1457/2401*T^33 + 1013/2401*T^32 - 1068/2401*T^31 - 3625/2401*T^30 - 
        2657/2401*T^29 + 2657/2401*T^27 + 3625/2401*T^26 + 1068/2401*T^25 - 
        1013/2401*T^24 - 1457/2401*T^23 + 663/2401*T^22 + 2277/2401*T^21 + 
        3747/2401*T^20 + 1599/2401*T^19 - 1219/2401*T^18 - 2038/2401*T^17 - 
        178/343*T^16 + 1/2401*T^15 + 494/2401*T^14 - 299/2401*T^13 - 2554/2401*T^12 
        - 3137/2401*T^11 - 267/343*T^10 + 710/2401*T^9 + 1504/2401*T^8 + 
        946/2401*T^7 - 24/49*T^6 - 2106/2401*T^5 - 1695/2401*T^4 - 32/343*T^3 + 
        6/7*T^2 + 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 4*X*Y^10 + X*Y^9 + X*Y^8 + 
        3*X*Y^7 + X*Y^6 + X*Y^5 + X*Y^4 + X*Y^3 + 2*X*Y^2 + 5*X*Y + X + 6*Y^30 + 
        Y^29 + 4*Y^28 + 6*Y^26 + 4*Y^25 + 2*Y^24 + 2*Y^23 + 4*Y^22 + 6*Y^21 + 5*Y^20
        + 6*Y^19 + Y^18 + Y^17 + 4*Y^16 + 2*Y^15 + 4*Y^14 + Y^13 + 4*Y^12 + 2*Y^11 +
        Y^10 + 3*Y^9 + 3*Y^7 + Y^6 + 5*Y^5 + Y^4 + 4*Y^3 + 3*Y^2 + 4*Y + 6,
    -T^56 - 11/7*T^55 - 83/49*T^54 - 104/49*T^53 - 3352/2401*T^52 - 1489/2401*T^51 -
        957/2401*T^50 - 309/2401*T^49 + 132/2401*T^48 + 2103/2401*T^47 + 
        3895/2401*T^46 + 4209/2401*T^45 + 4520/2401*T^44 + 3736/2401*T^43 + 
        282/2401*T^42 - 1735/2401*T^41 - 1277/2401*T^40 - 2453/2401*T^39 - 
        2938/2401*T^38 - 2313/2401*T^37 - 345/343*T^36 - 2579/2401*T^35 - 
        229/343*T^34 + 304/2401*T^33 + 2250/2401*T^32 + 1957/2401*T^31 + 
        1336/2401*T^30 + 2060/2401*T^29 - 2060/2401*T^27 - 1336/2401*T^26 - 
        1957/2401*T^25 - 2250/2401*T^24 - 304/2401*T^23 + 229/343*T^22 + 
        2579/2401*T^21 + 345/343*T^20 + 2313/2401*T^19 + 2938/2401*T^18 + 
        2453/2401*T^17 + 1277/2401*T^16 + 1735/2401*T^15 - 282/2401*T^14 - 
        3736/2401*T^13 - 4520/2401*T^12 - 4209/2401*T^11 - 3895/2401*T^10 - 
        2103/2401*T^9 - 132/2401*T^8 + 309/2401*T^7 + 957/2401*T^6 + 1489/2401*T^5 +
        3352/2401*T^4 + 104/49*T^3 + 83/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + X*Y^12 + 5*X*Y^10 + 5*X*Y^8 + 5*X*Y^7 + 
        5*X*Y^6 + 2*X*Y^5 + 6*X*Y^3 + 4*X*Y + X + Y^30 + 4*Y^28 + 2*Y^27 + 4*Y^26 + 
        4*Y^25 + 6*Y^23 + Y^22 + 3*Y^21 + 6*Y^19 + 2*Y^18 + 3*Y^17 + 3*Y^16 + 6*Y^15
        + 2*Y^14 + 4*Y^13 + 2*Y^12 + 6*Y^11 + 2*Y^10 + 3*Y^9 + 6*Y^8 + 5*Y^7 + 2*Y^6
        + 3*Y^5 + 2*Y^4 + 3*Y^3 + 4*Y^2 + 3*Y + 3,
    T^56 - 4/7*T^55 - 75/49*T^54 + 377/343*T^53 + 1142/2401*T^52 + 129/2401*T^51 - 
        1150/2401*T^50 - 2858/2401*T^49 + 3973/2401*T^48 + 885/2401*T^47 - 
        3442/2401*T^46 + 968/2401*T^45 + 268/2401*T^44 + 657/2401*T^43 - 
        808/2401*T^42 - 1888/2401*T^41 + 3961/2401*T^40 + 215/2401*T^39 - 
        4120/2401*T^38 + 1025/2401*T^37 + 681/2401*T^36 + 1345/2401*T^35 - 
        400/2401*T^34 - 3390/2401*T^33 + 3131/2401*T^32 + 1119/2401*T^31 - 
        2029/2401*T^30 + 550/2401*T^29 + 186/2401*T^28 + 550/2401*T^27 - 
        2029/2401*T^26 + 1119/2401*T^25 + 3131/2401*T^24 - 3390/2401*T^23 - 
        400/2401*T^22 + 1345/2401*T^21 + 681/2401*T^20 + 1025/2401*T^19 - 
        4120/2401*T^18 + 215/2401*T^17 + 3961/2401*T^16 - 1888/2401*T^15 - 
        808/2401*T^14 + 657/2401*T^13 + 268/2401*T^12 + 968/2401*T^11 - 
        3442/2401*T^10 + 885/2401*T^9 + 3973/2401*T^8 - 2858/2401*T^7 - 
        1150/2401*T^6 + 129/2401*T^5 + 1142/2401*T^4 + 377/343*T^3 - 75/49*T^2 - 
        4/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 5*X*Y^11 + X*Y^10 + 4*X*Y^9 + 5*X*Y^8 + 3*X*Y^7 + 
        3*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 5*X + 3*Y^30 + 2*Y^29 + 
        5*Y^28 + 4*Y^27 + 5*Y^25 + 4*Y^24 + 5*Y^23 + 2*Y^22 + 2*Y^21 + 2*Y^20 + 
        5*Y^19 + Y^17 + 2*Y^16 + 3*Y^15 + 6*Y^14 + 4*Y^13 + 6*Y^12 + 5*Y^11 + 4*Y^10
        + 2*Y^9 + Y^8 + Y^7 + Y^6 + 6*Y^5 + 6*Y^4 + 3*Y^3 + 3,
    -T^56 - 2/7*T^55 - 10/49*T^54 + 239/343*T^53 + 1390/2401*T^52 + 1305/2401*T^51 -
        981/2401*T^50 - 430/2401*T^49 - 201/343*T^48 - 4/343*T^47 - 13/49*T^46 + 
        569/2401*T^45 + 89/343*T^44 + 1402/2401*T^43 + 342/2401*T^42 + 60/2401*T^41 
        - 134/343*T^40 - 262/2401*T^39 - 3/7*T^38 + 2/343*T^37 - 57/2401*T^36 + 
        788/2401*T^35 + 1109/2401*T^34 - 876/2401*T^33 - 177/343*T^32 - 
        267/2401*T^31 + 801/2401*T^30 + 1368/2401*T^29 - 1368/2401*T^27 - 
        801/2401*T^26 + 267/2401*T^25 + 177/343*T^24 + 876/2401*T^23 - 
        1109/2401*T^22 - 788/2401*T^21 + 57/2401*T^20 - 2/343*T^19 + 3/7*T^18 + 
        262/2401*T^17 + 134/343*T^16 - 60/2401*T^15 - 342/2401*T^14 - 1402/2401*T^13
        - 89/343*T^12 - 569/2401*T^11 + 13/49*T^10 + 4/343*T^9 + 201/343*T^8 + 
        430/2401*T^7 + 981/2401*T^6 - 1305/2401*T^5 - 1390/2401*T^4 - 239/343*T^3 + 
        10/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 5*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + X*Y^9 + 4*X*Y^7 + 
        X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 4*X + Y^30 + 2*Y^29 + 5*Y^28
        + 4*Y^27 + 4*Y^26 + Y^25 + 5*Y^23 + Y^22 + 6*Y^21 + 6*Y^19 + 6*Y^18 + 4*Y^16
        + Y^15 + 3*Y^14 + 4*Y^13 + 6*Y^12 + 4*Y^11 + 5*Y^10 + 5*Y^9 + 6*Y^8 + 6*Y^6 
        + 4*Y^5 + 5*Y^3 + 6*Y^2 + 4,
    -T^56 + 5/7*T^55 - 6/7*T^54 - 295/343*T^53 + 1748/2401*T^52 - 2708/2401*T^51 + 
        227/343*T^50 - 1084/2401*T^49 + 283/343*T^48 - 774/2401*T^47 + 
        1863/2401*T^46 + 353/2401*T^45 - 331/2401*T^44 + 3410/2401*T^43 - 
        3825/2401*T^42 + 4268/2401*T^41 - 8/7*T^40 + 1921/2401*T^39 - 1313/2401*T^38
        + 249/2401*T^37 + 572/2401*T^36 - 2971/2401*T^35 + 500/343*T^34 - 
        5130/2401*T^33 + 3256/2401*T^32 - 530/343*T^31 + 807/2401*T^30 - 
        535/2401*T^29 + 535/2401*T^27 - 807/2401*T^26 + 530/343*T^25 - 
        3256/2401*T^24 + 5130/2401*T^23 - 500/343*T^22 + 2971/2401*T^21 - 
        572/2401*T^20 - 249/2401*T^19 + 1313/2401*T^18 - 1921/2401*T^17 + 8/7*T^16 -
        4268/2401*T^15 + 3825/2401*T^14 - 3410/2401*T^13 + 331/2401*T^12 - 
        353/2401*T^11 - 1863/2401*T^10 + 774/2401*T^9 - 283/343*T^8 + 1084/2401*T^7 
        - 227/343*T^6 + 2708/2401*T^5 - 1748/2401*T^4 + 295/343*T^3 + 6/7*T^2 - 
        5/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^10 + X*Y^8 + 4*X*Y^7 + 
        4*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 6*X*Y + 5*X + 6*Y^30 + 
        4*Y^29 + 3*Y^28 + 5*Y^27 + 5*Y^26 + Y^25 + 5*Y^23 + Y^22 + 3*Y^21 + 5*Y^20 +
        2*Y^19 + 3*Y^18 + Y^17 + 3*Y^16 + 3*Y^15 + 5*Y^14 + 3*Y^13 + 2*Y^12 + Y^11 +
        3*Y^10 + 2*Y^9 + Y^8 + 3*Y^7 + 2*Y^6 + 2*Y^5 + 5*Y^4 + Y^3 + 3*Y^2 + 6*Y + 
        6,
    -T^56 - 2*T^55 - 8/49*T^54 + 920/343*T^53 + 3126/2401*T^52 - 5359/2401*T^51 - 
        3177/2401*T^50 + 5603/2401*T^49 + 3153/2401*T^48 - 7026/2401*T^47 - 
        6681/2401*T^46 + 4086/2401*T^45 + 1247/343*T^44 + 748/2401*T^43 - 
        6903/2401*T^42 - 2812/2401*T^41 + 4903/2401*T^40 + 2347/2401*T^39 - 
        4800/2401*T^38 - 3638/2401*T^37 + 2621/2401*T^36 + 2578/2401*T^35 - 
        606/2401*T^34 - 751/2401*T^33 - 411/2401*T^32 - 1331/2401*T^31 + 
        304/2401*T^30 + 2185/2401*T^29 - 2185/2401*T^27 - 304/2401*T^26 + 
        1331/2401*T^25 + 411/2401*T^24 + 751/2401*T^23 + 606/2401*T^22 - 
        2578/2401*T^21 - 2621/2401*T^20 + 3638/2401*T^19 + 4800/2401*T^18 - 
        2347/2401*T^17 - 4903/2401*T^16 + 2812/2401*T^15 + 6903/2401*T^14 - 
        748/2401*T^13 - 1247/343*T^12 - 4086/2401*T^11 + 6681/2401*T^10 + 
        7026/2401*T^9 - 3153/2401*T^8 - 5603/2401*T^7 + 3177/2401*T^6 + 
        5359/2401*T^5 - 3126/2401*T^4 - 920/343*T^3 + 8/49*T^2 + 2*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 
        + X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + X*Y^4 + 6*X*Y^3 + X*Y^2 + 2*X*Y + 5*X + 2*Y^30
        + 3*Y^29 + 6*Y^26 + 3*Y^25 + 6*Y^23 + Y^22 + 3*Y^21 + 4*Y^20 + Y^19 + Y^18 +
        3*Y^17 + 2*Y^15 + Y^14 + 3*Y^13 + 3*Y^12 + Y^11 + 6*Y^9 + 4*Y^7 + 4*Y^5 + 
        4*Y^4 + 2*Y^3 + 2*Y^2 + 6*Y + 3,
    -T^56 - 9/7*T^55 - 1/7*T^54 + 317/343*T^53 + 3491/2401*T^52 + 1485/2401*T^51 - 
        227/2401*T^50 - 608/2401*T^49 - 408/2401*T^48 + 325/2401*T^47 - 
        432/2401*T^46 - 1782/2401*T^45 - 2045/2401*T^44 + 498/2401*T^43 + 
        2126/2401*T^42 + 1432/2401*T^41 + 317/2401*T^40 - 1227/2401*T^39 - 
        723/2401*T^38 + 449/2401*T^37 + 1583/2401*T^36 + 1444/2401*T^35 + 
        106/2401*T^34 - 935/2401*T^33 - 298/343*T^32 - 2316/2401*T^31 - 
        1227/2401*T^30 - 19/2401*T^29 + 19/2401*T^27 + 1227/2401*T^26 + 
        2316/2401*T^25 + 298/343*T^24 + 935/2401*T^23 - 106/2401*T^22 - 
        1444/2401*T^21 - 1583/2401*T^20 - 449/2401*T^19 + 723/2401*T^18 + 
        1227/2401*T^17 - 317/2401*T^16 - 1432/2401*T^15 - 2126/2401*T^14 - 
        498/2401*T^13 + 2045/2401*T^12 + 1782/2401*T^11 + 432/2401*T^10 - 
        325/2401*T^9 + 408/2401*T^8 + 608/2401*T^7 + 227/2401*T^6 - 1485/2401*T^5 - 
        3491/2401*T^4 - 317/343*T^3 + 1/7*T^2 + 9/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 2*X*Y^13 + X*Y^11 + X*Y^10 + 4*X*Y^9 + 6*X*Y^7 + 
        2*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + X*Y^3 + 5*X*Y^2 + 2*X*Y + Y^30 + 3*Y^29 + 
        2*Y^27 + 6*Y^26 + 5*Y^25 + Y^24 + Y^23 + Y^22 + 3*Y^21 + 2*Y^20 + 3*Y^19 + 
        6*Y^18 + 3*Y^17 + 3*Y^16 + 3*Y^15 + Y^14 + 2*Y^13 + 2*Y^12 + Y^11 + 4*Y^10 +
        4*Y^9 + 4*Y^8 + 4*Y^7 + 5*Y^5 + 5*Y^4 + 3*Y^3 + 6*Y + 6,
    -T^56 + 6/7*T^55 - 23/49*T^54 + 129/343*T^53 - 17/2401*T^52 - 932/2401*T^51 - 
        536/2401*T^50 - 169/2401*T^49 + 110/2401*T^48 - 737/2401*T^47 + 
        1622/2401*T^46 - 656/2401*T^45 + 1249/2401*T^44 - 325/343*T^43 + 
        269/343*T^42 - 1165/2401*T^41 + 334/2401*T^40 + 188/343*T^39 - 694/2401*T^38
        + 127/343*T^37 + 688/2401*T^36 + 305/2401*T^35 - 981/2401*T^34 + 
        1268/2401*T^33 - 1756/2401*T^32 + 2218/2401*T^31 - 685/2401*T^30 + 
        1081/2401*T^29 - 1081/2401*T^27 + 685/2401*T^26 - 2218/2401*T^25 + 
        1756/2401*T^24 - 1268/2401*T^23 + 981/2401*T^22 - 305/2401*T^21 - 
        688/2401*T^20 - 127/343*T^19 + 694/2401*T^18 - 188/343*T^17 - 334/2401*T^16 
        + 1165/2401*T^15 - 269/343*T^14 + 325/343*T^13 - 1249/2401*T^12 + 
        656/2401*T^11 - 1622/2401*T^10 + 737/2401*T^9 - 110/2401*T^8 + 169/2401*T^7 
        + 536/2401*T^6 + 932/2401*T^5 + 17/2401*T^4 - 129/343*T^3 + 23/49*T^2 - 
        6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^13 + X*Y^12 + X*Y^11 + 4*X*Y^9 + 4*X*Y^7 + 6*X*Y^5 + 
        4*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 4*X*Y + X + 5*Y^30 + Y^29 + Y^28 + Y^27 + Y^26
        + 4*Y^25 + 5*Y^24 + 2*Y^23 + 5*Y^22 + 2*Y^21 + 5*Y^20 + 4*Y^19 + 2*Y^18 + 
        6*Y^17 + 6*Y^16 + 2*Y^15 + 5*Y^14 + 4*Y^12 + 5*Y^11 + 4*Y^10 + 2*Y^8 + 3*Y^7
        + 4*Y^6 + 2*Y^3 + 4*Y^2 + 3,
    T^56 + 4/7*T^55 - 6/49*T^54 - 201/343*T^53 - 913/2401*T^52 + 88/343*T^51 + 
        933/2401*T^50 - 579/2401*T^49 - 2/7*T^48 - 984/2401*T^47 - 1037/2401*T^46 - 
        433/2401*T^45 - 1249/2401*T^44 - 207/2401*T^43 - 926/2401*T^42 - 
        451/2401*T^41 + 1040/2401*T^40 + 416/343*T^39 + 1298/2401*T^38 - 
        845/2401*T^37 - 2169/2401*T^36 + 121/343*T^35 + 2490/2401*T^34 + 
        202/343*T^33 + 6/343*T^32 - 250/343*T^31 - 724/2401*T^30 - 513/2401*T^29 - 
        8/49*T^28 - 513/2401*T^27 - 724/2401*T^26 - 250/343*T^25 + 6/343*T^24 + 
        202/343*T^23 + 2490/2401*T^22 + 121/343*T^21 - 2169/2401*T^20 - 
        845/2401*T^19 + 1298/2401*T^18 + 416/343*T^17 + 1040/2401*T^16 - 
        451/2401*T^15 - 926/2401*T^14 - 207/2401*T^13 - 1249/2401*T^12 - 
        433/2401*T^11 - 1037/2401*T^10 - 984/2401*T^9 - 2/7*T^8 - 579/2401*T^7 + 
        933/2401*T^6 + 88/343*T^5 - 913/2401*T^4 - 201/343*T^3 - 6/49*T^2 + 4/7*T + 
        1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 4*X*Y^8 + 5*X*Y^7 + 4*X*Y^5 + 
        5*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 5*X*Y + X + Y^30 + 6*Y^29 + 6*Y^28 + 6*Y^27 + 
        5*Y^26 + Y^25 + 3*Y^24 + 5*Y^22 + Y^21 + Y^20 + Y^19 + 4*Y^18 + 6*Y^16 + 
        3*Y^15 + Y^14 + 5*Y^13 + 4*Y^12 + 5*Y^11 + 4*Y^9 + 5*Y^8 + Y^6 + 5*Y^5 + 
        6*Y^3 + 2*Y + 1,
    T^56 - 8/7*T^55 + 33/49*T^54 + 45/343*T^53 - 1941/2401*T^52 + 823/2401*T^51 + 
        225/2401*T^50 - 1192/2401*T^49 - 51/2401*T^48 - 239/2401*T^47 - 44/343*T^46 
        + 752/2401*T^45 - 240/2401*T^44 + 1562/2401*T^43 - 1205/2401*T^42 + 
        2493/2401*T^41 - 2578/2401*T^40 + 2238/2401*T^39 - 407/2401*T^38 - 
        179/343*T^37 + 688/2401*T^36 - 492/2401*T^35 - 1511/2401*T^34 + 46/343*T^33 
        + 507/2401*T^32 - 1332/2401*T^31 + 319/343*T^30 - 191/343*T^29 + 4/7*T^28 - 
        191/343*T^27 + 319/343*T^26 - 1332/2401*T^25 + 507/2401*T^24 + 46/343*T^23 -
        1511/2401*T^22 - 492/2401*T^21 + 688/2401*T^20 - 179/343*T^19 - 
        407/2401*T^18 + 2238/2401*T^17 - 2578/2401*T^16 + 2493/2401*T^15 - 
        1205/2401*T^14 + 1562/2401*T^13 - 240/2401*T^12 + 752/2401*T^11 - 
        44/343*T^10 - 239/2401*T^9 - 51/2401*T^8 - 1192/2401*T^7 + 225/2401*T^6 + 
        823/2401*T^5 - 1941/2401*T^4 + 45/343*T^3 + 33/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^12 + 4*X*Y^10 + 3*X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 
        6*X*Y^4 + 3*X*Y^3 + X*Y^2 + 5*X*Y + 5*X + 5*Y^30 + 4*Y^29 + Y^28 + 5*Y^27 + 
        Y^26 + 3*Y^25 + 4*Y^24 + 5*Y^23 + 3*Y^22 + 6*Y^21 + 3*Y^20 + 6*Y^19 + 3*Y^18
        + 4*Y^16 + 6*Y^15 + 4*Y^14 + 6*Y^13 + 3*Y^12 + 6*Y^11 + 4*Y^10 + Y^9 + 3*Y^8
        + 6*Y^7 + Y^6 + 2*Y^5 + 4*Y^4 + 5*Y^3 + 6*Y^2 + 5*Y,
    T^56 + 2/7*T^55 - 43/49*T^54 + 34/343*T^53 + 807/2401*T^52 - 2178/2401*T^51 + 
        45/2401*T^50 + 2207/2401*T^49 - 2524/2401*T^48 - 120/2401*T^47 + 
        1593/2401*T^46 - 3411/2401*T^45 - 1844/2401*T^44 + 3379/2401*T^43 + 
        134/2401*T^42 - 453/2401*T^41 + 466/343*T^40 - 2048/2401*T^39 - 156/343*T^38
        + 3266/2401*T^37 - 76/343*T^36 - 1212/2401*T^35 + 3506/2401*T^34 - 
        307/2401*T^33 - 2502/2401*T^32 + 862/2401*T^31 - 2210/2401*T^30 - 
        1017/2401*T^29 + 2351/2401*T^28 - 1017/2401*T^27 - 2210/2401*T^26 + 
        862/2401*T^25 - 2502/2401*T^24 - 307/2401*T^23 + 3506/2401*T^22 - 
        1212/2401*T^21 - 76/343*T^20 + 3266/2401*T^19 - 156/343*T^18 - 
        2048/2401*T^17 + 466/343*T^16 - 453/2401*T^15 + 134/2401*T^14 + 
        3379/2401*T^13 - 1844/2401*T^12 - 3411/2401*T^11 + 1593/2401*T^10 - 
        120/2401*T^9 - 2524/2401*T^8 + 2207/2401*T^7 + 45/2401*T^6 - 2178/2401*T^5 +
        807/2401*T^4 + 34/343*T^3 - 43/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + X*Y^12 + 2*X*Y^11 + X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 
        6*X*Y^7 + 4*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + 3*X*Y + 4*X + Y^30 + Y^29 
        + 4*Y^28 + 3*Y^27 + Y^26 + 3*Y^25 + 5*Y^23 + 2*Y^22 + 5*Y^21 + 3*Y^20 + Y^18
        + 2*Y^17 + 3*Y^15 + 2*Y^13 + Y^12 + 5*Y^11 + 5*Y^10 + 6*Y^9 + 4*Y^8 + 3*Y^7 
        + Y^5 + 5*Y^4 + 2*Y^3 + 3*Y^2 + 3*Y + 6,
    -T^56 + 6/7*T^55 - 4/49*T^54 - 346/343*T^53 + 2603/2401*T^52 - 3655/2401*T^51 + 
        934/2401*T^50 + 1619/2401*T^49 - 3362/2401*T^48 + 1418/2401*T^47 + 
        383/2401*T^46 - 2903/2401*T^45 + 2249/2401*T^44 + 349/2401*T^43 - 
        457/343*T^42 + 3820/2401*T^41 - 2797/2401*T^40 + 25/343*T^39 + 
        1857/2401*T^38 - 2403/2401*T^37 + 633/2401*T^36 - 68/343*T^35 + 
        583/2401*T^34 - 993/2401*T^33 + 629/2401*T^32 - 969/2401*T^31 + 
        102/2401*T^30 + 414/2401*T^29 - 414/2401*T^27 - 102/2401*T^26 + 
        969/2401*T^25 - 629/2401*T^24 + 993/2401*T^23 - 583/2401*T^22 + 68/343*T^21 
        - 633/2401*T^20 + 2403/2401*T^19 - 1857/2401*T^18 - 25/343*T^17 + 
        2797/2401*T^16 - 3820/2401*T^15 + 457/343*T^14 - 349/2401*T^13 - 
        2249/2401*T^12 + 2903/2401*T^11 - 383/2401*T^10 - 1418/2401*T^9 + 
        3362/2401*T^8 - 1619/2401*T^7 - 934/2401*T^6 + 3655/2401*T^5 - 2603/2401*T^4
        + 346/343*T^3 + 4/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 3*X*Y^12 + 4*X*Y^9 + 5*X*Y^8 + 2*X*Y^7 + 4*X*Y^6 + 
        5*X*Y^5 + 5*X*Y^3 + 6*X*Y^2 + 6*X*Y + 4*X + 2*Y^30 + 5*Y^29 + 4*Y^28 + 
        4*Y^27 + 5*Y^26 + 2*Y^25 + 2*Y^24 + 6*Y^22 + Y^20 + 5*Y^19 + 6*Y^18 + 3*Y^17
        + 2*Y^16 + 5*Y^15 + Y^14 + 5*Y^13 + 2*Y^12 + 6*Y^11 + 4*Y^10 + 4*Y^9 + Y^8 +
        2*Y^6 + 3*Y^4 + 6*Y^3 + 6*Y^2 + 6*Y + 4,
    -T^56 + 8/7*T^55 - 6/7*T^54 + 102/343*T^53 + 856/2401*T^52 - 515/2401*T^51 + 
        1706/2401*T^50 - 2451/2401*T^49 + 2413/2401*T^48 - 999/2401*T^47 - 
        1101/2401*T^46 + 1079/2401*T^45 + 114/343*T^44 - 870/2401*T^43 - 
        633/2401*T^42 + 2376/2401*T^41 - 2403/2401*T^40 + 233/343*T^39 - 
        305/343*T^38 + 2185/2401*T^37 - 74/343*T^36 - 2305/2401*T^35 + 
        4404/2401*T^34 - 3321/2401*T^33 + 1116/2401*T^32 - 550/2401*T^31 + 
        100/343*T^30 - 1376/2401*T^29 + 1376/2401*T^27 - 100/343*T^26 + 
        550/2401*T^25 - 1116/2401*T^24 + 3321/2401*T^23 - 4404/2401*T^22 + 
        2305/2401*T^21 + 74/343*T^20 - 2185/2401*T^19 + 305/343*T^18 - 233/343*T^17 
        + 2403/2401*T^16 - 2376/2401*T^15 + 633/2401*T^14 + 870/2401*T^13 - 
        114/343*T^12 - 1079/2401*T^11 + 1101/2401*T^10 + 999/2401*T^9 - 
        2413/2401*T^8 + 2451/2401*T^7 - 1706/2401*T^6 + 515/2401*T^5 - 856/2401*T^4 
        - 102/343*T^3 + 6/7*T^2 - 8/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + X*Y^13 + 6*X*Y^11 + 6*X*Y^10 + X*Y^9 + 6*X*Y^8 + 
        5*X*Y^7 + X*Y^4 + 5*X*Y^3 + X*Y + 5*X + 6*Y^30 + 4*Y^29 + 6*Y^28 + Y^27 + 
        Y^26 + 6*Y^25 + Y^24 + Y^23 + 2*Y^22 + 3*Y^21 + Y^20 + 3*Y^19 + 6*Y^18 + 
        4*Y^17 + 5*Y^16 + 2*Y^15 + 4*Y^14 + 5*Y^12 + Y^10 + 6*Y^9 + 3*Y^8 + Y^7 + 
        4*Y^5 + Y^4 + 4*Y^2 + 4*Y,
    -T^56 + 8/7*T^55 + 12/49*T^54 - 526/343*T^53 + 2405/2401*T^52 + 1402/2401*T^51 -
        3435/2401*T^50 + 1913/2401*T^49 + 41/49*T^48 - 2006/2401*T^47 + 
        232/2401*T^46 + 1835/2401*T^45 - 1927/2401*T^44 - 8/343*T^43 + 
        2126/2401*T^42 - 2501/2401*T^41 + 188/2401*T^40 + 1955/2401*T^39 - 
        2976/2401*T^38 + 771/2401*T^37 + 2307/2401*T^36 - 3516/2401*T^35 + 
        1678/2401*T^34 + 2042/2401*T^33 - 3285/2401*T^32 + 1209/2401*T^31 + 
        2599/2401*T^30 - 3061/2401*T^29 + 3061/2401*T^27 - 2599/2401*T^26 - 
        1209/2401*T^25 + 3285/2401*T^24 - 2042/2401*T^23 - 1678/2401*T^22 + 
        3516/2401*T^21 - 2307/2401*T^20 - 771/2401*T^19 + 2976/2401*T^18 - 
        1955/2401*T^17 - 188/2401*T^16 + 2501/2401*T^15 - 2126/2401*T^14 + 
        8/343*T^13 + 1927/2401*T^12 - 1835/2401*T^11 - 232/2401*T^10 + 2006/2401*T^9
        - 41/49*T^8 - 1913/2401*T^7 + 3435/2401*T^6 - 1402/2401*T^5 - 2405/2401*T^4 
        + 526/343*T^3 - 12/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 
        2*X*Y^8 + X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 3*X*Y + 
        4*Y^30 + 3*Y^29 + 4*Y^28 + Y^26 + 6*Y^25 + 3*Y^24 + 6*Y^23 + 5*Y^22 + 3*Y^21
        + Y^20 + 4*Y^19 + 5*Y^17 + 6*Y^16 + 6*Y^15 + 2*Y^14 + Y^13 + 6*Y^12 + 2*Y^11
        + 4*Y^10 + Y^9 + 3*Y^8 + 4*Y^7 + 2*Y^6 + Y^5 + 6*Y^3 + 2*Y^2 + 4*Y + 6,
    -T^56 + 5/7*T^55 - 4/7*T^54 + 24/49*T^53 + 125/2401*T^52 + 2063/2401*T^51 - 
        789/2401*T^50 + 795/2401*T^49 + 188/2401*T^48 - 1795/2401*T^47 + 
        1132/2401*T^46 - 1759/2401*T^45 + 1564/2401*T^44 - 309/343*T^43 + 
        1906/2401*T^42 - 83/2401*T^41 - 61/2401*T^40 + 561/2401*T^39 - 898/2401*T^38
        + 569/2401*T^37 - 299/343*T^36 + 2319/2401*T^35 - 2323/2401*T^34 + 
        1732/2401*T^33 - 862/2401*T^32 + 173/343*T^31 - 1338/2401*T^30 + 
        961/2401*T^29 - 961/2401*T^27 + 1338/2401*T^26 - 173/343*T^25 + 
        862/2401*T^24 - 1732/2401*T^23 + 2323/2401*T^22 - 2319/2401*T^21 + 
        299/343*T^20 - 569/2401*T^19 + 898/2401*T^18 - 561/2401*T^17 + 61/2401*T^16 
        + 83/2401*T^15 - 1906/2401*T^14 + 309/343*T^13 - 1564/2401*T^12 + 
        1759/2401*T^11 - 1132/2401*T^10 + 1795/2401*T^9 - 188/2401*T^8 - 
        795/2401*T^7 + 789/2401*T^6 - 2063/2401*T^5 - 125/2401*T^4 - 24/49*T^3 + 
        4/7*T^2 - 5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + X*Y^8 + 
        4*X*Y^7 + 6*X*Y^6 + X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 6*X + 3*Y^30 + 4*Y^29 + 
        3*Y^28 + 6*Y^27 + 3*Y^26 + 4*Y^25 + 4*Y^24 + 4*Y^23 + 3*Y^22 + 2*Y^21 + 
        2*Y^20 + 3*Y^19 + 5*Y^18 + 5*Y^16 + Y^15 + 6*Y^14 + Y^13 + 3*Y^12 + 5*Y^11 +
        6*Y^10 + 4*Y^9 + 3*Y^8 + 6*Y^7 + 2*Y^6 + 4*Y^5 + 6*Y^4 + Y^3 + Y^2 + 5*Y + 
        6,
    T^56 - T^55 + 60/49*T^54 - 281/343*T^53 + 400/2401*T^52 + 13/343*T^51 - 
        1635/2401*T^50 + 3573/2401*T^49 - 3037/2401*T^48 + 276/343*T^47 - 
        204/2401*T^46 + 144/2401*T^45 + 358/2401*T^44 - 817/2401*T^43 + 
        857/2401*T^42 - 90/2401*T^41 - 639/2401*T^40 + 5/49*T^39 + 131/343*T^38 - 
        1090/2401*T^37 - 69/2401*T^36 + 75/343*T^35 - 202/2401*T^34 + 932/2401*T^33 
        - 864/2401*T^32 + 523/2401*T^31 - 318/2401*T^30 - 832/2401*T^29 + 
        750/2401*T^28 - 832/2401*T^27 - 318/2401*T^26 + 523/2401*T^25 - 
        864/2401*T^24 + 932/2401*T^23 - 202/2401*T^22 + 75/343*T^21 - 69/2401*T^20 -
        1090/2401*T^19 + 131/343*T^18 + 5/49*T^17 - 639/2401*T^16 - 90/2401*T^15 + 
        857/2401*T^14 - 817/2401*T^13 + 358/2401*T^12 + 144/2401*T^11 - 
        204/2401*T^10 + 276/343*T^9 - 3037/2401*T^8 + 3573/2401*T^7 - 1635/2401*T^6 
        + 13/343*T^5 + 400/2401*T^4 - 281/343*T^3 + 60/49*T^2 - T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 2*X*Y^11 + 6*X*Y^10 + 2*X*Y^8 + 5*X*Y^7 + 6*X*Y^6 + 
        4*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 3*X*Y + 6*X + 2*Y^30 + 6*Y^29 + 
        2*Y^28 + 5*Y^27 + 3*Y^26 + 6*Y^25 + 4*Y^24 + 4*Y^21 + 3*Y^20 + 2*Y^19 + 
        6*Y^18 + 6*Y^17 + 3*Y^16 + 5*Y^14 + 4*Y^13 + 4*Y^12 + 5*Y^11 + 2*Y^10 + Y^8 
        + 6*Y^7 + 2*Y^6 + 3*Y^5 + 5*Y^4 + 4*Y^3 + 3*Y^2 + 5,
    -T^56 - 1/7*T^55 - T^54 - 295/343*T^53 + 62/343*T^52 - 1287/2401*T^51 + 
        99/343*T^50 + 29/49*T^49 + 46/343*T^48 + 830/2401*T^47 - 181/2401*T^46 - 
        369/343*T^45 - 405/343*T^44 - 3509/2401*T^43 - 3333/2401*T^42 - 
        2166/2401*T^41 - 208/2401*T^40 - 2/49*T^39 + 942/2401*T^38 + 2554/2401*T^37 
        + 1075/2401*T^36 + 1016/2401*T^35 + 323/2401*T^34 - 3468/2401*T^33 - 
        2312/2401*T^32 - 2676/2401*T^31 - 3770/2401*T^30 + 11/343*T^29 - 11/343*T^27
        + 3770/2401*T^26 + 2676/2401*T^25 + 2312/2401*T^24 + 3468/2401*T^23 - 
        323/2401*T^22 - 1016/2401*T^21 - 1075/2401*T^20 - 2554/2401*T^19 - 
        942/2401*T^18 + 2/49*T^17 + 208/2401*T^16 + 2166/2401*T^15 + 3333/2401*T^14 
        + 3509/2401*T^13 + 405/343*T^12 + 369/343*T^11 + 181/2401*T^10 - 
        830/2401*T^9 - 46/343*T^8 - 29/49*T^7 - 99/343*T^6 + 1287/2401*T^5 - 
        62/343*T^4 + 295/343*T^3 + T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^13 + 3*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + X*Y^8 + 5*X*Y^7 + 
        3*X*Y^6 + X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 6*X*Y + 6*X + 2*Y^30 + 
        2*Y^29 + 3*Y^28 + 3*Y^27 + 6*Y^26 + Y^25 + 5*Y^24 + 6*Y^23 + 6*Y^22 + 5*Y^21
        + 6*Y^20 + 6*Y^19 + Y^18 + 2*Y^17 + Y^16 + 3*Y^15 + 5*Y^14 + 3*Y^13 + 6*Y^12
        + 4*Y^11 + 6*Y^10 + 4*Y^9 + 2*Y^7 + 2*Y^6 + 5*Y^4 + 2*Y^3 + Y + 5,
    T^56 - T^55 - 10/49*T^54 + 127/343*T^53 - 167/343*T^52 + 614/2401*T^51 - 
        186/2401*T^50 + 249/2401*T^49 + 1420/2401*T^48 - 747/2401*T^47 - 
        1852/2401*T^46 + 1391/2401*T^45 - 103/2401*T^44 - 19/343*T^43 + 
        411/2401*T^42 + 537/2401*T^41 - 304/2401*T^40 - 839/2401*T^39 + 
        188/2401*T^38 - 548/2401*T^37 + 12/343*T^36 + 657/2401*T^35 + 39/2401*T^34 -
        207/2401*T^33 + 475/2401*T^32 - 1091/2401*T^31 + 683/2401*T^30 + 
        1639/2401*T^29 - 3093/2401*T^28 + 1639/2401*T^27 + 683/2401*T^26 - 
        1091/2401*T^25 + 475/2401*T^24 - 207/2401*T^23 + 39/2401*T^22 + 
        657/2401*T^21 + 12/343*T^20 - 548/2401*T^19 + 188/2401*T^18 - 839/2401*T^17 
        - 304/2401*T^16 + 537/2401*T^15 + 411/2401*T^14 - 19/343*T^13 - 
        103/2401*T^12 + 1391/2401*T^11 - 1852/2401*T^10 - 747/2401*T^9 + 
        1420/2401*T^8 + 249/2401*T^7 - 186/2401*T^6 + 614/2401*T^5 - 167/343*T^4 + 
        127/343*T^3 - 10/49*T^2 - T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 
        + 3*X*Y^8 + 2*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + X*Y^2 + 6*X*Y 
        + 4*X + 6*Y^30 + 5*Y^29 + 2*Y^28 + 4*Y^27 + 5*Y^26 + 2*Y^25 + 4*Y^23 + 
        3*Y^22 + 2*Y^21 + 3*Y^20 + Y^19 + Y^18 + Y^17 + 5*Y^16 + 3*Y^15 + Y^14 + 
        3*Y^13 + 2*Y^12 + 6*Y^11 + 3*Y^10 + 6*Y^9 + 2*Y^8 + 4*Y^7 + 3*Y^6 + 5*Y^5 + 
        4*Y^4 + 5*Y^3 + 3*Y + 1,
    T^56 + 17/7*T^55 + 85/49*T^54 + 61/343*T^53 + 655/2401*T^52 + 208/343*T^51 + 
        2/343*T^50 - 244/2401*T^49 + 1182/2401*T^48 + 578/2401*T^47 - 1303/2401*T^46
        - 2708/2401*T^45 - 402/343*T^44 - 615/2401*T^43 - 615/2401*T^42 - 
        3286/2401*T^41 - 2787/2401*T^40 - 750/2401*T^39 - 20/49*T^38 - 
        1665/2401*T^37 - 1163/2401*T^36 - 1094/2401*T^35 - 597/2401*T^34 + 
        649/2401*T^33 + 331/2401*T^32 + 801/2401*T^31 + 2560/2401*T^30 + 
        275/343*T^29 + 768/2401*T^28 + 275/343*T^27 + 2560/2401*T^26 + 801/2401*T^25
        + 331/2401*T^24 + 649/2401*T^23 - 597/2401*T^22 - 1094/2401*T^21 - 
        1163/2401*T^20 - 1665/2401*T^19 - 20/49*T^18 - 750/2401*T^17 - 
        2787/2401*T^16 - 3286/2401*T^15 - 615/2401*T^14 - 615/2401*T^13 - 
        402/343*T^12 - 2708/2401*T^11 - 1303/2401*T^10 + 578/2401*T^9 + 
        1182/2401*T^8 - 244/2401*T^7 + 2/343*T^6 + 208/343*T^5 + 655/2401*T^4 + 
        61/343*T^3 + 85/49*T^2 + 17/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + X*Y^11 + 2*X*Y^10 + 2*X*Y^8 + 
        5*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + X*Y^4 + X*Y^3 + 2*X*Y^2 + 5*X*Y + 4*X + 3*Y^30
        + 3*Y^29 + 3*Y^27 + 2*Y^26 + Y^25 + 5*Y^24 + 4*Y^23 + Y^22 + Y^21 + 2*Y^20 +
        6*Y^19 + 2*Y^18 + 5*Y^17 + 5*Y^15 + 6*Y^14 + 3*Y^13 + 5*Y^12 + 6*Y^11 + 
        5*Y^9 + 2*Y^8 + Y^7 + 3*Y^6 + 3*Y^4 + 6*Y^3 + 5*Y^2 + 4*Y + 3,
    -T^56 + 3/7*T^55 + 3/49*T^54 - 74/343*T^53 + 2389/2401*T^52 - 1083/2401*T^51 + 
        944/2401*T^50 - 761/2401*T^49 - 1462/2401*T^48 + 628/2401*T^47 - 
        1367/2401*T^46 + 1373/2401*T^45 + 141/2401*T^44 + 25/343*T^43 + 
        788/2401*T^42 - 1791/2401*T^41 + 1028/2401*T^40 - 802/2401*T^39 - 
        450/2401*T^38 + 629/2401*T^37 - 20/49*T^36 + 1318/2401*T^35 - 60/343*T^34 - 
        33/2401*T^33 + 762/2401*T^32 - 1487/2401*T^31 + 710/2401*T^30 - 
        972/2401*T^29 + 972/2401*T^27 - 710/2401*T^26 + 1487/2401*T^25 - 
        762/2401*T^24 + 33/2401*T^23 + 60/343*T^22 - 1318/2401*T^21 + 20/49*T^20 - 
        629/2401*T^19 + 450/2401*T^18 + 802/2401*T^17 - 1028/2401*T^16 + 
        1791/2401*T^15 - 788/2401*T^14 - 25/343*T^13 - 141/2401*T^12 - 
        1373/2401*T^11 + 1367/2401*T^10 - 628/2401*T^9 + 1462/2401*T^8 + 
        761/2401*T^7 - 944/2401*T^6 + 1083/2401*T^5 - 2389/2401*T^4 + 74/343*T^3 - 
        3/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + X*Y^12 + X*Y^11 + X*Y^10 + 5*X*Y^9 + 
        4*X*Y^8 + 4*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + X*Y^2 + 3*X*Y + 
        6*Y^30 + 4*Y^28 + 2*Y^27 + Y^26 + Y^25 + 3*Y^23 + Y^22 + 3*Y^21 + 2*Y^20 + 
        2*Y^19 + 5*Y^18 + 3*Y^17 + Y^16 + 4*Y^15 + 5*Y^14 + 6*Y^13 + Y^12 + Y^11 + 
        4*Y^10 + Y^9 + 2*Y^8 + 6*Y^7 + Y^6 + 5*Y^5 + 5*Y^4 + Y^3 + 4*Y + 1,
    -T^56 - 46/49*T^54 - 247/343*T^53 - 1621/2401*T^52 - 1448/2401*T^51 - 
        1858/2401*T^50 - 50/343*T^49 + 1177/2401*T^48 - 173/343*T^47 + 
        1828/2401*T^46 + 992/2401*T^45 + 1294/2401*T^44 - 90/2401*T^43 + 
        2272/2401*T^42 - 852/2401*T^41 + 8/2401*T^40 + 1091/2401*T^39 + 
        367/2401*T^38 - 89/2401*T^37 + 1627/2401*T^36 + 1961/2401*T^35 + 
        1077/2401*T^34 + 3399/2401*T^33 + 1793/2401*T^32 + 2225/2401*T^31 + 
        902/2401*T^30 + 1557/2401*T^29 - 1557/2401*T^27 - 902/2401*T^26 - 
        2225/2401*T^25 - 1793/2401*T^24 - 3399/2401*T^23 - 1077/2401*T^22 - 
        1961/2401*T^21 - 1627/2401*T^20 + 89/2401*T^19 - 367/2401*T^18 - 
        1091/2401*T^17 - 8/2401*T^16 + 852/2401*T^15 - 2272/2401*T^14 + 90/2401*T^13
        - 1294/2401*T^12 - 992/2401*T^11 - 1828/2401*T^10 + 173/343*T^9 - 
        1177/2401*T^8 + 50/343*T^7 + 1858/2401*T^6 + 1448/2401*T^5 + 1621/2401*T^4 +
        247/343*T^3 + 46/49*T^2 + 1
*], [*
    X^3 + 4*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + X*Y^7 + 
        5*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + X*Y^3 + 2*X*Y^2 + 2*X*Y + 6*X + 3*Y^30 + 
        6*Y^29 + 3*Y^28 + 5*Y^27 + 4*Y^26 + 6*Y^25 + 2*Y^24 + Y^23 + 5*Y^22 + 5*Y^21
        + 6*Y^20 + Y^19 + 2*Y^18 + Y^17 + 2*Y^16 + 5*Y^15 + 5*Y^14 + 3*Y^13 + 3*Y^11
        + 3*Y^9 + 6*Y^8 + 5*Y^7 + 5*Y^6 + 5*Y^5 + 5*Y^4 + 5*Y^2 + 4*Y + 4,
    T^56 - 13/7*T^55 + 73/49*T^54 - 282/343*T^53 - 2484/2401*T^52 + 6555/2401*T^51 -
        6044/2401*T^50 + 4934/2401*T^49 - 2497/2401*T^48 - 20/49*T^47 + 384/343*T^46
        - 544/343*T^45 + 4455/2401*T^44 - 3123/2401*T^43 + 1159/2401*T^42 - 
        1063/2401*T^41 + 1390/2401*T^40 - 429/2401*T^39 - 684/2401*T^38 + 66/49*T^37
        - 6005/2401*T^36 + 5136/2401*T^35 - 46/49*T^34 + 711/2401*T^33 + 99/343*T^32
        - 1595/2401*T^31 + 1814/2401*T^30 - 3445/2401*T^29 + 4819/2401*T^28 - 
        3445/2401*T^27 + 1814/2401*T^26 - 1595/2401*T^25 + 99/343*T^24 + 
        711/2401*T^23 - 46/49*T^22 + 5136/2401*T^21 - 6005/2401*T^20 + 66/49*T^19 - 
        684/2401*T^18 - 429/2401*T^17 + 1390/2401*T^16 - 1063/2401*T^15 + 
        1159/2401*T^14 - 3123/2401*T^13 + 4455/2401*T^12 - 544/343*T^11 + 
        384/343*T^10 - 20/49*T^9 - 2497/2401*T^8 + 4934/2401*T^7 - 6044/2401*T^6 + 
        6555/2401*T^5 - 2484/2401*T^4 - 282/343*T^3 + 73/49*T^2 - 13/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 
        + 2*X*Y^8 + 4*X*Y^7 + 5*X*Y^5 + 5*X*Y^4 + X*Y^3 + 5*X*Y^2 + 3*X*Y + 4*X + 
        Y^30 + 4*Y^29 + Y^28 + Y^26 + 3*Y^25 + 5*Y^23 + 2*Y^22 + Y^20 + 4*Y^19 + 
        2*Y^18 + 3*Y^17 + 5*Y^16 + 2*Y^15 + 2*Y^14 + 2*Y^12 + 5*Y^11 + 3*Y^10 + Y^9 
        + Y^8 + 6*Y^7 + Y^6 + 2*Y^4 + 4*Y^3 + 6*Y^2 + Y,
    -T^56 + 15/7*T^55 - 60/49*T^54 + 29/49*T^53 - 4425/2401*T^52 + 4565/2401*T^51 - 
        27/49*T^50 + 1751/2401*T^49 - 4940/2401*T^48 + 3323/2401*T^47 + 
        729/2401*T^46 + 2119/2401*T^45 - 4833/2401*T^44 - 108/2401*T^43 + 
        1994/2401*T^42 + 2068/2401*T^41 - 2753/2401*T^40 - 694/2401*T^39 + 
        678/2401*T^38 + 2433/2401*T^37 - 449/2401*T^36 - 2909/2401*T^35 + 
        890/2401*T^34 + 795/2401*T^33 + 31/343*T^32 - 160/343*T^31 + 706/2401*T^30 +
        631/2401*T^29 - 631/2401*T^27 - 706/2401*T^26 + 160/343*T^25 - 31/343*T^24 -
        795/2401*T^23 - 890/2401*T^22 + 2909/2401*T^21 + 449/2401*T^20 - 
        2433/2401*T^19 - 678/2401*T^18 + 694/2401*T^17 + 2753/2401*T^16 - 
        2068/2401*T^15 - 1994/2401*T^14 + 108/2401*T^13 + 4833/2401*T^12 - 
        2119/2401*T^11 - 729/2401*T^10 - 3323/2401*T^9 + 4940/2401*T^8 - 
        1751/2401*T^7 + 27/49*T^6 - 4565/2401*T^5 + 4425/2401*T^4 - 29/49*T^3 + 
        60/49*T^2 - 15/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 5*X*Y^9 + 3*X*Y^8 + 3*X*Y^7 + 
        3*X*Y^6 + X*Y^5 + 5*X*Y^3 + 3*X*Y + 6*X + 3*Y^30 + 2*Y^29 + 3*Y^28 + 5*Y^27 
        + 4*Y^26 + 2*Y^25 + 2*Y^24 + 2*Y^23 + 5*Y^22 + 6*Y^21 + Y^20 + 4*Y^19 + 
        2*Y^17 + 3*Y^16 + 2*Y^14 + 6*Y^13 + 6*Y^12 + 2*Y^11 + 3*Y^10 + 3*Y^7 + 4*Y^5
        + 4*Y^4 + 5*Y^2 + 2*Y + 5,
    T^56 - 10/7*T^55 + 4/49*T^54 + 208/343*T^53 + 32/2401*T^52 + 530/2401*T^51 - 
        1919/2401*T^50 + 1485/2401*T^49 - 2260/2401*T^48 + 2382/2401*T^47 + 
        60/343*T^46 - 93/343*T^45 - 1679/2401*T^44 - 325/2401*T^43 + 3221/2401*T^42 
        - 1915/2401*T^41 + 254/2401*T^40 - 740/2401*T^39 + 1160/2401*T^38 - 
        1012/2401*T^37 + 736/2401*T^36 + 61/343*T^35 - 166/343*T^34 + 243/2401*T^33 
        + 16/2401*T^32 + 1265/2401*T^31 - 1810/2401*T^30 - 228/2401*T^29 + 
        1878/2401*T^28 - 228/2401*T^27 - 1810/2401*T^26 + 1265/2401*T^25 + 
        16/2401*T^24 + 243/2401*T^23 - 166/343*T^22 + 61/343*T^21 + 736/2401*T^20 - 
        1012/2401*T^19 + 1160/2401*T^18 - 740/2401*T^17 + 254/2401*T^16 - 
        1915/2401*T^15 + 3221/2401*T^14 - 325/2401*T^13 - 1679/2401*T^12 - 
        93/343*T^11 + 60/343*T^10 + 2382/2401*T^9 - 2260/2401*T^8 + 1485/2401*T^7 - 
        1919/2401*T^6 + 530/2401*T^5 + 32/2401*T^4 + 208/343*T^3 + 4/49*T^2 - 10/7*T
        + 1
*], [*
    X^3 + 6*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + X*Y^9 + X*Y^8 + 
        4*X*Y^5 + 5*X*Y^4 + X*Y^3 + 6*X*Y^2 + 2*X*Y + 3*X + 3*Y^30 + 5*Y^29 + 3*Y^28
        + 3*Y^27 + 3*Y^26 + 3*Y^25 + 5*Y^24 + 2*Y^22 + 6*Y^21 + 3*Y^19 + 6*Y^18 + 
        5*Y^17 + 5*Y^16 + 4*Y^15 + Y^14 + 5*Y^13 + 5*Y^12 + 3*Y^9 + 5*Y^8 + 6*Y^7 + 
        5*Y^5 + 5*Y^4 + 5*Y^3 + 5*Y^2 + 5*Y + 5,
    T^56 - 13/7*T^55 + 60/49*T^54 - 4/49*T^53 - 2363/2401*T^52 + 4607/2401*T^51 - 
        4817/2401*T^50 + 3240/2401*T^49 - 878/2401*T^48 - 1312/2401*T^47 + 
        1305/2401*T^46 - 2070/2401*T^45 + 3802/2401*T^44 - 3932/2401*T^43 + 
        3018/2401*T^42 - 2019/2401*T^41 - 1187/2401*T^40 + 713/343*T^39 - 
        6486/2401*T^38 + 5470/2401*T^37 - 207/343*T^36 - 2382/2401*T^35 + 
        3259/2401*T^34 - 475/343*T^33 + 53/49*T^32 - 142/2401*T^31 - 351/2401*T^30 +
        340/2401*T^29 - 1060/2401*T^28 + 340/2401*T^27 - 351/2401*T^26 - 
        142/2401*T^25 + 53/49*T^24 - 475/343*T^23 + 3259/2401*T^22 - 2382/2401*T^21 
        - 207/343*T^20 + 5470/2401*T^19 - 6486/2401*T^18 + 713/343*T^17 - 
        1187/2401*T^16 - 2019/2401*T^15 + 3018/2401*T^14 - 3932/2401*T^13 + 
        3802/2401*T^12 - 2070/2401*T^11 + 1305/2401*T^10 - 1312/2401*T^9 - 
        878/2401*T^8 + 3240/2401*T^7 - 4817/2401*T^6 + 4607/2401*T^5 - 2363/2401*T^4
        - 4/49*T^3 + 60/49*T^2 - 13/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + 6*X*Y^7 + 6*X*Y^6 + 
        5*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + X*Y^2 + 2*X*Y + 4*X + 4*Y^30 + 3*Y^29 + 4*Y^28
        + 6*Y^27 + 3*Y^26 + 4*Y^24 + 3*Y^23 + 2*Y^22 + 6*Y^21 + 3*Y^20 + 4*Y^19 + 
        Y^18 + Y^17 + 6*Y^16 + 3*Y^15 + 5*Y^14 + 5*Y^11 + 2*Y^10 + 2*Y^9 + 5*Y^8 + 
        5*Y^7 + 4*Y^6 + 2*Y^5 + 6*Y^4 + 5*Y^3 + 4*Y^2 + 4,
    -T^56 - 8/7*T^55 - 82/49*T^54 - 291/343*T^53 - 1128/2401*T^52 + 2236/2401*T^51 +
        1376/2401*T^50 + 2529/2401*T^49 + 1282/2401*T^48 - 83/2401*T^47 - 
        1985/2401*T^46 - 2246/2401*T^45 - 2357/2401*T^44 - 201/343*T^43 - 
        332/2401*T^42 - 309/2401*T^41 - 73/343*T^40 + 729/2401*T^39 + 990/2401*T^38 
        + 265/343*T^37 + 2610/2401*T^36 + 1641/2401*T^35 + 989/2401*T^34 - 
        1104/2401*T^33 - 2178/2401*T^32 - 3814/2401*T^31 - 2587/2401*T^30 - 
        2064/2401*T^29 + 2064/2401*T^27 + 2587/2401*T^26 + 3814/2401*T^25 + 
        2178/2401*T^24 + 1104/2401*T^23 - 989/2401*T^22 - 1641/2401*T^21 - 
        2610/2401*T^20 - 265/343*T^19 - 990/2401*T^18 - 729/2401*T^17 + 73/343*T^16 
        + 309/2401*T^15 + 332/2401*T^14 + 201/343*T^13 + 2357/2401*T^12 + 
        2246/2401*T^11 + 1985/2401*T^10 + 83/2401*T^9 - 1282/2401*T^8 - 
        2529/2401*T^7 - 1376/2401*T^6 - 2236/2401*T^5 + 1128/2401*T^4 + 291/343*T^3 
        + 82/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 
        + X*Y^8 + 5*X*Y^7 + X*Y^6 + X*Y^5 + X*Y^3 + 5*X*Y^2 + 5*X*Y + 5*X + 5*Y^30 +
        2*Y^29 + Y^28 + 5*Y^27 + 5*Y^26 + 5*Y^25 + 4*Y^24 + 5*Y^23 + 5*Y^22 + 4*Y^21
        + Y^20 + 6*Y^19 + 2*Y^18 + 5*Y^16 + 2*Y^15 + 4*Y^14 + 5*Y^13 + 2*Y^11 + 
        3*Y^10 + Y^8 + Y^7 + 5*Y^6 + 3*Y^5 + 3*Y^4 + 6*Y^3 + 2*Y^2 + 4*Y + 5,
    T^56 - 5/7*T^55 + 3/49*T^54 + 69/343*T^53 - 1583/2401*T^52 - 320/2401*T^51 + 
        298/2401*T^50 - 696/2401*T^49 + 1312/2401*T^48 + 815/2401*T^47 + 
        80/2401*T^46 + 370/2401*T^45 - 283/2401*T^44 - 705/2401*T^43 - 30/2401*T^42 
        - 1061/2401*T^41 + 239/2401*T^40 + 1146/2401*T^39 - 149/2401*T^38 + 
        640/2401*T^37 + 526/2401*T^36 - 34/343*T^35 - 394/2401*T^34 + 183/2401*T^33 
        - 2069/2401*T^32 + 1105/2401*T^31 - 383/2401*T^30 + 400/2401*T^29 + 
        1266/2401*T^28 + 400/2401*T^27 - 383/2401*T^26 + 1105/2401*T^25 - 
        2069/2401*T^24 + 183/2401*T^23 - 394/2401*T^22 - 34/343*T^21 + 526/2401*T^20
        + 640/2401*T^19 - 149/2401*T^18 + 1146/2401*T^17 + 239/2401*T^16 - 
        1061/2401*T^15 - 30/2401*T^14 - 705/2401*T^13 - 283/2401*T^12 + 
        370/2401*T^11 + 80/2401*T^10 + 815/2401*T^9 + 1312/2401*T^8 - 696/2401*T^7 +
        298/2401*T^6 - 320/2401*T^5 - 1583/2401*T^4 + 69/343*T^3 + 3/49*T^2 - 5/7*T 
        + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 6*X*Y^8 + 
        3*X*Y^7 + X*Y^6 + 6*X*Y^5 + X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 4*X*Y + 2*Y^30 + 
        Y^29 + 4*Y^28 + 5*Y^27 + 3*Y^26 + 6*Y^25 + 6*Y^24 + 3*Y^23 + 5*Y^22 + 2*Y^21
        + Y^20 + 4*Y^19 + 5*Y^18 + 4*Y^17 + 4*Y^16 + 5*Y^15 + 6*Y^14 + 6*Y^13 + 
        6*Y^12 + 6*Y^11 + 5*Y^9 + 4*Y^8 + 6*Y^6 + 3*Y^5 + 3*Y^4 + 5*Y^3 + 5*Y^2 + 
        3*Y + 4,
    T^56 + 8/7*T^55 + 40/49*T^54 + 62/343*T^53 - 2235/2401*T^52 - 660/343*T^51 - 
        4919/2401*T^50 - 1755/2401*T^49 + 354/2401*T^48 + 2421/2401*T^47 + 
        3467/2401*T^46 + 404/343*T^45 + 1053/2401*T^44 + 44/343*T^43 - 402/2401*T^42
        - 1145/2401*T^41 - 1779/2401*T^40 - 1317/2401*T^39 - 1317/2401*T^38 - 
        116/343*T^37 + 100/343*T^36 + 1095/2401*T^35 + 197/343*T^34 + 1663/2401*T^33
        + 1510/2401*T^32 + 97/2401*T^31 - 86/343*T^30 - 202/343*T^29 - 270/343*T^28 
        - 202/343*T^27 - 86/343*T^26 + 97/2401*T^25 + 1510/2401*T^24 + 
        1663/2401*T^23 + 197/343*T^22 + 1095/2401*T^21 + 100/343*T^20 - 116/343*T^19
        - 1317/2401*T^18 - 1317/2401*T^17 - 1779/2401*T^16 - 1145/2401*T^15 - 
        402/2401*T^14 + 44/343*T^13 + 1053/2401*T^12 + 404/343*T^11 + 3467/2401*T^10
        + 2421/2401*T^9 + 354/2401*T^8 - 1755/2401*T^7 - 4919/2401*T^6 - 660/343*T^5
        - 2235/2401*T^4 + 62/343*T^3 + 40/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 
        6*X*Y^8 + 2*X*Y^7 + 4*X*Y^6 + 4*X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + 5*X*Y + 3*X + 
        Y^30 + 2*Y^29 + 2*Y^28 + 6*Y^27 + 4*Y^26 + 6*Y^25 + 3*Y^24 + 6*Y^23 + 3*Y^21
        + 4*Y^20 + 2*Y^19 + 3*Y^18 + 3*Y^16 + 4*Y^15 + 3*Y^14 + 2*Y^13 + 3*Y^12 + 
        2*Y^11 + 5*Y^10 + 4*Y^9 + 3*Y^8 + 2*Y^7 + 3*Y^6 + 5*Y^5 + Y^4 + Y^2 + 3*Y + 
        1,
    -T^56 + 8/7*T^55 - 25/49*T^54 + 20/343*T^53 + 2514/2401*T^52 - 402/343*T^51 + 
        2189/2401*T^50 - 765/2401*T^49 - 1126/2401*T^48 + 179/343*T^47 - 4/343*T^46 
        - 958/2401*T^45 + 534/2401*T^44 + 53/343*T^43 - 89/343*T^42 - 2/343*T^41 + 
        444/2401*T^40 + 31/343*T^39 - 403/2401*T^38 + 656/2401*T^37 - 935/2401*T^36 
        + 699/2401*T^35 + 435/2401*T^34 - 1205/2401*T^33 + 1360/2401*T^32 - 
        300/343*T^31 + 153/343*T^30 - 1256/2401*T^29 + 1256/2401*T^27 - 153/343*T^26
        + 300/343*T^25 - 1360/2401*T^24 + 1205/2401*T^23 - 435/2401*T^22 - 
        699/2401*T^21 + 935/2401*T^20 - 656/2401*T^19 + 403/2401*T^18 - 31/343*T^17 
        - 444/2401*T^16 + 2/343*T^15 + 89/343*T^14 - 53/343*T^13 - 534/2401*T^12 + 
        958/2401*T^11 + 4/343*T^10 - 179/343*T^9 + 1126/2401*T^8 + 765/2401*T^7 - 
        2189/2401*T^6 + 402/343*T^5 - 2514/2401*T^4 - 20/343*T^3 + 25/49*T^2 - 8/7*T
        + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 6*X*Y^8 + 
        6*X*Y^7 + 2*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + X*Y^2 + X*Y + 5*Y^30 + 3*Y^29 + 
        4*Y^28 + 5*Y^27 + 2*Y^26 + 6*Y^23 + 2*Y^22 + 6*Y^21 + Y^20 + 6*Y^19 + 4*Y^17
        + Y^16 + 6*Y^15 + 4*Y^14 + Y^13 + 6*Y^12 + 5*Y^11 + 2*Y^10 + 2*Y^9 + 2*Y^8 +
        4*Y^7 + 4*Y^6 + 4*Y^4 + 6*Y^3 + 3*Y^2 + Y + 3,
    -T^56 + 9/7*T^55 + 25/49*T^54 - 481/343*T^53 + 3497/2401*T^52 - 2626/2401*T^51 -
        324/343*T^50 + 5638/2401*T^49 - 2320/2401*T^48 - 2363/2401*T^47 + 
        2497/2401*T^46 - 2432/2401*T^45 + 1910/2401*T^44 + 2323/2401*T^43 - 
        2924/2401*T^42 + 345/2401*T^41 + 381/2401*T^40 - 51/2401*T^39 + 
        1222/2401*T^38 - 1249/2401*T^37 - 2533/2401*T^36 + 274/343*T^35 + 
        328/343*T^34 - 3014/2401*T^33 + 1535/2401*T^32 + 5/343*T^31 - 3398/2401*T^30
        + 5829/2401*T^29 - 5829/2401*T^27 + 3398/2401*T^26 - 5/343*T^25 - 
        1535/2401*T^24 + 3014/2401*T^23 - 328/343*T^22 - 274/343*T^21 + 
        2533/2401*T^20 + 1249/2401*T^19 - 1222/2401*T^18 + 51/2401*T^17 - 
        381/2401*T^16 - 345/2401*T^15 + 2924/2401*T^14 - 2323/2401*T^13 - 
        1910/2401*T^12 + 2432/2401*T^11 - 2497/2401*T^10 + 2363/2401*T^9 + 
        2320/2401*T^8 - 5638/2401*T^7 + 324/343*T^6 + 2626/2401*T^5 - 3497/2401*T^4 
        + 481/343*T^3 - 25/49*T^2 - 9/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 4*X*Y^12 + 3*X*Y^11 + X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 
        2*X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + X*Y^3 + 3*X*Y^2 + 2*X*Y + 2*X + 6*Y^30 + 
        3*Y^29 + 6*Y^28 + 4*Y^25 + 4*Y^24 + 3*Y^23 + 2*Y^22 + 4*Y^20 + 3*Y^19 + 
        4*Y^18 + 3*Y^16 + 5*Y^15 + 3*Y^14 + 3*Y^13 + 4*Y^12 + 4*Y^11 + 5*Y^9 + 2*Y^8
        + 3*Y^7 + Y^6 + Y^5 + 6*Y^4 + 3*Y^2 + 5*Y + 3,
    -T^56 - 3/7*T^55 + 2/7*T^54 - 11/343*T^53 - 1451/2401*T^52 + 25/2401*T^51 - 
        72/343*T^50 - 872/2401*T^49 + 29/2401*T^48 + 81/2401*T^47 - 1760/2401*T^46 +
        9/2401*T^45 + 185/2401*T^44 - 624/2401*T^43 - 233/2401*T^42 + 15/49*T^41 + 
        128/2401*T^40 + 955/2401*T^39 + 1453/2401*T^38 - 114/2401*T^37 + 
        537/2401*T^36 + 2182/2401*T^35 + 72/2401*T^34 - 698/2401*T^33 + 
        992/2401*T^32 + 164/2401*T^31 + 75/2401*T^30 + 1233/2401*T^29 - 
        1233/2401*T^27 - 75/2401*T^26 - 164/2401*T^25 - 992/2401*T^24 + 
        698/2401*T^23 - 72/2401*T^22 - 2182/2401*T^21 - 537/2401*T^20 + 
        114/2401*T^19 - 1453/2401*T^18 - 955/2401*T^17 - 128/2401*T^16 - 15/49*T^15 
        + 233/2401*T^14 + 624/2401*T^13 - 185/2401*T^12 - 9/2401*T^11 + 
        1760/2401*T^10 - 81/2401*T^9 - 29/2401*T^8 + 872/2401*T^7 + 72/343*T^6 - 
        25/2401*T^5 + 1451/2401*T^4 + 11/343*T^3 - 2/7*T^2 + 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 3*X*Y^8 +
        5*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 3*X*Y + 6*X + 
        2*Y^30 + 5*Y^29 + 5*Y^28 + 6*Y^27 + 2*Y^26 + 2*Y^25 + 5*Y^24 + 3*Y^23 + Y^21
        + 5*Y^19 + Y^17 + 6*Y^16 + 2*Y^15 + 6*Y^14 + Y^13 + 4*Y^12 + 6*Y^11 + 5*Y^10
        + Y^9 + 5*Y^8 + 2*Y^7 + 2*Y^6 + 2*Y^3 + 2*Y^2 + 2*Y + 5,
    T^56 + 9/7*T^55 + 3/49*T^54 - 44/343*T^53 - 101/2401*T^52 - 142/343*T^51 - 
        655/2401*T^50 - 677/2401*T^49 + 180/2401*T^48 + 137/343*T^47 - 
        1334/2401*T^46 - 900/2401*T^45 + 795/2401*T^44 + 295/2401*T^43 - 
        230/2401*T^42 - 954/2401*T^41 - 309/2401*T^40 + 766/2401*T^39 + 
        339/2401*T^38 + 1198/2401*T^37 + 1993/2401*T^36 + 349/2401*T^35 - 
        95/343*T^34 - 1123/2401*T^33 - 941/2401*T^32 - 317/2401*T^31 - 
        1166/2401*T^30 - 4/7*T^29 - 890/2401*T^28 - 4/7*T^27 - 1166/2401*T^26 - 
        317/2401*T^25 - 941/2401*T^24 - 1123/2401*T^23 - 95/343*T^22 + 349/2401*T^21
        + 1993/2401*T^20 + 1198/2401*T^19 + 339/2401*T^18 + 766/2401*T^17 - 
        309/2401*T^16 - 954/2401*T^15 - 230/2401*T^14 + 295/2401*T^13 + 
        795/2401*T^12 - 900/2401*T^11 - 1334/2401*T^10 + 137/343*T^9 + 180/2401*T^8 
        - 677/2401*T^7 - 655/2401*T^6 - 142/343*T^5 - 101/2401*T^4 - 44/343*T^3 + 
        3/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 6*X*Y^10 + 4*X*Y^9 + 2*X*Y^8 +
        2*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + X*Y^2 + 5*X*Y + 2*Y^30 + 3*Y^28 + 6*Y^26 + 
        5*Y^25 + 6*Y^24 + 3*Y^23 + 3*Y^22 + 4*Y^20 + 6*Y^19 + 4*Y^18 + Y^17 + 6*Y^15
        + 6*Y^14 + 5*Y^13 + 2*Y^12 + 3*Y^11 + Y^10 + Y^9 + Y^8 + 3*Y^7 + 4*Y^5 + 
        2*Y^4 + 4*Y^2 + Y + 6,
    -T^56 + 1/7*T^55 - 30/49*T^54 + 34/343*T^53 + 2564/2401*T^52 + 1207/2401*T^51 + 
        753/2401*T^50 + 1723/2401*T^49 - 2417/2401*T^48 - 718/2401*T^47 - 
        482/2401*T^46 - 467/2401*T^45 + 342/343*T^44 + 2642/2401*T^43 + 
        1285/2401*T^42 + 327/2401*T^41 - 2454/2401*T^40 - 474/343*T^39 - 
        3282/2401*T^38 - 1019/2401*T^37 + 892/2401*T^36 + 2455/2401*T^35 + 
        2869/2401*T^34 + 1894/2401*T^33 - 174/343*T^32 - 2025/2401*T^31 - 
        3043/2401*T^30 - 2110/2401*T^29 + 2110/2401*T^27 + 3043/2401*T^26 + 
        2025/2401*T^25 + 174/343*T^24 - 1894/2401*T^23 - 2869/2401*T^22 - 
        2455/2401*T^21 - 892/2401*T^20 + 1019/2401*T^19 + 3282/2401*T^18 + 
        474/343*T^17 + 2454/2401*T^16 - 327/2401*T^15 - 1285/2401*T^14 - 
        2642/2401*T^13 - 342/343*T^12 + 467/2401*T^11 + 482/2401*T^10 + 718/2401*T^9
        + 2417/2401*T^8 - 1723/2401*T^7 - 753/2401*T^6 - 1207/2401*T^5 - 
        2564/2401*T^4 - 34/343*T^3 + 30/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        6*X*Y^8 + 3*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + X*Y + 
        5*X + Y^30 + 2*Y^28 + 3*Y^27 + 3*Y^26 + 5*Y^25 + 2*Y^24 + 4*Y^23 + 6*Y^22 + 
        2*Y^21 + 3*Y^20 + 5*Y^17 + 2*Y^16 + 6*Y^14 + 4*Y^13 + 3*Y^11 + 3*Y^10 + Y^8 
        + 5*Y^7 + 6*Y^6 + 4*Y^5 + 6*Y^4 + 5*Y^3 + 3*Y^2 + 6,
    -T^56 - 11/7*T^55 - 33/49*T^54 - 11/49*T^53 - 86/343*T^52 + 36/2401*T^51 + 
        1010/2401*T^50 + 1504/2401*T^49 + 925/2401*T^48 + 1084/2401*T^47 + 
        167/343*T^46 + 113/343*T^45 + 1263/2401*T^44 - 72/2401*T^43 - 2060/2401*T^42
        - 2000/2401*T^41 - 806/2401*T^40 + 55/2401*T^39 + 2/343*T^38 - 10/2401*T^37 
        - 4/49*T^36 - 244/2401*T^35 + 731/2401*T^34 + 1308/2401*T^33 + 
        1072/2401*T^32 + 428/2401*T^31 + 907/2401*T^30 + 1712/2401*T^29 - 
        1712/2401*T^27 - 907/2401*T^26 - 428/2401*T^25 - 1072/2401*T^24 - 
        1308/2401*T^23 - 731/2401*T^22 + 244/2401*T^21 + 4/49*T^20 + 10/2401*T^19 - 
        2/343*T^18 - 55/2401*T^17 + 806/2401*T^16 + 2000/2401*T^15 + 2060/2401*T^14 
        + 72/2401*T^13 - 1263/2401*T^12 - 113/343*T^11 - 167/343*T^10 - 
        1084/2401*T^9 - 925/2401*T^8 - 1504/2401*T^7 - 1010/2401*T^6 - 36/2401*T^5 +
        86/343*T^4 + 11/49*T^3 + 33/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 2*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 3*X*Y^9 + 5*X*Y^7 + X*Y^6 + 
        X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 2*X*Y + X + 5*Y^30 + 5*Y^29 + Y^27 + 
        4*Y^26 + 2*Y^25 + 2*Y^24 + 3*Y^23 + 3*Y^21 + Y^20 + 6*Y^19 + 3*Y^18 + 6*Y^17
        + 4*Y^16 + 5*Y^13 + 3*Y^12 + 2*Y^11 + 4*Y^10 + 6*Y^9 + 2*Y^8 + 4*Y^7 + Y^6 +
        Y^5 + Y^4 + 5*Y^3 + 5*Y^2 + 3*Y + 4,
    T^56 - 6/7*T^55 + 40/49*T^54 - 208/343*T^53 + 596/2401*T^52 + 1270/2401*T^51 - 
        3407/2401*T^50 + 3281/2401*T^49 - 2059/2401*T^48 + 839/2401*T^47 + 
        1768/2401*T^46 - 2851/2401*T^45 + 4694/2401*T^44 - 575/343*T^43 + 
        2021/2401*T^42 - 467/2401*T^41 - 1615/2401*T^40 + 403/343*T^39 - 
        3845/2401*T^38 + 2700/2401*T^37 - 849/2401*T^36 - 419/2401*T^35 + 
        1110/2401*T^34 - 1999/2401*T^33 + 1770/2401*T^32 - 906/2401*T^31 - 
        573/2401*T^30 + 715/2401*T^29 - 1390/2401*T^28 + 715/2401*T^27 - 
        573/2401*T^26 - 906/2401*T^25 + 1770/2401*T^24 - 1999/2401*T^23 + 
        1110/2401*T^22 - 419/2401*T^21 - 849/2401*T^20 + 2700/2401*T^19 - 
        3845/2401*T^18 + 403/343*T^17 - 1615/2401*T^16 - 467/2401*T^15 + 
        2021/2401*T^14 - 575/343*T^13 + 4694/2401*T^12 - 2851/2401*T^11 + 
        1768/2401*T^10 + 839/2401*T^9 - 2059/2401*T^8 + 3281/2401*T^7 - 
        3407/2401*T^6 + 1270/2401*T^5 + 596/2401*T^4 - 208/343*T^3 + 40/49*T^2 - 
        6/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 4*X*Y^13 + 3*X*Y^11 + 2*X*Y^10 + 4*X*Y^9 + 3*X*Y^8 + 
        5*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 2*X*Y^3 + 3*X*Y^2 + 5*X*Y + 5*X + 2*Y^30 + 
        4*Y^29 + 5*Y^28 + 6*Y^27 + 6*Y^26 + Y^25 + Y^24 + 6*Y^23 + 4*Y^22 + 4*Y^20 +
        6*Y^19 + 3*Y^18 + 5*Y^17 + 4*Y^16 + 4*Y^15 + 4*Y^14 + 2*Y^13 + 4*Y^12 + 
        5*Y^11 + 5*Y^10 + 6*Y^9 + 2*Y^7 + 6*Y^6 + 2*Y^5 + Y^3 + 3*Y^2 + 4*Y + 2,
    T^56 - 86/49*T^54 + 9/343*T^53 + 2011/2401*T^52 + 895/2401*T^51 + 1347/2401*T^50
        - 1773/2401*T^49 - 2715/2401*T^48 + 1210/2401*T^47 + 1238/2401*T^46 - 
        565/2401*T^45 + 1210/2401*T^44 + 444/2401*T^43 - 2356/2401*T^42 - 
        615/2401*T^41 + 230/343*T^40 + 934/2401*T^39 + 1088/2401*T^38 - 
        1620/2401*T^37 - 3439/2401*T^36 + 1621/2401*T^35 + 2916/2401*T^34 + 
        594/2401*T^33 - 559/2401*T^32 - 2519/2401*T^31 - 2053/2401*T^30 + 
        1312/2401*T^29 + 3392/2401*T^28 + 1312/2401*T^27 - 2053/2401*T^26 - 
        2519/2401*T^25 - 559/2401*T^24 + 594/2401*T^23 + 2916/2401*T^22 + 
        1621/2401*T^21 - 3439/2401*T^20 - 1620/2401*T^19 + 1088/2401*T^18 + 
        934/2401*T^17 + 230/343*T^16 - 615/2401*T^15 - 2356/2401*T^14 + 
        444/2401*T^13 + 1210/2401*T^12 - 565/2401*T^11 + 1238/2401*T^10 + 
        1210/2401*T^9 - 2715/2401*T^8 - 1773/2401*T^7 + 1347/2401*T^6 + 895/2401*T^5
        + 2011/2401*T^4 + 9/343*T^3 - 86/49*T^2 + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 4*X*Y^12 + 5*X*Y^11 + 6*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 
        X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 2*X*Y + 3*X + 2*Y^30 + 4*Y^29 + 4*Y^28 + 2*Y^27 
        + 2*Y^26 + 5*Y^25 + 5*Y^24 + 6*Y^23 + 3*Y^22 + Y^21 + 2*Y^19 + Y^18 + 6*Y^17
        + 6*Y^16 + 5*Y^15 + 5*Y^14 + Y^13 + 2*Y^12 + 5*Y^11 + Y^10 + Y^8 + 4*Y^7 + 
        6*Y^6 + Y^4 + 6*Y^2 + 5*Y + 2,
    -T^56 + T^55 + 59/49*T^54 - 27/49*T^53 - 4589/2401*T^52 + 471/2401*T^51 + 
        2902/2401*T^50 + 2770/2401*T^49 - 2614/2401*T^48 - 453/343*T^47 + 
        2022/2401*T^46 + 2831/2401*T^45 - 1389/2401*T^44 - 4290/2401*T^43 + 
        3776/2401*T^42 + 3202/2401*T^41 - 2126/2401*T^40 - 4909/2401*T^39 + 
        1174/2401*T^38 + 649/343*T^37 + 1031/2401*T^36 - 4787/2401*T^35 - 
        633/2401*T^34 + 3337/2401*T^33 - 47/343*T^32 - 2427/2401*T^31 + 93/2401*T^30
        + 3152/2401*T^29 - 3152/2401*T^27 - 93/2401*T^26 + 2427/2401*T^25 + 
        47/343*T^24 - 3337/2401*T^23 + 633/2401*T^22 + 4787/2401*T^21 - 
        1031/2401*T^20 - 649/343*T^19 - 1174/2401*T^18 + 4909/2401*T^17 + 
        2126/2401*T^16 - 3202/2401*T^15 - 3776/2401*T^14 + 4290/2401*T^13 + 
        1389/2401*T^12 - 2831/2401*T^11 - 2022/2401*T^10 + 453/343*T^9 + 
        2614/2401*T^8 - 2770/2401*T^7 - 2902/2401*T^6 - 471/2401*T^5 + 4589/2401*T^4
        + 27/49*T^3 - 59/49*T^2 - T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + X*Y^10 + 2*X*Y^9 + 2*X*Y^5 + 
        4*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 3*X*Y + 3*X + 4*Y^30 + 3*Y^29 + 4*Y^28 + 
        2*Y^25 + 6*Y^24 + 3*Y^23 + Y^22 + 5*Y^21 + 6*Y^20 + 5*Y^19 + 6*Y^17 + 4*Y^16
        + 4*Y^15 + 5*Y^14 + 5*Y^13 + Y^12 + 3*Y^11 + 3*Y^10 + Y^9 + 2*Y^8 + Y^7 + 
        2*Y^6 + 2*Y^5 + 2*Y^4 + 5*Y^3 + 5,
    T^56 + 15/7*T^55 + 103/49*T^54 + 92/49*T^53 + 4363/2401*T^52 + 760/343*T^51 + 
        6971/2401*T^50 + 6850/2401*T^49 + 6969/2401*T^48 + 7690/2401*T^47 + 
        6744/2401*T^46 + 6159/2401*T^45 + 6551/2401*T^44 + 7015/2401*T^43 + 
        7506/2401*T^42 + 7471/2401*T^41 + 1114/343*T^40 + 7338/2401*T^39 + 
        6015/2401*T^38 + 5972/2401*T^37 + 6406/2401*T^36 + 6228/2401*T^35 + 
        5162/2401*T^34 + 3390/2401*T^33 + 3161/2401*T^32 + 4085/2401*T^31 + 
        3719/2401*T^30 + 2882/2401*T^29 + 2624/2401*T^28 + 2882/2401*T^27 + 
        3719/2401*T^26 + 4085/2401*T^25 + 3161/2401*T^24 + 3390/2401*T^23 + 
        5162/2401*T^22 + 6228/2401*T^21 + 6406/2401*T^20 + 5972/2401*T^19 + 
        6015/2401*T^18 + 7338/2401*T^17 + 1114/343*T^16 + 7471/2401*T^15 + 
        7506/2401*T^14 + 7015/2401*T^13 + 6551/2401*T^12 + 6159/2401*T^11 + 
        6744/2401*T^10 + 7690/2401*T^9 + 6969/2401*T^8 + 6850/2401*T^7 + 
        6971/2401*T^6 + 760/343*T^5 + 4363/2401*T^4 + 92/49*T^3 + 103/49*T^2 + 
        15/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 4*X*Y^8 
        + 5*X*Y^6 + 3*X*Y^5 + 5*X*Y^3 + 5*X*Y^2 + X + Y^30 + 4*Y^29 + Y^28 + 3*Y^27 
        + 5*Y^26 + 3*Y^25 + 2*Y^24 + 2*Y^22 + 2*Y^21 + 4*Y^20 + 6*Y^19 + 2*Y^18 + 
        6*Y^17 + 6*Y^15 + 5*Y^14 + 5*Y^13 + 6*Y^12 + 5*Y^10 + 4*Y^9 + 5*Y^8 + 3*Y^7 
        + 5*Y^6 + 4*Y^5 + 3*Y^4 + 2*Y^3 + 3*Y + 1,
    T^56 - 3/7*T^55 - 13/49*T^54 - 86/343*T^53 + 2351/2401*T^52 - 1199/2401*T^51 - 
        290/2401*T^50 + 622/2401*T^49 + 879/2401*T^48 - 1549/2401*T^47 + 
        328/2401*T^46 - 18/2401*T^45 + 488/2401*T^44 + 276/2401*T^43 - 794/2401*T^42
        - 313/2401*T^41 - 279/2401*T^40 + 221/343*T^39 - 1495/2401*T^38 + 
        29/2401*T^37 + 573/2401*T^36 - 197/2401*T^35 - 1088/2401*T^34 - 
        293/2401*T^33 + 904/2401*T^32 + 138/2401*T^31 + 216/2401*T^30 - 
        150/2401*T^29 - 269/2401*T^28 - 150/2401*T^27 + 216/2401*T^26 + 
        138/2401*T^25 + 904/2401*T^24 - 293/2401*T^23 - 1088/2401*T^22 - 
        197/2401*T^21 + 573/2401*T^20 + 29/2401*T^19 - 1495/2401*T^18 + 221/343*T^17
        - 279/2401*T^16 - 313/2401*T^15 - 794/2401*T^14 + 276/2401*T^13 + 
        488/2401*T^12 - 18/2401*T^11 + 328/2401*T^10 - 1549/2401*T^9 + 879/2401*T^8 
        + 622/2401*T^7 - 290/2401*T^6 - 1199/2401*T^5 + 2351/2401*T^4 - 86/343*T^3 -
        13/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + 
        6*X*Y^8 + 2*X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + X*Y^4 + 4*X*Y^3 + 6*X*Y + 4*Y^30 + 
        4*Y^29 + 4*Y^28 + 2*Y^27 + 2*Y^26 + Y^25 + 6*Y^24 + 2*Y^23 + 6*Y^22 + 6*Y^21
        + 5*Y^20 + Y^19 + Y^18 + 4*Y^17 + 6*Y^16 + 2*Y^15 + 4*Y^14 + 5*Y^13 + 3*Y^12
        + Y^10 + 4*Y^9 + 4*Y^8 + 3*Y^7 + 2*Y^6 + 3*Y^4 + 5*Y^3 + 6*Y + 5,
    -T^56 + 8/7*T^55 - 39/49*T^54 + 4/7*T^53 + 412/2401*T^52 - 1847/2401*T^51 + 
        2980/2401*T^50 - 3205/2401*T^49 + 3183/2401*T^48 - 2164/2401*T^47 + 
        46/343*T^46 + 652/2401*T^45 - 2810/2401*T^44 + 4591/2401*T^43 - 
        4584/2401*T^42 + 4047/2401*T^41 - 2228/2401*T^40 + 270/2401*T^39 + 
        202/343*T^38 - 3352/2401*T^37 + 4498/2401*T^36 - 3380/2401*T^35 + 
        2115/2401*T^34 + 131/2401*T^33 - 1779/2401*T^32 + 1790/2401*T^31 - 
        1517/2401*T^30 + 1559/2401*T^29 - 1559/2401*T^27 + 1517/2401*T^26 - 
        1790/2401*T^25 + 1779/2401*T^24 - 131/2401*T^23 - 2115/2401*T^22 + 
        3380/2401*T^21 - 4498/2401*T^20 + 3352/2401*T^19 - 202/343*T^18 - 
        270/2401*T^17 + 2228/2401*T^16 - 4047/2401*T^15 + 4584/2401*T^14 - 
        4591/2401*T^13 + 2810/2401*T^12 - 652/2401*T^11 - 46/343*T^10 + 
        2164/2401*T^9 - 3183/2401*T^8 + 3205/2401*T^7 - 2980/2401*T^6 + 
        1847/2401*T^5 - 412/2401*T^4 - 4/7*T^3 + 39/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 
        + 3*X*Y^8 + 6*X*Y^6 + X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + 5*X + 6*Y^30 + 
        4*Y^29 + 6*Y^28 + 2*Y^27 + 5*Y^25 + 4*Y^23 + Y^21 + 2*Y^20 + 4*Y^19 + 3*Y^18
        + Y^17 + 6*Y^16 + 5*Y^14 + 4*Y^13 + 3*Y^12 + 5*Y^11 + 4*Y^10 + 5*Y^9 + 2*Y^8
        + Y^7 + Y^6 + 6*Y^4 + 5*Y^3 + 3*Y^2 + Y + 4,
    -T^56 - T^55 - 34/49*T^54 - 370/343*T^53 - 47/49*T^52 - 1532/2401*T^51 - 
        541/2401*T^50 - 1894/2401*T^49 - 1114/2401*T^48 + 256/343*T^47 + 
        590/2401*T^46 - 234/343*T^45 - 523/2401*T^44 - 46/2401*T^43 - 997/2401*T^42 
        - 572/2401*T^41 + 38/49*T^40 + 1052/2401*T^39 - 477/2401*T^38 + 
        902/2401*T^37 + 1770/2401*T^36 + 1160/2401*T^35 - 956/2401*T^34 - 
        265/2401*T^33 - 1210/2401*T^32 - 2215/2401*T^31 - 586/2401*T^30 + 
        26/343*T^29 - 26/343*T^27 + 586/2401*T^26 + 2215/2401*T^25 + 1210/2401*T^24 
        + 265/2401*T^23 + 956/2401*T^22 - 1160/2401*T^21 - 1770/2401*T^20 - 
        902/2401*T^19 + 477/2401*T^18 - 1052/2401*T^17 - 38/49*T^16 + 572/2401*T^15 
        + 997/2401*T^14 + 46/2401*T^13 + 523/2401*T^12 + 234/343*T^11 - 
        590/2401*T^10 - 256/343*T^9 + 1114/2401*T^8 + 1894/2401*T^7 + 541/2401*T^6 +
        1532/2401*T^5 + 47/49*T^4 + 370/343*T^3 + 34/49*T^2 + T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 
        + X*Y^8 + 3*X*Y^7 + 2*X*Y^5 + 2*X*Y^2 + 5*X + 5*Y^30 + 2*Y^28 + 4*Y^27 + 
        5*Y^23 + 5*Y^22 + Y^21 + 5*Y^20 + 5*Y^19 + 3*Y^18 + 5*Y^17 + 4*Y^16 + 5*Y^15
        + 2*Y^14 + 3*Y^13 + 4*Y^12 + 4*Y^11 + 5*Y^9 + 4*Y^8 + 2*Y^7 + 6*Y^6 + 6*Y^5 
        + 3*Y^3 + 5*Y^2 + Y,
    T^56 + 3/7*T^55 - 118/49*T^54 - 178/343*T^53 + 7011/2401*T^52 - 144/2401*T^51 - 
        4559/2401*T^50 + 740/2401*T^49 - 800/2401*T^48 - 206/2401*T^47 + 
        627/343*T^46 - 1461/2401*T^45 - 4803/2401*T^44 + 2591/2401*T^43 + 
        2426/2401*T^42 - 39/49*T^41 + 1422/2401*T^40 + 533/2401*T^39 - 
        3877/2401*T^38 + 1703/2401*T^37 + 4474/2401*T^36 - 3492/2401*T^35 - 
        3145/2401*T^34 + 3902/2401*T^33 + 262/343*T^32 - 2795/2401*T^31 - 
        2279/2401*T^30 + 765/2401*T^29 + 2596/2401*T^28 + 765/2401*T^27 - 
        2279/2401*T^26 - 2795/2401*T^25 + 262/343*T^24 + 3902/2401*T^23 - 
        3145/2401*T^22 - 3492/2401*T^21 + 4474/2401*T^20 + 1703/2401*T^19 - 
        3877/2401*T^18 + 533/2401*T^17 + 1422/2401*T^16 - 39/49*T^15 + 
        2426/2401*T^14 + 2591/2401*T^13 - 4803/2401*T^12 - 1461/2401*T^11 + 
        627/343*T^10 - 206/2401*T^9 - 800/2401*T^8 + 740/2401*T^7 - 4559/2401*T^6 - 
        144/2401*T^5 + 7011/2401*T^4 - 178/343*T^3 - 118/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + X*Y^8 + 
        6*X*Y^7 + X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 6*X*Y + 6*X + 2*Y^30 + 
        3*Y^29 + 3*Y^28 + Y^27 + 4*Y^25 + 4*Y^24 + Y^23 + 6*Y^21 + 5*Y^20 + Y^19 + 
        5*Y^18 + 6*Y^17 + 5*Y^16 + 2*Y^15 + 3*Y^13 + 6*Y^12 + 4*Y^11 + 2*Y^10 + 
        4*Y^7 + 6*Y^6 + 6*Y^5 + 6*Y^4 + 5*Y^3 + 2*Y^2 + 4*Y + 4,
    T^56 - 23/49*T^54 + 230/343*T^53 - 1161/2401*T^52 - 32/2401*T^51 + 
        1804/2401*T^50 - 57/343*T^49 - 136/2401*T^48 + 184/343*T^47 - 877/2401*T^46 
        - 940/2401*T^45 + 1202/2401*T^44 + 1396/2401*T^43 - 517/2401*T^42 - 
        131/2401*T^41 + 880/2401*T^40 - 1466/2401*T^39 + 965/2401*T^38 + 
        226/343*T^37 - 874/2401*T^36 - 955/2401*T^35 + 1322/2401*T^34 - 
        915/2401*T^33 - 1045/2401*T^32 + 2998/2401*T^31 - 576/2401*T^30 - 
        962/2401*T^29 + 1651/2401*T^28 - 962/2401*T^27 - 576/2401*T^26 + 
        2998/2401*T^25 - 1045/2401*T^24 - 915/2401*T^23 + 1322/2401*T^22 - 
        955/2401*T^21 - 874/2401*T^20 + 226/343*T^19 + 965/2401*T^18 - 
        1466/2401*T^17 + 880/2401*T^16 - 131/2401*T^15 - 517/2401*T^14 + 
        1396/2401*T^13 + 1202/2401*T^12 - 940/2401*T^11 - 877/2401*T^10 + 
        184/343*T^9 - 136/2401*T^8 - 57/343*T^7 + 1804/2401*T^6 - 32/2401*T^5 - 
        1161/2401*T^4 + 230/343*T^3 - 23/49*T^2 + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 5*X*Y^8 +
        X*Y^7 + 3*X*Y^6 + 2*X*Y^4 + 3*X*Y^3 + X*Y^2 + X*Y + 2*X + 3*Y^30 + 2*Y^29 + 
        2*Y^28 + 5*Y^26 + 4*Y^23 + 6*Y^22 + 6*Y^21 + 6*Y^20 + Y^19 + 6*Y^18 + 5*Y^17
        + 3*Y^16 + 3*Y^15 + 5*Y^14 + 5*Y^13 + 5*Y^11 + 5*Y^9 + 5*Y^7 + 2*Y^6 + 2*Y^5
        + 6*Y^4 + 3*Y^3 + 3*Y^2 + 4*Y + 1,
    T^56 + 4/7*T^55 - 57/49*T^54 - 46/343*T^53 + 1934/2401*T^52 - 2197/2401*T^51 - 
        946/2401*T^50 + 3368/2401*T^49 + 794/2401*T^48 - 1900/2401*T^47 + 1/7*T^46 -
        936/2401*T^45 - 891/2401*T^44 + 5/7*T^43 - 226/343*T^42 - 145/2401*T^41 + 
        4334/2401*T^40 - 957/2401*T^39 - 2309/2401*T^38 + 46/49*T^37 + 52/2401*T^36 
        - 2633/2401*T^35 + 1115/2401*T^34 + 1472/2401*T^33 - 167/2401*T^32 + 
        1517/2401*T^31 - 390/2401*T^30 - 1402/2401*T^29 + 1023/2401*T^28 - 
        1402/2401*T^27 - 390/2401*T^26 + 1517/2401*T^25 - 167/2401*T^24 + 
        1472/2401*T^23 + 1115/2401*T^22 - 2633/2401*T^21 + 52/2401*T^20 + 46/49*T^19
        - 2309/2401*T^18 - 957/2401*T^17 + 4334/2401*T^16 - 145/2401*T^15 - 
        226/343*T^14 + 5/7*T^13 - 891/2401*T^12 - 936/2401*T^11 + 1/7*T^10 - 
        1900/2401*T^9 + 794/2401*T^8 + 3368/2401*T^7 - 946/2401*T^6 - 2197/2401*T^5 
        + 1934/2401*T^4 - 46/343*T^3 - 57/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + X*Y^10 + 6*X*Y^9 + 3*X*Y^8 + 
        2*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 4*X*Y^3 + 4*X*Y^2 + 6*X*Y + 3*X + Y^30 + 
        3*Y^29 + 6*Y^28 + 5*Y^27 + 5*Y^26 + 6*Y^25 + 5*Y^24 + 3*Y^23 + 3*Y^22 + 
        2*Y^21 + 5*Y^19 + 5*Y^18 + 4*Y^17 + 6*Y^16 + 5*Y^12 + 3*Y^11 + 3*Y^10 + 
        2*Y^9 + 5*Y^8 + 6*Y^7 + 2*Y^6 + 4*Y^4 + 2*Y^3 + 5*Y^2 + 3*Y + 1,
    -T^56 + 16/7*T^55 - 54/49*T^54 - 853/343*T^53 + 9522/2401*T^52 - 1489/2401*T^51 
        - 8124/2401*T^50 + 6766/2401*T^49 + 3142/2401*T^48 - 10652/2401*T^47 + 
        7867/2401*T^46 + 3349/2401*T^45 - 11475/2401*T^44 + 8151/2401*T^43 + 
        3389/2401*T^42 - 9680/2401*T^41 + 3827/2401*T^40 + 7174/2401*T^39 - 
        11435/2401*T^38 + 4509/2401*T^37 + 6281/2401*T^36 - 10410/2401*T^35 + 
        5352/2401*T^34 + 3683/2401*T^33 - 7365/2401*T^32 + 822/2401*T^31 + 
        9566/2401*T^30 - 1591/343*T^29 + 1591/343*T^27 - 9566/2401*T^26 - 
        822/2401*T^25 + 7365/2401*T^24 - 3683/2401*T^23 - 5352/2401*T^22 + 
        10410/2401*T^21 - 6281/2401*T^20 - 4509/2401*T^19 + 11435/2401*T^18 - 
        7174/2401*T^17 - 3827/2401*T^16 + 9680/2401*T^15 - 3389/2401*T^14 - 
        8151/2401*T^13 + 11475/2401*T^12 - 3349/2401*T^11 - 7867/2401*T^10 + 
        10652/2401*T^9 - 3142/2401*T^8 - 6766/2401*T^7 + 8124/2401*T^6 + 
        1489/2401*T^5 - 9522/2401*T^4 + 853/343*T^3 + 54/49*T^2 - 16/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + X*Y^8 + 
        4*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + X*Y^2 + 2*X*Y + 2*X + 
        5*Y^30 + 3*Y^29 + 2*Y^27 + Y^26 + 6*Y^25 + 4*Y^23 + 3*Y^22 + 6*Y^21 + 6*Y^18
        + 5*Y^17 + 5*Y^14 + 5*Y^13 + 4*Y^12 + 6*Y^11 + 4*Y^10 + 4*Y^9 + Y^8 + 2*Y^7 
        + Y^6 + 2*Y^5 + 5*Y^4 + Y^3 + 6*Y^2 + 5*Y + 3,
    -T^56 - 2/7*T^55 + 31/49*T^54 + 19/49*T^53 + 4318/2401*T^52 + 1852/2401*T^51 - 
        2725/2401*T^50 - 452/343*T^49 - 4005/2401*T^48 - 16/49*T^47 + 3167/2401*T^46
        + 4369/2401*T^45 + 3315/2401*T^44 - 1375/2401*T^43 - 3433/2401*T^42 - 
        641/343*T^41 - 2953/2401*T^40 + 2473/2401*T^39 + 625/343*T^38 + 
        4969/2401*T^37 + 2258/2401*T^36 - 3310/2401*T^35 - 4653/2401*T^34 - 
        4747/2401*T^33 - 1996/2401*T^32 + 3877/2401*T^31 + 4671/2401*T^30 + 
        3868/2401*T^29 - 3868/2401*T^27 - 4671/2401*T^26 - 3877/2401*T^25 + 
        1996/2401*T^24 + 4747/2401*T^23 + 4653/2401*T^22 + 3310/2401*T^21 - 
        2258/2401*T^20 - 4969/2401*T^19 - 625/343*T^18 - 2473/2401*T^17 + 
        2953/2401*T^16 + 641/343*T^15 + 3433/2401*T^14 + 1375/2401*T^13 - 
        3315/2401*T^12 - 4369/2401*T^11 - 3167/2401*T^10 + 16/49*T^9 + 4005/2401*T^8
        + 452/343*T^7 + 2725/2401*T^6 - 1852/2401*T^5 - 4318/2401*T^4 - 19/49*T^3 - 
        31/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + X*Y^11 + 5*X*Y^10 + 3*X*Y^8 + 
        2*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 4*X*Y + 6*X + 
        6*Y^30 + Y^28 + Y^27 + 4*Y^24 + 5*Y^23 + 2*Y^22 + 4*Y^20 + Y^19 + 3*Y^18 + 
        4*Y^17 + 5*Y^16 + 2*Y^15 + 5*Y^14 + 3*Y^13 + 3*Y^12 + 2*Y^11 + 3*Y^10 + 
        5*Y^9 + Y^6 + 4*Y^5 + 4*Y^4 + Y^3 + 2*Y^2 + 6*Y + 2,
    -T^56 + 5/7*T^55 + 46/49*T^54 - 650/343*T^53 + 697/2401*T^52 + 1761/2401*T^51 - 
        2041/2401*T^50 + 1676/2401*T^49 - 32/49*T^48 - 1486/2401*T^47 + 
        3495/2401*T^46 - 1658/2401*T^45 - 1999/2401*T^44 + 359/343*T^43 + 
        180/2401*T^42 - 745/2401*T^41 + 159/2401*T^40 - 919/2401*T^39 + 
        1534/2401*T^38 + 2010/2401*T^37 - 1716/2401*T^36 - 1045/2401*T^35 + 
        1851/2401*T^34 + 1336/2401*T^33 - 345/2401*T^32 - 1257/2401*T^31 + 
        473/2401*T^30 + 1220/2401*T^29 - 1220/2401*T^27 - 473/2401*T^26 + 
        1257/2401*T^25 + 345/2401*T^24 - 1336/2401*T^23 - 1851/2401*T^22 + 
        1045/2401*T^21 + 1716/2401*T^20 - 2010/2401*T^19 - 1534/2401*T^18 + 
        919/2401*T^17 - 159/2401*T^16 + 745/2401*T^15 - 180/2401*T^14 - 359/343*T^13
        + 1999/2401*T^12 + 1658/2401*T^11 - 3495/2401*T^10 + 1486/2401*T^9 + 
        32/49*T^8 - 1676/2401*T^7 + 2041/2401*T^6 - 1761/2401*T^5 - 697/2401*T^4 + 
        650/343*T^3 - 46/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 6*X*Y^9 + 4*X*Y^8 +
        2*X*Y^7 + 5*X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + X*Y^2 + X*Y + 6*X + 5*Y^30
        + 4*Y^29 + 3*Y^28 + 5*Y^27 + 4*Y^26 + 5*Y^25 + 3*Y^24 + 5*Y^22 + 3*Y^21 + 
        3*Y^20 + 2*Y^19 + 3*Y^18 + 6*Y^17 + 5*Y^16 + 5*Y^15 + Y^14 + 5*Y^13 + 2*Y^12
        + 6*Y^11 + 4*Y^10 + 2*Y^9 + 5*Y^8 + 2*Y^7 + Y^6 + 6*Y^5 + 4*Y^4 + 6*Y^3 + 
        2*Y^2 + 6,
    T^56 + 8/7*T^55 + 15/49*T^54 + 89/343*T^53 + 1532/2401*T^52 + 1579/2401*T^51 + 
        3222/2401*T^50 + 349/343*T^49 - 166/343*T^48 - 276/343*T^47 + 380/2401*T^46 
        + 2265/2401*T^45 + 2123/2401*T^44 - 456/2401*T^43 - 3075/2401*T^42 - 
        1755/2401*T^41 + 1769/2401*T^40 + 3187/2401*T^39 + 935/2401*T^38 - 
        2440/2401*T^37 - 3145/2401*T^36 - 377/2401*T^35 + 2372/2401*T^34 + 
        1481/2401*T^33 - 2460/2401*T^32 - 6046/2401*T^31 - 5155/2401*T^30 - 
        1829/2401*T^29 + 146/2401*T^28 - 1829/2401*T^27 - 5155/2401*T^26 - 
        6046/2401*T^25 - 2460/2401*T^24 + 1481/2401*T^23 + 2372/2401*T^22 - 
        377/2401*T^21 - 3145/2401*T^20 - 2440/2401*T^19 + 935/2401*T^18 + 
        3187/2401*T^17 + 1769/2401*T^16 - 1755/2401*T^15 - 3075/2401*T^14 - 
        456/2401*T^13 + 2123/2401*T^12 + 2265/2401*T^11 + 380/2401*T^10 - 
        276/343*T^9 - 166/343*T^8 + 349/343*T^7 + 3222/2401*T^6 + 1579/2401*T^5 + 
        1532/2401*T^4 + 89/343*T^3 + 15/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 2*X*Y^13 + X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 3*X*Y^8 + 2*X*Y^7 + 
        3*X*Y^5 + X*Y^4 + 4*X*Y^2 + 2*X*Y + 6*X + 3*Y^30 + 4*Y^29 + Y^27 + 6*Y^25 + 
        3*Y^24 + 6*Y^23 + 4*Y^22 + 2*Y^21 + 4*Y^20 + 3*Y^18 + 4*Y^15 + 5*Y^14 + 
        4*Y^13 + 4*Y^12 + 5*Y^11 + 2*Y^10 + 3*Y^8 + 2*Y^7 + 2*Y^4 + 3*Y^3 + 3*Y^2 + 
        6*Y + 2,
    -T^56 + 9/7*T^55 - 37/49*T^54 - 199/343*T^53 + 3450/2401*T^52 - 2991/2401*T^51 +
        2084/2401*T^50 - 6/343*T^49 - 114/343*T^48 + 2036/2401*T^47 - 2064/2401*T^46
        + 1383/2401*T^45 + 741/2401*T^44 - 2777/2401*T^43 + 2778/2401*T^42 - 
        1476/2401*T^41 - 52/343*T^40 + 171/2401*T^39 - 1304/2401*T^38 + 
        2344/2401*T^37 - 2624/2401*T^36 + 1137/2401*T^35 + 619/2401*T^34 - 
        95/2401*T^33 + 20/2401*T^32 - 1074/2401*T^31 + 2132/2401*T^30 - 
        1626/2401*T^29 + 1626/2401*T^27 - 2132/2401*T^26 + 1074/2401*T^25 - 
        20/2401*T^24 + 95/2401*T^23 - 619/2401*T^22 - 1137/2401*T^21 + 
        2624/2401*T^20 - 2344/2401*T^19 + 1304/2401*T^18 - 171/2401*T^17 + 
        52/343*T^16 + 1476/2401*T^15 - 2778/2401*T^14 + 2777/2401*T^13 - 
        741/2401*T^12 - 1383/2401*T^11 + 2064/2401*T^10 - 2036/2401*T^9 + 
        114/343*T^8 + 6/343*T^7 - 2084/2401*T^6 + 2991/2401*T^5 - 3450/2401*T^4 + 
        199/343*T^3 + 37/49*T^2 - 9/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + X*Y^12 + 5*X*Y^11 + 5*X*Y^9 + 6*X*Y^6 + 
        3*X*Y^5 + 3*X*Y^4 + 4*X*Y^2 + 6*X*Y + 5*X + 6*Y^30 + 6*Y^29 + 6*Y^28 + 
        3*Y^27 + 6*Y^26 + 4*Y^25 + 6*Y^24 + Y^23 + 6*Y^22 + 3*Y^20 + 5*Y^19 + 2*Y^18
        + Y^17 + 6*Y^16 + 5*Y^15 + 5*Y^14 + Y^13 + 4*Y^12 + 3*Y^11 + 6*Y^10 + 2*Y^9 
        + 5*Y^8 + 5*Y^6 + 2*Y^5 + 6*Y^4 + Y^3 + 2*Y + 5,
    -T^56 - 12/7*T^55 - 73/49*T^54 - 468/343*T^53 - 2438/2401*T^52 + 1013/2401*T^51 
        + 5788/2401*T^50 + 942/343*T^49 + 4467/2401*T^48 + 2633/2401*T^47 - 
        790/2401*T^46 - 6001/2401*T^45 - 1181/343*T^44 - 6481/2401*T^43 - 
        2294/2401*T^42 + 2368/2401*T^41 + 6289/2401*T^40 + 7817/2401*T^39 + 
        6453/2401*T^38 + 2371/2401*T^37 - 3088/2401*T^36 - 5724/2401*T^35 - 
        5104/2401*T^34 - 3090/2401*T^33 - 67/2401*T^32 + 3478/2401*T^31 + 
        4610/2401*T^30 + 2706/2401*T^29 - 2706/2401*T^27 - 4610/2401*T^26 - 
        3478/2401*T^25 + 67/2401*T^24 + 3090/2401*T^23 + 5104/2401*T^22 + 
        5724/2401*T^21 + 3088/2401*T^20 - 2371/2401*T^19 - 6453/2401*T^18 - 
        7817/2401*T^17 - 6289/2401*T^16 - 2368/2401*T^15 + 2294/2401*T^14 + 
        6481/2401*T^13 + 1181/343*T^12 + 6001/2401*T^11 + 790/2401*T^10 - 
        2633/2401*T^9 - 4467/2401*T^8 - 942/343*T^7 - 5788/2401*T^6 - 1013/2401*T^5 
        + 2438/2401*T^4 + 468/343*T^3 + 73/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + X*Y^11 + 6*X*Y^9 + X*Y^8 + X*Y^7 + 
        2*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 4*X*Y + 4*X + Y^30 + 3*Y^28 + 5*Y^27
        + 6*Y^26 + 4*Y^25 + 6*Y^24 + 6*Y^22 + 2*Y^21 + Y^20 + 5*Y^17 + 2*Y^16 + Y^15
        + 5*Y^14 + 2*Y^13 + 4*Y^12 + 5*Y^11 + 6*Y^10 + 3*Y^9 + 6*Y^8 + 3*Y^7 + 2*Y^6
        + 2*Y^5 + 3*Y^4 + 3*Y^3 + 6*Y + 3,
    T^56 - 15/7*T^55 + 51/49*T^54 + 260/343*T^53 - 1275/2401*T^52 - 660/2401*T^51 - 
        596/2401*T^50 + 363/343*T^49 - 303/343*T^48 - 12/343*T^47 + 1289/2401*T^46 -
        386/2401*T^45 + 6/49*T^44 - 2204/2401*T^43 + 1502/2401*T^42 + 2388/2401*T^41
        - 2932/2401*T^40 + 668/2401*T^39 - 998/2401*T^38 + 2657/2401*T^37 - 
        2125/2401*T^36 - 384/2401*T^35 + 2287/2401*T^34 - 1747/2401*T^33 + 
        251/2401*T^32 - 1010/2401*T^31 + 1833/2401*T^30 + 1156/2401*T^29 - 
        531/343*T^28 + 1156/2401*T^27 + 1833/2401*T^26 - 1010/2401*T^25 + 
        251/2401*T^24 - 1747/2401*T^23 + 2287/2401*T^22 - 384/2401*T^21 - 
        2125/2401*T^20 + 2657/2401*T^19 - 998/2401*T^18 + 668/2401*T^17 - 
        2932/2401*T^16 + 2388/2401*T^15 + 1502/2401*T^14 - 2204/2401*T^13 + 
        6/49*T^12 - 386/2401*T^11 + 1289/2401*T^10 - 12/343*T^9 - 303/343*T^8 + 
        363/343*T^7 - 596/2401*T^6 - 660/2401*T^5 - 1275/2401*T^4 + 260/343*T^3 + 
        51/49*T^2 - 15/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 +
        X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + X + 5*Y^30 + Y^29 
        + 5*Y^28 + 2*Y^27 + 2*Y^26 + 3*Y^25 + 5*Y^24 + 2*Y^23 + 4*Y^22 + 3*Y^21 + 
        Y^19 + 6*Y^17 + 6*Y^16 + 6*Y^15 + 5*Y^14 + 6*Y^13 + 2*Y^11 + 5*Y^10 + 6*Y^9 
        + 6*Y^7 + 6*Y^6 + 6*Y^5 + 2*Y^4 + 4*Y^3 + 2*Y^2 + 2*Y + 3,
    T^56 - 5/7*T^55 + 38/49*T^54 - 222/343*T^53 + 111/343*T^52 - 69/2401*T^51 - 
        548/2401*T^50 - 1399/2401*T^49 + 779/2401*T^48 - 239/2401*T^47 + 
        40/2401*T^46 + 207/2401*T^45 - 132/343*T^44 - 372/2401*T^43 + 576/2401*T^42 
        + 254/2401*T^41 - 9/2401*T^40 + 108/343*T^39 - 1432/2401*T^38 + 
        925/2401*T^37 + 555/2401*T^36 - 834/2401*T^35 + 688/2401*T^34 - 
        697/2401*T^33 + 353/2401*T^32 + 30/343*T^31 + 141/343*T^30 - 2353/2401*T^29 
        + 1586/2401*T^28 - 2353/2401*T^27 + 141/343*T^26 + 30/343*T^25 + 
        353/2401*T^24 - 697/2401*T^23 + 688/2401*T^22 - 834/2401*T^21 + 
        555/2401*T^20 + 925/2401*T^19 - 1432/2401*T^18 + 108/343*T^17 - 9/2401*T^16 
        + 254/2401*T^15 + 576/2401*T^14 - 372/2401*T^13 - 132/343*T^12 + 
        207/2401*T^11 + 40/2401*T^10 - 239/2401*T^9 + 779/2401*T^8 - 1399/2401*T^7 -
        548/2401*T^6 - 69/2401*T^5 + 111/343*T^4 - 222/343*T^3 + 38/49*T^2 - 5/7*T +
        1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        X*Y^8 + 6*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + X*Y^3 + 6*X*Y^2 + 4*X*Y + 6*X + 3*Y^30
        + 3*Y^29 + 5*Y^27 + 3*Y^26 + 5*Y^25 + 3*Y^24 + 3*Y^21 + 6*Y^20 + 5*Y^19 + 
        5*Y^17 + 6*Y^15 + 2*Y^14 + 2*Y^13 + 4*Y^12 + 5*Y^11 + 2*Y^10 + 6*Y^8 + 2*Y^7
        + 3*Y^6 + 3*Y^5 + 3*Y^4 + Y^3 + 3*Y^2 + 6*Y + 1,
    -T^56 + 9/7*T^55 - 36/49*T^54 - 6/343*T^53 + 1714/2401*T^52 - 1339/2401*T^51 + 
        216/343*T^50 - 113/2401*T^49 - 691/2401*T^48 + 498/2401*T^47 - 863/2401*T^46
        + 450/2401*T^45 - 881/2401*T^44 - 116/2401*T^43 + 510/2401*T^42 - 
        195/2401*T^41 + 898/2401*T^40 - 443/2401*T^39 - 698/2401*T^38 + 
        1279/2401*T^37 - 946/2401*T^36 - 10/2401*T^35 - 60/2401*T^34 - 467/2401*T^33
        + 318/2401*T^32 + 142/343*T^31 - 754/2401*T^30 + 1024/2401*T^29 - 
        1024/2401*T^27 + 754/2401*T^26 - 142/343*T^25 - 318/2401*T^24 + 
        467/2401*T^23 + 60/2401*T^22 + 10/2401*T^21 + 946/2401*T^20 - 1279/2401*T^19
        + 698/2401*T^18 + 443/2401*T^17 - 898/2401*T^16 + 195/2401*T^15 - 
        510/2401*T^14 + 116/2401*T^13 + 881/2401*T^12 - 450/2401*T^11 + 
        863/2401*T^10 - 498/2401*T^9 + 691/2401*T^8 + 113/2401*T^7 - 216/343*T^6 + 
        1339/2401*T^5 - 1714/2401*T^4 + 6/343*T^3 + 36/49*T^2 - 9/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 5*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 5*X*Y^8 + 
        X*Y^7 + X*Y^6 + 6*X*Y^5 + X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 3*X*Y + 3*X + 6*Y^30 +
        Y^29 + 2*Y^28 + 5*Y^27 + 6*Y^26 + Y^24 + Y^23 + 3*Y^22 + 2*Y^21 + 6*Y^19 + 
        5*Y^18 + 2*Y^17 + 6*Y^16 + Y^15 + 3*Y^14 + 3*Y^13 + 4*Y^12 + 6*Y^11 + Y^10 +
        6*Y^9 + 4*Y^8 + 3*Y^7 + 4*Y^5 + 4*Y^4 + 4*Y^3 + 6*Y^2 + 5*Y + 2,
    -T^56 + 2/7*T^55 + 41/49*T^54 - 573/343*T^53 - 22/343*T^52 + 3086/2401*T^51 - 
        3992/2401*T^50 - 1248/2401*T^49 + 4126/2401*T^48 - 3172/2401*T^47 - 
        3615/2401*T^46 + 5721/2401*T^45 - 1635/2401*T^44 - 5882/2401*T^43 + 
        5906/2401*T^42 + 1228/2401*T^41 - 6687/2401*T^40 + 76/49*T^39 + 624/343*T^38
        - 5884/2401*T^37 + 881/2401*T^36 + 5646/2401*T^35 - 4604/2401*T^34 - 
        1492/2401*T^33 + 985/343*T^32 - 367/343*T^31 - 4566/2401*T^30 + 
        6211/2401*T^29 - 6211/2401*T^27 + 4566/2401*T^26 + 367/343*T^25 - 
        985/343*T^24 + 1492/2401*T^23 + 4604/2401*T^22 - 5646/2401*T^21 - 
        881/2401*T^20 + 5884/2401*T^19 - 624/343*T^18 - 76/49*T^17 + 6687/2401*T^16 
        - 1228/2401*T^15 - 5906/2401*T^14 + 5882/2401*T^13 + 1635/2401*T^12 - 
        5721/2401*T^11 + 3615/2401*T^10 + 3172/2401*T^9 - 4126/2401*T^8 + 
        1248/2401*T^7 + 3992/2401*T^6 - 3086/2401*T^5 + 22/343*T^4 + 573/343*T^3 - 
        41/49*T^2 - 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 4*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 2*X*Y + X + Y^30
        + 3*Y^29 + 5*Y^28 + 5*Y^27 + 2*Y^26 + 4*Y^25 + 5*Y^23 + 3*Y^22 + 4*Y^21 + 
        5*Y^20 + 5*Y^19 + 6*Y^18 + 2*Y^17 + 6*Y^16 + Y^14 + 2*Y^13 + 5*Y^12 + 5*Y^11
        + 4*Y^10 + 2*Y^9 + 5*Y^8 + 5*Y^7 + 3*Y^6 + 6*Y^5 + 2*Y^4 + 4*Y^2 + Y + 1,
    -T^56 - 5/7*T^54 - 34/343*T^53 + 346/2401*T^52 - 128/343*T^51 + 524/2401*T^50 - 
        1602/2401*T^49 - 1700/2401*T^48 - 193/343*T^47 - 596/2401*T^46 + 
        631/2401*T^45 + 135/343*T^44 - 5/343*T^43 + 402/2401*T^42 - 584/2401*T^41 + 
        174/2401*T^40 - 185/2401*T^39 + 102/343*T^38 + 1523/2401*T^37 + 
        685/2401*T^36 + 155/343*T^35 + 85/2401*T^34 + 291/2401*T^33 - 31/2401*T^32 +
        1075/2401*T^31 - 353/2401*T^30 + 74/343*T^29 - 74/343*T^27 + 353/2401*T^26 -
        1075/2401*T^25 + 31/2401*T^24 - 291/2401*T^23 - 85/2401*T^22 - 155/343*T^21 
        - 685/2401*T^20 - 1523/2401*T^19 - 102/343*T^18 + 185/2401*T^17 - 
        174/2401*T^16 + 584/2401*T^15 - 402/2401*T^14 + 5/343*T^13 - 135/343*T^12 - 
        631/2401*T^11 + 596/2401*T^10 + 193/343*T^9 + 1700/2401*T^8 + 1602/2401*T^7 
        - 524/2401*T^6 + 128/343*T^5 - 346/2401*T^4 + 34/343*T^3 + 5/7*T^2 + 1
*], [*
    X^3 + 6*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 +
        X*Y^7 + 6*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 2*X*Y + 4*X + Y^30 + 2*Y^29 
        + 4*Y^28 + 2*Y^26 + 3*Y^25 + Y^24 + 6*Y^23 + 4*Y^22 + 5*Y^21 + 5*Y^20 + Y^19
        + 2*Y^18 + 6*Y^17 + Y^16 + 4*Y^15 + 6*Y^14 + 4*Y^13 + Y^12 + 3*Y^11 + 6*Y^10
        + 3*Y^9 + 6*Y^8 + Y^7 + 2*Y^6 + Y^5 + 4*Y^4 + 4*Y^3 + 2*Y^2 + 5*Y + 4,
    T^56 - 18/7*T^55 + 171/49*T^54 - 1612/343*T^53 + 14513/2401*T^52 - 
        15471/2401*T^51 + 16448/2401*T^50 - 18101/2401*T^49 + 18093/2401*T^48 - 
        16596/2401*T^47 + 2152/343*T^46 - 2010/343*T^45 + 12321/2401*T^44 - 
        10298/2401*T^43 + 10407/2401*T^42 - 10809/2401*T^41 + 10288/2401*T^40 - 
        11679/2401*T^39 + 14268/2401*T^38 - 15049/2401*T^37 + 15567/2401*T^36 - 
        16742/2401*T^35 + 2292/343*T^34 - 14367/2401*T^33 + 13236/2401*T^32 - 
        11439/2401*T^31 + 1317/343*T^30 - 1096/343*T^29 + 7106/2401*T^28 - 
        1096/343*T^27 + 1317/343*T^26 - 11439/2401*T^25 + 13236/2401*T^24 - 
        14367/2401*T^23 + 2292/343*T^22 - 16742/2401*T^21 + 15567/2401*T^20 - 
        15049/2401*T^19 + 14268/2401*T^18 - 11679/2401*T^17 + 10288/2401*T^16 - 
        10809/2401*T^15 + 10407/2401*T^14 - 10298/2401*T^13 + 12321/2401*T^12 - 
        2010/343*T^11 + 2152/343*T^10 - 16596/2401*T^9 + 18093/2401*T^8 - 
        18101/2401*T^7 + 16448/2401*T^6 - 15471/2401*T^5 + 14513/2401*T^4 - 
        1612/343*T^3 + 171/49*T^2 - 18/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + X*Y^12 + 2*X*Y^11 + 4*X*Y^9 + 3*X*Y^8 + 
        6*X*Y^7 + X*Y^6 + 3*X*Y^5 + X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 6*X*Y + 3*X + 6*Y^30
        + 5*Y^28 + 4*Y^27 + 5*Y^26 + 4*Y^25 + 4*Y^24 + 5*Y^23 + 6*Y^22 + 5*Y^20 + 
        5*Y^19 + 2*Y^18 + Y^17 + 3*Y^16 + 4*Y^15 + 2*Y^13 + 4*Y^12 + 3*Y^11 + 6*Y^10
        + 2*Y^9 + 2*Y^8 + Y^7 + 5*Y^6 + Y^5 + 4*Y^4 + 2*Y^3 + Y^2 + Y + 5,
    T^56 + 4/7*T^55 - 43/49*T^54 + 1/49*T^53 + 115/343*T^52 - 1259/2401*T^51 + 
        30/2401*T^50 + 1937/2401*T^49 + 915/2401*T^48 - 2033/2401*T^47 - 
        1507/2401*T^46 + 542/2401*T^45 - 114/343*T^44 - 773/2401*T^43 + 
        1448/2401*T^42 + 738/2401*T^41 - 1178/2401*T^40 - 958/2401*T^39 + 
        318/2401*T^38 - 61/343*T^37 - 799/2401*T^36 + 1427/2401*T^35 + 4/49*T^34 - 
        1317/2401*T^33 + 743/2401*T^32 - 18/2401*T^31 - 502/2401*T^30 + 107/343*T^29
        + 912/2401*T^28 + 107/343*T^27 - 502/2401*T^26 - 18/2401*T^25 + 
        743/2401*T^24 - 1317/2401*T^23 + 4/49*T^22 + 1427/2401*T^21 - 799/2401*T^20 
        - 61/343*T^19 + 318/2401*T^18 - 958/2401*T^17 - 1178/2401*T^16 + 
        738/2401*T^15 + 1448/2401*T^14 - 773/2401*T^13 - 114/343*T^12 + 
        542/2401*T^11 - 1507/2401*T^10 - 2033/2401*T^9 + 915/2401*T^8 + 
        1937/2401*T^7 + 30/2401*T^6 - 1259/2401*T^5 + 115/343*T^4 + 1/49*T^3 - 
        43/49*T^2 + 4/7*T + 1
*], [*
    X^3 + X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 4*X*Y^9 + 6*X*Y^8 + X*Y^7 + 
        5*X*Y^6 + 3*X*Y^5 + 4*X*Y^3 + 4*X*Y^2 + 2*X*Y + 3*X + Y^30 + 2*Y^29 + Y^28 +
        6*Y^27 + 3*Y^26 + 4*Y^25 + 4*Y^24 + 4*Y^23 + 4*Y^22 + Y^21 + 3*Y^19 + 4*Y^18
        + Y^17 + 5*Y^16 + 2*Y^15 + 3*Y^14 + 4*Y^13 + 2*Y^12 + 2*Y^11 + 4*Y^10 + Y^9 
        + 3*Y^8 + 6*Y^7 + Y^6 + 5*Y^5 + 6*Y^4 + 5*Y^3 + 5*Y^2 + 3,
    -T^56 - 2/7*T^55 - 38/49*T^54 - 279/343*T^53 - 1636/2401*T^52 - 2684/2401*T^51 -
        1952/2401*T^50 - 561/2401*T^49 - 2880/2401*T^48 - 1294/2401*T^47 - 
        835/2401*T^46 - 1327/2401*T^45 + 361/2401*T^44 - 141/2401*T^43 + 
        895/2401*T^42 + 2901/2401*T^41 + 1562/2401*T^40 + 2218/2401*T^39 + 
        552/343*T^38 + 2920/2401*T^37 + 3613/2401*T^36 + 2978/2401*T^35 + 
        3408/2401*T^34 + 3568/2401*T^33 + 1992/2401*T^32 + 1023/2401*T^31 + 
        1298/2401*T^30 + 1502/2401*T^29 - 1502/2401*T^27 - 1298/2401*T^26 - 
        1023/2401*T^25 - 1992/2401*T^24 - 3568/2401*T^23 - 3408/2401*T^22 - 
        2978/2401*T^21 - 3613/2401*T^20 - 2920/2401*T^19 - 552/343*T^18 - 
        2218/2401*T^17 - 1562/2401*T^16 - 2901/2401*T^15 - 895/2401*T^14 + 
        141/2401*T^13 - 361/2401*T^12 + 1327/2401*T^11 + 835/2401*T^10 + 
        1294/2401*T^9 + 2880/2401*T^8 + 561/2401*T^7 + 1952/2401*T^6 + 2684/2401*T^5
        + 1636/2401*T^4 + 279/343*T^3 + 38/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + X*Y^13 + 4*X*Y^11 + X*Y^10 + 4*X*Y^9 + X*Y^7 + 
        4*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + X*Y + 4*X + 3*Y^30 + 
        4*Y^29 + 4*Y^28 + 4*Y^27 + 3*Y^26 + Y^25 + 4*Y^24 + 5*Y^23 + 3*Y^22 + 4*Y^21
        + Y^20 + 2*Y^17 + 2*Y^15 + 5*Y^14 + 2*Y^12 + 3*Y^11 + 2*Y^10 + 6*Y^9 + 2*Y^7
        + 2*Y^6 + 4*Y^5 + 3*Y^4 + 2*Y^3 + 4*Y + 1,
    -T^56 + 3/7*T^55 - 44/49*T^54 - 148/343*T^53 - 53/343*T^52 - 2839/2401*T^51 - 
        69/2401*T^50 - 1782/2401*T^49 + 570/2401*T^48 - 1179/2401*T^47 - 
        340/2401*T^46 - 171/343*T^45 - 449/2401*T^44 + 998/2401*T^43 - 
        1145/2401*T^42 + 724/2401*T^41 - 2108/2401*T^40 + 214/343*T^39 - 
        1243/2401*T^38 + 1392/2401*T^37 + 69/343*T^36 - 2402/2401*T^35 + 
        788/2401*T^34 - 1562/2401*T^33 + 1430/2401*T^32 - 1619/2401*T^31 + 
        6/343*T^30 - 1553/2401*T^29 + 1553/2401*T^27 - 6/343*T^26 + 1619/2401*T^25 -
        1430/2401*T^24 + 1562/2401*T^23 - 788/2401*T^22 + 2402/2401*T^21 - 
        69/343*T^20 - 1392/2401*T^19 + 1243/2401*T^18 - 214/343*T^17 + 
        2108/2401*T^16 - 724/2401*T^15 + 1145/2401*T^14 - 998/2401*T^13 + 
        449/2401*T^12 + 171/343*T^11 + 340/2401*T^10 + 1179/2401*T^9 - 570/2401*T^8 
        + 1782/2401*T^7 + 69/2401*T^6 + 2839/2401*T^5 + 53/343*T^4 + 148/343*T^3 + 
        44/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 6*X*Y^9 + 3*X*Y^8 + 
        X*Y^6 + X*Y^5 + X*Y^4 + X*Y^3 + 2*X*Y^2 + X*Y + 3*X + 4*Y^30 + 6*Y^29 + 
        5*Y^28 + 5*Y^27 + 4*Y^26 + 6*Y^25 + 3*Y^24 + 5*Y^23 + 4*Y^22 + Y^21 + Y^18 +
        3*Y^16 + Y^15 + 3*Y^14 + 5*Y^13 + 4*Y^12 + 2*Y^11 + 6*Y^10 + 5*Y^9 + 5*Y^8 +
        5*Y^7 + Y^5 + 6*Y^4 + Y^3 + 3*Y^2 + 5*Y + 4,
    -T^56 - 18/7*T^55 - 229/49*T^54 - 278/49*T^53 - 13689/2401*T^52 - 9916/2401*T^51
        - 5713/2401*T^50 - 309/343*T^49 - 1278/2401*T^48 - 390/343*T^47 - 
        4761/2401*T^46 - 6403/2401*T^45 - 5627/2401*T^44 - 3050/2401*T^43 + 
        320/2401*T^42 + 2445/2401*T^41 + 2972/2401*T^40 + 2300/2401*T^39 + 
        513/2401*T^38 - 1671/2401*T^37 - 4685/2401*T^36 - 1053/343*T^35 - 
        8159/2401*T^34 - 6129/2401*T^33 - 1585/2401*T^32 + 407/343*T^31 + 
        745/343*T^30 + 3887/2401*T^29 - 3887/2401*T^27 - 745/343*T^26 - 407/343*T^25
        + 1585/2401*T^24 + 6129/2401*T^23 + 8159/2401*T^22 + 1053/343*T^21 + 
        4685/2401*T^20 + 1671/2401*T^19 - 513/2401*T^18 - 2300/2401*T^17 - 
        2972/2401*T^16 - 2445/2401*T^15 - 320/2401*T^14 + 3050/2401*T^13 + 
        5627/2401*T^12 + 6403/2401*T^11 + 4761/2401*T^10 + 390/343*T^9 + 
        1278/2401*T^8 + 309/343*T^7 + 5713/2401*T^6 + 9916/2401*T^5 + 13689/2401*T^4
        + 278/49*T^3 + 229/49*T^2 + 18/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 
        X*Y^8 + 3*X*Y^7 + 6*X*Y^6 + 6*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 3*X*Y + X + 2*Y^30
        + 2*Y^29 + 4*Y^28 + 6*Y^27 + 5*Y^26 + Y^25 + 4*Y^24 + 3*Y^23 + 3*Y^22 + 
        4*Y^21 + 5*Y^20 + 4*Y^19 + 5*Y^17 + 3*Y^16 + 3*Y^15 + 3*Y^13 + 6*Y^12 + Y^11
        + 3*Y^10 + 3*Y^9 + 3*Y^8 + 4*Y^7 + Y^6 + 6*Y^5 + Y^4 + 5*Y^3 + 2*Y^2 + 6*Y +
        1,
    T^56 + 9/7*T^55 + 54/49*T^54 + 270/343*T^53 - 205/2401*T^52 + 640/2401*T^51 + 
        404/2401*T^50 + 1364/2401*T^49 + 367/343*T^48 + 285/343*T^47 + 
        2643/2401*T^46 - 188/2401*T^45 - 300/343*T^44 - 2061/2401*T^43 - 
        2507/2401*T^42 + 379/2401*T^41 + 114/2401*T^40 - 563/2401*T^39 - 
        234/2401*T^38 - 3046/2401*T^37 - 2851/2401*T^36 - 3441/2401*T^35 - 
        1917/2401*T^34 + 1779/2401*T^33 + 1310/2401*T^32 + 1980/2401*T^31 - 
        88/2401*T^30 - 2495/2401*T^29 - 1681/2401*T^28 - 2495/2401*T^27 - 
        88/2401*T^26 + 1980/2401*T^25 + 1310/2401*T^24 + 1779/2401*T^23 - 
        1917/2401*T^22 - 3441/2401*T^21 - 2851/2401*T^20 - 3046/2401*T^19 - 
        234/2401*T^18 - 563/2401*T^17 + 114/2401*T^16 + 379/2401*T^15 - 
        2507/2401*T^14 - 2061/2401*T^13 - 300/343*T^12 - 188/2401*T^11 + 
        2643/2401*T^10 + 285/343*T^9 + 367/343*T^8 + 1364/2401*T^7 + 404/2401*T^6 + 
        640/2401*T^5 - 205/2401*T^4 + 270/343*T^3 + 54/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 4*X*Y^7 
        + X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + X*Y + 5*Y^30 + 6*Y^29 + 
        Y^28 + Y^27 + 6*Y^26 + Y^25 + 2*Y^24 + 5*Y^23 + Y^22 + Y^21 + 4*Y^20 + 
        2*Y^19 + 3*Y^18 + 3*Y^17 + 2*Y^16 + 2*Y^15 + 2*Y^14 + 3*Y^13 + 6*Y^12 + Y^10
        + 4*Y^9 + 3*Y^8 + 3*Y^7 + Y^6 + 6*Y^5 + Y^4 + 5*Y^3 + 4*Y^2 + 4*Y + 6,
    T^56 + 20/7*T^55 + 204/49*T^54 + 1380/343*T^53 + 6192/2401*T^52 + 2378/2401*T^51
        + 943/2401*T^50 + 1907/2401*T^49 + 3898/2401*T^48 + 6644/2401*T^47 + 
        1254/343*T^46 + 8370/2401*T^45 + 5443/2401*T^44 + 2287/2401*T^43 + 
        1060/2401*T^42 + 2021/2401*T^41 + 460/343*T^40 + 3870/2401*T^39 + 
        4423/2401*T^38 + 444/343*T^37 - 426/2401*T^36 - 4744/2401*T^35 - 
        6633/2401*T^34 - 4832/2401*T^33 - 2173/2401*T^32 - 1179/2401*T^31 - 
        1518/2401*T^30 - 2189/2401*T^29 - 2630/2401*T^28 - 2189/2401*T^27 - 
        1518/2401*T^26 - 1179/2401*T^25 - 2173/2401*T^24 - 4832/2401*T^23 - 
        6633/2401*T^22 - 4744/2401*T^21 - 426/2401*T^20 + 444/343*T^19 + 
        4423/2401*T^18 + 3870/2401*T^17 + 460/343*T^16 + 2021/2401*T^15 + 
        1060/2401*T^14 + 2287/2401*T^13 + 5443/2401*T^12 + 8370/2401*T^11 + 
        1254/343*T^10 + 6644/2401*T^9 + 3898/2401*T^8 + 1907/2401*T^7 + 943/2401*T^6
        + 2378/2401*T^5 + 6192/2401*T^4 + 1380/343*T^3 + 204/49*T^2 + 20/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 2*X*Y^11 + 6*X*Y^10 + 2*X*Y^9 + 6*X*Y^8 +
        4*X*Y^7 + 4*X*Y^6 + 3*X*Y^4 + 6*X*Y^2 + 5*X*Y + 3*Y^30 + 3*Y^29 + 5*Y^27 + 
        2*Y^25 + 2*Y^24 + 3*Y^23 + 4*Y^22 + 4*Y^21 + 3*Y^20 + Y^19 + Y^18 + Y^17 + 
        Y^16 + 3*Y^15 + Y^14 + 4*Y^13 + 4*Y^12 + 5*Y^11 + 5*Y^10 + Y^9 + 4*Y^8 + 
        6*Y^7 + Y^6 + Y^5 + 2*Y^4 + 5*Y^3 + 6*Y^2 + Y + 2,
    -T^56 + 17/7*T^55 - 16/7*T^54 + 393/343*T^53 - 471/343*T^52 + 5108/2401*T^51 - 
        4609/2401*T^50 + 3460/2401*T^49 - 2490/2401*T^48 + 331/2401*T^47 + 
        843/2401*T^46 - 796/2401*T^45 + 2363/2401*T^44 - 5235/2401*T^43 + 
        6646/2401*T^42 - 7841/2401*T^41 + 8214/2401*T^40 - 914/343*T^39 + 
        765/343*T^38 - 6822/2401*T^37 + 6784/2401*T^36 - 5057/2401*T^35 + 
        3715/2401*T^34 - 2258/2401*T^33 + 1440/2401*T^32 - 38/49*T^31 + 
        1033/2401*T^30 + 590/2401*T^29 - 590/2401*T^27 - 1033/2401*T^26 + 38/49*T^25
        - 1440/2401*T^24 + 2258/2401*T^23 - 3715/2401*T^22 + 5057/2401*T^21 - 
        6784/2401*T^20 + 6822/2401*T^19 - 765/343*T^18 + 914/343*T^17 - 
        8214/2401*T^16 + 7841/2401*T^15 - 6646/2401*T^14 + 5235/2401*T^13 - 
        2363/2401*T^12 + 796/2401*T^11 - 843/2401*T^10 - 331/2401*T^9 + 
        2490/2401*T^8 - 3460/2401*T^7 + 4609/2401*T^6 - 5108/2401*T^5 + 471/343*T^4 
        - 393/343*T^3 + 16/7*T^2 - 17/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^10 + 2*X*Y^9 + 5*X*Y^7 +
        4*X*Y^6 + 5*X*Y^5 + 2*X*Y^3 + 6*X*Y^2 + 3*X*Y + Y^30 + 5*Y^29 + 4*Y^28 + 
        6*Y^27 + 6*Y^26 + 2*Y^25 + 6*Y^23 + 6*Y^22 + 4*Y^21 + 4*Y^20 + 5*Y^18 + 
        5*Y^17 + 5*Y^16 + 3*Y^15 + 5*Y^13 + 2*Y^12 + Y^11 + 6*Y^10 + 2*Y^9 + 5*Y^8 +
        3*Y^7 + 2*Y^6 + Y^5 + 4*Y^4 + 5*Y^3 + 3*Y^2 + 5*Y + 1,
    -T^56 + 6/7*T^55 + 27/49*T^54 - 121/343*T^53 + 278/2401*T^52 - 824/2401*T^51 - 
        757/2401*T^50 + 59/343*T^49 - 370/2401*T^48 + 279/2401*T^47 + 1465/2401*T^46
        + 398/2401*T^45 - 1772/2401*T^44 - 900/2401*T^43 + 634/2401*T^42 - 
        12/2401*T^41 + 241/343*T^40 - 223/2401*T^39 - 1222/2401*T^38 + 415/2401*T^37
        - 191/2401*T^36 - 803/2401*T^35 + 36/343*T^34 + 1387/2401*T^33 - 26/343*T^32
        - 757/2401*T^31 + 837/2401*T^30 - 1465/2401*T^29 + 1465/2401*T^27 - 
        837/2401*T^26 + 757/2401*T^25 + 26/343*T^24 - 1387/2401*T^23 - 36/343*T^22 +
        803/2401*T^21 + 191/2401*T^20 - 415/2401*T^19 + 1222/2401*T^18 + 
        223/2401*T^17 - 241/343*T^16 + 12/2401*T^15 - 634/2401*T^14 + 900/2401*T^13 
        + 1772/2401*T^12 - 398/2401*T^11 - 1465/2401*T^10 - 279/2401*T^9 + 
        370/2401*T^8 - 59/343*T^7 + 757/2401*T^6 + 824/2401*T^5 - 278/2401*T^4 + 
        121/343*T^3 - 27/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 2*X*Y^9 + 6*X*Y^8 + 
        4*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 3*X + Y^30 + 6*Y^29 + 
        3*Y^28 + 6*Y^27 + 2*Y^26 + Y^25 + 5*Y^24 + Y^23 + Y^21 + 4*Y^20 + Y^19 + 
        Y^18 + 2*Y^17 + 6*Y^16 + 3*Y^15 + 3*Y^14 + 3*Y^13 + 5*Y^12 + 3*Y^11 + 3*Y^9 
        + 4*Y^8 + Y^7 + 2*Y^6 + 5*Y^5 + 5*Y^4 + 4*Y^3 + 5*Y^2 + 2*Y + 6,
    T^56 + 10/7*T^55 - 467/343*T^53 - 1777/2401*T^52 + 661/2401*T^51 - 
        2110/2401*T^50 - 3751/2401*T^49 - 115/2401*T^48 + 5156/2401*T^47 + 
        3561/2401*T^46 - 841/2401*T^45 - 858/2401*T^44 - 32/343*T^43 - 89/343*T^42 -
        2405/2401*T^41 - 1845/2401*T^40 + 202/2401*T^39 + 2803/2401*T^38 + 
        54/49*T^37 + 317/2401*T^36 - 465/2401*T^35 - 1381/2401*T^34 - 1931/2401*T^33
        - 2860/2401*T^32 - 1271/2401*T^31 + 1800/2401*T^30 + 2032/2401*T^29 + 
        1483/2401*T^28 + 2032/2401*T^27 + 1800/2401*T^26 - 1271/2401*T^25 - 
        2860/2401*T^24 - 1931/2401*T^23 - 1381/2401*T^22 - 465/2401*T^21 + 
        317/2401*T^20 + 54/49*T^19 + 2803/2401*T^18 + 202/2401*T^17 - 1845/2401*T^16
        - 2405/2401*T^15 - 89/343*T^14 - 32/343*T^13 - 858/2401*T^12 - 841/2401*T^11
        + 3561/2401*T^10 + 5156/2401*T^9 - 115/2401*T^8 - 3751/2401*T^7 - 
        2110/2401*T^6 + 661/2401*T^5 - 1777/2401*T^4 - 467/343*T^3 + 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 
        3*X*Y^8 + 6*X*Y^7 + X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + X*Y^2 + X*Y + Y^30
        + Y^28 + Y^27 + 3*Y^26 + 6*Y^25 + 4*Y^24 + 3*Y^23 + Y^22 + 4*Y^21 + 3*Y^20 +
        5*Y^19 + 3*Y^18 + 6*Y^17 + 4*Y^16 + 3*Y^15 + 2*Y^14 + 4*Y^13 + 4*Y^12 + 
        2*Y^11 + 4*Y^10 + 3*Y^9 + 5*Y^8 + 4*Y^7 + 3*Y^6 + 4*Y^5 + Y^4 + 6*Y^3 + 
        2*Y^2 + 3*Y + 1,
    T^56 - T^55 + 22/49*T^54 - 23/343*T^53 - 1963/2401*T^52 + 1826/2401*T^51 - 
        1070/2401*T^50 - 188/2401*T^49 + 1523/2401*T^48 - 703/2401*T^47 + 
        531/2401*T^46 + 402/2401*T^45 - 1031/2401*T^44 + 1933/2401*T^43 - 
        1713/2401*T^42 + 1129/2401*T^41 - 1794/2401*T^40 - 886/2401*T^39 + 
        249/343*T^38 - 2847/2401*T^37 + 2334/2401*T^36 + 340/2401*T^35 - 
        698/2401*T^34 + 2962/2401*T^33 - 2439/2401*T^32 + 923/2401*T^31 + 
        24/2401*T^30 - 2241/2401*T^29 + 2333/2401*T^28 - 2241/2401*T^27 + 
        24/2401*T^26 + 923/2401*T^25 - 2439/2401*T^24 + 2962/2401*T^23 - 
        698/2401*T^22 + 340/2401*T^21 + 2334/2401*T^20 - 2847/2401*T^19 + 
        249/343*T^18 - 886/2401*T^17 - 1794/2401*T^16 + 1129/2401*T^15 - 
        1713/2401*T^14 + 1933/2401*T^13 - 1031/2401*T^12 + 402/2401*T^11 + 
        531/2401*T^10 - 703/2401*T^9 + 1523/2401*T^8 - 188/2401*T^7 - 1070/2401*T^6 
        + 1826/2401*T^5 - 1963/2401*T^4 - 23/343*T^3 + 22/49*T^2 - T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 
        6*X*Y^8 + 4*X*Y^7 + X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + X*Y^3 + 3*X*Y^2 + X*Y + 4*X 
        + 6*Y^30 + Y^29 + 2*Y^28 + 4*Y^26 + Y^25 + 2*Y^24 + 4*Y^23 + 2*Y^22 + 5*Y^21
        + 4*Y^20 + 5*Y^19 + 5*Y^15 + Y^14 + 2*Y^11 + 4*Y^10 + 2*Y^9 + 5*Y^8 + 4*Y^7 
        + 5*Y^6 + 6*Y^5 + 3*Y^4 + Y^3 + Y^2 + Y + 1,
    T^56 + T^55 - 4/7*T^54 - 550/343*T^53 - 3252/2401*T^52 + 285/2401*T^51 + 
        2231/2401*T^50 + 2712/2401*T^49 + 1746/2401*T^48 - 926/2401*T^47 - 
        1633/2401*T^46 - 753/2401*T^45 + 341/2401*T^44 - 377/2401*T^43 - 
        244/2401*T^42 + 613/2401*T^41 - 1098/2401*T^40 - 880/2401*T^39 + 
        1842/2401*T^38 + 3441/2401*T^37 + 599/2401*T^36 - 3068/2401*T^35 - 
        2141/2401*T^34 - 801/2401*T^33 - 443/2401*T^32 + 66/343*T^31 + 
        1233/2401*T^30 + 741/2401*T^29 - 416/2401*T^28 + 741/2401*T^27 + 
        1233/2401*T^26 + 66/343*T^25 - 443/2401*T^24 - 801/2401*T^23 - 
        2141/2401*T^22 - 3068/2401*T^21 + 599/2401*T^20 + 3441/2401*T^19 + 
        1842/2401*T^18 - 880/2401*T^17 - 1098/2401*T^16 + 613/2401*T^15 - 
        244/2401*T^14 - 377/2401*T^13 + 341/2401*T^12 - 753/2401*T^11 - 
        1633/2401*T^10 - 926/2401*T^9 + 1746/2401*T^8 + 2712/2401*T^7 + 
        2231/2401*T^6 + 285/2401*T^5 - 3252/2401*T^4 - 550/343*T^3 - 4/7*T^2 + T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^13 + 2*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 + 6*X*Y^7 + 
        6*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 5*X*Y + 4*X + 6*Y^30 + 
        6*Y^29 + 5*Y^28 + 3*Y^27 + 2*Y^25 + 4*Y^24 + Y^23 + 2*Y^22 + 5*Y^21 + 5*Y^20
        + 3*Y^19 + 5*Y^18 + 5*Y^17 + Y^16 + Y^15 + Y^14 + 5*Y^13 + 2*Y^12 + 6*Y^11 +
        2*Y^10 + Y^9 + 3*Y^8 + Y^7 + Y^6 + 2*Y^5 + Y^3 + 3*Y^2 + 6*Y + 6,
    T^56 - 8/7*T^55 + 16/49*T^54 - 227/343*T^53 + 1895/2401*T^52 - 646/2401*T^51 - 
        894/2401*T^50 + 152/2401*T^49 + 204/2401*T^48 + 2951/2401*T^47 - 
        3491/2401*T^46 + 173/343*T^45 - 1350/2401*T^44 + 2819/2401*T^43 - 
        1343/2401*T^42 - 12/49*T^41 - 359/2401*T^40 + 425/2401*T^39 + 300/343*T^38 -
        2565/2401*T^37 + 758/2401*T^36 - 1306/2401*T^35 + 2405/2401*T^34 - 
        213/343*T^33 - 745/2401*T^32 + 845/2401*T^31 - 156/2401*T^30 + 
        1668/2401*T^29 - 379/343*T^28 + 1668/2401*T^27 - 156/2401*T^26 + 
        845/2401*T^25 - 745/2401*T^24 - 213/343*T^23 + 2405/2401*T^22 - 
        1306/2401*T^21 + 758/2401*T^20 - 2565/2401*T^19 + 300/343*T^18 + 
        425/2401*T^17 - 359/2401*T^16 - 12/49*T^15 - 1343/2401*T^14 + 2819/2401*T^13
        - 1350/2401*T^12 + 173/343*T^11 - 3491/2401*T^10 + 2951/2401*T^9 + 
        204/2401*T^8 + 152/2401*T^7 - 894/2401*T^6 - 646/2401*T^5 + 1895/2401*T^4 - 
        227/343*T^3 + 16/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 2*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 4*X*Y^8 + 5*X*Y^7 + 
        5*X*Y^6 + X*Y^3 + 6*X*Y^2 + 6*X + 5*Y^30 + 5*Y^28 + 3*Y^27 + 5*Y^26 + 4*Y^25
        + 6*Y^24 + 6*Y^23 + 4*Y^22 + 2*Y^20 + 5*Y^19 + 3*Y^18 + 4*Y^17 + 6*Y^16 + 
        Y^15 + 4*Y^14 + 3*Y^13 + 3*Y^11 + 4*Y^9 + 4*Y^8 + 4*Y^7 + 3*Y^6 + 2*Y^5 + 
        Y^4 + 3*Y^3 + Y^2 + Y + 2,
    T^56 + 6/7*T^55 - 83/49*T^54 - 866/343*T^53 + 762/2401*T^52 + 6456/2401*T^51 + 
        3659/2401*T^50 - 4069/2401*T^49 - 4427/2401*T^48 + 1856/2401*T^47 + 
        3767/2401*T^46 + 764/2401*T^45 - 2512/2401*T^44 - 4505/2401*T^43 - 
        67/343*T^42 + 5016/2401*T^41 + 5146/2401*T^40 - 157/343*T^39 - 
        6984/2401*T^38 - 3161/2401*T^37 + 5639/2401*T^36 + 5216/2401*T^35 - 
        2266/2401*T^34 - 1013/343*T^33 - 2544/2401*T^32 + 6319/2401*T^31 + 
        888/343*T^30 - 2475/2401*T^29 - 976/343*T^28 - 2475/2401*T^27 + 888/343*T^26
        + 6319/2401*T^25 - 2544/2401*T^24 - 1013/343*T^23 - 2266/2401*T^22 + 
        5216/2401*T^21 + 5639/2401*T^20 - 3161/2401*T^19 - 6984/2401*T^18 - 
        157/343*T^17 + 5146/2401*T^16 + 5016/2401*T^15 - 67/343*T^14 - 
        4505/2401*T^13 - 2512/2401*T^12 + 764/2401*T^11 + 3767/2401*T^10 + 
        1856/2401*T^9 - 4427/2401*T^8 - 4069/2401*T^7 + 3659/2401*T^6 + 
        6456/2401*T^5 + 762/2401*T^4 - 866/343*T^3 - 83/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 
        + 6*X*Y^7 + 6*X*Y^6 + X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 4*X*Y + 5*X + 3*Y^30 + 
        4*Y^29 + 3*Y^28 + 6*Y^27 + Y^26 + 5*Y^25 + 5*Y^24 + 5*Y^23 + 5*Y^22 + 2*Y^20
        + Y^19 + 6*Y^18 + 6*Y^17 + 6*Y^16 + 5*Y^15 + 6*Y^14 + 6*Y^13 + 2*Y^12 + 
        2*Y^11 + 4*Y^10 + 4*Y^9 + 6*Y^8 + Y^7 + 4*Y^5 + 3*Y^4 + 6*Y^3 + 3*Y^2 + 6*Y 
        + 1,
    -T^56 + 4/7*T^55 + 2/49*T^54 + 269/343*T^53 + 3/7*T^52 - 576/2401*T^51 - 
        572/2401*T^50 - 1865/2401*T^49 - 321/2401*T^48 - 330/2401*T^47 + 
        1802/2401*T^46 - 1/49*T^45 + 402/2401*T^44 - 1388/2401*T^43 - 457/2401*T^42 
        + 566/2401*T^41 + 307/2401*T^40 + 1384/2401*T^39 + 299/2401*T^38 - 
        681/2401*T^37 - 368/2401*T^36 - 451/2401*T^35 - 451/2401*T^34 + 
        302/2401*T^33 + 852/2401*T^32 - 107/343*T^31 + 563/2401*T^30 - 
        1331/2401*T^29 + 1331/2401*T^27 - 563/2401*T^26 + 107/343*T^25 - 
        852/2401*T^24 - 302/2401*T^23 + 451/2401*T^22 + 451/2401*T^21 + 
        368/2401*T^20 + 681/2401*T^19 - 299/2401*T^18 - 1384/2401*T^17 - 
        307/2401*T^16 - 566/2401*T^15 + 457/2401*T^14 + 1388/2401*T^13 - 
        402/2401*T^12 + 1/49*T^11 - 1802/2401*T^10 + 330/2401*T^9 + 321/2401*T^8 + 
        1865/2401*T^7 + 572/2401*T^6 + 576/2401*T^5 - 3/7*T^4 - 269/343*T^3 - 
        2/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 4*X*Y^13 + X*Y^11 + 6*X*Y^10 + 4*X*Y^8 + 3*X*Y^7 + 
        2*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + X*Y^3 + 2*X*Y^2 + X*Y + X + 6*Y^30 + Y^28 + 
        2*Y^27 + 4*Y^25 + Y^24 + 2*Y^23 + 2*Y^21 + 2*Y^20 + 2*Y^19 + 4*Y^18 + 6*Y^17
        + 3*Y^16 + Y^15 + 2*Y^14 + 4*Y^13 + 4*Y^12 + 2*Y^11 + 2*Y^10 + 3*Y^9 + 4*Y^8
        + 3*Y^7 + 3*Y^5 + 6*Y^4 + 4*Y^3 + 3*Y^2 + Y + 4,
    T^56 + 1/7*T^55 - 9/49*T^54 - 90/343*T^53 - 2855/2401*T^52 - 1209/2401*T^51 - 
        4/343*T^50 + 426/2401*T^49 + 1789/2401*T^48 + 2381/2401*T^47 + 200/343*T^46 
        - 306/2401*T^45 - 639/2401*T^44 - 440/343*T^43 - 2396/2401*T^42 - 
        190/2401*T^41 - 982/2401*T^40 + 298/343*T^39 + 3050/2401*T^38 + 248/343*T^37
        + 1965/2401*T^36 + 24/343*T^35 - 2930/2401*T^34 - 3039/2401*T^33 - 
        2566/2401*T^32 - 2257/2401*T^31 + 174/343*T^30 + 3499/2401*T^29 + 
        2613/2401*T^28 + 3499/2401*T^27 + 174/343*T^26 - 2257/2401*T^25 - 
        2566/2401*T^24 - 3039/2401*T^23 - 2930/2401*T^22 + 24/343*T^21 + 
        1965/2401*T^20 + 248/343*T^19 + 3050/2401*T^18 + 298/343*T^17 - 
        982/2401*T^16 - 190/2401*T^15 - 2396/2401*T^14 - 440/343*T^13 - 
        639/2401*T^12 - 306/2401*T^11 + 200/343*T^10 + 2381/2401*T^9 + 1789/2401*T^8
        + 426/2401*T^7 - 4/343*T^6 - 1209/2401*T^5 - 2855/2401*T^4 - 90/343*T^3 - 
        9/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 
        4*X*Y^8 + X*Y^7 + 3*X*Y^6 + 2*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + X*Y + 4*X + 5*Y^30
        + Y^29 + 5*Y^28 + 2*Y^27 + 4*Y^26 + 5*Y^25 + 3*Y^24 + 4*Y^23 + 2*Y^22 + 
        2*Y^21 + 3*Y^20 + 4*Y^19 + 3*Y^18 + Y^17 + 2*Y^16 + 3*Y^15 + 4*Y^14 + 3*Y^13
        + Y^12 + 4*Y^11 + Y^10 + Y^9 + 3*Y^8 + 2*Y^7 + 6*Y^6 + 2*Y^5 + 4*Y^4 + 6*Y^3
        + 5*Y^2 + 2*Y + 6,
    -T^56 - 10/7*T^55 + 31/49*T^54 + 701/343*T^53 + 1966/2401*T^52 - 180/343*T^51 - 
        1016/2401*T^50 - 78/2401*T^49 + 542/2401*T^48 + 274/343*T^47 + 
        1605/2401*T^46 - 348/343*T^45 - 5316/2401*T^44 - 2204/2401*T^43 + 
        264/343*T^42 + 2400/2401*T^41 + 1755/2401*T^40 + 715/2401*T^39 - 
        1376/2401*T^38 - 253/343*T^37 + 1047/2401*T^36 + 1971/2401*T^35 - 
        12/2401*T^34 - 797/2401*T^33 - 131/2401*T^32 + 228/2401*T^31 - 132/2401*T^30
        - 419/2401*T^29 + 419/2401*T^27 + 132/2401*T^26 - 228/2401*T^25 + 
        131/2401*T^24 + 797/2401*T^23 + 12/2401*T^22 - 1971/2401*T^21 - 
        1047/2401*T^20 + 253/343*T^19 + 1376/2401*T^18 - 715/2401*T^17 - 
        1755/2401*T^16 - 2400/2401*T^15 - 264/343*T^14 + 2204/2401*T^13 + 
        5316/2401*T^12 + 348/343*T^11 - 1605/2401*T^10 - 274/343*T^9 - 542/2401*T^8 
        + 78/2401*T^7 + 1016/2401*T^6 + 180/343*T^5 - 1966/2401*T^4 - 701/343*T^3 - 
        31/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 2*X*Y^9 + 3*X*Y^6 +
        5*X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 3*X*Y + 3*X + 5*Y^30 + 4*Y^29 + 
        4*Y^28 + 5*Y^27 + 2*Y^26 + 6*Y^25 + 6*Y^24 + 2*Y^23 + 4*Y^21 + 2*Y^18 + 
        5*Y^17 + 2*Y^16 + 2*Y^15 + 5*Y^14 + 4*Y^12 + Y^11 + 2*Y^10 + 4*Y^9 + 2*Y^8 +
        5*Y^5 + Y^4 + 5*Y^3 + 6*Y^2 + 4,
    T^56 - 8/7*T^55 - 2/49*T^54 + 121/343*T^53 - 738/2401*T^52 + 965/2401*T^51 + 
        1238/2401*T^50 - 2105/2401*T^49 + 13/2401*T^48 + 1738/2401*T^47 - 
        2245/2401*T^46 + 923/2401*T^45 + 346/2401*T^44 - 2231/2401*T^43 + 
        2684/2401*T^42 - 151/2401*T^41 - 1588/2401*T^40 + 32/49*T^39 - 
        1822/2401*T^38 - 537/2401*T^37 + 2113/2401*T^36 - 538/2401*T^35 - 
        867/2401*T^34 + 1682/2401*T^33 - 1471/2401*T^32 + 148/2401*T^31 + 
        282/2401*T^30 + 155/2401*T^29 + 100/2401*T^28 + 155/2401*T^27 + 
        282/2401*T^26 + 148/2401*T^25 - 1471/2401*T^24 + 1682/2401*T^23 - 
        867/2401*T^22 - 538/2401*T^21 + 2113/2401*T^20 - 537/2401*T^19 - 
        1822/2401*T^18 + 32/49*T^17 - 1588/2401*T^16 - 151/2401*T^15 + 
        2684/2401*T^14 - 2231/2401*T^13 + 346/2401*T^12 + 923/2401*T^11 - 
        2245/2401*T^10 + 1738/2401*T^9 + 13/2401*T^8 - 2105/2401*T^7 + 1238/2401*T^6
        + 965/2401*T^5 - 738/2401*T^4 + 121/343*T^3 - 2/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + X*Y^10 + 4*X*Y^9 + 
        4*X*Y^7 + 4*X*Y^6 + 6*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 2*X*Y + X + 6*Y^30 + 
        6*Y^29 + 5*Y^28 + 5*Y^27 + 3*Y^26 + 6*Y^25 + 3*Y^24 + 3*Y^23 + 4*Y^21 + 
        3*Y^20 + 4*Y^19 + 6*Y^18 + Y^17 + Y^16 + 4*Y^15 + Y^14 + Y^13 + 3*Y^12 + 
        6*Y^11 + Y^10 + 3*Y^9 + 3*Y^8 + 3*Y^7 + 6*Y^6 + 4*Y^5 + 6*Y^4 + Y^3 + 6*Y,
    -T^56 + 5/7*T^55 - 16/49*T^54 + 312/343*T^53 - 283/2401*T^52 - 150/2401*T^51 - 
        347/2401*T^50 + 696/2401*T^49 - 127/2401*T^48 + 1079/2401*T^47 - 
        1779/2401*T^46 + 551/2401*T^45 + 115/2401*T^44 + 110/343*T^43 + 
        232/2401*T^42 - 99/2401*T^41 - 106/343*T^40 - 391/2401*T^39 - 519/2401*T^38 
        + 1087/2401*T^37 - 1360/2401*T^36 - 6/343*T^35 - 932/2401*T^34 + 
        408/2401*T^33 + 234/2401*T^32 + 158/343*T^31 - 666/2401*T^30 - 358/2401*T^29
        + 358/2401*T^27 + 666/2401*T^26 - 158/343*T^25 - 234/2401*T^24 - 
        408/2401*T^23 + 932/2401*T^22 + 6/343*T^21 + 1360/2401*T^20 - 1087/2401*T^19
        + 519/2401*T^18 + 391/2401*T^17 + 106/343*T^16 + 99/2401*T^15 - 
        232/2401*T^14 - 110/343*T^13 - 115/2401*T^12 - 551/2401*T^11 + 
        1779/2401*T^10 - 1079/2401*T^9 + 127/2401*T^8 - 696/2401*T^7 + 347/2401*T^6 
        + 150/2401*T^5 + 283/2401*T^4 - 312/343*T^3 + 16/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 
        2*X*Y^8 + 4*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + X*Y^2 + 3*X*Y + X + 5*Y^30
        + 4*Y^29 + 3*Y^28 + 5*Y^27 + Y^26 + 3*Y^25 + 6*Y^24 + Y^22 + Y^21 + 2*Y^20 +
        5*Y^19 + 6*Y^18 + Y^17 + 2*Y^16 + 5*Y^15 + Y^14 + Y^13 + 6*Y^12 + 5*Y^9 + 
        3*Y^8 + 5*Y^7 + 4*Y^6 + 5*Y^5 + 6*Y^4 + 3*Y^3 + 6,
    T^56 - 3/7*T^55 - 32/49*T^54 + 50/49*T^53 - 1096/2401*T^52 - 1766/2401*T^51 + 
        316/2401*T^50 + 916/2401*T^49 - 234/2401*T^48 - 55/343*T^47 + 1187/2401*T^46
        - 554/2401*T^45 + 3/49*T^44 + 1158/2401*T^43 - 1860/2401*T^42 + 
        884/2401*T^41 + 1111/2401*T^40 - 1705/2401*T^39 + 771/2401*T^38 + 
        144/2401*T^37 - 524/2401*T^36 + 47/343*T^35 - 1/49*T^34 - 523/2401*T^33 - 
        450/2401*T^32 + 1815/2401*T^31 - 1423/2401*T^30 - 1437/2401*T^29 + 
        3712/2401*T^28 - 1437/2401*T^27 - 1423/2401*T^26 + 1815/2401*T^25 - 
        450/2401*T^24 - 523/2401*T^23 - 1/49*T^22 + 47/343*T^21 - 524/2401*T^20 + 
        144/2401*T^19 + 771/2401*T^18 - 1705/2401*T^17 + 1111/2401*T^16 + 
        884/2401*T^15 - 1860/2401*T^14 + 1158/2401*T^13 + 3/49*T^12 - 554/2401*T^11 
        + 1187/2401*T^10 - 55/343*T^9 - 234/2401*T^8 + 916/2401*T^7 + 316/2401*T^6 -
        1766/2401*T^5 - 1096/2401*T^4 + 50/49*T^3 - 32/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + X*Y^11 + 3*X*Y^10 + X*Y^9 + 5*X*Y^8 + 2*X*Y^7 + 
        3*X*Y^6 + 2*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 6*X*Y + 2*X + 6*Y^30 + 6*Y^29 + Y^28
        + 6*Y^27 + 5*Y^26 + Y^25 + 5*Y^24 + 3*Y^22 + 6*Y^20 + 6*Y^18 + 4*Y^16 + Y^15
        + 5*Y^14 + 6*Y^13 + 4*Y^12 + 6*Y^11 + 3*Y^10 + 2*Y^9 + 5*Y^8 + 5*Y^6 + 3*Y^4
        + Y^2 + 2*Y,
    T^56 - 11/7*T^55 + 50/49*T^54 + 128/343*T^53 - 3617/2401*T^52 + 5673/2401*T^51 -
        551/343*T^50 + 1236/2401*T^49 + 1494/2401*T^48 - 2168/2401*T^47 + 
        1684/2401*T^46 - 26/2401*T^45 - 807/2401*T^44 + 680/2401*T^43 + 115/343*T^42
        - 1685/2401*T^41 + 258/343*T^40 - 360/343*T^39 + 2346/2401*T^38 - 
        382/2401*T^37 - 48/49*T^36 + 3842/2401*T^35 - 3558/2401*T^34 + 809/2401*T^33
        + 2085/2401*T^32 - 401/343*T^31 + 934/2401*T^30 + 1121/2401*T^29 - 
        260/343*T^28 + 1121/2401*T^27 + 934/2401*T^26 - 401/343*T^25 + 
        2085/2401*T^24 + 809/2401*T^23 - 3558/2401*T^22 + 3842/2401*T^21 - 
        48/49*T^20 - 382/2401*T^19 + 2346/2401*T^18 - 360/343*T^17 + 258/343*T^16 - 
        1685/2401*T^15 + 115/343*T^14 + 680/2401*T^13 - 807/2401*T^12 - 26/2401*T^11
        + 1684/2401*T^10 - 2168/2401*T^9 + 1494/2401*T^8 + 1236/2401*T^7 - 
        551/343*T^6 + 5673/2401*T^5 - 3617/2401*T^4 + 128/343*T^3 + 50/49*T^2 - 
        11/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        4*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 6*X*Y + 6*X + 
        6*Y^30 + 4*Y^29 + 4*Y^28 + 2*Y^27 + 2*Y^26 + 5*Y^25 + 4*Y^24 + 3*Y^21 + Y^20
        + Y^19 + 5*Y^17 + 5*Y^16 + Y^15 + Y^14 + 4*Y^12 + 4*Y^10 + 4*Y^9 + Y^8 + Y^7
        + 5*Y^6 + 5*Y^4 + Y^3 + 2*Y^2 + 4*Y + 3,
    -T^56 - 17/7*T^55 - 144/49*T^54 - 1102/343*T^53 - 6688/2401*T^52 - 
        4582/2401*T^51 - 5559/2401*T^50 - 5469/2401*T^49 - 2374/2401*T^48 + 
        484/2401*T^47 + 4653/2401*T^46 + 1101/343*T^45 + 6005/2401*T^44 + 
        3701/2401*T^43 + 2592/2401*T^42 + 516/2401*T^41 - 1284/2401*T^40 - 
        459/343*T^39 - 6684/2401*T^38 - 8185/2401*T^37 - 879/343*T^36 - 
        4432/2401*T^35 - 2867/2401*T^34 - 795/2401*T^33 - 897/2401*T^32 + 
        55/343*T^31 + 2503/2401*T^30 + 1027/2401*T^29 - 1027/2401*T^27 - 
        2503/2401*T^26 - 55/343*T^25 + 897/2401*T^24 + 795/2401*T^23 + 
        2867/2401*T^22 + 4432/2401*T^21 + 879/343*T^20 + 8185/2401*T^19 + 
        6684/2401*T^18 + 459/343*T^17 + 1284/2401*T^16 - 516/2401*T^15 - 
        2592/2401*T^14 - 3701/2401*T^13 - 6005/2401*T^12 - 1101/343*T^11 - 
        4653/2401*T^10 - 484/2401*T^9 + 2374/2401*T^8 + 5469/2401*T^7 + 
        5559/2401*T^6 + 4582/2401*T^5 + 6688/2401*T^4 + 1102/343*T^3 + 144/49*T^2 + 
        17/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 
        + 3*X*Y^8 + 6*X*Y^7 + X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 5*X + 4*Y^30 + 
        3*Y^29 + 3*Y^28 + 3*Y^27 + 3*Y^26 + 2*Y^25 + 5*Y^24 + 3*Y^23 + 6*Y^22 + 
        5*Y^21 + Y^20 + Y^19 + 3*Y^18 + 3*Y^17 + 3*Y^16 + 2*Y^15 + 4*Y^14 + Y^13 + 
        3*Y^12 + 2*Y^10 + 2*Y^8 + 4*Y^7 + 4*Y^6 + 3*Y^5 + 2*Y^3 + 2*Y^2 + 3*Y + 1,
    -T^56 - 11/7*T^55 - 40/49*T^54 - 278/343*T^53 - 2438/2401*T^52 - 317/2401*T^51 +
        874/2401*T^50 - 30/343*T^49 - 50/2401*T^48 - 291/2401*T^47 - 527/2401*T^46 -
        211/2401*T^45 - 1/2401*T^44 + 1543/2401*T^43 + 1642/2401*T^42 - 
        968/2401*T^41 - 1532/2401*T^40 - 1170/2401*T^39 - 3284/2401*T^38 - 
        2517/2401*T^37 + 2/2401*T^36 + 260/2401*T^35 + 1115/2401*T^34 + 
        1485/2401*T^33 - 424/2401*T^32 - 774/2401*T^31 - 33/343*T^30 - 
        1152/2401*T^29 + 1152/2401*T^27 + 33/343*T^26 + 774/2401*T^25 + 
        424/2401*T^24 - 1485/2401*T^23 - 1115/2401*T^22 - 260/2401*T^21 - 
        2/2401*T^20 + 2517/2401*T^19 + 3284/2401*T^18 + 1170/2401*T^17 + 
        1532/2401*T^16 + 968/2401*T^15 - 1642/2401*T^14 - 1543/2401*T^13 + 
        1/2401*T^12 + 211/2401*T^11 + 527/2401*T^10 + 291/2401*T^9 + 50/2401*T^8 + 
        30/343*T^7 - 874/2401*T^6 + 317/2401*T^5 + 2438/2401*T^4 + 278/343*T^3 + 
        40/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 4*X*Y^9 + 5*X*Y^6 + 
        6*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + X*Y + 6*Y^30 + 2*Y^28 + 4*Y^27 + 
        6*Y^26 + Y^25 + 2*Y^24 + 3*Y^23 + 5*Y^22 + 6*Y^20 + 5*Y^19 + 2*Y^18 + 3*Y^16
        + 3*Y^15 + 3*Y^13 + 4*Y^12 + 4*Y^11 + 5*Y^10 + Y^9 + 6*Y^8 + 4*Y^7 + 2*Y^6 +
        5*Y^5 + 4*Y^4 + 6*Y + 1,
    -T^56 + 9/7*T^55 - 27/49*T^54 - 251/343*T^53 + 786/2401*T^52 + 1018/2401*T^51 - 
        993/2401*T^50 - 1737/2401*T^49 + 2690/2401*T^48 - 390/2401*T^47 - 
        402/2401*T^46 - 26/2401*T^45 - 487/2401*T^44 + 2584/2401*T^43 - 
        1812/2401*T^42 - 905/2401*T^41 + 2342/2401*T^40 - 1194/2401*T^39 + 
        720/2401*T^38 - 264/343*T^37 + 1912/2401*T^36 - 1500/2401*T^35 + 
        290/2401*T^34 - 94/2401*T^33 - 828/2401*T^32 + 1483/2401*T^31 - 
        1728/2401*T^30 + 339/2401*T^29 - 339/2401*T^27 + 1728/2401*T^26 - 
        1483/2401*T^25 + 828/2401*T^24 + 94/2401*T^23 - 290/2401*T^22 + 
        1500/2401*T^21 - 1912/2401*T^20 + 264/343*T^19 - 720/2401*T^18 + 
        1194/2401*T^17 - 2342/2401*T^16 + 905/2401*T^15 + 1812/2401*T^14 - 
        2584/2401*T^13 + 487/2401*T^12 + 26/2401*T^11 + 402/2401*T^10 + 390/2401*T^9
        - 2690/2401*T^8 + 1737/2401*T^7 + 993/2401*T^6 - 1018/2401*T^5 - 
        786/2401*T^4 + 251/343*T^3 + 27/49*T^2 - 9/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 4*X*Y^13 + X*Y^12 + X*Y^11 + 4*X*Y^10 + 4*X*Y^6 + 
        5*X*Y^5 + X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 6*X*Y + 3*X + Y^30 + 6*Y^29 + 4*Y^28 +
        5*Y^27 + 4*Y^26 + 3*Y^25 + Y^24 + 3*Y^22 + 3*Y^21 + 5*Y^20 + 3*Y^19 + 2*Y^18
        + 3*Y^17 + 4*Y^16 + 5*Y^15 + 4*Y^14 + 5*Y^13 + 6*Y^12 + 3*Y^11 + Y^10 + 
        4*Y^9 + 5*Y^8 + 2*Y^6 + 6*Y^4 + 4*Y^3 + 4*Y^2 + 3*Y + 4,
    -T^56 + 12/7*T^55 - 37/49*T^54 - 72/343*T^53 - 556/2401*T^52 + 1/7*T^51 + 
        1677/2401*T^50 - 2090/2401*T^49 + 180/343*T^48 - 1892/2401*T^47 + 
        2337/2401*T^46 - 1941/2401*T^45 + 2931/2401*T^44 - 3012/2401*T^43 + 
        572/2401*T^42 + 221/2401*T^41 - 466/2401*T^40 + 1845/2401*T^39 - 
        1677/2401*T^38 + 898/2401*T^37 - 2568/2401*T^36 + 2724/2401*T^35 - 
        240/2401*T^34 + 30/343*T^33 - 2120/2401*T^32 + 1380/2401*T^31 + 
        159/2401*T^30 + 50/2401*T^29 - 50/2401*T^27 - 159/2401*T^26 - 1380/2401*T^25
        + 2120/2401*T^24 - 30/343*T^23 + 240/2401*T^22 - 2724/2401*T^21 + 
        2568/2401*T^20 - 898/2401*T^19 + 1677/2401*T^18 - 1845/2401*T^17 + 
        466/2401*T^16 - 221/2401*T^15 - 572/2401*T^14 + 3012/2401*T^13 - 
        2931/2401*T^12 + 1941/2401*T^11 - 2337/2401*T^10 + 1892/2401*T^9 - 
        180/343*T^8 + 2090/2401*T^7 - 1677/2401*T^6 - 1/7*T^5 + 556/2401*T^4 + 
        72/343*T^3 + 37/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + X*Y^12 + X*Y^11 + 3*X*Y^9 + 4*X*Y^8 + 
        4*X*Y^7 + 3*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 3*X + 5*Y^30 + 
        5*Y^27 + 4*Y^26 + 2*Y^25 + 5*Y^24 + 2*Y^22 + 5*Y^21 + 4*Y^18 + 6*Y^17 + 
        4*Y^15 + 4*Y^14 + Y^13 + 2*Y^12 + 4*Y^11 + 2*Y^10 + 5*Y^9 + 4*Y^8 + 4*Y^7 + 
        2*Y^6 + 6*Y^5 + 5*Y^4 + 2*Y^3 + Y^2 + Y,
    T^56 - 4/7*T^55 - 1/49*T^54 - 53/343*T^53 - 251/2401*T^52 + 13/343*T^51 + 
        205/2401*T^50 + 1464/2401*T^49 + 1630/2401*T^48 - 2475/2401*T^47 + 
        316/2401*T^46 - 1058/2401*T^45 + 421/2401*T^44 + 925/2401*T^43 + 
        600/2401*T^42 + 388/2401*T^41 + 876/2401*T^40 - 2132/2401*T^39 + 13/343*T^38
        - 927/2401*T^37 + 1424/2401*T^36 - 33/2401*T^35 + 830/2401*T^34 - 
        1681/2401*T^33 + 1342/2401*T^32 - 2032/2401*T^31 + 10/343*T^30 + 
        37/2401*T^29 + 1040/2401*T^28 + 37/2401*T^27 + 10/343*T^26 - 2032/2401*T^25 
        + 1342/2401*T^24 - 1681/2401*T^23 + 830/2401*T^22 - 33/2401*T^21 + 
        1424/2401*T^20 - 927/2401*T^19 + 13/343*T^18 - 2132/2401*T^17 + 
        876/2401*T^16 + 388/2401*T^15 + 600/2401*T^14 + 925/2401*T^13 + 
        421/2401*T^12 - 1058/2401*T^11 + 316/2401*T^10 - 2475/2401*T^9 + 
        1630/2401*T^8 + 1464/2401*T^7 + 205/2401*T^6 + 13/343*T^5 - 251/2401*T^4 - 
        53/343*T^3 - 1/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + X*Y^10 + X*Y^7 + 
        2*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 6*X*Y + 5*X + 3*Y^30 + 
        Y^29 + Y^28 + 5*Y^27 + 6*Y^26 + 2*Y^25 + 3*Y^24 + 2*Y^23 + 5*Y^22 + 4*Y^21 +
        5*Y^20 + 4*Y^19 + 3*Y^18 + Y^17 + 3*Y^16 + 4*Y^15 + 3*Y^14 + 2*Y^13 + 2*Y^12
        + 3*Y^11 + 2*Y^10 + 2*Y^9 + 2*Y^8 + 2*Y^7 + 6*Y^4 + 3*Y^3 + Y^2 + 5*Y,
    -T^56 + 10/7*T^55 - 5/49*T^54 - 57/49*T^53 + 1996/2401*T^52 - 878/2401*T^51 - 
        852/2401*T^50 + 3886/2401*T^49 - 4122/2401*T^48 + 5/7*T^47 + 33/2401*T^46 - 
        31/343*T^45 + 352/2401*T^44 + 915/2401*T^43 - 1150/2401*T^42 - 298/2401*T^41
        - 89/2401*T^40 + 2491/2401*T^39 - 2683/2401*T^38 + 1196/2401*T^37 - 
        23/49*T^36 + 165/2401*T^35 + 904/2401*T^34 + 397/2401*T^33 - 2528/2401*T^32 
        + 13/343*T^31 + 1693/2401*T^30 - 520/2401*T^29 + 520/2401*T^27 - 
        1693/2401*T^26 - 13/343*T^25 + 2528/2401*T^24 - 397/2401*T^23 - 
        904/2401*T^22 - 165/2401*T^21 + 23/49*T^20 - 1196/2401*T^19 + 2683/2401*T^18
        - 2491/2401*T^17 + 89/2401*T^16 + 298/2401*T^15 + 1150/2401*T^14 - 
        915/2401*T^13 - 352/2401*T^12 + 31/343*T^11 - 33/2401*T^10 - 5/7*T^9 + 
        4122/2401*T^8 - 3886/2401*T^7 + 852/2401*T^6 + 878/2401*T^5 - 1996/2401*T^4 
        + 57/49*T^3 + 5/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + X*Y^13 + X*Y^12 + 6*X*Y^11 + X*Y^9 + 4*X*Y^6 + 
        5*X*Y^5 + X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + X*Y + 5*X + 6*Y^30 + 6*Y^29 + 5*Y^28 +
        Y^27 + Y^26 + 6*Y^25 + 4*Y^24 + 2*Y^23 + Y^22 + 5*Y^21 + 5*Y^20 + Y^19 + 
        4*Y^18 + 2*Y^17 + 6*Y^16 + 4*Y^14 + 2*Y^13 + Y^12 + 6*Y^11 + 4*Y^10 + 2*Y^8 
        + 6*Y^7 + 3*Y^6 + 6*Y^5 + 3*Y^4 + 4*Y^3 + 3*Y^2 + 6*Y + 6,
    -T^56 - 13/7*T^55 - 73/49*T^54 - 250/343*T^53 + 475/2401*T^52 - 510/2401*T^51 - 
        2840/2401*T^50 - 3116/2401*T^49 - 502/2401*T^48 + 4203/2401*T^47 + 
        5235/2401*T^46 + 450/343*T^45 + 143/2401*T^44 - 212/2401*T^43 + 
        2461/2401*T^42 + 3727/2401*T^41 + 2871/2401*T^40 - 1427/2401*T^39 - 
        4180/2401*T^38 - 3674/2401*T^37 - 2701/2401*T^36 - 1088/2401*T^35 - 
        2297/2401*T^34 - 3944/2401*T^33 - 4085/2401*T^32 - 3202/2401*T^31 - 
        736/2401*T^30 - 88/2401*T^29 + 88/2401*T^27 + 736/2401*T^26 + 3202/2401*T^25
        + 4085/2401*T^24 + 3944/2401*T^23 + 2297/2401*T^22 + 1088/2401*T^21 + 
        2701/2401*T^20 + 3674/2401*T^19 + 4180/2401*T^18 + 1427/2401*T^17 - 
        2871/2401*T^16 - 3727/2401*T^15 - 2461/2401*T^14 + 212/2401*T^13 - 
        143/2401*T^12 - 450/343*T^11 - 5235/2401*T^10 - 4203/2401*T^9 + 502/2401*T^8
        + 3116/2401*T^7 + 2840/2401*T^6 + 510/2401*T^5 - 475/2401*T^4 + 250/343*T^3 
        + 73/49*T^2 + 13/7*T + 1
*], [*
    X^3 + 4*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 3*X*Y^8 + 5*X*Y^7 + 3*X*Y^6 + 
        6*X*Y^5 + X*Y^4 + X*Y^3 + 5*X*Y^2 + 4*X*Y + 4*X + Y^30 + 2*Y^29 + 4*Y^28 + 
        3*Y^27 + 4*Y^25 + 4*Y^24 + 3*Y^23 + 6*Y^22 + 3*Y^21 + 4*Y^20 + 5*Y^19 + Y^18
        + 6*Y^16 + Y^14 + 2*Y^13 + 5*Y^12 + 2*Y^11 + 6*Y^10 + Y^9 + 6*Y^8 + 2*Y^7 + 
        4*Y^6 + 6*Y^4 + 3*Y^2 + 2*Y + 3,
    T^56 - 8/7*T^54 - 15/343*T^53 + 454/2401*T^52 + 1264/2401*T^51 - 114/343*T^50 - 
        351/2401*T^49 + 1016/2401*T^48 - 1035/2401*T^47 - 16/2401*T^46 - 
        956/2401*T^45 + 1031/2401*T^44 + 1332/2401*T^43 - 1462/2401*T^42 - 
        1/2401*T^41 + 20/2401*T^40 + 242/2401*T^39 - 25/49*T^38 - 1/343*T^37 + 
        1894/2401*T^36 - 621/2401*T^35 - 911/2401*T^34 + 23/2401*T^33 + 
        1873/2401*T^32 - 296/2401*T^31 - 2019/2401*T^30 + 687/2401*T^29 + 
        1520/2401*T^28 + 687/2401*T^27 - 2019/2401*T^26 - 296/2401*T^25 + 
        1873/2401*T^24 + 23/2401*T^23 - 911/2401*T^22 - 621/2401*T^21 + 
        1894/2401*T^20 - 1/343*T^19 - 25/49*T^18 + 242/2401*T^17 + 20/2401*T^16 - 
        1/2401*T^15 - 1462/2401*T^14 + 1332/2401*T^13 + 1031/2401*T^12 - 
        956/2401*T^11 - 16/2401*T^10 - 1035/2401*T^9 + 1016/2401*T^8 - 351/2401*T^7 
        - 114/343*T^6 + 1264/2401*T^5 + 454/2401*T^4 - 15/343*T^3 - 8/7*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^13 + X*Y^12 + 5*X*Y^11 + X*Y^10 + X*Y^9 + 6*X*Y^7 + 2*X*Y^6
        + 6*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 3*X*Y + 4*X + 6*Y^30 + 6*Y^28 + 5*Y^26 + 
        4*Y^25 + Y^24 + 3*Y^22 + 5*Y^21 + 5*Y^20 + Y^19 + 2*Y^18 + 6*Y^17 + 5*Y^13 +
        6*Y^12 + 3*Y^11 + Y^10 + 3*Y^8 + 4*Y^7 + 6*Y^6 + 5*Y^5 + 5*Y^4 + 2*Y^3 + Y +
        3,
    T^56 + 11/7*T^55 + 47/49*T^54 + 69/343*T^53 - 782/2401*T^52 - 221/343*T^51 - 
        375/2401*T^50 + 363/2401*T^49 + 233/2401*T^48 - 202/2401*T^47 - 
        1199/2401*T^46 - 1689/2401*T^45 - 2420/2401*T^44 - 2164/2401*T^43 - 
        344/2401*T^42 + 107/2401*T^41 - 377/2401*T^40 - 744/2401*T^39 - 213/343*T^38
        - 1269/2401*T^37 - 261/2401*T^36 + 757/2401*T^35 + 2066/2401*T^34 + 
        1453/2401*T^33 + 27/2401*T^32 - 501/2401*T^31 - 312/2401*T^30 + 
        740/2401*T^29 + 278/343*T^28 + 740/2401*T^27 - 312/2401*T^26 - 501/2401*T^25
        + 27/2401*T^24 + 1453/2401*T^23 + 2066/2401*T^22 + 757/2401*T^21 - 
        261/2401*T^20 - 1269/2401*T^19 - 213/343*T^18 - 744/2401*T^17 - 
        377/2401*T^16 + 107/2401*T^15 - 344/2401*T^14 - 2164/2401*T^13 - 
        2420/2401*T^12 - 1689/2401*T^11 - 1199/2401*T^10 - 202/2401*T^9 + 
        233/2401*T^8 + 363/2401*T^7 - 375/2401*T^6 - 221/343*T^5 - 782/2401*T^4 + 
        69/343*T^3 + 47/49*T^2 + 11/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 4*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + X*Y^9 + 2*X*Y^8 + 
        6*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 5*X*Y + 6*X + 
        5*Y^30 + Y^29 + 2*Y^28 + 5*Y^27 + 2*Y^25 + 5*Y^24 + Y^23 + 4*Y^21 + 6*Y^20 +
        5*Y^19 + 3*Y^18 + 6*Y^17 + Y^16 + 3*Y^15 + Y^14 + Y^13 + 4*Y^11 + 3*Y^10 + 
        Y^9 + 3*Y^8 + 4*Y^7 + 5*Y^6 + 4*Y^5 + Y^4 + 2*Y^3 + 5*Y^2 + 4*Y + 1,
    T^56 - 11/7*T^55 + 62/49*T^54 - 410/343*T^53 + 293/343*T^52 - 1062/2401*T^51 - 
        6/2401*T^50 + 935/2401*T^49 - 2623/2401*T^48 + 3581/2401*T^47 - 
        3618/2401*T^46 + 4111/2401*T^45 - 3408/2401*T^44 + 2167/2401*T^43 - 
        1654/2401*T^42 + 976/2401*T^41 + 13/343*T^40 - 191/343*T^39 + 1080/2401*T^38
        - 915/2401*T^37 + 1700/2401*T^36 - 1244/2401*T^35 + 944/2401*T^34 - 
        1124/2401*T^33 + 31/2401*T^32 + 874/2401*T^31 + 346/2401*T^30 - 
        501/2401*T^29 - 381/2401*T^28 - 501/2401*T^27 + 346/2401*T^26 + 
        874/2401*T^25 + 31/2401*T^24 - 1124/2401*T^23 + 944/2401*T^22 - 
        1244/2401*T^21 + 1700/2401*T^20 - 915/2401*T^19 + 1080/2401*T^18 - 
        191/343*T^17 + 13/343*T^16 + 976/2401*T^15 - 1654/2401*T^14 + 2167/2401*T^13
        - 3408/2401*T^12 + 4111/2401*T^11 - 3618/2401*T^10 + 3581/2401*T^9 - 
        2623/2401*T^8 + 935/2401*T^7 - 6/2401*T^6 - 1062/2401*T^5 + 293/343*T^4 - 
        410/343*T^3 + 62/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 5*X*Y^12 + X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 + 
        5*X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 2*X*Y^2 + 6*X*Y + 3*Y^30 + 6*Y^29 + 
        5*Y^28 + 4*Y^27 + 5*Y^26 + 3*Y^25 + 3*Y^24 + 2*Y^23 + 5*Y^22 + 3*Y^21 + 
        6*Y^20 + 3*Y^18 + 4*Y^17 + 5*Y^16 + 2*Y^15 + Y^14 + 5*Y^13 + Y^12 + 4*Y^11 +
        5*Y^10 + 5*Y^9 + 2*Y^8 + 2*Y^7 + 2*Y^6 + Y^4 + 4*Y^3 + 2*Y^2 + 4*Y + 1,
    -T^56 + 13/7*T^55 - 108/49*T^54 + 957/343*T^53 - 4820/2401*T^52 + 164/343*T^51 +
        1257/2401*T^50 - 3630/2401*T^49 + 5188/2401*T^48 - 3496/2401*T^47 + 
        2957/2401*T^46 - 3814/2401*T^45 + 2505/2401*T^44 - 3488/2401*T^43 + 
        4756/2401*T^42 - 225/343*T^41 - 243/2401*T^40 + 309/2401*T^39 - 
        3230/2401*T^38 + 2528/2401*T^37 + 494/2401*T^36 - 636/2401*T^35 + 
        2284/2401*T^34 - 370/343*T^33 - 1054/2401*T^32 + 2314/2401*T^31 - 
        2049/2401*T^30 + 3524/2401*T^29 - 3524/2401*T^27 + 2049/2401*T^26 - 
        2314/2401*T^25 + 1054/2401*T^24 + 370/343*T^23 - 2284/2401*T^22 + 
        636/2401*T^21 - 494/2401*T^20 - 2528/2401*T^19 + 3230/2401*T^18 - 
        309/2401*T^17 + 243/2401*T^16 + 225/343*T^15 - 4756/2401*T^14 + 
        3488/2401*T^13 - 2505/2401*T^12 + 3814/2401*T^11 - 2957/2401*T^10 + 
        3496/2401*T^9 - 5188/2401*T^8 + 3630/2401*T^7 - 1257/2401*T^6 - 164/343*T^5 
        + 4820/2401*T^4 - 957/343*T^3 + 108/49*T^2 - 13/7*T + 1
*], [*
    X^3 + X*Y^14 + 4*X*Y^13 + 5*X*Y^11 + 6*X*Y^10 + X*Y^8 + X*Y^5 + 5*X*Y^4 + 
        3*X*Y^2 + 3*X*Y + X + Y^30 + 4*Y^29 + 3*Y^28 + 3*Y^27 + Y^26 + Y^25 + Y^24 +
        Y^23 + 4*Y^22 + 5*Y^19 + 2*Y^18 + 2*Y^17 + 6*Y^16 + 5*Y^15 + 2*Y^14 + 4*Y^13
        + 5*Y^12 + 6*Y^11 + Y^9 + 6*Y^8 + 6*Y^7 + 6*Y^6 + 4*Y^5 + 6*Y^4 + 3*Y^3 + 
        2*Y^2 + 5*Y + 3,
    -T^56 - T^55 - 23/49*T^54 + 107/343*T^53 + 1993/2401*T^52 + 3422/2401*T^51 + 
        3291/2401*T^50 + 605/2401*T^49 - 1320/2401*T^48 - 1464/2401*T^47 - 
        367/2401*T^46 + 358/2401*T^45 + 20/343*T^44 + 44/343*T^43 - 103/2401*T^42 - 
        1957/2401*T^41 - 2391/2401*T^40 - 922/2401*T^39 - 604/2401*T^38 - 
        506/2401*T^37 + 54/343*T^36 + 2336/2401*T^35 + 310/343*T^34 + 773/2401*T^33 
        - 138/2401*T^32 - 80/2401*T^31 - 936/2401*T^30 - 2003/2401*T^29 + 
        2003/2401*T^27 + 936/2401*T^26 + 80/2401*T^25 + 138/2401*T^24 - 
        773/2401*T^23 - 310/343*T^22 - 2336/2401*T^21 - 54/343*T^20 + 506/2401*T^19 
        + 604/2401*T^18 + 922/2401*T^17 + 2391/2401*T^16 + 1957/2401*T^15 + 
        103/2401*T^14 - 44/343*T^13 - 20/343*T^12 - 358/2401*T^11 + 367/2401*T^10 + 
        1464/2401*T^9 + 1320/2401*T^8 - 605/2401*T^7 - 3291/2401*T^6 - 3422/2401*T^5
        - 1993/2401*T^4 - 107/343*T^3 + 23/49*T^2 + T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 
        X*Y^8 + X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 2*X*Y^2 + 4*X*Y + 5*X + 5*Y^30
        + 4*Y^29 + 3*Y^28 + 5*Y^27 + 6*Y^26 + 2*Y^25 + 2*Y^24 + 3*Y^23 + Y^21 + 
        2*Y^20 + 5*Y^19 + 5*Y^18 + 4*Y^17 + 5*Y^16 + 2*Y^15 + 3*Y^13 + 5*Y^12 + 
        3*Y^11 + 2*Y^10 + 3*Y^9 + 3*Y^8 + 3*Y^7 + 2*Y^5 + 2*Y^4 + 6*Y^3 + Y^2 + 3,
    T^56 + 6/7*T^55 - 39/49*T^54 - 292/343*T^53 - 1523/2401*T^52 + 827/2401*T^51 + 
        4523/2401*T^50 + 1193/2401*T^49 - 3393/2401*T^48 - 3464/2401*T^47 + 
        452/2401*T^46 + 4794/2401*T^45 + 3238/2401*T^44 - 2041/2401*T^43 - 
        5170/2401*T^42 - 2598/2401*T^41 + 3974/2401*T^40 + 4727/2401*T^39 + 
        393/2401*T^38 - 3099/2401*T^37 - 4457/2401*T^36 + 753/2401*T^35 + 
        4602/2401*T^34 + 1482/2401*T^33 - 214/343*T^32 - 484/343*T^31 - 
        2438/2401*T^30 + 1825/2401*T^29 + 80/49*T^28 + 1825/2401*T^27 - 
        2438/2401*T^26 - 484/343*T^25 - 214/343*T^24 + 1482/2401*T^23 + 
        4602/2401*T^22 + 753/2401*T^21 - 4457/2401*T^20 - 3099/2401*T^19 + 
        393/2401*T^18 + 4727/2401*T^17 + 3974/2401*T^16 - 2598/2401*T^15 - 
        5170/2401*T^14 - 2041/2401*T^13 + 3238/2401*T^12 + 4794/2401*T^11 + 
        452/2401*T^10 - 3464/2401*T^9 - 3393/2401*T^8 + 1193/2401*T^7 + 
        4523/2401*T^6 + 827/2401*T^5 - 1523/2401*T^4 - 292/343*T^3 - 39/49*T^2 + 
        6/7*T + 1
*], [*
    X^3 + 5*X*Y^13 + X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + X*Y^9 + 5*X*Y^8 + 4*X*Y^7 + 
        X*Y^6 + X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 4*X*Y + 5*X + 3*Y^30 + 5*Y^29 
        + 5*Y^28 + Y^26 + 3*Y^25 + 3*Y^24 + Y^23 + 6*Y^22 + 2*Y^21 + 4*Y^19 + 3*Y^18
        + Y^17 + 5*Y^16 + 3*Y^14 + Y^13 + 3*Y^12 + 5*Y^11 + 6*Y^10 + 4*Y^9 + 4*Y^7 +
        6*Y^6 + Y^4 + 3*Y^3 + 2*Y^2 + 5*Y + 5,
    T^56 - 3/7*T^55 - 64/49*T^54 + 47/343*T^53 + 2409/2401*T^52 - 60/2401*T^51 - 
        694/2401*T^50 + 95/2401*T^49 + 305/2401*T^48 - 235/343*T^47 - 537/2401*T^46 
        + 2147/2401*T^45 + 505/2401*T^44 - 1096/2401*T^43 - 1073/2401*T^42 + 
        2550/2401*T^41 - 685/2401*T^40 - 2165/2401*T^39 + 211/343*T^38 + 
        1593/2401*T^37 - 1790/2401*T^36 - 947/2401*T^35 + 1938/2401*T^34 + 
        2074/2401*T^33 - 2162/2401*T^32 - 2614/2401*T^31 + 1411/2401*T^30 + 
        12/49*T^29 + 198/2401*T^28 + 12/49*T^27 + 1411/2401*T^26 - 2614/2401*T^25 - 
        2162/2401*T^24 + 2074/2401*T^23 + 1938/2401*T^22 - 947/2401*T^21 - 
        1790/2401*T^20 + 1593/2401*T^19 + 211/343*T^18 - 2165/2401*T^17 - 
        685/2401*T^16 + 2550/2401*T^15 - 1073/2401*T^14 - 1096/2401*T^13 + 
        505/2401*T^12 + 2147/2401*T^11 - 537/2401*T^10 - 235/343*T^9 + 305/2401*T^8 
        + 95/2401*T^7 - 694/2401*T^6 - 60/2401*T^5 + 2409/2401*T^4 + 47/343*T^3 - 
        64/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 6*X*Y^9 + 2*X*Y^8 +
        3*X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + 6*X*Y^3 + 3*X*Y^2 + 3*X*Y + 6*X + 3*Y^30 + 
        4*Y^29 + 5*Y^28 + Y^27 + 6*Y^26 + 5*Y^25 + 6*Y^24 + 3*Y^22 + 5*Y^21 + 4*Y^20
        + 6*Y^19 + 5*Y^17 + 3*Y^15 + 4*Y^14 + Y^13 + 4*Y^12 + 5*Y^10 + 4*Y^8 + Y^6 +
        4*Y^5 + 3*Y^4 + 3*Y^3 + 6*Y^2 + 4*Y + 1,
    -T^56 + 5/7*T^55 - 39/49*T^54 + 328/343*T^53 - 603/2401*T^52 + 820/2401*T^51 + 
        195/2401*T^50 - 219/2401*T^49 + 214/2401*T^48 + 25/343*T^47 + 612/2401*T^46 
        - 1492/2401*T^45 + 795/2401*T^44 - 2461/2401*T^43 + 202/343*T^42 - 
        883/2401*T^41 + 1300/2401*T^40 + 627/2401*T^39 + 1052/2401*T^38 - 
        669/2401*T^37 + 1521/2401*T^36 - 1712/2401*T^35 + 286/343*T^34 - 
        2116/2401*T^33 + 1492/2401*T^32 - 1439/2401*T^31 - 138/2401*T^30 - 
        537/2401*T^29 + 537/2401*T^27 + 138/2401*T^26 + 1439/2401*T^25 - 
        1492/2401*T^24 + 2116/2401*T^23 - 286/343*T^22 + 1712/2401*T^21 - 
        1521/2401*T^20 + 669/2401*T^19 - 1052/2401*T^18 - 627/2401*T^17 - 
        1300/2401*T^16 + 883/2401*T^15 - 202/343*T^14 + 2461/2401*T^13 - 
        795/2401*T^12 + 1492/2401*T^11 - 612/2401*T^10 - 25/343*T^9 - 214/2401*T^8 +
        219/2401*T^7 - 195/2401*T^6 - 820/2401*T^5 + 603/2401*T^4 - 328/343*T^3 + 
        39/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 
        + 2*X*Y^8 + 2*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 
        4*X*Y + 5*X + 5*Y^30 + 5*Y^29 + 6*Y^28 + 4*Y^27 + 5*Y^26 + 6*Y^25 + 5*Y^24 +
        3*Y^23 + 2*Y^22 + Y^20 + 4*Y^19 + 2*Y^18 + 3*Y^17 + 2*Y^16 + 6*Y^15 + 4*Y^14
        + 2*Y^13 + 3*Y^12 + 2*Y^11 + 4*Y^8 + 2*Y^6 + Y^5 + 2*Y^4 + 6*Y^2 + 2*Y,
    T^56 + 6/7*T^55 - 4/7*T^54 - 33/343*T^53 + 124/2401*T^52 - 333/343*T^51 + 
        440/2401*T^50 + 1280/2401*T^49 - 2559/2401*T^48 - 1045/2401*T^47 + 
        15/49*T^46 - 1300/2401*T^45 + 285/2401*T^44 + 1887/2401*T^43 - 284/2401*T^42
        + 563/2401*T^41 + 2337/2401*T^40 + 100/2401*T^39 - 1119/2401*T^38 - 
        974/2401*T^37 - 1544/2401*T^36 - 1327/2401*T^35 - 745/2401*T^34 - 
        633/2401*T^33 + 128/2401*T^32 + 454/2401*T^31 + 968/2401*T^30 + 
        1531/2401*T^29 + 205/343*T^28 + 1531/2401*T^27 + 968/2401*T^26 + 
        454/2401*T^25 + 128/2401*T^24 - 633/2401*T^23 - 745/2401*T^22 - 
        1327/2401*T^21 - 1544/2401*T^20 - 974/2401*T^19 - 1119/2401*T^18 + 
        100/2401*T^17 + 2337/2401*T^16 + 563/2401*T^15 - 284/2401*T^14 + 
        1887/2401*T^13 + 285/2401*T^12 - 1300/2401*T^11 + 15/49*T^10 - 1045/2401*T^9
        - 2559/2401*T^8 + 1280/2401*T^7 + 440/2401*T^6 - 333/343*T^5 + 124/2401*T^4 
        - 33/343*T^3 - 4/7*T^2 + 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + X*Y^10 + 5*X*Y^9 + 4*X*Y^8 + 
        4*X*Y^7 + 3*X*Y^6 + 3*X*Y^4 + 5*X*Y^3 + 6*X*Y + X + 2*Y^30 + 3*Y^29 + 5*Y^28
        + Y^27 + Y^26 + Y^25 + 5*Y^24 + 4*Y^23 + Y^20 + 2*Y^19 + Y^17 + 5*Y^16 + 
        3*Y^15 + 5*Y^14 + Y^13 + 5*Y^12 + 2*Y^10 + 2*Y^8 + 2*Y^7 + 5*Y^6 + 3*Y^5 + 
        6*Y^4 + 4*Y^3 + 3*Y^2,
    -T^56 + 10/7*T^55 - 76/49*T^54 + 626/343*T^53 - 7285/2401*T^52 + 8530/2401*T^51 
        - 8444/2401*T^50 + 6897/2401*T^49 - 6999/2401*T^48 + 6430/2401*T^47 - 
        5617/2401*T^46 + 2424/2401*T^45 - 670/2401*T^44 - 576/2401*T^43 + 
        797/2401*T^42 - 2819/2401*T^41 + 4383/2401*T^40 - 5127/2401*T^39 + 
        4183/2401*T^38 - 3883/2401*T^37 + 3742/2401*T^36 - 3571/2401*T^35 + 
        1903/2401*T^34 - 674/2401*T^33 + 50/2401*T^32 + 11/2401*T^31 - 340/2401*T^30
        + 338/2401*T^29 - 338/2401*T^27 + 340/2401*T^26 - 11/2401*T^25 - 
        50/2401*T^24 + 674/2401*T^23 - 1903/2401*T^22 + 3571/2401*T^21 - 
        3742/2401*T^20 + 3883/2401*T^19 - 4183/2401*T^18 + 5127/2401*T^17 - 
        4383/2401*T^16 + 2819/2401*T^15 - 797/2401*T^14 + 576/2401*T^13 + 
        670/2401*T^12 - 2424/2401*T^11 + 5617/2401*T^10 - 6430/2401*T^9 + 
        6999/2401*T^8 - 6897/2401*T^7 + 8444/2401*T^6 - 8530/2401*T^5 + 
        7285/2401*T^4 - 626/343*T^3 + 76/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 
        + 6*X*Y^7 + X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 2*X*Y + 5*X + 
        Y^30 + Y^29 + Y^28 + 4*Y^27 + Y^26 + 5*Y^25 + Y^23 + 5*Y^22 + 2*Y^21 + 
        4*Y^20 + Y^18 + Y^16 + 6*Y^15 + 6*Y^14 + 2*Y^13 + 2*Y^12 + 2*Y^10 + 2*Y^9 + 
        3*Y^8 + 3*Y^7 + 4*Y^6 + 4*Y^5 + 5*Y^4 + 3*Y^3 + 2*Y^2 + 2*Y + 6,
    T^56 - T^55 + 4/7*T^54 + 110/343*T^53 - 2776/2401*T^52 + 2846/2401*T^51 - 
        1405/2401*T^50 - 1642/2401*T^49 + 243/343*T^48 - 1524/2401*T^47 + 
        292/2401*T^46 - 940/2401*T^45 + 439/2401*T^44 - 202/2401*T^43 + 81/343*T^42 
        - 589/2401*T^41 + 1342/2401*T^40 - 215/343*T^39 + 990/2401*T^38 + 
        2348/2401*T^37 - 3280/2401*T^36 + 1933/2401*T^35 + 74/2401*T^34 - 
        2123/2401*T^33 + 3050/2401*T^32 - 1972/2401*T^31 - 46/2401*T^30 + 
        821/2401*T^29 - 641/2401*T^28 + 821/2401*T^27 - 46/2401*T^26 - 
        1972/2401*T^25 + 3050/2401*T^24 - 2123/2401*T^23 + 74/2401*T^22 + 
        1933/2401*T^21 - 3280/2401*T^20 + 2348/2401*T^19 + 990/2401*T^18 - 
        215/343*T^17 + 1342/2401*T^16 - 589/2401*T^15 + 81/343*T^14 - 202/2401*T^13 
        + 439/2401*T^12 - 940/2401*T^11 + 292/2401*T^10 - 1524/2401*T^9 + 
        243/343*T^8 - 1642/2401*T^7 - 1405/2401*T^6 + 2846/2401*T^5 - 2776/2401*T^4 
        + 110/343*T^3 + 4/7*T^2 - T + 1
*], [*
    X^3 + 6*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 +
        6*X*Y^6 + 2*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 3*X*Y + X + 4*Y^30 + 6*Y^29 + 5*Y^28
        + 4*Y^27 + 4*Y^26 + 3*Y^25 + Y^23 + 3*Y^22 + 3*Y^21 + 2*Y^20 + 3*Y^19 + 
        5*Y^17 + 6*Y^16 + 4*Y^15 + Y^14 + 3*Y^13 + 4*Y^12 + 2*Y^11 + 4*Y^10 + Y^9 + 
        6*Y^8 + 2*Y^6 + 3*Y^5 + 6*Y^3 + Y^2 + 5*Y + 4,
    -T^56 + 4/7*T^55 + 5/49*T^54 - 52/49*T^53 + 1296/2401*T^52 + 796/2401*T^51 + 
        507/2401*T^50 - 524/2401*T^49 + 1049/2401*T^48 + 883/2401*T^47 + 
        342/2401*T^46 - 1567/2401*T^45 + 523/2401*T^44 + 1609/2401*T^43 - 
        1425/2401*T^42 + 880/2401*T^41 - 549/2401*T^40 + 1237/2401*T^39 + 
        185/2401*T^38 - 1394/2401*T^37 + 351/2401*T^36 - 289/2401*T^35 - 
        129/2401*T^34 - 1350/2401*T^33 - 982/2401*T^32 - 324/2401*T^31 + 
        1753/2401*T^30 - 3250/2401*T^29 + 3250/2401*T^27 - 1753/2401*T^26 + 
        324/2401*T^25 + 982/2401*T^24 + 1350/2401*T^23 + 129/2401*T^22 + 
        289/2401*T^21 - 351/2401*T^20 + 1394/2401*T^19 - 185/2401*T^18 - 
        1237/2401*T^17 + 549/2401*T^16 - 880/2401*T^15 + 1425/2401*T^14 - 
        1609/2401*T^13 - 523/2401*T^12 + 1567/2401*T^11 - 342/2401*T^10 - 
        883/2401*T^9 - 1049/2401*T^8 + 524/2401*T^7 - 507/2401*T^6 - 796/2401*T^5 - 
        1296/2401*T^4 + 52/49*T^3 - 5/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 5*X*Y^8 + X*Y^7 + 3*X*Y^5 + 
        5*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 3*X*Y + 6*Y^30 + Y^28 + 4*Y^27 + 3*Y^26 + 
        4*Y^25 + Y^24 + Y^21 + 2*Y^20 + 2*Y^19 + 2*Y^18 + 3*Y^17 + 3*Y^16 + 4*Y^15 +
        3*Y^14 + 3*Y^13 + Y^12 + Y^11 + 2*Y^10 + 5*Y^9 + 5*Y^8 + 6*Y^7 + 3*Y^6 + 
        4*Y^5 + 6*Y^4 + 5*Y^3 + Y^2 + Y + 3,
    T^56 - T^55 + 32/49*T^54 + 244/343*T^53 - 1172/2401*T^52 - 687/2401*T^51 + 
        1325/2401*T^50 + 709/2401*T^49 - 2820/2401*T^48 + 2273/2401*T^47 - 
        577/2401*T^46 - 568/2401*T^45 - 611/2401*T^44 + 807/2401*T^43 - 5/7*T^42 - 
        451/2401*T^41 + 145/2401*T^40 - 2312/2401*T^39 + 1796/2401*T^38 - 
        1494/2401*T^37 - 13/49*T^36 + 617/2401*T^35 + 796/2401*T^34 - 1235/2401*T^33
        + 150/2401*T^32 + 330/343*T^31 - 1147/2401*T^30 + 324/2401*T^29 + 
        1796/2401*T^28 + 324/2401*T^27 - 1147/2401*T^26 + 330/343*T^25 + 
        150/2401*T^24 - 1235/2401*T^23 + 796/2401*T^22 + 617/2401*T^21 - 13/49*T^20 
        - 1494/2401*T^19 + 1796/2401*T^18 - 2312/2401*T^17 + 145/2401*T^16 - 
        451/2401*T^15 - 5/7*T^14 + 807/2401*T^13 - 611/2401*T^12 - 568/2401*T^11 - 
        577/2401*T^10 + 2273/2401*T^9 - 2820/2401*T^8 + 709/2401*T^7 + 1325/2401*T^6
        - 687/2401*T^5 - 1172/2401*T^4 + 244/343*T^3 + 32/49*T^2 - T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 2*X*Y^9 
        + 6*X*Y^8 + X*Y^7 + 4*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + X + 
        6*Y^30 + 3*Y^28 + Y^26 + 3*Y^25 + 2*Y^24 + 6*Y^23 + 5*Y^22 + 3*Y^21 + 2*Y^20
        + 2*Y^19 + 4*Y^18 + 3*Y^17 + 3*Y^16 + 5*Y^14 + 5*Y^13 + 5*Y^12 + 2*Y^11 + 
        6*Y^10 + 6*Y^9 + 3*Y^8 + 6*Y^7 + 3*Y^6 + 5*Y^5 + 3*Y^4 + Y^3 + 4*Y^2 + 3*Y +
        3,
    -T^56 - 2*T^55 - 10/7*T^54 - 127/343*T^53 + 288/2401*T^52 + 288/343*T^51 + 
        517/343*T^50 + 414/343*T^49 + 1180/2401*T^48 - 163/2401*T^47 - 
        2211/2401*T^46 - 4099/2401*T^45 - 2971/2401*T^44 + 711/2401*T^43 + 
        1625/2401*T^42 + 565/2401*T^41 + 1893/2401*T^40 + 599/343*T^39 + 
        4247/2401*T^38 + 3844/2401*T^37 + 3035/2401*T^36 + 839/2401*T^35 - 
        1289/2401*T^34 - 1165/2401*T^33 - 163/2401*T^32 - 570/2401*T^31 - 
        290/2401*T^30 + 648/2401*T^29 - 648/2401*T^27 + 290/2401*T^26 + 
        570/2401*T^25 + 163/2401*T^24 + 1165/2401*T^23 + 1289/2401*T^22 - 
        839/2401*T^21 - 3035/2401*T^20 - 3844/2401*T^19 - 4247/2401*T^18 - 
        599/343*T^17 - 1893/2401*T^16 - 565/2401*T^15 - 1625/2401*T^14 - 
        711/2401*T^13 + 2971/2401*T^12 + 4099/2401*T^11 + 2211/2401*T^10 + 
        163/2401*T^9 - 1180/2401*T^8 - 414/343*T^7 - 517/343*T^6 - 288/343*T^5 - 
        288/2401*T^4 + 127/343*T^3 + 10/7*T^2 + 2*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 2*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 3*X*Y^8 +
        5*X*Y^7 + 4*X*Y^6 + X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 4*X + Y^30 + Y^29 
        + 2*Y^28 + 5*Y^27 + 5*Y^26 + 5*Y^25 + Y^23 + 5*Y^22 + 5*Y^21 + 2*Y^20 + Y^19
        + 6*Y^18 + 3*Y^17 + Y^15 + 6*Y^14 + 2*Y^12 + 2*Y^11 + 2*Y^10 + 3*Y^8 + 6*Y^7
        + 6*Y^6 + 6*Y^5 + 6*Y^4 + 3*Y^2 + Y + 1,
    T^56 + T^55 + 3/7*T^54 - 389/343*T^53 - 11/7*T^52 - 1228/2401*T^51 + 
        1286/2401*T^50 + 2673/2401*T^49 + 38/2401*T^48 - 256/343*T^47 - 
        2867/2401*T^46 - 243/343*T^45 - 734/2401*T^44 + 1403/2401*T^43 + 
        1633/2401*T^42 + 2257/2401*T^41 + 215/2401*T^40 - 156/343*T^39 - 
        331/343*T^38 - 411/2401*T^37 + 318/343*T^36 + 437/343*T^35 + 1754/2401*T^34 
        - 1613/2401*T^33 - 2789/2401*T^32 - 3222/2401*T^31 - 162/2401*T^30 + 
        1989/2401*T^29 + 4124/2401*T^28 + 1989/2401*T^27 - 162/2401*T^26 - 
        3222/2401*T^25 - 2789/2401*T^24 - 1613/2401*T^23 + 1754/2401*T^22 + 
        437/343*T^21 + 318/343*T^20 - 411/2401*T^19 - 331/343*T^18 - 156/343*T^17 + 
        215/2401*T^16 + 2257/2401*T^15 + 1633/2401*T^14 + 1403/2401*T^13 - 
        734/2401*T^12 - 243/343*T^11 - 2867/2401*T^10 - 256/343*T^9 + 38/2401*T^8 + 
        2673/2401*T^7 + 1286/2401*T^6 - 1228/2401*T^5 - 11/7*T^4 - 389/343*T^3 + 
        3/7*T^2 + T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + X*Y^9 + 6*X*Y^8 + 
        6*X*Y^7 + 4*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 5*X*Y + 6*X + 5*Y^30 + 
        5*Y^29 + 5*Y^27 + 2*Y^26 + 5*Y^25 + 3*Y^24 + 4*Y^23 + 3*Y^22 + 3*Y^21 + 
        3*Y^19 + 2*Y^18 + 5*Y^17 + 4*Y^16 + 3*Y^15 + 6*Y^14 + Y^13 + Y^11 + 2*Y^10 +
        Y^9 + 5*Y^8 + 3*Y^7 + Y^6 + 6*Y^5 + Y^4 + 4*Y^3 + Y^2 + 3*Y + 5,
    T^56 - 4/7*T^55 - 73/49*T^54 + 373/343*T^53 + 1530/2401*T^52 - 2193/2401*T^51 - 
        1214/2401*T^50 + 2229/2401*T^49 + 253/343*T^48 - 2480/2401*T^47 - 
        206/2401*T^46 + 1011/2401*T^45 + 241/2401*T^44 - 1185/2401*T^43 - 
        1304/2401*T^42 + 69/49*T^41 - 408/2401*T^40 - 3611/2401*T^39 + 
        2735/2401*T^38 + 2418/2401*T^37 - 3162/2401*T^36 - 314/343*T^35 + 
        3937/2401*T^34 + 1081/2401*T^33 - 4457/2401*T^32 + 430/2401*T^31 + 
        2631/2401*T^30 - 467/2401*T^29 - 1082/2401*T^28 - 467/2401*T^27 + 
        2631/2401*T^26 + 430/2401*T^25 - 4457/2401*T^24 + 1081/2401*T^23 + 
        3937/2401*T^22 - 314/343*T^21 - 3162/2401*T^20 + 2418/2401*T^19 + 
        2735/2401*T^18 - 3611/2401*T^17 - 408/2401*T^16 + 69/49*T^15 - 
        1304/2401*T^14 - 1185/2401*T^13 + 241/2401*T^12 + 1011/2401*T^11 - 
        206/2401*T^10 - 2480/2401*T^9 + 253/343*T^8 + 2229/2401*T^7 - 1214/2401*T^6 
        - 2193/2401*T^5 + 1530/2401*T^4 + 373/343*T^3 - 73/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 2*X*Y^5 + X*Y^4 + X*Y^3 + 3*X*Y^2 + 2*X*Y + 4*X + 2*Y^30 + 2*Y^29 
        + 4*Y^28 + 5*Y^27 + Y^26 + 3*Y^25 + 5*Y^24 + 5*Y^23 + 2*Y^22 + 5*Y^21 + 
        5*Y^19 + 6*Y^18 + 3*Y^17 + 6*Y^16 + 2*Y^15 + Y^14 + 4*Y^13 + 6*Y^11 + 2*Y^10
        + 6*Y^9 + 4*Y^8 + 6*Y^7 + 6*Y^6 + Y^5 + 3*Y^4 + 6*Y^3 + 3*Y^2 + 5*Y + 6,
    -T^56 + 2/7*T^55 + 4/7*T^54 + 55/343*T^53 + 17/49*T^52 - 1363/2401*T^51 + 
        247/2401*T^50 + 39/2401*T^49 - 461/2401*T^48 + 701/2401*T^47 - 702/2401*T^46
        + 2630/2401*T^45 - 99/343*T^44 - 99/343*T^43 + 632/2401*T^42 - 
        2465/2401*T^41 + 1748/2401*T^40 - 766/2401*T^39 - 610/2401*T^38 + 
        2481/2401*T^37 - 885/2401*T^36 + 1095/2401*T^35 - 2209/2401*T^34 - 
        715/2401*T^33 + 869/2401*T^32 - 1189/2401*T^31 + 2722/2401*T^30 - 
        1296/2401*T^29 + 1296/2401*T^27 - 2722/2401*T^26 + 1189/2401*T^25 - 
        869/2401*T^24 + 715/2401*T^23 + 2209/2401*T^22 - 1095/2401*T^21 + 
        885/2401*T^20 - 2481/2401*T^19 + 610/2401*T^18 + 766/2401*T^17 - 
        1748/2401*T^16 + 2465/2401*T^15 - 632/2401*T^14 + 99/343*T^13 + 99/343*T^12 
        - 2630/2401*T^11 + 702/2401*T^10 - 701/2401*T^9 + 461/2401*T^8 - 39/2401*T^7
        - 247/2401*T^6 + 1363/2401*T^5 - 17/49*T^4 - 55/343*T^3 - 4/7*T^2 - 2/7*T + 
        1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 5*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 3*X*Y^7 + 
        2*X*Y^6 + 4*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 2*X*Y + 2*X + 2*Y^30 + 3*Y^29 + 
        2*Y^28 + 2*Y^27 + 5*Y^25 + 4*Y^23 + 4*Y^22 + 4*Y^21 + 5*Y^20 + 2*Y^19 + 
        4*Y^15 + 3*Y^14 + Y^13 + Y^12 + 3*Y^11 + 4*Y^6 + 4*Y^5 + 5*Y^4 + 4*Y^3 + 
        5*Y^2 + Y + 3,
    T^56 - 1/7*T^55 - 57/49*T^54 - 160/343*T^53 + 1643/2401*T^52 + 1371/2401*T^51 - 
        437/2401*T^50 - 1203/2401*T^49 + 246/2401*T^48 + 90/343*T^47 - 631/2401*T^46
        - 198/2401*T^45 + 1291/2401*T^44 - 810/2401*T^43 - 719/2401*T^42 - 
        16/2401*T^41 + 785/2401*T^40 + 599/2401*T^39 + 1271/2401*T^38 - 
        818/2401*T^37 - 206/343*T^36 - 657/2401*T^35 + 1546/2401*T^34 + 
        1284/2401*T^33 - 524/2401*T^32 - 233/343*T^31 + 942/2401*T^30 + 
        192/2401*T^29 - 934/2401*T^28 + 192/2401*T^27 + 942/2401*T^26 - 233/343*T^25
        - 524/2401*T^24 + 1284/2401*T^23 + 1546/2401*T^22 - 657/2401*T^21 - 
        206/343*T^20 - 818/2401*T^19 + 1271/2401*T^18 + 599/2401*T^17 + 
        785/2401*T^16 - 16/2401*T^15 - 719/2401*T^14 - 810/2401*T^13 + 
        1291/2401*T^12 - 198/2401*T^11 - 631/2401*T^10 + 90/343*T^9 + 246/2401*T^8 -
        1203/2401*T^7 - 437/2401*T^6 + 1371/2401*T^5 + 1643/2401*T^4 - 160/343*T^3 -
        57/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 6*X*Y^12 + 4*X*Y^11 + 4*X*Y^9 + 6*X*Y^8 + 6*X*Y^7 + 
        X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + X*Y + 4*X + 3*Y^30 + 3*Y^29 
        + 6*Y^28 + 6*Y^27 + 4*Y^26 + 3*Y^25 + 3*Y^24 + 4*Y^23 + 3*Y^20 + 3*Y^19 + 
        4*Y^18 + 2*Y^17 + Y^16 + 4*Y^15 + Y^13 + Y^12 + 6*Y^10 + 3*Y^9 + 2*Y^8 + 
        4*Y^7 + 2*Y^6 + 2*Y^5 + 4*Y^4 + 4*Y^3 + 4*Y^2 + 4*Y + 1,
    -T^56 - 5/7*T^55 - 53/49*T^54 - 1/7*T^53 + 1719/2401*T^52 + 3755/2401*T^51 + 
        3845/2401*T^50 + 2801/2401*T^49 + 141/343*T^48 - 1289/2401*T^47 - 
        1978/2401*T^46 - 473/343*T^45 - 3350/2401*T^44 - 465/343*T^43 - 
        1821/2401*T^42 - 101/343*T^41 + 1808/2401*T^40 + 3699/2401*T^39 + 
        4283/2401*T^38 + 4610/2401*T^37 + 2746/2401*T^36 + 963/2401*T^35 - 
        1730/2401*T^34 - 2390/2401*T^33 - 605/343*T^32 - 3824/2401*T^31 - 
        3344/2401*T^30 - 2098/2401*T^29 + 2098/2401*T^27 + 3344/2401*T^26 + 
        3824/2401*T^25 + 605/343*T^24 + 2390/2401*T^23 + 1730/2401*T^22 - 
        963/2401*T^21 - 2746/2401*T^20 - 4610/2401*T^19 - 4283/2401*T^18 - 
        3699/2401*T^17 - 1808/2401*T^16 + 101/343*T^15 + 1821/2401*T^14 + 
        465/343*T^13 + 3350/2401*T^12 + 473/343*T^11 + 1978/2401*T^10 + 
        1289/2401*T^9 - 141/343*T^8 - 2801/2401*T^7 - 3845/2401*T^6 - 3755/2401*T^5 
        - 1719/2401*T^4 + 1/7*T^3 + 53/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + X*Y^13 + 5*X*Y^12 + X*Y^11 + 4*X*Y^8 + 6*X*Y^7 + 
        5*X*Y^6 + X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 4*X*Y + 2*X + 2*Y^30 + Y^29 + 2*Y^28 +
        Y^27 + 2*Y^26 + 5*Y^25 + 5*Y^24 + 3*Y^23 + 5*Y^22 + 2*Y^21 + 3*Y^20 + 2*Y^19
        + 6*Y^18 + 5*Y^17 + 2*Y^16 + 5*Y^15 + 5*Y^14 + 4*Y^13 + Y^12 + 6*Y^6 + 2*Y^5
        + Y^4 + 3*Y^3 + 5*Y^2 + 1,
    -T^56 - 2/7*T^55 + 20/49*T^54 + 32/49*T^53 + 520/2401*T^52 + 342/2401*T^51 + 
        814/2401*T^50 - 1081/2401*T^49 - 1487/2401*T^48 - 58/343*T^47 + 
        426/2401*T^46 + 2123/2401*T^45 + 1969/2401*T^44 + 78/2401*T^43 - 
        1462/2401*T^42 - 1817/2401*T^41 - 408/2401*T^40 - 1318/2401*T^39 + 
        1466/2401*T^38 + 1926/2401*T^37 + 863/2401*T^36 - 919/2401*T^35 - 
        454/2401*T^34 - 692/2401*T^33 - 650/2401*T^32 - 204/2401*T^31 + 
        2181/2401*T^30 + 198/343*T^29 - 198/343*T^27 - 2181/2401*T^26 + 
        204/2401*T^25 + 650/2401*T^24 + 692/2401*T^23 + 454/2401*T^22 + 
        919/2401*T^21 - 863/2401*T^20 - 1926/2401*T^19 - 1466/2401*T^18 + 
        1318/2401*T^17 + 408/2401*T^16 + 1817/2401*T^15 + 1462/2401*T^14 - 
        78/2401*T^13 - 1969/2401*T^12 - 2123/2401*T^11 - 426/2401*T^10 + 58/343*T^9 
        + 1487/2401*T^8 + 1081/2401*T^7 - 814/2401*T^6 - 342/2401*T^5 - 520/2401*T^4
        - 32/49*T^3 - 20/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 
        + 6*X*Y^8 + 4*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 
        2*X*Y + 4*X + 4*Y^30 + 2*Y^29 + 2*Y^28 + 6*Y^27 + 5*Y^26 + 6*Y^25 + 3*Y^23 +
        5*Y^22 + 2*Y^21 + 6*Y^19 + 4*Y^18 + 5*Y^17 + 4*Y^16 + 3*Y^15 + 6*Y^13 + 
        3*Y^11 + 6*Y^9 + 4*Y^8 + 6*Y^7 + 3*Y^5 + 5*Y^4 + Y^2 + 3*Y + 3,
    -T^56 - 9/7*T^55 - 22/49*T^54 + 87/343*T^53 + 1206/2401*T^52 + 300/2401*T^51 + 
        428/2401*T^50 + 4/2401*T^49 + 1489/2401*T^48 + 2413/2401*T^47 - 
        999/2401*T^46 - 2928/2401*T^45 - 2570/2401*T^44 + 415/2401*T^43 + 
        568/2401*T^42 - 1581/2401*T^41 - 323/343*T^40 - 1590/2401*T^39 + 
        1912/2401*T^38 + 3025/2401*T^37 + 268/343*T^36 - 1460/2401*T^35 - 
        3096/2401*T^34 + 352/2401*T^33 + 2074/2401*T^32 + 383/2401*T^31 - 
        2451/2401*T^30 - 1920/2401*T^29 + 1920/2401*T^27 + 2451/2401*T^26 - 
        383/2401*T^25 - 2074/2401*T^24 - 352/2401*T^23 + 3096/2401*T^22 + 
        1460/2401*T^21 - 268/343*T^20 - 3025/2401*T^19 - 1912/2401*T^18 + 
        1590/2401*T^17 + 323/343*T^16 + 1581/2401*T^15 - 568/2401*T^14 - 
        415/2401*T^13 + 2570/2401*T^12 + 2928/2401*T^11 + 999/2401*T^10 - 
        2413/2401*T^9 - 1489/2401*T^8 - 4/2401*T^7 - 428/2401*T^6 - 300/2401*T^5 - 
        1206/2401*T^4 - 87/343*T^3 + 22/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 3*X*Y^13 + 4*X*Y^10 + 6*X*Y^8 + X*Y^7 + X*Y^6 + 
        5*X*Y^5 + 5*X*Y^4 + X*Y^3 + 5*X*Y^2 + 3*X*Y + 2*X + 2*Y^30 + Y^29 + 3*Y^28 +
        4*Y^27 + Y^26 + 3*Y^25 + 6*Y^23 + 6*Y^22 + 5*Y^21 + 4*Y^20 + 6*Y^19 + Y^18 +
        5*Y^17 + 5*Y^16 + 4*Y^15 + 6*Y^14 + 2*Y^12 + Y^11 + 2*Y^10 + 3*Y^9 + 5*Y^7 +
        5*Y^6 + 6*Y^5 + 2*Y^4 + Y^2,
    -T^56 + 3/7*T^55 + 3/7*T^54 + 3/49*T^53 - 268/2401*T^52 - 2911/2401*T^51 + 
        1994/2401*T^50 + 782/2401*T^49 + 429/2401*T^48 - 433/2401*T^47 - 
        1116/2401*T^46 + 2549/2401*T^45 - 324/2401*T^44 - 17/2401*T^43 - 
        562/2401*T^42 + 606/2401*T^41 + 1118/2401*T^40 - 1079/2401*T^39 + 
        216/2401*T^38 - 568/2401*T^37 + 628/2401*T^36 - 233/2401*T^35 - 
        1180/2401*T^34 + 787/2401*T^33 + 151/2401*T^32 + 622/2401*T^31 - 
        734/2401*T^30 - 1315/2401*T^29 + 1315/2401*T^27 + 734/2401*T^26 - 
        622/2401*T^25 - 151/2401*T^24 - 787/2401*T^23 + 1180/2401*T^22 + 
        233/2401*T^21 - 628/2401*T^20 + 568/2401*T^19 - 216/2401*T^18 + 
        1079/2401*T^17 - 1118/2401*T^16 - 606/2401*T^15 + 562/2401*T^14 + 
        17/2401*T^13 + 324/2401*T^12 - 2549/2401*T^11 + 1116/2401*T^10 + 
        433/2401*T^9 - 429/2401*T^8 - 782/2401*T^7 - 1994/2401*T^6 + 2911/2401*T^5 +
        268/2401*T^4 - 3/49*T^3 - 3/7*T^2 - 3/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + X*Y^13 + X*Y^12 + 5*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 
        4*X*Y^7 + 2*X*Y^6 + 3*X*Y^4 + X*Y^3 + 5*X*Y^2 + 4*X + 6*Y^30 + 4*Y^29 + Y^28
        + Y^26 + 5*Y^25 + 2*Y^24 + 2*Y^23 + 5*Y^22 + 3*Y^21 + 2*Y^20 + Y^19 + 2*Y^17
        + Y^16 + 6*Y^15 + 5*Y^14 + 2*Y^13 + Y^12 + 6*Y^11 + 5*Y^10 + 6*Y^8 + 3*Y^7 +
        2*Y^6 + 5*Y^5 + 2*Y^3 + 5*Y^2 + 4*Y + 3,
    -T^56 - 13/7*T^55 - 94/49*T^54 - 489/343*T^53 - 3621/2401*T^52 - 4968/2401*T^51 
        - 5326/2401*T^50 - 5571/2401*T^49 - 7439/2401*T^48 - 8292/2401*T^47 - 
        7339/2401*T^46 - 4761/2401*T^45 - 4269/2401*T^44 - 4484/2401*T^43 - 
        582/343*T^42 - 3909/2401*T^41 - 4155/2401*T^40 - 4846/2401*T^39 - 
        641/343*T^38 - 3762/2401*T^37 - 3870/2401*T^36 - 496/343*T^35 - 293/343*T^34
        - 1217/2401*T^33 - 390/343*T^32 - 4562/2401*T^31 - 3443/2401*T^30 - 
        1340/2401*T^29 + 1340/2401*T^27 + 3443/2401*T^26 + 4562/2401*T^25 + 
        390/343*T^24 + 1217/2401*T^23 + 293/343*T^22 + 496/343*T^21 + 3870/2401*T^20
        + 3762/2401*T^19 + 641/343*T^18 + 4846/2401*T^17 + 4155/2401*T^16 + 
        3909/2401*T^15 + 582/343*T^14 + 4484/2401*T^13 + 4269/2401*T^12 + 
        4761/2401*T^11 + 7339/2401*T^10 + 8292/2401*T^9 + 7439/2401*T^8 + 
        5571/2401*T^7 + 5326/2401*T^6 + 4968/2401*T^5 + 3621/2401*T^4 + 489/343*T^3 
        + 94/49*T^2 + 13/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 2*X*Y^13 + X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 4*X*Y^8 + 
        6*X*Y^7 + 5*X*Y^6 + 2*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 2*X*Y + 5*X + 4*Y^30 + 
        5*Y^29 + 5*Y^28 + 6*Y^27 + 4*Y^26 + 3*Y^25 + 3*Y^24 + 3*Y^22 + 3*Y^21 + 
        6*Y^20 + 5*Y^19 + 5*Y^18 + 4*Y^16 + 4*Y^15 + 4*Y^14 + 6*Y^11 + Y^10 + Y^9 + 
        5*Y^8 + 6*Y^7 + 5*Y^6 + 3*Y^5 + Y^3 + 6*Y^2 + 4*Y + 5,
    T^56 + 17/7*T^55 + 114/49*T^54 + 337/343*T^53 - 253/2401*T^52 - 558/2401*T^51 + 
        113/2401*T^50 - 85/2401*T^49 + 19/343*T^48 + 624/2401*T^47 - 1230/2401*T^46 
        - 3875/2401*T^45 - 4924/2401*T^44 - 626/343*T^43 - 3911/2401*T^42 - 
        3179/2401*T^41 - 318/343*T^40 - 1264/2401*T^39 - 809/2401*T^38 - 
        1149/2401*T^37 - 1333/2401*T^36 - 479/2401*T^35 + 109/343*T^34 + 
        2045/2401*T^33 + 3825/2401*T^32 + 744/343*T^31 + 4650/2401*T^30 + 
        1403/2401*T^29 - 568/2401*T^28 + 1403/2401*T^27 + 4650/2401*T^26 + 
        744/343*T^25 + 3825/2401*T^24 + 2045/2401*T^23 + 109/343*T^22 - 
        479/2401*T^21 - 1333/2401*T^20 - 1149/2401*T^19 - 809/2401*T^18 - 
        1264/2401*T^17 - 318/343*T^16 - 3179/2401*T^15 - 3911/2401*T^14 - 
        626/343*T^13 - 4924/2401*T^12 - 3875/2401*T^11 - 1230/2401*T^10 + 
        624/2401*T^9 + 19/343*T^8 - 85/2401*T^7 + 113/2401*T^6 - 558/2401*T^5 - 
        253/2401*T^4 + 337/343*T^3 + 114/49*T^2 + 17/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 2*X*Y^13 + X*Y^11 + 6*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 + 
        6*X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + X*Y^3 + 4*X*Y^2 + 2*X + 2*Y^30 + 6*Y^29 + 
        4*Y^28 + 5*Y^27 + 4*Y^26 + 2*Y^25 + Y^24 + 3*Y^23 + 5*Y^22 + 2*Y^21 + 5*Y^20
        + 4*Y^18 + 4*Y^17 + 6*Y^16 + 4*Y^15 + 6*Y^14 + 2*Y^13 + 3*Y^12 + 4*Y^11 + 
        3*Y^10 + 6*Y^9 + 5*Y^8 + 6*Y^7 + 4*Y^6 + Y^4 + 4*Y^2 + 6*Y,
    T^56 - 8/7*T^55 - 39/49*T^54 + 30/49*T^53 + 3849/2401*T^52 - 2379/2401*T^51 - 
        435/343*T^50 + 1635/2401*T^49 + 311/343*T^48 - 129/2401*T^47 - 200/343*T^46 
        - 74/343*T^45 + 979/2401*T^44 + 576/2401*T^43 - 1284/2401*T^42 - 
        739/2401*T^41 + 2164/2401*T^40 - 52/343*T^39 - 822/2401*T^38 - 
        1571/2401*T^37 + 2559/2401*T^36 + 293/2401*T^35 - 173/343*T^34 - 
        1557/2401*T^33 + 2353/2401*T^32 + 1376/2401*T^31 - 3648/2401*T^30 - 
        109/2401*T^29 + 3202/2401*T^28 - 109/2401*T^27 - 3648/2401*T^26 + 
        1376/2401*T^25 + 2353/2401*T^24 - 1557/2401*T^23 - 173/343*T^22 + 
        293/2401*T^21 + 2559/2401*T^20 - 1571/2401*T^19 - 822/2401*T^18 - 
        52/343*T^17 + 2164/2401*T^16 - 739/2401*T^15 - 1284/2401*T^14 + 
        576/2401*T^13 + 979/2401*T^12 - 74/343*T^11 - 200/343*T^10 - 129/2401*T^9 + 
        311/343*T^8 + 1635/2401*T^7 - 435/343*T^6 - 2379/2401*T^5 + 3849/2401*T^4 + 
        30/49*T^3 - 39/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 3*X*Y^11 + 5*X*Y^10 + 3*X*Y^8 + X*Y^7 + 
        4*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + X*Y + 6*X + 3*Y^30 + 3*Y^29 + 5*Y^28
        + Y^27 + 2*Y^25 + 2*Y^24 + 5*Y^23 + 5*Y^21 + 3*Y^20 + 6*Y^18 + 6*Y^17 + 
        6*Y^16 + 6*Y^15 + 6*Y^13 + 6*Y^12 + 2*Y^10 + 5*Y^9 + 6*Y^8 + 4*Y^7 + 6*Y^6 +
        5*Y^5 + 2*Y^4 + 6*Y^3 + Y^2 + Y + 1,
    -T^56 + 11/7*T^55 - 26/49*T^54 - 10/49*T^53 + 190/343*T^52 - 277/343*T^51 + 
        2221/2401*T^50 - 213/343*T^49 + 688/2401*T^48 - 1557/2401*T^47 + 
        505/2401*T^46 + 526/2401*T^45 + 295/2401*T^44 - 10/343*T^43 - 662/2401*T^42 
        + 197/343*T^41 - 999/2401*T^40 + 405/2401*T^39 - 416/2401*T^38 + 
        250/2401*T^37 - 739/2401*T^36 + 720/2401*T^35 + 37/343*T^34 - 31/49*T^33 + 
        2424/2401*T^32 - 2238/2401*T^31 + 2365/2401*T^30 - 1900/2401*T^29 + 
        1900/2401*T^27 - 2365/2401*T^26 + 2238/2401*T^25 - 2424/2401*T^24 + 
        31/49*T^23 - 37/343*T^22 - 720/2401*T^21 + 739/2401*T^20 - 250/2401*T^19 + 
        416/2401*T^18 - 405/2401*T^17 + 999/2401*T^16 - 197/343*T^15 + 662/2401*T^14
        + 10/343*T^13 - 295/2401*T^12 - 526/2401*T^11 - 505/2401*T^10 + 
        1557/2401*T^9 - 688/2401*T^8 + 213/343*T^7 - 2221/2401*T^6 + 277/343*T^5 - 
        190/343*T^4 + 10/49*T^3 + 26/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 +
        4*X*Y^7 + 2*X*Y^6 + X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 5*X*Y + X + Y^30 +
        5*Y^29 + 3*Y^28 + 3*Y^27 + 5*Y^24 + 6*Y^23 + 2*Y^22 + 5*Y^21 + Y^20 + 5*Y^19
        + 6*Y^16 + 5*Y^15 + 6*Y^14 + 4*Y^13 + 6*Y^12 + 2*Y^11 + 2*Y^10 + Y^9 + 5*Y^8
        + 6*Y^7 + 5*Y^6 + 5*Y^5 + 6*Y^4 + Y^3 + 3*Y^2 + 5*Y,
    -T^56 - 1/7*T^55 - 15/49*T^54 + 23/343*T^53 + 226/343*T^52 + 36/2401*T^51 - 
        8/49*T^50 - 814/2401*T^49 + 626/2401*T^48 + 620/2401*T^47 + 895/2401*T^46 - 
        17/2401*T^45 - 465/2401*T^44 + 402/2401*T^43 + 780/2401*T^42 + 
        1333/2401*T^41 - 55/2401*T^40 - 213/343*T^39 - 919/2401*T^38 - 236/2401*T^37
        + 640/2401*T^36 + 5/2401*T^35 - 153/2401*T^34 - 1882/2401*T^33 - 
        999/2401*T^32 - 104/343*T^31 + 362/2401*T^30 + 151/2401*T^29 - 151/2401*T^27
        - 362/2401*T^26 + 104/343*T^25 + 999/2401*T^24 + 1882/2401*T^23 + 
        153/2401*T^22 - 5/2401*T^21 - 640/2401*T^20 + 236/2401*T^19 + 919/2401*T^18 
        + 213/343*T^17 + 55/2401*T^16 - 1333/2401*T^15 - 780/2401*T^14 - 
        402/2401*T^13 + 465/2401*T^12 + 17/2401*T^11 - 895/2401*T^10 - 620/2401*T^9 
        - 626/2401*T^8 + 814/2401*T^7 + 8/49*T^6 - 36/2401*T^5 - 226/343*T^4 - 
        23/343*T^3 + 15/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + X*Y^11 + X*Y^10 + 6*X*Y^8 + 
        3*X*Y^7 + X*Y^6 + X*Y^4 + 3*X*Y^3 + X*Y^2 + 2*X*Y + 2*X + 3*Y^30 + 3*Y^29 + 
        6*Y^28 + 5*Y^27 + 5*Y^26 + 3*Y^25 + Y^24 + 4*Y^23 + 2*Y^22 + Y^21 + 6*Y^20 +
        4*Y^19 + 4*Y^18 + 5*Y^17 + 4*Y^16 + 2*Y^15 + 4*Y^13 + Y^12 + 6*Y^11 + 3*Y^10
        + 3*Y^9 + 5*Y^8 + 6*Y^7 + 4*Y^6 + 6*Y^5 + 4*Y^3 + 3*Y^2 + 4*Y + 1,
    T^56 - 2/7*T^55 - 60/49*T^54 + 163/343*T^53 + 460/343*T^52 - 1227/2401*T^51 - 
        4504/2401*T^50 + 1255/2401*T^49 + 4267/2401*T^48 - 1103/2401*T^47 - 
        4871/2401*T^46 + 1636/2401*T^45 + 6721/2401*T^44 - 51/49*T^43 - 
        7722/2401*T^42 + 2701/2401*T^41 + 1110/343*T^40 - 2346/2401*T^39 - 
        8450/2401*T^38 + 1811/2401*T^37 + 8959/2401*T^36 - 1333/2401*T^35 - 
        8901/2401*T^34 + 785/2401*T^33 + 9357/2401*T^32 - 680/2401*T^31 - 
        9924/2401*T^30 + 541/2401*T^29 + 9251/2401*T^28 + 541/2401*T^27 - 
        9924/2401*T^26 - 680/2401*T^25 + 9357/2401*T^24 + 785/2401*T^23 - 
        8901/2401*T^22 - 1333/2401*T^21 + 8959/2401*T^20 + 1811/2401*T^19 - 
        8450/2401*T^18 - 2346/2401*T^17 + 1110/343*T^16 + 2701/2401*T^15 - 
        7722/2401*T^14 - 51/49*T^13 + 6721/2401*T^12 + 1636/2401*T^11 - 
        4871/2401*T^10 - 1103/2401*T^9 + 4267/2401*T^8 + 1255/2401*T^7 - 
        4504/2401*T^6 - 1227/2401*T^5 + 460/343*T^4 + 163/343*T^3 - 60/49*T^2 - 
        2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 5*X*Y^9 + 5*X*Y^8 +
        4*X*Y^7 + 5*X*Y^6 + X*Y^5 + 6*X*Y^4 + X*Y^2 + 3*X + 3*Y^30 + 2*Y^29 + 6*Y^28
        + 3*Y^27 + 2*Y^24 + 4*Y^23 + 2*Y^22 + 5*Y^21 + 2*Y^20 + 3*Y^19 + 5*Y^18 + 
        5*Y^16 + 5*Y^15 + 4*Y^13 + 3*Y^12 + 5*Y^11 + 4*Y^9 + 5*Y^8 + 5*Y^7 + Y^6 + 
        3*Y^5 + 2*Y^4 + 4*Y^2 + 3*Y + 3,
    T^56 - 5/7*T^55 - 1/49*T^54 + 85/343*T^53 - 1817/2401*T^52 + 829/2401*T^51 + 
        256/2401*T^50 + 355/2401*T^49 - 359/2401*T^48 - 372/2401*T^47 + 
        750/2401*T^46 + 20/2401*T^45 - 991/2401*T^44 + 85/2401*T^43 - 859/2401*T^42 
        + 1354/2401*T^41 - 1392/2401*T^40 + 345/2401*T^39 + 207/2401*T^38 - 
        1336/2401*T^37 + 71/343*T^36 + 181/343*T^35 - 306/2401*T^34 - 443/2401*T^33 
        + 433/2401*T^32 - 464/2401*T^31 + 95/343*T^30 - 472/2401*T^29 + 184/343*T^28
        - 472/2401*T^27 + 95/343*T^26 - 464/2401*T^25 + 433/2401*T^24 - 
        443/2401*T^23 - 306/2401*T^22 + 181/343*T^21 + 71/343*T^20 - 1336/2401*T^19 
        + 207/2401*T^18 + 345/2401*T^17 - 1392/2401*T^16 + 1354/2401*T^15 - 
        859/2401*T^14 + 85/2401*T^13 - 991/2401*T^12 + 20/2401*T^11 + 750/2401*T^10 
        - 372/2401*T^9 - 359/2401*T^8 + 355/2401*T^7 + 256/2401*T^6 + 829/2401*T^5 -
        1817/2401*T^4 + 85/343*T^3 - 1/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 
        + 4*X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 
        5*X*Y + 4*X + Y^30 + 6*Y^29 + 6*Y^28 + 4*Y^25 + 5*Y^24 + 6*Y^23 + 2*Y^22 + 
        6*Y^21 + Y^20 + 2*Y^18 + 6*Y^17 + 3*Y^16 + 3*Y^15 + 6*Y^14 + 3*Y^13 + 6*Y^12
        + 5*Y^11 + 5*Y^10 + 4*Y^9 + Y^8 + Y^7 + 3*Y^6 + 5*Y^5 + 2*Y^4 + 2*Y^3 + 
        2*Y^2 + 1,
    T^56 - 6/7*T^55 - 19/49*T^54 + 130/343*T^53 - 1068/2401*T^52 + 1170/2401*T^51 - 
        727/2401*T^50 - 9/49*T^49 + 1585/2401*T^48 - 362/2401*T^47 - 202/2401*T^46 +
        437/2401*T^45 - 544/2401*T^44 + 31/343*T^43 - 6/2401*T^42 - 1434/2401*T^41 +
        167/343*T^40 - 919/2401*T^39 - 415/2401*T^38 + 1284/2401*T^37 - 
        342/2401*T^36 + 766/2401*T^35 - 352/2401*T^34 - 932/2401*T^33 + 
        1716/2401*T^32 - 984/2401*T^31 + 181/2401*T^30 + 1142/2401*T^29 - 
        2297/2401*T^28 + 1142/2401*T^27 + 181/2401*T^26 - 984/2401*T^25 + 
        1716/2401*T^24 - 932/2401*T^23 - 352/2401*T^22 + 766/2401*T^21 - 
        342/2401*T^20 + 1284/2401*T^19 - 415/2401*T^18 - 919/2401*T^17 + 
        167/343*T^16 - 1434/2401*T^15 - 6/2401*T^14 + 31/343*T^13 - 544/2401*T^12 + 
        437/2401*T^11 - 202/2401*T^10 - 362/2401*T^9 + 1585/2401*T^8 - 9/49*T^7 - 
        727/2401*T^6 + 1170/2401*T^5 - 1068/2401*T^4 + 130/343*T^3 - 19/49*T^2 - 
        6/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 + 
        X*Y^6 + 2*X*Y^5 + X*Y^4 + X*Y^3 + 3*X*Y^2 + 5*X*Y + 5*X + 6*Y^30 + 4*Y^29 + 
        4*Y^28 + 6*Y^27 + 3*Y^26 + 3*Y^24 + 5*Y^23 + 5*Y^22 + 5*Y^21 + Y^19 + 3*Y^18
        + 2*Y^16 + 4*Y^15 + 6*Y^14 + Y^13 + 5*Y^12 + 6*Y^10 + 4*Y^9 + 3*Y^8 + 4*Y^7 
        + 5*Y^6 + 2*Y^5 + 5*Y^4 + Y^3 + 2*Y^2 + 2*Y + 4,
    T^56 + 1/7*T^55 - 32/49*T^54 - 206/343*T^53 + 916/2401*T^52 + 1328/2401*T^51 + 
        113/2401*T^50 - 636/2401*T^49 - 221/343*T^48 - 715/2401*T^47 + 356/2401*T^46
        + 1105/2401*T^45 - 986/2401*T^44 - 1366/2401*T^43 + 571/2401*T^42 + 
        164/343*T^41 + 1140/2401*T^40 - 97/343*T^39 - 1255/2401*T^38 - 501/2401*T^37
        + 1234/2401*T^36 + 1852/2401*T^35 - 394/2401*T^34 - 221/343*T^33 - 
        407/2401*T^32 + 927/2401*T^31 + 956/2401*T^30 - 237/2401*T^29 - 
        1196/2401*T^28 - 237/2401*T^27 + 956/2401*T^26 + 927/2401*T^25 - 
        407/2401*T^24 - 221/343*T^23 - 394/2401*T^22 + 1852/2401*T^21 + 
        1234/2401*T^20 - 501/2401*T^19 - 1255/2401*T^18 - 97/343*T^17 + 
        1140/2401*T^16 + 164/343*T^15 + 571/2401*T^14 - 1366/2401*T^13 - 
        986/2401*T^12 + 1105/2401*T^11 + 356/2401*T^10 - 715/2401*T^9 - 221/343*T^8 
        - 636/2401*T^7 + 113/2401*T^6 + 1328/2401*T^5 + 916/2401*T^4 - 206/343*T^3 -
        32/49*T^2 + 1/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + X*Y^13 + 5*X*Y^11 + 3*X*Y^9 + 2*X*Y^8 + 4*X*Y^7 + 
        3*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 6*X*Y^2 + 3*X*Y + 4*X + 4*Y^30 + 3*Y^29 + Y^28
        + 4*Y^26 + 2*Y^25 + 6*Y^24 + 2*Y^23 + 2*Y^22 + Y^21 + 5*Y^20 + 5*Y^19 + 
        5*Y^18 + 4*Y^17 + 3*Y^16 + 6*Y^15 + 5*Y^14 + 4*Y^13 + 5*Y^12 + 4*Y^11 + 
        3*Y^10 + 2*Y^9 + 2*Y^7 + 4*Y^6 + Y^5 + Y^4 + 5*Y^3 + 5*Y^2 + 6,
    -T^56 + 4/7*T^55 + 73/49*T^54 - 240/343*T^53 + 608/2401*T^52 + 120/2401*T^51 - 
        3263/2401*T^50 - 33/343*T^49 + 125/2401*T^48 - 1304/2401*T^47 + 
        3887/2401*T^46 + 3345/2401*T^45 - 2661/2401*T^44 - 263/2401*T^43 - 
        2066/2401*T^42 - 3056/2401*T^41 + 3210/2401*T^40 + 311/2401*T^39 - 
        180/2401*T^38 + 3036/2401*T^37 - 1570/2401*T^36 + 151/2401*T^35 - 
        908/2401*T^34 - 3996/2401*T^33 + 3265/2401*T^32 + 2033/2401*T^31 - 
        2274/2401*T^30 + 1656/2401*T^29 - 1656/2401*T^27 + 2274/2401*T^26 - 
        2033/2401*T^25 - 3265/2401*T^24 + 3996/2401*T^23 + 908/2401*T^22 - 
        151/2401*T^21 + 1570/2401*T^20 - 3036/2401*T^19 + 180/2401*T^18 - 
        311/2401*T^17 - 3210/2401*T^16 + 3056/2401*T^15 + 2066/2401*T^14 + 
        263/2401*T^13 + 2661/2401*T^12 - 3345/2401*T^11 - 3887/2401*T^10 + 
        1304/2401*T^9 - 125/2401*T^8 + 33/343*T^7 + 3263/2401*T^6 - 120/2401*T^5 - 
        608/2401*T^4 + 240/343*T^3 - 73/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + X*Y^10 + 2*X*Y^9 + 
        5*X*Y^8 + 3*X*Y^7 + 3*X*Y^6 + 5*X*Y^3 + 4*X*Y^2 + 5*X*Y + 4*X + Y^30 + 
        6*Y^29 + 6*Y^28 + Y^27 + 2*Y^25 + 6*Y^23 + 3*Y^21 + 2*Y^20 + 6*Y^19 + 5*Y^17
        + 4*Y^15 + 3*Y^14 + 6*Y^13 + 4*Y^12 + 4*Y^11 + 3*Y^10 + Y^9 + 3*Y^7 + Y^6 + 
        2*Y^4 + 6*Y^3 + 5*Y + 4,
    T^56 + 6/7*T^55 - 38/49*T^54 - 69/49*T^53 - 880/2401*T^52 + 34/343*T^51 - 
        313/343*T^50 - 1858/2401*T^49 + 415/343*T^48 + 4493/2401*T^47 + 
        804/2401*T^46 - 1125/2401*T^45 + 351/2401*T^44 + 212/2401*T^43 - 
        3298/2401*T^42 - 3537/2401*T^41 + 831/2401*T^40 + 2077/2401*T^39 + 
        650/2401*T^38 + 1529/2401*T^37 + 3855/2401*T^36 + 855/2401*T^35 - 
        3592/2401*T^34 - 1727/2401*T^33 + 1996/2401*T^32 - 15/343*T^31 - 
        3557/2401*T^30 + 103/2401*T^29 + 502/343*T^28 + 103/2401*T^27 - 
        3557/2401*T^26 - 15/343*T^25 + 1996/2401*T^24 - 1727/2401*T^23 - 
        3592/2401*T^22 + 855/2401*T^21 + 3855/2401*T^20 + 1529/2401*T^19 + 
        650/2401*T^18 + 2077/2401*T^17 + 831/2401*T^16 - 3537/2401*T^15 - 
        3298/2401*T^14 + 212/2401*T^13 + 351/2401*T^12 - 1125/2401*T^11 + 
        804/2401*T^10 + 4493/2401*T^9 + 415/343*T^8 - 1858/2401*T^7 - 313/343*T^6 + 
        34/343*T^5 - 880/2401*T^4 - 69/49*T^3 - 38/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 
        + 2*X*Y^8 + 3*X*Y^5 + 5*X*Y^3 + X*Y^2 + 2*X*Y + 4*X + 6*Y^30 + 4*Y^29 + 
        5*Y^28 + Y^27 + 6*Y^25 + 4*Y^24 + 4*Y^22 + 5*Y^21 + 4*Y^20 + 5*Y^19 + 4*Y^18
        + 6*Y^17 + 5*Y^16 + 5*Y^15 + 2*Y^14 + 4*Y^13 + 3*Y^12 + 6*Y^10 + Y^9 + 5*Y^8
        + 5*Y^7 + 6*Y^6 + 2*Y^5 + Y^4 + 4*Y^3 + 4*Y + 4,
    T^56 - 2/7*T^55 - 11/49*T^54 + 18/343*T^53 - 37/49*T^52 + 284/2401*T^51 + 
        579/2401*T^50 + 1567/2401*T^49 + 216/2401*T^48 - 496/2401*T^47 + 
        746/2401*T^46 - 1466/2401*T^45 - 1319/2401*T^44 + 968/2401*T^43 + 
        859/2401*T^42 + 150/2401*T^41 + 478/2401*T^40 + 284/2401*T^39 - 
        2479/2401*T^38 - 622/2401*T^37 + 1042/2401*T^36 - 657/2401*T^35 + 
        895/2401*T^34 + 275/2401*T^33 + 430/2401*T^32 - 832/2401*T^31 - 
        200/2401*T^30 + 1101/2401*T^29 - 2575/2401*T^28 + 1101/2401*T^27 - 
        200/2401*T^26 - 832/2401*T^25 + 430/2401*T^24 + 275/2401*T^23 + 
        895/2401*T^22 - 657/2401*T^21 + 1042/2401*T^20 - 622/2401*T^19 - 
        2479/2401*T^18 + 284/2401*T^17 + 478/2401*T^16 + 150/2401*T^15 + 
        859/2401*T^14 + 968/2401*T^13 - 1319/2401*T^12 - 1466/2401*T^11 + 
        746/2401*T^10 - 496/2401*T^9 + 216/2401*T^8 + 1567/2401*T^7 + 579/2401*T^6 +
        284/2401*T^5 - 37/49*T^4 + 18/343*T^3 - 11/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 6*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 + 4*X*Y^6 + 
        2*X*Y^5 + 4*X*Y^4 + X*Y^3 + X*Y + 5*X + 5*Y^30 + 5*Y^29 + 4*Y^28 + Y^27 + 
        Y^26 + 4*Y^25 + 5*Y^24 + 5*Y^22 + 2*Y^20 + 2*Y^18 + 3*Y^17 + Y^16 + 4*Y^15 +
        6*Y^14 + Y^13 + 4*Y^12 + 2*Y^11 + 3*Y^10 + 2*Y^9 + Y^8 + 3*Y^7 + Y^6 + 4*Y^5
        + 3*Y^4 + 5*Y^3 + 5*Y,
    -T^56 + 1/7*T^55 + 67/49*T^54 - 153/343*T^53 - 1112/2401*T^52 + 1464/2401*T^51 -
        72/2401*T^50 - 848/2401*T^49 + 928/2401*T^48 - 1/7*T^47 - 2035/2401*T^46 + 
        167/2401*T^45 + 1941/2401*T^44 + 233/2401*T^43 - 702/2401*T^42 + 
        824/2401*T^41 - 240/2401*T^40 + 267/2401*T^39 + 20/343*T^38 - 657/2401*T^37 
        - 60/343*T^36 - 803/2401*T^35 + 430/2401*T^34 + 433/2401*T^33 - 38/2401*T^32
        + 380/2401*T^31 + 779/2401*T^30 - 323/2401*T^29 + 323/2401*T^27 - 
        779/2401*T^26 - 380/2401*T^25 + 38/2401*T^24 - 433/2401*T^23 - 430/2401*T^22
        + 803/2401*T^21 + 60/343*T^20 + 657/2401*T^19 - 20/343*T^18 - 267/2401*T^17 
        + 240/2401*T^16 - 824/2401*T^15 + 702/2401*T^14 - 233/2401*T^13 - 
        1941/2401*T^12 - 167/2401*T^11 + 2035/2401*T^10 + 1/7*T^9 - 928/2401*T^8 + 
        848/2401*T^7 + 72/2401*T^6 - 1464/2401*T^5 + 1112/2401*T^4 + 153/343*T^3 - 
        67/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + X*Y^10 + 2*X*Y^9 + 
        X*Y^8 + 3*X*Y^7 + 6*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 5*X*Y + 2*X + 2*Y^30 + Y^29 
        + 2*Y^28 + 2*Y^27 + 3*Y^25 + Y^24 + 3*Y^23 + 4*Y^22 + 2*Y^20 + 5*Y^19 + 
        3*Y^18 + 2*Y^16 + 3*Y^15 + 2*Y^14 + 6*Y^13 + 4*Y^12 + 5*Y^9 + Y^8 + 5*Y^7 + 
        6*Y^6 + 6*Y^5 + 6*Y^3 + 3*Y^2 + Y + 4,
    T^56 - T^55 - 32/49*T^54 + 242/343*T^53 - 841/2401*T^52 + 1205/2401*T^51 - 
        915/2401*T^50 + 1331/2401*T^49 + 1355/2401*T^48 - 3650/2401*T^47 - 
        1053/2401*T^46 + 3039/2401*T^45 + 432/2401*T^44 - 2413/2401*T^43 + 
        311/343*T^42 - 425/2401*T^41 + 1163/2401*T^40 - 2760/2401*T^39 - 
        1122/2401*T^38 + 4715/2401*T^37 - 373/343*T^36 + 1221/2401*T^35 - 
        103/343*T^34 - 108/2401*T^33 + 251/2401*T^32 - 1965/2401*T^31 + 
        1852/2401*T^30 - 208/2401*T^29 - 134/2401*T^28 - 208/2401*T^27 + 
        1852/2401*T^26 - 1965/2401*T^25 + 251/2401*T^24 - 108/2401*T^23 - 
        103/343*T^22 + 1221/2401*T^21 - 373/343*T^20 + 4715/2401*T^19 - 
        1122/2401*T^18 - 2760/2401*T^17 + 1163/2401*T^16 - 425/2401*T^15 + 
        311/343*T^14 - 2413/2401*T^13 + 432/2401*T^12 + 3039/2401*T^11 - 
        1053/2401*T^10 - 3650/2401*T^9 + 1355/2401*T^8 + 1331/2401*T^7 - 
        915/2401*T^6 + 1205/2401*T^5 - 841/2401*T^4 + 242/343*T^3 - 32/49*T^2 - T + 
        1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        2*X*Y^8 + 4*X*Y^6 + 5*X*Y^5 + 4*X*Y^3 + 4*X*Y + 3*X + 6*Y^30 + 2*Y^29 + 
        3*Y^28 + 6*Y^27 + 3*Y^26 + 6*Y^25 + 3*Y^24 + 4*Y^23 + 2*Y^20 + Y^19 + 6*Y^18
        + 3*Y^17 + 3*Y^16 + 4*Y^15 + 5*Y^14 + 4*Y^12 + 4*Y^11 + 3*Y^10 + 5*Y^9 + 
        3*Y^8 + 4*Y^7 + 5*Y^6 + 3*Y^5 + 5*Y^4 + 2*Y^2 + 2*Y + 6,
    -T^56 - 9/7*T^55 - 79/49*T^54 - 530/343*T^53 - 555/343*T^52 - 2155/2401*T^51 - 
        561/2401*T^50 + 232/343*T^49 + 2629/2401*T^48 + 564/343*T^47 + 
        3131/2401*T^46 + 3326/2401*T^45 + 312/343*T^44 + 1669/2401*T^43 + 
        858/2401*T^42 + 480/2401*T^41 + 215/2401*T^40 - 30/343*T^39 - 1226/2401*T^38
        - 2253/2401*T^37 - 3531/2401*T^36 - 3751/2401*T^35 - 4003/2401*T^34 - 
        3875/2401*T^33 - 516/343*T^32 - 2668/2401*T^31 - 1726/2401*T^30 - 
        1133/2401*T^29 + 1133/2401*T^27 + 1726/2401*T^26 + 2668/2401*T^25 + 
        516/343*T^24 + 3875/2401*T^23 + 4003/2401*T^22 + 3751/2401*T^21 + 
        3531/2401*T^20 + 2253/2401*T^19 + 1226/2401*T^18 + 30/343*T^17 - 
        215/2401*T^16 - 480/2401*T^15 - 858/2401*T^14 - 1669/2401*T^13 - 
        312/343*T^12 - 3326/2401*T^11 - 3131/2401*T^10 - 564/343*T^9 - 2629/2401*T^8
        - 232/343*T^7 + 561/2401*T^6 + 2155/2401*T^5 + 555/343*T^4 + 530/343*T^3 + 
        79/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + X*Y^13 + 3*X*Y^12 + X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 
        3*X*Y^8 + 6*X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 3*X*Y 
        + 2*X + 5*Y^30 + 4*Y^29 + 2*Y^28 + 5*Y^27 + 5*Y^26 + 3*Y^25 + 6*Y^24 + 
        6*Y^23 + 3*Y^22 + 2*Y^21 + 5*Y^20 + 6*Y^19 + 4*Y^18 + 2*Y^17 + 6*Y^16 + 
        5*Y^15 + 4*Y^14 + 6*Y^13 + 4*Y^12 + 6*Y^11 + 3*Y^10 + Y^9 + 2*Y^8 + 3*Y^7 + 
        3*Y^6 + 4*Y^5 + 3*Y^4 + 6*Y^3 + Y^2 + 3*Y,
    -T^56 - 12/7*T^55 + 19/49*T^54 + 545/343*T^53 - 367/2401*T^52 - 1608/2401*T^51 -
        1137/2401*T^50 - 1276/2401*T^49 + 2278/2401*T^48 + 1389/2401*T^47 - 
        3727/2401*T^46 - 906/2401*T^45 + 3222/2401*T^44 + 857/2401*T^43 - 
        136/343*T^42 - 191/343*T^41 - 15/49*T^40 + 2627/2401*T^39 + 2179/2401*T^38 -
        995/2401*T^37 - 1011/2401*T^36 + 295/2401*T^35 + 2880/2401*T^34 + 
        1726/2401*T^33 - 4009/2401*T^32 - 1440/2401*T^31 + 5009/2401*T^30 + 
        3498/2401*T^29 - 3498/2401*T^27 - 5009/2401*T^26 + 1440/2401*T^25 + 
        4009/2401*T^24 - 1726/2401*T^23 - 2880/2401*T^22 - 295/2401*T^21 + 
        1011/2401*T^20 + 995/2401*T^19 - 2179/2401*T^18 - 2627/2401*T^17 + 
        15/49*T^16 + 191/343*T^15 + 136/343*T^14 - 857/2401*T^13 - 3222/2401*T^12 + 
        906/2401*T^11 + 3727/2401*T^10 - 1389/2401*T^9 - 2278/2401*T^8 + 
        1276/2401*T^7 + 1137/2401*T^6 + 1608/2401*T^5 + 367/2401*T^4 - 545/343*T^3 -
        19/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + X*Y^13 + 2*X*Y^12 + 6*X*Y^10 + 4*X*Y^9 + 3*X*Y^8 + 
        5*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 2*X + 5*Y^30 + Y^29 + 
        6*Y^28 + 3*Y^26 + 2*Y^25 + 3*Y^24 + 4*Y^22 + 4*Y^21 + Y^20 + Y^19 + 5*Y^18 +
        6*Y^17 + 3*Y^16 + 4*Y^15 + 2*Y^14 + 2*Y^13 + 6*Y^12 + 6*Y^11 + 5*Y^10 + 
        3*Y^9 + Y^8 + 5*Y^7 + 2*Y^6 + 4*Y^5 + 3*Y^4 + 6*Y^3 + Y^2 + 2*Y + 4,
    -T^56 - 1/7*T^55 + 39/49*T^54 + 274/343*T^53 + 163/2401*T^52 - 549/2401*T^51 - 
        547/2401*T^50 - 1963/2401*T^49 + 283/2401*T^48 + 1335/2401*T^47 - 
        807/2401*T^46 - 192/343*T^45 + 962/2401*T^44 + 747/2401*T^43 - 114/343*T^42 
        + 100/343*T^41 + 458/2401*T^40 - 1030/2401*T^39 + 374/2401*T^38 + 
        216/343*T^37 - 1044/2401*T^36 - 235/343*T^35 + 687/2401*T^34 - 797/2401*T^33
        - 908/2401*T^32 + 1825/2401*T^31 + 1999/2401*T^30 - 1740/2401*T^29 + 
        1740/2401*T^27 - 1999/2401*T^26 - 1825/2401*T^25 + 908/2401*T^24 + 
        797/2401*T^23 - 687/2401*T^22 + 235/343*T^21 + 1044/2401*T^20 - 216/343*T^19
        - 374/2401*T^18 + 1030/2401*T^17 - 458/2401*T^16 - 100/343*T^15 + 
        114/343*T^14 - 747/2401*T^13 - 962/2401*T^12 + 192/343*T^11 + 807/2401*T^10 
        - 1335/2401*T^9 - 283/2401*T^8 + 1963/2401*T^7 + 547/2401*T^6 + 549/2401*T^5
        - 163/2401*T^4 - 274/343*T^3 - 39/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + X*Y^13 + 4*X*Y^12 + X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 3*X*Y^7 + 3*X*Y^6 + 5*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 3*X*Y + 2*X + 
        2*Y^30 + 6*Y^29 + 5*Y^28 + 3*Y^27 + 2*Y^26 + 5*Y^25 + 5*Y^24 + 3*Y^22 + 
        3*Y^21 + 5*Y^20 + 6*Y^19 + 6*Y^18 + 6*Y^17 + Y^16 + 6*Y^14 + 4*Y^13 + Y^12 +
        6*Y^11 + 5*Y^10 + 3*Y^9 + Y^8 + 4*Y^7 + 2*Y^6 + Y^4 + Y^3 + 3*Y,
    -T^56 + T^55 + 52/49*T^54 - 713/343*T^53 - 99/343*T^52 + 685/343*T^51 + 
        2027/2401*T^50 - 4708/2401*T^49 - 3300/2401*T^48 + 5510/2401*T^47 + 
        2735/2401*T^46 - 4161/2401*T^45 - 4068/2401*T^44 + 878/2401*T^43 + 
        7144/2401*T^42 - 890/2401*T^41 - 7717/2401*T^40 + 144/343*T^39 + 
        6428/2401*T^38 + 2574/2401*T^37 - 6927/2401*T^36 - 3688/2401*T^35 + 
        7086/2401*T^34 + 2614/2401*T^33 - 4629/2401*T^32 - 3391/2401*T^31 + 
        1297/2401*T^30 + 4853/2401*T^29 - 4853/2401*T^27 - 1297/2401*T^26 + 
        3391/2401*T^25 + 4629/2401*T^24 - 2614/2401*T^23 - 7086/2401*T^22 + 
        3688/2401*T^21 + 6927/2401*T^20 - 2574/2401*T^19 - 6428/2401*T^18 - 
        144/343*T^17 + 7717/2401*T^16 + 890/2401*T^15 - 7144/2401*T^14 - 
        878/2401*T^13 + 4068/2401*T^12 + 4161/2401*T^11 - 2735/2401*T^10 - 
        5510/2401*T^9 + 3300/2401*T^8 + 4708/2401*T^7 - 2027/2401*T^6 - 685/343*T^5 
        + 99/343*T^4 + 713/343*T^3 - 52/49*T^2 - T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^13 + 4*X*Y^11 + X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 2*X*Y^7 + 
        X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 5*X*Y + 6*X + 3*Y^30 + 
        5*Y^29 + 3*Y^28 + Y^27 + Y^26 + 4*Y^25 + 3*Y^24 + Y^23 + 3*Y^22 + 5*Y^21 + 
        4*Y^20 + 4*Y^19 + 5*Y^18 + 5*Y^17 + 3*Y^15 + Y^13 + 2*Y^12 + 6*Y^11 + 4*Y^10
        + 4*Y^9 + 6*Y^8 + 5*Y^7 + Y^6 + 2*Y^5 + 6*Y^4 + 6*Y^2 + 2*Y + 2,
    -T^56 + 5/7*T^55 + 45/49*T^54 - 264/343*T^53 + 1240/2401*T^52 - 713/2401*T^51 - 
        1282/2401*T^50 + 158/2401*T^49 + 678/2401*T^48 - 270/2401*T^47 - 
        1369/2401*T^46 + 263/343*T^45 + 747/2401*T^44 + 44/343*T^43 - 1024/2401*T^42
        - 862/2401*T^41 + 1553/2401*T^40 - 1172/2401*T^39 + 855/2401*T^38 - 
        65/2401*T^37 - 1707/2401*T^36 + 165/343*T^35 + 2070/2401*T^34 - 
        148/2401*T^33 - 1887/2401*T^32 + 60/2401*T^31 + 5/49*T^30 + 862/2401*T^29 - 
        862/2401*T^27 - 5/49*T^26 - 60/2401*T^25 + 1887/2401*T^24 + 148/2401*T^23 - 
        2070/2401*T^22 - 165/343*T^21 + 1707/2401*T^20 + 65/2401*T^19 - 
        855/2401*T^18 + 1172/2401*T^17 - 1553/2401*T^16 + 862/2401*T^15 + 
        1024/2401*T^14 - 44/343*T^13 - 747/2401*T^12 - 263/343*T^11 + 1369/2401*T^10
        + 270/2401*T^9 - 678/2401*T^8 - 158/2401*T^7 + 1282/2401*T^6 + 713/2401*T^5 
        - 1240/2401*T^4 + 264/343*T^3 - 45/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 5*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 4*X*Y^7 + 
        X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + X*Y^2 + 4*X*Y + 4*X + 4*Y^30 + Y^29 + Y^28 + 
        2*Y^27 + 6*Y^26 + 6*Y^25 + Y^24 + 2*Y^23 + Y^22 + 2*Y^21 + 2*Y^20 + 5*Y^18 +
        5*Y^17 + 3*Y^15 + Y^14 + 6*Y^13 + 4*Y^12 + 5*Y^11 + 6*Y^10 + 3*Y^9 + 4*Y^8 +
        6*Y^7 + 4*Y^6 + 2*Y^5 + 6*Y^3 + 2*Y^2 + 2*Y,
    -T^56 - 2*T^55 - 13/7*T^54 - 30/49*T^53 + 611/2401*T^52 + 353/343*T^51 + 
        3980/2401*T^50 + 3502/2401*T^49 + 1125/2401*T^48 + 405/2401*T^47 + 
        1342/2401*T^46 + 776/2401*T^45 - 1544/2401*T^44 - 2719/2401*T^43 - 
        2340/2401*T^42 - 1970/2401*T^41 - 790/2401*T^40 + 625/2401*T^39 + 
        1321/2401*T^38 - 29/2401*T^37 - 326/2401*T^36 + 747/2401*T^35 + 
        2358/2401*T^34 + 2573/2401*T^33 + 1775/2401*T^32 + 17/343*T^31 - 
        993/2401*T^30 - 894/2401*T^29 + 894/2401*T^27 + 993/2401*T^26 - 17/343*T^25 
        - 1775/2401*T^24 - 2573/2401*T^23 - 2358/2401*T^22 - 747/2401*T^21 + 
        326/2401*T^20 + 29/2401*T^19 - 1321/2401*T^18 - 625/2401*T^17 + 
        790/2401*T^16 + 1970/2401*T^15 + 2340/2401*T^14 + 2719/2401*T^13 + 
        1544/2401*T^12 - 776/2401*T^11 - 1342/2401*T^10 - 405/2401*T^9 - 
        1125/2401*T^8 - 3502/2401*T^7 - 3980/2401*T^6 - 353/343*T^5 - 611/2401*T^4 +
        30/49*T^3 + 13/7*T^2 + 2*T + 1
*], [*
    X^3 + 3*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 4*X*Y^8 + 3*X*Y^7 + 5*X*Y^6 + 
        X*Y^5 + 2*X*Y^4 + 6*X*Y^2 + 4*X*Y + 6*Y^30 + 4*Y^29 + 4*Y^28 + Y^27 + 6*Y^26
        + 2*Y^25 + 3*Y^24 + 2*Y^21 + 4*Y^20 + 2*Y^19 + Y^18 + 6*Y^17 + 6*Y^16 + 
        2*Y^15 + Y^14 + 6*Y^13 + 3*Y^12 + 6*Y^11 + 5*Y^10 + Y^9 + 6*Y^8 + 4*Y^7 + 
        6*Y^6 + Y^5 + 6*Y^4 + 6*Y^3 + 5*Y^2 + Y + 4,
    T^56 - 4/7*T^55 + 11/49*T^54 + 174/343*T^53 - 409/2401*T^52 + 566/2401*T^51 + 
        939/2401*T^50 + 283/2401*T^49 + 55/343*T^48 - 386/2401*T^47 + 1024/2401*T^46
        - 481/2401*T^45 + 1275/2401*T^44 + 149/2401*T^43 - 1021/2401*T^42 - 
        123/2401*T^41 - 411/2401*T^40 + 713/2401*T^39 - 1373/2401*T^38 + 
        256/2401*T^37 + 44/343*T^36 - 879/2401*T^35 - 628/2401*T^34 + 397/2401*T^33 
        + 68/2401*T^32 - 247/2401*T^31 - 999/2401*T^30 + 141/343*T^29 - 
        1458/2401*T^28 + 141/343*T^27 - 999/2401*T^26 - 247/2401*T^25 + 68/2401*T^24
        + 397/2401*T^23 - 628/2401*T^22 - 879/2401*T^21 + 44/343*T^20 + 
        256/2401*T^19 - 1373/2401*T^18 + 713/2401*T^17 - 411/2401*T^16 - 
        123/2401*T^15 - 1021/2401*T^14 + 149/2401*T^13 + 1275/2401*T^12 - 
        481/2401*T^11 + 1024/2401*T^10 - 386/2401*T^9 + 55/343*T^8 + 283/2401*T^7 + 
        939/2401*T^6 + 566/2401*T^5 - 409/2401*T^4 + 174/343*T^3 + 11/49*T^2 - 4/7*T
        + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + X*Y^10 + X*Y^9 + 
        2*X*Y^8 + X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + X*Y^3 + 3*X*Y^2 + X*Y + 
        6*Y^30 + 5*Y^29 + 6*Y^28 + 2*Y^27 + 6*Y^26 + 4*Y^25 + Y^24 + 4*Y^23 + 6*Y^22
        + 2*Y^21 + 5*Y^20 + 2*Y^19 + 3*Y^17 + 5*Y^16 + 3*Y^15 + Y^14 + 6*Y^13 + 
        2*Y^12 + 2*Y^11 + 4*Y^10 + 3*Y^9 + 2*Y^8 + 2*Y^7 + 2*Y^6 + 6*Y^5 + 5*Y^4 + 
        5*Y^3 + 3*Y^2 + 2*Y + 4,
    -T^56 - 6/7*T^55 + 3/49*T^54 + 130/343*T^53 + 1823/2401*T^52 + 2195/2401*T^51 + 
        139/343*T^50 - 44/2401*T^49 - 60/343*T^48 - 1367/2401*T^47 - 848/2401*T^46 -
        206/2401*T^45 + 201/2401*T^44 + 422/2401*T^43 - 3/49*T^42 - 78/2401*T^41 - 
        1500/2401*T^40 - 277/343*T^39 - 901/2401*T^38 - 170/2401*T^37 + 65/343*T^36 
        + 2014/2401*T^35 + 2770/2401*T^34 + 2040/2401*T^33 + 50/2401*T^32 - 
        1856/2401*T^31 - 2091/2401*T^30 - 27/49*T^29 + 27/49*T^27 + 2091/2401*T^26 +
        1856/2401*T^25 - 50/2401*T^24 - 2040/2401*T^23 - 2770/2401*T^22 - 
        2014/2401*T^21 - 65/343*T^20 + 170/2401*T^19 + 901/2401*T^18 + 277/343*T^17 
        + 1500/2401*T^16 + 78/2401*T^15 + 3/49*T^14 - 422/2401*T^13 - 201/2401*T^12 
        + 206/2401*T^11 + 848/2401*T^10 + 1367/2401*T^9 + 60/343*T^8 + 44/2401*T^7 -
        139/343*T^6 - 2195/2401*T^5 - 1823/2401*T^4 - 130/343*T^3 - 3/49*T^2 + 6/7*T
        + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + X*Y^8 + 
        2*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 6*X*Y + 6*Y^30 +
        5*Y^29 + 6*Y^28 + 4*Y^27 + 4*Y^26 + 2*Y^25 + 3*Y^24 + 3*Y^23 + Y^21 + 2*Y^20
        + 3*Y^19 + 6*Y^18 + 5*Y^17 + Y^16 + 3*Y^15 + Y^13 + 2*Y^10 + 5*Y^9 + Y^8 + 
        5*Y^5 + 6*Y^4 + 2*Y^3 + 6*Y^2 + 4*Y + 3,
    -T^56 - 1/7*T^55 - 34/49*T^54 - 141/343*T^53 - 720/2401*T^52 + 5/2401*T^51 + 
        1268/2401*T^50 + 253/343*T^49 + 1835/2401*T^48 + 2083/2401*T^47 + 
        194/343*T^46 + 1614/2401*T^45 + 178/2401*T^44 + 51/2401*T^43 - 
        1633/2401*T^42 - 214/2401*T^41 - 950/2401*T^40 - 578/2401*T^39 + 
        247/2401*T^38 + 472/2401*T^37 + 123/2401*T^36 - 85/2401*T^35 + 275/2401*T^34
        - 450/2401*T^33 - 1042/2401*T^32 - 534/2401*T^31 - 856/2401*T^30 + 
        26/343*T^29 - 26/343*T^27 + 856/2401*T^26 + 534/2401*T^25 + 1042/2401*T^24 +
        450/2401*T^23 - 275/2401*T^22 + 85/2401*T^21 - 123/2401*T^20 - 472/2401*T^19
        - 247/2401*T^18 + 578/2401*T^17 + 950/2401*T^16 + 214/2401*T^15 + 
        1633/2401*T^14 - 51/2401*T^13 - 178/2401*T^12 - 1614/2401*T^11 - 
        194/343*T^10 - 2083/2401*T^9 - 1835/2401*T^8 - 253/343*T^7 - 1268/2401*T^6 -
        5/2401*T^5 + 720/2401*T^4 + 141/343*T^3 + 34/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + X*Y^10 + 6*X*Y^9 + 
        3*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 4*X*Y^2 + 6*X*Y + 3*X + Y^30 + 
        5*Y^29 + 4*Y^28 + Y^27 + 6*Y^26 + 5*Y^25 + 5*Y^24 + 3*Y^23 + 5*Y^22 + 6*Y^21
        + Y^19 + 6*Y^18 + Y^17 + Y^16 + 5*Y^15 + 6*Y^14 + 3*Y^13 + 2*Y^12 + 5*Y^11 +
        5*Y^10 + 3*Y^9 + 2*Y^8 + 5*Y^7 + 2*Y^6 + 4*Y^5 + 3*Y^3 + Y + 4,
    -T^56 + 10/7*T^55 + 3/49*T^54 - 486/343*T^53 + 512/2401*T^52 + 2459/2401*T^51 - 
        1360/2401*T^50 - 1915/2401*T^49 + 2805/2401*T^48 + 236/2401*T^47 - 
        2846/2401*T^46 + 33/2401*T^45 + 2973/2401*T^44 - 944/2401*T^43 - 
        572/2401*T^42 + 5/343*T^41 + 1130/2401*T^40 - 2098/2401*T^39 + 
        1221/2401*T^38 + 3011/2401*T^37 - 3001/2401*T^36 - 813/2401*T^35 + 
        2560/2401*T^34 - 753/2401*T^33 - 1222/2401*T^32 + 1898/2401*T^31 + 
        23/49*T^30 - 3371/2401*T^29 + 3371/2401*T^27 - 23/49*T^26 - 1898/2401*T^25 +
        1222/2401*T^24 + 753/2401*T^23 - 2560/2401*T^22 + 813/2401*T^21 + 
        3001/2401*T^20 - 3011/2401*T^19 - 1221/2401*T^18 + 2098/2401*T^17 - 
        1130/2401*T^16 - 5/343*T^15 + 572/2401*T^14 + 944/2401*T^13 - 2973/2401*T^12
        - 33/2401*T^11 + 2846/2401*T^10 - 236/2401*T^9 - 2805/2401*T^8 + 
        1915/2401*T^7 + 1360/2401*T^6 - 2459/2401*T^5 - 512/2401*T^4 + 486/343*T^3 -
        3/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        X*Y^8 + 6*X*Y^7 + 5*X*Y^6 + X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 4*X*Y + X 
        + 2*Y^30 + 2*Y^29 + 3*Y^28 + 6*Y^27 + 5*Y^26 + 5*Y^23 + 4*Y^22 + 2*Y^21 + 
        6*Y^20 + 5*Y^19 + 2*Y^18 + 6*Y^17 + 4*Y^15 + 3*Y^14 + 5*Y^13 + 6*Y^12 + 
        5*Y^11 + 5*Y^10 + Y^9 + 4*Y^8 + 2*Y^7 + 4*Y^6 + 3*Y^5 + 4*Y^4 + 4*Y^3 + 6*Y 
        + 1,
    -T^56 + 1/7*T^55 + 75/49*T^54 - 50/343*T^53 - 2467/2401*T^52 - 143/2401*T^51 + 
        1475/2401*T^50 + 1116/2401*T^49 - 689/2401*T^48 - 1185/2401*T^47 + 
        436/2401*T^46 - 93/2401*T^45 - 95/343*T^44 + 909/2401*T^43 + 1467/2401*T^42 
        - 51/2401*T^41 - 2034/2401*T^40 - 1550/2401*T^39 + 45/49*T^38 + 440/343*T^37
        - 1562/2401*T^36 - 3050/2401*T^35 - 47/2401*T^34 + 1527/2401*T^33 + 
        1709/2401*T^32 - 618/2401*T^31 - 1249/2401*T^30 - 261/2401*T^29 + 
        261/2401*T^27 + 1249/2401*T^26 + 618/2401*T^25 - 1709/2401*T^24 - 
        1527/2401*T^23 + 47/2401*T^22 + 3050/2401*T^21 + 1562/2401*T^20 - 
        440/343*T^19 - 45/49*T^18 + 1550/2401*T^17 + 2034/2401*T^16 + 51/2401*T^15 -
        1467/2401*T^14 - 909/2401*T^13 + 95/343*T^12 + 93/2401*T^11 - 436/2401*T^10 
        + 1185/2401*T^9 + 689/2401*T^8 - 1116/2401*T^7 - 1475/2401*T^6 + 
        143/2401*T^5 + 2467/2401*T^4 + 50/343*T^3 - 75/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 
        5*X*Y^8 + X*Y^7 + 2*X*Y^6 + 6*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 6*Y^30 + 3*Y^29 + 
        2*Y^28 + 2*Y^27 + 4*Y^26 + 4*Y^25 + 5*Y^24 + 6*Y^22 + 4*Y^21 + 2*Y^20 + 
        4*Y^19 + 5*Y^18 + 6*Y^17 + 3*Y^16 + 3*Y^15 + 4*Y^14 + Y^13 + 6*Y^12 + Y^11 +
        6*Y^10 + 4*Y^9 + 4*Y^8 + 2*Y^7 + 3*Y^6 + 5*Y^5 + 4*Y^4 + 2*Y^3 + 5*Y^2 + 6*Y
        + 6,
    -T^56 - 20/7*T^55 - 163/49*T^54 - 495/343*T^53 + 2059/2401*T^52 + 3771/2401*T^51
        + 382/343*T^50 + 394/343*T^49 + 3879/2401*T^48 + 250/343*T^47 - 
        2405/2401*T^46 - 2887/2401*T^45 - 1328/2401*T^44 - 2725/2401*T^43 - 
        4586/2401*T^42 - 2071/2401*T^41 + 454/343*T^40 + 736/343*T^39 + 
        2038/2401*T^38 - 771/2401*T^37 + 54/2401*T^36 + 261/2401*T^35 - 
        2462/2401*T^34 - 3231/2401*T^33 + 271/2401*T^32 + 2949/2401*T^31 + 
        1847/2401*T^30 - 25/2401*T^29 + 25/2401*T^27 - 1847/2401*T^26 - 
        2949/2401*T^25 - 271/2401*T^24 + 3231/2401*T^23 + 2462/2401*T^22 - 
        261/2401*T^21 - 54/2401*T^20 + 771/2401*T^19 - 2038/2401*T^18 - 736/343*T^17
        - 454/343*T^16 + 2071/2401*T^15 + 4586/2401*T^14 + 2725/2401*T^13 + 
        1328/2401*T^12 + 2887/2401*T^11 + 2405/2401*T^10 - 250/343*T^9 - 
        3879/2401*T^8 - 394/343*T^7 - 382/343*T^6 - 3771/2401*T^5 - 2059/2401*T^4 + 
        495/343*T^3 + 163/49*T^2 + 20/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + X*Y^13 + 2*X*Y^12 + X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 
        X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 5*X*Y + 
        X + 2*Y^30 + 3*Y^29 + 3*Y^28 + Y^27 + 6*Y^26 + 4*Y^25 + 4*Y^23 + 4*Y^22 + 
        Y^20 + 5*Y^19 + 3*Y^18 + 3*Y^17 + 6*Y^16 + Y^15 + 5*Y^14 + 6*Y^13 + Y^12 + 
        3*Y^11 + 6*Y^10 + 6*Y^8 + 2*Y^7 + 5*Y^6 + 3*Y^5 + 3*Y^4 + Y,
    -T^56 - 1/7*T^55 + 17/49*T^54 + 338/343*T^53 + 1811/2401*T^52 + 737/2401*T^51 - 
        1117/2401*T^50 - 2213/2401*T^49 - 23/343*T^48 - 389/2401*T^47 + 96/343*T^46 
        + 207/343*T^45 + 421/2401*T^44 - 2140/2401*T^43 - 1207/2401*T^42 + 
        205/2401*T^41 + 297/2401*T^40 + 1194/2401*T^39 + 522/2401*T^38 - 
        600/2401*T^37 + 62/343*T^36 + 738/2401*T^35 - 421/2401*T^34 - 1060/2401*T^33
        + 1075/2401*T^32 - 194/2401*T^31 - 912/2401*T^30 - 2/2401*T^29 + 2/2401*T^27
        + 912/2401*T^26 + 194/2401*T^25 - 1075/2401*T^24 + 1060/2401*T^23 + 
        421/2401*T^22 - 738/2401*T^21 - 62/343*T^20 + 600/2401*T^19 - 522/2401*T^18 
        - 1194/2401*T^17 - 297/2401*T^16 - 205/2401*T^15 + 1207/2401*T^14 + 
        2140/2401*T^13 - 421/2401*T^12 - 207/343*T^11 - 96/343*T^10 + 389/2401*T^9 +
        23/343*T^8 + 2213/2401*T^7 + 1117/2401*T^6 - 737/2401*T^5 - 1811/2401*T^4 - 
        338/343*T^3 - 17/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 4*X*Y^12 + X*Y^11 + 5*X*Y^9 + 2*X*Y^8 + 5*X*Y^7 + 
        5*X*Y^6 + 3*X*Y^5 + 6*X*Y^2 + 2*X*Y + 6*X + 2*Y^30 + 3*Y^29 + 3*Y^28 + 
        4*Y^27 + 3*Y^26 + 3*Y^25 + 4*Y^24 + 5*Y^23 + 5*Y^22 + Y^21 + 4*Y^20 + Y^19 +
        5*Y^18 + 2*Y^17 + Y^13 + 2*Y^12 + 2*Y^11 + 4*Y^10 + 4*Y^9 + 3*Y^8 + 2*Y^7 + 
        4*Y^6 + 2*Y^5 + 3*Y^4 + 2*Y^3 + 2*Y^2 + 5,
    -T^56 - 4/7*T^55 - 10/49*T^54 - 330/343*T^53 - 297/2401*T^52 - 103/2401*T^51 - 
        1794/2401*T^50 + 372/2401*T^49 + 88/343*T^48 - 509/2401*T^47 + 607/2401*T^46
        + 453/2401*T^45 - 318/2401*T^44 + 2/2401*T^43 - 969/2401*T^42 - 
        759/2401*T^41 - 1280/2401*T^40 - 954/2401*T^39 - 463/2401*T^38 - 
        1545/2401*T^37 - 18/343*T^36 + 547/2401*T^35 - 164/2401*T^34 + 879/2401*T^33
        + 66/343*T^32 - 212/2401*T^31 + 501/2401*T^30 - 311/2401*T^29 + 
        311/2401*T^27 - 501/2401*T^26 + 212/2401*T^25 - 66/343*T^24 - 879/2401*T^23 
        + 164/2401*T^22 - 547/2401*T^21 + 18/343*T^20 + 1545/2401*T^19 + 
        463/2401*T^18 + 954/2401*T^17 + 1280/2401*T^16 + 759/2401*T^15 + 
        969/2401*T^14 - 2/2401*T^13 + 318/2401*T^12 - 453/2401*T^11 - 607/2401*T^10 
        + 509/2401*T^9 - 88/343*T^8 - 372/2401*T^7 + 1794/2401*T^6 + 103/2401*T^5 + 
        297/2401*T^4 + 330/343*T^3 + 10/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 4*X*Y^10 + 6*X*Y^9 + 2*X*Y^7 +
        2*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 4*X*Y + 2*X + 2*Y^30 + 
        6*Y^29 + 6*Y^28 + 2*Y^27 + 5*Y^26 + 2*Y^24 + 2*Y^23 + 2*Y^21 + 5*Y^20 + 
        2*Y^19 + 6*Y^18 + 3*Y^16 + 5*Y^14 + 2*Y^13 + 3*Y^12 + 6*Y^11 + Y^10 + 3*Y^9 
        + 4*Y^8 + Y^6 + 2*Y^5 + 4*Y^3 + 5*Y^2 + 4*Y + 3,
    T^56 - 1/7*T^55 - 62/49*T^54 + 442/343*T^53 + 437/2401*T^52 - 3775/2401*T^51 + 
        1860/2401*T^50 + 1704/2401*T^49 - 2260/2401*T^48 - 557/2401*T^47 + 
        1460/2401*T^46 - 1171/2401*T^45 - 961/2401*T^44 + 982/2401*T^43 - 
        1285/2401*T^42 - 758/2401*T^41 + 1164/2401*T^40 - 653/2401*T^39 - 
        1259/2401*T^38 + 152/343*T^37 + 5/343*T^36 - 1236/2401*T^35 + 1125/2401*T^34
        + 1417/2401*T^33 - 359/2401*T^32 - 1242/2401*T^31 + 1873/2401*T^30 + 
        1364/2401*T^29 - 2165/2401*T^28 + 1364/2401*T^27 + 1873/2401*T^26 - 
        1242/2401*T^25 - 359/2401*T^24 + 1417/2401*T^23 + 1125/2401*T^22 - 
        1236/2401*T^21 + 5/343*T^20 + 152/343*T^19 - 1259/2401*T^18 - 653/2401*T^17 
        + 1164/2401*T^16 - 758/2401*T^15 - 1285/2401*T^14 + 982/2401*T^13 - 
        961/2401*T^12 - 1171/2401*T^11 + 1460/2401*T^10 - 557/2401*T^9 - 
        2260/2401*T^8 + 1704/2401*T^7 + 1860/2401*T^6 - 3775/2401*T^5 + 437/2401*T^4
        + 442/343*T^3 - 62/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        3*X*Y^8 + 2*X*Y^7 + 5*X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 4*X*Y 
        + 6*X + 5*Y^30 + 3*Y^29 + 3*Y^28 + 6*Y^27 + 5*Y^25 + 2*Y^24 + 5*Y^23 + 
        2*Y^22 + 3*Y^21 + Y^20 + 5*Y^19 + Y^18 + 2*Y^17 + Y^16 + 6*Y^15 + 2*Y^14 + 
        3*Y^13 + 3*Y^12 + 2*Y^11 + 2*Y^10 + 5*Y^9 + 6*Y^8 + 3*Y^7 + Y^6 + 2*Y^4 + 
        6*Y^3 + 2*Y^2 + 6*Y + 3,
    T^56 + 16/49*T^54 + 74/343*T^53 - 2452/2401*T^52 + 822/2401*T^51 + 4/7*T^50 + 
        165/2401*T^49 + 2147/2401*T^48 + 137/2401*T^47 - 1447/2401*T^46 - 
        88/2401*T^45 + 1650/2401*T^44 + 662/2401*T^43 + 186/2401*T^42 + 
        1808/2401*T^41 - 2824/2401*T^40 - 155/2401*T^39 + 3173/2401*T^38 - 
        375/343*T^37 + 1459/2401*T^36 - 146/2401*T^35 - 4461/2401*T^34 + 
        1807/2401*T^33 + 1545/2401*T^32 - 162/2401*T^31 + 1878/2401*T^30 - 
        1625/2401*T^29 - 3257/2401*T^28 - 1625/2401*T^27 + 1878/2401*T^26 - 
        162/2401*T^25 + 1545/2401*T^24 + 1807/2401*T^23 - 4461/2401*T^22 - 
        146/2401*T^21 + 1459/2401*T^20 - 375/343*T^19 + 3173/2401*T^18 - 
        155/2401*T^17 - 2824/2401*T^16 + 1808/2401*T^15 + 186/2401*T^14 + 
        662/2401*T^13 + 1650/2401*T^12 - 88/2401*T^11 - 1447/2401*T^10 + 
        137/2401*T^9 + 2147/2401*T^8 + 165/2401*T^7 + 4/7*T^6 + 822/2401*T^5 - 
        2452/2401*T^4 + 74/343*T^3 + 16/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 6*X*Y^9 + 3*X*Y^8 +
        6*X*Y^7 + X*Y^6 + 6*X*Y^4 + 5*X*Y^3 + X*Y + 5*X + 5*Y^30 + 6*Y^28 + 3*Y^27 +
        6*Y^26 + 6*Y^25 + 3*Y^24 + 3*Y^23 + 2*Y^22 + 2*Y^21 + 3*Y^20 + 6*Y^19 + 
        4*Y^18 + 5*Y^16 + 2*Y^15 + 4*Y^14 + 5*Y^13 + Y^11 + Y^10 + 5*Y^8 + 5*Y^7 + 
        5*Y^6 + 2*Y^5 + 3*Y^4 + 2*Y^3 + 4*Y^2 + Y + 6,
    T^56 + 6/7*T^55 + 13/49*T^54 + 218/343*T^53 + 1942/2401*T^52 + 249/343*T^51 + 
        551/2401*T^50 + 638/2401*T^49 + 447/343*T^48 + 1795/2401*T^47 - 68/343*T^46 
        + 239/2401*T^45 + 188/343*T^44 + 73/2401*T^43 - 2109/2401*T^42 - 
        1238/2401*T^41 + 795/2401*T^40 + 179/2401*T^39 - 1945/2401*T^38 - 
        559/2401*T^37 + 281/343*T^36 - 297/2401*T^35 - 1978/2401*T^34 + 29/2401*T^33
        + 1268/2401*T^32 + 1471/2401*T^31 - 103/343*T^30 + 743/2401*T^29 + 
        3502/2401*T^28 + 743/2401*T^27 - 103/343*T^26 + 1471/2401*T^25 + 
        1268/2401*T^24 + 29/2401*T^23 - 1978/2401*T^22 - 297/2401*T^21 + 
        281/343*T^20 - 559/2401*T^19 - 1945/2401*T^18 + 179/2401*T^17 + 
        795/2401*T^16 - 1238/2401*T^15 - 2109/2401*T^14 + 73/2401*T^13 + 
        188/343*T^12 + 239/2401*T^11 - 68/343*T^10 + 1795/2401*T^9 + 447/343*T^8 + 
        638/2401*T^7 + 551/2401*T^6 + 249/343*T^5 + 1942/2401*T^4 + 218/343*T^3 + 
        13/49*T^2 + 6/7*T + 1
*], [*
    X^3 + X*Y^14 + 3*X*Y^13 + X*Y^11 + 3*X*Y^10 + X*Y^9 + 2*X*Y^8 + X*Y^7 + 3*X*Y^6 
        + X*Y^5 + 6*X*Y^4 + X*Y^3 + 3*X*Y^2 + 4*X*Y + 3*X + 2*Y^30 + 2*Y^29 + 6*Y^28
        + 4*Y^27 + 3*Y^25 + Y^24 + 3*Y^23 + 5*Y^22 + 3*Y^21 + 4*Y^20 + Y^19 + 5*Y^18
        + 4*Y^17 + 2*Y^16 + 5*Y^15 + 2*Y^13 + 3*Y^12 + Y^11 + 6*Y^10 + 5*Y^9 + 4*Y^8
        + 4*Y^7 + 3*Y^5 + 2*Y^4 + 2*Y^3 + 4*Y^2 + Y,
    T^56 + 8/7*T^55 + 25/49*T^54 - 230/343*T^53 - 442/343*T^52 + 408/2401*T^51 + 
        449/343*T^50 + 2014/2401*T^49 - 1259/2401*T^48 - 3893/2401*T^47 - 
        557/2401*T^46 + 3155/2401*T^45 + 4251/2401*T^44 + 1479/2401*T^43 - 
        3303/2401*T^42 - 2455/2401*T^41 + 1999/2401*T^40 + 6025/2401*T^39 + 
        3762/2401*T^38 - 3268/2401*T^37 - 6130/2401*T^36 - 272/343*T^35 + 
        4544/2401*T^34 + 5200/2401*T^33 - 660/2401*T^32 - 694/343*T^31 - 
        2724/2401*T^30 + 550/343*T^29 + 7254/2401*T^28 + 550/343*T^27 - 
        2724/2401*T^26 - 694/343*T^25 - 660/2401*T^24 + 5200/2401*T^23 + 
        4544/2401*T^22 - 272/343*T^21 - 6130/2401*T^20 - 3268/2401*T^19 + 
        3762/2401*T^18 + 6025/2401*T^17 + 1999/2401*T^16 - 2455/2401*T^15 - 
        3303/2401*T^14 + 1479/2401*T^13 + 4251/2401*T^12 + 3155/2401*T^11 - 
        557/2401*T^10 - 3893/2401*T^9 - 1259/2401*T^8 + 2014/2401*T^7 + 449/343*T^6 
        + 408/2401*T^5 - 442/343*T^4 - 230/343*T^3 + 25/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + 6*X*Y^8 + 2*X*Y^7 + 
        3*X*Y^6 + 2*X*Y^5 + X*Y^4 + 6*X*Y^3 + 4*X*Y + 3*X + 2*Y^30 + 3*Y^29 + 5*Y^28
        + 6*Y^27 + 3*Y^26 + 4*Y^25 + 2*Y^24 + 4*Y^23 + 2*Y^20 + 4*Y^19 + Y^17 + 
        4*Y^16 + 2*Y^15 + Y^14 + 2*Y^13 + 2*Y^12 + 3*Y^11 + 4*Y^10 + 3*Y^9 + 6*Y^8 +
        4*Y^7 + 4*Y^6 + 4*Y^3 + 6*Y^2 + 3,
    T^56 + 4/7*T^55 - 22/49*T^54 + 149/343*T^53 + 1516/2401*T^52 + 1068/2401*T^51 + 
        979/2401*T^50 + 1773/2401*T^49 - 25/2401*T^48 - 1027/2401*T^47 + 
        310/343*T^46 + 544/2401*T^45 - 66/343*T^44 + 1065/2401*T^43 - 880/2401*T^42 
        - 1786/2401*T^41 - 113/343*T^40 + 562/2401*T^39 - 712/2401*T^38 - 
        345/343*T^37 - 701/2401*T^36 - 733/2401*T^35 - 312/2401*T^34 - 130/2401*T^33
        - 1046/2401*T^32 - 402/2401*T^31 - 54/2401*T^30 - 310/2401*T^29 - 
        758/2401*T^28 - 310/2401*T^27 - 54/2401*T^26 - 402/2401*T^25 - 
        1046/2401*T^24 - 130/2401*T^23 - 312/2401*T^22 - 733/2401*T^21 - 
        701/2401*T^20 - 345/343*T^19 - 712/2401*T^18 + 562/2401*T^17 - 113/343*T^16 
        - 1786/2401*T^15 - 880/2401*T^14 + 1065/2401*T^13 - 66/343*T^12 + 
        544/2401*T^11 + 310/343*T^10 - 1027/2401*T^9 - 25/2401*T^8 + 1773/2401*T^7 +
        979/2401*T^6 + 1068/2401*T^5 + 1516/2401*T^4 + 149/343*T^3 - 22/49*T^2 + 
        4/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 
        X*Y^7 + X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + X*Y^3 + 2*X*Y^2 + 5*X + Y^30 + 2*Y^29 + 
        Y^28 + Y^27 + 6*Y^26 + 5*Y^25 + 3*Y^24 + 6*Y^23 + 5*Y^22 + 4*Y^21 + 6*Y^20 +
        6*Y^19 + 6*Y^18 + 6*Y^17 + 4*Y^16 + 4*Y^15 + 4*Y^14 + 5*Y^13 + Y^12 + Y^11 +
        6*Y^10 + 2*Y^9 + 4*Y^8 + 4*Y^7 + Y^6 + 3*Y^5 + 4*Y^4 + Y^3 + 4*Y^2 + 2,
    -T^56 + 5/7*T^55 + 45/49*T^54 - 396/343*T^53 - 535/2401*T^52 + 1619/2401*T^51 - 
        1570/2401*T^50 + 670/2401*T^49 + 428/2401*T^48 - 1567/2401*T^47 + 
        1853/2401*T^46 + 396/2401*T^45 - 1875/2401*T^44 + 1227/2401*T^43 + 
        213/2401*T^42 - 1259/2401*T^41 + 1499/2401*T^40 - 667/2401*T^39 - 
        156/2401*T^38 + 1548/2401*T^37 - 2180/2401*T^36 + 213/2401*T^35 + 
        1910/2401*T^34 - 1845/2401*T^33 + 750/2401*T^32 - 407/2401*T^31 - 
        284/343*T^30 + 3816/2401*T^29 - 3816/2401*T^27 + 284/343*T^26 + 
        407/2401*T^25 - 750/2401*T^24 + 1845/2401*T^23 - 1910/2401*T^22 - 
        213/2401*T^21 + 2180/2401*T^20 - 1548/2401*T^19 + 156/2401*T^18 + 
        667/2401*T^17 - 1499/2401*T^16 + 1259/2401*T^15 - 213/2401*T^14 - 
        1227/2401*T^13 + 1875/2401*T^12 - 396/2401*T^11 - 1853/2401*T^10 + 
        1567/2401*T^9 - 428/2401*T^8 - 670/2401*T^7 + 1570/2401*T^6 - 1619/2401*T^5 
        + 535/2401*T^4 + 396/343*T^3 - 45/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 
        3*X*Y^8 + 3*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + X*Y^2 + 3*X + 
        Y^30 + Y^29 + 6*Y^28 + 2*Y^26 + 6*Y^25 + Y^24 + 3*Y^23 + 6*Y^21 + Y^20 + 
        6*Y^19 + 4*Y^18 + Y^16 + 6*Y^15 + Y^14 + 4*Y^13 + 2*Y^12 + 2*Y^11 + 3*Y^10 +
        4*Y^9 + 6*Y^8 + 3*Y^7 + Y^6 + 5*Y^5 + 5*Y^4 + 2*Y^3 + 4*Y + 1,
    -T^56 - 4/7*T^55 + 9/49*T^54 - 1/49*T^53 + 2804/2401*T^52 + 2528/2401*T^51 - 
        591/2401*T^50 + 1154/2401*T^49 - 145/343*T^48 - 3096/2401*T^47 + 
        1357/2401*T^46 - 456/2401*T^45 - 43/343*T^44 + 517/343*T^43 - 865/2401*T^42 
        - 2052/2401*T^41 + 860/2401*T^40 - 2476/2401*T^39 + 25/343*T^38 + 
        2572/2401*T^37 - 246/343*T^36 + 491/2401*T^35 + 1042/2401*T^34 - 
        3155/2401*T^33 + 1646/2401*T^32 + 50/49*T^31 - 467/2401*T^30 + 
        3399/2401*T^29 - 3399/2401*T^27 + 467/2401*T^26 - 50/49*T^25 - 
        1646/2401*T^24 + 3155/2401*T^23 - 1042/2401*T^22 - 491/2401*T^21 + 
        246/343*T^20 - 2572/2401*T^19 - 25/343*T^18 + 2476/2401*T^17 - 860/2401*T^16
        + 2052/2401*T^15 + 865/2401*T^14 - 517/343*T^13 + 43/343*T^12 + 
        456/2401*T^11 - 1357/2401*T^10 + 3096/2401*T^9 + 145/343*T^8 - 1154/2401*T^7
        + 591/2401*T^6 - 2528/2401*T^5 - 2804/2401*T^4 + 1/49*T^3 - 9/49*T^2 + 4/7*T
        + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + X*Y^10 + X*Y^9 + 
        4*X*Y^6 + X*Y^5 + X*Y^4 + 2*X*Y^3 + X*Y^2 + 2*X*Y + X + 4*Y^30 + 4*Y^29 + 
        Y^28 + 2*Y^27 + 2*Y^26 + 3*Y^25 + Y^24 + Y^23 + 5*Y^21 + 3*Y^20 + 4*Y^19 + 
        3*Y^18 + 4*Y^17 + 5*Y^16 + 4*Y^15 + 3*Y^14 + 5*Y^13 + Y^12 + 3*Y^11 + Y^10 +
        4*Y^9 + 3*Y^8 + 3*Y^7 + Y^6 + 5*Y^4 + 3*Y^3 + 4*Y^2 + 4*Y + 6,
    -T^56 - 3/7*T^55 - T^54 - 6/49*T^53 - 1320/2401*T^52 + 215/343*T^51 + 
        752/2401*T^50 + 1927/2401*T^49 + 523/2401*T^48 + 1464/2401*T^47 - 
        328/2401*T^46 + 402/2401*T^45 - 65/2401*T^44 + 349/2401*T^43 + 24/2401*T^42 
        - 45/343*T^41 - 121/2401*T^40 - 1035/2401*T^39 - 1413/2401*T^38 - 23/49*T^37
        - 201/2401*T^36 + 152/2401*T^35 + 582/2401*T^34 + 295/2401*T^33 + 
        558/2401*T^32 - 153/2401*T^31 - 165/2401*T^30 - 260/2401*T^29 + 
        260/2401*T^27 + 165/2401*T^26 + 153/2401*T^25 - 558/2401*T^24 - 
        295/2401*T^23 - 582/2401*T^22 - 152/2401*T^21 + 201/2401*T^20 + 23/49*T^19 +
        1413/2401*T^18 + 1035/2401*T^17 + 121/2401*T^16 + 45/343*T^15 - 24/2401*T^14
        - 349/2401*T^13 + 65/2401*T^12 - 402/2401*T^11 + 328/2401*T^10 - 
        1464/2401*T^9 - 523/2401*T^8 - 1927/2401*T^7 - 752/2401*T^6 - 215/343*T^5 + 
        1320/2401*T^4 + 6/49*T^3 + T^2 + 3/7*T + 1
*], [*
    X^3 + X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 5*X*Y^10 + 6*X*Y^9 + X*Y^8 + 5*X*Y^7 + 
        3*X*Y^6 + 2*X*Y^5 + 5*X*Y^3 + 4*X*Y^2 + 3*X*Y + 2*X + 3*Y^30 + Y^29 + 5*Y^27
        + Y^26 + 5*Y^25 + 5*Y^24 + 5*Y^23 + 4*Y^22 + 6*Y^21 + 6*Y^20 + 5*Y^19 + Y^18
        + 2*Y^17 + 2*Y^15 + 6*Y^14 + 2*Y^13 + Y^12 + Y^11 + 3*Y^10 + Y^9 + 2*Y^8 + 
        5*Y^7 + 6*Y^6 + 4*Y^5 + 3*Y^4 + Y + 4,
    T^56 - 4/7*T^55 - 31/49*T^54 + 46/343*T^53 + 461/2401*T^52 - 573/2401*T^51 - 
        751/2401*T^50 + 432/2401*T^49 + 1276/2401*T^48 + 1087/2401*T^47 - 
        1882/2401*T^46 - 1216/2401*T^45 + 184/343*T^44 + 18/49*T^43 - 832/2401*T^42 
        - 981/2401*T^41 + 1262/2401*T^40 + 431/2401*T^39 - 627/2401*T^38 - 
        452/2401*T^37 + 96/2401*T^36 + 1472/2401*T^35 + 718/2401*T^34 - 
        1601/2401*T^33 - 1335/2401*T^32 + 1212/2401*T^31 + 10/2401*T^30 - 
        1038/2401*T^29 + 1854/2401*T^28 - 1038/2401*T^27 + 10/2401*T^26 + 
        1212/2401*T^25 - 1335/2401*T^24 - 1601/2401*T^23 + 718/2401*T^22 + 
        1472/2401*T^21 + 96/2401*T^20 - 452/2401*T^19 - 627/2401*T^18 + 
        431/2401*T^17 + 1262/2401*T^16 - 981/2401*T^15 - 832/2401*T^14 + 18/49*T^13 
        + 184/343*T^12 - 1216/2401*T^11 - 1882/2401*T^10 + 1087/2401*T^9 + 
        1276/2401*T^8 + 432/2401*T^7 - 751/2401*T^6 - 573/2401*T^5 + 461/2401*T^4 + 
        46/343*T^3 - 31/49*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 6*X*Y^13 + 2*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 2*X*Y^8 + 
        3*X*Y^7 + X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 5*X + Y^30 + 
        4*Y^28 + 5*Y^26 + 2*Y^25 + 2*Y^24 + 5*Y^23 + 4*Y^22 + Y^21 + 3*Y^20 + 5*Y^18
        + 3*Y^17 + 2*Y^16 + 6*Y^15 + 6*Y^13 + 2*Y^12 + 3*Y^11 + 6*Y^10 + Y^9 + 3*Y^8
        + 2*Y^7 + 2*Y^6 + 3*Y^5 + 5*Y^4 + 2*Y^3 + 2*Y^2 + 4*Y + 5,
    T^56 - 5/7*T^55 + 37/49*T^54 - 264/343*T^53 + 1145/2401*T^52 - 562/2401*T^51 + 
        1177/2401*T^50 + 310/2401*T^49 + 20/343*T^48 - 155/2401*T^47 - 439/2401*T^46
        - 355/2401*T^45 + 177/2401*T^44 + 218/2401*T^43 + 272/2401*T^42 - 
        75/343*T^41 + 244/2401*T^40 - 691/2401*T^39 - 596/2401*T^38 + 212/2401*T^37 
        - 199/2401*T^36 + 548/2401*T^35 - 342/2401*T^34 - 96/2401*T^33 - 
        442/2401*T^32 + 719/2401*T^31 - 505/2401*T^30 + 148/343*T^29 - 859/2401*T^28
        + 148/343*T^27 - 505/2401*T^26 + 719/2401*T^25 - 442/2401*T^24 - 
        96/2401*T^23 - 342/2401*T^22 + 548/2401*T^21 - 199/2401*T^20 + 212/2401*T^19
        - 596/2401*T^18 - 691/2401*T^17 + 244/2401*T^16 - 75/343*T^15 + 
        272/2401*T^14 + 218/2401*T^13 + 177/2401*T^12 - 355/2401*T^11 - 
        439/2401*T^10 - 155/2401*T^9 + 20/343*T^8 + 310/2401*T^7 + 1177/2401*T^6 - 
        562/2401*T^5 + 1145/2401*T^4 - 264/343*T^3 + 37/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^8 
        + 6*X*Y^7 + X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 5*X*Y + 5*X + 2*Y^30 + 
        Y^29 + Y^28 + 6*Y^27 + 6*Y^26 + 4*Y^25 + 4*Y^24 + 6*Y^23 + 4*Y^22 + 3*Y^21 +
        Y^20 + 3*Y^19 + 2*Y^17 + 5*Y^16 + 6*Y^15 + 5*Y^14 + Y^13 + 3*Y^12 + 6*Y^11 +
        6*Y^10 + 6*Y^9 + 3*Y^7 + 4*Y^6 + Y^5 + 2*Y^3 + 3*Y^2 + 2*Y + 6,
    T^56 + 9/7*T^55 - 5/7*T^54 - 669/343*T^53 - 1509/2401*T^52 + 1371/2401*T^51 - 
        1021/2401*T^50 - 2517/2401*T^49 - 650/2401*T^48 + 1833/2401*T^47 + 
        3464/2401*T^46 + 2448/2401*T^45 - 69/343*T^44 - 212/343*T^43 + 115/343*T^42 
        + 255/343*T^41 - 570/2401*T^40 - 1167/2401*T^39 + 92/343*T^38 + 
        1383/2401*T^37 - 1132/2401*T^36 - 3741/2401*T^35 - 2227/2401*T^34 - 
        17/343*T^33 - 194/2401*T^32 - 1602/2401*T^31 - 346/2401*T^30 + 
        3426/2401*T^29 + 5107/2401*T^28 + 3426/2401*T^27 - 346/2401*T^26 - 
        1602/2401*T^25 - 194/2401*T^24 - 17/343*T^23 - 2227/2401*T^22 - 
        3741/2401*T^21 - 1132/2401*T^20 + 1383/2401*T^19 + 92/343*T^18 - 
        1167/2401*T^17 - 570/2401*T^16 + 255/343*T^15 + 115/343*T^14 - 212/343*T^13 
        - 69/343*T^12 + 2448/2401*T^11 + 3464/2401*T^10 + 1833/2401*T^9 - 
        650/2401*T^8 - 2517/2401*T^7 - 1021/2401*T^6 + 1371/2401*T^5 - 1509/2401*T^4
        - 669/343*T^3 - 5/7*T^2 + 9/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 2*X*Y^9 + 2*X*Y^8 + 6*X*Y^7 + 
        5*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 4*X*Y + 2*X + 4*Y^30 + 
        4*Y^29 + 4*Y^28 + 2*Y^26 + 2*Y^24 + 3*Y^23 + Y^21 + 5*Y^20 + 4*Y^19 + 2*Y^18
        + 5*Y^16 + 5*Y^14 + 5*Y^13 + 3*Y^12 + Y^11 + 2*Y^10 + 5*Y^9 + Y^8 + 2*Y^7 + 
        5*Y^6 + Y^5 + 2*Y^4 + 6*Y^3 + 2*Y^2 + 4*Y + 4,
    T^56 + 6/7*T^55 + 8/7*T^54 + 302/343*T^53 - 249/2401*T^52 - 1608/2401*T^51 - 
        531/343*T^50 - 3184/2401*T^49 - 2042/2401*T^48 - 156/343*T^47 + 
        2344/2401*T^46 + 2055/2401*T^45 + 400/343*T^44 + 1543/2401*T^43 - 
        695/2401*T^42 - 1908/2401*T^41 - 521/343*T^40 - 1754/2401*T^39 - 78/343*T^38
        + 1653/2401*T^37 + 443/343*T^36 + 2867/2401*T^35 + 1948/2401*T^34 + 
        150/2401*T^33 - 1070/2401*T^32 - 24/49*T^31 - 1622/2401*T^30 - 488/2401*T^29
        - 919/2401*T^28 - 488/2401*T^27 - 1622/2401*T^26 - 24/49*T^25 - 
        1070/2401*T^24 + 150/2401*T^23 + 1948/2401*T^22 + 2867/2401*T^21 + 
        443/343*T^20 + 1653/2401*T^19 - 78/343*T^18 - 1754/2401*T^17 - 521/343*T^16 
        - 1908/2401*T^15 - 695/2401*T^14 + 1543/2401*T^13 + 400/343*T^12 + 
        2055/2401*T^11 + 2344/2401*T^10 - 156/343*T^9 - 2042/2401*T^8 - 
        3184/2401*T^7 - 531/343*T^6 - 1608/2401*T^5 - 249/2401*T^4 + 302/343*T^3 + 
        8/7*T^2 + 6/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 6*X*Y^8 +
        4*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 4*X*Y + 2*X + 
        3*Y^30 + Y^28 + 2*Y^27 + Y^26 + 3*Y^25 + 4*Y^24 + 6*Y^23 + 4*Y^22 + 6*Y^21 +
        3*Y^20 + 4*Y^19 + 6*Y^18 + 3*Y^17 + 5*Y^16 + 4*Y^15 + 4*Y^14 + 6*Y^13 + 
        3*Y^12 + 2*Y^11 + Y^10 + 2*Y^8 + 3*Y^7 + Y^6 + Y^5 + 6*Y^4 + 5*Y^3 + 5*Y^2 +
        Y + 3,
    T^56 - 2*T^55 + 72/49*T^54 + 321/343*T^53 - 828/343*T^52 + 3065/2401*T^51 + 
        2161/2401*T^50 - 3455/2401*T^49 - 1256/2401*T^48 + 4568/2401*T^47 - 
        304/343*T^46 - 3191/2401*T^45 + 4353/2401*T^44 - 512/2401*T^43 - 
        361/343*T^42 + 82/343*T^41 + 3680/2401*T^40 - 4463/2401*T^39 + 5/49*T^38 + 
        4586/2401*T^37 - 6145/2401*T^36 + 3202/2401*T^35 + 390/2401*T^34 - 
        2101/2401*T^33 + 1518/2401*T^32 + 229/2401*T^31 - 888/2401*T^30 - 
        117/2401*T^29 + 1317/2401*T^28 - 117/2401*T^27 - 888/2401*T^26 + 
        229/2401*T^25 + 1518/2401*T^24 - 2101/2401*T^23 + 390/2401*T^22 + 
        3202/2401*T^21 - 6145/2401*T^20 + 4586/2401*T^19 + 5/49*T^18 - 
        4463/2401*T^17 + 3680/2401*T^16 + 82/343*T^15 - 361/343*T^14 - 512/2401*T^13
        + 4353/2401*T^12 - 3191/2401*T^11 - 304/343*T^10 + 4568/2401*T^9 - 
        1256/2401*T^8 - 3455/2401*T^7 + 2161/2401*T^6 + 3065/2401*T^5 - 828/343*T^4 
        + 321/343*T^3 + 72/49*T^2 - 2*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 4*X*Y^11 + X*Y^10 + X*Y^9 + 4*X*Y^8 + 3*X*Y^6 + 
        2*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y + 6*X + Y^30 + 5*Y^29 + 2*Y^27 + 6*Y^26 
        + 4*Y^25 + 6*Y^23 + 3*Y^22 + 2*Y^20 + 6*Y^19 + 5*Y^18 + 4*Y^17 + 5*Y^16 + 
        5*Y^15 + 3*Y^14 + 4*Y^11 + 6*Y^10 + 5*Y^9 + 4*Y^8 + 5*Y^7 + 5*Y^6 + 6*Y^5 + 
        4*Y^4 + 4*Y^3 + 6*Y^2 + 6*Y,
    T^56 - 9/7*T^55 - 43/49*T^54 + 629/343*T^53 + 937/2401*T^52 - 4266/2401*T^51 - 
        26/2401*T^50 + 88/49*T^49 - 191/343*T^48 - 3268/2401*T^47 + 2808/2401*T^46 +
        1013/2401*T^45 - 347/343*T^44 - 1277/2401*T^43 + 3846/2401*T^42 - 
        534/2401*T^41 - 3939/2401*T^40 + 4064/2401*T^39 + 180/343*T^38 - 
        4937/2401*T^37 + 561/2401*T^36 + 4821/2401*T^35 - 2236/2401*T^34 - 
        736/343*T^33 + 5265/2401*T^32 + 3027/2401*T^31 - 6240/2401*T^30 - 
        439/2401*T^29 + 5308/2401*T^28 - 439/2401*T^27 - 6240/2401*T^26 + 
        3027/2401*T^25 + 5265/2401*T^24 - 736/343*T^23 - 2236/2401*T^22 + 
        4821/2401*T^21 + 561/2401*T^20 - 4937/2401*T^19 + 180/343*T^18 + 
        4064/2401*T^17 - 3939/2401*T^16 - 534/2401*T^15 + 3846/2401*T^14 - 
        1277/2401*T^13 - 347/343*T^12 + 1013/2401*T^11 + 2808/2401*T^10 - 
        3268/2401*T^9 - 191/343*T^8 + 88/49*T^7 - 26/2401*T^6 - 4266/2401*T^5 + 
        937/2401*T^4 + 629/343*T^3 - 43/49*T^2 - 9/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 6*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + X*Y^3 + 2*X*Y + 3*X + 
        3*Y^30 + 4*Y^29 + 6*Y^28 + 3*Y^27 + 5*Y^26 + 4*Y^25 + 4*Y^24 + 6*Y^23 + Y^22
        + 2*Y^21 + 2*Y^19 + 5*Y^18 + 2*Y^17 + Y^16 + 6*Y^15 + Y^13 + 2*Y^12 + 6*Y^9 
        + Y^8 + 4*Y^7 + 6*Y^6 + 2*Y^5 + 2*Y^4 + 3*Y^3 + 3*Y^2 + 6*Y + 6,
    -T^56 + 9/7*T^55 - 100/49*T^54 + 131/49*T^53 - 5437/2401*T^52 + 4653/2401*T^51 -
        2543/2401*T^50 + 555/2401*T^49 + 1212/2401*T^48 - 2623/2401*T^47 + 
        3460/2401*T^46 - 3594/2401*T^45 + 443/343*T^44 - 3065/2401*T^43 + 
        1951/2401*T^42 - 1972/2401*T^41 + 2927/2401*T^40 - 2101/2401*T^39 + 
        2774/2401*T^38 - 2300/2401*T^37 + 1083/2401*T^36 - 71/2401*T^35 - 
        391/2401*T^34 + 1236/2401*T^33 - 1143/2401*T^32 + 52/343*T^31 - 139/343*T^30
        - 297/2401*T^29 + 297/2401*T^27 + 139/343*T^26 - 52/343*T^25 + 
        1143/2401*T^24 - 1236/2401*T^23 + 391/2401*T^22 + 71/2401*T^21 - 
        1083/2401*T^20 + 2300/2401*T^19 - 2774/2401*T^18 + 2101/2401*T^17 - 
        2927/2401*T^16 + 1972/2401*T^15 - 1951/2401*T^14 + 3065/2401*T^13 - 
        443/343*T^12 + 3594/2401*T^11 - 3460/2401*T^10 + 2623/2401*T^9 - 
        1212/2401*T^8 - 555/2401*T^7 + 2543/2401*T^6 - 4653/2401*T^5 + 5437/2401*T^4
        - 131/49*T^3 + 100/49*T^2 - 9/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 
        + 2*X*Y^8 + 4*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 4*X*Y + 2*Y^30
        + 3*Y^29 + 3*Y^27 + 6*Y^26 + 2*Y^25 + 6*Y^24 + 6*Y^23 + 4*Y^22 + Y^21 + 
        3*Y^20 + Y^19 + 4*Y^17 + Y^16 + 5*Y^15 + 2*Y^14 + 3*Y^13 + 4*Y^12 + 5*Y^11 +
        Y^10 + 5*Y^8 + 6*Y^7 + 4*Y^6 + 2*Y^5 + 2*Y^4 + 4*Y^3 + 4*Y^2 + 5*Y + 3,
    T^56 - T^55 - 16/49*T^53 + 222/2401*T^52 + 473/2401*T^51 + 1513/2401*T^50 - 
        78/2401*T^49 - 2515/2401*T^48 + 1485/2401*T^47 - 2078/2401*T^46 + 
        270/343*T^45 + 370/2401*T^44 + 326/2401*T^43 - 1852/2401*T^42 + 
        655/2401*T^41 - 639/2401*T^40 + 1181/2401*T^39 + 1023/2401*T^38 - 
        155/343*T^37 + 415/2401*T^36 - 585/2401*T^35 + 109/2401*T^34 + 556/2401*T^33
        + 1098/2401*T^32 - 2896/2401*T^31 + 626/2401*T^30 + 1023/2401*T^29 - 
        710/2401*T^28 + 1023/2401*T^27 + 626/2401*T^26 - 2896/2401*T^25 + 
        1098/2401*T^24 + 556/2401*T^23 + 109/2401*T^22 - 585/2401*T^21 + 
        415/2401*T^20 - 155/343*T^19 + 1023/2401*T^18 + 1181/2401*T^17 - 
        639/2401*T^16 + 655/2401*T^15 - 1852/2401*T^14 + 326/2401*T^13 + 
        370/2401*T^12 + 270/343*T^11 - 2078/2401*T^10 + 1485/2401*T^9 - 
        2515/2401*T^8 - 78/2401*T^7 + 1513/2401*T^6 + 473/2401*T^5 + 222/2401*T^4 - 
        16/49*T^3 - T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 
        + 5*X*Y^8 + 6*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + X*Y^4 + X*Y^3 + X*Y + 2*X + 5*Y^30
        + 5*Y^28 + 3*Y^27 + 2*Y^26 + 3*Y^25 + 4*Y^24 + 6*Y^23 + 6*Y^20 + Y^19 + 
        4*Y^18 + 6*Y^16 + 3*Y^15 + 3*Y^13 + Y^12 + Y^11 + 2*Y^9 + 3*Y^8 + 5*Y^7 + 
        5*Y^6 + 2*Y^5 + Y^4 + 2*Y^3 + 6*Y^2 + 3,
    -T^56 + 26/49*T^54 + 2/343*T^53 + 1969/2401*T^52 + 180/343*T^51 + 312/2401*T^50 
        + 82/2401*T^49 - 1235/2401*T^48 - 312/2401*T^47 - 832/2401*T^46 - 
        1870/2401*T^45 + 586/2401*T^44 - 319/2401*T^43 - 635/2401*T^42 + 
        109/343*T^41 + 528/2401*T^40 + 661/2401*T^39 - 211/2401*T^38 + 
        1682/2401*T^37 + 1521/2401*T^36 - 1046/2401*T^35 + 645/2401*T^34 - 
        1481/2401*T^33 - 1292/2401*T^32 - 55/343*T^31 - 1413/2401*T^30 + 
        825/2401*T^29 - 825/2401*T^27 + 1413/2401*T^26 + 55/343*T^25 + 
        1292/2401*T^24 + 1481/2401*T^23 - 645/2401*T^22 + 1046/2401*T^21 - 
        1521/2401*T^20 - 1682/2401*T^19 + 211/2401*T^18 - 661/2401*T^17 - 
        528/2401*T^16 - 109/343*T^15 + 635/2401*T^14 + 319/2401*T^13 - 586/2401*T^12
        + 1870/2401*T^11 + 832/2401*T^10 + 312/2401*T^9 + 1235/2401*T^8 - 
        82/2401*T^7 - 312/2401*T^6 - 180/343*T^5 - 1969/2401*T^4 - 2/343*T^3 - 
        26/49*T^2 + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 
        + X*Y^8 + X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + X*Y^2 + 5*X*Y + 
        5*X + 5*Y^30 + 4*Y^29 + Y^28 + 3*Y^27 + 4*Y^26 + 6*Y^25 + 6*Y^24 + 3*Y^23 + 
        3*Y^22 + 2*Y^21 + 4*Y^19 + 4*Y^18 + 3*Y^17 + Y^15 + 4*Y^14 + 2*Y^13 + Y^12 +
        3*Y^11 + 3*Y^10 + Y^9 + 5*Y^8 + 6*Y^7 + 6*Y^6 + 2*Y^5 + 2*Y^4 + 6*Y + 2,
    -T^56 + 2/7*T^55 - 3/49*T^54 + 38/49*T^53 - 1453/2401*T^52 + 2913/2401*T^51 - 
        880/2401*T^50 + 127/343*T^49 - 2988/2401*T^48 + 2270/2401*T^47 - 
        279/343*T^46 + 517/2401*T^45 - 1774/2401*T^44 + 1699/2401*T^43 - 
        901/2401*T^42 + 341/2401*T^41 - 1126/2401*T^40 + 1467/2401*T^39 + 
        243/2401*T^38 + 66/343*T^37 - 293/2401*T^36 + 1238/2401*T^35 + 458/2401*T^34
        - 1560/2401*T^33 - 967/2401*T^32 + 971/2401*T^31 - 646/2401*T^30 - 
        1870/2401*T^29 + 1870/2401*T^27 + 646/2401*T^26 - 971/2401*T^25 + 
        967/2401*T^24 + 1560/2401*T^23 - 458/2401*T^22 - 1238/2401*T^21 + 
        293/2401*T^20 - 66/343*T^19 - 243/2401*T^18 - 1467/2401*T^17 + 
        1126/2401*T^16 - 341/2401*T^15 + 901/2401*T^14 - 1699/2401*T^13 + 
        1774/2401*T^12 - 517/2401*T^11 + 279/343*T^10 - 2270/2401*T^9 + 
        2988/2401*T^8 - 127/343*T^7 + 880/2401*T^6 - 2913/2401*T^5 + 1453/2401*T^4 -
        38/49*T^3 + 3/49*T^2 - 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 
        3*X*Y^7 + 5*X*Y^6 + X*Y^5 + X*Y^3 + X*Y^2 + 4*X*Y + 5*X + Y^30 + Y^29 + 
        6*Y^28 + 6*Y^27 + 6*Y^26 + 4*Y^24 + 4*Y^23 + 5*Y^22 + 2*Y^21 + 6*Y^19 + Y^17
        + Y^16 + 4*Y^15 + 4*Y^14 + 3*Y^13 + 2*Y^12 + 5*Y^11 + 4*Y^10 + Y^9 + 2*Y^8 +
        3*Y^7 + 5*Y^6 + 2*Y^5 + 5*Y^4 + 5*Y^2 + 4*Y + 3,
    -T^56 + 5/7*T^55 + 23/49*T^54 + 169/343*T^53 - 2112/2401*T^52 + 15/343*T^51 + 
        934/2401*T^50 + 1292/2401*T^49 - 1140/2401*T^48 - 1061/2401*T^47 + 
        66/2401*T^46 - 603/2401*T^45 + 501/2401*T^44 - 552/2401*T^43 + 533/2401*T^42
        - 138/2401*T^41 + 387/2401*T^40 - 205/2401*T^39 + 1021/2401*T^38 + 
        461/2401*T^37 - 27/2401*T^36 - 879/2401*T^35 + 590/2401*T^34 - 30/343*T^33 -
        542/2401*T^32 - 107/343*T^31 - 381/2401*T^30 + 429/2401*T^29 - 429/2401*T^27
        + 381/2401*T^26 + 107/343*T^25 + 542/2401*T^24 + 30/343*T^23 - 590/2401*T^22
        + 879/2401*T^21 + 27/2401*T^20 - 461/2401*T^19 - 1021/2401*T^18 + 
        205/2401*T^17 - 387/2401*T^16 + 138/2401*T^15 - 533/2401*T^14 + 
        552/2401*T^13 - 501/2401*T^12 + 603/2401*T^11 - 66/2401*T^10 + 1061/2401*T^9
        + 1140/2401*T^8 - 1292/2401*T^7 - 934/2401*T^6 - 15/343*T^5 + 2112/2401*T^4 
        - 169/343*T^3 - 23/49*T^2 - 5/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 
        3*X*Y^8 + 2*X*Y^7 + X*Y^6 + 5*X*Y^5 + X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + X*Y + 3*X 
        + 4*Y^30 + Y^29 + Y^28 + 3*Y^27 + Y^26 + 4*Y^25 + 2*Y^24 + Y^23 + 4*Y^22 + 
        3*Y^21 + Y^20 + 2*Y^19 + 6*Y^18 + 6*Y^17 + Y^15 + 3*Y^14 + 2*Y^12 + Y^11 + 
        3*Y^10 + Y^9 + Y^8 + 5*Y^7 + 4*Y^6 + 2*Y^5 + Y^4 + 2*Y^3 + 2*Y^2 + Y + 2,
    -T^56 + 55/49*T^54 + 33/343*T^53 - 1726/2401*T^52 - 1497/2401*T^51 + 
        1240/2401*T^50 + 837/2401*T^49 - 123/2401*T^48 - 80/2401*T^47 - 
        475/2401*T^46 - 8/343*T^45 + 81/2401*T^44 + 29/49*T^43 + 608/2401*T^42 - 
        1220/2401*T^41 - 1935/2401*T^40 - 338/2401*T^39 + 2385/2401*T^38 + 
        773/2401*T^37 - 43/343*T^36 - 221/343*T^35 - 1257/2401*T^34 + 372/2401*T^33 
        + 211/343*T^32 + 1751/2401*T^31 - 1811/2401*T^30 - 1685/2401*T^29 + 
        1685/2401*T^27 + 1811/2401*T^26 - 1751/2401*T^25 - 211/343*T^24 - 
        372/2401*T^23 + 1257/2401*T^22 + 221/343*T^21 + 43/343*T^20 - 773/2401*T^19 
        - 2385/2401*T^18 + 338/2401*T^17 + 1935/2401*T^16 + 1220/2401*T^15 - 
        608/2401*T^14 - 29/49*T^13 - 81/2401*T^12 + 8/343*T^11 + 475/2401*T^10 + 
        80/2401*T^9 + 123/2401*T^8 - 837/2401*T^7 - 1240/2401*T^6 + 1497/2401*T^5 + 
        1726/2401*T^4 - 33/343*T^3 - 55/49*T^2 + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 
        6*X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 5*X*Y + 
        X + 6*Y^30 + Y^28 + 5*Y^27 + 5*Y^26 + 6*Y^25 + 5*Y^24 + 3*Y^23 + 4*Y^22 + 
        Y^21 + 4*Y^20 + 3*Y^19 + 2*Y^18 + 5*Y^17 + Y^16 + 3*Y^15 + 2*Y^14 + Y^13 + 
        4*Y^12 + 3*Y^11 + 5*Y^10 + 2*Y^8 + 6*Y^7 + 5*Y^6 + 2*Y^5 + 3*Y^4 + 6*Y^3 + 
        4*Y^2 + 2*Y + 6,
    -T^56 - 1/7*T^55 + 16/49*T^54 + 194/343*T^53 - 163/2401*T^52 + 1230/2401*T^51 + 
        313/2401*T^50 - 488/2401*T^49 - 790/2401*T^48 + 968/2401*T^47 + 
        1429/2401*T^46 - 73/2401*T^45 - 626/2401*T^44 + 15/2401*T^43 - 456/2401*T^42
        - 1613/2401*T^41 - 249/2401*T^40 - 187/2401*T^39 + 139/343*T^38 - 
        848/2401*T^37 - 397/2401*T^36 + 9/343*T^35 + 1524/2401*T^34 - 262/2401*T^33 
        + 393/2401*T^32 + 215/343*T^31 + 684/2401*T^30 - 583/2401*T^29 + 
        583/2401*T^27 - 684/2401*T^26 - 215/343*T^25 - 393/2401*T^24 + 262/2401*T^23
        - 1524/2401*T^22 - 9/343*T^21 + 397/2401*T^20 + 848/2401*T^19 - 139/343*T^18
        + 187/2401*T^17 + 249/2401*T^16 + 1613/2401*T^15 + 456/2401*T^14 - 
        15/2401*T^13 + 626/2401*T^12 + 73/2401*T^11 - 1429/2401*T^10 - 968/2401*T^9 
        + 790/2401*T^8 + 488/2401*T^7 - 313/2401*T^6 - 1230/2401*T^5 + 163/2401*T^4 
        - 194/343*T^3 - 16/49*T^2 + 1/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 4*X*Y^9 + 
        X*Y^8 + 3*X*Y^7 + 5*X*Y^5 + 5*X*Y^4 + X*Y^3 + X*Y^2 + 2*X*Y + 6*X + 5*Y^30 +
        4*Y^29 + 3*Y^28 + 4*Y^27 + 5*Y^26 + 3*Y^25 + 3*Y^24 + Y^23 + 2*Y^21 + 3*Y^20
        + Y^18 + 2*Y^17 + 4*Y^16 + 2*Y^15 + 5*Y^13 + 6*Y^12 + 5*Y^10 + 6*Y^8 + 2*Y^7
        + 6*Y^6 + 2*Y^5 + 3*Y^4 + 5*Y^3 + 5*Y^2 + 4*Y + 3,
    -T^56 + 6/7*T^55 + 71/49*T^54 - 564/343*T^53 - 2190/2401*T^52 + 3904/2401*T^51 +
        206/2401*T^50 - 2339/2401*T^49 - 251/2401*T^48 + 29/49*T^47 + 1656/2401*T^46
        - 2581/2401*T^45 - 137/2401*T^44 + 3007/2401*T^43 - 1688/2401*T^42 - 
        2714/2401*T^41 + 332/343*T^40 + 1686/2401*T^39 - 188/343*T^38 - 
        758/2401*T^37 + 508/2401*T^36 + 17/49*T^35 - 1328/2401*T^34 - 243/2401*T^33 
        + 767/2401*T^32 + 211/2401*T^31 - 744/2401*T^30 + 1032/2401*T^29 - 
        1032/2401*T^27 + 744/2401*T^26 - 211/2401*T^25 - 767/2401*T^24 + 
        243/2401*T^23 + 1328/2401*T^22 - 17/49*T^21 - 508/2401*T^20 + 758/2401*T^19 
        + 188/343*T^18 - 1686/2401*T^17 - 332/343*T^16 + 2714/2401*T^15 + 
        1688/2401*T^14 - 3007/2401*T^13 + 137/2401*T^12 + 2581/2401*T^11 - 
        1656/2401*T^10 - 29/49*T^9 + 251/2401*T^8 + 2339/2401*T^7 - 206/2401*T^6 - 
        3904/2401*T^5 + 2190/2401*T^4 + 564/343*T^3 - 71/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + X*Y^12 + X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 
        3*X*Y^8 + 3*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + X*Y^2 + 3*X*Y + 
        4*X + 6*Y^30 + 4*Y^29 + 6*Y^28 + 3*Y^27 + 2*Y^26 + 5*Y^24 + 4*Y^23 + 6*Y^22 
        + 6*Y^21 + 3*Y^20 + Y^19 + 6*Y^18 + 6*Y^17 + 6*Y^16 + 2*Y^15 + 4*Y^14 + 
        6*Y^13 + 6*Y^12 + 4*Y^11 + Y^10 + 4*Y^9 + 3*Y^8 + 6*Y^7 + 6*Y^6 + 2*Y^4 + 
        6*Y^3 + 4*Y + 3,
    T^56 + 1/7*T^55 - 2*T^54 - 17/49*T^53 + 3580/2401*T^52 + 1985/2401*T^51 - 
        226/343*T^50 - 2357/2401*T^49 + 1150/2401*T^48 + 643/2401*T^47 - 78/343*T^46
        + 1234/2401*T^45 - 54/343*T^44 - 1718/2401*T^43 - 999/2401*T^42 + 18/49*T^41
        + 2665/2401*T^40 - 92/343*T^39 - 1214/2401*T^38 + 806/2401*T^37 - 
        295/343*T^36 - 1627/2401*T^35 + 2452/2401*T^34 + 418/343*T^33 - 
        666/2401*T^32 - 3032/2401*T^31 - 335/2401*T^30 + 1383/2401*T^29 + 
        696/2401*T^28 + 1383/2401*T^27 - 335/2401*T^26 - 3032/2401*T^25 - 
        666/2401*T^24 + 418/343*T^23 + 2452/2401*T^22 - 1627/2401*T^21 - 
        295/343*T^20 + 806/2401*T^19 - 1214/2401*T^18 - 92/343*T^17 + 2665/2401*T^16
        + 18/49*T^15 - 999/2401*T^14 - 1718/2401*T^13 - 54/343*T^12 + 1234/2401*T^11
        - 78/343*T^10 + 643/2401*T^9 + 1150/2401*T^8 - 2357/2401*T^7 - 226/343*T^6 +
        1985/2401*T^5 + 3580/2401*T^4 - 17/49*T^3 - 2*T^2 + 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 
        + 4*X*Y^8 + X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 5*X*Y + 
        X + 6*Y^30 + 6*Y^29 + Y^28 + 3*Y^27 + 2*Y^26 + 4*Y^25 + 4*Y^23 + 5*Y^22 + 
        5*Y^21 + 6*Y^20 + Y^18 + 3*Y^17 + Y^15 + 2*Y^14 + 6*Y^12 + 6*Y^11 + Y^10 + 
        2*Y^9 + 2*Y^7 + 5*Y^6 + 2*Y^5 + 3*Y^4 + 2*Y^3 + Y^2 + Y + 6,
    T^56 - 1/7*T^55 - 43/49*T^54 + 254/343*T^53 + 634/2401*T^52 - 1032/2401*T^51 + 
        639/2401*T^50 - 316/2401*T^49 - 227/2401*T^48 + 1784/2401*T^47 - 
        1087/2401*T^46 - 1552/2401*T^45 + 332/343*T^44 - 138/2401*T^43 - 
        2413/2401*T^42 + 1287/2401*T^41 + 1366/2401*T^40 - 155/343*T^39 + 
        132/2401*T^38 + 12/343*T^37 - 1123/2401*T^36 + 157/2401*T^35 + 106/343*T^34 
        - 930/2401*T^33 - 114/2401*T^32 + 242/343*T^31 - 1349/2401*T^30 - 
        650/2401*T^29 + 2369/2401*T^28 - 650/2401*T^27 - 1349/2401*T^26 + 
        242/343*T^25 - 114/2401*T^24 - 930/2401*T^23 + 106/343*T^22 + 157/2401*T^21 
        - 1123/2401*T^20 + 12/343*T^19 + 132/2401*T^18 - 155/343*T^17 + 
        1366/2401*T^16 + 1287/2401*T^15 - 2413/2401*T^14 - 138/2401*T^13 + 
        332/343*T^12 - 1552/2401*T^11 - 1087/2401*T^10 + 1784/2401*T^9 - 
        227/2401*T^8 - 316/2401*T^7 + 639/2401*T^6 - 1032/2401*T^5 + 634/2401*T^4 + 
        254/343*T^3 - 43/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 5*X*Y^13 + 6*X*Y^12 + X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 3*X*Y^7 + 
        6*X*Y^6 + 2*X*Y^5 + 3*X*Y^3 + 5*X*Y^2 + 6*X*Y + 6*X + 2*Y^30 + 6*Y^28 + 
        4*Y^27 + 6*Y^26 + 5*Y^25 + 3*Y^24 + 3*Y^23 + 3*Y^22 + 3*Y^21 + 4*Y^20 + 
        3*Y^18 + 3*Y^17 + 3*Y^16 + 5*Y^14 + 6*Y^13 + 5*Y^12 + 5*Y^11 + Y^10 + 3*Y^9 
        + 5*Y^8 + 5*Y^7 + 5*Y^6 + Y^4 + 2*Y^3 + Y^2 + 3*Y + 1,
    -T^56 + 6/7*T^55 + 74/49*T^54 - 132/343*T^53 - 100/49*T^52 + 775/2401*T^51 + 
        2540/2401*T^50 - 295/2401*T^49 - 1975/2401*T^48 + 1545/2401*T^47 + 
        2509/2401*T^46 - 2967/2401*T^45 - 1828/2401*T^44 + 9/7*T^43 + 5/7*T^42 - 
        3607/2401*T^41 - 1872/2401*T^40 + 3401/2401*T^39 + 1663/2401*T^38 - 
        2942/2401*T^37 - 1700/2401*T^36 + 5380/2401*T^35 + 265/2401*T^34 - 
        842/343*T^33 - 200/343*T^32 + 6303/2401*T^31 + 646/2401*T^30 - 631/343*T^29 
        + 631/343*T^27 - 646/2401*T^26 - 6303/2401*T^25 + 200/343*T^24 + 
        842/343*T^23 - 265/2401*T^22 - 5380/2401*T^21 + 1700/2401*T^20 + 
        2942/2401*T^19 - 1663/2401*T^18 - 3401/2401*T^17 + 1872/2401*T^16 + 
        3607/2401*T^15 - 5/7*T^14 - 9/7*T^13 + 1828/2401*T^12 + 2967/2401*T^11 - 
        2509/2401*T^10 - 1545/2401*T^9 + 1975/2401*T^8 + 295/2401*T^7 - 
        2540/2401*T^6 - 775/2401*T^5 + 100/49*T^4 + 132/343*T^3 - 74/49*T^2 - 6/7*T 
        + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 
        + 3*X*Y^8 + 6*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 6*X*Y^2 + 2*X*Y + 5*X + 
        4*Y^30 + 6*Y^29 + 6*Y^28 + 4*Y^27 + 4*Y^26 + 6*Y^25 + 4*Y^24 + 6*Y^23 + 
        5*Y^22 + 4*Y^21 + 2*Y^20 + 2*Y^18 + 3*Y^17 + 6*Y^15 + Y^14 + 2*Y^13 + 5*Y^12
        + 4*Y^11 + 2*Y^9 + 3*Y^8 + Y^7 + 6*Y^6 + 5*Y^5 + 4*Y^4 + 6*Y^3 + 2,
    T^56 + 5/7*T^55 - 3/49*T^54 - 247/343*T^53 - 1987/2401*T^52 - 1396/2401*T^51 + 
        775/2401*T^50 + 1020/2401*T^49 - 177/2401*T^48 - 726/2401*T^47 - 
        626/2401*T^46 - 614/2401*T^45 - 227/2401*T^44 + 1082/2401*T^43 + 87/343*T^42
        + 421/2401*T^41 - 779/2401*T^40 - 215/343*T^39 - 643/2401*T^38 + 
        325/2401*T^37 + 290/343*T^36 + 379/343*T^35 + 166/343*T^34 - 1063/2401*T^33 
        - 1338/2401*T^32 - 1024/2401*T^31 - 32/343*T^30 - 213/2401*T^29 + 
        459/2401*T^28 - 213/2401*T^27 - 32/343*T^26 - 1024/2401*T^25 - 
        1338/2401*T^24 - 1063/2401*T^23 + 166/343*T^22 + 379/343*T^21 + 290/343*T^20
        + 325/2401*T^19 - 643/2401*T^18 - 215/343*T^17 - 779/2401*T^16 + 
        421/2401*T^15 + 87/343*T^14 + 1082/2401*T^13 - 227/2401*T^12 - 614/2401*T^11
        - 626/2401*T^10 - 726/2401*T^9 - 177/2401*T^8 + 1020/2401*T^7 + 775/2401*T^6
        - 1396/2401*T^5 - 1987/2401*T^4 - 247/343*T^3 - 3/49*T^2 + 5/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        4*X*Y^7 + X*Y^6 + 3*X*Y^5 + 5*X*Y^3 + 6*X*Y^2 + 4*X*Y + 4*X + 5*Y^30 + 
        6*Y^29 + 4*Y^28 + Y^27 + 5*Y^26 + 3*Y^24 + 5*Y^23 + 4*Y^22 + 4*Y^21 + 5*Y^20
        + 6*Y^19 + 3*Y^18 + 5*Y^17 + 2*Y^16 + Y^15 + 3*Y^14 + 5*Y^13 + 3*Y^12 + 
        6*Y^10 + 5*Y^9 + 5*Y^8 + Y^7 + 6*Y^6 + 3*Y^4 + 4*Y^3 + 4*Y^2 + 6*Y + 1,
    -T^56 - 11/7*T^55 - 78/49*T^54 - 549/343*T^53 - 755/2401*T^52 + 1003/2401*T^51 +
        2076/2401*T^50 + 1492/2401*T^49 + 58/343*T^48 + 257/2401*T^47 - 
        943/2401*T^46 - 16/2401*T^45 + 1115/2401*T^44 + 1931/2401*T^43 + 
        2312/2401*T^42 + 2960/2401*T^41 + 2519/2401*T^40 + 990/2401*T^39 + 
        839/2401*T^38 - 86/2401*T^37 - 1035/2401*T^36 - 2000/2401*T^35 - 
        1369/2401*T^34 - 423/2401*T^33 + 400/2401*T^32 + 2703/2401*T^31 + 
        2540/2401*T^30 + 1181/2401*T^29 - 1181/2401*T^27 - 2540/2401*T^26 - 
        2703/2401*T^25 - 400/2401*T^24 + 423/2401*T^23 + 1369/2401*T^22 + 
        2000/2401*T^21 + 1035/2401*T^20 + 86/2401*T^19 - 839/2401*T^18 - 
        990/2401*T^17 - 2519/2401*T^16 - 2960/2401*T^15 - 2312/2401*T^14 - 
        1931/2401*T^13 - 1115/2401*T^12 + 16/2401*T^11 + 943/2401*T^10 - 
        257/2401*T^9 - 58/343*T^8 - 1492/2401*T^7 - 2076/2401*T^6 - 1003/2401*T^5 + 
        755/2401*T^4 + 549/343*T^3 + 78/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^13 + 3*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 5*X*Y^8 + X*Y^7 + 
        4*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + X*Y^3 + 2*X*Y^2 + 6*X*Y + X + Y^30 + 4*Y^28 + 
        4*Y^26 + Y^24 + 5*Y^23 + Y^22 + 6*Y^21 + Y^20 + Y^19 + 3*Y^18 + 5*Y^17 + 
        4*Y^16 + 6*Y^14 + Y^13 + 5*Y^12 + 3*Y^11 + 2*Y^9 + 6*Y^6 + 3*Y^5 + Y^4 + 
        5*Y^3 + 4*Y^2 + 2*Y + 6,
    -T^56 - 4/7*T^55 + 5/7*T^54 - 120/343*T^53 - 2906/2401*T^52 + 1723/2401*T^51 + 
        2374/2401*T^50 - 278/343*T^49 + 262/2401*T^48 + 368/343*T^47 - 
        1859/2401*T^46 - 2011/2401*T^45 + 2158/2401*T^44 - 1006/2401*T^43 - 
        4100/2401*T^42 + 2083/2401*T^41 + 2822/2401*T^40 - 446/343*T^39 + 
        47/343*T^38 + 5064/2401*T^37 - 783/2401*T^36 - 1261/2401*T^35 + 543/343*T^34
        - 1370/2401*T^33 - 4507/2401*T^32 + 2132/2401*T^31 + 1151/2401*T^30 - 
        5399/2401*T^29 + 5399/2401*T^27 - 1151/2401*T^26 - 2132/2401*T^25 + 
        4507/2401*T^24 + 1370/2401*T^23 - 543/343*T^22 + 1261/2401*T^21 + 
        783/2401*T^20 - 5064/2401*T^19 - 47/343*T^18 + 446/343*T^17 - 2822/2401*T^16
        - 2083/2401*T^15 + 4100/2401*T^14 + 1006/2401*T^13 - 2158/2401*T^12 + 
        2011/2401*T^11 + 1859/2401*T^10 - 368/343*T^9 - 262/2401*T^8 + 278/343*T^7 -
        2374/2401*T^6 - 1723/2401*T^5 + 2906/2401*T^4 + 120/343*T^3 - 5/7*T^2 + 
        4/7*T + 1
*], [*
    X^3 + 5*X*Y^13 + 6*X*Y^12 + 3*X*Y^10 + X*Y^9 + X*Y^8 + 3*X*Y^7 + 2*X*Y^6 + 
        6*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + X*Y + X + 6*Y^30 + 5*Y^29 + Y^28 + 
        Y^27 + 3*Y^26 + 6*Y^25 + 2*Y^24 + 4*Y^22 + 5*Y^19 + 2*Y^18 + Y^17 + 4*Y^16 +
        Y^15 + 4*Y^14 + Y^13 + 5*Y^12 + 3*Y^11 + 4*Y^10 + 4*Y^9 + 4*Y^7 + 4*Y^5 + 
        4*Y^4 + 2*Y^3 + 5*Y + 3,
    T^56 + 15/7*T^55 + 54/49*T^54 - 255/343*T^53 - 372/343*T^52 - 1140/2401*T^51 - 
        1387/2401*T^50 - 4915/2401*T^49 - 5150/2401*T^48 + 834/2401*T^47 + 
        4372/2401*T^46 + 3330/2401*T^45 + 3442/2401*T^44 + 4873/2401*T^43 + 
        4175/2401*T^42 - 19/2401*T^41 - 3614/2401*T^40 - 1406/2401*T^39 + 
        351/2401*T^38 - 656/343*T^37 - 1042/343*T^36 - 2068/2401*T^35 + 
        2349/2401*T^34 + 1545/2401*T^33 - 1135/2401*T^32 - 1353/2401*T^31 + 
        1856/2401*T^30 + 1874/2401*T^29 - 166/2401*T^28 + 1874/2401*T^27 + 
        1856/2401*T^26 - 1353/2401*T^25 - 1135/2401*T^24 + 1545/2401*T^23 + 
        2349/2401*T^22 - 2068/2401*T^21 - 1042/343*T^20 - 656/343*T^19 + 
        351/2401*T^18 - 1406/2401*T^17 - 3614/2401*T^16 - 19/2401*T^15 + 
        4175/2401*T^14 + 4873/2401*T^13 + 3442/2401*T^12 + 3330/2401*T^11 + 
        4372/2401*T^10 + 834/2401*T^9 - 5150/2401*T^8 - 4915/2401*T^7 - 
        1387/2401*T^6 - 1140/2401*T^5 - 372/343*T^4 - 255/343*T^3 + 54/49*T^2 + 
        15/7*T + 1
*], [*
    X^3 + 6*X*Y^13 + 5*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 2*X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 
        4*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 5*X*Y + 5*Y^30 + 3*Y^29 + 4*Y^28 + 6*Y^27 + 
        3*Y^26 + 4*Y^25 + 3*Y^24 + Y^23 + Y^20 + 5*Y^19 + Y^18 + 2*Y^17 + Y^16 + 
        Y^14 + 5*Y^12 + 4*Y^11 + 3*Y^10 + 6*Y^8 + Y^6 + 3*Y^5 + 3*Y^4 + 2*Y^2 + 1,
    -T^56 + 2/7*T^55 + 37/49*T^54 + 198/343*T^53 - 890/2401*T^52 - 996/2401*T^51 + 
        943/2401*T^50 + 597/2401*T^49 - 2435/2401*T^48 - 613/2401*T^47 + 
        293/343*T^46 + 1690/2401*T^45 - 114/2401*T^44 - 1199/2401*T^43 - 
        452/2401*T^42 - 166/2401*T^41 - 12/49*T^40 + 414/2401*T^39 - 55/2401*T^38 + 
        180/2401*T^37 + 1136/2401*T^36 + 498/2401*T^35 - 1690/2401*T^34 - 
        2818/2401*T^33 + 1131/2401*T^32 + 3316/2401*T^31 + 334/2401*T^30 - 
        309/343*T^29 + 309/343*T^27 - 334/2401*T^26 - 3316/2401*T^25 - 
        1131/2401*T^24 + 2818/2401*T^23 + 1690/2401*T^22 - 498/2401*T^21 - 
        1136/2401*T^20 - 180/2401*T^19 + 55/2401*T^18 - 414/2401*T^17 + 12/49*T^16 +
        166/2401*T^15 + 452/2401*T^14 + 1199/2401*T^13 + 114/2401*T^12 - 
        1690/2401*T^11 - 293/343*T^10 + 613/2401*T^9 + 2435/2401*T^8 - 597/2401*T^7 
        - 943/2401*T^6 + 996/2401*T^5 + 890/2401*T^4 - 198/343*T^3 - 37/49*T^2 - 
        2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 4*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 5*X*Y^7 + 
        2*X*Y^6 + X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 3*Y^30 + Y^29 + 3*Y^28 + 6*Y^27 + Y^26
        + Y^25 + Y^24 + 3*Y^22 + 6*Y^21 + 5*Y^20 + 5*Y^19 + 5*Y^18 + 5*Y^17 + 4*Y^14
        + 4*Y^13 + 2*Y^12 + Y^10 + Y^9 + 3*Y^7 + 3*Y^6 + 6*Y^3 + 5*Y^2 + 5,
    T^56 - 12/7*T^55 + 19/49*T^54 + 416/343*T^53 - 1858/2401*T^52 - 2403/2401*T^51 +
        4266/2401*T^50 - 2187/2401*T^49 - 629/2401*T^48 + 188/343*T^47 - 
        463/2401*T^46 - 1891/2401*T^45 + 3856/2401*T^44 - 2441/2401*T^43 + 
        158/2401*T^42 - 106/2401*T^41 + 950/2401*T^40 - 1607/2401*T^39 + 
        2008/2401*T^38 - 2287/2401*T^37 + 2815/2401*T^36 - 2306/2401*T^35 + 
        290/2401*T^34 + 465/2401*T^33 + 1287/2401*T^32 - 3359/2401*T^31 + 64/49*T^30
        - 348/2401*T^29 - 1571/2401*T^28 - 348/2401*T^27 + 64/49*T^26 - 
        3359/2401*T^25 + 1287/2401*T^24 + 465/2401*T^23 + 290/2401*T^22 - 
        2306/2401*T^21 + 2815/2401*T^20 - 2287/2401*T^19 + 2008/2401*T^18 - 
        1607/2401*T^17 + 950/2401*T^16 - 106/2401*T^15 + 158/2401*T^14 - 
        2441/2401*T^13 + 3856/2401*T^12 - 1891/2401*T^11 - 463/2401*T^10 + 
        188/343*T^9 - 629/2401*T^8 - 2187/2401*T^7 + 4266/2401*T^6 - 2403/2401*T^5 -
        1858/2401*T^4 + 416/343*T^3 + 19/49*T^2 - 12/7*T + 1
*], [*
    X^3 + X*Y^14 + X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 4*X*Y^7 + 5*X*Y^6 + 
        2*X*Y^5 + 6*X*Y^4 + X*Y^3 + X*Y^2 + 4*X*Y + 5*X + 6*Y^30 + 2*Y^29 + 2*Y^28 +
        3*Y^27 + 2*Y^26 + Y^25 + 2*Y^24 + 5*Y^23 + 4*Y^22 + 5*Y^21 + Y^20 + 6*Y^19 +
        5*Y^17 + 5*Y^16 + Y^15 + 2*Y^14 + Y^13 + 3*Y^12 + 3*Y^11 + Y^10 + 3*Y^9 + 
        3*Y^7 + 4*Y^6 + 2*Y^5 + 6*Y^4 + 3*Y^3 + 6*Y^2 + 6*Y + 1,
    T^56 + 1/7*T^55 + 10/49*T^54 - 187/343*T^53 - 1389/2401*T^52 - 230/2401*T^51 - 
        265/2401*T^50 - 314/2401*T^49 + 649/2401*T^48 - 251/343*T^47 + 380/2401*T^46
        - 284/2401*T^45 - 744/2401*T^44 + 759/2401*T^43 - 891/2401*T^42 + 
        787/2401*T^41 + 138/343*T^40 + 292/2401*T^39 + 1199/2401*T^38 + 
        180/2401*T^37 - 64/2401*T^36 + 1333/2401*T^35 - 1284/2401*T^34 + 
        69/2401*T^33 - 764/2401*T^32 - 122/2401*T^31 - 43/343*T^30 + 3/2401*T^29 - 
        41/2401*T^28 + 3/2401*T^27 - 43/343*T^26 - 122/2401*T^25 - 764/2401*T^24 + 
        69/2401*T^23 - 1284/2401*T^22 + 1333/2401*T^21 - 64/2401*T^20 + 
        180/2401*T^19 + 1199/2401*T^18 + 292/2401*T^17 + 138/343*T^16 + 
        787/2401*T^15 - 891/2401*T^14 + 759/2401*T^13 - 744/2401*T^12 - 
        284/2401*T^11 + 380/2401*T^10 - 251/343*T^9 + 649/2401*T^8 - 314/2401*T^7 - 
        265/2401*T^6 - 230/2401*T^5 - 1389/2401*T^4 - 187/343*T^3 + 10/49*T^2 + 
        1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 
        + 3*X*Y^8 + 2*X*Y^7 + 3*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 2*X*Y + X + 
        6*Y^30 + 6*Y^29 + 3*Y^28 + 2*Y^27 + 4*Y^26 + 2*Y^25 + Y^24 + 3*Y^22 + 6*Y^21
        + 3*Y^20 + 3*Y^18 + 6*Y^17 + 2*Y^16 + 4*Y^15 + 6*Y^14 + 3*Y^12 + Y^11 + 
        6*Y^10 + 3*Y^8 + 2*Y^7 + 6*Y^6 + 6*Y^5 + Y^4 + Y^3 + 4*Y^2 + 5*Y + 3,
    T^56 + 3/7*T^55 - 94/49*T^54 - 523/343*T^53 + 4324/2401*T^52 + 5326/2401*T^51 - 
        2488/2401*T^50 - 6697/2401*T^49 + 694/2401*T^48 + 6439/2401*T^47 + 
        984/2401*T^46 - 3631/2401*T^45 - 1360/2401*T^44 + 998/2401*T^43 + 
        720/2401*T^42 + 92/343*T^41 + 123/2401*T^40 - 1581/2401*T^39 - 
        1648/2401*T^38 + 1047/2401*T^37 + 2067/2401*T^36 + 921/2401*T^35 - 
        1369/2401*T^34 - 2668/2401*T^33 - 1083/2401*T^32 + 3025/2401*T^31 + 
        4132/2401*T^30 - 1187/2401*T^29 - 5765/2401*T^28 - 1187/2401*T^27 + 
        4132/2401*T^26 + 3025/2401*T^25 - 1083/2401*T^24 - 2668/2401*T^23 - 
        1369/2401*T^22 + 921/2401*T^21 + 2067/2401*T^20 + 1047/2401*T^19 - 
        1648/2401*T^18 - 1581/2401*T^17 + 123/2401*T^16 + 92/343*T^15 + 
        720/2401*T^14 + 998/2401*T^13 - 1360/2401*T^12 - 3631/2401*T^11 + 
        984/2401*T^10 + 6439/2401*T^9 + 694/2401*T^8 - 6697/2401*T^7 - 2488/2401*T^6
        + 5326/2401*T^5 + 4324/2401*T^4 - 523/343*T^3 - 94/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 6*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 +
        2*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 3*X*Y^2 + 5*X*Y + 3*X + 4*Y^30 + 
        5*Y^29 + 4*Y^28 + 4*Y^27 + 4*Y^26 + 6*Y^25 + 3*Y^24 + 5*Y^23 + 4*Y^21 + 
        6*Y^20 + Y^19 + 5*Y^17 + 5*Y^16 + 3*Y^15 + Y^12 + 4*Y^11 + 5*Y^10 + 6*Y^9 + 
        4*Y^8 + 4*Y^7 + 2*Y^6 + 4*Y^3 + 5*Y^2 + 3*Y + 1,
    -T^56 + 4/7*T^55 + 6/49*T^54 - 52/343*T^53 - 463/2401*T^52 + 137/2401*T^51 + 
        1024/2401*T^50 - 62/343*T^49 + 122/2401*T^48 + 23/343*T^47 + 1194/2401*T^46 
        - 1046/2401*T^45 - 106/2401*T^44 + 143/2401*T^43 - 466/2401*T^42 + 
        734/2401*T^41 + 256/2401*T^40 - 93/343*T^39 - 125/343*T^38 + 1404/2401*T^37 
        + 19/343*T^36 + 41/2401*T^35 - 62/2401*T^34 + 356/2401*T^33 + 759/2401*T^32 
        - 311/2401*T^31 - 289/2401*T^30 + 1542/2401*T^29 - 1542/2401*T^27 + 
        289/2401*T^26 + 311/2401*T^25 - 759/2401*T^24 - 356/2401*T^23 + 62/2401*T^22
        - 41/2401*T^21 - 19/343*T^20 - 1404/2401*T^19 + 125/343*T^18 + 93/343*T^17 -
        256/2401*T^16 - 734/2401*T^15 + 466/2401*T^14 - 143/2401*T^13 + 
        106/2401*T^12 + 1046/2401*T^11 - 1194/2401*T^10 - 23/343*T^9 - 122/2401*T^8 
        + 62/343*T^7 - 1024/2401*T^6 - 137/2401*T^5 + 463/2401*T^4 + 52/343*T^3 - 
        6/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 5*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 6*X*Y^8 +
        2*X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + X*Y + 4*Y^30 + 
        4*Y^27 + 6*Y^26 + Y^25 + Y^24 + 2*Y^23 + 3*Y^22 + 2*Y^21 + 3*Y^19 + 6*Y^18 +
        3*Y^17 + 3*Y^14 + 2*Y^13 + 5*Y^12 + 2*Y^11 + Y^10 + 5*Y^9 + 5*Y^8 + 2*Y^7 + 
        5*Y^6 + Y^5 + 6*Y^4 + 6*Y^3 + 3*Y^2 + 5*Y + 2,
    -T^56 + 2/7*T^55 + 27/49*T^54 - 174/343*T^53 + 548/2401*T^52 - 64/343*T^51 - 
        1107/2401*T^50 - 380/2401*T^49 + 193/343*T^48 - 918/2401*T^47 + 
        572/2401*T^46 + 746/2401*T^45 + 75/343*T^44 - 75/343*T^43 - 1598/2401*T^42 +
        3443/2401*T^41 - 922/2401*T^40 + 34/343*T^39 + 337/2401*T^38 - 871/2401*T^37
        - 55/2401*T^36 + 803/2401*T^35 + 440/2401*T^34 - 1291/2401*T^33 + 
        1409/2401*T^32 - 1462/2401*T^31 + 1170/2401*T^30 - 1584/2401*T^29 + 
        1584/2401*T^27 - 1170/2401*T^26 + 1462/2401*T^25 - 1409/2401*T^24 + 
        1291/2401*T^23 - 440/2401*T^22 - 803/2401*T^21 + 55/2401*T^20 + 
        871/2401*T^19 - 337/2401*T^18 - 34/343*T^17 + 922/2401*T^16 - 3443/2401*T^15
        + 1598/2401*T^14 + 75/343*T^13 - 75/343*T^12 - 746/2401*T^11 - 572/2401*T^10
        + 918/2401*T^9 - 193/343*T^8 + 380/2401*T^7 + 1107/2401*T^6 + 64/343*T^5 - 
        548/2401*T^4 + 174/343*T^3 - 27/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + 3*X*Y^9 + 6*X*Y^8 +
        X*Y^7 + 5*X*Y^6 + 4*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 3*X*Y + Y^30 + 6*Y^29 + 
        5*Y^28 + 2*Y^27 + 2*Y^26 + 6*Y^25 + Y^24 + 4*Y^23 + 5*Y^22 + 5*Y^21 + 5*Y^20
        + 3*Y^19 + 3*Y^18 + Y^17 + 6*Y^16 + Y^15 + Y^14 + 4*Y^13 + 6*Y^12 + 3*Y^11 +
        3*Y^10 + 2*Y^9 + 3*Y^8 + 3*Y^7 + 3*Y^5 + 4*Y^4 + 6*Y^3 + 3*Y^2 + 6*Y + 6,
    -T^56 - 5/7*T^55 + 69/49*T^54 + 578/343*T^53 + 69/343*T^52 - 1535/2401*T^51 - 
        1580/2401*T^50 - 177/343*T^49 - 312/343*T^48 - 1987/2401*T^47 + 
        2341/2401*T^46 + 4751/2401*T^45 + 1900/2401*T^44 - 821/2401*T^43 - 
        1695/2401*T^42 - 2299/2401*T^41 - 2076/2401*T^40 - 997/2401*T^39 + 
        846/2401*T^38 + 335/343*T^37 + 1252/2401*T^36 - 220/2401*T^35 + 
        703/2401*T^34 + 1984/2401*T^33 - 1016/2401*T^32 - 3616/2401*T^31 - 
        629/2401*T^30 + 1706/2401*T^29 - 1706/2401*T^27 + 629/2401*T^26 + 
        3616/2401*T^25 + 1016/2401*T^24 - 1984/2401*T^23 - 703/2401*T^22 + 
        220/2401*T^21 - 1252/2401*T^20 - 335/343*T^19 - 846/2401*T^18 + 
        997/2401*T^17 + 2076/2401*T^16 + 2299/2401*T^15 + 1695/2401*T^14 + 
        821/2401*T^13 - 1900/2401*T^12 - 4751/2401*T^11 - 2341/2401*T^10 + 
        1987/2401*T^9 + 312/343*T^8 + 177/343*T^7 + 1580/2401*T^6 + 1535/2401*T^5 - 
        69/343*T^4 - 578/343*T^3 - 69/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 4*X*Y^13 + X*Y^12 + X*Y^11 + 4*X*Y^10 + X*Y^9 + X*Y^8 + 5*X*Y^7
        + X*Y^6 + X*Y^5 + X*Y^4 + 6*X*Y^3 + 3*X*Y + X + 3*Y^30 + 6*Y^29 + 3*Y^26 + 
        Y^25 + 5*Y^23 + Y^21 + 2*Y^20 + 4*Y^19 + 2*Y^18 + 4*Y^17 + 4*Y^16 + 6*Y^15 +
        4*Y^14 + 4*Y^13 + 5*Y^12 + 4*Y^11 + 5*Y^9 + 3*Y^8 + 4*Y^7 + 3*Y^6 + 3*Y^5 + 
        2*Y^4 + 3*Y^2 + 5*Y + 3,
    -T^56 - 5/7*T^55 + 59/49*T^54 + 417/343*T^53 - 1761/2401*T^52 - 1843/2401*T^51 +
        1915/2401*T^50 + 37/2401*T^49 - 2797/2401*T^48 + 632/2401*T^47 + 
        451/343*T^46 - 1017/2401*T^45 - 3075/2401*T^44 + 969/2401*T^43 + 
        1963/2401*T^42 - 1300/2401*T^41 - 71/343*T^40 + 3771/2401*T^39 + 
        1592/2401*T^38 - 3457/2401*T^37 - 2895/2401*T^36 + 1423/2401*T^35 + 
        298/343*T^34 + 127/2401*T^33 + 636/2401*T^32 + 890/2401*T^31 - 
        1011/2401*T^30 - 1871/2401*T^29 + 1871/2401*T^27 + 1011/2401*T^26 - 
        890/2401*T^25 - 636/2401*T^24 - 127/2401*T^23 - 298/343*T^22 - 
        1423/2401*T^21 + 2895/2401*T^20 + 3457/2401*T^19 - 1592/2401*T^18 - 
        3771/2401*T^17 + 71/343*T^16 + 1300/2401*T^15 - 1963/2401*T^14 - 
        969/2401*T^13 + 3075/2401*T^12 + 1017/2401*T^11 - 451/343*T^10 - 
        632/2401*T^9 + 2797/2401*T^8 - 37/2401*T^7 - 1915/2401*T^6 + 1843/2401*T^5 +
        1761/2401*T^4 - 417/343*T^3 - 59/49*T^2 + 5/7*T + 1
*], [*
    X^3 + X*Y^14 + X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 5*X*Y^8 + 
        2*X*Y^7 + 2*X*Y^6 + 2*X*Y^4 + X*Y^3 + 2*X*Y^2 + 6*X*Y + 5*X + 6*Y^30 + 
        3*Y^29 + 5*Y^28 + 3*Y^27 + 3*Y^26 + 6*Y^25 + 5*Y^24 + 2*Y^23 + 6*Y^22 + Y^21
        + Y^20 + 6*Y^19 + Y^18 + 3*Y^17 + 6*Y^16 + 6*Y^15 + Y^14 + 2*Y^13 + Y^12 + 
        4*Y^11 + 4*Y^10 + 4*Y^9 + Y^8 + 2*Y^7 + 6*Y^6 + 5*Y^5 + 3*Y^4 + 5*Y^3 + 
        3*Y^2 + 3*Y + 2,
    T^56 + 10/7*T^55 + 61/49*T^54 + 5/343*T^53 - 2998/2401*T^52 - 478/343*T^51 - 
        767/2401*T^50 + 551/343*T^49 + 4588/2401*T^48 + 2073/2401*T^47 - 
        4766/2401*T^46 - 8429/2401*T^45 - 6751/2401*T^44 - 520/2401*T^43 + 
        5630/2401*T^42 + 144/49*T^41 + 2171/2401*T^40 - 4985/2401*T^39 - 
        7603/2401*T^38 - 4002/2401*T^37 + 3288/2401*T^36 + 8627/2401*T^35 + 
        7380/2401*T^34 + 2/7*T^33 - 6299/2401*T^32 - 8279/2401*T^31 - 2927/2401*T^30
        + 3993/2401*T^29 + 7720/2401*T^28 + 3993/2401*T^27 - 2927/2401*T^26 - 
        8279/2401*T^25 - 6299/2401*T^24 + 2/7*T^23 + 7380/2401*T^22 + 8627/2401*T^21
        + 3288/2401*T^20 - 4002/2401*T^19 - 7603/2401*T^18 - 4985/2401*T^17 + 
        2171/2401*T^16 + 144/49*T^15 + 5630/2401*T^14 - 520/2401*T^13 - 
        6751/2401*T^12 - 8429/2401*T^11 - 4766/2401*T^10 + 2073/2401*T^9 + 
        4588/2401*T^8 + 551/343*T^7 - 767/2401*T^6 - 478/343*T^5 - 2998/2401*T^4 + 
        5/343*T^3 + 61/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 
        3*X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + X*Y + 
        3*X + Y^30 + Y^29 + 5*Y^28 + 6*Y^26 + 6*Y^25 + 6*Y^24 + 6*Y^23 + 3*Y^22 + 
        3*Y^21 + 4*Y^20 + 2*Y^19 + 6*Y^18 + 4*Y^17 + 6*Y^16 + 2*Y^15 + 3*Y^14 + 
        5*Y^13 + 6*Y^12 + 4*Y^11 + 4*Y^10 + Y^8 + 5*Y^7 + 2*Y^6 + 5*Y^5 + 4*Y^4 + 
        3*Y^3 + Y + 2,
    -T^56 + 4/7*T^55 - 38/49*T^54 + 33/343*T^53 + 279/2401*T^52 - 1335/2401*T^51 + 
        43/49*T^50 - 1817/2401*T^49 + 1517/2401*T^48 + 733/2401*T^47 - 178/343*T^46 
        + 2600/2401*T^45 - 2652/2401*T^44 + 1273/2401*T^43 + 233/2401*T^42 - 
        2257/2401*T^41 + 3049/2401*T^40 - 1707/2401*T^39 - 163/2401*T^38 + 
        2195/2401*T^37 - 449/343*T^36 + 3251/2401*T^35 - 1926/2401*T^34 + 
        292/2401*T^33 + 2465/2401*T^32 - 4497/2401*T^31 + 4420/2401*T^30 - 
        2614/2401*T^29 + 2614/2401*T^27 - 4420/2401*T^26 + 4497/2401*T^25 - 
        2465/2401*T^24 - 292/2401*T^23 + 1926/2401*T^22 - 3251/2401*T^21 + 
        449/343*T^20 - 2195/2401*T^19 + 163/2401*T^18 + 1707/2401*T^17 - 
        3049/2401*T^16 + 2257/2401*T^15 - 233/2401*T^14 - 1273/2401*T^13 + 
        2652/2401*T^12 - 2600/2401*T^11 + 178/343*T^10 - 733/2401*T^9 - 
        1517/2401*T^8 + 1817/2401*T^7 - 43/49*T^6 + 1335/2401*T^5 - 279/2401*T^4 - 
        33/343*T^3 + 38/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 5*X*Y^10 + 6*X*Y^9 + X*Y^8 + 3*X*Y^7 + 
        4*X*Y^5 + 2*X*Y^4 + X*Y + X + Y^30 + 5*Y^29 + 3*Y^28 + 3*Y^25 + 4*Y^24 + 
        3*Y^23 + 5*Y^22 + 4*Y^21 + 6*Y^20 + 2*Y^19 + 6*Y^18 + 2*Y^17 + 5*Y^16 + 
        3*Y^15 + Y^14 + 6*Y^13 + Y^12 + 2*Y^11 + 4*Y^8 + 2*Y^7 + 6*Y^6 + 5*Y^5 + 
        2*Y^4 + 4*Y^3 + Y^2 + 3,
    -T^56 + 16/7*T^55 - 138/49*T^54 + 912/343*T^53 - 4338/2401*T^52 + 3113/2401*T^51
        - 1730/2401*T^50 - 368/2401*T^49 + 838/2401*T^48 + 428/2401*T^47 - 
        461/343*T^46 + 1030/343*T^45 - 1355/343*T^44 + 1306/343*T^43 - 
        7354/2401*T^42 + 4210/2401*T^41 - 1556/2401*T^40 - 195/343*T^39 + 
        661/343*T^38 - 4836/2401*T^37 + 3334/2401*T^36 - 722/2401*T^35 - 
        2123/2401*T^34 + 486/343*T^33 - 4191/2401*T^32 + 586/343*T^31 - 
        3519/2401*T^30 + 342/343*T^29 - 342/343*T^27 + 3519/2401*T^26 - 586/343*T^25
        + 4191/2401*T^24 - 486/343*T^23 + 2123/2401*T^22 + 722/2401*T^21 - 
        3334/2401*T^20 + 4836/2401*T^19 - 661/343*T^18 + 195/343*T^17 + 
        1556/2401*T^16 - 4210/2401*T^15 + 7354/2401*T^14 - 1306/343*T^13 + 
        1355/343*T^12 - 1030/343*T^11 + 461/343*T^10 - 428/2401*T^9 - 838/2401*T^8 +
        368/2401*T^7 + 1730/2401*T^6 - 3113/2401*T^5 + 4338/2401*T^4 - 912/343*T^3 +
        138/49*T^2 - 16/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 6*X*Y^11 + 5*X*Y^10 + X*Y^9 + X*Y^8 + 4*X*Y^7 + 
        X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + X*Y + 2*X + 5*Y^30 + 4*Y^29 
        + 2*Y^28 + 4*Y^27 + 2*Y^26 + Y^25 + Y^24 + 4*Y^23 + 2*Y^22 + 5*Y^21 + 5*Y^20
        + Y^19 + 5*Y^18 + 4*Y^16 + 5*Y^15 + Y^14 + 6*Y^12 + 2*Y^11 + Y^10 + 6*Y^9 + 
        5*Y^8 + 6*Y^7 + 6*Y^5 + 4*Y^4 + 5*Y^3 + 6*Y,
    T^56 - 1/7*T^55 - 83/49*T^54 + 139/343*T^53 + 2705/2401*T^52 - 2837/2401*T^51 - 
        54/343*T^50 + 69/49*T^49 + 236/2401*T^48 - 2484/2401*T^47 + 839/2401*T^46 + 
        1200/2401*T^45 - 2640/2401*T^44 - 1200/2401*T^43 + 526/343*T^42 - 
        37/343*T^41 - 382/343*T^40 + 2404/2401*T^39 + 1278/2401*T^38 - 
        3006/2401*T^37 - 376/2401*T^36 + 2332/2401*T^35 - 577/2401*T^34 - 38/49*T^33
        + 863/2401*T^32 + 1301/2401*T^31 - 1154/2401*T^30 - 27/343*T^29 + 
        1046/2401*T^28 - 27/343*T^27 - 1154/2401*T^26 + 1301/2401*T^25 + 
        863/2401*T^24 - 38/49*T^23 - 577/2401*T^22 + 2332/2401*T^21 - 376/2401*T^20 
        - 3006/2401*T^19 + 1278/2401*T^18 + 2404/2401*T^17 - 382/343*T^16 - 
        37/343*T^15 + 526/343*T^14 - 1200/2401*T^13 - 2640/2401*T^12 + 
        1200/2401*T^11 + 839/2401*T^10 - 2484/2401*T^9 + 236/2401*T^8 + 69/49*T^7 - 
        54/343*T^6 - 2837/2401*T^5 + 2705/2401*T^4 + 139/343*T^3 - 83/49*T^2 - 1/7*T
        + 1
*], [*
    X^3 + 5*X*Y^14 + 2*X*Y^12 + X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 3*X*Y^8 + 6*X*Y^7 + 
        2*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 5*X*Y + 3*Y^30 + 3*Y^29 + 2*Y^28 + 3*Y^27 + 
        6*Y^26 + 6*Y^25 + 6*Y^24 + 5*Y^23 + 6*Y^22 + 3*Y^20 + 6*Y^19 + 2*Y^18 + 
        2*Y^17 + 3*Y^16 + 6*Y^15 + 5*Y^14 + 6*Y^13 + 4*Y^12 + Y^11 + 6*Y^9 + 3*Y^8 +
        4*Y^7 + 5*Y^6 + 2*Y^4 + Y^2 + 4*Y + 4,
    -T^56 + 2/7*T^55 + 22/49*T^54 + 248/343*T^53 - 36/2401*T^52 - 2021/2401*T^51 + 
        192/2401*T^50 + 523/2401*T^49 + 1916/2401*T^48 - 176/2401*T^47 - 
        1721/2401*T^46 - 646/2401*T^45 - 1067/2401*T^44 + 179/343*T^43 + 
        185/2401*T^42 + 3/49*T^41 + 1173/2401*T^40 - 1334/2401*T^39 + 720/2401*T^38 
        - 262/343*T^37 + 2322/2401*T^36 + 608/2401*T^35 + 403/2401*T^34 - 
        848/2401*T^33 - 3215/2401*T^32 + 250/2401*T^31 + 850/2401*T^30 + 
        2234/2401*T^29 - 2234/2401*T^27 - 850/2401*T^26 - 250/2401*T^25 + 
        3215/2401*T^24 + 848/2401*T^23 - 403/2401*T^22 - 608/2401*T^21 - 
        2322/2401*T^20 + 262/343*T^19 - 720/2401*T^18 + 1334/2401*T^17 - 
        1173/2401*T^16 - 3/49*T^15 - 185/2401*T^14 - 179/343*T^13 + 1067/2401*T^12 +
        646/2401*T^11 + 1721/2401*T^10 + 176/2401*T^9 - 1916/2401*T^8 - 523/2401*T^7
        - 192/2401*T^6 + 2021/2401*T^5 + 36/2401*T^4 - 248/343*T^3 - 22/49*T^2 - 
        2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + X*Y^13 + 2*X*Y^12 + X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 
        2*X*Y^8 + 3*X*Y^7 + 5*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + X*Y + 5*X + 3*Y^30 + Y^29 
        + 3*Y^25 + 3*Y^24 + 6*Y^22 + 4*Y^21 + 6*Y^19 + 2*Y^18 + 5*Y^17 + Y^15 + Y^14
        + Y^12 + 5*Y^10 + 4*Y^9 + 5*Y^8 + 5*Y^6 + 5*Y^4 + 2*Y^3 + 2*Y + 4,
    -T^56 + 5/7*T^55 - 17/49*T^54 - 54/343*T^53 + 900/2401*T^52 - 51/2401*T^51 - 
        493/2401*T^50 + 250/2401*T^49 + 2238/2401*T^48 - 2656/2401*T^47 + 
        1776/2401*T^46 + 8/343*T^45 - 1290/2401*T^44 - 424/2401*T^43 + 758/2401*T^42
        - 755/2401*T^41 - 263/2401*T^40 + 3081/2401*T^39 - 1735/2401*T^38 + 
        523/2401*T^37 + 663/2401*T^36 - 753/2401*T^35 + 733/2401*T^34 + 94/2401*T^33
        + 17/343*T^32 - 1511/2401*T^31 + 918/2401*T^30 - 155/343*T^29 + 155/343*T^27
        - 918/2401*T^26 + 1511/2401*T^25 - 17/343*T^24 - 94/2401*T^23 - 
        733/2401*T^22 + 753/2401*T^21 - 663/2401*T^20 - 523/2401*T^19 + 
        1735/2401*T^18 - 3081/2401*T^17 + 263/2401*T^16 + 755/2401*T^15 - 
        758/2401*T^14 + 424/2401*T^13 + 1290/2401*T^12 - 8/343*T^11 - 1776/2401*T^10
        + 2656/2401*T^9 - 2238/2401*T^8 - 250/2401*T^7 + 493/2401*T^6 + 51/2401*T^5 
        - 900/2401*T^4 + 54/343*T^3 + 17/49*T^2 - 5/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 5*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 5*X*Y^8 + X*Y^7 + 
        4*X*Y^6 + X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 2*X + 3*Y^30 + 3*Y^29 + 
        3*Y^28 + Y^27 + 3*Y^26 + 4*Y^25 + 4*Y^23 + Y^22 + Y^21 + 3*Y^19 + 3*Y^18 + 
        3*Y^17 + 4*Y^16 + 2*Y^15 + 2*Y^14 + Y^13 + 6*Y^12 + Y^11 + 5*Y^10 + Y^9 + 
        5*Y^8 + 4*Y^7 + 6*Y^6 + 6*Y^5 + 5*Y^4 + 2*Y^3 + Y^2 + 5*Y + 6,
    -T^56 + 10/7*T^55 - 12/49*T^54 - 274/343*T^53 + 220/343*T^52 + 698/2401*T^51 - 
        1187/2401*T^50 - 1769/2401*T^49 + 1894/2401*T^48 + 1887/2401*T^47 - 
        3403/2401*T^46 - 18/343*T^45 + 4385/2401*T^44 - 415/343*T^43 - 
        1359/2401*T^42 + 317/343*T^41 + 634/2401*T^40 - 2922/2401*T^39 + 
        1286/2401*T^38 + 243/343*T^37 - 1406/2401*T^36 - 1559/2401*T^35 + 
        3854/2401*T^34 - 1585/2401*T^33 - 2335/2401*T^32 + 276/343*T^31 + 
        2052/2401*T^30 - 3679/2401*T^29 + 3679/2401*T^27 - 2052/2401*T^26 - 
        276/343*T^25 + 2335/2401*T^24 + 1585/2401*T^23 - 3854/2401*T^22 + 
        1559/2401*T^21 + 1406/2401*T^20 - 243/343*T^19 - 1286/2401*T^18 + 
        2922/2401*T^17 - 634/2401*T^16 - 317/343*T^15 + 1359/2401*T^14 + 
        415/343*T^13 - 4385/2401*T^12 + 18/343*T^11 + 3403/2401*T^10 - 1887/2401*T^9
        - 1894/2401*T^8 + 1769/2401*T^7 + 1187/2401*T^6 - 698/2401*T^5 - 220/343*T^4
        + 274/343*T^3 + 12/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 4*X*Y^13 + X*Y^12 + 2*X*Y^11 + 2*X*Y^9 + 2*X*Y^8 + 6*X*Y^7 + 
        4*X*Y^6 + 2*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 5*X*Y + 2*X + Y^30 + 6*Y^29 + 6*Y^28
        + 4*Y^27 + 3*Y^26 + 5*Y^24 + 5*Y^23 + 3*Y^22 + 3*Y^21 + 2*Y^20 + 6*Y^19 + 
        4*Y^18 + 4*Y^17 + 2*Y^16 + 5*Y^15 + 5*Y^14 + 4*Y^13 + Y^11 + 3*Y^10 + 3*Y^9 
        + 4*Y^7 + Y^6 + 5*Y^5 + 3*Y^4 + 4*Y^2 + Y + 6,
    -T^56 + 2/7*T^55 + 31/49*T^54 - 92/343*T^53 + 319/2401*T^52 - 701/2401*T^51 + 
        697/2401*T^50 + 1194/2401*T^49 - 144/343*T^48 + 803/2401*T^47 + 53/2401*T^46
        + 187/2401*T^45 + 949/2401*T^44 + 115/2401*T^43 + 1005/2401*T^42 - 
        459/2401*T^41 - 1627/2401*T^40 + 1000/2401*T^39 - 24/343*T^38 - 
        1408/2401*T^37 + 123/2401*T^36 + 125/2401*T^35 - 263/2401*T^34 - 
        1122/2401*T^33 - 827/2401*T^32 + 719/2401*T^31 - 782/2401*T^30 - 
        703/2401*T^29 + 703/2401*T^27 + 782/2401*T^26 - 719/2401*T^25 + 
        827/2401*T^24 + 1122/2401*T^23 + 263/2401*T^22 - 125/2401*T^21 - 
        123/2401*T^20 + 1408/2401*T^19 + 24/343*T^18 - 1000/2401*T^17 + 
        1627/2401*T^16 + 459/2401*T^15 - 1005/2401*T^14 - 115/2401*T^13 - 
        949/2401*T^12 - 187/2401*T^11 - 53/2401*T^10 - 803/2401*T^9 + 144/343*T^8 - 
        1194/2401*T^7 - 697/2401*T^6 + 701/2401*T^5 - 319/2401*T^4 + 92/343*T^3 - 
        31/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 
        + X*Y^8 + 6*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 6*X + 
        2*Y^30 + 6*Y^29 + 5*Y^28 + 4*Y^27 + 3*Y^25 + 6*Y^24 + Y^23 + 5*Y^22 + 5*Y^21
        + 2*Y^20 + Y^19 + 2*Y^18 + 6*Y^17 + Y^16 + 6*Y^15 + 3*Y^14 + Y^13 + 3*Y^11 +
        3*Y^9 + 3*Y^8 + 4*Y^7 + 2*Y^6 + 3*Y^5 + 5*Y^3 + 2*Y + 4,
    -T^56 - 5/7*T^55 + 53/49*T^54 + 269/343*T^53 - 19/2401*T^52 - 867/2401*T^51 - 
        1450/2401*T^50 - 17/2401*T^49 + 1688/2401*T^48 + 1405/2401*T^47 + 
        513/2401*T^46 + 41/343*T^45 - 652/2401*T^44 - 1818/2401*T^43 - 27/49*T^42 + 
        1188/2401*T^41 + 2274/2401*T^40 + 118/2401*T^39 - 2312/2401*T^38 - 
        1595/2401*T^37 + 891/2401*T^36 + 1373/2401*T^35 + 30/343*T^34 - 
        1112/2401*T^33 + 153/2401*T^32 + 173/343*T^31 - 568/2401*T^30 - 
        122/2401*T^29 + 122/2401*T^27 + 568/2401*T^26 - 173/343*T^25 - 153/2401*T^24
        + 1112/2401*T^23 - 30/343*T^22 - 1373/2401*T^21 - 891/2401*T^20 + 
        1595/2401*T^19 + 2312/2401*T^18 - 118/2401*T^17 - 2274/2401*T^16 - 
        1188/2401*T^15 + 27/49*T^14 + 1818/2401*T^13 + 652/2401*T^12 - 41/343*T^11 -
        513/2401*T^10 - 1405/2401*T^9 - 1688/2401*T^8 + 17/2401*T^7 + 1450/2401*T^6 
        + 867/2401*T^5 + 19/2401*T^4 - 269/343*T^3 - 53/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 3*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 3*X*Y^8 +
        4*X*Y^7 + 2*X*Y^6 + 6*X*Y^3 + 4*X*Y^2 + 6*X*Y + 5*X + Y^30 + 3*Y^28 + 6*Y^26
        + 2*Y^25 + 6*Y^24 + 4*Y^23 + 6*Y^22 + Y^21 + 3*Y^20 + 6*Y^19 + 3*Y^18 + 
        6*Y^17 + 2*Y^16 + Y^15 + Y^14 + 2*Y^13 + 4*Y^12 + 4*Y^11 + 6*Y^10 + 4*Y^9 + 
        4*Y^8 + 2*Y^7 + Y^6 + 6*Y^4 + 2*Y^3 + 3*Y^2 + 5*Y + 6,
    -T^56 - T^55 - 3/49*T^54 + 256/343*T^53 + 956/2401*T^52 + 352/2401*T^51 + 
        461/2401*T^50 + 776/2401*T^49 - 668/2401*T^48 - 3256/2401*T^47 - 
        2327/2401*T^46 + 22/49*T^45 + 3103/2401*T^44 + 1535/2401*T^43 + 
        368/2401*T^42 - 243/2401*T^41 - 146/2401*T^40 - 257/343*T^39 - 438/343*T^38 
        - 235/343*T^37 + 863/2401*T^36 + 2215/2401*T^35 + 780/2401*T^34 + 
        193/2401*T^33 - 601/2401*T^32 - 103/343*T^31 - 1527/2401*T^30 - 
        1118/2401*T^29 + 1118/2401*T^27 + 1527/2401*T^26 + 103/343*T^25 + 
        601/2401*T^24 - 193/2401*T^23 - 780/2401*T^22 - 2215/2401*T^21 - 
        863/2401*T^20 + 235/343*T^19 + 438/343*T^18 + 257/343*T^17 + 146/2401*T^16 +
        243/2401*T^15 - 368/2401*T^14 - 1535/2401*T^13 - 3103/2401*T^12 - 22/49*T^11
        + 2327/2401*T^10 + 3256/2401*T^9 + 668/2401*T^8 - 776/2401*T^7 - 
        461/2401*T^6 - 352/2401*T^5 - 956/2401*T^4 - 256/343*T^3 + 3/49*T^2 + T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 
        X*Y^8 + 4*X*Y^7 + X*Y^6 + X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 6*X*Y + Y^30 + 3*Y^26 
        + 5*Y^25 + 6*Y^24 + Y^23 + 3*Y^21 + 2*Y^20 + 6*Y^19 + 2*Y^18 + Y^17 + Y^14 +
        5*Y^13 + 3*Y^12 + 6*Y^11 + Y^10 + 5*Y^9 + 2*Y^8 + 5*Y^7 + 5*Y^6 + 3*Y^5 + 
        6*Y^4 + 4*Y^2 + 3*Y + 4,
    -T^56 - 1/7*T^55 - 12/49*T^54 + 37/343*T^53 - 166/343*T^52 + 352/2401*T^51 - 
        983/2401*T^50 - 794/2401*T^49 + 17/49*T^48 - 1/343*T^47 - 1311/2401*T^46 - 
        348/2401*T^45 + 257/2401*T^44 - 428/2401*T^43 + 750/2401*T^42 - 
        186/2401*T^41 - 117/343*T^40 - 995/2401*T^39 + 1340/2401*T^38 - 
        1612/2401*T^37 + 737/2401*T^36 + 11/2401*T^35 - 435/2401*T^34 - 151/343*T^33
        + 565/2401*T^32 - 1117/2401*T^31 - 171/343*T^30 + 1095/2401*T^29 - 
        1095/2401*T^27 + 171/343*T^26 + 1117/2401*T^25 - 565/2401*T^24 + 
        151/343*T^23 + 435/2401*T^22 - 11/2401*T^21 - 737/2401*T^20 + 1612/2401*T^19
        - 1340/2401*T^18 + 995/2401*T^17 + 117/343*T^16 + 186/2401*T^15 - 
        750/2401*T^14 + 428/2401*T^13 - 257/2401*T^12 + 348/2401*T^11 + 
        1311/2401*T^10 + 1/343*T^9 - 17/49*T^8 + 794/2401*T^7 + 983/2401*T^6 - 
        352/2401*T^5 + 166/343*T^4 - 37/343*T^3 + 12/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 6*X*Y^13 + 2*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + X*Y^8 + 2*X*Y^7 + 
        6*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + X*Y^2 + 3*X*Y + 5*X + 5*Y^30 + 
        5*Y^29 + 5*Y^28 + 3*Y^27 + 2*Y^26 + 2*Y^24 + 4*Y^23 + 6*Y^22 + 6*Y^20 + 
        4*Y^19 + 6*Y^18 + 4*Y^16 + Y^15 + 3*Y^14 + 4*Y^13 + Y^10 + 4*Y^9 + 4*Y^8 + 
        6*Y^7 + 2*Y^6 + 6*Y^4 + 4*Y^3 + 5*Y^2 + Y + 6,
    -T^56 - 12/7*T^55 - 26/49*T^54 + 351/343*T^53 + 3117/2401*T^52 + 362/343*T^51 + 
        1885/2401*T^50 - 2038/2401*T^49 - 5036/2401*T^48 - 2602/2401*T^47 + 
        171/2401*T^46 - 391/2401*T^45 + 999/2401*T^44 + 3659/2401*T^43 + 
        263/343*T^42 - 1158/2401*T^41 - 2200/2401*T^40 - 2187/2401*T^39 - 
        1522/2401*T^38 + 824/2401*T^37 + 393/343*T^36 + 2033/2401*T^35 - 
        94/2401*T^34 - 1941/2401*T^33 - 1969/2401*T^32 - 12/343*T^31 + 
        1384/2401*T^30 + 606/2401*T^29 - 606/2401*T^27 - 1384/2401*T^26 + 
        12/343*T^25 + 1969/2401*T^24 + 1941/2401*T^23 + 94/2401*T^22 - 
        2033/2401*T^21 - 393/343*T^20 - 824/2401*T^19 + 1522/2401*T^18 + 
        2187/2401*T^17 + 2200/2401*T^16 + 1158/2401*T^15 - 263/343*T^14 - 
        3659/2401*T^13 - 999/2401*T^12 + 391/2401*T^11 - 171/2401*T^10 + 
        2602/2401*T^9 + 5036/2401*T^8 + 2038/2401*T^7 - 1885/2401*T^6 - 362/343*T^5 
        - 3117/2401*T^4 - 351/343*T^3 + 26/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 6*X*Y^9 + X*Y^8 + 
        5*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 6*X*Y^3 + 6*X*Y^2 + 3*Y^30 + 3*Y^29 + 5*Y^28 +
        5*Y^26 + Y^25 + 4*Y^24 + 5*Y^23 + 3*Y^22 + Y^20 + 2*Y^19 + 2*Y^18 + 2*Y^17 +
        2*Y^16 + 6*Y^15 + 3*Y^14 + 4*Y^13 + 4*Y^12 + 6*Y^11 + 5*Y^10 + 6*Y^9 + Y^8 +
        3*Y^7 + 3*Y^6 + 3*Y^5 + 5*Y^4 + 6*Y^3 + 6*Y^2 + 3*Y + 4,
    T^56 - 4/7*T^55 + 5/49*T^54 + 82/343*T^53 - 10/343*T^52 + 599/2401*T^51 + 
        289/2401*T^50 + 589/2401*T^49 + 1103/2401*T^48 - 557/2401*T^47 + 
        803/2401*T^46 - 79/343*T^45 + 236/2401*T^44 + 190/343*T^43 - 5/343*T^42 - 
        775/2401*T^41 + 72/343*T^40 + 646/2401*T^39 + 433/2401*T^38 - 258/2401*T^37 
        + 306/2401*T^36 + 2/343*T^35 + 663/2401*T^34 - 747/2401*T^33 - 31/2401*T^32 
        - 212/2401*T^31 + 1004/2401*T^30 - 4/2401*T^29 - 1025/2401*T^28 - 
        4/2401*T^27 + 1004/2401*T^26 - 212/2401*T^25 - 31/2401*T^24 - 747/2401*T^23 
        + 663/2401*T^22 + 2/343*T^21 + 306/2401*T^20 - 258/2401*T^19 + 433/2401*T^18
        + 646/2401*T^17 + 72/343*T^16 - 775/2401*T^15 - 5/343*T^14 + 190/343*T^13 + 
        236/2401*T^12 - 79/343*T^11 + 803/2401*T^10 - 557/2401*T^9 + 1103/2401*T^8 +
        589/2401*T^7 + 289/2401*T^6 + 599/2401*T^5 - 10/343*T^4 + 82/343*T^3 + 
        5/49*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 
        X*Y^8 + X*Y^7 + X*Y^6 + 5*X*Y^5 + X*Y^4 + 6*X*Y + 5*X + 4*Y^30 + 3*Y^29 + 
        Y^28 + 2*Y^27 + 4*Y^26 + 6*Y^25 + 5*Y^24 + 6*Y^23 + 3*Y^22 + 5*Y^21 + 5*Y^20
        + 2*Y^19 + 6*Y^17 + 3*Y^16 + 5*Y^15 + Y^14 + 3*Y^12 + 3*Y^11 + 6*Y^10 + 
        6*Y^9 + 5*Y^8 + 3*Y^7 + 2*Y^5 + 6*Y^4 + Y^3 + 6*Y^2 + 4*Y + 5,
    -T^56 - 4/7*T^55 + 75/49*T^54 + 45/49*T^53 - 2515/2401*T^52 - 4233/2401*T^51 + 
        296/2401*T^50 + 6306/2401*T^49 + 2370/2401*T^48 - 5434/2401*T^47 - 
        4651/2401*T^46 + 3082/2401*T^45 + 5891/2401*T^44 - 464/2401*T^43 - 
        4638/2401*T^42 - 120/343*T^41 + 3774/2401*T^40 + 2746/2401*T^39 - 
        2438/2401*T^38 - 3758/2401*T^37 + 240/2401*T^36 + 2853/2401*T^35 + 
        744/2401*T^34 - 2370/2401*T^33 - 1501/2401*T^32 + 786/2401*T^31 + 
        1087/2401*T^30 + 195/343*T^29 - 195/343*T^27 - 1087/2401*T^26 - 
        786/2401*T^25 + 1501/2401*T^24 + 2370/2401*T^23 - 744/2401*T^22 - 
        2853/2401*T^21 - 240/2401*T^20 + 3758/2401*T^19 + 2438/2401*T^18 - 
        2746/2401*T^17 - 3774/2401*T^16 + 120/343*T^15 + 4638/2401*T^14 + 
        464/2401*T^13 - 5891/2401*T^12 - 3082/2401*T^11 + 4651/2401*T^10 + 
        5434/2401*T^9 - 2370/2401*T^8 - 6306/2401*T^7 - 296/2401*T^6 + 4233/2401*T^5
        + 2515/2401*T^4 - 45/49*T^3 - 75/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 2*X*Y^8 
        + 3*X*Y^7 + X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + X*Y^2 + 4*X*Y + 5*X + Y^30
        + 3*Y^29 + Y^28 + 6*Y^27 + 3*Y^26 + 6*Y^25 + 3*Y^24 + Y^23 + 2*Y^22 + Y^21 +
        6*Y^20 + 3*Y^19 + Y^18 + 5*Y^17 + 3*Y^16 + 3*Y^15 + 6*Y^12 + 5*Y^11 + Y^9 + 
        6*Y^8 + 6*Y^7 + 6*Y^6 + 5*Y^5 + 4*Y^4 + 6*Y^3 + 4*Y^2 + 5*Y + 5,
    T^56 - 6/7*T^55 + 13/49*T^54 - 187/343*T^53 + 1447/2401*T^52 - 467/2401*T^51 + 
        404/2401*T^50 - 774/2401*T^49 - 201/2401*T^48 + 452/2401*T^47 - 
        711/2401*T^46 + 1158/2401*T^45 - 1397/2401*T^44 + 19/2401*T^43 - 
        628/2401*T^42 + 1840/2401*T^41 - 1419/2401*T^40 + 1067/2401*T^39 - 
        1496/2401*T^38 + 2430/2401*T^37 - 1018/2401*T^36 + 115/2401*T^35 + 
        911/2401*T^34 - 655/2401*T^33 - 384/2401*T^32 - 1049/2401*T^31 + 
        1851/2401*T^30 - 2085/2401*T^29 + 2199/2401*T^28 - 2085/2401*T^27 + 
        1851/2401*T^26 - 1049/2401*T^25 - 384/2401*T^24 - 655/2401*T^23 + 
        911/2401*T^22 + 115/2401*T^21 - 1018/2401*T^20 + 2430/2401*T^19 - 
        1496/2401*T^18 + 1067/2401*T^17 - 1419/2401*T^16 + 1840/2401*T^15 - 
        628/2401*T^14 + 19/2401*T^13 - 1397/2401*T^12 + 1158/2401*T^11 - 
        711/2401*T^10 + 452/2401*T^9 - 201/2401*T^8 - 774/2401*T^7 + 404/2401*T^6 - 
        467/2401*T^5 + 1447/2401*T^4 - 187/343*T^3 + 13/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 5*X*Y^12 + 2*X*Y^11 + X*Y^10 + 2*X*Y^9 + X*Y^8 + 
        6*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 6*X + 2*Y^30 + 
        3*Y^29 + Y^28 + Y^27 + 2*Y^26 + 2*Y^25 + 3*Y^24 + 3*Y^23 + 3*Y^22 + 6*Y^21 +
        5*Y^20 + 3*Y^19 + 3*Y^18 + 5*Y^17 + 5*Y^16 + 5*Y^14 + 3*Y^13 + 4*Y^12 + 
        4*Y^11 + 3*Y^10 + Y^9 + Y^8 + 6*Y^7 + 5*Y^6 + 5*Y^5 + Y^4 + 5*Y^3 + 3*Y^2 + 
        6*Y + 4,
    -T^56 - 4/7*T^55 + 10/49*T^54 + 241/343*T^53 + 82/2401*T^52 - 984/2401*T^51 - 
        671/2401*T^50 - 131/2401*T^49 - 309/2401*T^48 - 104/2401*T^47 + 
        773/2401*T^46 + 1277/2401*T^45 + 613/2401*T^44 - 88/2401*T^43 - 
        297/2401*T^42 + 806/2401*T^41 + 851/2401*T^40 + 73/2401*T^39 - 332/2401*T^38
        + 663/2401*T^37 + 1023/2401*T^36 + 111/2401*T^35 - 15/49*T^34 - 
        193/2401*T^33 + 612/2401*T^32 + 383/2401*T^31 - 94/343*T^30 - 559/2401*T^29 
        + 559/2401*T^27 + 94/343*T^26 - 383/2401*T^25 - 612/2401*T^24 + 
        193/2401*T^23 + 15/49*T^22 - 111/2401*T^21 - 1023/2401*T^20 - 663/2401*T^19 
        + 332/2401*T^18 - 73/2401*T^17 - 851/2401*T^16 - 806/2401*T^15 + 
        297/2401*T^14 + 88/2401*T^13 - 613/2401*T^12 - 1277/2401*T^11 - 
        773/2401*T^10 + 104/2401*T^9 + 309/2401*T^8 + 131/2401*T^7 + 671/2401*T^6 + 
        984/2401*T^5 - 82/2401*T^4 - 241/343*T^3 - 10/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 5*X*Y^10 + 5*X*Y^8 + 4*X*Y^7 +
        3*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 5*X*Y + 6*Y^30 + 3*Y^29 + 
        4*Y^28 + 3*Y^27 + 2*Y^26 + 2*Y^25 + 3*Y^24 + Y^23 + 3*Y^22 + 5*Y^21 + 4*Y^20
        + 4*Y^19 + 5*Y^18 + Y^17 + 4*Y^16 + 4*Y^15 + 6*Y^13 + 4*Y^12 + 3*Y^11 + 
        4*Y^10 + 5*Y^9 + 2*Y^8 + 6*Y^7 + 2*Y^6 + 5*Y^4 + 2*Y^3 + 2*Y^2 + 6,
    T^56 + T^55 + 11/49*T^54 - 109/343*T^53 - 124/2401*T^52 + 2666/2401*T^51 + 
        4623/2401*T^50 + 2678/2401*T^49 - 22/49*T^48 - 1968/2401*T^47 + 
        1215/2401*T^46 + 3966/2401*T^45 + 3181/2401*T^44 - 494/2401*T^43 - 
        2747/2401*T^42 - 11/2401*T^41 + 507/343*T^40 + 3574/2401*T^39 + 
        505/2401*T^38 - 1822/2401*T^37 - 1102/2401*T^36 + 1699/2401*T^35 + 
        4159/2401*T^34 + 2202/2401*T^33 - 775/2401*T^32 - 258/343*T^31 - 
        559/2401*T^30 + 242/343*T^29 + 2958/2401*T^28 + 242/343*T^27 - 559/2401*T^26
        - 258/343*T^25 - 775/2401*T^24 + 2202/2401*T^23 + 4159/2401*T^22 + 
        1699/2401*T^21 - 1102/2401*T^20 - 1822/2401*T^19 + 505/2401*T^18 + 
        3574/2401*T^17 + 507/343*T^16 - 11/2401*T^15 - 2747/2401*T^14 - 
        494/2401*T^13 + 3181/2401*T^12 + 3966/2401*T^11 + 1215/2401*T^10 - 
        1968/2401*T^9 - 22/49*T^8 + 2678/2401*T^7 + 4623/2401*T^6 + 2666/2401*T^5 - 
        124/2401*T^4 - 109/343*T^3 + 11/49*T^2 + T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 +
        6*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 5*X*Y + 5*X + 5*Y^30 + 
        6*Y^29 + 6*Y^28 + 5*Y^27 + 2*Y^26 + Y^25 + 4*Y^24 + 6*Y^23 + 4*Y^21 + 2*Y^20
        + 5*Y^18 + 3*Y^17 + 3*Y^16 + 2*Y^15 + 6*Y^14 + 2*Y^13 + 5*Y^12 + 3*Y^10 + 
        4*Y^9 + 3*Y^8 + 4*Y^7 + 2*Y^6 + 3*Y^3 + Y^2 + 4*Y + 6,
    -T^56 - 8/7*T^55 - 61/49*T^54 - 6/7*T^53 - 43/49*T^52 - 568/2401*T^51 - 
        768/2401*T^50 - 789/2401*T^49 + 341/2401*T^48 + 901/2401*T^47 + 
        499/2401*T^46 + 468/2401*T^45 + 566/2401*T^44 - 1586/2401*T^43 - 
        218/343*T^42 - 1629/2401*T^41 - 1366/2401*T^40 - 2098/2401*T^39 - 
        899/2401*T^38 - 1572/2401*T^37 - 1305/2401*T^36 - 55/2401*T^35 + 
        549/2401*T^34 + 1185/2401*T^33 + 1940/2401*T^32 + 2280/2401*T^31 + 
        1380/2401*T^30 + 816/2401*T^29 - 816/2401*T^27 - 1380/2401*T^26 - 
        2280/2401*T^25 - 1940/2401*T^24 - 1185/2401*T^23 - 549/2401*T^22 + 
        55/2401*T^21 + 1305/2401*T^20 + 1572/2401*T^19 + 899/2401*T^18 + 
        2098/2401*T^17 + 1366/2401*T^16 + 1629/2401*T^15 + 218/343*T^14 + 
        1586/2401*T^13 - 566/2401*T^12 - 468/2401*T^11 - 499/2401*T^10 - 
        901/2401*T^9 - 341/2401*T^8 + 789/2401*T^7 + 768/2401*T^6 + 568/2401*T^5 + 
        43/49*T^4 + 6/7*T^3 + 61/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + X*Y^13 + 3*X*Y^12 + 4*X*Y^10 + X*Y^9 + X*Y^8 + 
        6*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + X*Y + 6*X + 6*Y^30
        + 2*Y^29 + Y^28 + 4*Y^27 + 5*Y^26 + 4*Y^24 + 5*Y^22 + 6*Y^21 + 4*Y^20 + Y^19
        + Y^18 + Y^17 + 3*Y^16 + 4*Y^15 + Y^14 + 6*Y^13 + 6*Y^11 + Y^9 + 6*Y^8 + 
        4*Y^7 + 6*Y^5 + Y^4 + 3*Y^3 + 2*Y^2 + 5*Y + 4,
    -T^56 + 1/7*T^55 + 38/49*T^54 - 10/49*T^53 + 38/343*T^52 + 235/2401*T^51 + 
        29/343*T^50 - 387/2401*T^49 - 769/2401*T^48 - 69/2401*T^47 + 678/2401*T^46 +
        178/2401*T^45 - 53/343*T^44 - 1798/2401*T^43 + 106/2401*T^42 + 
        1343/2401*T^41 - 1121/2401*T^40 + 566/2401*T^39 + 109/2401*T^38 + 
        808/2401*T^37 + 733/2401*T^36 - 522/2401*T^35 + 128/2401*T^34 - 
        1049/2401*T^33 + 53/343*T^32 - 382/2401*T^31 - 1195/2401*T^30 + 
        1268/2401*T^29 - 1268/2401*T^27 + 1195/2401*T^26 + 382/2401*T^25 - 
        53/343*T^24 + 1049/2401*T^23 - 128/2401*T^22 + 522/2401*T^21 - 733/2401*T^20
        - 808/2401*T^19 - 109/2401*T^18 - 566/2401*T^17 + 1121/2401*T^16 - 
        1343/2401*T^15 - 106/2401*T^14 + 1798/2401*T^13 + 53/343*T^12 - 
        178/2401*T^11 - 678/2401*T^10 + 69/2401*T^9 + 769/2401*T^8 + 387/2401*T^7 - 
        29/343*T^6 - 235/2401*T^5 - 38/343*T^4 + 10/49*T^3 - 38/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + X*Y^13 + X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 
        4*X*Y^8 + X*Y^7 + X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 5*X*Y + 
        5*X + 4*Y^30 + 6*Y^29 + 6*Y^28 + 2*Y^27 + 5*Y^26 + 3*Y^25 + Y^23 + 3*Y^22 + 
        6*Y^21 + Y^20 + Y^18 + 2*Y^17 + 2*Y^16 + 3*Y^15 + 4*Y^14 + 6*Y^12 + Y^10 + 
        4*Y^9 + 5*Y^8 + Y^7 + Y^6 + 5*Y^5 + Y^4 + 3*Y^3 + Y + 3,
    -T^56 - 18/7*T^55 - 158/49*T^54 - 608/343*T^53 + 612/2401*T^52 + 4017/2401*T^51 
        + 2381/2401*T^50 - 2764/2401*T^49 - 6679/2401*T^48 - 3972/2401*T^47 + 
        2973/2401*T^46 + 9981/2401*T^45 + 11852/2401*T^44 + 7498/2401*T^43 + 
        715/2401*T^42 - 3081/2401*T^41 - 2066/2401*T^40 + 2633/2401*T^39 + 
        7025/2401*T^38 + 6170/2401*T^37 + 97/343*T^36 - 5455/2401*T^35 - 
        7991/2401*T^34 - 5742/2401*T^33 - 1349/2401*T^32 + 561/2401*T^31 + 
        647/2401*T^30 + 547/2401*T^29 - 547/2401*T^27 - 647/2401*T^26 - 
        561/2401*T^25 + 1349/2401*T^24 + 5742/2401*T^23 + 7991/2401*T^22 + 
        5455/2401*T^21 - 97/343*T^20 - 6170/2401*T^19 - 7025/2401*T^18 - 
        2633/2401*T^17 + 2066/2401*T^16 + 3081/2401*T^15 - 715/2401*T^14 - 
        7498/2401*T^13 - 11852/2401*T^12 - 9981/2401*T^11 - 2973/2401*T^10 + 
        3972/2401*T^9 + 6679/2401*T^8 + 2764/2401*T^7 - 2381/2401*T^6 - 
        4017/2401*T^5 - 612/2401*T^4 + 608/343*T^3 + 158/49*T^2 + 18/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + X*Y^10 + 2*X*Y^9 + 
        5*X*Y^8 + 5*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 2*X*Y 
        + X + Y^30 + 5*Y^29 + 6*Y^28 + 6*Y^26 + 2*Y^25 + 4*Y^24 + 4*Y^23 + 3*Y^22 + 
        5*Y^21 + Y^20 + 6*Y^19 + 5*Y^18 + 3*Y^17 + 6*Y^14 + 3*Y^13 + 5*Y^12 + 5*Y^11
        + 5*Y^10 + Y^9 + 2*Y^7 + 6*Y^5 + 3*Y^3 + 4*Y,
    T^56 - 3/49*T^54 + 32/343*T^53 - 794/2401*T^52 + 457/2401*T^51 - 72/2401*T^50 + 
        1016/2401*T^49 - 1698/2401*T^48 - 58/343*T^47 - 412/2401*T^46 - 
        457/2401*T^45 - 227/2401*T^44 - 55/343*T^43 - 22/343*T^42 - 6/49*T^41 + 
        19/49*T^40 - 47/343*T^39 + 796/2401*T^38 - 921/2401*T^37 + 219/343*T^36 - 
        548/2401*T^35 + 667/2401*T^34 + 289/2401*T^33 - 1185/2401*T^32 - 
        71/2401*T^31 - 478/2401*T^30 + 1153/2401*T^29 - 1777/2401*T^28 + 
        1153/2401*T^27 - 478/2401*T^26 - 71/2401*T^25 - 1185/2401*T^24 + 
        289/2401*T^23 + 667/2401*T^22 - 548/2401*T^21 + 219/343*T^20 - 921/2401*T^19
        + 796/2401*T^18 - 47/343*T^17 + 19/49*T^16 - 6/49*T^15 - 22/343*T^14 - 
        55/343*T^13 - 227/2401*T^12 - 457/2401*T^11 - 412/2401*T^10 - 58/343*T^9 - 
        1698/2401*T^8 + 1016/2401*T^7 - 72/2401*T^6 + 457/2401*T^5 - 794/2401*T^4 + 
        32/343*T^3 - 3/49*T^2 + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 2*X*Y^12 + 6*X*Y^10 + 4*X*Y^9 + 4*X*Y^8 + 5*X*Y^7 + 
        5*X*Y^6 + 4*X*Y^4 + 5*X*Y^3 + X*Y^2 + 3*X*Y + 4*Y^30 + 3*Y^29 + Y^28 + 
        4*Y^27 + 3*Y^26 + 5*Y^25 + 6*Y^23 + 3*Y^21 + 5*Y^20 + 5*Y^19 + 6*Y^18 + 
        4*Y^17 + Y^16 + 6*Y^15 + 6*Y^14 + 6*Y^13 + 4*Y^12 + 3*Y^11 + 3*Y^10 + 3*Y^9 
        + 6*Y^8 + 3*Y^7 + 6*Y^6 + 5*Y^5 + 2*Y^4 + 2*Y^3 + 5*Y^2 + 3,
    -T^56 - 1/7*T^55 + 30/49*T^54 - 115/343*T^53 - 2980/2401*T^52 + 445/2401*T^51 + 
        1713/2401*T^50 - 1069/2401*T^49 - 859/2401*T^48 + 151/343*T^47 - 
        1340/2401*T^46 - 563/2401*T^45 + 1233/2401*T^44 - 659/2401*T^43 - 
        2050/2401*T^42 + 369/2401*T^41 + 831/2401*T^40 - 108/343*T^39 + 
        195/2401*T^38 + 699/2401*T^37 - 886/2401*T^36 + 654/2401*T^35 + 
        1522/2401*T^34 - 1402/2401*T^33 - 1488/2401*T^32 + 1873/2401*T^31 + 
        89/343*T^30 - 60/49*T^29 + 60/49*T^27 - 89/343*T^26 - 1873/2401*T^25 + 
        1488/2401*T^24 + 1402/2401*T^23 - 1522/2401*T^22 - 654/2401*T^21 + 
        886/2401*T^20 - 699/2401*T^19 - 195/2401*T^18 + 108/343*T^17 - 831/2401*T^16
        - 369/2401*T^15 + 2050/2401*T^14 + 659/2401*T^13 - 1233/2401*T^12 + 
        563/2401*T^11 + 1340/2401*T^10 - 151/343*T^9 + 859/2401*T^8 + 1069/2401*T^7 
        - 1713/2401*T^6 - 445/2401*T^5 + 2980/2401*T^4 + 115/343*T^3 - 30/49*T^2 + 
        1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 6*X*Y^13 + X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 2*X*Y^8 + 
        4*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + X*Y^2 + 6*X*Y + 5*X + 
        5*Y^30 + 4*Y^29 + Y^28 + 5*Y^27 + 4*Y^26 + 5*Y^25 + 3*Y^24 + Y^23 + 2*Y^22 +
        4*Y^20 + 2*Y^19 + 6*Y^18 + 6*Y^17 + 5*Y^16 + 3*Y^15 + Y^14 + 3*Y^13 + 3*Y^11
        + Y^10 + 2*Y^9 + 3*Y^8 + 5*Y^7 + 6*Y^6 + 3*Y^5 + 6*Y^4 + 6*Y^3 + 6*Y,
    -T^56 - 4/7*T^55 + 55/49*T^54 + 330/343*T^53 - 2752/2401*T^52 - 3365/2401*T^51 +
        1627/2401*T^50 + 2490/2401*T^49 - 1749/2401*T^48 - 1901/2401*T^47 + 
        1665/2401*T^46 + 1203/2401*T^45 - 1378/2401*T^44 - 543/2401*T^43 + 
        256/2401*T^42 + 68/2401*T^41 + 3/49*T^40 + 97/2401*T^39 - 555/2401*T^38 - 
        771/2401*T^37 + 559/2401*T^36 + 316/2401*T^35 - 1340/2401*T^34 - 
        130/343*T^33 + 454/2401*T^32 + 379/2401*T^31 - 163/2401*T^30 - 309/2401*T^29
        + 309/2401*T^27 + 163/2401*T^26 - 379/2401*T^25 - 454/2401*T^24 + 
        130/343*T^23 + 1340/2401*T^22 - 316/2401*T^21 - 559/2401*T^20 + 
        771/2401*T^19 + 555/2401*T^18 - 97/2401*T^17 - 3/49*T^16 - 68/2401*T^15 - 
        256/2401*T^14 + 543/2401*T^13 + 1378/2401*T^12 - 1203/2401*T^11 - 
        1665/2401*T^10 + 1901/2401*T^9 + 1749/2401*T^8 - 2490/2401*T^7 - 
        1627/2401*T^6 + 3365/2401*T^5 + 2752/2401*T^4 - 330/343*T^3 - 55/49*T^2 + 
        4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + X*Y^8 + X*Y^7 + X*Y^6
        + 6*X*Y^5 + X*Y^4 + 5*X*Y^3 + X*Y^2 + X*Y + 4*X + 3*Y^30 + 4*Y^29 + 2*Y^28 +
        4*Y^27 + 2*Y^26 + 5*Y^25 + 5*Y^24 + 4*Y^23 + 5*Y^22 + 2*Y^21 + Y^19 + 6*Y^18
        + 4*Y^17 + 6*Y^16 + 4*Y^15 + 6*Y^14 + 3*Y^13 + 2*Y^12 + 6*Y^11 + Y^10 + 
        3*Y^9 + 3*Y^8 + 4*Y^7 + Y^6 + 6*Y^5 + Y^4 + 2*Y^3 + 2*Y^2 + 2*Y,
    T^56 - T^55 - 27/49*T^54 - 40/343*T^53 + 241/2401*T^52 + 2461/2401*T^51 + 
        104/2401*T^50 - 326/2401*T^49 - 1636/2401*T^48 - 422/2401*T^47 + 
        944/2401*T^46 + 323/2401*T^45 + 159/343*T^44 - 521/2401*T^43 + 230/2401*T^42
        - 244/343*T^41 - 156/343*T^40 + 1669/2401*T^39 + 429/2401*T^38 + 48/49*T^37 
        - 671/2401*T^36 - 2797/2401*T^35 - 1605/2401*T^34 + 885/2401*T^33 + 
        1301/2401*T^32 + 1460/2401*T^31 - 33/2401*T^30 - 758/2401*T^29 - 
        676/2401*T^28 - 758/2401*T^27 - 33/2401*T^26 + 1460/2401*T^25 + 
        1301/2401*T^24 + 885/2401*T^23 - 1605/2401*T^22 - 2797/2401*T^21 - 
        671/2401*T^20 + 48/49*T^19 + 429/2401*T^18 + 1669/2401*T^17 - 156/343*T^16 -
        244/343*T^15 + 230/2401*T^14 - 521/2401*T^13 + 159/343*T^12 + 323/2401*T^11 
        + 944/2401*T^10 - 422/2401*T^9 - 1636/2401*T^8 - 326/2401*T^7 + 104/2401*T^6
        + 2461/2401*T^5 + 241/2401*T^4 - 40/343*T^3 - 27/49*T^2 - T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + X*Y^13 + 2*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 + 
        5*X*Y^7 + 3*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 5*X*Y + X + 4*Y^30 + 
        5*Y^29 + Y^28 + 3*Y^27 + 4*Y^26 + 6*Y^25 + Y^24 + 4*Y^23 + Y^22 + 3*Y^21 + 
        6*Y^20 + 6*Y^19 + 4*Y^18 + 5*Y^17 + 5*Y^16 + 2*Y^15 + 2*Y^14 + 5*Y^13 + 
        2*Y^12 + 4*Y^11 + 5*Y^10 + 6*Y^8 + Y^7 + 5*Y^6 + 6*Y^5 + 2*Y^4 + 4*Y^3 + 
        6*Y^2 + Y,
    -T^56 - 6/7*T^55 - 45/49*T^54 - 206/343*T^53 - 1653/2401*T^52 - 1272/2401*T^51 -
        429/2401*T^50 + 370/2401*T^49 - 72/2401*T^48 + 65/2401*T^47 + 111/2401*T^46 
        + 1406/2401*T^45 + 1398/2401*T^44 + 604/2401*T^43 + 144/343*T^42 + 
        583/2401*T^41 + 2119/2401*T^40 + 222/343*T^39 + 1419/2401*T^38 + 
        1229/2401*T^37 + 1727/2401*T^36 + 921/2401*T^35 - 33/343*T^34 - 
        692/2401*T^33 + 206/2401*T^32 + 363/2401*T^31 + 253/2401*T^30 - 13/49*T^29 +
        13/49*T^27 - 253/2401*T^26 - 363/2401*T^25 - 206/2401*T^24 + 692/2401*T^23 +
        33/343*T^22 - 921/2401*T^21 - 1727/2401*T^20 - 1229/2401*T^19 - 
        1419/2401*T^18 - 222/343*T^17 - 2119/2401*T^16 - 583/2401*T^15 - 
        144/343*T^14 - 604/2401*T^13 - 1398/2401*T^12 - 1406/2401*T^11 - 
        111/2401*T^10 - 65/2401*T^9 + 72/2401*T^8 - 370/2401*T^7 + 429/2401*T^6 + 
        1272/2401*T^5 + 1653/2401*T^4 + 206/343*T^3 + 45/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + 5*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + X*Y^7 + 
        6*X*Y^6 + X*Y^5 + 4*X*Y^4 + X*Y^2 + 3*X*Y + 6*X + 2*Y^30 + 6*Y^29 + 6*Y^28 +
        6*Y^27 + 3*Y^26 + 2*Y^24 + 4*Y^23 + 5*Y^21 + Y^20 + Y^19 + 5*Y^18 + 6*Y^17 +
        4*Y^16 + 2*Y^15 + Y^14 + 6*Y^13 + 2*Y^11 + 3*Y^9 + Y^8 + 6*Y^7 + 5*Y^6 + 
        5*Y^5 + 5*Y^4 + 4*Y^2 + 1,
    -T^56 + 8/7*T^55 + 61/49*T^54 - 870/343*T^53 - 486/2401*T^52 + 8661/2401*T^51 - 
        4244/2401*T^50 - 8970/2401*T^49 + 10635/2401*T^48 + 5070/2401*T^47 - 
        15410/2401*T^46 + 2122/2401*T^45 + 2312/343*T^44 - 1507/343*T^43 - 
        10777/2401*T^42 + 17119/2401*T^41 + 221/343*T^40 - 19134/2401*T^39 + 
        8520/2401*T^38 + 14401/2401*T^37 - 16251/2401*T^36 - 5503/2401*T^35 + 
        19399/2401*T^34 - 4572/2401*T^33 - 17944/2401*T^32 + 14568/2401*T^31 + 
        10282/2401*T^30 - 20247/2401*T^29 + 20247/2401*T^27 - 10282/2401*T^26 - 
        14568/2401*T^25 + 17944/2401*T^24 + 4572/2401*T^23 - 19399/2401*T^22 + 
        5503/2401*T^21 + 16251/2401*T^20 - 14401/2401*T^19 - 8520/2401*T^18 + 
        19134/2401*T^17 - 221/343*T^16 - 17119/2401*T^15 + 10777/2401*T^14 + 
        1507/343*T^13 - 2312/343*T^12 - 2122/2401*T^11 + 15410/2401*T^10 - 
        5070/2401*T^9 - 10635/2401*T^8 + 8970/2401*T^7 + 4244/2401*T^6 - 
        8661/2401*T^5 + 486/2401*T^4 + 870/343*T^3 - 61/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 
        2*X*Y^8 + 3*X*Y^7 + X*Y^6 + 4*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 6*X*Y + 6*X + 
        3*Y^30 + 4*Y^29 + Y^28 + 2*Y^27 + 5*Y^26 + 2*Y^25 + 3*Y^24 + 6*Y^23 + Y^22 +
        3*Y^21 + 6*Y^20 + 2*Y^18 + 4*Y^17 + 5*Y^16 + 2*Y^15 + 3*Y^14 + Y^12 + 5*Y^10
        + 3*Y^9 + 2*Y^8 + 3*Y^7 + Y^6 + 6*Y^4 + 6*Y^3 + 6*Y^2 + 5,
    T^56 - T^55 + 54/49*T^54 - 281/343*T^53 - 898/2401*T^52 + 2123/2401*T^51 - 
        435/343*T^50 + 3007/2401*T^49 - 639/2401*T^48 - 1082/2401*T^47 + 
        417/343*T^46 - 4232/2401*T^45 + 2465/2401*T^44 - 99/343*T^43 - 
        2682/2401*T^42 + 3772/2401*T^41 - 4415/2401*T^40 + 3079/2401*T^39 - 
        354/2401*T^38 - 1706/2401*T^37 + 2417/2401*T^36 - 2038/2401*T^35 + 
        99/343*T^34 + 647/2401*T^33 - 1401/2401*T^32 + 5/7*T^31 - 24/343*T^30 - 
        124/2401*T^29 + 109/343*T^28 - 124/2401*T^27 - 24/343*T^26 + 5/7*T^25 - 
        1401/2401*T^24 + 647/2401*T^23 + 99/343*T^22 - 2038/2401*T^21 + 
        2417/2401*T^20 - 1706/2401*T^19 - 354/2401*T^18 + 3079/2401*T^17 - 
        4415/2401*T^16 + 3772/2401*T^15 - 2682/2401*T^14 - 99/343*T^13 + 
        2465/2401*T^12 - 4232/2401*T^11 + 417/343*T^10 - 1082/2401*T^9 - 
        639/2401*T^8 + 3007/2401*T^7 - 435/343*T^6 + 2123/2401*T^5 - 898/2401*T^4 - 
        281/343*T^3 + 54/49*T^2 - T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + X*Y^7 + 
        3*X*Y^6 + 6*X*Y^5 + X*Y^4 + X*Y^2 + Y^30 + 4*Y^29 + 5*Y^28 + 2*Y^27 + 6*Y^26
        + Y^25 + 3*Y^24 + 4*Y^22 + 3*Y^21 + 5*Y^19 + 4*Y^18 + 5*Y^17 + Y^16 + 3*Y^15
        + 3*Y^14 + 4*Y^13 + Y^11 + 6*Y^10 + Y^9 + 4*Y^8 + 2*Y^7 + 4*Y^6 + 5*Y^5 + 
        4*Y^4 + 4*Y^3 + 3*Y^2 + 5*Y + 1,
    -T^56 + 12/7*T^55 - 16/49*T^54 - 436/343*T^53 + 2621/2401*T^52 + 314/2401*T^51 -
        345/2401*T^50 - 1158/2401*T^49 + 589/2401*T^48 + 374/2401*T^47 - 
        104/343*T^46 - 428/2401*T^45 + 32/49*T^44 + 272/2401*T^43 - 2397/2401*T^42 +
        187/343*T^41 + 282/343*T^40 - 1835/2401*T^39 - 298/343*T^38 + 2342/2401*T^37
        + 901/2401*T^36 - 1010/2401*T^35 - 1153/2401*T^34 + 587/2401*T^33 + 
        297/343*T^32 - 158/343*T^31 - 2767/2401*T^30 + 3285/2401*T^29 - 
        3285/2401*T^27 + 2767/2401*T^26 + 158/343*T^25 - 297/343*T^24 - 
        587/2401*T^23 + 1153/2401*T^22 + 1010/2401*T^21 - 901/2401*T^20 - 
        2342/2401*T^19 + 298/343*T^18 + 1835/2401*T^17 - 282/343*T^16 - 187/343*T^15
        + 2397/2401*T^14 - 272/2401*T^13 - 32/49*T^12 + 428/2401*T^11 + 104/343*T^10
        - 374/2401*T^9 - 589/2401*T^8 + 1158/2401*T^7 + 345/2401*T^6 - 314/2401*T^5 
        - 2621/2401*T^4 + 436/343*T^3 + 16/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 4*X*Y^9 
        + 5*X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + X*Y^3 + 2*X*Y^2 + 3*X*Y 
        + 4*X + 4*Y^30 + 2*Y^29 + 3*Y^28 + 5*Y^27 + 5*Y^26 + 2*Y^25 + 3*Y^24 + 
        3*Y^23 + 2*Y^22 + 4*Y^21 + Y^20 + Y^19 + 6*Y^18 + Y^17 + 3*Y^16 + 3*Y^12 + 
        3*Y^11 + 5*Y^10 + 6*Y^9 + 3*Y^8 + Y^7 + 3*Y^6 + Y^5 + 6*Y^4 + Y^3 + 6*Y^2 + 
        3*Y + 3,
    T^56 - 3/7*T^55 - 39/49*T^54 + 176/343*T^53 - 681/2401*T^52 + 458/2401*T^51 + 
        464/2401*T^50 - 3314/2401*T^49 + 1763/2401*T^48 + 68/49*T^47 - 
        2754/2401*T^46 - 1297/2401*T^45 + 963/2401*T^44 + 1326/2401*T^43 + 
        578/2401*T^42 - 1292/2401*T^41 - 2277/2401*T^40 + 2374/2401*T^39 + 
        2522/2401*T^38 - 3158/2401*T^37 - 2684/2401*T^36 + 2407/2401*T^35 + 
        1199/2401*T^34 - 779/2401*T^33 - 491/2401*T^32 - 905/2401*T^31 + 
        3032/2401*T^30 + 597/2401*T^29 - 584/343*T^28 + 597/2401*T^27 + 
        3032/2401*T^26 - 905/2401*T^25 - 491/2401*T^24 - 779/2401*T^23 + 
        1199/2401*T^22 + 2407/2401*T^21 - 2684/2401*T^20 - 3158/2401*T^19 + 
        2522/2401*T^18 + 2374/2401*T^17 - 2277/2401*T^16 - 1292/2401*T^15 + 
        578/2401*T^14 + 1326/2401*T^13 + 963/2401*T^12 - 1297/2401*T^11 - 
        2754/2401*T^10 + 68/49*T^9 + 1763/2401*T^8 - 3314/2401*T^7 + 464/2401*T^6 + 
        458/2401*T^5 - 681/2401*T^4 + 176/343*T^3 - 39/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^13 + X*Y^12 + 6*X*Y^11 + 4*X*Y^8 + 4*X*Y^7 + 6*X*Y^6 + 
        X*Y^5 + X*Y^3 + 5*X*Y^2 + 4*X*Y + 6*X + 4*Y^30 + 6*Y^29 + 3*Y^26 + 4*Y^25 + 
        3*Y^24 + 2*Y^22 + 2*Y^21 + 4*Y^20 + 3*Y^19 + 3*Y^18 + 6*Y^17 + 6*Y^16 + 
        4*Y^15 + 2*Y^14 + 3*Y^13 + Y^12 + 6*Y^11 + 2*Y^10 + 5*Y^8 + 4*Y^7 + Y^6 + 
        Y^5 + 6*Y^4 + 5*Y^3 + 6*Y^2 + 3*Y + 2,
    T^56 + 4/7*T^55 - 36/49*T^54 - 242/343*T^53 + 505/2401*T^52 + 461/2401*T^51 - 
        744/2401*T^50 - 558/2401*T^49 - 1132/2401*T^48 - 1068/2401*T^47 + 
        2295/2401*T^46 + 419/343*T^45 - 1430/2401*T^44 - 3411/2401*T^43 + 
        1187/2401*T^42 + 3005/2401*T^41 - 152/2401*T^40 - 1461/2401*T^39 - 
        1209/2401*T^38 - 1081/2401*T^37 + 1632/2401*T^36 + 507/343*T^35 - 
        1644/2401*T^34 - 4436/2401*T^33 - 53/343*T^32 + 3320/2401*T^31 + 
        1339/2401*T^30 - 867/2401*T^29 - 114/343*T^28 - 867/2401*T^27 + 
        1339/2401*T^26 + 3320/2401*T^25 - 53/343*T^24 - 4436/2401*T^23 - 
        1644/2401*T^22 + 507/343*T^21 + 1632/2401*T^20 - 1081/2401*T^19 - 
        1209/2401*T^18 - 1461/2401*T^17 - 152/2401*T^16 + 3005/2401*T^15 + 
        1187/2401*T^14 - 3411/2401*T^13 - 1430/2401*T^12 + 419/343*T^11 + 
        2295/2401*T^10 - 1068/2401*T^9 - 1132/2401*T^8 - 558/2401*T^7 - 744/2401*T^6
        + 461/2401*T^5 + 505/2401*T^4 - 242/343*T^3 - 36/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 3*X*Y^13 + 2*X*Y^11 + 5*X*Y^10 + X*Y^9 + X*Y^8 + X*Y^7
        + 6*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 6*X*Y + 6*X + 2*Y^30 + 2*Y^28 + 
        5*Y^27 + 6*Y^26 + 5*Y^25 + 5*Y^24 + 6*Y^23 + 2*Y^22 + 2*Y^21 + 4*Y^20 + 
        6*Y^19 + 5*Y^18 + 4*Y^16 + Y^15 + 2*Y^14 + 4*Y^13 + 3*Y^12 + 3*Y^11 + 3*Y^10
        + Y^8 + Y^7 + 6*Y^6 + 2*Y^5 + 2*Y^3 + 3*Y^2 + 3*Y + 2,
    -T^56 - 6/7*T^55 + 24/49*T^54 + 549/343*T^53 + 3063/2401*T^52 - 752/2401*T^51 - 
        4609/2401*T^50 - 3649/2401*T^49 + 95/343*T^48 + 4399/2401*T^47 + 
        4850/2401*T^46 + 1291/2401*T^45 - 4437/2401*T^44 - 5765/2401*T^43 - 
        52/49*T^42 + 3396/2401*T^41 + 835/343*T^40 + 3247/2401*T^39 - 2564/2401*T^38
        - 4649/2401*T^37 - 2088/2401*T^36 + 906/2401*T^35 + 2664/2401*T^34 + 
        2494/2401*T^33 + 61/2401*T^32 - 1222/2401*T^31 - 1711/2401*T^30 - 
        305/343*T^29 + 305/343*T^27 + 1711/2401*T^26 + 1222/2401*T^25 - 61/2401*T^24
        - 2494/2401*T^23 - 2664/2401*T^22 - 906/2401*T^21 + 2088/2401*T^20 + 
        4649/2401*T^19 + 2564/2401*T^18 - 3247/2401*T^17 - 835/343*T^16 - 
        3396/2401*T^15 + 52/49*T^14 + 5765/2401*T^13 + 4437/2401*T^12 - 
        1291/2401*T^11 - 4850/2401*T^10 - 4399/2401*T^9 - 95/343*T^8 + 3649/2401*T^7
        + 4609/2401*T^6 + 752/2401*T^5 - 3063/2401*T^4 - 549/343*T^3 - 24/49*T^2 + 
        6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 
        + 6*X*Y^8 + 2*X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 
        3*X*Y + 5*X + 4*Y^30 + 3*Y^28 + 3*Y^27 + Y^26 + 3*Y^25 + 6*Y^24 + Y^23 + 
        2*Y^22 + 2*Y^21 + 3*Y^20 + 4*Y^19 + 6*Y^17 + 5*Y^16 + 4*Y^14 + 4*Y^13 + 
        3*Y^12 + 6*Y^11 + 2*Y^10 + Y^9 + 5*Y^8 + 5*Y^7 + 2*Y^6 + 6*Y^5 + 5*Y^4 + 
        3*Y^3 + 3*Y^2 + 4*Y + 3,
    -T^56 - 2/7*T^55 + 1/7*T^54 + 143/343*T^53 + 1615/2401*T^52 + 975/2401*T^51 + 
        44/343*T^50 - 1366/2401*T^49 - 173/2401*T^48 - 324/2401*T^47 - 220/2401*T^46
        + 1072/2401*T^45 + 128/343*T^44 + 1033/2401*T^43 - 381/2401*T^42 - 
        109/343*T^41 - 1380/2401*T^40 - 1683/2401*T^39 - 24/343*T^38 + 165/2401*T^37
        + 449/2401*T^36 + 664/2401*T^35 + 878/2401*T^34 + 506/2401*T^33 - 
        1361/2401*T^32 + 82/343*T^31 - 389/2401*T^30 - 408/2401*T^29 + 408/2401*T^27
        + 389/2401*T^26 - 82/343*T^25 + 1361/2401*T^24 - 506/2401*T^23 - 
        878/2401*T^22 - 664/2401*T^21 - 449/2401*T^20 - 165/2401*T^19 + 24/343*T^18 
        + 1683/2401*T^17 + 1380/2401*T^16 + 109/343*T^15 + 381/2401*T^14 - 
        1033/2401*T^13 - 128/343*T^12 - 1072/2401*T^11 + 220/2401*T^10 + 
        324/2401*T^9 + 173/2401*T^8 + 1366/2401*T^7 - 44/343*T^6 - 975/2401*T^5 - 
        1615/2401*T^4 - 143/343*T^3 - 1/7*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 
        + 3*X*Y^8 + X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + X*Y^3 + 2*X*Y^2 + 4*X*Y + 
        2*X + 2*Y^30 + 2*Y^29 + 2*Y^26 + 2*Y^25 + 6*Y^24 + 2*Y^23 + 5*Y^22 + 2*Y^21 
        + 4*Y^19 + 5*Y^18 + Y^16 + 2*Y^15 + 5*Y^14 + 6*Y^13 + 2*Y^12 + 3*Y^11 + 
        2*Y^10 + 3*Y^8 + 6*Y^7 + Y^6 + Y^5 + 4*Y^4 + 2*Y^3 + 2*Y^2 + 6*Y,
    -T^56 + T^55 + 5/49*T^54 - 109/343*T^53 + 1380/2401*T^52 - 407/343*T^51 - 
        269/2401*T^50 + 3195/2401*T^49 - 732/2401*T^48 - 241/2401*T^47 + 
        1040/2401*T^46 - 2413/2401*T^45 + 109/2401*T^44 + 2266/2401*T^43 - 6/7*T^42 
        + 1508/2401*T^41 + 366/2401*T^40 - 1991/2401*T^39 + 547/2401*T^38 - 
        3/49*T^37 - 869/2401*T^36 + 1640/2401*T^35 + 145/343*T^34 - 1856/2401*T^33 +
        262/2401*T^32 - 734/2401*T^31 + 111/2401*T^30 + 2253/2401*T^29 - 
        2253/2401*T^27 - 111/2401*T^26 + 734/2401*T^25 - 262/2401*T^24 + 
        1856/2401*T^23 - 145/343*T^22 - 1640/2401*T^21 + 869/2401*T^20 + 3/49*T^19 -
        547/2401*T^18 + 1991/2401*T^17 - 366/2401*T^16 - 1508/2401*T^15 + 6/7*T^14 -
        2266/2401*T^13 - 109/2401*T^12 + 2413/2401*T^11 - 1040/2401*T^10 + 
        241/2401*T^9 + 732/2401*T^8 - 3195/2401*T^7 + 269/2401*T^6 + 407/343*T^5 - 
        1380/2401*T^4 + 109/343*T^3 - 5/49*T^2 - T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 2*X*Y^9 
        + 5*X*Y^8 + 2*X*Y^7 + X*Y^6 + 4*X*Y^5 + 6*X*Y^3 + 6*X*Y + 6*X + 3*Y^30 + 
        6*Y^29 + Y^28 + 5*Y^27 + 6*Y^26 + 3*Y^24 + 2*Y^23 + 6*Y^21 + 6*Y^20 + 3*Y^19
        + 5*Y^18 + 4*Y^17 + Y^16 + 3*Y^15 + 3*Y^14 + 4*Y^13 + 5*Y^12 + 4*Y^11 + 
        2*Y^10 + Y^9 + 2*Y^8 + Y^6 + 2*Y^5 + 5*Y^4 + 2*Y^2 + 5*Y + 2,
    T^56 - 2*T^55 + 82/49*T^54 - 215/343*T^53 + 262/2401*T^52 + 907/2401*T^51 - 
        1737/2401*T^50 + 2721/2401*T^49 - 96/49*T^48 + 5442/2401*T^47 - 
        4692/2401*T^46 + 3361/2401*T^45 - 1976/2401*T^44 - 605/2401*T^43 + 
        1809/2401*T^42 - 2403/2401*T^41 + 2740/2401*T^40 - 3524/2401*T^39 + 
        2719/2401*T^38 - 1735/2401*T^37 + 1104/2401*T^36 - 1093/2401*T^35 + 
        1335/2401*T^34 - 970/2401*T^33 - 13/2401*T^32 + 1496/2401*T^31 - 
        250/343*T^30 + 1782/2401*T^29 - 1167/2401*T^28 + 1782/2401*T^27 - 
        250/343*T^26 + 1496/2401*T^25 - 13/2401*T^24 - 970/2401*T^23 + 
        1335/2401*T^22 - 1093/2401*T^21 + 1104/2401*T^20 - 1735/2401*T^19 + 
        2719/2401*T^18 - 3524/2401*T^17 + 2740/2401*T^16 - 2403/2401*T^15 + 
        1809/2401*T^14 - 605/2401*T^13 - 1976/2401*T^12 + 3361/2401*T^11 - 
        4692/2401*T^10 + 5442/2401*T^9 - 96/49*T^8 + 2721/2401*T^7 - 1737/2401*T^6 +
        907/2401*T^5 + 262/2401*T^4 - 215/343*T^3 + 82/49*T^2 - 2*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 
        5*X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + 5*X*Y^4 + 2*X*Y^3 + 2*X*Y + 3*X + Y^30 + 
        4*Y^29 + 3*Y^28 + 5*Y^27 + 2*Y^26 + 2*Y^25 + Y^24 + 5*Y^23 + 6*Y^22 + 2*Y^21
        + 5*Y^20 + 4*Y^19 + 2*Y^18 + 5*Y^17 + 6*Y^16 + 5*Y^15 + 5*Y^14 + 2*Y^13 + 
        Y^11 + Y^9 + 5*Y^8 + 3*Y^7 + 6*Y^6 + 2*Y^5 + 5*Y^4 + 6*Y^3 + 6*Y^2 + 2*Y + 
        2,
    -T^56 + 6/7*T^55 + 22/49*T^54 - 201/343*T^53 + 906/2401*T^52 - 1844/2401*T^51 + 
        498/343*T^50 - 2005/2401*T^49 - 25/343*T^48 + 1989/2401*T^47 - 
        3481/2401*T^46 + 2904/2401*T^45 - 1513/2401*T^44 + 1077/2401*T^43 - 
        122/2401*T^42 - 533/343*T^41 + 681/343*T^40 - 2064/2401*T^39 - 592/2401*T^38
        + 2861/2401*T^37 - 4264/2401*T^36 + 3763/2401*T^35 - 5/7*T^34 - 5/343*T^33 +
        3202/2401*T^32 - 6332/2401*T^31 + 5239/2401*T^30 - 1860/2401*T^29 + 
        1860/2401*T^27 - 5239/2401*T^26 + 6332/2401*T^25 - 3202/2401*T^24 + 
        5/343*T^23 + 5/7*T^22 - 3763/2401*T^21 + 4264/2401*T^20 - 2861/2401*T^19 + 
        592/2401*T^18 + 2064/2401*T^17 - 681/343*T^16 + 533/343*T^15 + 122/2401*T^14
        - 1077/2401*T^13 + 1513/2401*T^12 - 2904/2401*T^11 + 3481/2401*T^10 - 
        1989/2401*T^9 + 25/343*T^8 + 2005/2401*T^7 - 498/343*T^6 + 1844/2401*T^5 - 
        906/2401*T^4 + 201/343*T^3 - 22/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + X*Y^10 + 4*X*Y^9 + 5*X*Y^8 + X*Y^6 + 
        5*X*Y^4 + X*Y^3 + 5*X*Y^2 + 6*X*Y + 5*Y^30 + 2*Y^29 + 6*Y^28 + 2*Y^26 + 
        6*Y^25 + 2*Y^24 + 5*Y^23 + 6*Y^21 + 4*Y^20 + 4*Y^19 + 3*Y^18 + Y^17 + 6*Y^16
        + Y^15 + 5*Y^14 + Y^13 + Y^12 + 5*Y^11 + 2*Y^10 + Y^9 + 5*Y^8 + 5*Y^7 + Y^6 
        + 6*Y^5 + 4*Y^4 + Y^3 + 5*Y^2 + Y + 1,
    -T^56 + T^55 - 4/7*T^54 + 195/343*T^53 - 1292/2401*T^52 + 355/2401*T^51 + 
        82/343*T^50 - 779/2401*T^49 + 223/343*T^48 - 1951/2401*T^47 + 1726/2401*T^46
        - 1177/2401*T^45 + 565/2401*T^44 - 479/2401*T^43 + 138/2401*T^42 + 
        711/2401*T^41 - 1885/2401*T^40 + 1620/2401*T^39 - 1458/2401*T^38 + 
        519/2401*T^37 - 23/343*T^36 - 114/2401*T^35 + 1408/2401*T^34 - 
        1874/2401*T^33 + 2189/2401*T^32 - 2168/2401*T^31 + 1462/2401*T^30 - 
        414/2401*T^29 + 414/2401*T^27 - 1462/2401*T^26 + 2168/2401*T^25 - 
        2189/2401*T^24 + 1874/2401*T^23 - 1408/2401*T^22 + 114/2401*T^21 + 
        23/343*T^20 - 519/2401*T^19 + 1458/2401*T^18 - 1620/2401*T^17 + 
        1885/2401*T^16 - 711/2401*T^15 - 138/2401*T^14 + 479/2401*T^13 - 
        565/2401*T^12 + 1177/2401*T^11 - 1726/2401*T^10 + 1951/2401*T^9 - 
        223/343*T^8 + 779/2401*T^7 - 82/343*T^6 - 355/2401*T^5 + 1292/2401*T^4 - 
        195/343*T^3 + 4/7*T^2 - T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 2*X*Y^7 + 4*X*Y^6 +
        X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 2*X*Y + 6*X + 6*Y^30 + 5*Y^29 + 3*Y^28 + Y^27 + 
        2*Y^26 + 2*Y^25 + 5*Y^24 + 6*Y^23 + 4*Y^22 + 6*Y^21 + 5*Y^20 + 2*Y^19 + Y^18
        + 4*Y^17 + 5*Y^16 + 6*Y^15 + 2*Y^14 + Y^13 + 6*Y^12 + Y^11 + 3*Y^10 + 6*Y^9 
        + 6*Y^8 + 3*Y^6 + 2*Y^5 + 3*Y^4 + 5*Y^3 + 3*Y^2 + Y + 2,
    T^56 + 4/7*T^55 + 22/49*T^54 - 155/343*T^53 + 27/2401*T^52 - 87/343*T^51 - 
        276/2401*T^50 + 382/2401*T^49 + 373/2401*T^48 - 291/343*T^47 - 
        3044/2401*T^46 - 1632/2401*T^45 + 593/2401*T^44 + 456/2401*T^43 - 
        38/343*T^42 - 489/2401*T^41 - 1521/2401*T^40 - 1/7*T^39 + 710/2401*T^38 + 
        2871/2401*T^37 + 1516/2401*T^36 + 29/343*T^35 - 1137/2401*T^34 + 
        36/2401*T^33 + 134/343*T^32 + 1732/2401*T^31 - 151/2401*T^30 - 857/2401*T^29
        - 2158/2401*T^28 - 857/2401*T^27 - 151/2401*T^26 + 1732/2401*T^25 + 
        134/343*T^24 + 36/2401*T^23 - 1137/2401*T^22 + 29/343*T^21 + 1516/2401*T^20 
        + 2871/2401*T^19 + 710/2401*T^18 - 1/7*T^17 - 1521/2401*T^16 - 489/2401*T^15
        - 38/343*T^14 + 456/2401*T^13 + 593/2401*T^12 - 1632/2401*T^11 - 
        3044/2401*T^10 - 291/343*T^9 + 373/2401*T^8 + 382/2401*T^7 - 276/2401*T^6 - 
        87/343*T^5 + 27/2401*T^4 - 155/343*T^3 + 22/49*T^2 + 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 2*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + X*Y^8 + 
        4*X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + X*Y^3 + 4*X*Y + 4*X + 5*Y^30 + 
        4*Y^29 + 2*Y^27 + Y^26 + 6*Y^25 + Y^24 + 5*Y^23 + 2*Y^22 + 4*Y^20 + 2*Y^19 +
        6*Y^18 + 3*Y^17 + 2*Y^15 + 2*Y^14 + 4*Y^13 + 4*Y^9 + 5*Y^7 + 2*Y^6 + 5*Y^5 +
        2*Y^4 + Y^3 + 4*Y^2 + Y + 4,
    -T^56 - 1/7*T^55 + 6/7*T^54 + 65/343*T^53 - 41/2401*T^52 + 1095/2401*T^51 - 
        1766/2401*T^50 - 1945/2401*T^49 + 1084/2401*T^48 + 155/343*T^47 + 
        102/2401*T^46 + 1025/2401*T^45 - 149/2401*T^44 - 1734/2401*T^43 - 
        867/2401*T^42 + 46/343*T^41 - 25/2401*T^40 - 466/2401*T^39 + 709/2401*T^38 +
        1339/2401*T^37 + 803/2401*T^36 + 328/2401*T^35 - 111/343*T^34 - 
        2615/2401*T^33 - 1129/2401*T^32 + 171/343*T^31 + 2102/2401*T^30 + 
        1977/2401*T^29 - 1977/2401*T^27 - 2102/2401*T^26 - 171/343*T^25 + 
        1129/2401*T^24 + 2615/2401*T^23 + 111/343*T^22 - 328/2401*T^21 - 
        803/2401*T^20 - 1339/2401*T^19 - 709/2401*T^18 + 466/2401*T^17 + 
        25/2401*T^16 - 46/343*T^15 + 867/2401*T^14 + 1734/2401*T^13 + 149/2401*T^12 
        - 1025/2401*T^11 - 102/2401*T^10 - 155/343*T^9 - 1084/2401*T^8 + 
        1945/2401*T^7 + 1766/2401*T^6 - 1095/2401*T^5 + 41/2401*T^4 - 65/343*T^3 - 
        6/7*T^2 + 1/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 5*X*Y^9 + 2*X*Y^8 + 3*X*Y^7 + 
        3*X*Y^6 + X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + X*Y + 3*X + 4*Y^30 + 3*Y^29 
        + 4*Y^28 + 6*Y^27 + 5*Y^25 + 4*Y^24 + 2*Y^23 + 3*Y^22 + 3*Y^21 + 4*Y^20 + 
        3*Y^18 + 3*Y^17 + Y^16 + 6*Y^15 + Y^13 + 5*Y^12 + 6*Y^11 + 6*Y^10 + 4*Y^9 + 
        5*Y^8 + 5*Y^7 + 2*Y^6 + 6*Y^5 + 6*Y^4 + 4*Y^3 + 4*Y^2 + Y + 2,
    T^56 + T^55 + 25/49*T^54 + 29/49*T^53 - 232/343*T^52 - 40/343*T^51 + 
        1153/2401*T^50 - 57/343*T^49 + 2570/2401*T^48 + 747/2401*T^47 - 
        1264/2401*T^46 + 228/2401*T^45 - 2187/2401*T^44 - 253/2401*T^43 + 
        1177/2401*T^42 - 1412/2401*T^41 + 673/2401*T^40 - 17/343*T^39 - 
        1098/2401*T^38 + 1340/2401*T^37 + 398/2401*T^36 + 1993/2401*T^35 + 
        2175/2401*T^34 - 451/2401*T^33 - 16/2401*T^32 - 779/2401*T^31 + 
        538/2401*T^30 + 2448/2401*T^29 + 1544/2401*T^28 + 2448/2401*T^27 + 
        538/2401*T^26 - 779/2401*T^25 - 16/2401*T^24 - 451/2401*T^23 + 
        2175/2401*T^22 + 1993/2401*T^21 + 398/2401*T^20 + 1340/2401*T^19 - 
        1098/2401*T^18 - 17/343*T^17 + 673/2401*T^16 - 1412/2401*T^15 + 
        1177/2401*T^14 - 253/2401*T^13 - 2187/2401*T^12 + 228/2401*T^11 - 
        1264/2401*T^10 + 747/2401*T^9 + 2570/2401*T^8 - 57/343*T^7 + 1153/2401*T^6 -
        40/343*T^5 - 232/343*T^4 + 29/49*T^3 + 25/49*T^2 + T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + X*Y^12 + X*Y^11 + X*Y^10 + 6*X*Y^9 + 
        6*X*Y^8 + X*Y^7 + 2*X*Y^6 + X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 4*X*Y + 
        6*X + 5*Y^30 + 2*Y^29 + 4*Y^28 + 4*Y^27 + 6*Y^25 + Y^23 + Y^22 + 3*Y^21 + 
        2*Y^20 + 6*Y^18 + 2*Y^17 + 6*Y^16 + 4*Y^15 + Y^14 + 6*Y^12 + 3*Y^11 + 6*Y^10
        + 5*Y^9 + 4*Y^8 + 4*Y^7 + 4*Y^6 + 3*Y^5 + 4*Y^4 + Y^3 + 3*Y + 4,
    T^56 - 6/7*T^55 + 36/49*T^54 - 106/343*T^53 - 194/2401*T^52 + 467/2401*T^51 - 
        1333/2401*T^50 + 90/343*T^49 - 2036/2401*T^48 + 1896/2401*T^47 - 
        1564/2401*T^46 + 576/2401*T^45 + 162/2401*T^44 + 349/2401*T^43 + 
        949/2401*T^42 - 302/2401*T^41 + 1293/2401*T^40 - 1160/2401*T^39 + 
        985/2401*T^38 - 209/343*T^37 + 120/2401*T^36 + 79/2401*T^35 - 2024/2401*T^34
        + 1235/2401*T^33 - 1093/2401*T^32 + 262/2401*T^31 + 837/2401*T^30 - 
        12/343*T^29 + 772/2401*T^28 - 12/343*T^27 + 837/2401*T^26 + 262/2401*T^25 - 
        1093/2401*T^24 + 1235/2401*T^23 - 2024/2401*T^22 + 79/2401*T^21 + 
        120/2401*T^20 - 209/343*T^19 + 985/2401*T^18 - 1160/2401*T^17 + 
        1293/2401*T^16 - 302/2401*T^15 + 949/2401*T^14 + 349/2401*T^13 + 
        162/2401*T^12 + 576/2401*T^11 - 1564/2401*T^10 + 1896/2401*T^9 - 
        2036/2401*T^8 + 90/343*T^7 - 1333/2401*T^6 + 467/2401*T^5 - 194/2401*T^4 - 
        106/343*T^3 + 36/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 2*X*Y^10 + 2*X*Y^9 + 3*X*Y^7 +
        5*X*Y^6 + 5*X*Y^5 + 3*X*Y^3 + X*Y^2 + 2*X + 5*Y^30 + 5*Y^29 + 6*Y^28 + 
        6*Y^27 + 6*Y^26 + Y^25 + 6*Y^23 + Y^22 + 2*Y^21 + 6*Y^20 + 3*Y^19 + Y^18 + 
        2*Y^17 + 6*Y^16 + Y^15 + Y^14 + 5*Y^13 + 4*Y^12 + 2*Y^11 + 2*Y^10 + 6*Y^9 + 
        2*Y^8 + 2*Y^6 + 5*Y^5 + 5*Y^4 + 2*Y^3 + 5*Y + 3,
    -T^56 - 2*T^55 - 85/49*T^54 - 415/343*T^53 - 382/343*T^52 - 2416/2401*T^51 - 
        3411/2401*T^50 - 5881/2401*T^49 - 7502/2401*T^48 - 6292/2401*T^47 - 
        3469/2401*T^46 - 1174/2401*T^45 - 699/2401*T^44 - 3/7*T^43 - 258/2401*T^42 +
        76/343*T^41 + 1056/2401*T^40 + 2586/2401*T^39 + 4063/2401*T^38 + 
        5183/2401*T^37 + 6494/2401*T^36 + 6869/2401*T^35 + 5825/2401*T^34 + 
        3627/2401*T^33 + 2922/2401*T^32 + 3880/2401*T^31 + 3802/2401*T^30 + 
        1977/2401*T^29 - 1977/2401*T^27 - 3802/2401*T^26 - 3880/2401*T^25 - 
        2922/2401*T^24 - 3627/2401*T^23 - 5825/2401*T^22 - 6869/2401*T^21 - 
        6494/2401*T^20 - 5183/2401*T^19 - 4063/2401*T^18 - 2586/2401*T^17 - 
        1056/2401*T^16 - 76/343*T^15 + 258/2401*T^14 + 3/7*T^13 + 699/2401*T^12 + 
        1174/2401*T^11 + 3469/2401*T^10 + 6292/2401*T^9 + 7502/2401*T^8 + 
        5881/2401*T^7 + 3411/2401*T^6 + 2416/2401*T^5 + 382/343*T^4 + 415/343*T^3 + 
        85/49*T^2 + 2*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 4*X*Y^8 + 
        5*X*Y^7 + 5*X*Y^6 + X*Y^5 + 5*X*Y^2 + 5*X*Y + 4*X + 3*Y^30 + 4*Y^28 + 5*Y^27
        + 5*Y^25 + Y^24 + 2*Y^23 + 5*Y^22 + 3*Y^21 + 5*Y^20 + 2*Y^19 + Y^18 + Y^17 +
        3*Y^16 + Y^15 + 5*Y^14 + 4*Y^13 + 3*Y^12 + 3*Y^11 + Y^10 + 5*Y^9 + 2*Y^8 + 
        3*Y^7 + 6*Y^6 + 3*Y^5 + 2*Y^4 + 5*Y^3 + 6*Y^2 + 5*Y + 1,
    T^56 + 2/7*T^55 + 2/7*T^54 - 279/343*T^53 - 145/2401*T^52 - 411/2401*T^51 + 
        2299/2401*T^50 - 40/343*T^49 + 34/2401*T^48 - 1580/2401*T^47 + 29/49*T^46 - 
        46/343*T^45 + 1406/2401*T^44 - 174/2401*T^43 + 22/2401*T^42 - 1182/2401*T^41
        + 472/2401*T^40 - 244/2401*T^39 - 241/2401*T^38 - 692/2401*T^37 - 
        79/343*T^36 + 102/343*T^35 + 394/2401*T^34 + 278/2401*T^33 - 1543/2401*T^32 
        + 94/343*T^31 - 71/343*T^30 + 1037/2401*T^29 - 1286/2401*T^28 + 
        1037/2401*T^27 - 71/343*T^26 + 94/343*T^25 - 1543/2401*T^24 + 278/2401*T^23 
        + 394/2401*T^22 + 102/343*T^21 - 79/343*T^20 - 692/2401*T^19 - 241/2401*T^18
        - 244/2401*T^17 + 472/2401*T^16 - 1182/2401*T^15 + 22/2401*T^14 - 
        174/2401*T^13 + 1406/2401*T^12 - 46/343*T^11 + 29/49*T^10 - 1580/2401*T^9 + 
        34/2401*T^8 - 40/343*T^7 + 2299/2401*T^6 - 411/2401*T^5 - 145/2401*T^4 - 
        279/343*T^3 + 2/7*T^2 + 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + X*Y^9 + 4*X*Y^8 + 5*X*Y^7 + 
        X*Y^6 + 6*X*Y + 4*Y^30 + 4*Y^29 + Y^28 + Y^26 + 2*Y^25 + 2*Y^24 + Y^23 + 
        2*Y^22 + 3*Y^21 + 6*Y^20 + 3*Y^18 + Y^17 + 3*Y^16 + 3*Y^15 + 6*Y^12 + 3*Y^11
        + 5*Y^10 + Y^9 + Y^8 + 2*Y^7 + Y^6 + Y^5 + 4*Y^4 + 3*Y^3 + Y^2 + 2*Y + 5,
    T^56 + 13/7*T^55 + 53/49*T^54 - 132/343*T^53 - 3845/2401*T^52 - 5571/2401*T^51 -
        6109/2401*T^50 - 464/343*T^49 + 3436/2401*T^48 + 7852/2401*T^47 + 
        760/343*T^46 - 758/2401*T^45 - 5695/2401*T^44 - 6390/2401*T^43 - 
        2608/2401*T^42 + 3208/2401*T^41 + 194/49*T^40 + 11337/2401*T^39 + 
        4574/2401*T^38 - 6767/2401*T^37 - 13935/2401*T^36 - 11783/2401*T^35 - 
        3142/2401*T^34 + 5532/2401*T^33 + 10956/2401*T^32 + 10940/2401*T^31 + 
        3110/2401*T^30 - 1129/343*T^29 - 12875/2401*T^28 - 1129/343*T^27 + 
        3110/2401*T^26 + 10940/2401*T^25 + 10956/2401*T^24 + 5532/2401*T^23 - 
        3142/2401*T^22 - 11783/2401*T^21 - 13935/2401*T^20 - 6767/2401*T^19 + 
        4574/2401*T^18 + 11337/2401*T^17 + 194/49*T^16 + 3208/2401*T^15 - 
        2608/2401*T^14 - 6390/2401*T^13 - 5695/2401*T^12 - 758/2401*T^11 + 
        760/343*T^10 + 7852/2401*T^9 + 3436/2401*T^8 - 464/343*T^7 - 6109/2401*T^6 -
        5571/2401*T^5 - 3845/2401*T^4 - 132/343*T^3 + 53/49*T^2 + 13/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + X*Y^13 + 5*X*Y^12 + X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 
        5*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 5*X*Y + 4*X + Y^30
        + 5*Y^29 + 5*Y^28 + 5*Y^27 + 4*Y^26 + 5*Y^25 + 4*Y^24 + 2*Y^23 + 6*Y^22 + 
        2*Y^21 + 4*Y^20 + 2*Y^19 + 2*Y^17 + Y^16 + 5*Y^15 + 4*Y^14 + 6*Y^13 + 2*Y^12
        + 2*Y^11 + 5*Y^10 + 2*Y^9 + Y^8 + 6*Y^6 + 2*Y^5 + 2*Y^4 + 4*Y^3 + 4*Y^2 + Y 
        + 1,
    T^56 + 6/7*T^55 + 31/49*T^54 + 122/343*T^53 - 1062/2401*T^52 - 974/2401*T^51 - 
        2046/2401*T^50 - 4142/2401*T^49 - 388/343*T^48 - 283/343*T^47 - 199/343*T^46
        + 38/343*T^45 + 464/2401*T^44 + 648/2401*T^43 + 3152/2401*T^42 + 
        1325/2401*T^41 + 1445/2401*T^40 + 2999/2401*T^39 + 120/343*T^38 + 
        1702/2401*T^37 + 1324/2401*T^36 - 1986/2401*T^35 - 3/49*T^34 - 852/2401*T^33
        - 2462/2401*T^32 + 186/2401*T^31 - 886/2401*T^30 - 983/2401*T^29 + 
        30/49*T^28 - 983/2401*T^27 - 886/2401*T^26 + 186/2401*T^25 - 2462/2401*T^24 
        - 852/2401*T^23 - 3/49*T^22 - 1986/2401*T^21 + 1324/2401*T^20 + 
        1702/2401*T^19 + 120/343*T^18 + 2999/2401*T^17 + 1445/2401*T^16 + 
        1325/2401*T^15 + 3152/2401*T^14 + 648/2401*T^13 + 464/2401*T^12 + 
        38/343*T^11 - 199/343*T^10 - 283/343*T^9 - 388/343*T^8 - 4142/2401*T^7 - 
        2046/2401*T^6 - 974/2401*T^5 - 1062/2401*T^4 + 122/343*T^3 + 31/49*T^2 + 
        6/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 2*X*Y^9 + 6*X*Y^8 + 4*X*Y^7 + 
        3*X*Y^6 + 4*X*Y^5 + 4*X*Y^3 + 5*X*Y^2 + X*Y + 2*X + 5*Y^30 + 6*Y^29 + 2*Y^28
        + 6*Y^27 + 4*Y^26 + 3*Y^25 + 4*Y^24 + 5*Y^23 + Y^22 + Y^20 + 2*Y^19 + Y^18 +
        3*Y^17 + 6*Y^16 + Y^15 + 2*Y^13 + Y^12 + 5*Y^11 + 4*Y^10 + Y^9 + 3*Y^8 + 
        6*Y^7 + 2*Y^5 + 2*Y^3 + 4*Y + 4,
    -T^56 + 4/7*T^55 + 6/7*T^54 + 151/343*T^53 - 3632/2401*T^52 - 1164/2401*T^51 + 
        1824/2401*T^50 + 1564/2401*T^49 - 2105/2401*T^48 + 753/2401*T^47 + 
        1119/2401*T^46 - 467/2401*T^45 - 4071/2401*T^44 + 3264/2401*T^43 + 
        2157/2401*T^42 - 466/2401*T^41 - 4236/2401*T^40 + 1587/2401*T^39 + 
        2026/2401*T^38 + 583/2401*T^37 - 291/343*T^36 + 292/2401*T^35 + 9/2401*T^34 
        + 187/2401*T^33 + 192/2401*T^32 + 1482/2401*T^31 - 1065/2401*T^30 - 
        1552/2401*T^29 + 1552/2401*T^27 + 1065/2401*T^26 - 1482/2401*T^25 - 
        192/2401*T^24 - 187/2401*T^23 - 9/2401*T^22 - 292/2401*T^21 + 291/343*T^20 -
        583/2401*T^19 - 2026/2401*T^18 - 1587/2401*T^17 + 4236/2401*T^16 + 
        466/2401*T^15 - 2157/2401*T^14 - 3264/2401*T^13 + 4071/2401*T^12 + 
        467/2401*T^11 - 1119/2401*T^10 - 753/2401*T^9 + 2105/2401*T^8 - 
        1564/2401*T^7 - 1824/2401*T^6 + 1164/2401*T^5 + 3632/2401*T^4 - 151/343*T^3 
        - 6/7*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 4*X*Y^9 + 2*X*Y^7 +
        2*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + X*Y^3 + X*Y^2 + 4*X*Y + 3*X + 5*Y^30 + 6*Y^29 
        + 5*Y^28 + 2*Y^27 + Y^25 + 6*Y^24 + Y^22 + 6*Y^21 + 4*Y^20 + 2*Y^18 + Y^17 +
        Y^16 + 2*Y^15 + 5*Y^11 + 2*Y^10 + Y^9 + 2*Y^8 + 6*Y^7 + 3*Y^6 + 2*Y^3 + 3*Y 
        + 6,
    T^56 + 2/7*T^55 - 43/49*T^54 + 12/343*T^53 + 117/343*T^52 - 1324/2401*T^51 + 
        132/2401*T^50 + 167/343*T^49 - 2102/2401*T^48 - 1457/2401*T^47 + 
        1837/2401*T^46 + 1007/2401*T^45 - 911/2401*T^44 + 93/2401*T^43 + 
        208/2401*T^42 - 268/2401*T^41 + 151/2401*T^40 + 955/2401*T^39 - 
        701/2401*T^38 - 36/49*T^37 + 626/2401*T^36 + 1170/2401*T^35 - 381/2401*T^34 
        + 431/2401*T^33 + 124/2401*T^32 - 1373/2401*T^31 + 30/343*T^30 + 
        811/2401*T^29 - 4/343*T^28 + 811/2401*T^27 + 30/343*T^26 - 1373/2401*T^25 + 
        124/2401*T^24 + 431/2401*T^23 - 381/2401*T^22 + 1170/2401*T^21 + 
        626/2401*T^20 - 36/49*T^19 - 701/2401*T^18 + 955/2401*T^17 + 151/2401*T^16 -
        268/2401*T^15 + 208/2401*T^14 + 93/2401*T^13 - 911/2401*T^12 + 
        1007/2401*T^11 + 1837/2401*T^10 - 1457/2401*T^9 - 2102/2401*T^8 + 
        167/343*T^7 + 132/2401*T^6 - 1324/2401*T^5 + 117/343*T^4 + 12/343*T^3 - 
        43/49*T^2 + 2/7*T + 1
*], [*
    X^3 + X*Y^13 + 4*X*Y^11 + 6*X*Y^10 + 2*X*Y^9 + 2*X*Y^8 + 3*X*Y^7 + 6*X*Y^5 + 
        2*X*Y^4 + 2*X*Y^3 + 5*X*Y + 3*X + 3*Y^30 + 4*Y^29 + 4*Y^28 + 2*Y^26 + Y^25 +
        2*Y^24 + Y^21 + 5*Y^19 + 2*Y^18 + 2*Y^17 + 4*Y^16 + Y^15 + 3*Y^13 + 5*Y^12 +
        6*Y^11 + 6*Y^10 + 5*Y^9 + 4*Y^8 + Y^7 + Y^6 + 4*Y^4 + 5*Y^3 + 5*Y^2 + 5*Y + 
        6,
    T^56 - 9/7*T^55 - 1/49*T^54 + 155/343*T^53 + 1457/2401*T^52 - 1061/2401*T^51 - 
        2050/2401*T^50 + 2155/2401*T^49 + 1174/2401*T^48 - 1742/2401*T^47 - 
        802/2401*T^46 - 484/2401*T^45 + 347/343*T^44 - 590/2401*T^43 - 940/2401*T^42
        - 729/2401*T^41 - 550/2401*T^40 + 411/343*T^39 - 1562/2401*T^38 - 
        1655/2401*T^37 + 43/343*T^36 + 2187/2401*T^35 - 53/2401*T^34 - 
        1975/2401*T^33 + 180/2401*T^32 + 1553/2401*T^31 - 612/2401*T^30 + 
        1258/2401*T^29 - 1908/2401*T^28 + 1258/2401*T^27 - 612/2401*T^26 + 
        1553/2401*T^25 + 180/2401*T^24 - 1975/2401*T^23 - 53/2401*T^22 + 
        2187/2401*T^21 + 43/343*T^20 - 1655/2401*T^19 - 1562/2401*T^18 + 
        411/343*T^17 - 550/2401*T^16 - 729/2401*T^15 - 940/2401*T^14 - 590/2401*T^13
        + 347/343*T^12 - 484/2401*T^11 - 802/2401*T^10 - 1742/2401*T^9 + 
        1174/2401*T^8 + 2155/2401*T^7 - 2050/2401*T^6 - 1061/2401*T^5 + 
        1457/2401*T^4 + 155/343*T^3 - 1/49*T^2 - 9/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + X*Y^10 + 4*X*Y^9 + 4*X*Y^8 + 
        5*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 3*X*Y + 2*X + 4*Y^30 + Y^29 + 4*Y^28
        + Y^27 + Y^26 + 6*Y^25 + 2*Y^23 + 4*Y^22 + Y^20 + 2*Y^19 + Y^18 + 2*Y^17 + 
        5*Y^16 + 5*Y^15 + 4*Y^14 + 6*Y^13 + 4*Y^11 + 5*Y^10 + 3*Y^9 + 6*Y^7 + 3*Y^6 
        + 4*Y^5 + 4*Y^4 + 3*Y^2 + 4*Y + 6,
    T^56 + 9/7*T^55 - 16/49*T^54 - 111/49*T^53 - 6256/2401*T^52 + 388/2401*T^51 + 
        6631/2401*T^50 + 894/343*T^49 - 584/2401*T^48 - 6273/2401*T^47 - 
        4514/2401*T^46 + 1332/2401*T^45 + 4873/2401*T^44 + 1679/2401*T^43 - 
        1861/2401*T^42 - 250/343*T^41 + 1723/2401*T^40 + 2739/2401*T^39 - 
        1227/2401*T^38 - 4149/2401*T^37 - 3748/2401*T^36 + 1313/2401*T^35 + 
        683/343*T^34 + 3618/2401*T^33 - 1003/2401*T^32 - 4061/2401*T^31 - 
        2174/2401*T^30 + 194/343*T^29 + 3684/2401*T^28 + 194/343*T^27 - 
        2174/2401*T^26 - 4061/2401*T^25 - 1003/2401*T^24 + 3618/2401*T^23 + 
        683/343*T^22 + 1313/2401*T^21 - 3748/2401*T^20 - 4149/2401*T^19 - 
        1227/2401*T^18 + 2739/2401*T^17 + 1723/2401*T^16 - 250/343*T^15 - 
        1861/2401*T^14 + 1679/2401*T^13 + 4873/2401*T^12 + 1332/2401*T^11 - 
        4514/2401*T^10 - 6273/2401*T^9 - 584/2401*T^8 + 894/343*T^7 + 6631/2401*T^6 
        + 388/2401*T^5 - 6256/2401*T^4 - 111/49*T^3 - 16/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 5*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 +
        6*X*Y^7 + X*Y^5 + 4*X*Y^4 + 2*X*Y^2 + 6*X + 2*Y^30 + 5*Y^28 + 3*Y^27 + 
        4*Y^26 + 3*Y^25 + 6*Y^24 + 3*Y^23 + 3*Y^22 + 6*Y^21 + 6*Y^19 + 3*Y^18 + 
        4*Y^17 + 2*Y^16 + 2*Y^14 + 6*Y^12 + Y^11 + 4*Y^10 + 6*Y^9 + 3*Y^7 + 2*Y^6 + 
        3*Y^4 + 6*Y^3 + 2*Y^2 + 3*Y + 6,
    -T^56 - 19/7*T^55 - 177/49*T^54 - 1033/343*T^53 - 3985/2401*T^52 - 569/2401*T^51
        + 2843/2401*T^50 + 5102/2401*T^49 + 15/7*T^48 + 3050/2401*T^47 + 
        841/2401*T^46 + 45/2401*T^45 + 467/2401*T^44 - 286/2401*T^43 - 
        1609/2401*T^42 - 2172/2401*T^41 - 335/343*T^40 - 2565/2401*T^39 - 
        2880/2401*T^38 - 568/343*T^37 - 5909/2401*T^36 - 5720/2401*T^35 - 
        2277/2401*T^34 + 1900/2401*T^33 + 4776/2401*T^32 + 7500/2401*T^31 + 
        8621/2401*T^30 + 6059/2401*T^29 - 6059/2401*T^27 - 8621/2401*T^26 - 
        7500/2401*T^25 - 4776/2401*T^24 - 1900/2401*T^23 + 2277/2401*T^22 + 
        5720/2401*T^21 + 5909/2401*T^20 + 568/343*T^19 + 2880/2401*T^18 + 
        2565/2401*T^17 + 335/343*T^16 + 2172/2401*T^15 + 1609/2401*T^14 + 
        286/2401*T^13 - 467/2401*T^12 - 45/2401*T^11 - 841/2401*T^10 - 3050/2401*T^9
        - 15/7*T^8 - 5102/2401*T^7 - 2843/2401*T^6 + 569/2401*T^5 + 3985/2401*T^4 + 
        1033/343*T^3 + 177/49*T^2 + 19/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 
        + 2*X*Y^8 + 4*X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 
        3*X*Y + 4*X + 6*Y^30 + 3*Y^29 + 5*Y^28 + 3*Y^27 + 6*Y^26 + 2*Y^25 + 6*Y^24 +
        4*Y^23 + 5*Y^22 + 5*Y^21 + 2*Y^20 + 4*Y^19 + 2*Y^18 + 4*Y^17 + 4*Y^16 + 
        2*Y^15 + 3*Y^14 + 3*Y^13 + 2*Y^12 + 4*Y^11 + 5*Y^10 + 5*Y^8 + 6*Y^7 + 5*Y^6 
        + 3*Y^4 + Y^3 + 6*Y^2 + 4*Y + 6,
    -T^56 + 3/7*T^55 + 12/49*T^54 - 466/343*T^53 + 3631/2401*T^52 + 54/343*T^51 - 
        1143/2401*T^50 + 1459/2401*T^49 - 436/2401*T^48 + 1058/2401*T^47 - 
        1881/2401*T^46 + 207/343*T^45 + 684/2401*T^44 - 2676/2401*T^43 + 
        1315/2401*T^42 - 54/343*T^41 - 729/2401*T^40 - 641/2401*T^39 + 510/2401*T^38
        + 970/2401*T^37 - 2000/2401*T^36 + 1140/2401*T^35 + 20/49*T^34 - 
        1395/2401*T^33 + 220/343*T^32 + 37/343*T^31 - 839/2401*T^30 + 1206/2401*T^29
        - 1206/2401*T^27 + 839/2401*T^26 - 37/343*T^25 - 220/343*T^24 + 
        1395/2401*T^23 - 20/49*T^22 - 1140/2401*T^21 + 2000/2401*T^20 - 
        970/2401*T^19 - 510/2401*T^18 + 641/2401*T^17 + 729/2401*T^16 + 54/343*T^15 
        - 1315/2401*T^14 + 2676/2401*T^13 - 684/2401*T^12 - 207/343*T^11 + 
        1881/2401*T^10 - 1058/2401*T^9 + 436/2401*T^8 - 1459/2401*T^7 + 
        1143/2401*T^6 - 54/343*T^5 - 3631/2401*T^4 + 466/343*T^3 - 12/49*T^2 - 3/7*T
        + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 3*X*Y^9 + X*Y^8 + 
        3*X*Y^6 + 4*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 6*X + 2*Y^30 + 6*Y^29 + 2*Y^28 + 
        2*Y^27 + 3*Y^26 + 5*Y^25 + 2*Y^24 + 5*Y^23 + 3*Y^22 + Y^21 + 2*Y^20 + 3*Y^18
        + 6*Y^17 + 2*Y^16 + 3*Y^15 + 4*Y^14 + 5*Y^13 + 2*Y^12 + Y^11 + 2*Y^9 + Y^8 +
        6*Y^7 + 3*Y^6 + 3*Y^5 + 3*Y^3 + 5*Y^2 + 3*Y,
    -T^56 + 2/7*T^55 + 5/7*T^54 - 65/343*T^53 - 1044/2401*T^52 - 468/2401*T^51 - 
        418/2401*T^50 - 855/2401*T^49 + 2480/2401*T^48 - 73/2401*T^47 - 
        898/2401*T^46 - 591/2401*T^45 + 570/2401*T^44 + 31/2401*T^43 - 
        1360/2401*T^42 + 1363/2401*T^41 - 181/2401*T^40 + 424/2401*T^39 - 
        722/2401*T^38 - 278/2401*T^37 - 99/343*T^36 - 944/2401*T^35 + 2005/2401*T^34
        + 230/2401*T^33 - 633/2401*T^32 - 901/2401*T^31 + 1275/2401*T^30 - 
        1236/2401*T^29 + 1236/2401*T^27 - 1275/2401*T^26 + 901/2401*T^25 + 
        633/2401*T^24 - 230/2401*T^23 - 2005/2401*T^22 + 944/2401*T^21 + 99/343*T^20
        + 278/2401*T^19 + 722/2401*T^18 - 424/2401*T^17 + 181/2401*T^16 - 
        1363/2401*T^15 + 1360/2401*T^14 - 31/2401*T^13 - 570/2401*T^12 + 
        591/2401*T^11 + 898/2401*T^10 + 73/2401*T^9 - 2480/2401*T^8 + 855/2401*T^7 +
        418/2401*T^6 + 468/2401*T^5 + 1044/2401*T^4 + 65/343*T^3 - 5/7*T^2 - 2/7*T +
        1
*], [*
    X^3 + 2*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 2*X*Y^9 + 6*X*Y^8 + 3*X*Y^7 + 
        3*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 4*X*Y + 4*X + 5*Y^30 + 
        Y^29 + 4*Y^28 + 3*Y^27 + 4*Y^25 + 4*Y^24 + Y^23 + Y^22 + 4*Y^20 + 5*Y^19 + 
        3*Y^18 + 5*Y^17 + 4*Y^15 + 3*Y^14 + 5*Y^12 + Y^11 + 6*Y^10 + 6*Y^9 + 6*Y^8 +
        5*Y^7 + Y^6 + 5*Y^5 + 2*Y^3 + Y,
    -T^56 + 4/7*T^55 + 2/7*T^54 - 470/343*T^53 + 1923/2401*T^52 + 50/2401*T^51 - 
        1789/2401*T^50 + 1982/2401*T^49 - 1578/2401*T^48 - 1118/2401*T^47 + 
        2591/2401*T^46 - 1472/2401*T^45 - 471/2401*T^44 + 1551/2401*T^43 - 
        118/343*T^42 + 127/2401*T^41 + 598/2401*T^40 + 19/343*T^39 - 704/2401*T^38 +
        299/2401*T^37 + 1928/2401*T^36 - 549/2401*T^35 - 24/2401*T^34 + 
        1377/2401*T^33 - 657/2401*T^32 + 573/2401*T^31 + 835/2401*T^30 - 29/49*T^29 
        + 29/49*T^27 - 835/2401*T^26 - 573/2401*T^25 + 657/2401*T^24 - 
        1377/2401*T^23 + 24/2401*T^22 + 549/2401*T^21 - 1928/2401*T^20 - 
        299/2401*T^19 + 704/2401*T^18 - 19/343*T^17 - 598/2401*T^16 - 127/2401*T^15 
        + 118/343*T^14 - 1551/2401*T^13 + 471/2401*T^12 + 1472/2401*T^11 - 
        2591/2401*T^10 + 1118/2401*T^9 + 1578/2401*T^8 - 1982/2401*T^7 + 
        1789/2401*T^6 - 50/2401*T^5 - 1923/2401*T^4 + 470/343*T^3 - 2/7*T^2 - 4/7*T 
        + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 2*X*Y^10 + 5*X*Y^9 + X*Y^7 + 
        6*X*Y^6 + 6*X*Y^5 + X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 2*X*Y + 2*Y^30 + 2*Y^29 + 
        5*Y^28 + Y^27 + 2*Y^26 + 3*Y^25 + 2*Y^24 + Y^23 + 4*Y^22 + 2*Y^21 + 3*Y^20 +
        4*Y^19 + 2*Y^17 + 6*Y^15 + 5*Y^14 + Y^13 + 2*Y^12 + 4*Y^11 + 4*Y^9 + 4*Y^8 +
        Y^7 + Y^6 + 4*Y^5 + 3*Y^3 + 3*Y^2 + 1,
    -T^56 + 1/7*T^55 + 1/7*T^54 + 1/49*T^53 - 244/2401*T^52 - 479/2401*T^51 + 
        1577/2401*T^50 + 2/2401*T^49 + 841/2401*T^48 - 513/2401*T^47 - 104/2401*T^46
        + 1075/2401*T^45 - 209/343*T^44 + 1924/2401*T^43 - 76/343*T^42 + 
        519/2401*T^41 + 248/2401*T^40 - 334/2401*T^39 + 1391/2401*T^38 - 
        2132/2401*T^37 + 432/2401*T^36 - 1118/2401*T^35 + 269/2401*T^34 + 
        256/2401*T^33 - 348/343*T^32 + 1594/2401*T^31 - 961/2401*T^30 + 
        949/2401*T^29 - 949/2401*T^27 + 961/2401*T^26 - 1594/2401*T^25 + 
        348/343*T^24 - 256/2401*T^23 - 269/2401*T^22 + 1118/2401*T^21 - 
        432/2401*T^20 + 2132/2401*T^19 - 1391/2401*T^18 + 334/2401*T^17 - 
        248/2401*T^16 - 519/2401*T^15 + 76/343*T^14 - 1924/2401*T^13 + 209/343*T^12 
        - 1075/2401*T^11 + 104/2401*T^10 + 513/2401*T^9 - 841/2401*T^8 - 2/2401*T^7 
        - 1577/2401*T^6 + 479/2401*T^5 + 244/2401*T^4 - 1/49*T^3 - 1/7*T^2 - 1/7*T +
        1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 2*X*Y^9 + 2*X*Y^8 + 
        4*X*Y^7 + 6*X*Y^4 + 4*X*Y + 3*Y^30 + 5*Y^29 + 3*Y^28 + 5*Y^27 + Y^25 + 
        4*Y^24 + 5*Y^23 + 3*Y^22 + 4*Y^21 + 4*Y^20 + Y^19 + 2*Y^18 + 2*Y^17 + 6*Y^16
        + 4*Y^14 + 2*Y^13 + 2*Y^11 + 2*Y^10 + 2*Y^9 + 5*Y^8 + 5*Y^7 + 3*Y^6 + 4*Y^5 
        + 5*Y^4 + 4*Y^3 + 4*Y^2 + 6*Y + 6,
    -T^56 - 1/7*T^55 + 17/49*T^54 - 2/49*T^53 - 474/2401*T^52 - 2299/2401*T^51 - 
        326/2401*T^50 + 2201/2401*T^49 + 134/343*T^48 - 851/2401*T^47 - 
        1810/2401*T^46 - 1326/2401*T^45 + 1563/2401*T^44 + 537/2401*T^43 + 
        410/2401*T^42 - 1662/2401*T^41 - 1550/2401*T^40 + 655/2401*T^39 + 
        922/2401*T^38 + 2159/2401*T^37 + 10/49*T^36 - 2518/2401*T^35 - 
        1377/2401*T^34 + 990/2401*T^33 + 2349/2401*T^32 + 1874/2401*T^31 - 
        2966/2401*T^30 - 2529/2401*T^29 + 2529/2401*T^27 + 2966/2401*T^26 - 
        1874/2401*T^25 - 2349/2401*T^24 - 990/2401*T^23 + 1377/2401*T^22 + 
        2518/2401*T^21 - 10/49*T^20 - 2159/2401*T^19 - 922/2401*T^18 - 655/2401*T^17
        + 1550/2401*T^16 + 1662/2401*T^15 - 410/2401*T^14 - 537/2401*T^13 - 
        1563/2401*T^12 + 1326/2401*T^11 + 1810/2401*T^10 + 851/2401*T^9 - 
        134/343*T^8 - 2201/2401*T^7 + 326/2401*T^6 + 2299/2401*T^5 + 474/2401*T^4 + 
        2/49*T^3 - 17/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 
        + 3*X*Y^8 + 3*X*Y^7 + 4*X*Y^6 + X*Y^5 + X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 4*X*Y + 
        5*X + 2*Y^30 + 5*Y^28 + 4*Y^27 + 4*Y^26 + 5*Y^25 + 6*Y^24 + 6*Y^23 + 5*Y^22 
        + 5*Y^21 + 3*Y^20 + 4*Y^19 + 5*Y^15 + 6*Y^14 + 4*Y^13 + 5*Y^12 + 3*Y^11 + 
        Y^10 + 3*Y^8 + 4*Y^7 + 3*Y^6 + 2*Y^5 + Y^4 + 6*Y^2 + 5*Y + 5,
    T^56 + 9/49*T^54 - 47/49*T^53 - 1025/2401*T^52 + 1427/2401*T^51 + 1801/2401*T^50
        + 1214/2401*T^49 - 1819/2401*T^48 - 2003/2401*T^47 - 971/2401*T^46 + 
        846/2401*T^45 + 608/2401*T^44 - 158/2401*T^43 - 107/343*T^42 - 29/49*T^41 + 
        312/2401*T^40 - 74/2401*T^39 + 1501/2401*T^38 + 216/2401*T^37 - 
        891/2401*T^36 - 25/343*T^35 - 453/2401*T^34 + 1237/2401*T^33 + 741/2401*T^32
        - 251/2401*T^31 - 86/343*T^30 + 145/2401*T^29 + 586/2401*T^28 + 
        145/2401*T^27 - 86/343*T^26 - 251/2401*T^25 + 741/2401*T^24 + 1237/2401*T^23
        - 453/2401*T^22 - 25/343*T^21 - 891/2401*T^20 + 216/2401*T^19 + 
        1501/2401*T^18 - 74/2401*T^17 + 312/2401*T^16 - 29/49*T^15 - 107/343*T^14 - 
        158/2401*T^13 + 608/2401*T^12 + 846/2401*T^11 - 971/2401*T^10 - 
        2003/2401*T^9 - 1819/2401*T^8 + 1214/2401*T^7 + 1801/2401*T^6 + 
        1427/2401*T^5 - 1025/2401*T^4 - 47/49*T^3 + 9/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 
        X*Y^8 + X*Y^7 + 4*X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + X*Y^2 + 3*X*Y + 4*X + 2*Y^30 +
        2*Y^29 + 6*Y^28 + 6*Y^27 + 4*Y^26 + 3*Y^25 + 2*Y^23 + 2*Y^22 + 4*Y^21 + 
        5*Y^20 + Y^19 + 3*Y^18 + 6*Y^17 + Y^16 + 5*Y^15 + 6*Y^14 + 3*Y^13 + Y^12 + 
        4*Y^11 + 4*Y^9 + 6*Y^7 + 2*Y^6 + Y^5 + 4*Y^4 + 3*Y^3 + Y^2 + Y,
    T^56 - 4/7*T^55 - 6/49*T^54 + 26/49*T^53 - 1816/2401*T^52 - 542/2401*T^51 - 
        383/2401*T^50 + 204/343*T^49 + 306/2401*T^48 - 1338/2401*T^47 + 
        2003/2401*T^46 - 338/2401*T^45 - 1564/2401*T^44 + 265/2401*T^43 + 
        592/2401*T^42 - 598/2401*T^41 - 647/2401*T^40 + 212/343*T^39 + 779/2401*T^38
        - 635/2401*T^37 - 275/2401*T^36 + 692/2401*T^35 - 142/343*T^34 - 
        1237/2401*T^33 + 614/2401*T^32 + 468/2401*T^31 - 379/2401*T^30 + 
        29/2401*T^29 + 683/2401*T^28 + 29/2401*T^27 - 379/2401*T^26 + 468/2401*T^25 
        + 614/2401*T^24 - 1237/2401*T^23 - 142/343*T^22 + 692/2401*T^21 - 
        275/2401*T^20 - 635/2401*T^19 + 779/2401*T^18 + 212/343*T^17 - 647/2401*T^16
        - 598/2401*T^15 + 592/2401*T^14 + 265/2401*T^13 - 1564/2401*T^12 - 
        338/2401*T^11 + 2003/2401*T^10 - 1338/2401*T^9 + 306/2401*T^8 + 204/343*T^7 
        - 383/2401*T^6 - 542/2401*T^5 - 1816/2401*T^4 + 26/49*T^3 - 6/49*T^2 - 4/7*T
        + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + X*Y^13 + 6*X*Y^12 + X*Y^11 + 4*X*Y^10 + 3*X*Y^8 + 
        2*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 5*X*Y + 2*X + 6*Y^30 + 
        6*Y^29 + 5*Y^28 + 6*Y^27 + 2*Y^26 + 6*Y^25 + 6*Y^24 + 4*Y^23 + 6*Y^22 + 
        2*Y^20 + 6*Y^19 + 6*Y^18 + Y^16 + 6*Y^15 + 2*Y^14 + 2*Y^13 + 5*Y^12 + Y^10 +
        6*Y^8 + 3*Y^7 + 4*Y^5 + 4*Y^4 + 2*Y^3 + 6*Y^2 + 2*Y + 3,
    T^56 + 5/7*T^55 - 64/49*T^54 - 246/343*T^53 + 3161/2401*T^52 + 30/2401*T^51 - 
        4910/2401*T^50 + 958/2401*T^49 + 4663/2401*T^48 - 1040/2401*T^47 - 
        3443/2401*T^46 + 335/2401*T^45 + 3212/2401*T^44 - 10/343*T^43 - 538/343*T^42
        - 1262/2401*T^41 + 4828/2401*T^40 + 1389/2401*T^39 - 6784/2401*T^38 - 
        1208/2401*T^37 + 6683/2401*T^36 - 12/343*T^35 - 7130/2401*T^34 + 
        1259/2401*T^33 + 7375/2401*T^32 - 254/2401*T^31 - 5353/2401*T^30 - 
        106/2401*T^29 + 4534/2401*T^28 - 106/2401*T^27 - 5353/2401*T^26 - 
        254/2401*T^25 + 7375/2401*T^24 + 1259/2401*T^23 - 7130/2401*T^22 - 
        12/343*T^21 + 6683/2401*T^20 - 1208/2401*T^19 - 6784/2401*T^18 + 
        1389/2401*T^17 + 4828/2401*T^16 - 1262/2401*T^15 - 538/343*T^14 - 
        10/343*T^13 + 3212/2401*T^12 + 335/2401*T^11 - 3443/2401*T^10 - 
        1040/2401*T^9 + 4663/2401*T^8 + 958/2401*T^7 - 4910/2401*T^6 + 30/2401*T^5 +
        3161/2401*T^4 - 246/343*T^3 - 64/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + X*Y^13 + 4*X*Y^12 + 3*X*Y^10 + 2*X*Y^9 + X*Y^8 + 
        5*X*Y^7 + X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 2*X*Y^2 + 3*X*Y + 5*Y^30 + 6*Y^28 + 
        2*Y^27 + 2*Y^26 + 2*Y^25 + 5*Y^24 + 5*Y^23 + 3*Y^22 + 4*Y^20 + 6*Y^19 + 
        3*Y^18 + 6*Y^17 + 6*Y^16 + 5*Y^15 + 3*Y^13 + Y^12 + 2*Y^11 + 6*Y^10 + Y^9 + 
        5*Y^8 + 3*Y^7 + 2*Y^6 + 4*Y^4 + 2*Y^3 + 5*Y^2 + 2*Y + 4,
    T^56 + 9/7*T^55 + 26/49*T^54 + 90/343*T^53 + 389/2401*T^52 + 1469/2401*T^51 + 
        517/2401*T^50 - 447/2401*T^49 + 220/343*T^48 + 1881/2401*T^47 + 179/343*T^46
        + 37/49*T^45 + 1118/2401*T^44 + 1373/2401*T^43 + 157/343*T^42 + 
        653/2401*T^41 + 333/343*T^40 + 2077/2401*T^39 + 2157/2401*T^38 + 
        2489/2401*T^37 + 1434/2401*T^36 + 1469/2401*T^35 + 2220/2401*T^34 + 
        362/343*T^33 + 2348/2401*T^32 + 799/2401*T^31 + 412/2401*T^30 + 
        1182/2401*T^29 + 1096/2401*T^28 + 1182/2401*T^27 + 412/2401*T^26 + 
        799/2401*T^25 + 2348/2401*T^24 + 362/343*T^23 + 2220/2401*T^22 + 
        1469/2401*T^21 + 1434/2401*T^20 + 2489/2401*T^19 + 2157/2401*T^18 + 
        2077/2401*T^17 + 333/343*T^16 + 653/2401*T^15 + 157/343*T^14 + 
        1373/2401*T^13 + 1118/2401*T^12 + 37/49*T^11 + 179/343*T^10 + 1881/2401*T^9 
        + 220/343*T^8 - 447/2401*T^7 + 517/2401*T^6 + 1469/2401*T^5 + 389/2401*T^4 +
        90/343*T^3 + 26/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 5*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 +
        3*X*Y^7 + 4*X*Y^6 + 6*X*Y^5 + 5*X*Y^3 + 2*X*Y + 3*X + 6*Y^30 + 6*Y^29 + 
        3*Y^27 + 4*Y^26 + 2*Y^25 + 3*Y^23 + 4*Y^22 + Y^21 + 4*Y^20 + 2*Y^19 + 3*Y^18
        + Y^17 + 4*Y^16 + 4*Y^14 + 6*Y^13 + 4*Y^12 + 4*Y^11 + 3*Y^10 + 2*Y^7 + Y^6 +
        6*Y^5 + 5*Y^4 + Y^3 + 3*Y^2 + 5*Y + 2,
    T^56 + 4/7*T^55 - 68/49*T^54 - 237/343*T^53 + 2176/2401*T^52 + 3/2401*T^51 - 
        657/2401*T^50 + 1005/2401*T^49 - 48/343*T^48 + 190/2401*T^47 + 
        1489/2401*T^46 - 174/343*T^45 - 1161/2401*T^44 + 780/2401*T^43 - 
        67/2401*T^42 + 57/343*T^41 + 2039/2401*T^40 + 627/2401*T^39 - 2031/2401*T^38
        - 1539/2401*T^37 + 404/2401*T^36 + 451/2401*T^35 - 622/2401*T^34 + 
        198/2401*T^33 + 913/2401*T^32 + 421/2401*T^31 + 332/2401*T^30 - 34/343*T^29 
        - 1431/2401*T^28 - 34/343*T^27 + 332/2401*T^26 + 421/2401*T^25 + 
        913/2401*T^24 + 198/2401*T^23 - 622/2401*T^22 + 451/2401*T^21 + 
        404/2401*T^20 - 1539/2401*T^19 - 2031/2401*T^18 + 627/2401*T^17 + 
        2039/2401*T^16 + 57/343*T^15 - 67/2401*T^14 + 780/2401*T^13 - 1161/2401*T^12
        - 174/343*T^11 + 1489/2401*T^10 + 190/2401*T^9 - 48/343*T^8 + 1005/2401*T^7 
        - 657/2401*T^6 + 3/2401*T^5 + 2176/2401*T^4 - 237/343*T^3 - 68/49*T^2 + 
        4/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        2*X*Y^8 + 5*X*Y^6 + 2*X*Y^5 + 6*X*Y^3 + 2*X*Y^2 + 2*X*Y + 5*X + 5*Y^30 + 
        6*Y^29 + 2*Y^28 + 2*Y^27 + 4*Y^26 + 3*Y^25 + Y^24 + 4*Y^23 + 4*Y^22 + 3*Y^21
        + 2*Y^20 + 5*Y^19 + 5*Y^18 + Y^17 + 4*Y^16 + 2*Y^15 + 2*Y^14 + 4*Y^13 + 
        2*Y^12 + 5*Y^11 + 6*Y^10 + Y^9 + 3*Y^8 + 6*Y^7 + 5*Y^6 + 6*Y^5 + Y^4 + 3*Y^3
        + 5*Y^2 + 4*Y + 4,
    T^56 - 4/7*T^55 - 68/49*T^54 + 326/343*T^53 + 1200/2401*T^52 - 2111/2401*T^51 + 
        187/343*T^50 + 1/343*T^49 - 913/2401*T^48 + 249/2401*T^47 - 148/343*T^46 + 
        2174/2401*T^45 + 806/2401*T^44 - 4595/2401*T^43 + 1455/2401*T^42 + 
        4456/2401*T^41 - 1766/2401*T^40 - 1865/2401*T^39 + 969/2401*T^38 + 
        877/2401*T^37 - 1811/2401*T^36 - 2063/2401*T^35 + 2598/2401*T^34 + 
        1973/2401*T^33 - 3653/2401*T^32 - 1/2401*T^31 + 3618/2401*T^30 - 
        19/2401*T^29 - 3670/2401*T^28 - 19/2401*T^27 + 3618/2401*T^26 - 1/2401*T^25 
        - 3653/2401*T^24 + 1973/2401*T^23 + 2598/2401*T^22 - 2063/2401*T^21 - 
        1811/2401*T^20 + 877/2401*T^19 + 969/2401*T^18 - 1865/2401*T^17 - 
        1766/2401*T^16 + 4456/2401*T^15 + 1455/2401*T^14 - 4595/2401*T^13 + 
        806/2401*T^12 + 2174/2401*T^11 - 148/343*T^10 + 249/2401*T^9 - 913/2401*T^8 
        + 1/343*T^7 + 187/343*T^6 - 2111/2401*T^5 + 1200/2401*T^4 + 326/343*T^3 - 
        68/49*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^13 + X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + X*Y^7 + X*Y^6 + 2*X*Y^5 + 5*X*Y^4 +
        4*X*Y^3 + 5*X*Y^2 + 2*X*Y + 4*X + 3*Y^30 + 5*Y^28 + 4*Y^27 + 6*Y^26 + 5*Y^25
        + 5*Y^24 + 6*Y^23 + 3*Y^22 + 3*Y^21 + 4*Y^20 + 4*Y^19 + Y^18 + 5*Y^17 + 
        3*Y^16 + Y^15 + Y^14 + 5*Y^13 + 3*Y^12 + 2*Y^11 + 5*Y^10 + 2*Y^9 + 4*Y^8 + 
        5*Y^6 + 2*Y^5 + 2*Y^4 + Y^3 + 3*Y^2 + 6*Y + 4,
    T^56 - T^55 + 15/49*T^54 + 142/343*T^53 - 3364/2401*T^52 + 1969/2401*T^51 + 
        313/2401*T^50 - 18/2401*T^49 - 990/2401*T^48 + 470/2401*T^47 + 594/2401*T^46
        - 3404/2401*T^45 + 3383/2401*T^44 + 46/2401*T^43 - 2363/2401*T^42 + 
        328/343*T^41 - 867/2401*T^40 - 580/2401*T^39 - 375/2401*T^38 + 201/343*T^37 
        - 383/2401*T^36 - 1212/2401*T^35 + 2193/2401*T^34 - 1157/2401*T^33 - 
        137/2401*T^32 + 752/2401*T^31 - 353/2401*T^30 - 61/2401*T^29 + 228/2401*T^28
        - 61/2401*T^27 - 353/2401*T^26 + 752/2401*T^25 - 137/2401*T^24 - 
        1157/2401*T^23 + 2193/2401*T^22 - 1212/2401*T^21 - 383/2401*T^20 + 
        201/343*T^19 - 375/2401*T^18 - 580/2401*T^17 - 867/2401*T^16 + 328/343*T^15 
        - 2363/2401*T^14 + 46/2401*T^13 + 3383/2401*T^12 - 3404/2401*T^11 + 
        594/2401*T^10 + 470/2401*T^9 - 990/2401*T^8 - 18/2401*T^7 + 313/2401*T^6 + 
        1969/2401*T^5 - 3364/2401*T^4 + 142/343*T^3 + 15/49*T^2 - T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + X*Y^12 + X*Y^11 + 6*X*Y^10 + 2*X*Y^9 + 
        6*X*Y^8 + 6*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + X*Y^2 + 6*X*Y + 
        2*Y^30 + 5*Y^29 + 3*Y^28 + 6*Y^27 + 6*Y^26 + 5*Y^24 + Y^23 + Y^22 + 5*Y^21 +
        6*Y^20 + Y^19 + 2*Y^17 + 3*Y^16 + 4*Y^15 + 6*Y^14 + 4*Y^13 + 2*Y^11 + 3*Y^10
        + 5*Y^9 + Y^8 + Y^7 + 2*Y^6 + 3*Y^5 + 5*Y^4 + Y^2 + 5*Y + 5,
    -T^56 - T^55 + 27/49*T^54 + 129/343*T^53 - 1791/2401*T^52 + 249/2401*T^51 + 
        2802/2401*T^50 + 488/2401*T^49 - 926/2401*T^48 + 431/2401*T^47 + 
        895/2401*T^46 - 1594/2401*T^45 - 2955/2401*T^44 - 746/2401*T^43 + 
        1702/2401*T^42 + 1263/2401*T^41 + 450/2401*T^40 + 1062/2401*T^39 + 
        1115/2401*T^38 + 439/2401*T^37 - 62/2401*T^36 + 116/2401*T^35 + 
        153/2401*T^34 - 403/2401*T^33 - 1215/2401*T^32 + 346/2401*T^31 + 
        1738/2401*T^30 + 608/2401*T^29 - 608/2401*T^27 - 1738/2401*T^26 - 
        346/2401*T^25 + 1215/2401*T^24 + 403/2401*T^23 - 153/2401*T^22 - 
        116/2401*T^21 + 62/2401*T^20 - 439/2401*T^19 - 1115/2401*T^18 - 
        1062/2401*T^17 - 450/2401*T^16 - 1263/2401*T^15 - 1702/2401*T^14 + 
        746/2401*T^13 + 2955/2401*T^12 + 1594/2401*T^11 - 895/2401*T^10 - 
        431/2401*T^9 + 926/2401*T^8 - 488/2401*T^7 - 2802/2401*T^6 - 249/2401*T^5 + 
        1791/2401*T^4 - 129/343*T^3 - 27/49*T^2 + T + 1
*], [*
    X^3 + 4*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 5*X*Y^8 + 
        X*Y^7 + X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 6*X*Y + X + Y^30 + 
        4*Y^29 + 4*Y^28 + 6*Y^26 + 6*Y^25 + 3*Y^21 + 5*Y^20 + 2*Y^19 + 5*Y^18 + 
        5*Y^17 + Y^16 + 4*Y^15 + 3*Y^14 + 6*Y^13 + 3*Y^12 + Y^11 + 5*Y^10 + Y^9 + 
        6*Y^8 + 2*Y^6 + 4*Y^5 + Y^4 + Y^3 + 4*Y^2 + 6,
    -T^56 + 9/7*T^55 - 62/49*T^54 + 57/343*T^53 + 306/343*T^52 - 4122/2401*T^51 + 
        2599/2401*T^50 - 327/2401*T^49 - 982/2401*T^48 + 739/2401*T^47 + 
        1525/2401*T^46 - 274/343*T^45 + 624/2401*T^44 + 2607/2401*T^43 - 
        3471/2401*T^42 + 2729/2401*T^41 + 96/343*T^40 - 2410/2401*T^39 + 
        2391/2401*T^38 + 706/2401*T^37 - 283/343*T^36 + 1380/2401*T^35 + 
        1398/2401*T^34 - 395/343*T^33 + 2259/2401*T^32 + 165/343*T^31 - 
        3322/2401*T^30 + 2739/2401*T^29 - 2739/2401*T^27 + 3322/2401*T^26 - 
        165/343*T^25 - 2259/2401*T^24 + 395/343*T^23 - 1398/2401*T^22 - 
        1380/2401*T^21 + 283/343*T^20 - 706/2401*T^19 - 2391/2401*T^18 + 
        2410/2401*T^17 - 96/343*T^16 - 2729/2401*T^15 + 3471/2401*T^14 - 
        2607/2401*T^13 - 624/2401*T^12 + 274/343*T^11 - 1525/2401*T^10 - 
        739/2401*T^9 + 982/2401*T^8 + 327/2401*T^7 - 2599/2401*T^6 + 4122/2401*T^5 -
        306/343*T^4 - 57/343*T^3 + 62/49*T^2 - 9/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 4*X*Y^13 + X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 
        4*X*Y^7 + 3*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + X*Y + 6*X + 3*Y^30 + Y^29 
        + 5*Y^28 + 2*Y^27 + 5*Y^26 + 3*Y^25 + Y^24 + Y^23 + 3*Y^21 + 6*Y^20 + 4*Y^19
        + 4*Y^18 + 2*Y^17 + 3*Y^15 + 3*Y^13 + 4*Y^12 + 2*Y^11 + 6*Y^10 + 4*Y^9 + 
        2*Y^7 + 3*Y^6 + 3*Y^5 + 3*Y^4 + 3*Y^2 + Y + 5,
    T^56 - 8/7*T^55 + 9/49*T^54 + 29/49*T^53 + 1096/2401*T^52 - 3442/2401*T^51 + 
        2193/2401*T^50 - 121/2401*T^49 - 139/2401*T^48 - 2266/2401*T^47 + 
        2031/2401*T^46 + 184/2401*T^45 - 377/2401*T^44 - 2266/2401*T^43 + 
        1824/2401*T^42 + 250/343*T^41 - 1775/2401*T^40 - 33/49*T^39 + 2153/2401*T^38
        + 1026/2401*T^37 - 2085/2401*T^36 - 897/2401*T^35 + 1776/2401*T^34 + 
        1289/2401*T^33 - 2533/2401*T^32 - 773/2401*T^31 + 3404/2401*T^30 + 
        61/2401*T^29 - 2266/2401*T^28 + 61/2401*T^27 + 3404/2401*T^26 - 
        773/2401*T^25 - 2533/2401*T^24 + 1289/2401*T^23 + 1776/2401*T^22 - 
        897/2401*T^21 - 2085/2401*T^20 + 1026/2401*T^19 + 2153/2401*T^18 - 
        33/49*T^17 - 1775/2401*T^16 + 250/343*T^15 + 1824/2401*T^14 - 2266/2401*T^13
        - 377/2401*T^12 + 184/2401*T^11 + 2031/2401*T^10 - 2266/2401*T^9 - 
        139/2401*T^8 - 121/2401*T^7 + 2193/2401*T^6 - 3442/2401*T^5 + 1096/2401*T^4 
        + 29/49*T^3 + 9/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 4*X*Y^12 + 4*X*Y^11 + X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 
        4*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 4*X*Y^3 + 4*X*Y^2 + 4*X + 3*Y^30 + Y^29 + 
        3*Y^28 + 4*Y^26 + 2*Y^25 + 2*Y^24 + 3*Y^23 + 5*Y^22 + 4*Y^21 + 4*Y^20 + Y^19
        + 3*Y^18 + 3*Y^16 + 2*Y^15 + 3*Y^14 + 6*Y^12 + 4*Y^11 + 6*Y^10 + Y^9 + 4*Y^7
        + 6*Y^6 + 6*Y^5 + 6*Y^4 + 4*Y^3 + 4*Y + 6,
    -T^56 + 16/7*T^55 - 65/49*T^54 - 274/343*T^53 + 2727/2401*T^52 + 901/2401*T^51 -
        4945/2401*T^50 + 5297/2401*T^49 - 6/343*T^48 - 825/343*T^47 + 4715/2401*T^46
        + 2003/2401*T^45 - 5683/2401*T^44 + 402/343*T^43 + 2615/2401*T^42 - 
        5524/2401*T^41 + 2824/2401*T^40 + 2763/2401*T^39 - 4182/2401*T^38 + 
        624/2401*T^37 + 2901/2401*T^36 - 4360/2401*T^35 + 2634/2401*T^34 + 
        1774/2401*T^33 - 2530/2401*T^32 - 1516/2401*T^31 + 3670/2401*T^30 - 
        2236/2401*T^29 + 2236/2401*T^27 - 3670/2401*T^26 + 1516/2401*T^25 + 
        2530/2401*T^24 - 1774/2401*T^23 - 2634/2401*T^22 + 4360/2401*T^21 - 
        2901/2401*T^20 - 624/2401*T^19 + 4182/2401*T^18 - 2763/2401*T^17 - 
        2824/2401*T^16 + 5524/2401*T^15 - 2615/2401*T^14 - 402/343*T^13 + 
        5683/2401*T^12 - 2003/2401*T^11 - 4715/2401*T^10 + 825/343*T^9 + 6/343*T^8 -
        5297/2401*T^7 + 4945/2401*T^6 - 901/2401*T^5 - 2727/2401*T^4 + 274/343*T^3 +
        65/49*T^2 - 16/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 6*X*Y^9 + X*Y^8 + 
        3*X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 6*X*Y + X + 
        2*Y^30 + 4*Y^29 + 3*Y^28 + 6*Y^27 + 5*Y^26 + 6*Y^25 + 3*Y^24 + 6*Y^23 + 
        4*Y^22 + 3*Y^21 + 4*Y^19 + 3*Y^18 + 2*Y^17 + 5*Y^16 + 2*Y^15 + 3*Y^14 + 
        4*Y^13 + Y^12 + 4*Y^11 + 2*Y^10 + 4*Y^9 + 6*Y^7 + 4*Y^6 + 3*Y^5 + 4*Y^4 + 
        6*Y^3 + 2*Y^2 + 2*Y + 4,
    -T^56 + 19/7*T^55 - 166/49*T^54 + 831/343*T^53 - 58/49*T^52 + 41/49*T^51 - 
        412/343*T^50 + 2799/2401*T^49 - 1908/2401*T^48 + 2200/2401*T^47 - 
        3807/2401*T^46 + 4873/2401*T^45 - 5296/2401*T^44 + 5091/2401*T^43 - 
        4337/2401*T^42 + 2160/2401*T^41 + 418/2401*T^40 - 1054/2401*T^39 + 
        760/2401*T^38 - 306/343*T^37 + 4525/2401*T^36 - 4632/2401*T^35 + 
        851/2401*T^34 + 3075/2401*T^33 - 3114/2401*T^32 + 25/49*T^31 - 100/343*T^30 
        + 99/343*T^29 - 99/343*T^27 + 100/343*T^26 - 25/49*T^25 + 3114/2401*T^24 - 
        3075/2401*T^23 - 851/2401*T^22 + 4632/2401*T^21 - 4525/2401*T^20 + 
        306/343*T^19 - 760/2401*T^18 + 1054/2401*T^17 - 418/2401*T^16 - 
        2160/2401*T^15 + 4337/2401*T^14 - 5091/2401*T^13 + 5296/2401*T^12 - 
        4873/2401*T^11 + 3807/2401*T^10 - 2200/2401*T^9 + 1908/2401*T^8 - 
        2799/2401*T^7 + 412/343*T^6 - 41/49*T^5 + 58/49*T^4 - 831/343*T^3 + 
        166/49*T^2 - 19/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^13 + 6*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 2*X*Y^8 + 5*X*Y^7 + 
        5*X*Y^6 + X*Y^5 + 2*X*Y^3 + 4*X*Y^2 + 2*X*Y + 6*X + Y^30 + 5*Y^29 + 6*Y^27 +
        6*Y^26 + 6*Y^25 + 3*Y^24 + 2*Y^23 + 4*Y^22 + 5*Y^21 + Y^20 + 2*Y^19 + Y^18 +
        Y^16 + 6*Y^15 + 4*Y^14 + 5*Y^12 + 4*Y^11 + 3*Y^9 + 4*Y^8 + 3*Y^7 + Y^6 + 
        4*Y^5 + 5*Y^4 + 3*Y^2 + 3*Y,
    -T^56 + 16/7*T^55 - 73/49*T^54 - 395/343*T^53 + 7781/2401*T^52 - 6655/2401*T^51 
        + 258/2401*T^50 + 101/49*T^49 - 5226/2401*T^48 + 1557/2401*T^47 + 
        2437/2401*T^46 - 3921/2401*T^45 + 592/343*T^44 - 2846/2401*T^43 - 
        1513/2401*T^42 + 6667/2401*T^41 - 7124/2401*T^40 + 823/2401*T^39 + 
        6400/2401*T^38 - 8244/2401*T^37 + 4371/2401*T^36 + 2481/2401*T^35 - 
        7927/2401*T^34 + 8136/2401*T^33 - 535/343*T^32 - 2725/2401*T^31 + 
        7194/2401*T^30 - 5911/2401*T^29 + 5911/2401*T^27 - 7194/2401*T^26 + 
        2725/2401*T^25 + 535/343*T^24 - 8136/2401*T^23 + 7927/2401*T^22 - 
        2481/2401*T^21 - 4371/2401*T^20 + 8244/2401*T^19 - 6400/2401*T^18 - 
        823/2401*T^17 + 7124/2401*T^16 - 6667/2401*T^15 + 1513/2401*T^14 + 
        2846/2401*T^13 - 592/343*T^12 + 3921/2401*T^11 - 2437/2401*T^10 - 
        1557/2401*T^9 + 5226/2401*T^8 - 101/49*T^7 - 258/2401*T^6 + 6655/2401*T^5 - 
        7781/2401*T^4 + 395/343*T^3 + 73/49*T^2 - 16/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 2*X*Y^10 + 4*X*Y^9 + 3*X*Y^8 + 5*X*Y^7 + 
        3*X*Y^6 + 5*X*Y^4 + 2*X*Y^3 + X*Y^2 + 6*X*Y + 6*X + Y^30 + 6*Y^29 + 6*Y^26 +
        2*Y^25 + 6*Y^24 + Y^23 + 4*Y^22 + 6*Y^21 + 2*Y^20 + 2*Y^19 + 6*Y^18 + Y^17 +
        5*Y^16 + 2*Y^15 + 2*Y^14 + 5*Y^13 + 2*Y^11 + 6*Y^10 + 3*Y^9 + 6*Y^8 + 3*Y^7 
        + 5*Y^6 + 2*Y^5 + 5*Y^4 + 5*Y^3 + 6*Y^2 + 6,
    T^56 + 5/7*T^55 + 12/49*T^54 + 255/343*T^53 + 2617/2401*T^52 + 1669/2401*T^51 - 
        556/2401*T^50 + 643/2401*T^49 + 930/2401*T^48 - 1567/2401*T^47 - 
        307/343*T^46 - 1123/2401*T^45 - 942/2401*T^44 - 2073/2401*T^43 - 
        2832/2401*T^42 - 1544/2401*T^41 + 68/2401*T^40 - 1749/2401*T^39 - 
        2656/2401*T^38 - 1465/2401*T^37 - 150/2401*T^36 - 373/2401*T^35 - 
        2521/2401*T^34 - 44/343*T^33 + 2677/2401*T^32 + 2041/2401*T^31 + 
        419/2401*T^30 + 2325/2401*T^29 + 4789/2401*T^28 + 2325/2401*T^27 + 
        419/2401*T^26 + 2041/2401*T^25 + 2677/2401*T^24 - 44/343*T^23 - 
        2521/2401*T^22 - 373/2401*T^21 - 150/2401*T^20 - 1465/2401*T^19 - 
        2656/2401*T^18 - 1749/2401*T^17 + 68/2401*T^16 - 1544/2401*T^15 - 
        2832/2401*T^14 - 2073/2401*T^13 - 942/2401*T^12 - 1123/2401*T^11 - 
        307/343*T^10 - 1567/2401*T^9 + 930/2401*T^8 + 643/2401*T^7 - 556/2401*T^6 + 
        1669/2401*T^5 + 2617/2401*T^4 + 255/343*T^3 + 12/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + X*Y^10 + X*Y^9 + 
        X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 4*X*Y + X + 3*Y^30
        + 3*Y^29 + 4*Y^28 + 6*Y^27 + 6*Y^26 + 5*Y^24 + 4*Y^23 + 3*Y^22 + 6*Y^21 + 
        2*Y^20 + 6*Y^19 + 6*Y^17 + 5*Y^16 + 3*Y^14 + Y^13 + Y^12 + 5*Y^11 + 2*Y^10 +
        3*Y^8 + 3*Y^6 + 3*Y^5 + 2*Y^4 + 3*Y^3 + 5*Y^2 + 6*Y + 1,
    T^56 - 20/7*T^55 + 171/49*T^54 - 880/343*T^53 + 1780/2401*T^52 + 3861/2401*T^51 
        - 7485/2401*T^50 + 8126/2401*T^49 - 6725/2401*T^48 + 3055/2401*T^47 + 
        503/2401*T^46 - 919/2401*T^45 - 213/343*T^44 + 4954/2401*T^43 - 922/343*T^42
        + 3863/2401*T^41 + 1188/2401*T^40 - 6563/2401*T^39 + 11108/2401*T^38 - 
        12941/2401*T^37 + 10527/2401*T^36 - 5077/2401*T^35 - 523/2401*T^34 + 
        4663/2401*T^33 - 6732/2401*T^32 + 6292/2401*T^31 - 4463/2401*T^30 + 
        3155/2401*T^29 - 2824/2401*T^28 + 3155/2401*T^27 - 4463/2401*T^26 + 
        6292/2401*T^25 - 6732/2401*T^24 + 4663/2401*T^23 - 523/2401*T^22 - 
        5077/2401*T^21 + 10527/2401*T^20 - 12941/2401*T^19 + 11108/2401*T^18 - 
        6563/2401*T^17 + 1188/2401*T^16 + 3863/2401*T^15 - 922/343*T^14 + 
        4954/2401*T^13 - 213/343*T^12 - 919/2401*T^11 + 503/2401*T^10 + 
        3055/2401*T^9 - 6725/2401*T^8 + 8126/2401*T^7 - 7485/2401*T^6 + 
        3861/2401*T^5 + 1780/2401*T^4 - 880/343*T^3 + 171/49*T^2 - 20/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 3*X*Y^10 + 3*X*Y^8 + 2*X*Y^6 + 2*X*Y^5 + 
        6*X*Y^4 + X*Y^3 + X*Y^2 + 4*X*Y + 2*X + 2*Y^30 + 2*Y^29 + 4*Y^28 + 2*Y^27 + 
        2*Y^26 + 3*Y^25 + 6*Y^24 + Y^23 + Y^22 + 6*Y^20 + Y^18 + 6*Y^17 + Y^16 + 
        5*Y^14 + 4*Y^13 + Y^12 + 3*Y^11 + 6*Y^10 + 2*Y^9 + 2*Y^8 + 4*Y^7 + 4*Y^6 + 
        2*Y^5 + 3*Y^4 + 5*Y^3 + 6*Y^2 + Y,
    -T^56 - 6/7*T^55 + 8/7*T^54 + 249/343*T^53 - 1670/2401*T^52 - 187/343*T^51 - 
        939/2401*T^50 - 445/2401*T^49 - 425/2401*T^48 - 60/2401*T^47 + 873/2401*T^46
        - 1737/2401*T^45 - 3953/2401*T^44 - 1431/2401*T^43 + 2510/2401*T^42 + 
        2866/2401*T^41 - 1612/2401*T^40 - 3632/2401*T^39 - 1632/2401*T^38 - 
        1033/2401*T^37 + 1031/2401*T^36 + 358/343*T^35 - 83/343*T^34 - 
        2768/2401*T^33 - 3229/2401*T^32 - 722/2401*T^31 + 3448/2401*T^30 + 
        3043/2401*T^29 - 3043/2401*T^27 - 3448/2401*T^26 + 722/2401*T^25 + 
        3229/2401*T^24 + 2768/2401*T^23 + 83/343*T^22 - 358/343*T^21 - 
        1031/2401*T^20 + 1033/2401*T^19 + 1632/2401*T^18 + 3632/2401*T^17 + 
        1612/2401*T^16 - 2866/2401*T^15 - 2510/2401*T^14 + 1431/2401*T^13 + 
        3953/2401*T^12 + 1737/2401*T^11 - 873/2401*T^10 + 60/2401*T^9 + 425/2401*T^8
        + 445/2401*T^7 + 939/2401*T^6 + 187/343*T^5 + 1670/2401*T^4 - 249/343*T^3 - 
        8/7*T^2 + 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 
        3*X*Y^8 + 4*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + X*Y^2 + X*Y + 
        6*Y^30 + 3*Y^29 + 5*Y^28 + 4*Y^27 + 5*Y^26 + 6*Y^24 + Y^23 + Y^22 + 6*Y^21 +
        5*Y^19 + Y^18 + 6*Y^15 + 6*Y^14 + 5*Y^13 + Y^12 + 6*Y^11 + 5*Y^10 + 2*Y^9 + 
        6*Y^7 + 6*Y^6 + Y^3 + 6*Y^2 + 5*Y + 5,
    -T^56 + 10/49*T^54 + 48/49*T^53 + 33/2401*T^52 - 2974/2401*T^51 - 661/2401*T^50 
        - 975/2401*T^49 + 1832/2401*T^48 + 1630/2401*T^47 - 1164/2401*T^46 + 
        488/2401*T^45 - 1965/2401*T^44 + 300/2401*T^43 + 688/2401*T^42 - 65/343*T^41
        + 3033/2401*T^40 - 296/2401*T^39 - 494/2401*T^38 - 638/2401*T^37 - 
        1318/2401*T^36 + 381/343*T^35 + 480/2401*T^34 + 822/2401*T^33 + 86/343*T^32 
        - 1804/2401*T^31 + 901/2401*T^30 - 1090/2401*T^29 + 1090/2401*T^27 - 
        901/2401*T^26 + 1804/2401*T^25 - 86/343*T^24 - 822/2401*T^23 - 480/2401*T^22
        - 381/343*T^21 + 1318/2401*T^20 + 638/2401*T^19 + 494/2401*T^18 + 
        296/2401*T^17 - 3033/2401*T^16 + 65/343*T^15 - 688/2401*T^14 - 300/2401*T^13
        + 1965/2401*T^12 - 488/2401*T^11 + 1164/2401*T^10 - 1630/2401*T^9 - 
        1832/2401*T^8 + 975/2401*T^7 + 661/2401*T^6 + 2974/2401*T^5 - 33/2401*T^4 - 
        48/49*T^3 - 10/49*T^2 + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 6*X*Y^9 + 6*X*Y^7 + 
        X*Y^6 + 2*X*Y^5 + X*Y^4 + X*Y + 5*Y^30 + 2*Y^29 + 2*Y^28 + 6*Y^27 + 3*Y^26 +
        5*Y^24 + 4*Y^23 + 5*Y^22 + 2*Y^21 + 5*Y^20 + 6*Y^19 + 5*Y^18 + 2*Y^17 + 
        3*Y^16 + 2*Y^15 + 5*Y^14 + 4*Y^13 + 6*Y^12 + Y^11 + 2*Y^10 + 3*Y^9 + Y^8 + 
        Y^7 + 3*Y^5 + Y^3 + Y^2 + 6*Y + 5,
    -T^56 - 8/7*T^55 - 19/49*T^54 - 64/343*T^53 - 981/2401*T^52 + 79/343*T^51 + 
        1826/2401*T^50 - 24/2401*T^49 - 965/2401*T^48 + 1030/2401*T^47 + 
        710/2401*T^46 - 223/2401*T^45 + 682/2401*T^44 + 1055/2401*T^43 - 
        1423/2401*T^42 - 2466/2401*T^41 - 331/2401*T^40 - 766/2401*T^39 - 
        276/343*T^38 - 104/2401*T^37 + 1356/2401*T^36 + 345/2401*T^35 - 
        104/2401*T^34 + 1675/2401*T^33 + 2094/2401*T^32 + 1129/2401*T^31 + 
        1573/2401*T^30 + 1786/2401*T^29 - 1786/2401*T^27 - 1573/2401*T^26 - 
        1129/2401*T^25 - 2094/2401*T^24 - 1675/2401*T^23 + 104/2401*T^22 - 
        345/2401*T^21 - 1356/2401*T^20 + 104/2401*T^19 + 276/343*T^18 + 
        766/2401*T^17 + 331/2401*T^16 + 2466/2401*T^15 + 1423/2401*T^14 - 
        1055/2401*T^13 - 682/2401*T^12 + 223/2401*T^11 - 710/2401*T^10 - 
        1030/2401*T^9 + 965/2401*T^8 + 24/2401*T^7 - 1826/2401*T^6 - 79/343*T^5 + 
        981/2401*T^4 + 64/343*T^3 + 19/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 
        2*X*Y^8 + 6*X*Y^7 + 6*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 2*X*Y + X + 
        4*Y^30 + 6*Y^29 + 3*Y^28 + 5*Y^27 + 4*Y^25 + 6*Y^24 + 2*Y^23 + 3*Y^22 + 
        6*Y^21 + Y^20 + 2*Y^18 + 2*Y^17 + 3*Y^16 + 2*Y^14 + 4*Y^13 + 2*Y^12 + Y^11 +
        Y^10 + 6*Y^9 + 3*Y^8 + 4*Y^7 + 6*Y^6 + 2*Y^5 + 4*Y^4 + 6*Y^3 + Y^2 + Y,
    T^56 + 15/7*T^55 + 83/49*T^54 + 135/343*T^53 - 416/2401*T^52 - 628/2401*T^51 - 
        3376/2401*T^50 - 768/343*T^49 - 3373/2401*T^48 - 897/2401*T^47 - 
        104/343*T^46 + 150/2401*T^45 + 3763/2401*T^44 + 5907/2401*T^43 + 
        4940/2401*T^42 + 601/343*T^41 + 5295/2401*T^40 + 4133/2401*T^39 - 
        1560/2401*T^38 - 6955/2401*T^37 - 8097/2401*T^36 - 7996/2401*T^35 - 
        1187/343*T^34 - 904/343*T^33 - 1735/2401*T^32 + 1320/2401*T^31 + 
        3040/2401*T^30 + 6317/2401*T^29 + 8289/2401*T^28 + 6317/2401*T^27 + 
        3040/2401*T^26 + 1320/2401*T^25 - 1735/2401*T^24 - 904/343*T^23 - 
        1187/343*T^22 - 7996/2401*T^21 - 8097/2401*T^20 - 6955/2401*T^19 - 
        1560/2401*T^18 + 4133/2401*T^17 + 5295/2401*T^16 + 601/343*T^15 + 
        4940/2401*T^14 + 5907/2401*T^13 + 3763/2401*T^12 + 150/2401*T^11 - 
        104/343*T^10 - 897/2401*T^9 - 3373/2401*T^8 - 768/343*T^7 - 3376/2401*T^6 - 
        628/2401*T^5 - 416/2401*T^4 + 135/343*T^3 + 83/49*T^2 + 15/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 6*X*Y^8 + 
        5*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 2*X*Y^2 + X*Y + 5*Y^30 + 4*Y^29 + 
        5*Y^27 + 4*Y^24 + 2*Y^22 + Y^21 + 4*Y^19 + 5*Y^18 + 6*Y^17 + 3*Y^16 + 3*Y^15
        + 5*Y^14 + 2*Y^13 + 4*Y^12 + 6*Y^11 + 2*Y^10 + Y^9 + 2*Y^8 + 3*Y^7 + Y^6 + 
        3*Y^5 + 6*Y^4 + 5*Y^3 + 4*Y^2 + 4*Y + 1,
    T^56 - 12/7*T^54 - 33/343*T^53 + 2027/2401*T^52 - 694/2401*T^51 - 1/49*T^50 + 
        1691/2401*T^49 + 1677/2401*T^48 - 373/2401*T^47 - 2678/2401*T^46 + 
        116/2401*T^45 + 271/343*T^44 - 2652/2401*T^43 - 19/49*T^42 + 3834/2401*T^41 
        - 15/2401*T^40 - 2613/2401*T^39 + 221/2401*T^38 + 1312/2401*T^37 + 
        965/2401*T^36 - 531/2401*T^35 - 1059/2401*T^34 + 1325/2401*T^33 - 
        1063/2401*T^32 - 2158/2401*T^31 + 2568/2401*T^30 + 1198/2401*T^29 - 
        58/49*T^28 + 1198/2401*T^27 + 2568/2401*T^26 - 2158/2401*T^25 - 
        1063/2401*T^24 + 1325/2401*T^23 - 1059/2401*T^22 - 531/2401*T^21 + 
        965/2401*T^20 + 1312/2401*T^19 + 221/2401*T^18 - 2613/2401*T^17 - 
        15/2401*T^16 + 3834/2401*T^15 - 19/49*T^14 - 2652/2401*T^13 + 271/343*T^12 +
        116/2401*T^11 - 2678/2401*T^10 - 373/2401*T^9 + 1677/2401*T^8 + 
        1691/2401*T^7 - 1/49*T^6 - 694/2401*T^5 + 2027/2401*T^4 - 33/343*T^3 - 
        12/7*T^2 + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 4*X*Y^11 + 4*X*Y^10 + X*Y^9 + 5*X*Y^7 + 6*X*Y^6 + 
        3*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 3*X*Y + 6*X + 5*Y^30 + 5*Y^29 + Y^28 + 5*Y^27 
        + 3*Y^26 + 5*Y^25 + 4*Y^24 + 3*Y^23 + 2*Y^21 + 4*Y^18 + 2*Y^17 + 6*Y^16 + 
        6*Y^15 + Y^14 + 5*Y^13 + 2*Y^12 + 6*Y^11 + 4*Y^10 + Y^9 + 3*Y^8 + 4*Y^7 + 
        3*Y^6 + 5*Y^5 + 6*Y^4 + 5*Y^2 + 4*Y + 3,
    -T^56 - 10/7*T^55 - 9/49*T^54 + 80/343*T^53 - 1898/2401*T^52 - 2235/2401*T^51 - 
        2175/2401*T^50 - 2435/2401*T^49 + 1041/2401*T^48 + 3006/2401*T^47 - 
        190/2401*T^46 - 2770/2401*T^45 - 823/2401*T^44 + 928/2401*T^43 + 
        149/2401*T^42 - 37/2401*T^41 - 232/2401*T^40 - 2126/2401*T^39 - 
        1557/2401*T^38 + 1394/2401*T^37 + 1140/2401*T^36 + 50/2401*T^35 + 
        1023/2401*T^34 + 232/2401*T^33 - 493/2401*T^32 + 666/2401*T^31 + 
        1619/2401*T^30 + 888/2401*T^29 - 888/2401*T^27 - 1619/2401*T^26 - 
        666/2401*T^25 + 493/2401*T^24 - 232/2401*T^23 - 1023/2401*T^22 - 
        50/2401*T^21 - 1140/2401*T^20 - 1394/2401*T^19 + 1557/2401*T^18 + 
        2126/2401*T^17 + 232/2401*T^16 + 37/2401*T^15 - 149/2401*T^14 - 
        928/2401*T^13 + 823/2401*T^12 + 2770/2401*T^11 + 190/2401*T^10 - 
        3006/2401*T^9 - 1041/2401*T^8 + 2435/2401*T^7 + 2175/2401*T^6 + 
        2235/2401*T^5 + 1898/2401*T^4 - 80/343*T^3 + 9/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 3*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 5*X*Y^7 + 
        X*Y^6 + X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 4*X*Y + 6*X + Y^30 + 5*Y^29 + 
        3*Y^27 + Y^26 + 5*Y^25 + 5*Y^24 + 2*Y^23 + Y^22 + 6*Y^21 + 6*Y^20 + 6*Y^19 +
        3*Y^18 + 3*Y^17 + 3*Y^16 + 4*Y^15 + 2*Y^14 + 3*Y^13 + 5*Y^12 + 6*Y^11 + 
        3*Y^10 + 2*Y^9 + 6*Y^8 + 4*Y^7 + 3*Y^6 + 3*Y^5 + 4*Y^4 + 5*Y^3 + Y^2 + 3*Y +
        5,
    T^56 + 1/7*T^55 + 19/49*T^54 - 207/343*T^53 + 765/2401*T^52 - 2022/2401*T^51 + 
        1607/2401*T^50 - 775/2401*T^49 + 1314/2401*T^48 - 64/2401*T^47 + 
        1038/2401*T^46 - 856/2401*T^45 - 1271/2401*T^44 + 303/2401*T^43 - 
        1153/2401*T^42 + 1342/2401*T^41 - 1056/2401*T^40 + 2542/2401*T^39 - 
        1872/2401*T^38 + 772/2401*T^37 - 2148/2401*T^36 + 67/2401*T^35 - 
        1247/2401*T^34 + 1399/2401*T^33 + 1017/2401*T^32 + 152/2401*T^31 + 
        1016/2401*T^30 - 962/2401*T^29 - 904/2401*T^28 - 962/2401*T^27 + 
        1016/2401*T^26 + 152/2401*T^25 + 1017/2401*T^24 + 1399/2401*T^23 - 
        1247/2401*T^22 + 67/2401*T^21 - 2148/2401*T^20 + 772/2401*T^19 - 
        1872/2401*T^18 + 2542/2401*T^17 - 1056/2401*T^16 + 1342/2401*T^15 - 
        1153/2401*T^14 + 303/2401*T^13 - 1271/2401*T^12 - 856/2401*T^11 + 
        1038/2401*T^10 - 64/2401*T^9 + 1314/2401*T^8 - 775/2401*T^7 + 1607/2401*T^6 
        - 2022/2401*T^5 + 765/2401*T^4 - 207/343*T^3 + 19/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 + X*Y^7 + 
        5*X*Y^6 + X*Y^5 + 4*X*Y^4 + X*Y^3 + 2*X*Y^2 + Y^30 + 6*Y^29 + 4*Y^27 + 
        6*Y^26 + 2*Y^25 + 5*Y^23 + 4*Y^22 + 3*Y^21 + 2*Y^19 + Y^18 + 3*Y^17 + Y^16 +
        5*Y^14 + Y^13 + 6*Y^12 + 2*Y^11 + 5*Y^9 + 6*Y^8 + Y^7 + 5*Y^6 + 4*Y^5 + 
        6*Y^3 + 6*Y^2 + 4*Y + 2,
    T^56 - 8/7*T^55 - 8/49*T^54 - 254/343*T^53 + 2935/2401*T^52 + 1983/2401*T^51 - 
        107/343*T^50 - 354/343*T^49 - 2144/2401*T^48 + 1016/2401*T^47 + 
        3909/2401*T^46 + 1145/2401*T^45 + 165/2401*T^44 - 6532/2401*T^43 - 
        1184/2401*T^42 + 2921/2401*T^41 + 635/343*T^40 + 1879/2401*T^39 - 
        4622/2401*T^38 - 3403/2401*T^37 + 45/343*T^36 + 2237/2401*T^35 + 
        3662/2401*T^34 - 1304/2401*T^33 - 57/343*T^32 - 3905/2401*T^31 - 
        187/2401*T^30 + 1457/2401*T^29 + 2703/2401*T^28 + 1457/2401*T^27 - 
        187/2401*T^26 - 3905/2401*T^25 - 57/343*T^24 - 1304/2401*T^23 + 
        3662/2401*T^22 + 2237/2401*T^21 + 45/343*T^20 - 3403/2401*T^19 - 
        4622/2401*T^18 + 1879/2401*T^17 + 635/343*T^16 + 2921/2401*T^15 - 
        1184/2401*T^14 - 6532/2401*T^13 + 165/2401*T^12 + 1145/2401*T^11 + 
        3909/2401*T^10 + 1016/2401*T^9 - 2144/2401*T^8 - 354/343*T^7 - 107/343*T^6 +
        1983/2401*T^5 + 2935/2401*T^4 - 254/343*T^3 - 8/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 2*X*Y^9 + 6*X*Y^8 + 2*X*Y^7 + 
        4*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + X*Y^3 + 2*X*Y^2 + 4*X*Y + 3*Y^30 + Y^28 + 
        4*Y^27 + 6*Y^25 + 5*Y^24 + 6*Y^23 + 2*Y^22 + 5*Y^21 + Y^20 + 6*Y^19 + Y^18 +
        3*Y^16 + 2*Y^14 + 5*Y^13 + 5*Y^12 + 4*Y^11 + Y^10 + 5*Y^9 + 6*Y^8 + 5*Y^7 + 
        4*Y^6 + 3*Y^5 + 4*Y^4 + 3*Y^3 + 3*Y^2 + 4*Y + 6,
    -T^56 + 3/7*T^55 + 8/49*T^54 - 351/343*T^53 + 265/2401*T^52 + 290/343*T^51 - 
        1065/2401*T^50 + 39/2401*T^49 + 1445/2401*T^48 + 57/2401*T^47 + 
        256/2401*T^46 - 254/2401*T^45 - 430/2401*T^44 - 102/343*T^43 + 689/2401*T^42
        - 304/343*T^41 - 1049/2401*T^40 + 1844/2401*T^39 - 930/2401*T^38 - 
        1403/2401*T^37 + 1863/2401*T^36 + 732/2401*T^35 - 475/2401*T^34 + 
        283/2401*T^33 + 219/2401*T^32 + 1/7*T^31 - 345/2401*T^30 + 157/2401*T^29 - 
        157/2401*T^27 + 345/2401*T^26 - 1/7*T^25 - 219/2401*T^24 - 283/2401*T^23 + 
        475/2401*T^22 - 732/2401*T^21 - 1863/2401*T^20 + 1403/2401*T^19 + 
        930/2401*T^18 - 1844/2401*T^17 + 1049/2401*T^16 + 304/343*T^15 - 
        689/2401*T^14 + 102/343*T^13 + 430/2401*T^12 + 254/2401*T^11 - 256/2401*T^10
        - 57/2401*T^9 - 1445/2401*T^8 - 39/2401*T^7 + 1065/2401*T^6 - 290/343*T^5 - 
        265/2401*T^4 + 351/343*T^3 - 8/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        5*X*Y^6 + 6*X*Y^5 + 2*X*Y^3 + 2*X*Y^2 + 5*X*Y + 5*X + 4*Y^30 + 3*Y^27 + 
        5*Y^26 + 5*Y^25 + 2*Y^24 + 6*Y^22 + 2*Y^19 + 4*Y^18 + 2*Y^17 + 6*Y^16 + 
        3*Y^15 + 4*Y^14 + 4*Y^13 + 4*Y^12 + 4*Y^11 + 2*Y^10 + Y^9 + 6*Y^8 + 6*Y^7 + 
        4*Y^6 + 6*Y^5 + 6*Y^4 + 4*Y^3 + 3*Y^2 + 4*Y + 5,
    T^56 + 3*T^55 + 240/49*T^54 + 40/7*T^53 + 11114/2401*T^52 + 787/343*T^51 - 
        2076/2401*T^50 - 10706/2401*T^49 - 18227/2401*T^48 - 21778/2401*T^47 - 
        20488/2401*T^46 - 15429/2401*T^45 - 7986/2401*T^44 + 457/2401*T^43 + 
        10022/2401*T^42 + 17893/2401*T^41 + 21986/2401*T^40 + 2994/343*T^39 + 
        14622/2401*T^38 + 5175/2401*T^37 - 5610/2401*T^36 - 14330/2401*T^35 - 
        18500/2401*T^34 - 17083/2401*T^33 - 11171/2401*T^32 - 2451/2401*T^31 + 
        6147/2401*T^30 + 11978/2401*T^29 + 14269/2401*T^28 + 11978/2401*T^27 + 
        6147/2401*T^26 - 2451/2401*T^25 - 11171/2401*T^24 - 17083/2401*T^23 - 
        18500/2401*T^22 - 14330/2401*T^21 - 5610/2401*T^20 + 5175/2401*T^19 + 
        14622/2401*T^18 + 2994/343*T^17 + 21986/2401*T^16 + 17893/2401*T^15 + 
        10022/2401*T^14 + 457/2401*T^13 - 7986/2401*T^12 - 15429/2401*T^11 - 
        20488/2401*T^10 - 21778/2401*T^9 - 18227/2401*T^8 - 10706/2401*T^7 - 
        2076/2401*T^6 + 787/343*T^5 + 11114/2401*T^4 + 40/7*T^3 + 240/49*T^2 + 3*T +
        1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + X*Y^10 + 4*X*Y^9 + 
        4*X*Y^8 + 2*X*Y^7 + 2*X*Y^6 + 2*X*Y^4 + 6*X*Y^2 + 4*X*Y + 2*X + 2*Y^30 + 
        2*Y^29 + 2*Y^28 + 4*Y^27 + 2*Y^26 + 4*Y^25 + Y^23 + 2*Y^22 + Y^21 + 3*Y^18 +
        5*Y^17 + 3*Y^16 + 5*Y^15 + Y^14 + 6*Y^13 + 4*Y^12 + 2*Y^11 + Y^10 + 4*Y^9 + 
        6*Y^8 + 5*Y^7 + 4*Y^6 + 3*Y^5 + 2*Y^4 + 2*Y^3 + 4*Y^2 + 6*Y + 4,
    -T^56 + 12/7*T^55 - 33/49*T^54 - 30/49*T^53 + 13/49*T^52 + 1037/2401*T^51 + 
        867/2401*T^50 - 1894/2401*T^49 - 382/2401*T^48 + 1898/2401*T^47 - 
        114/343*T^46 + 68/2401*T^45 - 1441/2401*T^44 + 1483/2401*T^43 + 
        977/2401*T^42 - 2319/2401*T^41 + 81/343*T^40 + 752/2401*T^39 + 953/2401*T^38
        - 741/2401*T^37 - 2031/2401*T^36 + 2304/2401*T^35 + 871/2401*T^34 - 
        2287/2401*T^33 + 1122/2401*T^32 - 667/2401*T^31 + 1065/2401*T^30 - 
        894/2401*T^29 + 894/2401*T^27 - 1065/2401*T^26 + 667/2401*T^25 - 
        1122/2401*T^24 + 2287/2401*T^23 - 871/2401*T^22 - 2304/2401*T^21 + 
        2031/2401*T^20 + 741/2401*T^19 - 953/2401*T^18 - 752/2401*T^17 - 81/343*T^16
        + 2319/2401*T^15 - 977/2401*T^14 - 1483/2401*T^13 + 1441/2401*T^12 - 
        68/2401*T^11 + 114/343*T^10 - 1898/2401*T^9 + 382/2401*T^8 + 1894/2401*T^7 -
        867/2401*T^6 - 1037/2401*T^5 - 13/49*T^4 + 30/49*T^3 + 33/49*T^2 - 12/7*T + 
        1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + 6*X*Y^8 
        + X*Y^6 + X*Y^4 + X*Y^3 + 2*X*Y^2 + 6*X + 2*Y^30 + 5*Y^29 + 4*Y^28 + 4*Y^27 
        + 5*Y^26 + 2*Y^25 + 2*Y^24 + 4*Y^23 + 5*Y^22 + 3*Y^21 + 4*Y^20 + 4*Y^19 + 
        6*Y^18 + Y^17 + 2*Y^15 + 2*Y^14 + 5*Y^13 + 2*Y^12 + Y^11 + 4*Y^10 + Y^9 + 
        3*Y^8 + 5*Y^6 + 6*Y^5 + 5*Y^4 + 4*Y^3 + 2*Y^2 + 5*Y + 6,
    -T^56 + 3/7*T^55 + 8/7*T^54 - 185/343*T^53 + 877/2401*T^52 + 1863/2401*T^51 - 
        1832/2401*T^50 - 1384/2401*T^49 + 1072/2401*T^48 - 1284/2401*T^47 - 
        2945/2401*T^46 + 1697/2401*T^45 + 2697/2401*T^44 - 439/2401*T^43 + 
        351/2401*T^42 + 1795/2401*T^41 - 530/2401*T^40 - 468/343*T^39 + 
        345/2401*T^38 + 340/2401*T^37 - 1901/2401*T^36 + 141/2401*T^35 + 
        3475/2401*T^34 + 47/2401*T^33 - 1616/2401*T^32 + 1783/2401*T^31 + 
        13/2401*T^30 - 1945/2401*T^29 + 1945/2401*T^27 - 13/2401*T^26 - 
        1783/2401*T^25 + 1616/2401*T^24 - 47/2401*T^23 - 3475/2401*T^22 - 
        141/2401*T^21 + 1901/2401*T^20 - 340/2401*T^19 - 345/2401*T^18 + 
        468/343*T^17 + 530/2401*T^16 - 1795/2401*T^15 - 351/2401*T^14 + 
        439/2401*T^13 - 2697/2401*T^12 - 1697/2401*T^11 + 2945/2401*T^10 + 
        1284/2401*T^9 - 1072/2401*T^8 + 1384/2401*T^7 + 1832/2401*T^6 - 
        1863/2401*T^5 - 877/2401*T^4 + 185/343*T^3 - 8/7*T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 2*X*Y^8 + 2*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + 
        4*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 6*X*Y + 6*X + Y^30 + 3*Y^28 + 4*Y^27 + Y^26 + 
        2*Y^25 + 5*Y^24 + Y^23 + 5*Y^22 + 3*Y^21 + 4*Y^20 + 3*Y^19 + 5*Y^18 + 4*Y^15
        + 6*Y^13 + 5*Y^12 + 3*Y^10 + 5*Y^9 + 3*Y^7 + 6*Y^6 + 5*Y^5 + 4*Y^4 + Y^3 + 
        2*Y + 1,
    -T^56 + T^55 - 6/7*T^54 - 45/343*T^53 + 716/2401*T^52 + 523/2401*T^51 + 
        985/2401*T^50 - 596/2401*T^49 + 4062/2401*T^48 - 1996/2401*T^47 + 
        2603/2401*T^46 - 1935/2401*T^45 + 1793/2401*T^44 - 1997/2401*T^43 - 
        409/2401*T^42 - 884/2401*T^41 - 1332/2401*T^40 + 62/2401*T^39 - 
        1581/2401*T^38 + 2055/2401*T^37 - 2512/2401*T^36 + 55/49*T^35 - 
        2029/2401*T^34 + 3208/2401*T^33 - 414/343*T^32 + 2780/2401*T^31 - 
        163/343*T^30 + 87/2401*T^29 - 87/2401*T^27 + 163/343*T^26 - 2780/2401*T^25 +
        414/343*T^24 - 3208/2401*T^23 + 2029/2401*T^22 - 55/49*T^21 + 2512/2401*T^20
        - 2055/2401*T^19 + 1581/2401*T^18 - 62/2401*T^17 + 1332/2401*T^16 + 
        884/2401*T^15 + 409/2401*T^14 + 1997/2401*T^13 - 1793/2401*T^12 + 
        1935/2401*T^11 - 2603/2401*T^10 + 1996/2401*T^9 - 4062/2401*T^8 + 
        596/2401*T^7 - 985/2401*T^6 - 523/2401*T^5 - 716/2401*T^4 + 45/343*T^3 + 
        6/7*T^2 - T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 4*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 5*X*Y^7 +
        2*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 4*X*Y + 6*X + 6*Y^30 + 6*Y^29 + Y^28
        + 5*Y^27 + 6*Y^26 + 3*Y^24 + 3*Y^23 + 6*Y^22 + Y^21 + 2*Y^20 + 6*Y^19 + 
        4*Y^18 + Y^17 + 6*Y^16 + 4*Y^15 + 6*Y^14 + 4*Y^13 + 2*Y^12 + Y^11 + 3*Y^10 +
        2*Y^9 + 3*Y^8 + Y^6 + 4*Y^5 + 6*Y^4 + 2*Y^3 + 6*Y^2 + 5*Y + 6,
    T^56 + 12/7*T^55 + 79/49*T^54 - 5127/2401*T^52 - 6217/2401*T^51 - 4328/2401*T^50
        - 1297/2401*T^49 + 50/343*T^48 - 562/2401*T^47 + 550/2401*T^46 + 
        398/343*T^45 + 5547/2401*T^44 + 5576/2401*T^43 + 1552/2401*T^42 - 
        2269/2401*T^41 - 3664/2401*T^40 - 2102/2401*T^39 - 1325/2401*T^38 - 
        1703/2401*T^37 - 471/343*T^36 - 1791/2401*T^35 + 2430/2401*T^34 + 
        5262/2401*T^33 + 860/343*T^32 + 2161/2401*T^31 - 1979/2401*T^30 - 
        3800/2401*T^29 - 5646/2401*T^28 - 3800/2401*T^27 - 1979/2401*T^26 + 
        2161/2401*T^25 + 860/343*T^24 + 5262/2401*T^23 + 2430/2401*T^22 - 
        1791/2401*T^21 - 471/343*T^20 - 1703/2401*T^19 - 1325/2401*T^18 - 
        2102/2401*T^17 - 3664/2401*T^16 - 2269/2401*T^15 + 1552/2401*T^14 + 
        5576/2401*T^13 + 5547/2401*T^12 + 398/343*T^11 + 550/2401*T^10 - 
        562/2401*T^9 + 50/343*T^8 - 1297/2401*T^7 - 4328/2401*T^6 - 6217/2401*T^5 - 
        5127/2401*T^4 + 79/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 
        + 6*X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 6*X*Y 
        + 5*X + 4*Y^30 + 3*Y^29 + 6*Y^28 + Y^26 + 4*Y^25 + 6*Y^24 + 4*Y^23 + Y^21 + 
        Y^20 + 4*Y^19 + Y^18 + 5*Y^17 + 4*Y^16 + Y^15 + 5*Y^13 + 3*Y^11 + 6*Y^10 + 
        6*Y^9 + 6*Y^8 + 6*Y^7 + 4*Y^6 + 6*Y^5 + 4*Y^4 + 3*Y^2 + 6,
    -T^56 - 2/7*T^55 - 71/49*T^54 - 3/7*T^53 - 3365/2401*T^52 - 1616/2401*T^51 - 
        2691/2401*T^50 - 1384/2401*T^49 - 190/2401*T^48 + 22/2401*T^47 + 
        286/343*T^46 + 918/2401*T^45 + 3303/2401*T^44 + 2088/2401*T^43 + 
        3847/2401*T^42 + 2080/2401*T^41 + 376/343*T^40 + 1606/2401*T^39 + 
        1714/2401*T^38 + 495/2401*T^37 + 464/2401*T^36 - 1032/2401*T^35 - 
        613/2401*T^34 - 1749/2401*T^33 + 73/2401*T^32 - 1948/2401*T^31 - 
        75/2401*T^30 - 1150/2401*T^29 + 1150/2401*T^27 + 75/2401*T^26 + 
        1948/2401*T^25 - 73/2401*T^24 + 1749/2401*T^23 + 613/2401*T^22 + 
        1032/2401*T^21 - 464/2401*T^20 - 495/2401*T^19 - 1714/2401*T^18 - 
        1606/2401*T^17 - 376/343*T^16 - 2080/2401*T^15 - 3847/2401*T^14 - 
        2088/2401*T^13 - 3303/2401*T^12 - 918/2401*T^11 - 286/343*T^10 - 22/2401*T^9
        + 190/2401*T^8 + 1384/2401*T^7 + 2691/2401*T^6 + 1616/2401*T^5 + 
        3365/2401*T^4 + 3/7*T^3 + 71/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 
        2*X*Y^8 + 2*X*Y^6 + 4*X*Y^4 + X*Y^3 + X*Y + 5*X + 5*Y^30 + 6*Y^28 + 5*Y^27 +
        5*Y^26 + 5*Y^25 + 6*Y^24 + Y^22 + 6*Y^21 + 2*Y^20 + 4*Y^19 + 4*Y^18 + 3*Y^17
        + 5*Y^16 + 5*Y^15 + Y^13 + Y^12 + 6*Y^11 + 5*Y^10 + Y^9 + 3*Y^8 + 6*Y^7 + 
        Y^6 + 3*Y^5 + 3*Y^4 + Y^3 + 5*Y^2 + 3,
    T^56 + 6/7*T^55 - 17/49*T^54 - 346/343*T^53 - 2008/2401*T^52 - 221/343*T^51 - 
        1237/2401*T^50 + 101/343*T^49 + 1669/2401*T^48 + 171/343*T^47 - 80/2401*T^46
        + 160/2401*T^45 + 601/2401*T^44 - 895/2401*T^43 - 831/2401*T^42 + 
        312/2401*T^41 + 1255/2401*T^40 + 632/2401*T^39 + 197/2401*T^38 + 
        249/2401*T^37 - 102/343*T^36 - 1606/2401*T^35 - 1702/2401*T^34 - 
        705/2401*T^33 - 94/2401*T^32 + 197/2401*T^31 + 962/2401*T^30 + 
        1311/2401*T^29 + 32/49*T^28 + 1311/2401*T^27 + 962/2401*T^26 + 197/2401*T^25
        - 94/2401*T^24 - 705/2401*T^23 - 1702/2401*T^22 - 1606/2401*T^21 - 
        102/343*T^20 + 249/2401*T^19 + 197/2401*T^18 + 632/2401*T^17 + 
        1255/2401*T^16 + 312/2401*T^15 - 831/2401*T^14 - 895/2401*T^13 + 
        601/2401*T^12 + 160/2401*T^11 - 80/2401*T^10 + 171/343*T^9 + 1669/2401*T^8 +
        101/343*T^7 - 1237/2401*T^6 - 221/343*T^5 - 2008/2401*T^4 - 346/343*T^3 - 
        17/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 
        + 6*X*Y^8 + 2*X*Y^7 + 3*X*Y^6 + X*Y^5 + 3*X*Y^3 + 6*X*Y^2 + 3*X*Y + 6*X + 
        2*Y^30 + 2*Y^29 + 3*Y^28 + Y^27 + 4*Y^26 + 3*Y^25 + 4*Y^24 + 5*Y^22 + 5*Y^21
        + 5*Y^20 + 3*Y^19 + 3*Y^18 + 4*Y^17 + 4*Y^16 + 2*Y^15 + 4*Y^14 + 2*Y^13 + 
        Y^11 + 4*Y^10 + 6*Y^9 + 2*Y^8 + 2*Y^7 + 3*Y^6 + 2*Y^5 + 5*Y^4 + 3*Y^3 + 
        2*Y^2 + 5*Y + 6,
    -T^56 + 9/7*T^55 - 24/49*T^54 - 453/343*T^53 + 2644/2401*T^52 + 1942/2401*T^51 -
        4014/2401*T^50 + 16/49*T^49 + 3134/2401*T^48 - 1285/2401*T^47 - 
        1740/2401*T^46 + 1093/2401*T^45 + 1815/2401*T^44 - 955/2401*T^43 - 
        2117/2401*T^42 + 1622/2401*T^41 + 577/2401*T^40 - 1630/2401*T^39 - 
        23/343*T^38 - 373/2401*T^37 + 1772/2401*T^36 - 774/2401*T^35 - 
        1824/2401*T^34 + 2986/2401*T^33 + 561/2401*T^32 - 1720/2401*T^31 + 
        1007/2401*T^30 + 927/2401*T^29 - 927/2401*T^27 - 1007/2401*T^26 + 
        1720/2401*T^25 - 561/2401*T^24 - 2986/2401*T^23 + 1824/2401*T^22 + 
        774/2401*T^21 - 1772/2401*T^20 + 373/2401*T^19 + 23/343*T^18 + 
        1630/2401*T^17 - 577/2401*T^16 - 1622/2401*T^15 + 2117/2401*T^14 + 
        955/2401*T^13 - 1815/2401*T^12 - 1093/2401*T^11 + 1740/2401*T^10 + 
        1285/2401*T^9 - 3134/2401*T^8 - 16/49*T^7 + 4014/2401*T^6 - 1942/2401*T^5 - 
        2644/2401*T^4 + 453/343*T^3 + 24/49*T^2 - 9/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 
        + 4*X*Y^7 + X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 4*X*Y + 3*X + 2*Y^30 + Y^29 + 4*Y^28
        + 5*Y^26 + 2*Y^24 + 3*Y^23 + Y^22 + 3*Y^21 + 6*Y^20 + 4*Y^19 + 6*Y^18 + 
        3*Y^17 + 2*Y^16 + 3*Y^14 + 3*Y^13 + 5*Y^12 + 4*Y^11 + 2*Y^10 + 5*Y^9 + 3*Y^8
        + 4*Y^7 + 4*Y^6 + 4*Y^5 + 6*Y^4 + 2*Y^3 + 2*Y^2 + Y + 4,
    T^56 - 2/7*T^55 - 45/49*T^54 + 213/343*T^53 - 1602/2401*T^52 - 311/2401*T^51 + 
        8/7*T^50 - 68/343*T^49 - 341/2401*T^48 + 1041/2401*T^47 - 1383/2401*T^46 - 
        2194/2401*T^45 + 712/2401*T^44 + 1046/2401*T^43 - 102/2401*T^42 + 
        1058/2401*T^41 + 387/2401*T^40 + 219/2401*T^39 - 612/2401*T^38 - 
        507/2401*T^37 - 96/2401*T^36 - 131/343*T^35 + 135/343*T^34 + 439/2401*T^33 +
        16/2401*T^32 + 180/343*T^31 - 11/2401*T^30 - 23/49*T^29 - 1009/2401*T^28 - 
        23/49*T^27 - 11/2401*T^26 + 180/343*T^25 + 16/2401*T^24 + 439/2401*T^23 + 
        135/343*T^22 - 131/343*T^21 - 96/2401*T^20 - 507/2401*T^19 - 612/2401*T^18 +
        219/2401*T^17 + 387/2401*T^16 + 1058/2401*T^15 - 102/2401*T^14 + 
        1046/2401*T^13 + 712/2401*T^12 - 2194/2401*T^11 - 1383/2401*T^10 + 
        1041/2401*T^9 - 341/2401*T^8 - 68/343*T^7 + 8/7*T^6 - 311/2401*T^5 - 
        1602/2401*T^4 + 213/343*T^3 - 45/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 
        5*X*Y^8 + 2*X*Y^7 + 4*X*Y^6 + X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 2*X*Y + 2*X + 
        6*Y^30 + 6*Y^28 + 3*Y^27 + 2*Y^26 + 3*Y^25 + 2*Y^24 + Y^23 + 4*Y^22 + 3*Y^21
        + 2*Y^20 + 6*Y^19 + 6*Y^17 + 3*Y^16 + 5*Y^15 + 5*Y^14 + Y^13 + 4*Y^12 + 
        2*Y^11 + 3*Y^10 + 6*Y^9 + 6*Y^7 + 3*Y^6 + 4*Y^4 + 5*Y^3 + 4*Y^2 + 4,
    -T^56 - 8/7*T^55 + 17/49*T^54 - 52/343*T^53 - 2557/2401*T^52 - 1149/2401*T^51 - 
        886/2401*T^50 - 482/2401*T^49 + 8/49*T^48 - 1359/2401*T^47 - 2244/2401*T^46 
        - 463/2401*T^45 + 80/343*T^44 - 925/2401*T^43 - 264/343*T^42 - 467/2401*T^41
        + 206/2401*T^40 - 162/2401*T^39 - 932/2401*T^38 - 1754/2401*T^37 - 
        809/2401*T^36 + 18/343*T^35 - 1129/2401*T^34 - 899/2401*T^33 + 46/2401*T^32 
        - 508/2401*T^31 + 138/2401*T^30 + 955/2401*T^29 - 955/2401*T^27 - 
        138/2401*T^26 + 508/2401*T^25 - 46/2401*T^24 + 899/2401*T^23 + 
        1129/2401*T^22 - 18/343*T^21 + 809/2401*T^20 + 1754/2401*T^19 + 
        932/2401*T^18 + 162/2401*T^17 - 206/2401*T^16 + 467/2401*T^15 + 264/343*T^14
        + 925/2401*T^13 - 80/343*T^12 + 463/2401*T^11 + 2244/2401*T^10 + 
        1359/2401*T^9 - 8/49*T^8 + 482/2401*T^7 + 886/2401*T^6 + 1149/2401*T^5 + 
        2557/2401*T^4 + 52/343*T^3 - 17/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 5*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 4*X*Y^8 + 5*X*Y^6 +
        5*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + X*Y^2 + 3*X*Y + 4*X + Y^30 + 2*Y^29 + 4*Y^27 +
        Y^26 + 6*Y^25 + 4*Y^24 + Y^23 + 5*Y^21 + Y^20 + 4*Y^19 + 3*Y^18 + 6*Y^16 + 
        3*Y^15 + 6*Y^14 + 5*Y^13 + Y^12 + Y^11 + 2*Y^10 + Y^8 + Y^7 + 2*Y^6 + Y^5 + 
        4*Y^4 + 4*Y^3 + 3,
    -T^56 - 5/7*T^55 - 1/49*T^54 + 307/343*T^53 - 94/343*T^52 - 272/2401*T^51 - 
        5/2401*T^50 + 15/49*T^49 + 408/2401*T^48 + 1087/2401*T^47 + 99/343*T^46 - 
        1273/2401*T^45 - 367/2401*T^44 - 1048/2401*T^43 - 288/2401*T^42 + 
        195/2401*T^41 + 2187/2401*T^40 + 194/2401*T^39 - 169/343*T^38 - 
        228/2401*T^37 + 55/2401*T^36 + 80/343*T^35 + 116/2401*T^34 + 1173/2401*T^33 
        - 465/2401*T^32 + 415/2401*T^31 + 381/2401*T^30 + 612/2401*T^29 - 
        612/2401*T^27 - 381/2401*T^26 - 415/2401*T^25 + 465/2401*T^24 - 
        1173/2401*T^23 - 116/2401*T^22 - 80/343*T^21 - 55/2401*T^20 + 228/2401*T^19 
        + 169/343*T^18 - 194/2401*T^17 - 2187/2401*T^16 - 195/2401*T^15 + 
        288/2401*T^14 + 1048/2401*T^13 + 367/2401*T^12 + 1273/2401*T^11 - 
        99/343*T^10 - 1087/2401*T^9 - 408/2401*T^8 - 15/49*T^7 + 5/2401*T^6 + 
        272/2401*T^5 + 94/343*T^4 - 307/343*T^3 + 1/49*T^2 + 5/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 4*X*Y^9 + X*Y^8 + 5*X*Y^7 + X*Y^5 + 3*X*Y^4
        + X*Y^3 + 6*X*Y^2 + 6*X*Y + 4*X + Y^30 + 5*Y^28 + 5*Y^27 + 3*Y^26 + 2*Y^25 +
        4*Y^24 + 5*Y^23 + 3*Y^22 + 6*Y^21 + 4*Y^20 + Y^17 + 6*Y^15 + Y^14 + 4*Y^13 +
        Y^12 + 6*Y^11 + 6*Y^10 + Y^9 + 4*Y^8 + 3*Y^7 + 6*Y^6 + 6*Y^5 + 5*Y^4 + 5*Y^2
        + Y + 4,
    -T^56 + 5/7*T^55 - 3/49*T^54 + 74/343*T^53 + 255/343*T^52 - 2689/2401*T^51 + 
        779/2401*T^50 + 120/2401*T^49 - 383/2401*T^48 + 1670/2401*T^47 - 
        769/2401*T^46 - 47/343*T^45 + 53/343*T^44 - 583/2401*T^43 + 1221/2401*T^42 -
        955/2401*T^41 - 829/2401*T^40 + 10/49*T^39 + 209/2401*T^38 + 74/343*T^37 + 
        696/2401*T^36 - 159/343*T^35 - 440/2401*T^34 + 596/2401*T^33 + 603/2401*T^32
        + 822/2401*T^31 - 706/2401*T^30 - 1419/2401*T^29 + 1419/2401*T^27 + 
        706/2401*T^26 - 822/2401*T^25 - 603/2401*T^24 - 596/2401*T^23 + 
        440/2401*T^22 + 159/343*T^21 - 696/2401*T^20 - 74/343*T^19 - 209/2401*T^18 -
        10/49*T^17 + 829/2401*T^16 + 955/2401*T^15 - 1221/2401*T^14 + 583/2401*T^13 
        - 53/343*T^12 + 47/343*T^11 + 769/2401*T^10 - 1670/2401*T^9 + 383/2401*T^8 -
        120/2401*T^7 - 779/2401*T^6 + 2689/2401*T^5 - 255/343*T^4 - 74/343*T^3 + 
        3/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 3*X*Y^10 + X*Y^9 + 2*X*Y^7 + 
        X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + X*Y + 5*X + Y^30 + 2*Y^29 + Y^28 + 
        5*Y^27 + 2*Y^26 + 4*Y^25 + 3*Y^24 + Y^23 + Y^22 + 4*Y^21 + Y^19 + 4*Y^18 + 
        5*Y^16 + 6*Y^14 + 4*Y^13 + 3*Y^11 + 6*Y^10 + Y^9 + 2*Y^8 + Y^7 + 2*Y^6 + 
        6*Y^5 + 5*Y^4 + 5*Y^3 + Y^2 + Y + 4,
    T^56 - 13/7*T^55 + 78/49*T^54 - 228/343*T^53 - 2637/2401*T^52 + 494/343*T^51 - 
        1963/2401*T^50 - 335/2401*T^49 + 459/343*T^48 - 2483/2401*T^47 + 
        1143/2401*T^46 + 964/2401*T^45 - 2447/2401*T^44 + 249/343*T^43 - 
        1110/2401*T^42 - 223/343*T^41 + 3013/2401*T^40 - 2559/2401*T^39 + 
        1224/2401*T^38 + 1304/2401*T^37 - 1501/2401*T^36 + 122/343*T^35 - 
        172/2401*T^34 - 782/2401*T^33 + 706/2401*T^32 + 187/2401*T^31 - 
        745/2401*T^30 + 855/2401*T^29 - 1025/2401*T^28 + 855/2401*T^27 - 
        745/2401*T^26 + 187/2401*T^25 + 706/2401*T^24 - 782/2401*T^23 - 
        172/2401*T^22 + 122/343*T^21 - 1501/2401*T^20 + 1304/2401*T^19 + 
        1224/2401*T^18 - 2559/2401*T^17 + 3013/2401*T^16 - 223/343*T^15 - 
        1110/2401*T^14 + 249/343*T^13 - 2447/2401*T^12 + 964/2401*T^11 + 
        1143/2401*T^10 - 2483/2401*T^9 + 459/343*T^8 - 335/2401*T^7 - 1963/2401*T^6 
        + 494/343*T^5 - 2637/2401*T^4 - 228/343*T^3 + 78/49*T^2 - 13/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 2*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 6*X*Y^8 + 6*X*Y^7 + 
        2*X*Y^6 + X*Y^5 + 2*X*Y^3 + 5*X*Y^2 + 5*X + 3*Y^30 + 4*Y^29 + 5*Y^28 + 
        5*Y^27 + 2*Y^26 + 6*Y^25 + 2*Y^24 + Y^23 + 5*Y^22 + 2*Y^20 + 4*Y^19 + Y^18 +
        3*Y^17 + 3*Y^16 + 6*Y^15 + 4*Y^13 + 5*Y^12 + 3*Y^11 + 6*Y^10 + Y^8 + 4*Y^7 +
        6*Y^6 + 5*Y^4 + 6*Y^2 + 6,
    -T^56 + T^55 + 30/49*T^54 - 415/343*T^53 - 430/2401*T^52 + 1318/2401*T^51 + 
        803/2401*T^50 - 1010/2401*T^49 + 96/343*T^48 - 1051/2401*T^47 + 
        615/2401*T^46 + 725/2401*T^45 - 1634/2401*T^44 + 1590/2401*T^43 - 
        425/2401*T^42 - 582/2401*T^41 - 144/2401*T^40 + 601/2401*T^39 - 
        888/2401*T^38 - 199/2401*T^37 + 1539/2401*T^36 - 566/2401*T^35 - 
        1005/2401*T^34 - 643/2401*T^33 + 40/49*T^32 + 696/2401*T^31 - 536/2401*T^30 
        - 1650/2401*T^29 + 1650/2401*T^27 + 536/2401*T^26 - 696/2401*T^25 - 
        40/49*T^24 + 643/2401*T^23 + 1005/2401*T^22 + 566/2401*T^21 - 1539/2401*T^20
        + 199/2401*T^19 + 888/2401*T^18 - 601/2401*T^17 + 144/2401*T^16 + 
        582/2401*T^15 + 425/2401*T^14 - 1590/2401*T^13 + 1634/2401*T^12 - 
        725/2401*T^11 - 615/2401*T^10 + 1051/2401*T^9 - 96/343*T^8 + 1010/2401*T^7 -
        803/2401*T^6 - 1318/2401*T^5 + 430/2401*T^4 + 415/343*T^3 - 30/49*T^2 - T + 
        1
*], [*
    X^3 + 2*X*Y^14 + 3*X*Y^12 + 5*X*Y^9 + X*Y^8 + X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + 
        4*X*Y^4 + 4*X*Y^3 + 2*X*Y + 3*X + 3*Y^30 + 2*Y^29 + Y^28 + 5*Y^27 + 4*Y^26 +
        6*Y^25 + 6*Y^24 + Y^23 + 3*Y^22 + 6*Y^21 + 3*Y^20 + 6*Y^19 + 2*Y^18 + 4*Y^17
        + 4*Y^16 + 6*Y^15 + 5*Y^13 + 5*Y^12 + 3*Y^11 + 4*Y^10 + 2*Y^9 + 5*Y^8 + Y^7 
        + 3*Y^6 + Y^5 + 2*Y^4 + 6*Y + 6,
    T^56 + 1/7*T^55 + 16/49*T^54 + 123/343*T^53 + 30/2401*T^52 - 801/2401*T^51 - 
        2834/2401*T^50 - 563/2401*T^49 - 2213/2401*T^48 - 544/2401*T^47 - 
        661/2401*T^46 + 731/2401*T^45 + 2099/2401*T^44 + 1646/2401*T^43 + 
        1942/2401*T^42 + 1910/2401*T^41 + 995/2401*T^40 - 394/2401*T^39 - 
        750/2401*T^38 - 1585/2401*T^37 - 1991/2401*T^36 - 3212/2401*T^35 - 
        986/2401*T^34 - 248/343*T^33 - 522/2401*T^32 + 776/2401*T^31 + 
        1098/2401*T^30 + 2496/2401*T^29 + 1396/2401*T^28 + 2496/2401*T^27 + 
        1098/2401*T^26 + 776/2401*T^25 - 522/2401*T^24 - 248/343*T^23 - 
        986/2401*T^22 - 3212/2401*T^21 - 1991/2401*T^20 - 1585/2401*T^19 - 
        750/2401*T^18 - 394/2401*T^17 + 995/2401*T^16 + 1910/2401*T^15 + 
        1942/2401*T^14 + 1646/2401*T^13 + 2099/2401*T^12 + 731/2401*T^11 - 
        661/2401*T^10 - 544/2401*T^9 - 2213/2401*T^8 - 563/2401*T^7 - 2834/2401*T^6 
        - 801/2401*T^5 + 30/2401*T^4 + 123/343*T^3 + 16/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + X*Y^13 + X*Y^12 + X*Y^11 + 5*X*Y^10 + X*Y^9 + X*Y^8 
        + X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 4*X*Y + 6*X + 5*Y^30 + 
        Y^28 + 3*Y^27 + Y^26 + 6*Y^25 + Y^24 + 5*Y^23 + 2*Y^22 + 6*Y^21 + 5*Y^20 + 
        4*Y^19 + Y^18 + 5*Y^17 + Y^16 + 6*Y^15 + 5*Y^14 + 2*Y^13 + 3*Y^12 + 3*Y^10 +
        2*Y^9 + 6*Y^8 + 5*Y^7 + 2*Y^6 + 3*Y^5 + 4*Y^4 + 3*Y^3 + 4*Y^2 + 2*Y + 2,
    T^56 + T^55 + 10/49*T^54 + 297/343*T^53 + 10/7*T^52 + 81/343*T^51 - 
        543/2401*T^50 + 1343/2401*T^49 + 221/2401*T^48 - 1080/2401*T^47 - 
        2566/2401*T^46 - 1793/2401*T^45 - 648/2401*T^44 - 2440/2401*T^43 - 
        2473/2401*T^42 - 17/2401*T^41 + 772/2401*T^40 + 492/2401*T^39 + 
        2102/2401*T^38 + 2456/2401*T^37 + 2957/2401*T^36 + 1728/2401*T^35 - 
        295/2401*T^34 + 184/2401*T^33 - 30/343*T^32 - 2575/2401*T^31 - 
        3506/2401*T^30 - 3455/2401*T^29 - 4043/2401*T^28 - 3455/2401*T^27 - 
        3506/2401*T^26 - 2575/2401*T^25 - 30/343*T^24 + 184/2401*T^23 - 
        295/2401*T^22 + 1728/2401*T^21 + 2957/2401*T^20 + 2456/2401*T^19 + 
        2102/2401*T^18 + 492/2401*T^17 + 772/2401*T^16 - 17/2401*T^15 - 
        2473/2401*T^14 - 2440/2401*T^13 - 648/2401*T^12 - 1793/2401*T^11 - 
        2566/2401*T^10 - 1080/2401*T^9 + 221/2401*T^8 + 1343/2401*T^7 - 543/2401*T^6
        + 81/343*T^5 + 10/7*T^4 + 297/343*T^3 + 10/49*T^2 + T + 1
*], [*
    X^3 + 3*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 +
        3*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 4*X*Y^2 + 5*X*Y + 6*X + 2*Y^30 + 
        Y^29 + Y^28 + 6*Y^26 + 5*Y^25 + 3*Y^24 + 4*Y^23 + Y^22 + Y^21 + Y^20 + 
        3*Y^19 + 5*Y^18 + 2*Y^17 + 3*Y^16 + 5*Y^15 + 4*Y^14 + 4*Y^13 + Y^12 + 5*Y^10
        + Y^9 + 3*Y^8 + 3*Y^7 + 2*Y^6 + 6*Y^5 + 4*Y^4 + 6*Y^3 + 2*Y^2 + 5*Y,
    T^56 + 9/7*T^55 + 9/49*T^54 + 183/343*T^53 + 2344/2401*T^52 - 963/2401*T^51 - 
        2831/2401*T^50 + 81/343*T^49 + 829/2401*T^48 - 1133/2401*T^47 + 
        1132/2401*T^46 + 43/49*T^45 + 169/343*T^44 + 383/2401*T^43 + 244/2401*T^42 +
        388/2401*T^41 - 122/343*T^40 - 899/2401*T^39 + 395/2401*T^38 + 551/2401*T^37
        - 1056/2401*T^36 + 167/2401*T^35 + 2376/2401*T^34 - 99/343*T^33 - 
        887/2401*T^32 + 159/343*T^31 + 44/343*T^30 + 284/2401*T^29 + 62/343*T^28 + 
        284/2401*T^27 + 44/343*T^26 + 159/343*T^25 - 887/2401*T^24 - 99/343*T^23 + 
        2376/2401*T^22 + 167/2401*T^21 - 1056/2401*T^20 + 551/2401*T^19 + 
        395/2401*T^18 - 899/2401*T^17 - 122/343*T^16 + 388/2401*T^15 + 244/2401*T^14
        + 383/2401*T^13 + 169/343*T^12 + 43/49*T^11 + 1132/2401*T^10 - 1133/2401*T^9
        + 829/2401*T^8 + 81/343*T^7 - 2831/2401*T^6 - 963/2401*T^5 + 2344/2401*T^4 +
        183/343*T^3 + 9/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 +
        6*X*Y^7 + 2*X*Y^5 + 6*X*Y^4 + X*Y^3 + 3*X*Y^2 + 6*X*Y + 6*Y^30 + 3*Y^29 + 
        Y^28 + 2*Y^25 + 6*Y^24 + 2*Y^23 + 6*Y^22 + 5*Y^21 + 5*Y^19 + Y^18 + 3*Y^17 +
        5*Y^16 + 5*Y^15 + 6*Y^14 + 3*Y^13 + 2*Y^12 + 2*Y^11 + 2*Y^10 + 4*Y^9 + 4*Y^8
        + 4*Y^7 + 4*Y^6 + 5*Y^5 + 3*Y^4 + Y^3 + 5*Y^2 + 6*Y + 4,
    T^56 + 10/7*T^55 + 22/49*T^54 - 18/49*T^53 - 2760/2401*T^52 - 5134/2401*T^51 - 
        3672/2401*T^50 - 796/2401*T^49 + 895/2401*T^48 + 3196/2401*T^47 + 
        4005/2401*T^46 + 1220/2401*T^45 - 198/343*T^44 - 2430/2401*T^43 - 
        2773/2401*T^42 - 618/2401*T^41 + 2019/2401*T^40 + 1814/2401*T^39 + 
        1054/2401*T^38 + 941/2401*T^37 - 212/2401*T^36 - 211/2401*T^35 + 
        611/2401*T^34 + 176/2401*T^33 + 523/2401*T^32 + 1623/2401*T^31 - 
        601/2401*T^30 - 2347/2401*T^29 - 2279/2401*T^28 - 2347/2401*T^27 - 
        601/2401*T^26 + 1623/2401*T^25 + 523/2401*T^24 + 176/2401*T^23 + 
        611/2401*T^22 - 211/2401*T^21 - 212/2401*T^20 + 941/2401*T^19 + 
        1054/2401*T^18 + 1814/2401*T^17 + 2019/2401*T^16 - 618/2401*T^15 - 
        2773/2401*T^14 - 2430/2401*T^13 - 198/343*T^12 + 1220/2401*T^11 + 
        4005/2401*T^10 + 3196/2401*T^9 + 895/2401*T^8 - 796/2401*T^7 - 3672/2401*T^6
        - 5134/2401*T^5 - 2760/2401*T^4 - 18/49*T^3 + 22/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 
        5*X*Y^8 + X*Y^7 + 2*X*Y^5 + 6*X*Y^3 + 5*X*Y^2 + 3*X*Y + 6*X + 5*Y^30 + 
        6*Y^28 + 5*Y^27 + Y^26 + 4*Y^25 + 6*Y^23 + 4*Y^22 + 2*Y^21 + 4*Y^20 + 6*Y^19
        + 4*Y^18 + 4*Y^17 + 6*Y^16 + 5*Y^15 + 3*Y^14 + 6*Y^13 + 5*Y^12 + 3*Y^11 + 
        2*Y^10 + 5*Y^9 + 5*Y^8 + 6*Y^7 + 6*Y^6 + Y^5 + 6*Y^4 + 4*Y^3 + 3*Y^2 + Y + 
        3,
    -T^56 - 11/7*T^55 - 46/49*T^54 + 72/343*T^53 + 3887/2401*T^52 + 5206/2401*T^51 +
        3772/2401*T^50 - 111/2401*T^49 - 3246/2401*T^48 - 82/49*T^47 - 
        1396/2401*T^46 + 2570/2401*T^45 + 3977/2401*T^44 + 2157/2401*T^43 - 
        2294/2401*T^42 - 5290/2401*T^41 - 5615/2401*T^40 - 2027/2401*T^39 + 
        4492/2401*T^38 + 7622/2401*T^37 + 5266/2401*T^36 - 255/2401*T^35 - 
        4674/2401*T^34 - 6037/2401*T^33 - 3631/2401*T^32 + 1163/2401*T^31 + 
        4129/2401*T^30 + 3973/2401*T^29 - 3973/2401*T^27 - 4129/2401*T^26 - 
        1163/2401*T^25 + 3631/2401*T^24 + 6037/2401*T^23 + 4674/2401*T^22 + 
        255/2401*T^21 - 5266/2401*T^20 - 7622/2401*T^19 - 4492/2401*T^18 + 
        2027/2401*T^17 + 5615/2401*T^16 + 5290/2401*T^15 + 2294/2401*T^14 - 
        2157/2401*T^13 - 3977/2401*T^12 - 2570/2401*T^11 + 1396/2401*T^10 + 
        82/49*T^9 + 3246/2401*T^8 + 111/2401*T^7 - 3772/2401*T^6 - 5206/2401*T^5 - 
        3887/2401*T^4 - 72/343*T^3 + 46/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 
        6*X*Y^8 + 4*X*Y^7 + 4*X*Y^5 + X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 2*X*Y + 6*X + 
        2*Y^30 + 4*Y^29 + 3*Y^28 + Y^27 + 5*Y^25 + 4*Y^24 + 2*Y^23 + Y^22 + Y^21 + 
        Y^20 + 5*Y^19 + 2*Y^17 + 2*Y^16 + 4*Y^15 + 3*Y^14 + 3*Y^13 + 3*Y^12 + 4*Y^11
        + Y^9 + 3*Y^8 + 2*Y^7 + 3*Y^6 + 6*Y^5 + 6*Y^4 + Y^3 + 2*Y + 6,
    -T^56 + 9/7*T^55 - 138/49*T^54 + 997/343*T^53 - 1124/343*T^52 + 7535/2401*T^51 -
        6408/2401*T^50 + 8451/2401*T^49 - 8557/2401*T^48 + 11939/2401*T^47 - 
        12190/2401*T^46 + 12531/2401*T^45 - 10294/2401*T^44 + 8059/2401*T^43 - 
        6003/2401*T^42 + 4577/2401*T^41 - 5483/2401*T^40 + 4951/2401*T^39 - 
        926/343*T^38 + 4350/2401*T^37 - 3358/2401*T^36 + 367/2401*T^35 + 
        1784/2401*T^34 - 1506/2401*T^33 + 1231/2401*T^32 + 1509/2401*T^31 - 
        1858/2401*T^30 + 1867/2401*T^29 - 1867/2401*T^27 + 1858/2401*T^26 - 
        1509/2401*T^25 - 1231/2401*T^24 + 1506/2401*T^23 - 1784/2401*T^22 - 
        367/2401*T^21 + 3358/2401*T^20 - 4350/2401*T^19 + 926/343*T^18 - 
        4951/2401*T^17 + 5483/2401*T^16 - 4577/2401*T^15 + 6003/2401*T^14 - 
        8059/2401*T^13 + 10294/2401*T^12 - 12531/2401*T^11 + 12190/2401*T^10 - 
        11939/2401*T^9 + 8557/2401*T^8 - 8451/2401*T^7 + 6408/2401*T^6 - 
        7535/2401*T^5 + 1124/343*T^4 - 997/343*T^3 + 138/49*T^2 - 9/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 5*X*Y^11 + X*Y^10 + 2*X*Y^9 + 3*X*Y^8 + 4*X*Y^7 + 
        6*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 6*X*Y + 5*X + Y^30 + Y^29 
        + 3*Y^28 + Y^27 + 2*Y^25 + 6*Y^24 + 2*Y^23 + 6*Y^21 + 2*Y^20 + 6*Y^19 + 
        4*Y^18 + Y^17 + 2*Y^16 + 2*Y^15 + 3*Y^14 + 2*Y^13 + 5*Y^12 + Y^11 + 4*Y^10 +
        6*Y^9 + Y^8 + Y^5 + 5*Y^4 + 4*Y^3 + Y^2 + 3*Y + 3,
    -T^56 + 10/7*T^55 + 19/49*T^54 - 316/343*T^53 - 150/343*T^52 + 872/2401*T^51 + 
        1349/2401*T^50 - 2025/2401*T^49 + 431/2401*T^48 + 1676/2401*T^47 - 
        60/2401*T^46 - 943/2401*T^45 - 1385/2401*T^44 + 1516/2401*T^43 - 
        200/2401*T^42 - 313/2401*T^41 + 316/2401*T^40 + 771/2401*T^39 - 
        410/2401*T^38 - 935/2401*T^37 + 248/2401*T^36 + 12/49*T^35 - 69/2401*T^34 - 
        379/2401*T^33 - 169/2401*T^32 + 835/2401*T^31 - 418/2401*T^30 - 30/343*T^29 
        + 30/343*T^27 + 418/2401*T^26 - 835/2401*T^25 + 169/2401*T^24 + 
        379/2401*T^23 + 69/2401*T^22 - 12/49*T^21 - 248/2401*T^20 + 935/2401*T^19 + 
        410/2401*T^18 - 771/2401*T^17 - 316/2401*T^16 + 313/2401*T^15 + 
        200/2401*T^14 - 1516/2401*T^13 + 1385/2401*T^12 + 943/2401*T^11 + 
        60/2401*T^10 - 1676/2401*T^9 - 431/2401*T^8 + 2025/2401*T^7 - 1349/2401*T^6 
        - 872/2401*T^5 + 150/343*T^4 + 316/343*T^3 - 19/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + X*Y^10 + X*Y^9 + 
        6*X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 2*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 3*X*Y + 2*X + 
        2*Y^30 + 6*Y^29 + 2*Y^28 + Y^27 + Y^26 + 5*Y^25 + 4*Y^24 + 6*Y^23 + 5*Y^22 +
        4*Y^21 + Y^20 + 4*Y^19 + 6*Y^18 + 3*Y^17 + 3*Y^15 + 6*Y^13 + 3*Y^11 + 2*Y^10
        + 6*Y^9 + 2*Y^8 + 6*Y^7 + 2*Y^6 + 3*Y^5 + 5*Y^4 + 2*Y^3 + 2*Y^2 + 5*Y + 6,
    T^56 - 1/7*T^55 - 13/49*T^54 + 100/343*T^53 + 1102/2401*T^52 + 916/2401*T^51 - 
        1119/2401*T^50 + 1748/2401*T^49 + 673/2401*T^48 - 1377/2401*T^47 - 
        1128/2401*T^46 + 2243/2401*T^45 - 776/2401*T^44 - 2119/2401*T^43 - 
        395/2401*T^42 + 904/2401*T^41 - 561/2401*T^40 - 3713/2401*T^39 + 
        716/2401*T^38 + 720/2401*T^37 - 1409/2401*T^36 - 1787/2401*T^35 + 
        2496/2401*T^34 + 1105/2401*T^33 - 1595/2401*T^32 - 451/2401*T^31 + 
        2284/2401*T^30 + 2328/2401*T^29 - 2131/2401*T^28 + 2328/2401*T^27 + 
        2284/2401*T^26 - 451/2401*T^25 - 1595/2401*T^24 + 1105/2401*T^23 + 
        2496/2401*T^22 - 1787/2401*T^21 - 1409/2401*T^20 + 720/2401*T^19 + 
        716/2401*T^18 - 3713/2401*T^17 - 561/2401*T^16 + 904/2401*T^15 - 
        395/2401*T^14 - 2119/2401*T^13 - 776/2401*T^12 + 2243/2401*T^11 - 
        1128/2401*T^10 - 1377/2401*T^9 + 673/2401*T^8 + 1748/2401*T^7 - 
        1119/2401*T^6 + 916/2401*T^5 + 1102/2401*T^4 + 100/343*T^3 - 13/49*T^2 - 
        1/7*T + 1
*], [*
    X^3 + 6*X*Y^13 + 4*X*Y^12 + X*Y^11 + X*Y^10 + 6*X*Y^9 + 5*X*Y^8 + 5*X*Y^7 + 
        X*Y^6 + 5*X*Y^4 + 5*X*Y^2 + 6*X*Y + 6*X + 2*Y^30 + 2*Y^29 + 6*Y^28 + 6*Y^27 
        + 4*Y^26 + 5*Y^25 + 3*Y^24 + 6*Y^23 + 6*Y^22 + 5*Y^21 + 5*Y^20 + Y^19 + Y^18
        + 4*Y^17 + 3*Y^16 + 3*Y^14 + 6*Y^13 + 4*Y^12 + 6*Y^11 + 4*Y^10 + Y^9 + 6*Y^8
        + 4*Y^7 + 4*Y^6 + 6*Y^5 + 5*Y^4 + Y^3 + 3*Y^2 + Y + 3,
    -T^56 + 1/7*T^55 + 18/49*T^54 - 194/343*T^53 + 131/343*T^52 + 188/343*T^51 - 
        732/2401*T^50 + 1269/2401*T^49 + 375/2401*T^48 - 2360/2401*T^47 + 
        1709/2401*T^46 - 922/2401*T^45 - 22/49*T^44 + 3284/2401*T^43 - 
        1551/2401*T^42 - 1126/2401*T^41 + 418/343*T^40 - 39/49*T^39 - 687/2401*T^38 
        + 2937/2401*T^37 - 2193/2401*T^36 + 493/2401*T^35 + 2066/2401*T^34 - 
        498/343*T^33 + 1520/2401*T^32 + 262/2401*T^31 - 3541/2401*T^30 + 
        1973/2401*T^29 - 1973/2401*T^27 + 3541/2401*T^26 - 262/2401*T^25 - 
        1520/2401*T^24 + 498/343*T^23 - 2066/2401*T^22 - 493/2401*T^21 + 
        2193/2401*T^20 - 2937/2401*T^19 + 687/2401*T^18 + 39/49*T^17 - 418/343*T^16 
        + 1126/2401*T^15 + 1551/2401*T^14 - 3284/2401*T^13 + 22/49*T^12 + 
        922/2401*T^11 - 1709/2401*T^10 + 2360/2401*T^9 - 375/2401*T^8 - 
        1269/2401*T^7 + 732/2401*T^6 - 188/343*T^5 - 131/343*T^4 + 194/343*T^3 - 
        18/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 3*X*Y^12 + 5*X*Y^11 + X*Y^10 + 5*X*Y^9 + 3*X*Y^7 + 
        2*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + X*Y^3 + 5*X*Y^2 + 3*X*Y + 5*X + 2*Y^30 + 
        6*Y^29 + 2*Y^27 + 2*Y^25 + 6*Y^24 + 3*Y^23 + 6*Y^22 + 3*Y^21 + 4*Y^20 + Y^18
        + 2*Y^17 + 6*Y^15 + 2*Y^14 + 3*Y^13 + 2*Y^12 + 4*Y^11 + 4*Y^9 + Y^7 + 3*Y^6 
        + Y^5 + Y^4 + 3*Y^3 + Y^2 + 3*Y,
    T^56 - 1/7*T^55 - 17/49*T^54 - 66/343*T^53 - 624/2401*T^52 + 852/2401*T^51 - 
        708/2401*T^50 - 8/49*T^49 + 153/2401*T^48 - 221/343*T^47 - 761/2401*T^46 + 
        855/2401*T^45 - 583/2401*T^44 + 820/2401*T^43 + 891/2401*T^42 + 
        274/2401*T^41 + 33/343*T^40 - 921/2401*T^39 + 355/2401*T^38 + 1753/2401*T^37
        - 655/2401*T^36 + 381/2401*T^35 + 229/2401*T^34 - 1073/2401*T^33 + 
        605/2401*T^32 - 1061/2401*T^31 - 58/2401*T^30 + 856/2401*T^29 - 
        1221/2401*T^28 + 856/2401*T^27 - 58/2401*T^26 - 1061/2401*T^25 + 
        605/2401*T^24 - 1073/2401*T^23 + 229/2401*T^22 + 381/2401*T^21 - 
        655/2401*T^20 + 1753/2401*T^19 + 355/2401*T^18 - 921/2401*T^17 + 33/343*T^16
        + 274/2401*T^15 + 891/2401*T^14 + 820/2401*T^13 - 583/2401*T^12 + 
        855/2401*T^11 - 761/2401*T^10 - 221/343*T^9 + 153/2401*T^8 - 8/49*T^7 - 
        708/2401*T^6 + 852/2401*T^5 - 624/2401*T^4 - 66/343*T^3 - 17/49*T^2 - 1/7*T 
        + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 3*X*Y^2 + 3*X*Y + Y^30 + 3*Y^29 + 
        4*Y^28 + 3*Y^27 + 3*Y^26 + 3*Y^25 + 5*Y^24 + 5*Y^22 + 3*Y^21 + 4*Y^20 + 
        5*Y^19 + 5*Y^17 + 5*Y^15 + 4*Y^14 + 3*Y^12 + 6*Y^11 + 2*Y^10 + 4*Y^9 + 3*Y^8
        + 5*Y^7 + 2*Y^6 + 4*Y^5 + 6*Y^4 + 6*Y^3 + 3*Y^2 + 3*Y + 6,
    T^56 - 2/7*T^55 + 9/49*T^54 + 29/343*T^53 - 811/2401*T^52 + 2304/2401*T^51 - 
        2094/2401*T^50 + 156/343*T^49 + 302/2401*T^48 - 1231/2401*T^47 + 
        654/2401*T^46 - 1639/2401*T^45 + 1391/2401*T^44 - 85/2401*T^43 - 
        1291/2401*T^42 - 207/2401*T^41 - 488/2401*T^40 - 361/2401*T^39 - 
        363/2401*T^38 - 242/2401*T^37 + 62/2401*T^36 + 136/343*T^35 - 289/343*T^34 +
        1185/2401*T^33 + 620/2401*T^32 + 946/2401*T^31 + 1353/2401*T^30 - 
        1181/2401*T^29 + 2633/2401*T^28 - 1181/2401*T^27 + 1353/2401*T^26 + 
        946/2401*T^25 + 620/2401*T^24 + 1185/2401*T^23 - 289/343*T^22 + 136/343*T^21
        + 62/2401*T^20 - 242/2401*T^19 - 363/2401*T^18 - 361/2401*T^17 - 
        488/2401*T^16 - 207/2401*T^15 - 1291/2401*T^14 - 85/2401*T^13 + 
        1391/2401*T^12 - 1639/2401*T^11 + 654/2401*T^10 - 1231/2401*T^9 + 
        302/2401*T^8 + 156/343*T^7 - 2094/2401*T^6 + 2304/2401*T^5 - 811/2401*T^4 + 
        29/343*T^3 + 9/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + X*Y^9 + 3*X*Y^7 + 3*X*Y^6 + 
        3*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + X*Y + X + 3*Y^30 + Y^28 + 4*Y^27 + 
        2*Y^26 + Y^25 + 6*Y^24 + 5*Y^23 + 2*Y^22 + 4*Y^21 + 2*Y^20 + 3*Y^19 + 5*Y^18
        + 3*Y^17 + Y^16 + Y^15 + Y^14 + Y^13 + 2*Y^12 + 2*Y^11 + 6*Y^10 + 3*Y^9 + 
        4*Y^8 + Y^7 + 3*Y^6 + Y^5 + Y^4 + Y^2 + Y + 3,
    T^56 + 8/7*T^55 + 29/49*T^54 - 407/343*T^53 - 2162/2401*T^52 - 3048/2401*T^51 - 
        2725/2401*T^50 - 461/343*T^49 + 218/343*T^48 + 638/343*T^47 + 4742/2401*T^46
        + 2545/2401*T^45 - 151/2401*T^44 - 1850/2401*T^43 - 4203/2401*T^42 - 
        2945/2401*T^41 - 2071/2401*T^40 + 1480/2401*T^39 + 3285/2401*T^38 + 
        4446/2401*T^37 + 1922/2401*T^36 - 111/2401*T^35 - 789/2401*T^34 - 
        358/343*T^33 - 2769/2401*T^32 - 2598/2401*T^31 + 1114/2401*T^30 + 
        1077/2401*T^29 + 2570/2401*T^28 + 1077/2401*T^27 + 1114/2401*T^26 - 
        2598/2401*T^25 - 2769/2401*T^24 - 358/343*T^23 - 789/2401*T^22 - 
        111/2401*T^21 + 1922/2401*T^20 + 4446/2401*T^19 + 3285/2401*T^18 + 
        1480/2401*T^17 - 2071/2401*T^16 - 2945/2401*T^15 - 4203/2401*T^14 - 
        1850/2401*T^13 - 151/2401*T^12 + 2545/2401*T^11 + 4742/2401*T^10 + 
        638/343*T^9 + 218/343*T^8 - 461/343*T^7 - 2725/2401*T^6 - 3048/2401*T^5 - 
        2162/2401*T^4 - 407/343*T^3 + 29/49*T^2 + 8/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 6*X*Y^13 + X*Y^12 + 4*X*Y^11 + X*Y^10 + X*Y^9 + 3*X*Y^8 
        + 2*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 3*X*Y + 3*X + 
        5*Y^30 + 2*Y^29 + 3*Y^28 + 3*Y^27 + 5*Y^26 + 2*Y^25 + 6*Y^24 + 4*Y^23 + 
        3*Y^22 + 2*Y^20 + 4*Y^19 + 3*Y^18 + 3*Y^17 + 2*Y^16 + 3*Y^15 + 3*Y^14 + 
        3*Y^13 + 3*Y^11 + Y^10 + 2*Y^9 + 3*Y^8 + 3*Y^7 + 2*Y^6 + Y^5 + Y^4 + Y^3 + 
        2*Y^2 + 2,
    T^56 + 2/7*T^55 - 39/49*T^54 + 202/343*T^53 + 1178/2401*T^52 - 1066/2401*T^51 + 
        1529/2401*T^50 - 17/343*T^49 - 1112/2401*T^48 + 163/2401*T^47 - 
        598/2401*T^46 + 451/2401*T^45 - 1620/2401*T^44 - 65/2401*T^43 + 
        1976/2401*T^42 - 1467/2401*T^41 - 494/2401*T^40 + 659/2401*T^39 - 
        554/2401*T^38 + 921/2401*T^37 - 1035/2401*T^36 + 456/2401*T^35 + 
        858/2401*T^34 - 1021/2401*T^33 + 1952/2401*T^32 - 151/2401*T^31 - 
        1107/2401*T^30 + 185/343*T^29 + 1411/2401*T^28 + 185/343*T^27 - 
        1107/2401*T^26 - 151/2401*T^25 + 1952/2401*T^24 - 1021/2401*T^23 + 
        858/2401*T^22 + 456/2401*T^21 - 1035/2401*T^20 + 921/2401*T^19 - 
        554/2401*T^18 + 659/2401*T^17 - 494/2401*T^16 - 1467/2401*T^15 + 
        1976/2401*T^14 - 65/2401*T^13 - 1620/2401*T^12 + 451/2401*T^11 - 
        598/2401*T^10 + 163/2401*T^9 - 1112/2401*T^8 - 17/343*T^7 + 1529/2401*T^6 - 
        1066/2401*T^5 + 1178/2401*T^4 + 202/343*T^3 - 39/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + X*Y^10 + X*Y^9 + 4*X*Y^8 + 
        X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 3*X*Y + 3*X + 3*Y^30 + 3*Y^29 + 2*Y^25
        + Y^24 + 4*Y^23 + 2*Y^22 + Y^21 + Y^20 + Y^18 + 3*Y^17 + 6*Y^15 + 5*Y^14 + 
        4*Y^13 + 5*Y^12 + 4*Y^11 + 5*Y^10 + 5*Y^9 + 4*Y^8 + 6*Y^7 + Y^6 + 3*Y^5 + 
        2*Y^4 + 5*Y^3 + 6*Y^2 + 4*Y + 1,
    T^56 - 10/7*T^55 + 31/49*T^54 + 302/343*T^53 - 2082/2401*T^52 - 186/343*T^51 + 
        1112/2401*T^50 + 393/343*T^49 - 5333/2401*T^48 + 2341/2401*T^47 + 
        1679/2401*T^46 - 2512/2401*T^45 - 290/2401*T^44 + 1339/2401*T^43 + 
        921/2401*T^42 - 593/343*T^41 + 3625/2401*T^40 + 527/2401*T^39 - 
        3449/2401*T^38 + 2417/2401*T^37 + 1138/2401*T^36 - 1891/2401*T^35 - 
        1137/2401*T^34 + 3838/2401*T^33 - 1741/2401*T^32 - 3159/2401*T^31 + 
        4252/2401*T^30 + 218/2401*T^29 - 2805/2401*T^28 + 218/2401*T^27 + 
        4252/2401*T^26 - 3159/2401*T^25 - 1741/2401*T^24 + 3838/2401*T^23 - 
        1137/2401*T^22 - 1891/2401*T^21 + 1138/2401*T^20 + 2417/2401*T^19 - 
        3449/2401*T^18 + 527/2401*T^17 + 3625/2401*T^16 - 593/343*T^15 + 
        921/2401*T^14 + 1339/2401*T^13 - 290/2401*T^12 - 2512/2401*T^11 + 
        1679/2401*T^10 + 2341/2401*T^9 - 5333/2401*T^8 + 393/343*T^7 + 1112/2401*T^6
        - 186/343*T^5 - 2082/2401*T^4 + 302/343*T^3 + 31/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 6*X*Y^8 
        + 4*X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + X*Y^4 + 2*X*Y^3 + 6*X*Y + 6*X + 3*Y^30 + 
        4*Y^29 + 6*Y^28 + 4*Y^27 + Y^25 + 3*Y^24 + 4*Y^23 + 6*Y^22 + Y^21 + 6*Y^20 +
        4*Y^19 + 5*Y^18 + 2*Y^16 + Y^15 + 4*Y^14 + 6*Y^13 + 3*Y^12 + 3*Y^11 + Y^10 +
        Y^9 + 4*Y^8 + Y^7 + 3*Y^6 + Y^5 + Y^3 + 6*Y^2 + 3*Y + 6,
    -T^56 + 33/49*T^54 + 36/49*T^53 - 976/2401*T^52 - 851/2401*T^51 + 288/2401*T^50 
        - 151/343*T^49 + 337/2401*T^48 - 447/2401*T^47 + 958/2401*T^46 - 51/343*T^45
        + 625/2401*T^44 - 5/2401*T^43 - 685/2401*T^42 - 444/2401*T^41 - 
        636/2401*T^40 - 172/2401*T^39 + 1352/2401*T^38 + 1857/2401*T^37 - 
        554/2401*T^36 - 1957/2401*T^35 - 200/343*T^34 + 1033/2401*T^33 - 
        143/2401*T^32 + 844/2401*T^31 + 202/2401*T^30 + 144/343*T^29 - 144/343*T^27 
        - 202/2401*T^26 - 844/2401*T^25 + 143/2401*T^24 - 1033/2401*T^23 + 
        200/343*T^22 + 1957/2401*T^21 + 554/2401*T^20 - 1857/2401*T^19 - 
        1352/2401*T^18 + 172/2401*T^17 + 636/2401*T^16 + 444/2401*T^15 + 
        685/2401*T^14 + 5/2401*T^13 - 625/2401*T^12 + 51/343*T^11 - 958/2401*T^10 + 
        447/2401*T^9 - 337/2401*T^8 + 151/343*T^7 - 288/2401*T^6 + 851/2401*T^5 + 
        976/2401*T^4 - 36/49*T^3 - 33/49*T^2 + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 3*X*Y^11 + 2*X*Y^10 + 2*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + 
        4*X*Y^4 + 2*X*Y^3 + 4*X*Y + 6*X + 4*Y^30 + 5*Y^29 + 5*Y^28 + 2*Y^27 + 2*Y^26
        + Y^25 + Y^24 + 6*Y^22 + 3*Y^21 + Y^20 + Y^19 + Y^18 + Y^17 + 2*Y^16 + 
        2*Y^14 + 3*Y^13 + Y^12 + 6*Y^11 + Y^10 + 2*Y^9 + 3*Y^8 + 4*Y^7 + Y^6 + 6*Y^4
        + 3*Y^3 + 2*Y^2 + 1,
    -T^56 + 5/7*T^55 + 37/49*T^54 - 425/343*T^53 + 963/2401*T^52 + 383/2401*T^51 + 
        373/2401*T^50 + 1438/2401*T^49 - 2270/2401*T^48 + 1147/2401*T^47 + 
        1240/2401*T^46 - 788/2401*T^45 + 1011/2401*T^44 - 307/343*T^43 + 
        1000/2401*T^42 + 1258/2401*T^41 - 1767/2401*T^40 + 937/2401*T^39 - 
        1228/2401*T^38 + 1047/2401*T^37 + 153/2401*T^36 - 2617/2401*T^35 + 
        2291/2401*T^34 - 159/343*T^33 - 107/2401*T^32 + 1446/2401*T^31 - 
        2883/2401*T^30 + 2299/2401*T^29 - 2299/2401*T^27 + 2883/2401*T^26 - 
        1446/2401*T^25 + 107/2401*T^24 + 159/343*T^23 - 2291/2401*T^22 + 
        2617/2401*T^21 - 153/2401*T^20 - 1047/2401*T^19 + 1228/2401*T^18 - 
        937/2401*T^17 + 1767/2401*T^16 - 1258/2401*T^15 - 1000/2401*T^14 + 
        307/343*T^13 - 1011/2401*T^12 + 788/2401*T^11 - 1240/2401*T^10 - 
        1147/2401*T^9 + 2270/2401*T^8 - 1438/2401*T^7 - 373/2401*T^6 - 383/2401*T^5 
        - 963/2401*T^4 + 425/343*T^3 - 37/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 
        + 2*X*Y^8 + 6*X*Y^7 + X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 2*X*Y + 4*X + 2*Y^30 + 
        Y^29 + 4*Y^25 + 3*Y^24 + 2*Y^22 + 6*Y^21 + 5*Y^20 + 3*Y^18 + Y^17 + 2*Y^16 +
        Y^15 + 2*Y^14 + 5*Y^13 + 5*Y^12 + 4*Y^11 + 5*Y^10 + 5*Y^8 + 5*Y^6 + 2*Y^5 + 
        Y^4 + 6*Y^3 + 4*Y^2 + 5*Y + 6,
    T^56 + 1/7*T^55 - 4/49*T^54 + 183/343*T^53 - 958/2401*T^52 + 674/2401*T^51 + 
        283/2401*T^50 - 40/343*T^49 + 1165/2401*T^48 - 2344/2401*T^47 + 
        1073/2401*T^46 + 1228/2401*T^45 - 1553/2401*T^44 + 1759/2401*T^43 - 
        1048/2401*T^42 - 9/343*T^41 - 425/2401*T^40 - 836/2401*T^39 + 2288/2401*T^38
        - 3225/2401*T^37 + 688/2401*T^36 + 787/2401*T^35 - 1919/2401*T^34 + 
        1595/2401*T^33 - 2423/2401*T^32 + 188/343*T^31 - 611/2401*T^30 - 
        2925/2401*T^29 + 557/343*T^28 - 2925/2401*T^27 - 611/2401*T^26 + 
        188/343*T^25 - 2423/2401*T^24 + 1595/2401*T^23 - 1919/2401*T^22 + 
        787/2401*T^21 + 688/2401*T^20 - 3225/2401*T^19 + 2288/2401*T^18 - 
        836/2401*T^17 - 425/2401*T^16 - 9/343*T^15 - 1048/2401*T^14 + 1759/2401*T^13
        - 1553/2401*T^12 + 1228/2401*T^11 + 1073/2401*T^10 - 2344/2401*T^9 + 
        1165/2401*T^8 - 40/343*T^7 + 283/2401*T^6 + 674/2401*T^5 - 958/2401*T^4 + 
        183/343*T^3 - 4/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 3*X*Y^9 + 5*X*Y^7 + 6*X*Y^5 + 
        6*X*Y^4 + 3*X*Y^3 + X*Y^2 + 4*X*Y + 6*X + 3*Y^30 + 2*Y^29 + 4*Y^28 + 2*Y^27 
        + 2*Y^26 + 2*Y^25 + 5*Y^24 + 2*Y^23 + 3*Y^22 + 4*Y^21 + 2*Y^20 + 2*Y^19 + 
        4*Y^18 + 5*Y^17 + 2*Y^16 + 3*Y^15 + 4*Y^14 + 2*Y^13 + 5*Y^12 + 6*Y^11 + 
        3*Y^10 + 5*Y^9 + 2*Y^8 + Y^7 + 5*Y^6 + 3*Y^5 + 5*Y^4 + 3*Y^3 + 4*Y^2 + 4,
    T^56 - 8/7*T^55 - 33/49*T^54 + 765/343*T^53 - 719/2401*T^52 - 5525/2401*T^51 + 
        2865/2401*T^50 + 5328/2401*T^49 - 4598/2401*T^48 - 3104/2401*T^47 + 
        3909/2401*T^46 + 1406/2401*T^45 - 2055/2401*T^44 - 170/343*T^43 - 
        65/343*T^42 + 2768/2401*T^41 - 95/343*T^40 - 1886/2401*T^39 - 6/343*T^38 + 
        1291/2401*T^37 + 85/2401*T^36 + 874/2401*T^35 - 1373/2401*T^34 - 
        3925/2401*T^33 + 5591/2401*T^32 + 3265/2401*T^31 - 8111/2401*T^30 - 
        1733/2401*T^29 + 10049/2401*T^28 - 1733/2401*T^27 - 8111/2401*T^26 + 
        3265/2401*T^25 + 5591/2401*T^24 - 3925/2401*T^23 - 1373/2401*T^22 + 
        874/2401*T^21 + 85/2401*T^20 + 1291/2401*T^19 - 6/343*T^18 - 1886/2401*T^17 
        - 95/343*T^16 + 2768/2401*T^15 - 65/343*T^14 - 170/343*T^13 - 2055/2401*T^12
        + 1406/2401*T^11 + 3909/2401*T^10 - 3104/2401*T^9 - 4598/2401*T^8 + 
        5328/2401*T^7 + 2865/2401*T^6 - 5525/2401*T^5 - 719/2401*T^4 + 765/343*T^3 -
        33/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 3*X*Y^8 + 6*X*Y^7 +
        4*X*Y^6 + 2*X*Y^5 + X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 3*X*Y + 4*Y^30 + 2*Y^29 + 
        6*Y^28 + 2*Y^27 + 2*Y^26 + 6*Y^25 + Y^24 + 6*Y^22 + 6*Y^21 + 3*Y^20 + Y^19 +
        5*Y^18 + 6*Y^16 + 3*Y^15 + Y^14 + 6*Y^13 + 2*Y^12 + Y^10 + 2*Y^9 + 6*Y^8 + 
        Y^7 + 2*Y^6 + Y^5 + Y^4 + 2*Y^2 + 6*Y + 4,
    T^56 - 2/7*T^55 - 47/49*T^54 + 363/343*T^53 - 172/2401*T^52 - 71/49*T^51 + 
        80/2401*T^50 + 2740/2401*T^49 - 1882/2401*T^48 - 47/49*T^47 + 3329/2401*T^46
        + 1205/2401*T^45 - 468/343*T^44 + 911/2401*T^43 + 3650/2401*T^42 - 
        297/343*T^41 - 1892/2401*T^40 + 3454/2401*T^39 - 132/2401*T^38 - 
        2477/2401*T^37 + 912/2401*T^36 + 1058/2401*T^35 - 1483/2401*T^34 - 
        1949/2401*T^33 + 1373/2401*T^32 + 835/2401*T^31 - 2242/2401*T^30 + 
        229/2401*T^29 + 3275/2401*T^28 + 229/2401*T^27 - 2242/2401*T^26 + 
        835/2401*T^25 + 1373/2401*T^24 - 1949/2401*T^23 - 1483/2401*T^22 + 
        1058/2401*T^21 + 912/2401*T^20 - 2477/2401*T^19 - 132/2401*T^18 + 
        3454/2401*T^17 - 1892/2401*T^16 - 297/343*T^15 + 3650/2401*T^14 + 
        911/2401*T^13 - 468/343*T^12 + 1205/2401*T^11 + 3329/2401*T^10 - 47/49*T^9 -
        1882/2401*T^8 + 2740/2401*T^7 + 80/2401*T^6 - 71/49*T^5 - 172/2401*T^4 + 
        363/343*T^3 - 47/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + X*Y^9 + X*Y^7 + 6*X*Y^6 + 
        X*Y^4 + 5*X*Y^2 + 2*X*Y + 2*X + 4*Y^30 + 4*Y^29 + 3*Y^28 + 3*Y^26 + 4*Y^25 +
        4*Y^22 + 3*Y^21 + 6*Y^19 + Y^18 + Y^17 + 4*Y^16 + Y^15 + 6*Y^14 + 4*Y^13 + 
        Y^12 + 6*Y^10 + Y^9 + 3*Y^7 + 4*Y^6 + 3*Y^5 + 6*Y^4 + 2*Y^2 + 5*Y + 6,
    T^56 - 4/7*T^55 - 8/49*T^54 + 296/343*T^53 - 1399/2401*T^52 - 1178/2401*T^51 + 
        1942/2401*T^50 - 580/2401*T^49 - 123/343*T^48 + 1732/2401*T^47 + 
        1104/2401*T^46 - 1489/2401*T^45 + 1150/2401*T^44 + 615/2401*T^43 - 
        2418/2401*T^42 + 124/2401*T^41 + 16/343*T^40 - 100/2401*T^39 + 251/2401*T^38
        + 250/2401*T^37 + 1187/2401*T^36 - 59/343*T^35 - 1224/2401*T^34 + 
        1399/2401*T^33 - 998/2401*T^32 - 242/343*T^31 + 1608/2401*T^30 + 
        874/2401*T^29 - 1310/2401*T^28 + 874/2401*T^27 + 1608/2401*T^26 - 
        242/343*T^25 - 998/2401*T^24 + 1399/2401*T^23 - 1224/2401*T^22 - 59/343*T^21
        + 1187/2401*T^20 + 250/2401*T^19 + 251/2401*T^18 - 100/2401*T^17 + 
        16/343*T^16 + 124/2401*T^15 - 2418/2401*T^14 + 615/2401*T^13 + 
        1150/2401*T^12 - 1489/2401*T^11 + 1104/2401*T^10 + 1732/2401*T^9 - 
        123/343*T^8 - 580/2401*T^7 + 1942/2401*T^6 - 1178/2401*T^5 - 1399/2401*T^4 +
        296/343*T^3 - 8/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^13 + 3*X*Y^12 + 2*X*Y^10 + 5*X*Y^9 + X*Y^8 + 5*X*Y^7 + 
        4*X*Y^6 + 6*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 3*X*Y + 4*Y^30 + 6*Y^29 + 3*Y^28 + 
        5*Y^27 + 3*Y^25 + 2*Y^23 + 4*Y^22 + 5*Y^21 + 4*Y^20 + 5*Y^19 + 2*Y^18 + 
        5*Y^17 + 6*Y^16 + Y^13 + 3*Y^12 + 3*Y^11 + 3*Y^10 + 6*Y^9 + 5*Y^8 + 5*Y^7 + 
        6*Y^6 + 6*Y^5 + 6*Y^3 + 2*Y + 6,
    T^56 + 2/7*T^55 - 18/49*T^54 + 117/343*T^53 - 9/343*T^52 - 60/343*T^51 + 
        1630/2401*T^50 - 188/2401*T^49 - 1314/2401*T^48 + 1506/2401*T^47 + 
        722/2401*T^46 - 97/343*T^45 + 260/2401*T^44 - 369/2401*T^43 - 1172/2401*T^42
        + 1171/2401*T^41 + 513/2401*T^40 - 727/2401*T^39 - 254/2401*T^38 + 
        314/2401*T^37 - 743/2401*T^36 - 839/2401*T^35 - 221/2401*T^34 - 
        1012/2401*T^33 - 211/2401*T^32 + 291/2401*T^31 - 246/2401*T^30 - 
        369/2401*T^29 - 247/2401*T^28 - 369/2401*T^27 - 246/2401*T^26 + 
        291/2401*T^25 - 211/2401*T^24 - 1012/2401*T^23 - 221/2401*T^22 - 
        839/2401*T^21 - 743/2401*T^20 + 314/2401*T^19 - 254/2401*T^18 - 
        727/2401*T^17 + 513/2401*T^16 + 1171/2401*T^15 - 1172/2401*T^14 - 
        369/2401*T^13 + 260/2401*T^12 - 97/343*T^11 + 722/2401*T^10 + 1506/2401*T^9 
        - 1314/2401*T^8 - 188/2401*T^7 + 1630/2401*T^6 - 60/343*T^5 - 9/343*T^4 + 
        117/343*T^3 - 18/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + X*Y^10 + 3*X*Y^9 + 
        2*X*Y^8 + X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 4*X*Y + 
        6*X + 6*Y^30 + 4*Y^29 + 2*Y^28 + 3*Y^27 + 6*Y^26 + 2*Y^25 + 3*Y^24 + 2*Y^23 
        + 3*Y^22 + Y^21 + 5*Y^20 + 2*Y^19 + 3*Y^18 + 4*Y^17 + 2*Y^16 + Y^14 + Y^13 +
        6*Y^12 + 3*Y^11 + 6*Y^10 + 5*Y^8 + 6*Y^7 + 5*Y^6 + 3*Y^5 + 5*Y^4 + 6*Y^3 + 
        5*Y^2 + 3*Y + 4,
    T^56 - 2/7*T^55 - 3/49*T^54 + 1/7*T^53 - 2428/2401*T^52 - 41/2401*T^51 + 
        870/2401*T^50 - 1385/2401*T^49 + 1179/2401*T^48 + 884/2401*T^47 - 
        766/2401*T^46 + 20/343*T^45 + 62/343*T^44 - 64/2401*T^43 - 13/343*T^42 - 
        214/2401*T^41 - 120/343*T^40 + 57/2401*T^39 - 542/2401*T^38 + 397/2401*T^37 
        - 6/343*T^36 - 145/343*T^35 + 1338/2401*T^34 + 727/2401*T^33 - 900/2401*T^32
        + 368/343*T^31 - 676/2401*T^30 - 2124/2401*T^29 + 1374/2401*T^28 - 
        2124/2401*T^27 - 676/2401*T^26 + 368/343*T^25 - 900/2401*T^24 + 
        727/2401*T^23 + 1338/2401*T^22 - 145/343*T^21 - 6/343*T^20 + 397/2401*T^19 -
        542/2401*T^18 + 57/2401*T^17 - 120/343*T^16 - 214/2401*T^15 - 13/343*T^14 - 
        64/2401*T^13 + 62/343*T^12 + 20/343*T^11 - 766/2401*T^10 + 884/2401*T^9 + 
        1179/2401*T^8 - 1385/2401*T^7 + 870/2401*T^6 - 41/2401*T^5 - 2428/2401*T^4 +
        1/7*T^3 - 3/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + X*Y^9 + 3*X*Y^8 + 4*X*Y^7 + 
        5*X*Y^6 + X*Y^5 + X*Y^3 + X*Y^2 + X*Y + X + 6*Y^30 + 3*Y^29 + Y^28 + Y^25 + 
        4*Y^24 + Y^23 + 6*Y^22 + 2*Y^21 + Y^20 + 6*Y^18 + 5*Y^17 + 6*Y^16 + 4*Y^15 +
        Y^14 + 6*Y^13 + 4*Y^11 + 5*Y^10 + 2*Y^9 + 3*Y^8 + 6*Y^7 + 5*Y^6 + Y^5 + 
        4*Y^4 + Y^3 + Y^2 + 3,
    T^56 + 11/7*T^55 + 69/49*T^54 + 262/343*T^53 - 930/2401*T^52 - 3929/2401*T^51 - 
        3840/2401*T^50 - 1261/2401*T^49 + 1382/2401*T^48 + 2706/2401*T^47 + 
        2784/2401*T^46 + 284/2401*T^45 - 3090/2401*T^44 - 3698/2401*T^43 - 
        2830/2401*T^42 - 304/343*T^41 + 892/2401*T^40 + 2978/2401*T^39 + 
        2447/2401*T^38 + 242/343*T^37 + 685/2401*T^36 - 685/2401*T^35 - 
        1558/2401*T^34 - 901/2401*T^33 - 599/2401*T^32 - 746/2401*T^31 + 
        101/2401*T^30 - 261/2401*T^29 - 1196/2401*T^28 - 261/2401*T^27 + 
        101/2401*T^26 - 746/2401*T^25 - 599/2401*T^24 - 901/2401*T^23 - 
        1558/2401*T^22 - 685/2401*T^21 + 685/2401*T^20 + 242/343*T^19 + 
        2447/2401*T^18 + 2978/2401*T^17 + 892/2401*T^16 - 304/343*T^15 - 
        2830/2401*T^14 - 3698/2401*T^13 - 3090/2401*T^12 + 284/2401*T^11 + 
        2784/2401*T^10 + 2706/2401*T^9 + 1382/2401*T^8 - 1261/2401*T^7 - 
        3840/2401*T^6 - 3929/2401*T^5 - 930/2401*T^4 + 262/343*T^3 + 69/49*T^2 + 
        11/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + 4*X*Y^10 + 3*X*Y^9 + 3*X*Y^7 + 
        X*Y^6 + 5*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 2*X*Y + 5*X + 2*Y^30 + Y^29 + 2*Y^28 +
        Y^27 + 4*Y^26 + 3*Y^25 + 6*Y^24 + 3*Y^23 + 4*Y^21 + 6*Y^20 + 4*Y^19 + 4*Y^18
        + 2*Y^16 + Y^14 + 4*Y^13 + Y^11 + Y^10 + 2*Y^9 + 4*Y^8 + 6*Y^6 + Y^5 + Y^4 +
        5*Y^3 + 6*Y + 5,
    T^56 + 1/7*T^55 + 38/49*T^54 - 206/343*T^53 - 1837/2401*T^52 - 4203/2401*T^51 - 
        1149/2401*T^50 - 132/2401*T^49 + 495/343*T^48 + 1748/2401*T^47 + 
        2721/2401*T^46 - 3009/2401*T^45 - 3282/2401*T^44 - 2676/2401*T^43 - 
        759/2401*T^42 + 1957/2401*T^41 + 558/343*T^40 + 3382/2401*T^39 - 72/343*T^38
        - 1329/2401*T^37 - 2626/2401*T^36 - 1709/2401*T^35 - 15/343*T^34 + 
        3814/2401*T^33 + 2694/2401*T^32 + 1754/2401*T^31 - 463/2401*T^30 - 
        2218/2401*T^29 - 5204/2401*T^28 - 2218/2401*T^27 - 463/2401*T^26 + 
        1754/2401*T^25 + 2694/2401*T^24 + 3814/2401*T^23 - 15/343*T^22 - 
        1709/2401*T^21 - 2626/2401*T^20 - 1329/2401*T^19 - 72/343*T^18 + 
        3382/2401*T^17 + 558/343*T^16 + 1957/2401*T^15 - 759/2401*T^14 - 
        2676/2401*T^13 - 3282/2401*T^12 - 3009/2401*T^11 + 2721/2401*T^10 + 
        1748/2401*T^9 + 495/343*T^8 - 132/2401*T^7 - 1149/2401*T^6 - 4203/2401*T^5 -
        1837/2401*T^4 - 206/343*T^3 + 38/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + X*Y^12 + 3*X*Y^11 + X*Y^8 + 6*X*Y^7 + 3*X*Y^6 + 
        4*X*Y^5 + 6*X*Y^4 + X*Y^3 + 2*X*Y^2 + 5*X*Y + 6*X + 5*Y^30 + 5*Y^29 + 6*Y^28
        + 3*Y^27 + 2*Y^26 + 2*Y^25 + 2*Y^24 + 2*Y^23 + 6*Y^22 + 6*Y^21 + 3*Y^20 + 
        5*Y^18 + 5*Y^17 + Y^16 + 2*Y^15 + 6*Y^14 + 4*Y^12 + 2*Y^11 + Y^10 + 3*Y^9 + 
        3*Y^8 + 3*Y^6 + 3*Y^5 + Y^4 + 6*Y^3 + 3*Y^2 + 4*Y + 2,
    T^56 - 8/49*T^54 + 3/49*T^53 + 71/2401*T^52 + 41/2401*T^51 - 760/2401*T^50 + 
        10/2401*T^49 - 377/343*T^48 - 326/2401*T^47 + 134/2401*T^46 - 1020/2401*T^45
        + 517/2401*T^44 - 145/343*T^43 + 97/2401*T^42 + 206/2401*T^41 + 
        1857/2401*T^40 - 558/2401*T^39 - 239/2401*T^38 + 1440/2401*T^37 - 
        46/343*T^36 + 1517/2401*T^35 + 376/2401*T^34 - 869/2401*T^33 - 332/2401*T^32
        + 184/343*T^31 - 16/343*T^30 - 1760/2401*T^29 + 488/2401*T^28 - 
        1760/2401*T^27 - 16/343*T^26 + 184/343*T^25 - 332/2401*T^24 - 869/2401*T^23 
        + 376/2401*T^22 + 1517/2401*T^21 - 46/343*T^20 + 1440/2401*T^19 - 
        239/2401*T^18 - 558/2401*T^17 + 1857/2401*T^16 + 206/2401*T^15 + 
        97/2401*T^14 - 145/343*T^13 + 517/2401*T^12 - 1020/2401*T^11 + 134/2401*T^10
        - 326/2401*T^9 - 377/343*T^8 + 10/2401*T^7 - 760/2401*T^6 + 41/2401*T^5 + 
        71/2401*T^4 + 3/49*T^3 - 8/49*T^2 + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + X*Y^10 + 3*X*Y^9 + 
        2*X*Y^8 + 2*X*Y^7 + 3*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 6*X*Y + 6*X + 2*Y^30 + 
        Y^29 + 6*Y^28 + 3*Y^27 + 3*Y^26 + Y^25 + 4*Y^24 + 2*Y^23 + 4*Y^22 + 6*Y^21 +
        3*Y^20 + 5*Y^19 + Y^18 + 3*Y^17 + Y^16 + 2*Y^15 + 2*Y^14 + 4*Y^13 + 6*Y^11 +
        4*Y^10 + 2*Y^9 + 3*Y^8 + 3*Y^7 + 2*Y^6 + 2*Y^4 + 6*Y^2 + 5*Y + 5,
    T^56 + T^55 - 46/49*T^54 - 582/343*T^53 + 1824/2401*T^52 + 4500/2401*T^51 - 
        964/2401*T^50 - 3408/2401*T^49 + 2059/2401*T^48 + 2736/2401*T^47 - 
        3951/2401*T^46 - 2836/2401*T^45 + 6273/2401*T^44 + 4437/2401*T^43 - 
        5594/2401*T^42 - 3264/2401*T^41 + 880/343*T^40 + 2888/2401*T^39 - 
        6565/2401*T^38 - 1747/2401*T^37 + 8706/2401*T^36 + 2664/2401*T^35 - 
        8991/2401*T^34 - 2270/2401*T^33 + 8944/2401*T^32 + 2375/2401*T^31 - 
        7408/2401*T^30 - 502/2401*T^29 + 7304/2401*T^28 - 502/2401*T^27 - 
        7408/2401*T^26 + 2375/2401*T^25 + 8944/2401*T^24 - 2270/2401*T^23 - 
        8991/2401*T^22 + 2664/2401*T^21 + 8706/2401*T^20 - 1747/2401*T^19 - 
        6565/2401*T^18 + 2888/2401*T^17 + 880/343*T^16 - 3264/2401*T^15 - 
        5594/2401*T^14 + 4437/2401*T^13 + 6273/2401*T^12 - 2836/2401*T^11 - 
        3951/2401*T^10 + 2736/2401*T^9 + 2059/2401*T^8 - 3408/2401*T^7 - 
        964/2401*T^6 + 4500/2401*T^5 + 1824/2401*T^4 - 582/343*T^3 - 46/49*T^2 + T +
        1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 3*X*Y^9 + 3*X*Y^8 +
        4*X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + X*Y^2 + 4*X*Y + 3*X + 
        6*Y^30 + 2*Y^29 + 5*Y^28 + 4*Y^27 + 5*Y^26 + 6*Y^25 + 3*Y^24 + 6*Y^23 + 
        2*Y^22 + 6*Y^21 + 2*Y^20 + 6*Y^19 + 4*Y^18 + 4*Y^17 + 3*Y^16 + 5*Y^14 + 
        3*Y^13 + 6*Y^12 + Y^11 + Y^9 + 3*Y^8 + 4*Y^7 + Y^6 + 6*Y^5 + 4*Y^4 + 3*Y^3 +
        Y^2 + 6*Y + 4,
    T^56 - 23/49*T^54 - 275/343*T^53 - 2337/2401*T^52 + 2252/2401*T^51 + 20/343*T^50
        - 37/2401*T^49 + 59/2401*T^48 - 264/2401*T^47 + 1587/2401*T^46 + 
        572/2401*T^45 - 181/2401*T^44 + 25/343*T^43 - 184/2401*T^42 - 153/343*T^41 +
        179/2401*T^40 - 130/343*T^39 - 765/2401*T^38 + 184/2401*T^37 - 303/2401*T^36
        + 1951/2401*T^35 + 1314/2401*T^34 - 180/343*T^33 + 206/2401*T^32 - 
        30/2401*T^31 + 558/2401*T^30 + 123/2401*T^29 - 2550/2401*T^28 + 
        123/2401*T^27 + 558/2401*T^26 - 30/2401*T^25 + 206/2401*T^24 - 180/343*T^23 
        + 1314/2401*T^22 + 1951/2401*T^21 - 303/2401*T^20 + 184/2401*T^19 - 
        765/2401*T^18 - 130/343*T^17 + 179/2401*T^16 - 153/343*T^15 - 184/2401*T^14 
        + 25/343*T^13 - 181/2401*T^12 + 572/2401*T^11 + 1587/2401*T^10 - 
        264/2401*T^9 + 59/2401*T^8 - 37/2401*T^7 + 20/343*T^6 + 2252/2401*T^5 - 
        2337/2401*T^4 - 275/343*T^3 - 23/49*T^2 + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 4*X*Y^11 + 6*X*Y^10 + 2*X*Y^9 + 4*X*Y^8 + X*Y^7 + 
        3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 4*X*Y + 3*X + 2*Y^30 + 
        5*Y^29 + Y^28 + 3*Y^27 + 3*Y^26 + 2*Y^25 + 6*Y^23 + 6*Y^22 + Y^21 + 4*Y^20 +
        6*Y^19 + 3*Y^18 + 4*Y^16 + 4*Y^15 + 2*Y^14 + 5*Y^12 + 2*Y^10 + 2*Y^9 + 6*Y^8
        + 4*Y^7 + 2*Y^6 + Y^5 + 2*Y^4 + 5*Y^3 + 3*Y^2 + 2*Y + 6,
    -T^56 - 12/7*T^55 - 60/49*T^54 - 379/343*T^53 - 366/343*T^52 - 3247/2401*T^51 - 
        4898/2401*T^50 - 3956/2401*T^49 - 2795/2401*T^48 - 3370/2401*T^47 - 
        697/343*T^46 - 6551/2401*T^45 - 5454/2401*T^44 - 2444/2401*T^43 - 
        940/2401*T^42 - 1934/2401*T^41 - 2805/2401*T^40 - 1984/2401*T^39 - 
        123/343*T^38 + 346/2401*T^37 + 228/2401*T^36 - 1388/2401*T^35 - 
        641/2401*T^34 + 1241/2401*T^33 + 2356/2401*T^32 + 1931/2401*T^31 + 
        85/2401*T^30 - 387/2401*T^29 + 387/2401*T^27 - 85/2401*T^26 - 1931/2401*T^25
        - 2356/2401*T^24 - 1241/2401*T^23 + 641/2401*T^22 + 1388/2401*T^21 - 
        228/2401*T^20 - 346/2401*T^19 + 123/343*T^18 + 1984/2401*T^17 + 
        2805/2401*T^16 + 1934/2401*T^15 + 940/2401*T^14 + 2444/2401*T^13 + 
        5454/2401*T^12 + 6551/2401*T^11 + 697/343*T^10 + 3370/2401*T^9 + 
        2795/2401*T^8 + 3956/2401*T^7 + 4898/2401*T^6 + 3247/2401*T^5 + 366/343*T^4 
        + 379/343*T^3 + 60/49*T^2 + 12/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 
        X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 3*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 4*X + Y^30 + 
        4*Y^27 + 5*Y^26 + 5*Y^25 + 2*Y^24 + 4*Y^23 + Y^22 + Y^21 + 5*Y^20 + 3*Y^18 +
        5*Y^16 + 4*Y^15 + 3*Y^14 + 6*Y^13 + 3*Y^12 + 2*Y^11 + 5*Y^10 + 2*Y^9 + 6*Y^8
        + 5*Y^7 + 6*Y^6 + 2*Y^4 + 5*Y^3 + 6*Y^2 + Y + 3,
    T^56 - T^55 - 3/7*T^54 + 416/343*T^53 - 2311/2401*T^52 + 38/49*T^51 + 
        1040/2401*T^50 - 2530/2401*T^49 + 811/2401*T^48 + 869/2401*T^47 - 
        1593/2401*T^46 + 131/343*T^45 + 45/49*T^44 - 2950/2401*T^43 + 517/2401*T^42 
        + 1000/2401*T^41 - 1885/2401*T^40 + 251/343*T^39 + 650/2401*T^38 - 
        2071/2401*T^37 - 110/2401*T^36 + 265/343*T^35 - 2025/2401*T^34 + 
        265/2401*T^33 + 2396/2401*T^32 - 3508/2401*T^31 + 8/49*T^30 + 1973/2401*T^29
        - 57/49*T^28 + 1973/2401*T^27 + 8/49*T^26 - 3508/2401*T^25 + 2396/2401*T^24 
        + 265/2401*T^23 - 2025/2401*T^22 + 265/343*T^21 - 110/2401*T^20 - 
        2071/2401*T^19 + 650/2401*T^18 + 251/343*T^17 - 1885/2401*T^16 + 
        1000/2401*T^15 + 517/2401*T^14 - 2950/2401*T^13 + 45/49*T^12 + 131/343*T^11 
        - 1593/2401*T^10 + 869/2401*T^9 + 811/2401*T^8 - 2530/2401*T^7 + 
        1040/2401*T^6 + 38/49*T^5 - 2311/2401*T^4 + 416/343*T^3 - 3/7*T^2 - T + 1
*], [*
    X^3 + 5*X*Y^14 + X*Y^13 + 2*X*Y^9 + 3*X*Y^8 + X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 
        5*X*Y^3 + 6*X*Y^2 + 3*X*Y + 2*X + Y^30 + 3*Y^29 + 3*Y^28 + 6*Y^27 + 3*Y^26 +
        3*Y^25 + 4*Y^24 + 6*Y^23 + 3*Y^22 + 3*Y^21 + 4*Y^20 + 2*Y^19 + 4*Y^16 + Y^15
        + 5*Y^14 + 2*Y^13 + 2*Y^12 + 4*Y^10 + 4*Y^8 + 4*Y^7 + 3*Y^4 + Y^3 + 4*Y^2 + 
        4,
    -T^56 + 4/7*T^55 + 9/49*T^54 - 194/343*T^53 + 788/2401*T^52 - 1398/2401*T^51 + 
        200/343*T^50 - 500/2401*T^49 - 94/343*T^48 + 932/2401*T^47 - 1270/2401*T^46 
        + 1264/2401*T^45 + 466/2401*T^44 - 158/2401*T^43 + 62/343*T^42 + 
        681/2401*T^41 - 76/2401*T^40 - 1079/2401*T^39 + 265/343*T^38 - 536/2401*T^37
        + 415/2401*T^36 + 88/343*T^35 - 614/2401*T^34 + 1108/2401*T^33 - 
        422/2401*T^32 - 52/2401*T^31 + 243/2401*T^30 - 752/2401*T^29 + 752/2401*T^27
        - 243/2401*T^26 + 52/2401*T^25 + 422/2401*T^24 - 1108/2401*T^23 + 
        614/2401*T^22 - 88/343*T^21 - 415/2401*T^20 + 536/2401*T^19 - 265/343*T^18 +
        1079/2401*T^17 + 76/2401*T^16 - 681/2401*T^15 - 62/343*T^14 + 158/2401*T^13 
        - 466/2401*T^12 - 1264/2401*T^11 + 1270/2401*T^10 - 932/2401*T^9 + 
        94/343*T^8 + 500/2401*T^7 - 200/343*T^6 + 1398/2401*T^5 - 788/2401*T^4 + 
        194/343*T^3 - 9/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 4*X*Y^13 + 4*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 6*X*Y^7 + 
        X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 6*X*Y + 4*X + 4*Y^30 + Y^29 
        + 4*Y^28 + 5*Y^27 + 4*Y^26 + Y^25 + 6*Y^24 + 3*Y^23 + 6*Y^22 + 3*Y^21 + 
        6*Y^19 + 6*Y^18 + 4*Y^17 + 4*Y^15 + 2*Y^13 + 2*Y^12 + 3*Y^10 + 3*Y^9 + 4*Y^8
        + Y^7 + Y^6 + 2*Y^5 + 2*Y^2 + 3,
    T^56 + 4/7*T^55 + 3/49*T^54 - 132/343*T^53 - 1551/2401*T^52 + 81/2401*T^51 + 
        449/2401*T^50 + 1492/2401*T^49 + 881/2401*T^48 - 340/2401*T^47 - 
        1171/2401*T^46 - 67/2401*T^45 + 46/343*T^44 - 447/2401*T^43 - 906/2401*T^42 
        - 1402/2401*T^41 + 1032/2401*T^40 + 99/343*T^39 + 913/2401*T^38 - 
        61/343*T^37 - 1142/2401*T^36 - 436/2401*T^35 + 396/2401*T^34 + 122/2401*T^33
        - 45/2401*T^32 - 1587/2401*T^31 - 1388/2401*T^30 + 1038/2401*T^29 + 
        1024/2401*T^28 + 1038/2401*T^27 - 1388/2401*T^26 - 1587/2401*T^25 - 
        45/2401*T^24 + 122/2401*T^23 + 396/2401*T^22 - 436/2401*T^21 - 
        1142/2401*T^20 - 61/343*T^19 + 913/2401*T^18 + 99/343*T^17 + 1032/2401*T^16 
        - 1402/2401*T^15 - 906/2401*T^14 - 447/2401*T^13 + 46/343*T^12 - 
        67/2401*T^11 - 1171/2401*T^10 - 340/2401*T^9 + 881/2401*T^8 + 1492/2401*T^7 
        + 449/2401*T^6 + 81/2401*T^5 - 1551/2401*T^4 - 132/343*T^3 + 3/49*T^2 + 
        4/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + X*Y^12 + 3*X*Y^11 + 5*X*Y^9 + 5*X*Y^8 + 
        6*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 5*X*Y + 3*X + 6*Y^30 + 3*Y^29 + 
        3*Y^28 + 3*Y^27 + 5*Y^26 + 2*Y^25 + 4*Y^24 + Y^23 + 5*Y^22 + 5*Y^21 + 4*Y^19
        + Y^18 + Y^17 + 5*Y^16 + 3*Y^15 + 5*Y^14 + 4*Y^13 + 3*Y^11 + 3*Y^10 + 5*Y^9 
        + Y^8 + 2*Y^7 + 5*Y^6 + 2*Y^5 + 3*Y^4 + Y^3 + 2*Y^2 + 6*Y + 1,
    T^56 - 2/7*T^55 + 6/49*T^54 - 34/343*T^53 - 3565/2401*T^52 + 271/2401*T^51 - 
        561/2401*T^50 + 205/2401*T^49 + 2859/2401*T^48 + 60/2401*T^47 + 
        674/2401*T^46 + 249/2401*T^45 - 1100/2401*T^44 - 1577/2401*T^43 + 
        239/2401*T^42 - 723/2401*T^41 + 566/2401*T^40 + 1874/2401*T^39 - 
        237/2401*T^38 - 801/2401*T^37 - 57/343*T^36 - 194/343*T^35 + 541/2401*T^34 +
        986/2401*T^33 + 458/2401*T^32 + 650/2401*T^31 - 101/2401*T^30 - 
        1072/2401*T^29 + 191/2401*T^28 - 1072/2401*T^27 - 101/2401*T^26 + 
        650/2401*T^25 + 458/2401*T^24 + 986/2401*T^23 + 541/2401*T^22 - 194/343*T^21
        - 57/343*T^20 - 801/2401*T^19 - 237/2401*T^18 + 1874/2401*T^17 + 
        566/2401*T^16 - 723/2401*T^15 + 239/2401*T^14 - 1577/2401*T^13 - 
        1100/2401*T^12 + 249/2401*T^11 + 674/2401*T^10 + 60/2401*T^9 + 2859/2401*T^8
        + 205/2401*T^7 - 561/2401*T^6 + 271/2401*T^5 - 3565/2401*T^4 - 34/343*T^3 + 
        6/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 
        + 6*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 5*X + 4*Y^30 + 3*Y^29 + 
        6*Y^28 + 6*Y^27 + 5*Y^26 + 5*Y^25 + 2*Y^24 + 5*Y^22 + Y^21 + 2*Y^20 + 4*Y^19
        + 3*Y^18 + 2*Y^17 + Y^16 + 3*Y^15 + 2*Y^14 + 6*Y^13 + 5*Y^12 + 2*Y^11 + 
        3*Y^7 + 4*Y^6 + Y^5 + Y^4 + 4*Y^3 + 5*Y + 3,
    T^56 + T^55 + 2/7*T^54 - 44/49*T^53 - 352/343*T^52 - 50/2401*T^51 + 151/343*T^50
        + 1182/2401*T^49 + 292/2401*T^48 + 512/2401*T^47 + 534/2401*T^46 + 
        144/2401*T^45 - 566/2401*T^44 - 103/2401*T^43 + 571/2401*T^42 + 41/343*T^41 
        - 988/2401*T^40 - 1214/2401*T^39 - 976/2401*T^38 - 405/2401*T^37 - 
        334/2401*T^36 - 58/2401*T^35 + 1165/2401*T^34 + 885/2401*T^33 + 
        874/2401*T^32 - 121/2401*T^31 - 964/2401*T^30 - 844/2401*T^29 - 
        1647/2401*T^28 - 844/2401*T^27 - 964/2401*T^26 - 121/2401*T^25 + 
        874/2401*T^24 + 885/2401*T^23 + 1165/2401*T^22 - 58/2401*T^21 - 
        334/2401*T^20 - 405/2401*T^19 - 976/2401*T^18 - 1214/2401*T^17 - 
        988/2401*T^16 + 41/343*T^15 + 571/2401*T^14 - 103/2401*T^13 - 566/2401*T^12 
        + 144/2401*T^11 + 534/2401*T^10 + 512/2401*T^9 + 292/2401*T^8 + 
        1182/2401*T^7 + 151/343*T^6 - 50/2401*T^5 - 352/343*T^4 - 44/49*T^3 + 
        2/7*T^2 + T + 1
*], [*
    X^3 + 2*X*Y^14 + 3*X*Y^13 + 2*X*Y^11 + X*Y^10 + 5*X*Y^9 + 5*X*Y^8 + X*Y^5 + 
        2*X*Y^3 + X*Y^2 + X + Y^30 + 5*Y^29 + 5*Y^26 + 3*Y^25 + 2*Y^24 + 4*Y^23 + 
        5*Y^22 + Y^21 + 4*Y^20 + 3*Y^19 + 6*Y^18 + 5*Y^17 + 3*Y^16 + 2*Y^15 + 5*Y^14
        + Y^13 + 3*Y^12 + 5*Y^11 + 5*Y^10 + Y^9 + 5*Y^8 + 6*Y^7 + 4*Y^6 + 3*Y^5 + 
        6*Y^4 + 5*Y^3 + 5*Y^2 + 4*Y + 4,
    T^56 - 10/7*T^55 + 3/49*T^54 - 69/343*T^53 + 485/343*T^52 - 2210/2401*T^51 + 
        5/7*T^50 - 2815/2401*T^49 + 20/2401*T^48 + 902/2401*T^47 + 138/343*T^46 + 
        1436/2401*T^45 - 2153/2401*T^44 - 457/2401*T^43 - 1606/2401*T^42 + 
        2815/2401*T^41 + 76/2401*T^40 + 813/2401*T^39 - 1164/2401*T^38 - 
        1325/2401*T^37 - 642/2401*T^36 + 1782/2401*T^35 + 1380/2401*T^34 - 
        41/2401*T^33 - 2207/2401*T^32 + 317/2401*T^31 - 773/2401*T^30 + 
        1914/2401*T^29 - 1425/2401*T^28 + 1914/2401*T^27 - 773/2401*T^26 + 
        317/2401*T^25 - 2207/2401*T^24 - 41/2401*T^23 + 1380/2401*T^22 + 
        1782/2401*T^21 - 642/2401*T^20 - 1325/2401*T^19 - 1164/2401*T^18 + 
        813/2401*T^17 + 76/2401*T^16 + 2815/2401*T^15 - 1606/2401*T^14 - 
        457/2401*T^13 - 2153/2401*T^12 + 1436/2401*T^11 + 138/343*T^10 + 
        902/2401*T^9 + 20/2401*T^8 - 2815/2401*T^7 + 5/7*T^6 - 2210/2401*T^5 + 
        485/343*T^4 - 69/343*T^3 + 3/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 2*X*Y^13 + 4*X*Y^11 + 2*X*Y^10 + X*Y^9 + 6*X*Y^8 + 
        4*X*Y^7 + 2*X*Y^4 + 2*X*Y^3 + X*Y^2 + X*Y + 4*Y^30 + 6*Y^29 + 4*Y^28 + 
        5*Y^25 + 4*Y^24 + 5*Y^23 + 5*Y^22 + 5*Y^21 + 4*Y^20 + 3*Y^19 + 5*Y^18 + Y^17
        + 5*Y^16 + 5*Y^14 + 6*Y^13 + Y^12 + 5*Y^11 + 6*Y^10 + 5*Y^9 + Y^8 + 3*Y^7 + 
        6*Y^6 + 2*Y^5 + 4*Y^3 + 2*Y^2 + 6*Y + 6,
    T^56 + 1/7*T^55 - 33/49*T^54 - 57/343*T^53 - 58/2401*T^52 + 113/343*T^51 + 
        913/2401*T^50 + 592/2401*T^49 - 484/2401*T^48 - 774/2401*T^47 - 
        796/2401*T^46 + 1275/2401*T^45 + 391/2401*T^44 + 576/2401*T^43 + 
        1080/2401*T^42 - 180/343*T^41 - 137/343*T^40 + 46/343*T^39 + 876/2401*T^38 -
        181/2401*T^37 - 407/2401*T^36 + 396/2401*T^35 + 177/2401*T^34 - 
        862/2401*T^33 + 216/2401*T^32 + 83/2401*T^31 - 990/2401*T^30 + 498/2401*T^29
        + 1339/2401*T^28 + 498/2401*T^27 - 990/2401*T^26 + 83/2401*T^25 + 
        216/2401*T^24 - 862/2401*T^23 + 177/2401*T^22 + 396/2401*T^21 - 
        407/2401*T^20 - 181/2401*T^19 + 876/2401*T^18 + 46/343*T^17 - 137/343*T^16 -
        180/343*T^15 + 1080/2401*T^14 + 576/2401*T^13 + 391/2401*T^12 + 
        1275/2401*T^11 - 796/2401*T^10 - 774/2401*T^9 - 484/2401*T^8 + 592/2401*T^7 
        + 913/2401*T^6 + 113/343*T^5 - 58/2401*T^4 - 57/343*T^3 - 33/49*T^2 + 1/7*T 
        + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + X*Y^8 + 
        2*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 4*X*Y + 5*X + 
        2*Y^30 + 6*Y^29 + 3*Y^28 + 6*Y^27 + 3*Y^26 + 3*Y^25 + 4*Y^23 + Y^22 + Y^21 +
        2*Y^19 + 3*Y^18 + Y^16 + 3*Y^15 + 5*Y^14 + 2*Y^13 + 6*Y^12 + 3*Y^11 + 4*Y^10
        + Y^9 + 2*Y^8 + Y^7 + 2*Y^6 + 3*Y^5 + 5*Y^4 + 2*Y^3 + 2*Y^2 + 2*Y + 6,
    -T^56 - 2/7*T^55 + 27/343*T^53 - 148/2401*T^52 - 165/343*T^51 + 1255/2401*T^50 -
        391/2401*T^49 + 66/343*T^48 - 736/2401*T^47 - 1753/2401*T^46 + 151/2401*T^45
        - 671/2401*T^44 + 1770/2401*T^43 - 125/2401*T^42 + 379/2401*T^41 + 
        1705/2401*T^40 - 12/2401*T^39 + 1096/2401*T^38 - 1489/2401*T^37 + 
        705/2401*T^36 + 220/2401*T^35 + 582/2401*T^34 + 941/2401*T^33 - 
        792/2401*T^32 + 1198/2401*T^31 + 254/2401*T^30 + 908/2401*T^29 - 
        908/2401*T^27 - 254/2401*T^26 - 1198/2401*T^25 + 792/2401*T^24 - 
        941/2401*T^23 - 582/2401*T^22 - 220/2401*T^21 - 705/2401*T^20 + 
        1489/2401*T^19 - 1096/2401*T^18 + 12/2401*T^17 - 1705/2401*T^16 - 
        379/2401*T^15 + 125/2401*T^14 - 1770/2401*T^13 + 671/2401*T^12 - 
        151/2401*T^11 + 1753/2401*T^10 + 736/2401*T^9 - 66/343*T^8 + 391/2401*T^7 - 
        1255/2401*T^6 + 165/343*T^5 + 148/2401*T^4 - 27/343*T^3 + 2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 
        5*X*Y^7 + 3*X*Y^6 + X*Y^5 + X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 6*X*Y + 2*Y^30 + 
        3*Y^29 + 2*Y^28 + 5*Y^27 + 5*Y^25 + 5*Y^24 + 3*Y^23 + 3*Y^22 + 4*Y^21 + 
        5*Y^20 + Y^19 + 5*Y^18 + 3*Y^16 + 5*Y^15 + 6*Y^14 + Y^13 + 2*Y^12 + 3*Y^11 +
        Y^10 + 4*Y^9 + 6*Y^7 + 6*Y^6 + 2*Y^5 + 2*Y^4 + 5*Y^3 + 4*Y + 3,
    T^56 - 12/7*T^55 + 2/7*T^54 + 670/343*T^53 - 6988/2401*T^52 + 4269/2401*T^51 + 
        1535/2401*T^50 - 1082/343*T^49 + 8818/2401*T^48 - 1565/2401*T^47 - 
        6268/2401*T^46 + 7214/2401*T^45 - 1858/2401*T^44 - 3352/2401*T^43 + 
        4875/2401*T^42 - 2868/2401*T^41 - 2056/2401*T^40 + 605/343*T^39 - 
        2333/2401*T^38 - 543/2401*T^37 + 1807/2401*T^36 - 1377/2401*T^35 + 
        1327/2401*T^34 - 256/2401*T^33 - 970/2401*T^32 + 797/2401*T^31 + 
        87/2401*T^30 - 183/2401*T^29 - 468/2401*T^28 - 183/2401*T^27 + 87/2401*T^26 
        + 797/2401*T^25 - 970/2401*T^24 - 256/2401*T^23 + 1327/2401*T^22 - 
        1377/2401*T^21 + 1807/2401*T^20 - 543/2401*T^19 - 2333/2401*T^18 + 
        605/343*T^17 - 2056/2401*T^16 - 2868/2401*T^15 + 4875/2401*T^14 - 
        3352/2401*T^13 - 1858/2401*T^12 + 7214/2401*T^11 - 6268/2401*T^10 - 
        1565/2401*T^9 + 8818/2401*T^8 - 1082/343*T^7 + 1535/2401*T^6 + 4269/2401*T^5
        - 6988/2401*T^4 + 670/343*T^3 + 2/7*T^2 - 12/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + X*Y^10 + X*Y^9 + 3*X*Y^8 + 
        2*X*Y^7 + X*Y^6 + 4*X*Y^5 + 2*X*Y^3 + 5*X*Y^2 + 2*X + Y^30 + 6*Y^29 + 4*Y^28
        + Y^26 + 6*Y^25 + 3*Y^24 + 4*Y^23 + 3*Y^22 + 6*Y^21 + 5*Y^20 + 6*Y^19 + 
        5*Y^18 + Y^17 + 5*Y^16 + 4*Y^15 + Y^14 + 3*Y^13 + 3*Y^10 + 2*Y^9 + 6*Y^8 + 
        5*Y^7 + 3*Y^6 + 4*Y^5 + 6*Y^4 + Y^3 + Y^2 + 4*Y + 3,
    -T^56 + 5/7*T^55 + 31/49*T^54 - 73/343*T^53 - 806/2401*T^52 - 1650/2401*T^51 + 
        2613/2401*T^50 + 1326/2401*T^49 - 1836/2401*T^48 - 1448/2401*T^47 - 
        121/2401*T^46 + 1530/2401*T^45 + 1592/2401*T^44 - 2582/2401*T^43 + 
        115/2401*T^42 + 397/2401*T^41 + 1307/2401*T^40 - 512/2401*T^39 - 
        276/343*T^38 + 183/343*T^37 + 57/343*T^36 + 1147/2401*T^35 - 2649/2401*T^34 
        - 10/2401*T^33 + 1045/2401*T^32 + 1381/2401*T^31 - 388/2401*T^30 - 
        2682/2401*T^29 + 2682/2401*T^27 + 388/2401*T^26 - 1381/2401*T^25 - 
        1045/2401*T^24 + 10/2401*T^23 + 2649/2401*T^22 - 1147/2401*T^21 - 
        57/343*T^20 - 183/343*T^19 + 276/343*T^18 + 512/2401*T^17 - 1307/2401*T^16 -
        397/2401*T^15 - 115/2401*T^14 + 2582/2401*T^13 - 1592/2401*T^12 - 
        1530/2401*T^11 + 121/2401*T^10 + 1448/2401*T^9 + 1836/2401*T^8 - 
        1326/2401*T^7 - 2613/2401*T^6 + 1650/2401*T^5 + 806/2401*T^4 + 73/343*T^3 - 
        31/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 
        4*X*Y^8 + 2*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + X*Y^2 + 3*X + 
        4*Y^30 + 5*Y^29 + 4*Y^28 + 4*Y^27 + 2*Y^26 + 2*Y^25 + 6*Y^24 + 5*Y^23 + 
        6*Y^21 + 6*Y^20 + 4*Y^19 + 2*Y^18 + Y^17 + 2*Y^16 + 6*Y^15 + 4*Y^14 + 3*Y^13
        + 3*Y^12 + 6*Y^11 + 4*Y^10 + 3*Y^9 + 2*Y^8 + 3*Y^7 + 6*Y^6 + 4*Y^5 + 5*Y^4 +
        2*Y^3 + 5*Y^2 + 6*Y + 1,
    -T^56 + 2/7*T^55 + 55/49*T^54 - 124/343*T^53 - 1910/2401*T^52 + 1622/2401*T^51 +
        466/343*T^50 - 2297/2401*T^49 - 2862/2401*T^48 + 1263/2401*T^47 + 
        2286/2401*T^46 - 312/343*T^45 - 3162/2401*T^44 + 3034/2401*T^43 + 
        2122/2401*T^42 - 256/343*T^41 - 1496/2401*T^40 + 1844/2401*T^39 + 
        118/343*T^38 - 1306/2401*T^37 - 558/2401*T^36 + 384/2401*T^35 + 
        678/2401*T^34 - 547/2401*T^33 + 390/2401*T^32 - 710/2401*T^31 - 
        200/2401*T^30 + 792/2401*T^29 - 792/2401*T^27 + 200/2401*T^26 + 
        710/2401*T^25 - 390/2401*T^24 + 547/2401*T^23 - 678/2401*T^22 - 
        384/2401*T^21 + 558/2401*T^20 + 1306/2401*T^19 - 118/343*T^18 - 
        1844/2401*T^17 + 1496/2401*T^16 + 256/343*T^15 - 2122/2401*T^14 - 
        3034/2401*T^13 + 3162/2401*T^12 + 312/343*T^11 - 2286/2401*T^10 - 
        1263/2401*T^9 + 2862/2401*T^8 + 2297/2401*T^7 - 466/343*T^6 - 1622/2401*T^5 
        + 1910/2401*T^4 + 124/343*T^3 - 55/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 
        + 4*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 2*X*Y + X + 
        6*Y^30 + 2*Y^28 + 6*Y^27 + 3*Y^25 + 6*Y^24 + Y^22 + Y^20 + 2*Y^19 + 6*Y^18 +
        5*Y^16 + 4*Y^15 + Y^14 + 2*Y^13 + 2*Y^12 + 6*Y^11 + 6*Y^10 + 2*Y^9 + 3*Y^8 +
        5*Y^7 + 6*Y^5 + Y^4 + 4*Y^3 + 5*Y^2 + 2*Y + 3,
    -T^56 - T^55 - 22/49*T^54 + 61/343*T^53 + 655/2401*T^52 - 563/2401*T^51 - 
        965/2401*T^50 - 3295/2401*T^49 - 1748/2401*T^48 - 582/2401*T^47 - 
        1185/2401*T^46 - 2064/2401*T^45 - 1149/2401*T^44 - 233/2401*T^43 - 
        831/2401*T^42 - 15/343*T^41 - 438/2401*T^40 - 1231/2401*T^39 - 
        1486/2401*T^38 - 94/2401*T^37 - 424/2401*T^36 - 1326/2401*T^35 + 
        537/2401*T^34 + 1361/2401*T^33 + 1088/2401*T^32 + 135/2401*T^31 - 
        1616/2401*T^30 - 1971/2401*T^29 + 1971/2401*T^27 + 1616/2401*T^26 - 
        135/2401*T^25 - 1088/2401*T^24 - 1361/2401*T^23 - 537/2401*T^22 + 
        1326/2401*T^21 + 424/2401*T^20 + 94/2401*T^19 + 1486/2401*T^18 + 
        1231/2401*T^17 + 438/2401*T^16 + 15/343*T^15 + 831/2401*T^14 + 233/2401*T^13
        + 1149/2401*T^12 + 2064/2401*T^11 + 1185/2401*T^10 + 582/2401*T^9 + 
        1748/2401*T^8 + 3295/2401*T^7 + 965/2401*T^6 + 563/2401*T^5 - 655/2401*T^4 -
        61/343*T^3 + 22/49*T^2 + T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^12 + 2*X*Y^11 + X*Y^10 + 4*X*Y^9 + X*Y^8 + 2*X*Y^7 + 
        3*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + X*Y^2 + X*Y + 3*X + 3*Y^30 + 3*Y^29 
        + 6*Y^28 + 6*Y^27 + 2*Y^26 + 6*Y^25 + 3*Y^24 + 4*Y^23 + 2*Y^22 + 5*Y^21 + 
        6*Y^20 + 5*Y^19 + 2*Y^18 + 3*Y^17 + Y^16 + 4*Y^15 + 3*Y^14 + 4*Y^13 + Y^12 +
        3*Y^11 + 4*Y^10 + 6*Y^8 + 4*Y^7 + 2*Y^6 + 2*Y^5 + Y^4 + 2*Y^2 + 4*Y + 6,
    -T^56 + 10/7*T^55 + 1/49*T^54 - 89/49*T^53 + 2234/2401*T^52 + 2025/2401*T^51 - 
        1548/2401*T^50 - 2083/2401*T^49 + 1376/2401*T^48 + 929/2401*T^47 - 
        92/343*T^46 - 991/2401*T^45 + 155/2401*T^44 + 957/2401*T^43 - 407/2401*T^42 
        - 307/2401*T^41 - 1389/2401*T^40 + 2491/2401*T^39 - 1095/2401*T^38 - 
        1121/2401*T^37 + 248/343*T^36 - 925/2401*T^35 - 965/2401*T^34 + 
        1098/2401*T^33 + 1306/2401*T^32 - 2992/2401*T^31 - 129/2401*T^30 + 
        2880/2401*T^29 - 2880/2401*T^27 + 129/2401*T^26 + 2992/2401*T^25 - 
        1306/2401*T^24 - 1098/2401*T^23 + 965/2401*T^22 + 925/2401*T^21 - 
        248/343*T^20 + 1121/2401*T^19 + 1095/2401*T^18 - 2491/2401*T^17 + 
        1389/2401*T^16 + 307/2401*T^15 + 407/2401*T^14 - 957/2401*T^13 - 
        155/2401*T^12 + 991/2401*T^11 + 92/343*T^10 - 929/2401*T^9 - 1376/2401*T^8 +
        2083/2401*T^7 + 1548/2401*T^6 - 2025/2401*T^5 - 2234/2401*T^4 + 89/49*T^3 - 
        1/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + X*Y^13 + 3*X*Y^12 + 5*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 + 
        3*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 2*X*Y + 4*X + 
        6*Y^30 + 5*Y^29 + 4*Y^28 + Y^27 + 4*Y^26 + 5*Y^25 + Y^24 + 2*Y^23 + 2*Y^22 +
        3*Y^21 + 4*Y^20 + Y^19 + 3*Y^18 + 6*Y^17 + 4*Y^16 + Y^15 + 3*Y^14 + 6*Y^13 +
        4*Y^12 + 3*Y^10 + 6*Y^8 + 5*Y^6 + 6*Y^4 + Y^3 + 6*Y^2 + 6*Y + 4,
    -T^56 + 4/7*T^55 + 9/49*T^54 - 312/343*T^53 + 29/2401*T^52 + 440/2401*T^51 - 
        12/2401*T^50 - 542/2401*T^49 + 359/2401*T^48 + 1062/2401*T^47 - 
        622/2401*T^46 - 40/2401*T^45 + 2071/2401*T^44 - 205/343*T^43 + 43/343*T^42 +
        1350/2401*T^41 - 1035/2401*T^40 - 339/2401*T^39 + 180/343*T^38 + 5/343*T^37 
        - 1031/2401*T^36 + 586/2401*T^35 + 1049/2401*T^34 + 558/2401*T^33 - 
        720/2401*T^32 + 1192/2401*T^31 + 838/2401*T^30 - 104/343*T^29 + 104/343*T^27
        - 838/2401*T^26 - 1192/2401*T^25 + 720/2401*T^24 - 558/2401*T^23 - 
        1049/2401*T^22 - 586/2401*T^21 + 1031/2401*T^20 - 5/343*T^19 - 180/343*T^18 
        + 339/2401*T^17 + 1035/2401*T^16 - 1350/2401*T^15 - 43/343*T^14 + 
        205/343*T^13 - 2071/2401*T^12 + 40/2401*T^11 + 622/2401*T^10 - 1062/2401*T^9
        - 359/2401*T^8 + 542/2401*T^7 + 12/2401*T^6 - 440/2401*T^5 - 29/2401*T^4 + 
        312/343*T^3 - 9/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + X*Y^11 + 4*X*Y^9 + 4*X*Y^8 + 
        2*X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + 3*X*Y^3 + X*Y^2 + 3*X*Y + 4*X + 6*Y^30 + 
        6*Y^29 + 3*Y^28 + 4*Y^25 + 2*Y^24 + 6*Y^22 + 3*Y^21 + 3*Y^20 + 4*Y^19 + Y^18
        + 3*Y^17 + 5*Y^16 + 3*Y^14 + 4*Y^13 + Y^12 + 5*Y^11 + 6*Y^10 + 3*Y^9 + 5*Y^8
        + 6*Y^6 + Y^4 + Y^3 + 4*Y^2 + 6*Y + 4,
    -T^56 - 5/7*T^55 + 5/49*T^54 - 330/343*T^53 - 1245/2401*T^52 + 3537/2401*T^51 + 
        1341/2401*T^50 - 915/2401*T^49 + 3132/2401*T^48 + 2168/2401*T^47 - 
        1321/2401*T^46 + 242/2401*T^45 + 1422/2401*T^44 - 740/2401*T^43 - 
        1625/2401*T^42 - 34/2401*T^41 + 247/2401*T^40 - 1684/2401*T^39 - 
        555/2401*T^38 + 1042/2401*T^37 - 302/2401*T^36 - 948/2401*T^35 + 
        1669/2401*T^34 + 695/2401*T^33 - 824/2401*T^32 + 1546/2401*T^31 + 
        1745/2401*T^30 - 137/343*T^29 + 137/343*T^27 - 1745/2401*T^26 - 
        1546/2401*T^25 + 824/2401*T^24 - 695/2401*T^23 - 1669/2401*T^22 + 
        948/2401*T^21 + 302/2401*T^20 - 1042/2401*T^19 + 555/2401*T^18 + 
        1684/2401*T^17 - 247/2401*T^16 + 34/2401*T^15 + 1625/2401*T^14 + 
        740/2401*T^13 - 1422/2401*T^12 - 242/2401*T^11 + 1321/2401*T^10 - 
        2168/2401*T^9 - 3132/2401*T^8 + 915/2401*T^7 - 1341/2401*T^6 - 3537/2401*T^5
        + 1245/2401*T^4 + 330/343*T^3 - 5/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 2*X*Y^8 + 2*X*Y^7 +
        3*X*Y^6 + X*Y^5 + 2*X*Y^3 + 2*X*Y^2 + 4*X*Y + 3*X + 2*Y^30 + Y^29 + Y^28 + 
        Y^27 + 5*Y^26 + 2*Y^25 + 4*Y^24 + 2*Y^23 + 2*Y^22 + Y^21 + 3*Y^20 + 2*Y^19 +
        3*Y^18 + Y^16 + Y^15 + Y^14 + Y^13 + 4*Y^12 + 6*Y^11 + 4*Y^8 + 2*Y^7 + 5*Y^6
        + 6*Y^5 + 5*Y^4 + 3*Y^3 + 4*Y^2 + 3*Y + 4,
    -T^56 + 6/7*T^55 + 1/49*T^54 - 213/343*T^53 + 1455/2401*T^52 - 1212/2401*T^51 + 
        1565/2401*T^50 - 81/2401*T^49 - 556/2401*T^48 + 1529/2401*T^47 - 
        429/2401*T^46 - 60/343*T^45 + 33/343*T^44 + 506/2401*T^43 - 1094/2401*T^42 -
        337/2401*T^41 + 1289/2401*T^40 - 804/2401*T^39 - 649/2401*T^38 + 
        286/2401*T^37 + 132/343*T^36 - 573/2401*T^35 - 257/2401*T^34 - 8/343*T^33 + 
        1356/2401*T^32 - 128/2401*T^31 - 1031/2401*T^30 + 169/343*T^29 - 
        169/343*T^27 + 1031/2401*T^26 + 128/2401*T^25 - 1356/2401*T^24 + 8/343*T^23 
        + 257/2401*T^22 + 573/2401*T^21 - 132/343*T^20 - 286/2401*T^19 + 
        649/2401*T^18 + 804/2401*T^17 - 1289/2401*T^16 + 337/2401*T^15 + 
        1094/2401*T^14 - 506/2401*T^13 - 33/343*T^12 + 60/343*T^11 + 429/2401*T^10 -
        1529/2401*T^9 + 556/2401*T^8 + 81/2401*T^7 - 1565/2401*T^6 + 1212/2401*T^5 -
        1455/2401*T^4 + 213/343*T^3 - 1/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + X*Y^10 + 2*X*Y^9 + 4*X*Y^8 + 
        X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 3*X*Y + X + 4*Y^30
        + 5*Y^29 + 3*Y^28 + 2*Y^27 + 2*Y^26 + 4*Y^25 + 5*Y^24 + 6*Y^23 + 4*Y^22 + 
        2*Y^21 + 4*Y^20 + 2*Y^19 + 2*Y^18 + 5*Y^17 + 3*Y^16 + Y^15 + 6*Y^14 + 3*Y^13
        + 4*Y^12 + 2*Y^11 + 2*Y^10 + 2*Y^9 + 6*Y^8 + 5*Y^7 + 5*Y^6 + 4*Y^4 + 5*Y^3 +
        4*Y^2 + 4*Y,
    T^56 + 1/7*T^55 + 43/49*T^54 - 47/343*T^53 + 1067/2401*T^52 - 2949/2401*T^51 + 
        1447/2401*T^50 - 173/343*T^49 + 1837/2401*T^48 - 47/2401*T^47 + 
        2332/2401*T^46 - 604/2401*T^45 + 440/2401*T^44 - 120/2401*T^43 - 
        534/2401*T^42 + 906/2401*T^41 + 528/2401*T^40 + 1377/2401*T^39 - 
        387/2401*T^38 + 1907/2401*T^37 - 1858/2401*T^36 + 206/343*T^35 + 
        349/2401*T^34 + 2566/2401*T^33 + 937/2401*T^32 + 2964/2401*T^31 - 
        428/2401*T^30 - 135/2401*T^29 - 1367/2401*T^28 - 135/2401*T^27 - 
        428/2401*T^26 + 2964/2401*T^25 + 937/2401*T^24 + 2566/2401*T^23 + 
        349/2401*T^22 + 206/343*T^21 - 1858/2401*T^20 + 1907/2401*T^19 - 
        387/2401*T^18 + 1377/2401*T^17 + 528/2401*T^16 + 906/2401*T^15 - 
        534/2401*T^14 - 120/2401*T^13 + 440/2401*T^12 - 604/2401*T^11 + 
        2332/2401*T^10 - 47/2401*T^9 + 1837/2401*T^8 - 173/343*T^7 + 1447/2401*T^6 -
        2949/2401*T^5 + 1067/2401*T^4 - 47/343*T^3 + 43/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 
        + 4*X*Y^8 + 5*X*Y^7 + 3*X*Y^3 + 6*X*Y + 6*X + 6*Y^30 + Y^29 + Y^28 + 3*Y^27 
        + Y^26 + 6*Y^25 + 4*Y^24 + 2*Y^23 + 5*Y^22 + 5*Y^21 + 6*Y^20 + 6*Y^19 + 
        4*Y^18 + 6*Y^16 + 4*Y^15 + 5*Y^13 + 2*Y^11 + 4*Y^10 + Y^9 + 3*Y^8 + 6*Y^7 + 
        4*Y^6 + 4*Y^5 + 6*Y^4 + 6*Y^3 + Y^2 + 4,
    T^56 - 8/7*T^55 + 5/7*T^54 + 142/343*T^53 - 358/2401*T^52 - 255/2401*T^51 - 
        736/2401*T^50 + 2284/2401*T^49 - 1648/2401*T^48 + 550/2401*T^47 - 
        1385/2401*T^46 + 2262/2401*T^45 - 1244/2401*T^44 - 99/2401*T^43 + 
        339/2401*T^42 - 145/2401*T^41 + 225/343*T^40 - 2447/2401*T^39 + 
        1525/2401*T^38 - 90/2401*T^37 - 585/2401*T^36 - 4/49*T^35 - 16/343*T^34 + 
        627/2401*T^33 - 2/7*T^32 - 473/2401*T^31 + 741/2401*T^30 + 488/2401*T^29 - 
        1347/2401*T^28 + 488/2401*T^27 + 741/2401*T^26 - 473/2401*T^25 - 2/7*T^24 + 
        627/2401*T^23 - 16/343*T^22 - 4/49*T^21 - 585/2401*T^20 - 90/2401*T^19 + 
        1525/2401*T^18 - 2447/2401*T^17 + 225/343*T^16 - 145/2401*T^15 + 
        339/2401*T^14 - 99/2401*T^13 - 1244/2401*T^12 + 2262/2401*T^11 - 
        1385/2401*T^10 + 550/2401*T^9 - 1648/2401*T^8 + 2284/2401*T^7 - 736/2401*T^6
        - 255/2401*T^5 - 358/2401*T^4 + 142/343*T^3 + 5/7*T^2 - 8/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 4*X*Y^8 
        + 3*X*Y^7 + 4*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 4*X*Y + 5*X + 4*Y^30 + 
        Y^28 + 5*Y^27 + 3*Y^25 + 5*Y^24 + 3*Y^23 + Y^22 + 6*Y^21 + Y^20 + 4*Y^19 + 
        2*Y^18 + Y^17 + 6*Y^16 + 4*Y^13 + 3*Y^12 + 3*Y^11 + 6*Y^10 + 3*Y^8 + 4*Y^7 +
        2*Y^6 + 3*Y^5 + 4*Y^4 + Y^3 + 6,
    T^56 + 6/7*T^55 + 51/49*T^54 + 250/343*T^53 + 400/2401*T^52 + 958/2401*T^51 - 
        1355/2401*T^50 + 666/2401*T^49 - 543/2401*T^48 - 1775/2401*T^47 - 
        570/2401*T^46 - 2306/2401*T^45 + 564/2401*T^44 - 1221/2401*T^43 - 
        198/343*T^42 - 276/2401*T^41 - 2784/2401*T^40 + 465/2401*T^39 - 
        2108/2401*T^38 - 360/2401*T^37 - 683/2401*T^36 - 2729/2401*T^35 + 
        1284/2401*T^34 - 1343/2401*T^33 + 2091/2401*T^32 + 930/2401*T^31 + 
        662/2401*T^30 + 3293/2401*T^29 - 723/2401*T^28 + 3293/2401*T^27 + 
        662/2401*T^26 + 930/2401*T^25 + 2091/2401*T^24 - 1343/2401*T^23 + 
        1284/2401*T^22 - 2729/2401*T^21 - 683/2401*T^20 - 360/2401*T^19 - 
        2108/2401*T^18 + 465/2401*T^17 - 2784/2401*T^16 - 276/2401*T^15 - 
        198/343*T^14 - 1221/2401*T^13 + 564/2401*T^12 - 2306/2401*T^11 - 
        570/2401*T^10 - 1775/2401*T^9 - 543/2401*T^8 + 666/2401*T^7 - 1355/2401*T^6 
        + 958/2401*T^5 + 400/2401*T^4 + 250/343*T^3 + 51/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 2*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 2*X*Y^8 + 3*X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + 
        2*X*Y^3 + X*Y + 2*X + 6*Y^30 + 6*Y^29 + 3*Y^28 + 2*Y^27 + 3*Y^26 + 4*Y^25 + 
        6*Y^24 + 2*Y^23 + Y^22 + 4*Y^20 + 3*Y^18 + Y^17 + 3*Y^16 + 5*Y^15 + 2*Y^14 +
        Y^13 + 2*Y^12 + Y^11 + 3*Y^10 + 4*Y^9 + Y^8 + 4*Y^7 + 2*Y^6 + 6*Y^5 + 5*Y^4 
        + 6*Y^3 + 2*Y + 3,
    T^56 + 10/7*T^55 - 6/7*T^54 - 978/343*T^53 - 67/49*T^52 + 634/343*T^51 + 
        7732/2401*T^50 + 2286/2401*T^49 - 6723/2401*T^48 - 8263/2401*T^47 + 
        32/2401*T^46 + 8289/2401*T^45 + 7396/2401*T^44 - 1045/2401*T^43 - 
        9294/2401*T^42 - 7668/2401*T^41 + 3937/2401*T^40 + 11006/2401*T^39 + 
        4762/2401*T^38 - 7338/2401*T^37 - 11439/2401*T^36 - 899/2401*T^35 + 
        11647/2401*T^34 + 9981/2401*T^33 - 3033/2401*T^32 - 13011/2401*T^31 - 
        9089/2401*T^30 + 5805/2401*T^29 + 14370/2401*T^28 + 5805/2401*T^27 - 
        9089/2401*T^26 - 13011/2401*T^25 - 3033/2401*T^24 + 9981/2401*T^23 + 
        11647/2401*T^22 - 899/2401*T^21 - 11439/2401*T^20 - 7338/2401*T^19 + 
        4762/2401*T^18 + 11006/2401*T^17 + 3937/2401*T^16 - 7668/2401*T^15 - 
        9294/2401*T^14 - 1045/2401*T^13 + 7396/2401*T^12 + 8289/2401*T^11 + 
        32/2401*T^10 - 8263/2401*T^9 - 6723/2401*T^8 + 2286/2401*T^7 + 7732/2401*T^6
        + 634/343*T^5 - 67/49*T^4 - 978/343*T^3 - 6/7*T^2 + 10/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 3*X*Y^9 + X*Y^8 + 5*X*Y^6 + 
        2*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 2*X*Y + 5*X + Y^30 + 3*Y^28 + 2*Y^26
        + Y^25 + Y^24 + 4*Y^23 + Y^21 + 4*Y^19 + 5*Y^18 + Y^17 + Y^14 + Y^13 + 
        4*Y^12 + Y^11 + 5*Y^10 + 4*Y^9 + 3*Y^8 + Y^7 + 2*Y^6 + Y^3 + 3*Y^2 + 6,
    T^56 - 1/7*T^55 - 16/49*T^54 - 9/49*T^53 - 300/2401*T^52 - 296/2401*T^51 + 
        6/343*T^50 - 516/2401*T^49 - 110/343*T^48 - 571/2401*T^47 + 874/2401*T^46 - 
        285/2401*T^45 - 752/2401*T^44 + 100/343*T^43 - 510/2401*T^42 + 159/343*T^41 
        + 1367/2401*T^40 - 353/2401*T^39 + 478/2401*T^38 + 326/2401*T^37 - 
        419/2401*T^36 - 148/2401*T^35 - 72/2401*T^34 + 274/2401*T^33 - 720/2401*T^32
        + 534/2401*T^31 - 97/2401*T^30 - 344/2401*T^29 - 655/2401*T^28 - 
        344/2401*T^27 - 97/2401*T^26 + 534/2401*T^25 - 720/2401*T^24 + 274/2401*T^23
        - 72/2401*T^22 - 148/2401*T^21 - 419/2401*T^20 + 326/2401*T^19 + 
        478/2401*T^18 - 353/2401*T^17 + 1367/2401*T^16 + 159/343*T^15 - 
        510/2401*T^14 + 100/343*T^13 - 752/2401*T^12 - 285/2401*T^11 + 874/2401*T^10
        - 571/2401*T^9 - 110/343*T^8 - 516/2401*T^7 + 6/343*T^6 - 296/2401*T^5 - 
        300/2401*T^4 - 9/49*T^3 - 16/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 4*X*Y^8 
        + 6*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + X*Y^3 + 5*X*Y^2 + 4*X*Y + 5*Y^30 + Y^29 + 
        2*Y^26 + 6*Y^25 + 6*Y^24 + 4*Y^22 + 4*Y^21 + 6*Y^19 + 3*Y^18 + 6*Y^17 + 
        2*Y^16 + 6*Y^15 + 4*Y^14 + Y^13 + 6*Y^12 + 3*Y^11 + 6*Y^10 + Y^9 + 2*Y^8 + 
        5*Y^7 + Y^6 + 5*Y^5 + 3*Y^4 + 2*Y^3 + 6*Y^2 + 6*Y + 6,
    -T^56 - 15/7*T^55 - 95/49*T^54 - 144/343*T^53 + 3372/2401*T^52 + 6360/2401*T^51 
        + 5262/2401*T^50 + 37/2401*T^49 - 5112/2401*T^48 - 7544/2401*T^47 - 
        6694/2401*T^46 - 2846/2401*T^45 + 358/343*T^44 + 5840/2401*T^43 + 
        5653/2401*T^42 + 2183/2401*T^41 - 3025/2401*T^40 - 7683/2401*T^39 - 
        1118/343*T^38 - 3669/2401*T^37 + 2052/2401*T^36 + 6680/2401*T^35 + 
        8371/2401*T^34 + 4946/2401*T^33 - 1924/2401*T^32 - 7148/2401*T^31 - 
        8527/2401*T^30 - 6046/2401*T^29 + 6046/2401*T^27 + 8527/2401*T^26 + 
        7148/2401*T^25 + 1924/2401*T^24 - 4946/2401*T^23 - 8371/2401*T^22 - 
        6680/2401*T^21 - 2052/2401*T^20 + 3669/2401*T^19 + 1118/343*T^18 + 
        7683/2401*T^17 + 3025/2401*T^16 - 2183/2401*T^15 - 5653/2401*T^14 - 
        5840/2401*T^13 - 358/343*T^12 + 2846/2401*T^11 + 6694/2401*T^10 + 
        7544/2401*T^9 + 5112/2401*T^8 - 37/2401*T^7 - 5262/2401*T^6 - 6360/2401*T^5 
        - 3372/2401*T^4 + 144/343*T^3 + 95/49*T^2 + 15/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + X*Y^13 + X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 + 
        3*X*Y^7 + X*Y^6 + 3*X*Y^4 + X*Y^3 + 6*X*Y^2 + X*Y + 2*X + 6*Y^30 + 2*Y^29 + 
        4*Y^28 + 5*Y^27 + 5*Y^26 + 3*Y^25 + 2*Y^24 + 4*Y^23 + Y^22 + 4*Y^20 + 4*Y^19
        + 2*Y^18 + 2*Y^17 + 5*Y^16 + 3*Y^14 + 3*Y^13 + 2*Y^12 + 4*Y^11 + 5*Y^10 + 
        Y^9 + 4*Y^8 + Y^7 + 2*Y^6 + 2*Y^5 + 2*Y^4 + 3*Y^3 + 2*Y^2 + 5*Y + 6,
    -T^56 - 4/7*T^55 - 22/49*T^54 + 1/7*T^53 - 1516/2401*T^52 - 463/2401*T^51 - 
        1168/2401*T^50 + 215/2401*T^49 - 15/343*T^48 - 1826/2401*T^47 - 
        1703/2401*T^46 + 30/2401*T^45 + 123/343*T^44 - 310/2401*T^43 + 348/2401*T^42
        + 459/2401*T^41 + 104/343*T^40 + 986/2401*T^39 - 24/2401*T^38 + 23/343*T^37 
        + 684/2401*T^36 + 26/49*T^35 - 960/2401*T^34 + 34/343*T^33 + 828/2401*T^32 +
        1241/2401*T^31 - 584/2401*T^30 - 549/2401*T^29 + 549/2401*T^27 + 
        584/2401*T^26 - 1241/2401*T^25 - 828/2401*T^24 - 34/343*T^23 + 960/2401*T^22
        - 26/49*T^21 - 684/2401*T^20 - 23/343*T^19 + 24/2401*T^18 - 986/2401*T^17 - 
        104/343*T^16 - 459/2401*T^15 - 348/2401*T^14 + 310/2401*T^13 - 123/343*T^12 
        - 30/2401*T^11 + 1703/2401*T^10 + 1826/2401*T^9 + 15/343*T^8 - 215/2401*T^7 
        + 1168/2401*T^6 + 463/2401*T^5 + 1516/2401*T^4 - 1/7*T^3 + 22/49*T^2 + 4/7*T
        + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 +
        X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 3*X*Y + 3*X + 
        3*Y^30 + Y^29 + 2*Y^28 + Y^27 + 6*Y^26 + 6*Y^24 + 5*Y^23 + 2*Y^22 + 4*Y^20 +
        4*Y^19 + 5*Y^18 + 6*Y^17 + 6*Y^15 + 2*Y^14 + 3*Y^13 + 2*Y^12 + 6*Y^11 + 
        2*Y^10 + Y^9 + 2*Y^8 + 3*Y^5 + Y^4 + 4*Y^3 + 5*Y^2 + 3*Y,
    -T^56 + 11/7*T^55 - 75/49*T^54 + 472/343*T^53 - 2319/2401*T^52 + 3565/2401*T^51 
        - 2172/2401*T^50 - 984/2401*T^49 + 2841/2401*T^48 - 4581/2401*T^47 + 
        646/343*T^46 - 5484/2401*T^45 + 6036/2401*T^44 - 4338/2401*T^43 + 
        3189/2401*T^42 - 2711/2401*T^41 + 1982/2401*T^40 - 279/2401*T^39 - 
        1618/2401*T^38 + 2868/2401*T^37 - 2869/2401*T^36 + 5380/2401*T^35 - 
        8539/2401*T^34 + 9423/2401*T^33 - 1242/343*T^32 + 7034/2401*T^31 - 
        6512/2401*T^30 + 4308/2401*T^29 - 4308/2401*T^27 + 6512/2401*T^26 - 
        7034/2401*T^25 + 1242/343*T^24 - 9423/2401*T^23 + 8539/2401*T^22 - 
        5380/2401*T^21 + 2869/2401*T^20 - 2868/2401*T^19 + 1618/2401*T^18 + 
        279/2401*T^17 - 1982/2401*T^16 + 2711/2401*T^15 - 3189/2401*T^14 + 
        4338/2401*T^13 - 6036/2401*T^12 + 5484/2401*T^11 - 646/343*T^10 + 
        4581/2401*T^9 - 2841/2401*T^8 + 984/2401*T^7 + 2172/2401*T^6 - 3565/2401*T^5
        + 2319/2401*T^4 - 472/343*T^3 + 75/49*T^2 - 11/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^13 + 5*X*Y^12 + 2*X*Y^7 + 5*X*Y^6 + X*Y^4 + 6*X*Y^3 + X*Y^2
        + 6*X*Y + 3*X + 2*Y^30 + 6*Y^29 + 5*Y^28 + 5*Y^27 + Y^26 + 3*Y^25 + 6*Y^24 +
        3*Y^22 + 2*Y^21 + Y^19 + 4*Y^18 + 6*Y^17 + 2*Y^16 + 5*Y^13 + 6*Y^12 + 5*Y^11
        + Y^7 + 2*Y^6 + 2*Y^5 + 5*Y^4 + 5*Y^3 + 4*Y^2 + Y + 6,
    -T^56 - 2/7*T^55 - 4/49*T^54 + 118/343*T^53 + 353/2401*T^52 + 470/2401*T^51 + 
        1458/2401*T^50 + 821/2401*T^49 + 1039/2401*T^48 - 1010/2401*T^47 - 
        1012/2401*T^46 - 829/2401*T^45 - 793/2401*T^44 - 1250/2401*T^43 - 
        2165/2401*T^42 + 701/2401*T^41 + 1003/2401*T^40 + 978/2401*T^39 + 
        254/2401*T^38 + 1634/2401*T^37 + 1790/2401*T^36 + 892/2401*T^35 - 
        193/2401*T^34 - 304/343*T^33 - 68/343*T^32 - 1338/2401*T^31 - 181/343*T^30 -
        283/343*T^29 + 283/343*T^27 + 181/343*T^26 + 1338/2401*T^25 + 68/343*T^24 + 
        304/343*T^23 + 193/2401*T^22 - 892/2401*T^21 - 1790/2401*T^20 - 
        1634/2401*T^19 - 254/2401*T^18 - 978/2401*T^17 - 1003/2401*T^16 - 
        701/2401*T^15 + 2165/2401*T^14 + 1250/2401*T^13 + 793/2401*T^12 + 
        829/2401*T^11 + 1012/2401*T^10 + 1010/2401*T^9 - 1039/2401*T^8 - 
        821/2401*T^7 - 1458/2401*T^6 - 470/2401*T^5 - 353/2401*T^4 - 118/343*T^3 + 
        4/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 3*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 4*X*Y^8 + 
        3*X*Y^7 + 6*X*Y^6 + 6*X*Y^4 + X*Y^3 + 6*X*Y + 4*X + 5*Y^30 + 2*Y^27 + 3*Y^25
        + 2*Y^24 + 2*Y^23 + Y^22 + 3*Y^21 + 4*Y^20 + Y^19 + 3*Y^18 + 5*Y^17 + 3*Y^16
        + 3*Y^15 + 6*Y^14 + 3*Y^11 + 3*Y^10 + Y^9 + 5*Y^8 + 6*Y^6 + 2*Y^5 + 6*Y^4 + 
        5*Y^3 + 2*Y^2 + 5*Y + 6,
    T^56 + 2/7*T^55 - 39/49*T^54 + 58/343*T^53 + 1368/2401*T^52 - 355/2401*T^51 - 
        2906/2401*T^50 + 228/2401*T^49 + 2759/2401*T^48 - 873/2401*T^47 - 
        1558/2401*T^46 + 88/2401*T^45 + 209/343*T^44 - 1096/2401*T^43 - 
        2292/2401*T^42 + 78/343*T^41 + 132/2401*T^40 + 397/2401*T^39 - 775/2401*T^38
        - 597/2401*T^37 + 986/2401*T^36 + 38/2401*T^35 - 1202/2401*T^34 - 
        1217/2401*T^33 + 1956/2401*T^32 + 1020/2401*T^31 - 1451/2401*T^30 + 
        701/2401*T^29 + 2125/2401*T^28 + 701/2401*T^27 - 1451/2401*T^26 + 
        1020/2401*T^25 + 1956/2401*T^24 - 1217/2401*T^23 - 1202/2401*T^22 + 
        38/2401*T^21 + 986/2401*T^20 - 597/2401*T^19 - 775/2401*T^18 + 397/2401*T^17
        + 132/2401*T^16 + 78/343*T^15 - 2292/2401*T^14 - 1096/2401*T^13 + 
        209/343*T^12 + 88/2401*T^11 - 1558/2401*T^10 - 873/2401*T^9 + 2759/2401*T^8 
        + 228/2401*T^7 - 2906/2401*T^6 - 355/2401*T^5 + 1368/2401*T^4 + 58/343*T^3 -
        39/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 
        + 3*X*Y^8 + 6*X*Y^7 + 3*X*Y^6 + 2*X*Y^4 + 6*X*Y^3 + 2*X*Y + 2*X + 4*Y^30 + 
        2*Y^29 + 6*Y^28 + 3*Y^27 + 2*Y^26 + Y^25 + 3*Y^24 + Y^23 + Y^22 + Y^21 + 
        6*Y^20 + 6*Y^19 + Y^18 + 2*Y^17 + 3*Y^16 + 4*Y^15 + 3*Y^14 + 3*Y^13 + 2*Y^11
        + 5*Y^10 + 5*Y^9 + 5*Y^8 + 3*Y^6 + 5*Y^5 + 3*Y^3 + 4*Y^2 + 6,
    T^56 - 10/49*T^54 - 116/343*T^53 + 101/2401*T^52 + 250/2401*T^51 + 774/2401*T^50
        + 1553/2401*T^49 + 12/49*T^48 - 869/2401*T^47 - 2276/2401*T^46 - 
        249/2401*T^45 + 1726/2401*T^44 + 1726/2401*T^43 + 120/2401*T^42 - 
        1221/2401*T^41 - 9/343*T^40 - 1688/2401*T^39 - 702/2401*T^38 + 205/343*T^37 
        + 1164/2401*T^36 + 181/2401*T^35 - 1966/2401*T^34 - 753/2401*T^33 + 
        475/2401*T^32 + 67/343*T^31 - 722/2401*T^30 - 286/2401*T^29 - 288/2401*T^28 
        - 286/2401*T^27 - 722/2401*T^26 + 67/343*T^25 + 475/2401*T^24 - 
        753/2401*T^23 - 1966/2401*T^22 + 181/2401*T^21 + 1164/2401*T^20 + 
        205/343*T^19 - 702/2401*T^18 - 1688/2401*T^17 - 9/343*T^16 - 1221/2401*T^15 
        + 120/2401*T^14 + 1726/2401*T^13 + 1726/2401*T^12 - 249/2401*T^11 - 
        2276/2401*T^10 - 869/2401*T^9 + 12/49*T^8 + 1553/2401*T^7 + 774/2401*T^6 + 
        250/2401*T^5 + 101/2401*T^4 - 116/343*T^3 - 10/49*T^2 + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 5*X*Y^13 + 5*X*Y^11 + 6*X*Y^9 + 2*X*Y^8 + 2*X*Y^7 + 
        3*X*Y^6 + 2*X*Y^5 + 6*X*Y^3 + 6*X*Y^2 + 3*X*Y + 6*Y^30 + 2*Y^29 + 6*Y^26 + 
        5*Y^25 + 4*Y^24 + Y^23 + 6*Y^22 + 4*Y^21 + 3*Y^19 + 3*Y^17 + 2*Y^16 + 3*Y^15
        + 6*Y^14 + 4*Y^13 + Y^12 + 5*Y^10 + 6*Y^9 + Y^6 + 3*Y^4 + 4*Y^3 + 3*Y^2 + 
        2*Y + 4,
    T^56 + 10/7*T^55 + 131/49*T^54 + 1082/343*T^53 + 1264/343*T^52 + 9295/2401*T^51 
        + 8423/2401*T^50 + 7428/2401*T^49 + 575/343*T^48 + 1759/2401*T^47 - 
        1660/2401*T^46 - 4154/2401*T^45 - 6091/2401*T^44 - 8607/2401*T^43 - 
        8733/2401*T^42 - 10272/2401*T^41 - 9175/2401*T^40 - 8860/2401*T^39 - 
        7563/2401*T^38 - 5935/2401*T^37 - 4951/2401*T^36 - 1976/2401*T^35 - 
        797/2401*T^34 + 2823/2401*T^33 + 4103/2401*T^32 + 6087/2401*T^31 + 
        8181/2401*T^30 + 8423/2401*T^29 + 10086/2401*T^28 + 8423/2401*T^27 + 
        8181/2401*T^26 + 6087/2401*T^25 + 4103/2401*T^24 + 2823/2401*T^23 - 
        797/2401*T^22 - 1976/2401*T^21 - 4951/2401*T^20 - 5935/2401*T^19 - 
        7563/2401*T^18 - 8860/2401*T^17 - 9175/2401*T^16 - 10272/2401*T^15 - 
        8733/2401*T^14 - 8607/2401*T^13 - 6091/2401*T^12 - 4154/2401*T^11 - 
        1660/2401*T^10 + 1759/2401*T^9 + 575/343*T^8 + 7428/2401*T^7 + 8423/2401*T^6
        + 9295/2401*T^5 + 1264/343*T^4 + 1082/343*T^3 + 131/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + X*Y^8 + 3*X*Y^7 + 
        5*X*Y^6 + 5*X*Y^5 + X*Y^4 + 5*X*Y^2 + 5*X + 3*Y^30 + 2*Y^29 + 2*Y^28 + 
        4*Y^27 + 2*Y^26 + Y^25 + Y^24 + Y^23 + 2*Y^22 + 4*Y^20 + Y^19 + 3*Y^18 + 
        6*Y^17 + 5*Y^16 + Y^15 + 2*Y^14 + 3*Y^12 + 4*Y^10 + 6*Y^9 + 6*Y^6 + 3*Y^5 + 
        5*Y^4 + 2*Y^3 + 5*Y^2 + 6*Y + 3,
    T^56 - 4/7*T^55 - 54/49*T^54 + 410/343*T^53 + 1380/2401*T^52 - 1752/2401*T^51 - 
        40/2401*T^50 - 242/2401*T^49 + 922/2401*T^48 + 15/49*T^47 - 912/2401*T^46 - 
        251/2401*T^45 + 5/343*T^44 - 650/2401*T^43 + 248/343*T^42 - 659/2401*T^41 - 
        267/343*T^40 + 899/2401*T^39 + 659/2401*T^38 - 251/2401*T^37 - 239/2401*T^36
        - 197/343*T^35 + 380/2401*T^34 + 1044/2401*T^33 + 715/2401*T^32 - 
        1037/2401*T^31 - 1371/2401*T^30 + 95/2401*T^29 + 1719/2401*T^28 + 
        95/2401*T^27 - 1371/2401*T^26 - 1037/2401*T^25 + 715/2401*T^24 + 
        1044/2401*T^23 + 380/2401*T^22 - 197/343*T^21 - 239/2401*T^20 - 
        251/2401*T^19 + 659/2401*T^18 + 899/2401*T^17 - 267/343*T^16 - 659/2401*T^15
        + 248/343*T^14 - 650/2401*T^13 + 5/343*T^12 - 251/2401*T^11 - 912/2401*T^10 
        + 15/49*T^9 + 922/2401*T^8 - 242/2401*T^7 - 40/2401*T^6 - 1752/2401*T^5 + 
        1380/2401*T^4 + 410/343*T^3 - 54/49*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + X*Y^8 + 
        6*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 5*X*Y^2 + X*Y + 6*X + 2*Y^30 + Y^29 
        + Y^28 + 5*Y^27 + 3*Y^26 + 5*Y^25 + 3*Y^24 + 4*Y^23 + 5*Y^22 + 6*Y^21 + 
        3*Y^20 + 5*Y^19 + 4*Y^17 + 5*Y^15 + 2*Y^14 + 4*Y^13 + 4*Y^12 + 2*Y^11 + 
        4*Y^10 + Y^9 + 3*Y^8 + Y^7 + 3*Y^6 + 5*Y^5 + Y^3 + Y^2 + 3*Y + 4,
    T^56 + 5/7*T^55 + 30/49*T^54 + 379/343*T^53 + 2350/2401*T^52 + 1903/2401*T^51 + 
        3538/2401*T^50 + 461/343*T^49 + 2651/2401*T^48 + 3022/2401*T^47 + 
        4027/2401*T^46 + 2722/2401*T^45 + 3540/2401*T^44 + 5176/2401*T^43 + 
        4461/2401*T^42 + 5109/2401*T^41 + 5510/2401*T^40 + 4180/2401*T^39 + 
        5554/2401*T^38 + 6233/2401*T^37 + 5479/2401*T^36 + 6688/2401*T^35 + 
        7925/2401*T^34 + 6191/2401*T^33 + 6953/2401*T^32 + 1040/343*T^31 + 
        6190/2401*T^30 + 6865/2401*T^29 + 9055/2401*T^28 + 6865/2401*T^27 + 
        6190/2401*T^26 + 1040/343*T^25 + 6953/2401*T^24 + 6191/2401*T^23 + 
        7925/2401*T^22 + 6688/2401*T^21 + 5479/2401*T^20 + 6233/2401*T^19 + 
        5554/2401*T^18 + 4180/2401*T^17 + 5510/2401*T^16 + 5109/2401*T^15 + 
        4461/2401*T^14 + 5176/2401*T^13 + 3540/2401*T^12 + 2722/2401*T^11 + 
        4027/2401*T^10 + 3022/2401*T^9 + 2651/2401*T^8 + 461/343*T^7 + 3538/2401*T^6
        + 1903/2401*T^5 + 2350/2401*T^4 + 379/343*T^3 + 30/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 3*X*Y^9 + X*Y^8 + 
        4*X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + X*Y + 6*X + 
        3*Y^30 + 6*Y^29 + 6*Y^27 + Y^26 + 2*Y^25 + 5*Y^24 + 2*Y^23 + 2*Y^21 + 5*Y^20
        + 2*Y^18 + 5*Y^15 + 2*Y^14 + 2*Y^13 + Y^12 + 4*Y^11 + 4*Y^10 + 5*Y^9 + 6*Y^8
        + 5*Y^6 + 6*Y^5 + 4*Y^4 + Y^3 + 5*Y + 1,
    -T^56 + 11/7*T^55 - 2/49*T^54 - 555/343*T^53 + 4580/2401*T^52 - 2010/2401*T^51 -
        1290/2401*T^50 + 536/343*T^49 - 690/343*T^48 + 1915/2401*T^47 + 
        2047/2401*T^46 - 3335/2401*T^45 + 3294/2401*T^44 - 220/343*T^43 - 
        607/2401*T^42 + 1733/2401*T^41 - 1877/2401*T^40 + 1027/2401*T^39 - 
        956/2401*T^38 + 1109/2401*T^37 - 370/2401*T^36 - 1879/2401*T^35 + 
        4801/2401*T^34 - 3925/2401*T^33 + 117/2401*T^32 + 3561/2401*T^31 - 
        6512/2401*T^30 + 5038/2401*T^29 - 5038/2401*T^27 + 6512/2401*T^26 - 
        3561/2401*T^25 - 117/2401*T^24 + 3925/2401*T^23 - 4801/2401*T^22 + 
        1879/2401*T^21 + 370/2401*T^20 - 1109/2401*T^19 + 956/2401*T^18 - 
        1027/2401*T^17 + 1877/2401*T^16 - 1733/2401*T^15 + 607/2401*T^14 + 
        220/343*T^13 - 3294/2401*T^12 + 3335/2401*T^11 - 2047/2401*T^10 - 
        1915/2401*T^9 + 690/343*T^8 - 536/343*T^7 + 1290/2401*T^6 + 2010/2401*T^5 - 
        4580/2401*T^4 + 555/343*T^3 + 2/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 5*X*Y^8 
        + 6*X*Y^7 + 6*X*Y^6 + X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 6*X*Y + 2*X + 4*Y^30 + 
        6*Y^29 + Y^28 + 5*Y^27 + 5*Y^26 + 6*Y^25 + 4*Y^24 + 2*Y^23 + 4*Y^22 + 6*Y^20
        + 5*Y^19 + Y^18 + 4*Y^17 + 5*Y^16 + 4*Y^15 + 5*Y^14 + 4*Y^13 + 6*Y^12 + 
        6*Y^10 + 6*Y^9 + 2*Y^8 + 6*Y^7 + 4*Y^6 + 5*Y^5 + 2*Y^4 + 3*Y^2 + 6*Y + 4,
    -T^56 + 3/7*T^55 + 58/49*T^54 - 23/343*T^53 - 3469/2401*T^52 + 624/2401*T^51 + 
        2277/2401*T^50 - 757/2401*T^49 - 1627/2401*T^48 + 1573/2401*T^47 + 
        1606/2401*T^46 - 1182/2401*T^45 - 1637/2401*T^44 + 366/2401*T^43 + 
        1398/2401*T^42 + 1325/2401*T^41 - 1131/2401*T^40 - 1965/2401*T^39 + 
        1598/2401*T^38 + 2041/2401*T^37 - 1949/2401*T^36 - 2645/2401*T^35 + 
        1987/2401*T^34 + 2323/2401*T^33 - 776/2401*T^32 - 366/343*T^31 + 
        706/2401*T^30 + 1969/2401*T^29 - 1969/2401*T^27 - 706/2401*T^26 + 
        366/343*T^25 + 776/2401*T^24 - 2323/2401*T^23 - 1987/2401*T^22 + 
        2645/2401*T^21 + 1949/2401*T^20 - 2041/2401*T^19 - 1598/2401*T^18 + 
        1965/2401*T^17 + 1131/2401*T^16 - 1325/2401*T^15 - 1398/2401*T^14 - 
        366/2401*T^13 + 1637/2401*T^12 + 1182/2401*T^11 - 1606/2401*T^10 - 
        1573/2401*T^9 + 1627/2401*T^8 + 757/2401*T^7 - 2277/2401*T^6 - 624/2401*T^5 
        + 3469/2401*T^4 + 23/343*T^3 - 58/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 3*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 5*X*Y^8 +
        5*X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 5*X*Y^2 + 4*X*Y + 3*X + 4*Y^30 + 
        4*Y^28 + 2*Y^27 + 4*Y^26 + 5*Y^25 + 5*Y^24 + 5*Y^23 + Y^22 + 4*Y^20 + 3*Y^19
        + Y^18 + Y^15 + 3*Y^14 + 5*Y^12 + 4*Y^11 + 6*Y^10 + 4*Y^9 + 4*Y^8 + 3*Y^7 + 
        6*Y^6 + 5*Y^5 + 2*Y^4 + Y^3 + 2*Y^2 + Y + 4,
    -T^56 - 12/7*T^55 - 82/49*T^54 - 520/343*T^53 - 1226/2401*T^52 + 72/343*T^51 + 
        1643/2401*T^50 + 34/49*T^49 + 585/2401*T^48 + 188/2401*T^47 + 152/2401*T^46 
        + 1643/2401*T^45 + 898/2401*T^44 - 52/343*T^43 - 757/2401*T^42 - 
        3284/2401*T^41 - 3550/2401*T^40 - 3225/2401*T^39 - 1738/2401*T^38 + 
        111/343*T^37 + 998/2401*T^36 + 1307/2401*T^35 + 212/2401*T^34 + 
        144/2401*T^33 + 638/2401*T^32 + 300/2401*T^31 + 2043/2401*T^30 + 
        838/2401*T^29 - 838/2401*T^27 - 2043/2401*T^26 - 300/2401*T^25 - 
        638/2401*T^24 - 144/2401*T^23 - 212/2401*T^22 - 1307/2401*T^21 - 
        998/2401*T^20 - 111/343*T^19 + 1738/2401*T^18 + 3225/2401*T^17 + 
        3550/2401*T^16 + 3284/2401*T^15 + 757/2401*T^14 + 52/343*T^13 - 
        898/2401*T^12 - 1643/2401*T^11 - 152/2401*T^10 - 188/2401*T^9 - 585/2401*T^8
        - 34/49*T^7 - 1643/2401*T^6 - 72/343*T^5 + 1226/2401*T^4 + 520/343*T^3 + 
        82/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 2*X*Y^12 + 6*X*Y^11 + 3*X*Y^9 + X*Y^8 + 6*X*Y^7 + 
        6*X*Y^6 + 2*X*Y^5 + X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 3*X*Y + X + 4*Y^30 + 3*Y^29 
        + Y^28 + 5*Y^27 + 5*Y^25 + 4*Y^24 + 6*Y^23 + 3*Y^22 + 6*Y^21 + 4*Y^19 + 
        3*Y^18 + 2*Y^17 + 2*Y^16 + 6*Y^15 + Y^14 + 2*Y^12 + 5*Y^11 + 6*Y^10 + 3*Y^9 
        + 3*Y^8 + 6*Y^7 + 5*Y^6 + 4*Y^5 + 4*Y^4 + 3*Y^3 + 6*Y^2 + 6*Y,
    -T^56 + T^55 - 24/49*T^54 + 507/343*T^53 - 2741/2401*T^52 - 521/2401*T^51 - 
        606/2401*T^50 - 750/2401*T^49 + 4316/2401*T^48 - 2452/2401*T^47 + 
        313/343*T^46 - 671/343*T^45 + 682/2401*T^44 + 188/2401*T^43 + 1530/2401*T^42
        + 2266/2401*T^41 - 2815/2401*T^40 + 240/2401*T^39 - 3322/2401*T^38 + 
        2881/2401*T^37 + 573/2401*T^36 + 2008/2401*T^35 - 213/343*T^34 - 
        1770/2401*T^33 - 451/2401*T^32 - 424/2401*T^31 + 2098/2401*T^30 + 
        87/343*T^29 - 87/343*T^27 - 2098/2401*T^26 + 424/2401*T^25 + 451/2401*T^24 +
        1770/2401*T^23 + 213/343*T^22 - 2008/2401*T^21 - 573/2401*T^20 - 
        2881/2401*T^19 + 3322/2401*T^18 - 240/2401*T^17 + 2815/2401*T^16 - 
        2266/2401*T^15 - 1530/2401*T^14 - 188/2401*T^13 - 682/2401*T^12 + 
        671/343*T^11 - 313/343*T^10 + 2452/2401*T^9 - 4316/2401*T^8 + 750/2401*T^7 +
        606/2401*T^6 + 521/2401*T^5 + 2741/2401*T^4 - 507/343*T^3 + 24/49*T^2 - T + 
        1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + X*Y^11 + 6*X*Y^10 + 2*X*Y^9 + 
        5*X*Y^8 + 4*X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 3*X*Y + 3*X + 
        Y^30 + Y^29 + 2*Y^28 + 4*Y^27 + 3*Y^26 + 4*Y^25 + 3*Y^23 + 4*Y^22 + 2*Y^21 +
        5*Y^20 + Y^19 + 5*Y^18 + 2*Y^17 + Y^16 + Y^15 + 5*Y^14 + 3*Y^12 + 2*Y^10 + 
        Y^9 + 4*Y^8 + 4*Y^7 + Y^6 + 3*Y^5 + 4*Y^4 + Y^2 + 4*Y + 4,
    -T^56 + 6/7*T^55 - 20/49*T^54 - 1/7*T^53 + 106/2401*T^52 + 1431/2401*T^51 - 
        486/2401*T^50 - 676/2401*T^49 + 1937/2401*T^48 - 316/343*T^47 + 
        1242/2401*T^46 - 204/2401*T^45 + 22/343*T^44 - 465/2401*T^43 - 321/2401*T^42
        + 1076/2401*T^41 - 1885/2401*T^40 + 290/2401*T^39 + 85/2401*T^38 + 
        81/343*T^37 - 410/2401*T^36 + 376/2401*T^35 + 800/2401*T^34 - 45/343*T^33 + 
        22/343*T^32 - 82/2401*T^31 + 18/2401*T^30 + 12/343*T^29 - 12/343*T^27 - 
        18/2401*T^26 + 82/2401*T^25 - 22/343*T^24 + 45/343*T^23 - 800/2401*T^22 - 
        376/2401*T^21 + 410/2401*T^20 - 81/343*T^19 - 85/2401*T^18 - 290/2401*T^17 +
        1885/2401*T^16 - 1076/2401*T^15 + 321/2401*T^14 + 465/2401*T^13 - 
        22/343*T^12 + 204/2401*T^11 - 1242/2401*T^10 + 316/343*T^9 - 1937/2401*T^8 +
        676/2401*T^7 + 486/2401*T^6 - 1431/2401*T^5 - 106/2401*T^4 + 1/7*T^3 + 
        20/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + X*Y^11 + 5*X*Y^9 + 2*X*Y^8 + 
        X*Y^7 + 5*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 4*X*Y + 5*X + Y^30
        + 6*Y^29 + 5*Y^28 + 2*Y^27 + 2*Y^26 + 2*Y^25 + 6*Y^24 + 2*Y^23 + 4*Y^22 + 
        3*Y^21 + 5*Y^20 + 2*Y^18 + 4*Y^17 + Y^15 + 4*Y^14 + 6*Y^13 + 2*Y^12 + 4*Y^10
        + 5*Y^9 + 6*Y^8 + 5*Y^7 + 3*Y^5 + 3*Y^4 + 3*Y^3 + Y^2 + 2,
    T^56 + 5/7*T^55 + 30/49*T^54 - 5/49*T^53 + 485/2401*T^52 - 234/2401*T^51 - 
        215/343*T^50 - 299/343*T^49 - 180/343*T^48 + 2241/2401*T^47 + 222/343*T^46 +
        1513/2401*T^45 - 849/2401*T^44 + 1458/2401*T^43 + 313/2401*T^42 - 
        575/2401*T^41 - 2578/2401*T^40 - 293/2401*T^39 + 643/2401*T^38 + 
        737/2401*T^37 + 258/2401*T^36 + 331/2401*T^35 + 1497/2401*T^34 + 
        607/2401*T^33 + 466/2401*T^32 - 738/2401*T^31 + 614/2401*T^30 - 
        1040/2401*T^29 + 375/2401*T^28 - 1040/2401*T^27 + 614/2401*T^26 - 
        738/2401*T^25 + 466/2401*T^24 + 607/2401*T^23 + 1497/2401*T^22 + 
        331/2401*T^21 + 258/2401*T^20 + 737/2401*T^19 + 643/2401*T^18 - 
        293/2401*T^17 - 2578/2401*T^16 - 575/2401*T^15 + 313/2401*T^14 + 
        1458/2401*T^13 - 849/2401*T^12 + 1513/2401*T^11 + 222/343*T^10 + 
        2241/2401*T^9 - 180/343*T^8 - 299/343*T^7 - 215/343*T^6 - 234/2401*T^5 + 
        485/2401*T^4 - 5/49*T^3 + 30/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 4*X*Y^13 + X*Y^12 + X*Y^11 + X*Y^10 + 2*X*Y^9 + 
        3*X*Y^8 + X*Y^7 + 2*X*Y^6 + X*Y^2 + X*Y + 4*X + 3*Y^30 + 4*Y^29 + 3*Y^28 + 
        Y^27 + 6*Y^26 + Y^25 + 2*Y^24 + 6*Y^23 + 4*Y^22 + 6*Y^19 + 6*Y^18 + 5*Y^16 +
        4*Y^14 + 5*Y^13 + Y^12 + Y^11 + 5*Y^9 + 5*Y^7 + 4*Y^5 + 5*Y^4 + 3*Y^3 + 
        3*Y^2 + 4*Y,
    -T^56 + 6/7*T^55 + 46/49*T^54 - 143/343*T^53 + 1131/2401*T^52 - 1137/2401*T^51 -
        3320/2401*T^50 - 185/2401*T^49 + 25/49*T^48 - 4/2401*T^47 + 59/49*T^46 + 
        362/343*T^45 - 1446/2401*T^44 - 1597/2401*T^43 - 2862/2401*T^42 - 
        2508/2401*T^41 + 696/2401*T^40 + 3084/2401*T^39 + 302/343*T^38 + 
        2626/2401*T^37 + 1782/2401*T^36 - 5104/2401*T^35 - 3735/2401*T^34 - 
        1433/2401*T^33 - 2019/2401*T^32 + 3652/2401*T^31 + 6646/2401*T^30 + 
        911/2401*T^29 - 911/2401*T^27 - 6646/2401*T^26 - 3652/2401*T^25 + 
        2019/2401*T^24 + 1433/2401*T^23 + 3735/2401*T^22 + 5104/2401*T^21 - 
        1782/2401*T^20 - 2626/2401*T^19 - 302/343*T^18 - 3084/2401*T^17 - 
        696/2401*T^16 + 2508/2401*T^15 + 2862/2401*T^14 + 1597/2401*T^13 + 
        1446/2401*T^12 - 362/343*T^11 - 59/49*T^10 + 4/2401*T^9 - 25/49*T^8 + 
        185/2401*T^7 + 3320/2401*T^6 + 1137/2401*T^5 - 1131/2401*T^4 + 143/343*T^3 -
        46/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 4*X*Y^8 +
        6*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + X*Y^2 + 3*X + 6*Y^30 + Y^29 + 6*Y^28 + 5*Y^27 
        + 4*Y^25 + Y^24 + 6*Y^23 + 2*Y^22 + 3*Y^21 + 3*Y^20 + 4*Y^19 + 6*Y^18 + 
        6*Y^17 + 2*Y^15 + Y^14 + Y^12 + 2*Y^11 + 6*Y^9 + 5*Y^8 + 2*Y^7 + 4*Y^6 + 
        5*Y^4 + 4*Y^3 + Y^2 + 3,
    T^56 + 13/7*T^55 + 110/49*T^54 + 647/343*T^53 + 531/343*T^52 + 4022/2401*T^51 + 
        2939/2401*T^50 + 8/49*T^49 + 786/2401*T^48 + 1889/2401*T^47 + 2516/2401*T^46
        + 1632/2401*T^45 + 757/2401*T^44 + 1535/2401*T^43 - 102/2401*T^42 - 
        2882/2401*T^41 - 3233/2401*T^40 - 2304/2401*T^39 - 2250/2401*T^38 - 
        2770/2401*T^37 - 2642/2401*T^36 - 421/2401*T^35 - 44/2401*T^34 - 
        1268/2401*T^33 - 1053/2401*T^32 - 475/2401*T^31 - 421/2401*T^30 - 
        1838/2401*T^29 - 471/343*T^28 - 1838/2401*T^27 - 421/2401*T^26 - 
        475/2401*T^25 - 1053/2401*T^24 - 1268/2401*T^23 - 44/2401*T^22 - 
        421/2401*T^21 - 2642/2401*T^20 - 2770/2401*T^19 - 2250/2401*T^18 - 
        2304/2401*T^17 - 3233/2401*T^16 - 2882/2401*T^15 - 102/2401*T^14 + 
        1535/2401*T^13 + 757/2401*T^12 + 1632/2401*T^11 + 2516/2401*T^10 + 
        1889/2401*T^9 + 786/2401*T^8 + 8/49*T^7 + 2939/2401*T^6 + 4022/2401*T^5 + 
        531/343*T^4 + 647/343*T^3 + 110/49*T^2 + 13/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + X*Y^13 + X*Y^12 + 3*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 + 
        X*Y^7 + 6*X*Y^6 + 4*X*Y^4 + 2*X*Y^3 + X*Y^2 + 4*X*Y + 6*X + 5*Y^30 + 5*Y^29 
        + 2*Y^28 + 2*Y^27 + 2*Y^26 + 3*Y^25 + 2*Y^24 + 3*Y^23 + 2*Y^22 + Y^20 + 
        4*Y^19 + 2*Y^18 + 6*Y^16 + 4*Y^15 + 3*Y^14 + 4*Y^13 + 4*Y^12 + 4*Y^11 + Y^10
        + 2*Y^8 + 3*Y^7 + 4*Y^6 + 3*Y^5 + 2*Y^4 + 2*Y^3 + 2*Y^2 + 6,
    -T^56 - 6/7*T^55 + 59/49*T^54 + 145/343*T^53 - 2356/2401*T^52 + 1444/2401*T^51 +
        851/2401*T^50 - 3156/2401*T^49 - 241/2401*T^48 + 799/2401*T^47 - 
        2390/2401*T^46 - 9/2401*T^45 + 2446/2401*T^44 - 123/2401*T^43 - 
        606/2401*T^42 + 72/2401*T^41 - 209/343*T^40 - 80/2401*T^39 + 1343/2401*T^38 
        - 1009/2401*T^37 - 59/2401*T^36 + 1574/2401*T^35 - 606/2401*T^34 - 
        587/2401*T^33 + 75/343*T^32 - 111/343*T^31 - 86/2401*T^30 + 249/343*T^29 - 
        249/343*T^27 + 86/2401*T^26 + 111/343*T^25 - 75/343*T^24 + 587/2401*T^23 + 
        606/2401*T^22 - 1574/2401*T^21 + 59/2401*T^20 + 1009/2401*T^19 - 
        1343/2401*T^18 + 80/2401*T^17 + 209/343*T^16 - 72/2401*T^15 + 606/2401*T^14 
        + 123/2401*T^13 - 2446/2401*T^12 + 9/2401*T^11 + 2390/2401*T^10 - 
        799/2401*T^9 + 241/2401*T^8 + 3156/2401*T^7 - 851/2401*T^6 - 1444/2401*T^5 +
        2356/2401*T^4 - 145/343*T^3 - 59/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 4*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 5*X*Y^7 + 5*X*Y^5 +
        2*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 6*X*Y + 3*X + 5*Y^30 + Y^29 + Y^28 + 5*Y^27 + 
        4*Y^26 + 6*Y^25 + 2*Y^24 + 4*Y^23 + Y^22 + Y^21 + 5*Y^20 + 3*Y^18 + 3*Y^17 +
        2*Y^15 + 2*Y^14 + 6*Y^13 + 6*Y^12 + 5*Y^10 + 3*Y^8 + 2*Y^7 + 6*Y^6 + 2*Y^5 +
        6*Y^4 + 4*Y^3 + Y^2 + 6*Y + 6,
    T^56 + 5/7*T^55 + 11/49*T^54 - 135/343*T^53 - 4101/2401*T^52 - 1667/2401*T^51 - 
        835/2401*T^50 + 1749/2401*T^49 + 3065/2401*T^48 + 1551/2401*T^47 + 
        387/2401*T^46 - 2542/2401*T^45 - 2439/2401*T^44 - 1648/2401*T^43 + 
        52/343*T^42 + 2274/2401*T^41 + 1495/2401*T^40 - 356/2401*T^39 - 
        848/2401*T^38 - 2087/2401*T^37 - 138/2401*T^36 + 1277/2401*T^35 + 
        396/2401*T^34 + 2242/2401*T^33 - 51/343*T^32 + 537/2401*T^31 + 158/2401*T^30
        - 2025/2401*T^29 + 76/2401*T^28 - 2025/2401*T^27 + 158/2401*T^26 + 
        537/2401*T^25 - 51/343*T^24 + 2242/2401*T^23 + 396/2401*T^22 + 
        1277/2401*T^21 - 138/2401*T^20 - 2087/2401*T^19 - 848/2401*T^18 - 
        356/2401*T^17 + 1495/2401*T^16 + 2274/2401*T^15 + 52/343*T^14 - 
        1648/2401*T^13 - 2439/2401*T^12 - 2542/2401*T^11 + 387/2401*T^10 + 
        1551/2401*T^9 + 3065/2401*T^8 + 1749/2401*T^7 - 835/2401*T^6 - 1667/2401*T^5
        - 4101/2401*T^4 - 135/343*T^3 + 11/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 2*X*Y^9 + 3*X*Y^8 +
        X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 5*X*Y + X + 5*Y^30
        + 5*Y^29 + 2*Y^28 + 4*Y^27 + 4*Y^26 + Y^24 + 6*Y^23 + 4*Y^22 + Y^21 + 6*Y^20
        + 6*Y^19 + 5*Y^18 + 2*Y^17 + 4*Y^16 + 2*Y^15 + 4*Y^14 + 2*Y^13 + 6*Y^12 + 
        4*Y^11 + 4*Y^10 + 5*Y^9 + 5*Y^8 + 6*Y^7 + Y^6 + Y^3 + 4*Y^2 + 4*Y + 3,
    T^56 + 10/7*T^55 + 4/49*T^54 - 103/49*T^53 - 6228/2401*T^52 - 535/2401*T^51 + 
        4234/2401*T^50 + 3592/2401*T^49 - 433/2401*T^48 - 367/343*T^47 + 
        1277/2401*T^46 + 3074/2401*T^45 - 992/2401*T^44 - 6225/2401*T^43 - 
        4962/2401*T^42 + 2405/2401*T^41 + 790/343*T^40 + 3085/2401*T^39 - 
        1045/2401*T^38 - 13/49*T^37 + 303/343*T^36 + 1325/2401*T^35 - 2668/2401*T^34
        - 5269/2401*T^33 - 1167/2401*T^32 + 533/343*T^31 + 3538/2401*T^30 - 
        359/2401*T^29 - 3602/2401*T^28 - 359/2401*T^27 + 3538/2401*T^26 + 
        533/343*T^25 - 1167/2401*T^24 - 5269/2401*T^23 - 2668/2401*T^22 + 
        1325/2401*T^21 + 303/343*T^20 - 13/49*T^19 - 1045/2401*T^18 + 3085/2401*T^17
        + 790/343*T^16 + 2405/2401*T^15 - 4962/2401*T^14 - 6225/2401*T^13 - 
        992/2401*T^12 + 3074/2401*T^11 + 1277/2401*T^10 - 367/343*T^9 - 433/2401*T^8
        + 3592/2401*T^7 + 4234/2401*T^6 - 535/2401*T^5 - 6228/2401*T^4 - 103/49*T^3 
        + 4/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 3*X*Y^8 +
        6*X*Y^7 + 5*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + X*Y^3 + 4*X*Y^2 + 6*X + 4*Y^30 + 
        3*Y^29 + 3*Y^27 + 5*Y^26 + Y^24 + 6*Y^23 + Y^22 + 2*Y^20 + 6*Y^19 + 3*Y^18 +
        5*Y^17 + 3*Y^16 + 5*Y^13 + Y^12 + 4*Y^11 + 4*Y^10 + Y^9 + 5*Y^8 + 3*Y^7 + 
        6*Y^6 + 5*Y^5 + 5*Y^4 + 2*Y^3 + 5*Y^2 + Y + 3,
    -T^56 - 9/7*T^55 - 65/49*T^54 - 76/49*T^53 - 3247/2401*T^52 - 2147/2401*T^51 - 
        1994/2401*T^50 - 1667/2401*T^49 + 387/2401*T^48 + 1282/2401*T^47 + 
        2241/2401*T^46 + 2950/2401*T^45 + 2022/2401*T^44 + 2113/2401*T^43 + 
        2281/2401*T^42 + 1480/2401*T^41 + 1935/2401*T^40 + 1420/2401*T^39 + 
        540/2401*T^38 + 34/343*T^37 + 943/2401*T^36 - 276/2401*T^35 - 27/343*T^34 - 
        377/2401*T^33 - 236/343*T^32 - 1289/2401*T^31 - 985/2401*T^30 - 
        1279/2401*T^29 + 1279/2401*T^27 + 985/2401*T^26 + 1289/2401*T^25 + 
        236/343*T^24 + 377/2401*T^23 + 27/343*T^22 + 276/2401*T^21 - 943/2401*T^20 -
        34/343*T^19 - 540/2401*T^18 - 1420/2401*T^17 - 1935/2401*T^16 - 
        1480/2401*T^15 - 2281/2401*T^14 - 2113/2401*T^13 - 2022/2401*T^12 - 
        2950/2401*T^11 - 2241/2401*T^10 - 1282/2401*T^9 - 387/2401*T^8 + 
        1667/2401*T^7 + 1994/2401*T^6 + 2147/2401*T^5 + 3247/2401*T^4 + 76/49*T^3 + 
        65/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + X*Y^13 + X*Y^11 + 4*X*Y^10 + X*Y^9 + 6*X*Y^8 + 5*X*Y^7 + 
        2*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 4*X*Y + 4*X + 3*Y^30 + 
        2*Y^29 + 4*Y^28 + 5*Y^27 + 2*Y^26 + 5*Y^25 + 6*Y^24 + 2*Y^23 + 2*Y^20 + 
        2*Y^19 + 3*Y^18 + 4*Y^17 + 3*Y^15 + Y^13 + 4*Y^12 + 2*Y^11 + 3*Y^10 + 4*Y^9 
        + Y^8 + 5*Y^7 + Y^6 + Y^5 + 2*Y^4 + 3*Y^3 + 4*Y^2 + 3*Y + 4,
    T^56 - 8/49*T^54 - 30/49*T^53 - 2357/2401*T^52 + 2675/2401*T^51 - 695/2401*T^50 
        + 264/2401*T^49 - 40/2401*T^48 - 177/343*T^47 + 2061/2401*T^46 - 
        762/2401*T^45 - 286/2401*T^44 - 170/2401*T^43 - 1196/2401*T^42 + 22/343*T^41
        - 295/2401*T^40 - 170/2401*T^39 + 683/2401*T^38 + 841/2401*T^37 + 
        216/2401*T^36 + 323/2401*T^35 - 1534/2401*T^34 + 486/2401*T^33 + 
        559/2401*T^32 + 248/2401*T^31 + 536/2401*T^30 - 1132/2401*T^29 + 
        778/2401*T^28 - 1132/2401*T^27 + 536/2401*T^26 + 248/2401*T^25 + 
        559/2401*T^24 + 486/2401*T^23 - 1534/2401*T^22 + 323/2401*T^21 + 
        216/2401*T^20 + 841/2401*T^19 + 683/2401*T^18 - 170/2401*T^17 - 
        295/2401*T^16 + 22/343*T^15 - 1196/2401*T^14 - 170/2401*T^13 - 286/2401*T^12
        - 762/2401*T^11 + 2061/2401*T^10 - 177/343*T^9 - 40/2401*T^8 + 264/2401*T^7 
        - 695/2401*T^6 + 2675/2401*T^5 - 2357/2401*T^4 - 30/49*T^3 - 8/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 
        X*Y^8 + X*Y^7 + X*Y^6 + X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 2*X*Y + 3*X + 
        5*Y^30 + 2*Y^28 + 3*Y^27 + 3*Y^26 + 4*Y^25 + 4*Y^24 + 3*Y^23 + 2*Y^22 + 
        4*Y^21 + 4*Y^20 + 6*Y^19 + 4*Y^18 + 2*Y^17 + 2*Y^16 + 5*Y^15 + 2*Y^13 + 
        6*Y^12 + 4*Y^11 + 5*Y^10 + 4*Y^8 + 5*Y^7 + 2*Y^6 + 6*Y^5 + 4*Y^4 + 5*Y^3 + 
        5*Y^2 + 6*Y + 5,
    -T^56 - 1/7*T^55 + 31/49*T^54 + 45/343*T^53 + 163/343*T^52 - 436/2401*T^51 + 
        717/2401*T^50 + 1346/2401*T^49 - 643/2401*T^48 + 768/2401*T^47 - 
        1229/2401*T^46 - 2234/2401*T^45 + 496/2401*T^44 - 38/2401*T^43 + 
        1277/2401*T^42 - 1395/2401*T^41 - 2280/2401*T^40 + 2230/2401*T^39 + 
        986/2401*T^38 + 1550/2401*T^37 + 1144/2401*T^36 - 1892/2401*T^35 + 
        1114/2401*T^34 - 1012/2401*T^33 - 534/2401*T^32 + 134/343*T^31 - 
        3169/2401*T^30 - 1096/2401*T^29 + 1096/2401*T^27 + 3169/2401*T^26 - 
        134/343*T^25 + 534/2401*T^24 + 1012/2401*T^23 - 1114/2401*T^22 + 
        1892/2401*T^21 - 1144/2401*T^20 - 1550/2401*T^19 - 986/2401*T^18 - 
        2230/2401*T^17 + 2280/2401*T^16 + 1395/2401*T^15 - 1277/2401*T^14 + 
        38/2401*T^13 - 496/2401*T^12 + 2234/2401*T^11 + 1229/2401*T^10 - 
        768/2401*T^9 + 643/2401*T^8 - 1346/2401*T^7 - 717/2401*T^6 + 436/2401*T^5 - 
        163/343*T^4 - 45/343*T^3 - 31/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + X*Y^9 + 4*X*Y^7 + 6*X*Y^6 + 
        5*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + X*Y^2 + X + 3*Y^30 + 6*Y^29 + 4*Y^28 + 3*Y^27 
        + 4*Y^26 + Y^25 + 2*Y^24 + 2*Y^23 + 3*Y^22 + 4*Y^21 + 3*Y^20 + 3*Y^19 + 
        2*Y^18 + 2*Y^17 + 5*Y^15 + 3*Y^14 + 4*Y^13 + 2*Y^11 + 6*Y^10 + 5*Y^9 + 6*Y^8
        + 5*Y^7 + Y^4 + 6*Y^2 + Y + 1,
    -T^56 + 5/7*T^55 - 8/49*T^54 - 29/49*T^53 + 142/2401*T^52 + 1217/2401*T^51 - 
        192/343*T^50 + 1172/2401*T^49 + 32/2401*T^48 - 215/2401*T^47 + 737/2401*T^46
        + 317/2401*T^45 - 11/343*T^44 - 23/2401*T^43 + 822/2401*T^42 - 25/49*T^41 + 
        891/2401*T^40 - 123/2401*T^39 - 214/2401*T^38 - 66/343*T^37 + 877/2401*T^36 
        - 1845/2401*T^35 + 976/2401*T^34 - 46/2401*T^33 - 170/343*T^32 + 
        311/2401*T^31 + 23/49*T^30 - 1462/2401*T^29 + 1462/2401*T^27 - 23/49*T^26 - 
        311/2401*T^25 + 170/343*T^24 + 46/2401*T^23 - 976/2401*T^22 + 1845/2401*T^21
        - 877/2401*T^20 + 66/343*T^19 + 214/2401*T^18 + 123/2401*T^17 - 
        891/2401*T^16 + 25/49*T^15 - 822/2401*T^14 + 23/2401*T^13 + 11/343*T^12 - 
        317/2401*T^11 - 737/2401*T^10 + 215/2401*T^9 - 32/2401*T^8 - 1172/2401*T^7 +
        192/343*T^6 - 1217/2401*T^5 - 142/2401*T^4 + 29/49*T^3 + 8/49*T^2 - 5/7*T + 
        1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 
        + 3*X*Y^8 + 5*X*Y^7 + 3*X*Y^6 + 5*X*Y^4 + 4*X*Y^2 + 5*X*Y + 2*Y^30 + 4*Y^29 
        + 3*Y^28 + 5*Y^27 + 2*Y^25 + 2*Y^24 + 2*Y^23 + 2*Y^22 + 3*Y^21 + 5*Y^20 + 
        3*Y^18 + 2*Y^17 + Y^16 + 4*Y^15 + 2*Y^14 + 2*Y^13 + 6*Y^12 + 4*Y^9 + 6*Y^8 +
        6*Y^7 + 5*Y^6 + 4*Y^5 + 5*Y^4 + 2*Y^3 + 4*Y^2 + 6*Y + 4,
    T^56 + 1/7*T^55 + 18/49*T^54 + 360/343*T^53 + 1672/2401*T^52 + 13/343*T^51 + 
        185/343*T^50 + 323/2401*T^49 - 10/49*T^48 - 2323/2401*T^47 - 183/2401*T^46 -
        163/2401*T^45 - 2001/2401*T^44 - 1308/2401*T^43 + 1058/2401*T^42 - 
        617/2401*T^41 - 1188/2401*T^40 - 32/2401*T^39 + 62/2401*T^38 - 
        1389/2401*T^37 - 1465/2401*T^36 + 9/343*T^35 - 60/343*T^34 - 745/2401*T^33 +
        52/343*T^32 + 1111/2401*T^31 + 430/2401*T^30 + 1257/2401*T^29 + 
        1528/2401*T^28 + 1257/2401*T^27 + 430/2401*T^26 + 1111/2401*T^25 + 
        52/343*T^24 - 745/2401*T^23 - 60/343*T^22 + 9/343*T^21 - 1465/2401*T^20 - 
        1389/2401*T^19 + 62/2401*T^18 - 32/2401*T^17 - 1188/2401*T^16 - 
        617/2401*T^15 + 1058/2401*T^14 - 1308/2401*T^13 - 2001/2401*T^12 - 
        163/2401*T^11 - 183/2401*T^10 - 2323/2401*T^9 - 10/49*T^8 + 323/2401*T^7 + 
        185/343*T^6 + 13/343*T^5 + 1672/2401*T^4 + 360/343*T^3 + 18/49*T^2 + 1/7*T +
        1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 3*X*Y^8 
        + 6*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + X*Y^4 + 2*X*Y^2 + 3*Y^30 + 6*Y^29 + 5*Y^28 +
        5*Y^27 + 4*Y^26 + 6*Y^25 + 2*Y^24 + 4*Y^22 + 3*Y^21 + 3*Y^20 + 3*Y^19 + 
        6*Y^17 + 5*Y^16 + 3*Y^15 + Y^14 + 6*Y^13 + 5*Y^12 + 2*Y^11 + 4*Y^9 + Y^8 + 
        5*Y^7 + Y^6 + 5*Y^5 + 3*Y^4 + Y^3 + 4*Y + 5,
    T^56 - 10/7*T^55 + 23/49*T^54 - 122/343*T^53 - 1012/2401*T^52 + 4399/2401*T^51 -
        2295/2401*T^50 - 18/2401*T^49 - 911/2401*T^48 - 279/2401*T^47 + 
        1510/2401*T^46 + 306/2401*T^45 - 228/2401*T^44 - 2533/2401*T^43 + 
        2007/2401*T^42 - 453/2401*T^41 + 1692/2401*T^40 - 968/2401*T^39 - 
        1373/2401*T^38 + 593/2401*T^37 + 4/343*T^36 + 2438/2401*T^35 - 
        3585/2401*T^34 + 1622/2401*T^33 - 1571/2401*T^32 + 1635/2401*T^31 + 
        2735/2401*T^30 - 3578/2401*T^29 + 1334/2401*T^28 - 3578/2401*T^27 + 
        2735/2401*T^26 + 1635/2401*T^25 - 1571/2401*T^24 + 1622/2401*T^23 - 
        3585/2401*T^22 + 2438/2401*T^21 + 4/343*T^20 + 593/2401*T^19 - 
        1373/2401*T^18 - 968/2401*T^17 + 1692/2401*T^16 - 453/2401*T^15 + 
        2007/2401*T^14 - 2533/2401*T^13 - 228/2401*T^12 + 306/2401*T^11 + 
        1510/2401*T^10 - 279/2401*T^9 - 911/2401*T^8 - 18/2401*T^7 - 2295/2401*T^6 +
        4399/2401*T^5 - 1012/2401*T^4 - 122/343*T^3 + 23/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 4*X*Y^8 +
        5*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 4*X*Y^2 + 4*X*Y + 4*Y^30 + 5*Y^29 + 3*Y^28 + 
        6*Y^27 + 2*Y^26 + Y^25 + 2*Y^24 + 2*Y^23 + 4*Y^22 + 2*Y^21 + Y^20 + 2*Y^19 +
        3*Y^18 + Y^17 + Y^16 + 6*Y^15 + Y^14 + 6*Y^13 + 5*Y^12 + 4*Y^11 + 3*Y^9 + 
        3*Y^8 + 6*Y^7 + 4*Y^6 + 3*Y^5 + 3*Y^4 + 6*Y^3 + 5*Y + 1,
    T^56 - 18/49*T^54 - 122/343*T^53 - 407/2401*T^52 + 1577/2401*T^51 - 
        249/2401*T^50 - 1010/2401*T^49 - 438/2401*T^48 + 159/2401*T^47 + 
        495/2401*T^46 - 45/343*T^45 - 599/2401*T^44 + 239/2401*T^43 - 557/2401*T^42 
        - 143/343*T^41 + 146/2401*T^40 + 103/2401*T^39 + 37/343*T^38 + 283/2401*T^37
        - 1070/2401*T^36 + 978/2401*T^35 + 1123/2401*T^34 - 942/2401*T^33 + 
        472/2401*T^32 + 11/2401*T^31 + 474/2401*T^30 + 492/2401*T^29 - 
        1452/2401*T^28 + 492/2401*T^27 + 474/2401*T^26 + 11/2401*T^25 + 
        472/2401*T^24 - 942/2401*T^23 + 1123/2401*T^22 + 978/2401*T^21 - 
        1070/2401*T^20 + 283/2401*T^19 + 37/343*T^18 + 103/2401*T^17 + 146/2401*T^16
        - 143/343*T^15 - 557/2401*T^14 + 239/2401*T^13 - 599/2401*T^12 - 45/343*T^11
        + 495/2401*T^10 + 159/2401*T^9 - 438/2401*T^8 - 1010/2401*T^7 - 249/2401*T^6
        + 1577/2401*T^5 - 407/2401*T^4 - 122/343*T^3 - 18/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + X*Y^12 + 6*X*Y^11 + X*Y^10 + 3*X*Y^9 + 2*X*Y^8 + 
        6*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + X*Y + X + 2*Y^30
        + Y^28 + 4*Y^27 + 5*Y^26 + 2*Y^25 + 5*Y^24 + 3*Y^23 + Y^22 + 4*Y^21 + 3*Y^20
        + 5*Y^19 + Y^18 + 6*Y^17 + 5*Y^16 + 3*Y^15 + 4*Y^14 + 6*Y^13 + 6*Y^12 + 
        3*Y^11 + 2*Y^9 + 6*Y^7 + Y^6 + 3*Y^5 + Y^4 + 2*Y^3 + 5*Y^2 + 3*Y + 3,
    T^56 + 3/7*T^55 - 20/49*T^54 - 197/343*T^53 - 1487/2401*T^52 + 134/2401*T^51 + 
        243/2401*T^50 - 229/343*T^49 + 137/343*T^48 + 1408/2401*T^47 - 856/2401*T^46
        - 465/2401*T^45 - 913/2401*T^44 - 902/2401*T^43 + 1381/2401*T^42 - 
        596/2401*T^41 + 93/2401*T^40 + 2151/2401*T^39 + 6/49*T^38 + 1375/2401*T^37 +
        856/2401*T^36 - 1590/2401*T^35 - 527/2401*T^34 + 19/2401*T^33 - 
        608/2401*T^32 + 1389/2401*T^31 - 499/2401*T^30 - 1430/2401*T^29 + 
        215/2401*T^28 - 1430/2401*T^27 - 499/2401*T^26 + 1389/2401*T^25 - 
        608/2401*T^24 + 19/2401*T^23 - 527/2401*T^22 - 1590/2401*T^21 + 
        856/2401*T^20 + 1375/2401*T^19 + 6/49*T^18 + 2151/2401*T^17 + 93/2401*T^16 -
        596/2401*T^15 + 1381/2401*T^14 - 902/2401*T^13 - 913/2401*T^12 - 
        465/2401*T^11 - 856/2401*T^10 + 1408/2401*T^9 + 137/343*T^8 - 229/343*T^7 + 
        243/2401*T^6 + 134/2401*T^5 - 1487/2401*T^4 - 197/343*T^3 - 20/49*T^2 + 
        3/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 3*X*Y^13 + X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 3*X*Y^8 + 
        2*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 3*X*Y^2 + 2*X*Y + 2*X + 6*Y^30 + 
        4*Y^29 + Y^28 + 6*Y^27 + 2*Y^26 + 3*Y^23 + 6*Y^22 + Y^21 + 6*Y^20 + 4*Y^19 +
        5*Y^18 + 4*Y^17 + 6*Y^15 + 3*Y^14 + 4*Y^13 + 6*Y^12 + 4*Y^11 + 3*Y^10 + 
        2*Y^9 + 2*Y^8 + Y^7 + 5*Y^6 + 3*Y^4 + 6*Y^3 + 4*Y^2 + 1,
    T^56 + 8/7*T^55 + 4/49*T^54 - 16/49*T^53 - 661/2401*T^52 - 332/2401*T^51 + 
        465/2401*T^50 + 251/2401*T^49 + 509/2401*T^48 + 435/2401*T^47 - 
        354/2401*T^46 + 6/343*T^45 + 627/2401*T^44 + 1069/2401*T^43 + 464/2401*T^42 
        + 729/2401*T^41 + 2356/2401*T^40 + 29/49*T^39 - 685/2401*T^38 - 
        654/2401*T^37 - 3/7*T^36 - 753/2401*T^35 - 54/2401*T^34 + 401/2401*T^33 + 
        1114/2401*T^32 + 192/2401*T^31 - 4/2401*T^30 + 1223/2401*T^29 + 
        1678/2401*T^28 + 1223/2401*T^27 - 4/2401*T^26 + 192/2401*T^25 + 
        1114/2401*T^24 + 401/2401*T^23 - 54/2401*T^22 - 753/2401*T^21 - 3/7*T^20 - 
        654/2401*T^19 - 685/2401*T^18 + 29/49*T^17 + 2356/2401*T^16 + 729/2401*T^15 
        + 464/2401*T^14 + 1069/2401*T^13 + 627/2401*T^12 + 6/343*T^11 - 
        354/2401*T^10 + 435/2401*T^9 + 509/2401*T^8 + 251/2401*T^7 + 465/2401*T^6 - 
        332/2401*T^5 - 661/2401*T^4 - 16/49*T^3 + 4/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + X*Y^13 + 5*X*Y^12 + 6*X*Y^10 + X*Y^9 + 4*X*Y^8 + 
        6*X*Y^7 + X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 4*X*Y^2 + 3*X*Y + 4*X + 5*Y^30 + 
        5*Y^29 + Y^28 + 5*Y^27 + 3*Y^26 + 3*Y^25 + Y^24 + 5*Y^22 + 6*Y^21 + 2*Y^19 +
        5*Y^18 + Y^17 + 6*Y^16 + 6*Y^15 + 3*Y^14 + 2*Y^13 + 4*Y^11 + 5*Y^10 + 5*Y^9 
        + 3*Y^8 + 4*Y^7 + 4*Y^6 + 5*Y^4 + 6*Y^3 + 2*Y^2 + 3*Y,
    -T^56 + 2/7*T^55 + 33/49*T^54 - 93/343*T^53 + 1305/2401*T^52 - 1704/2401*T^51 - 
        1913/2401*T^50 + 268/2401*T^49 + 1101/2401*T^48 + 2267/2401*T^47 + 
        61/343*T^46 - 326/2401*T^45 - 2615/2401*T^44 + 683/2401*T^43 + 
        1948/2401*T^42 - 478/2401*T^41 + 2250/2401*T^40 - 1513/2401*T^39 - 
        724/2401*T^38 + 771/2401*T^37 - 213/343*T^36 + 1447/2401*T^35 - 
        293/2401*T^34 - 173/343*T^33 + 383/2401*T^32 - 331/2401*T^31 - 226/2401*T^30
        - 8/2401*T^29 + 8/2401*T^27 + 226/2401*T^26 + 331/2401*T^25 - 383/2401*T^24 
        + 173/343*T^23 + 293/2401*T^22 - 1447/2401*T^21 + 213/343*T^20 - 
        771/2401*T^19 + 724/2401*T^18 + 1513/2401*T^17 - 2250/2401*T^16 + 
        478/2401*T^15 - 1948/2401*T^14 - 683/2401*T^13 + 2615/2401*T^12 + 
        326/2401*T^11 - 61/343*T^10 - 2267/2401*T^9 - 1101/2401*T^8 - 268/2401*T^7 +
        1913/2401*T^6 + 1704/2401*T^5 - 1305/2401*T^4 + 93/343*T^3 - 33/49*T^2 - 
        2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 6*X*Y^12 + X*Y^11 + 2*X*Y^10 + 3*X*Y^9 + 5*X*Y^7 + 
        X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + X*Y^2 + 5*X + 5*Y^30 + Y^29 + 3*Y^28 +
        3*Y^27 + 6*Y^25 + 4*Y^24 + 5*Y^23 + 4*Y^22 + 6*Y^21 + 2*Y^19 + 4*Y^17 + 
        4*Y^16 + 4*Y^15 + 4*Y^14 + 4*Y^13 + 3*Y^12 + 4*Y^11 + 5*Y^9 + 5*Y^8 + 2*Y^7 
        + Y^6 + 4*Y^5 + 2*Y^4 + 3*Y^3 + 5*Y^2 + 6*Y,
    -T^56 + 3/7*T^55 + 6/49*T^54 - 5/7*T^53 + 988/2401*T^52 - 401/2401*T^51 - 
        269/2401*T^50 + 194/2401*T^49 - 190/343*T^48 + 309/2401*T^47 - 13/2401*T^46 
        - 207/2401*T^45 + 626/2401*T^44 - 928/2401*T^43 - 222/2401*T^42 - 
        235/2401*T^41 - 814/2401*T^40 + 643/2401*T^39 - 1241/2401*T^38 + 
        739/2401*T^37 + 65/343*T^36 - 1116/2401*T^35 + 766/2401*T^34 - 
        1503/2401*T^33 + 538/2401*T^32 + 1496/2401*T^31 - 1354/2401*T^30 + 
        1387/2401*T^29 - 1387/2401*T^27 + 1354/2401*T^26 - 1496/2401*T^25 - 
        538/2401*T^24 + 1503/2401*T^23 - 766/2401*T^22 + 1116/2401*T^21 - 
        65/343*T^20 - 739/2401*T^19 + 1241/2401*T^18 - 643/2401*T^17 + 814/2401*T^16
        + 235/2401*T^15 + 222/2401*T^14 + 928/2401*T^13 - 626/2401*T^12 + 
        207/2401*T^11 + 13/2401*T^10 - 309/2401*T^9 + 190/343*T^8 - 194/2401*T^7 + 
        269/2401*T^6 + 401/2401*T^5 - 988/2401*T^4 + 5/7*T^3 - 6/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 
        + 5*X*Y^8 + 3*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 6*X*Y^2 + 2*X*Y + 5*X + 
        Y^30 + 6*Y^29 + 3*Y^28 + 3*Y^27 + 6*Y^26 + 4*Y^24 + 3*Y^23 + 6*Y^22 + 2*Y^20
        + 5*Y^19 + 5*Y^18 + Y^17 + 6*Y^16 + 6*Y^14 + Y^13 + 4*Y^11 + 6*Y^10 + Y^7 + 
        Y^6 + 2*Y^5 + 5*Y^4 + Y^3 + Y^2 + Y + 3,
    -T^56 + 2/7*T^55 - 2/7*T^54 + 72/343*T^53 - 193/2401*T^52 + 250/343*T^51 - 
        2057/2401*T^50 + 241/343*T^49 + 116/2401*T^48 + 719/2401*T^47 - 
        984/2401*T^46 + 1716/2401*T^45 - 1762/2401*T^44 + 790/2401*T^43 - 
        774/2401*T^42 + 1178/2401*T^41 - 853/2401*T^40 - 4/343*T^39 - 1037/2401*T^38
        + 583/2401*T^37 - 87/343*T^36 + 1200/2401*T^35 - 113/2401*T^34 - 
        1151/2401*T^33 + 313/2401*T^32 + 278/2401*T^31 - 405/2401*T^30 + 
        855/2401*T^29 - 855/2401*T^27 + 405/2401*T^26 - 278/2401*T^25 - 
        313/2401*T^24 + 1151/2401*T^23 + 113/2401*T^22 - 1200/2401*T^21 + 
        87/343*T^20 - 583/2401*T^19 + 1037/2401*T^18 + 4/343*T^17 + 853/2401*T^16 - 
        1178/2401*T^15 + 774/2401*T^14 - 790/2401*T^13 + 1762/2401*T^12 - 
        1716/2401*T^11 + 984/2401*T^10 - 719/2401*T^9 - 116/2401*T^8 - 241/343*T^7 +
        2057/2401*T^6 - 250/343*T^5 + 193/2401*T^4 - 72/343*T^3 + 2/7*T^2 - 2/7*T + 
        1
*], [*
    X^3 + X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 4*X*Y^9 + 6*X*Y^8 + X*Y^7 + 
        3*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 3*X*Y + 3*X + Y^30 + 
        3*Y^28 + 4*Y^27 + 6*Y^26 + 6*Y^25 + 6*Y^23 + Y^22 + 5*Y^20 + 6*Y^19 + 4*Y^18
        + 3*Y^17 + 5*Y^16 + 5*Y^13 + 4*Y^12 + 4*Y^11 + 5*Y^10 + 6*Y^8 + 5*Y^7 + 
        5*Y^5 + 4*Y^4 + 2*Y^3 + 2*Y^2 + 5,
    -T^56 + 17/7*T^55 - 146/49*T^54 + 858/343*T^53 - 4057/2401*T^52 + 1734/2401*T^51
        + 1122/2401*T^50 - 3383/2401*T^49 + 3302/2401*T^48 - 101/343*T^47 - 
        2928/2401*T^46 + 5632/2401*T^45 - 6137/2401*T^44 + 3583/2401*T^43 + 
        1229/2401*T^42 - 5508/2401*T^41 + 7439/2401*T^40 - 6525/2401*T^39 + 
        2376/2401*T^38 + 3394/2401*T^37 - 8097/2401*T^36 + 9559/2401*T^35 - 
        7440/2401*T^34 + 2386/2401*T^33 + 3317/2401*T^32 - 1063/343*T^31 + 
        8130/2401*T^30 - 5153/2401*T^29 + 5153/2401*T^27 - 8130/2401*T^26 + 
        1063/343*T^25 - 3317/2401*T^24 - 2386/2401*T^23 + 7440/2401*T^22 - 
        9559/2401*T^21 + 8097/2401*T^20 - 3394/2401*T^19 - 2376/2401*T^18 + 
        6525/2401*T^17 - 7439/2401*T^16 + 5508/2401*T^15 - 1229/2401*T^14 - 
        3583/2401*T^13 + 6137/2401*T^12 - 5632/2401*T^11 + 2928/2401*T^10 + 
        101/343*T^9 - 3302/2401*T^8 + 3383/2401*T^7 - 1122/2401*T^6 - 1734/2401*T^5 
        + 4057/2401*T^4 - 858/343*T^3 + 146/49*T^2 - 17/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + X*Y^11 + 4*X*Y^9 + 3*X*Y^6 + 
        2*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 2*X + 3*Y^30 + 3*Y^29 + 6*Y^28 + 
        Y^26 + 6*Y^25 + 5*Y^22 + 2*Y^21 + 2*Y^20 + Y^19 + 4*Y^18 + 6*Y^17 + 2*Y^16 +
        5*Y^15 + 3*Y^14 + 3*Y^13 + Y^12 + 6*Y^11 + 2*Y^9 + 4*Y^8 + 6*Y^7 + 6*Y^6 + 
        Y^5 + 2*Y^4 + 6*Y^3 + 3*Y^2 + 4*Y + 6,
    -T^56 + 12/7*T^55 - 68/49*T^54 + 374/343*T^53 - 3616/2401*T^52 + 2109/2401*T^51 
        + 1279/2401*T^50 - 290/343*T^49 + 545/2401*T^48 - 380/2401*T^47 + 
        2356/2401*T^46 - 2946/2401*T^45 + 2033/2401*T^44 - 2601/2401*T^43 + 
        625/343*T^42 - 3155/2401*T^41 + 38/343*T^40 + 1003/2401*T^39 - 38/343*T^38 +
        365/2401*T^37 - 46/2401*T^36 - 1528/2401*T^35 + 3110/2401*T^34 - 
        2271/2401*T^33 + 263/2401*T^32 + 16/343*T^31 - 107/343*T^30 + 1425/2401*T^29
        - 1425/2401*T^27 + 107/343*T^26 - 16/343*T^25 - 263/2401*T^24 + 
        2271/2401*T^23 - 3110/2401*T^22 + 1528/2401*T^21 + 46/2401*T^20 - 
        365/2401*T^19 + 38/343*T^18 - 1003/2401*T^17 - 38/343*T^16 + 3155/2401*T^15 
        - 625/343*T^14 + 2601/2401*T^13 - 2033/2401*T^12 + 2946/2401*T^11 - 
        2356/2401*T^10 + 380/2401*T^9 - 545/2401*T^8 + 290/343*T^7 - 1279/2401*T^6 -
        2109/2401*T^5 + 3616/2401*T^4 - 374/343*T^3 + 68/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + X*Y^10 + X*Y^9 + 
        X*Y^8 + 2*X*Y^7 + 3*X*Y^6 + X*Y^5 + 2*X*Y^3 + 5*X*Y^2 + 3*X + 4*Y^30 + 
        2*Y^29 + 6*Y^28 + 6*Y^27 + Y^26 + 2*Y^24 + 2*Y^23 + 4*Y^21 + 4*Y^20 + 2*Y^19
        + Y^18 + 6*Y^17 + 6*Y^16 + 4*Y^15 + 3*Y^14 + 6*Y^13 + 6*Y^12 + 3*Y^11 + 
        5*Y^10 + 2*Y^8 + 3*Y^7 + 5*Y^6 + Y^5 + Y^4 + 6*Y^3 + 3*Y^2 + 3*Y + 5,
    T^56 - 5/49*T^54 + 204/343*T^53 + 2269/2401*T^52 - 752/2401*T^51 + 117/343*T^50 
        + 202/343*T^49 + 419/2401*T^48 + 71/343*T^47 + 491/2401*T^46 - 793/2401*T^45
        - 2203/2401*T^44 + 90/343*T^43 - 422/2401*T^42 - 2299/2401*T^41 - 
        2826/2401*T^40 - 818/2401*T^39 - 515/2401*T^38 - 2433/2401*T^37 - 
        2143/2401*T^36 + 506/2401*T^35 + 755/2401*T^34 - 1388/2401*T^33 + 
        1152/2401*T^32 + 2066/2401*T^31 - 289/2401*T^30 + 123/343*T^29 + 
        3412/2401*T^28 + 123/343*T^27 - 289/2401*T^26 + 2066/2401*T^25 + 
        1152/2401*T^24 - 1388/2401*T^23 + 755/2401*T^22 + 506/2401*T^21 - 
        2143/2401*T^20 - 2433/2401*T^19 - 515/2401*T^18 - 818/2401*T^17 - 
        2826/2401*T^16 - 2299/2401*T^15 - 422/2401*T^14 + 90/343*T^13 - 
        2203/2401*T^12 - 793/2401*T^11 + 491/2401*T^10 + 71/343*T^9 + 419/2401*T^8 +
        202/343*T^7 + 117/343*T^6 - 752/2401*T^5 + 2269/2401*T^4 + 204/343*T^3 - 
        5/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 
        4*X*Y^8 + 3*X*Y^6 + 3*X*Y^4 + 2*X + 2*Y^30 + 5*Y^29 + 4*Y^28 + 2*Y^26 + Y^25
        + 5*Y^24 + 4*Y^22 + 6*Y^21 + 2*Y^20 + Y^19 + 5*Y^18 + 5*Y^17 + 6*Y^16 + 
        4*Y^15 + 2*Y^14 + 5*Y^12 + Y^11 + 6*Y^10 + 5*Y^9 + Y^8 + 2*Y^7 + 6*Y^6 + Y^4
        + 6*Y^3 + 5*Y + 1,
    T^56 + 3/49*T^54 - 9/49*T^53 - 101/2401*T^52 - 36/343*T^51 - 272/2401*T^50 + 
        1223/2401*T^49 - 1136/2401*T^48 + 1051/2401*T^47 + 237/2401*T^46 + 
        753/2401*T^45 - 1049/2401*T^44 - 304/2401*T^43 - 480/2401*T^42 - 
        860/2401*T^41 + 1/343*T^40 + 195/2401*T^39 + 509/2401*T^38 - 529/2401*T^37 +
        981/2401*T^36 - 38/343*T^35 - 226/2401*T^34 - 17/49*T^33 - 706/2401*T^32 - 
        561/2401*T^31 + 5/2401*T^30 + 779/2401*T^29 - 400/2401*T^28 + 779/2401*T^27 
        + 5/2401*T^26 - 561/2401*T^25 - 706/2401*T^24 - 17/49*T^23 - 226/2401*T^22 -
        38/343*T^21 + 981/2401*T^20 - 529/2401*T^19 + 509/2401*T^18 + 195/2401*T^17 
        + 1/343*T^16 - 860/2401*T^15 - 480/2401*T^14 - 304/2401*T^13 - 
        1049/2401*T^12 + 753/2401*T^11 + 237/2401*T^10 + 1051/2401*T^9 - 
        1136/2401*T^8 + 1223/2401*T^7 - 272/2401*T^6 - 36/343*T^5 - 101/2401*T^4 - 
        9/49*T^3 + 3/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + X*Y^10 + 5*X*Y^9 + X*Y^8 + 
        X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 5*X*Y + 6*X + Y^30 + 4*Y^29 
        + 3*Y^28 + 2*Y^26 + Y^25 + Y^24 + 6*Y^23 + 6*Y^22 + 2*Y^21 + Y^20 + 5*Y^18 +
        5*Y^17 + 5*Y^16 + 5*Y^15 + 6*Y^14 + 3*Y^13 + Y^11 + Y^9 + 6*Y^8 + Y^7 + Y^5 
        + 2*Y^4 + 4*Y^2 + 5*Y,
    T^56 - 11/7*T^55 - 10/49*T^54 + 397/343*T^53 + 1486/2401*T^52 - 3064/2401*T^51 -
        237/2401*T^50 + 2057/2401*T^49 - 10/7*T^48 + 3236/2401*T^47 + 2180/2401*T^46
        - 3555/2401*T^45 - 2868/2401*T^44 + 3650/2401*T^43 + 2269/2401*T^42 - 
        4041/2401*T^41 + 1805/2401*T^40 + 11/2401*T^39 - 2414/2401*T^38 + 
        2463/2401*T^37 + 1765/2401*T^36 - 2791/2401*T^35 - 3011/2401*T^34 + 
        5949/2401*T^33 - 592/2401*T^32 - 3846/2401*T^31 + 1804/2401*T^30 + 
        905/2401*T^29 - 176/343*T^28 + 905/2401*T^27 + 1804/2401*T^26 - 
        3846/2401*T^25 - 592/2401*T^24 + 5949/2401*T^23 - 3011/2401*T^22 - 
        2791/2401*T^21 + 1765/2401*T^20 + 2463/2401*T^19 - 2414/2401*T^18 + 
        11/2401*T^17 + 1805/2401*T^16 - 4041/2401*T^15 + 2269/2401*T^14 + 
        3650/2401*T^13 - 2868/2401*T^12 - 3555/2401*T^11 + 2180/2401*T^10 + 
        3236/2401*T^9 - 10/7*T^8 + 2057/2401*T^7 - 237/2401*T^6 - 3064/2401*T^5 + 
        1486/2401*T^4 + 397/343*T^3 - 10/49*T^2 - 11/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 3*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + X*Y^8 + 
        6*X*Y^7 + 2*X*Y^6 + 4*X*Y^3 + X*Y^2 + 2*X*Y + X + 3*Y^30 + Y^29 + 2*Y^28 + 
        6*Y^27 + 6*Y^26 + 5*Y^25 + 3*Y^24 + 3*Y^23 + 2*Y^22 + 6*Y^21 + 6*Y^19 + 
        6*Y^18 + Y^17 + 6*Y^15 + 4*Y^14 + 3*Y^13 + Y^12 + 4*Y^11 + 2*Y^10 + 2*Y^9 + 
        5*Y^8 + 2*Y^7 + Y^6 + 2*Y^5 + 2*Y^4 + 2*Y^3 + Y^2 + 5*Y + 4,
    T^56 - 12/7*T^55 + 96/49*T^54 - 41/49*T^53 - 181/2401*T^52 + 116/343*T^51 + 
        313/2401*T^50 - 274/343*T^49 + 1436/2401*T^48 + 253/2401*T^47 - 
        2411/2401*T^46 + 2522/2401*T^45 - 967/2401*T^44 - 822/2401*T^43 + 
        632/2401*T^42 + 1478/2401*T^41 - 3090/2401*T^40 + 2565/2401*T^39 - 
        158/2401*T^38 - 1269/2401*T^37 + 205/2401*T^36 + 356/343*T^35 - 
        3292/2401*T^34 + 1607/2401*T^33 + 1200/2401*T^32 - 2355/2401*T^31 + 
        1133/2401*T^30 + 1084/2401*T^29 - 2473/2401*T^28 + 1084/2401*T^27 + 
        1133/2401*T^26 - 2355/2401*T^25 + 1200/2401*T^24 + 1607/2401*T^23 - 
        3292/2401*T^22 + 356/343*T^21 + 205/2401*T^20 - 1269/2401*T^19 - 
        158/2401*T^18 + 2565/2401*T^17 - 3090/2401*T^16 + 1478/2401*T^15 + 
        632/2401*T^14 - 822/2401*T^13 - 967/2401*T^12 + 2522/2401*T^11 - 
        2411/2401*T^10 + 253/2401*T^9 + 1436/2401*T^8 - 274/343*T^7 + 313/2401*T^6 +
        116/343*T^5 - 181/2401*T^4 - 41/49*T^3 + 96/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 4*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 +
        3*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 6*X*Y + 2*X + 
        6*Y^30 + 2*Y^29 + 2*Y^28 + 6*Y^27 + 4*Y^26 + 6*Y^25 + 6*Y^24 + Y^23 + 3*Y^21
        + 4*Y^20 + 6*Y^19 + 3*Y^18 + 2*Y^17 + 5*Y^16 + 3*Y^14 + 6*Y^13 + 2*Y^12 + 
        4*Y^11 + Y^10 + 4*Y^9 + 3*Y^8 + 5*Y^7 + 3*Y^6 + 2*Y^5 + 6*Y^4 + 2*Y^3 + 3*Y 
        + 6,
    T^56 - 3/49*T^54 - 132/343*T^53 + 856/2401*T^52 + 1270/2401*T^51 - 717/2401*T^50
        + 2033/2401*T^49 + 30/2401*T^48 + 884/2401*T^47 + 187/2401*T^46 + 
        1334/2401*T^45 + 1426/2401*T^44 - 995/2401*T^43 + 410/2401*T^42 + 
        691/2401*T^41 + 789/2401*T^40 + 297/343*T^39 + 226/2401*T^38 - 6/343*T^37 + 
        230/2401*T^36 + 11/343*T^35 + 1313/2401*T^34 - 811/2401*T^33 + 211/343*T^32 
        + 390/2401*T^31 - 1195/2401*T^30 + 1410/2401*T^29 + 220/2401*T^28 + 
        1410/2401*T^27 - 1195/2401*T^26 + 390/2401*T^25 + 211/343*T^24 - 
        811/2401*T^23 + 1313/2401*T^22 + 11/343*T^21 + 230/2401*T^20 - 6/343*T^19 + 
        226/2401*T^18 + 297/343*T^17 + 789/2401*T^16 + 691/2401*T^15 + 410/2401*T^14
        - 995/2401*T^13 + 1426/2401*T^12 + 1334/2401*T^11 + 187/2401*T^10 + 
        884/2401*T^9 + 30/2401*T^8 + 2033/2401*T^7 - 717/2401*T^6 + 1270/2401*T^5 + 
        856/2401*T^4 - 132/343*T^3 - 3/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^10 + 2*X*Y^9 + 6*X*Y^8 + 5*X*Y^7 + X*Y^6 + 5*X*Y^5 + 
        6*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 5*X + 4*Y^30 + 5*Y^28 + 6*Y^26 + 3*Y^25 + 
        3*Y^24 + 5*Y^22 + 3*Y^21 + 6*Y^19 + 4*Y^18 + 3*Y^17 + 4*Y^16 + 6*Y^15 + 
        2*Y^14 + 2*Y^13 + 6*Y^12 + 3*Y^11 + 5*Y^10 + 2*Y^9 + 4*Y^8 + 6*Y^7 + 2*Y^6 +
        2*Y^4 + 4*Y^3 + 2*Y + 3,
    -T^56 - 4/7*T^55 + 38/49*T^54 - 19/343*T^53 - 1741/2401*T^52 - 445/2401*T^51 - 
        31/343*T^50 + 272/2401*T^49 - 222/2401*T^48 - 1304/2401*T^47 + 62/343*T^46 +
        810/2401*T^45 - 724/2401*T^44 - 934/2401*T^43 + 150/2401*T^42 + 
        997/2401*T^41 + 769/2401*T^40 - 563/2401*T^39 - 1342/2401*T^38 - 
        94/2401*T^37 + 1040/2401*T^36 + 285/2401*T^35 - 1192/2401*T^34 - 
        1090/2401*T^33 - 359/2401*T^32 + 1286/2401*T^31 + 395/2401*T^30 - 
        298/343*T^29 + 298/343*T^27 - 395/2401*T^26 - 1286/2401*T^25 + 359/2401*T^24
        + 1090/2401*T^23 + 1192/2401*T^22 - 285/2401*T^21 - 1040/2401*T^20 + 
        94/2401*T^19 + 1342/2401*T^18 + 563/2401*T^17 - 769/2401*T^16 - 
        997/2401*T^15 - 150/2401*T^14 + 934/2401*T^13 + 724/2401*T^12 - 
        810/2401*T^11 - 62/343*T^10 + 1304/2401*T^9 + 222/2401*T^8 - 272/2401*T^7 + 
        31/343*T^6 + 445/2401*T^5 + 1741/2401*T^4 + 19/343*T^3 - 38/49*T^2 + 4/7*T +
        1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 
        + X*Y^8 + 3*X*Y^7 + 6*X*Y^6 + X*Y^4 + 3*X*Y^2 + 3*X*Y + 3*Y^30 + 6*Y^28 + 
        2*Y^27 + 4*Y^26 + Y^25 + 3*Y^24 + 6*Y^23 + Y^21 + 5*Y^19 + 3*Y^18 + 3*Y^17 +
        6*Y^16 + 5*Y^14 + 4*Y^13 + 5*Y^12 + 6*Y^10 + 2*Y^9 + 3*Y^8 + 4*Y^7 + 6*Y^6 +
        5*Y^5 + 6*Y^4 + Y^3 + Y^2 + Y + 5,
    -T^56 + 9/7*T^55 - 6/7*T^54 + 173/343*T^53 - 1486/2401*T^52 + 547/2401*T^51 + 
        592/2401*T^50 + 463/2401*T^49 - 923/2401*T^48 + 256/2401*T^47 - 130/343*T^46
        + 3358/2401*T^45 - 2354/2401*T^44 + 347/2401*T^43 - 915/2401*T^42 + 
        615/2401*T^41 + 1184/2401*T^40 - 1151/2401*T^39 - 1949/2401*T^38 + 
        1790/2401*T^37 - 814/2401*T^36 + 1829/2401*T^35 - 1894/2401*T^34 - 
        613/2401*T^33 + 2218/2401*T^32 - 1306/2401*T^31 + 2110/2401*T^30 - 
        405/343*T^29 + 405/343*T^27 - 2110/2401*T^26 + 1306/2401*T^25 - 
        2218/2401*T^24 + 613/2401*T^23 + 1894/2401*T^22 - 1829/2401*T^21 + 
        814/2401*T^20 - 1790/2401*T^19 + 1949/2401*T^18 + 1151/2401*T^17 - 
        1184/2401*T^16 - 615/2401*T^15 + 915/2401*T^14 - 347/2401*T^13 + 
        2354/2401*T^12 - 3358/2401*T^11 + 130/343*T^10 - 256/2401*T^9 + 923/2401*T^8
        - 463/2401*T^7 - 592/2401*T^6 - 547/2401*T^5 + 1486/2401*T^4 - 173/343*T^3 +
        6/7*T^2 - 9/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        X*Y^8 + 3*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + X*Y + 
        4*X + 6*Y^30 + Y^29 + 6*Y^28 + Y^25 + 3*Y^24 + 4*Y^23 + 3*Y^22 + 3*Y^21 + 
        6*Y^20 + 4*Y^19 + 6*Y^18 + 4*Y^17 + 6*Y^16 + 2*Y^15 + 2*Y^14 + 3*Y^13 + 
        5*Y^12 + 6*Y^11 + 4*Y^10 + 6*Y^9 + Y^8 + 5*Y^7 + 6*Y^6 + 5*Y^5 + 3*Y^4 + 
        6*Y^3 + 5*Y^2 + 2*Y + 3,
    -T^56 + 4/7*T^55 + 24/49*T^54 - 148/343*T^53 - 148/2401*T^52 + 1287/2401*T^51 + 
        127/2401*T^50 - 498/2401*T^49 + 1874/2401*T^48 + 135/2401*T^47 - 
        1163/2401*T^46 + 265/2401*T^45 + 249/2401*T^44 - 1054/2401*T^43 - 
        615/2401*T^42 + 41/343*T^41 + 163/2401*T^40 - 855/2401*T^39 - 558/2401*T^38 
        + 821/2401*T^37 + 677/2401*T^36 - 1137/2401*T^35 + 986/2401*T^34 + 
        689/2401*T^33 - 578/2401*T^32 + 235/2401*T^31 + 897/2401*T^30 - 
        1234/2401*T^29 + 1234/2401*T^27 - 897/2401*T^26 - 235/2401*T^25 + 
        578/2401*T^24 - 689/2401*T^23 - 986/2401*T^22 + 1137/2401*T^21 - 
        677/2401*T^20 - 821/2401*T^19 + 558/2401*T^18 + 855/2401*T^17 - 
        163/2401*T^16 - 41/343*T^15 + 615/2401*T^14 + 1054/2401*T^13 - 249/2401*T^12
        - 265/2401*T^11 + 1163/2401*T^10 - 135/2401*T^9 - 1874/2401*T^8 + 
        498/2401*T^7 - 127/2401*T^6 - 1287/2401*T^5 + 148/2401*T^4 + 148/343*T^3 - 
        24/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 5*X*Y^7 +
        6*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 3*X*Y + 6*X + 6*Y^30 + 
        3*Y^29 + 6*Y^28 + 3*Y^26 + 2*Y^25 + 2*Y^24 + 2*Y^22 + Y^21 + 5*Y^20 + 3*Y^19
        + 6*Y^18 + 6*Y^16 + 2*Y^15 + 4*Y^14 + 3*Y^13 + 6*Y^12 + 4*Y^11 + 3*Y^10 + 
        4*Y^9 + 2*Y^8 + Y^7 + Y^6 + 4*Y^5 + 4*Y^4 + 6*Y^3 + Y^2 + 6*Y + 2,
    T^56 - 3/7*T^55 - 6/7*T^54 + 25/343*T^53 + 936/2401*T^52 + 254/2401*T^51 - 
        213/343*T^50 + 2515/2401*T^49 - 1138/2401*T^48 - 561/2401*T^47 + 61/343*T^46
        + 1543/2401*T^45 + 442/2401*T^44 - 2433/2401*T^43 + 1914/2401*T^42 - 
        582/2401*T^41 + 97/2401*T^40 - 1388/2401*T^39 - 715/2401*T^38 + 
        827/2401*T^37 - 43/2401*T^36 + 6/7*T^35 - 1384/2401*T^34 + 128/343*T^33 - 
        277/2401*T^32 - 93/2401*T^31 + 19/49*T^30 - 1804/2401*T^29 + 681/2401*T^28 -
        1804/2401*T^27 + 19/49*T^26 - 93/2401*T^25 - 277/2401*T^24 + 128/343*T^23 - 
        1384/2401*T^22 + 6/7*T^21 - 43/2401*T^20 + 827/2401*T^19 - 715/2401*T^18 - 
        1388/2401*T^17 + 97/2401*T^16 - 582/2401*T^15 + 1914/2401*T^14 - 
        2433/2401*T^13 + 442/2401*T^12 + 1543/2401*T^11 + 61/343*T^10 - 561/2401*T^9
        - 1138/2401*T^8 + 2515/2401*T^7 - 213/343*T^6 + 254/2401*T^5 + 936/2401*T^4 
        + 25/343*T^3 - 6/7*T^2 - 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^12 + 6*X*Y^9 + X*Y^8 + 5*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + 
        5*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + X*Y + 6*X + 3*Y^30 + Y^29 + 6*Y^28 + 2*Y^27 + 
        6*Y^25 + 3*Y^24 + 6*Y^23 + 6*Y^22 + 4*Y^21 + 5*Y^20 + Y^18 + 6*Y^17 + Y^16 +
        3*Y^15 + 3*Y^14 + 6*Y^13 + Y^12 + 4*Y^11 + 5*Y^10 + 2*Y^9 + 5*Y^8 + 5*Y^7 + 
        3*Y^6 + 2*Y^5 + 6*Y^4 + 3*Y^3 + 6*Y^2 + 6*Y + 3,
    -T^56 + 3/7*T^55 + 12/49*T^54 - 27/343*T^53 + 902/2401*T^52 - 1606/2401*T^51 - 
        527/2401*T^50 + 1520/2401*T^49 + 255/2401*T^48 + 517/2401*T^47 + 
        99/2401*T^46 - 442/2401*T^45 - 141/2401*T^44 + 278/2401*T^43 - 27/343*T^42 +
        118/343*T^41 - 283/2401*T^40 - 408/2401*T^39 - 480/2401*T^38 - 389/2401*T^37
        + 716/2401*T^36 + 47/2401*T^35 - 613/2401*T^34 - 450/2401*T^33 + 
        33/2401*T^32 + 109/2401*T^31 - 74/2401*T^30 - 432/2401*T^29 + 432/2401*T^27 
        + 74/2401*T^26 - 109/2401*T^25 - 33/2401*T^24 + 450/2401*T^23 + 
        613/2401*T^22 - 47/2401*T^21 - 716/2401*T^20 + 389/2401*T^19 + 480/2401*T^18
        + 408/2401*T^17 + 283/2401*T^16 - 118/343*T^15 + 27/343*T^14 - 278/2401*T^13
        + 141/2401*T^12 + 442/2401*T^11 - 99/2401*T^10 - 517/2401*T^9 - 255/2401*T^8
        - 1520/2401*T^7 + 527/2401*T^6 + 1606/2401*T^5 - 902/2401*T^4 + 27/343*T^3 -
        12/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + X*Y^12 + 6*X*Y^11 + 3*X*Y^9 + X*Y^8 + 
        5*X*Y^7 + 4*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 6*X*Y + 5*X + 
        3*Y^30 + 5*Y^29 + Y^28 + 3*Y^27 + 6*Y^26 + 5*Y^25 + 2*Y^24 + 4*Y^23 + 3*Y^22
        + 2*Y^20 + 2*Y^19 + 3*Y^18 + 3*Y^17 + 4*Y^14 + 4*Y^13 + 5*Y^12 + 3*Y^11 + 
        3*Y^10 + 3*Y^9 + 5*Y^8 + 6*Y^7 + 4*Y^6 + 2*Y^5 + 6*Y^4 + 4*Y^3 + 6*Y^2 + 
        5*Y,
    T^56 - T^55 + 11/7*T^54 - 634/343*T^53 + 2476/2401*T^52 - 4003/2401*T^51 + 
        397/343*T^50 - 458/343*T^49 + 4418/2401*T^48 - 3364/2401*T^47 + 
        5069/2401*T^46 - 540/343*T^45 + 3445/2401*T^44 - 3210/2401*T^43 + 
        1567/2401*T^42 - 370/343*T^41 + 811/2401*T^40 - 1324/2401*T^39 - 
        278/2401*T^38 + 1623/2401*T^37 - 1487/2401*T^36 + 2976/2401*T^35 - 
        1986/2401*T^34 + 2417/2401*T^33 - 2025/2401*T^32 + 2410/2401*T^31 - 
        3298/2401*T^30 + 3518/2401*T^29 - 4570/2401*T^28 + 3518/2401*T^27 - 
        3298/2401*T^26 + 2410/2401*T^25 - 2025/2401*T^24 + 2417/2401*T^23 - 
        1986/2401*T^22 + 2976/2401*T^21 - 1487/2401*T^20 + 1623/2401*T^19 - 
        278/2401*T^18 - 1324/2401*T^17 + 811/2401*T^16 - 370/343*T^15 + 
        1567/2401*T^14 - 3210/2401*T^13 + 3445/2401*T^12 - 540/343*T^11 + 
        5069/2401*T^10 - 3364/2401*T^9 + 4418/2401*T^8 - 458/343*T^7 + 397/343*T^6 -
        4003/2401*T^5 + 2476/2401*T^4 - 634/343*T^3 + 11/7*T^2 - T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + X*Y^13 + X*Y^12 + 5*X*Y^9 + 2*X*Y^8 + 5*X*Y^7 + 
        5*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 6*X*Y + X + Y^30 + 2*Y^29 
        + 5*Y^28 + 3*Y^27 + 3*Y^26 + 4*Y^25 + 6*Y^24 + 6*Y^23 + 6*Y^21 + 5*Y^20 + 
        3*Y^19 + 3*Y^18 + 6*Y^17 + 4*Y^16 + 3*Y^15 + 6*Y^13 + 6*Y^12 + 6*Y^10 + 
        6*Y^9 + 4*Y^8 + 2*Y^7 + 2*Y^6 + 3*Y^5 + 5*Y^4 + Y^2 + 4,
    T^56 - 2/7*T^55 + 20/49*T^54 - 67/343*T^53 - 937/2401*T^52 + 125/2401*T^51 - 
        734/2401*T^50 - 748/2401*T^49 - 1336/2401*T^48 - 33/343*T^47 - 183/2401*T^46
        + 1403/2401*T^45 + 1261/2401*T^44 + 1002/2401*T^43 + 977/2401*T^42 + 
        352/2401*T^41 + 515/2401*T^40 - 1522/2401*T^39 + 838/2401*T^38 - 
        2145/2401*T^37 - 202/2401*T^36 - 937/2401*T^35 - 1013/2401*T^34 - 
        370/2401*T^33 + 65/343*T^32 + 1065/2401*T^31 + 930/2401*T^30 + 
        1193/2401*T^29 - 604/2401*T^28 + 1193/2401*T^27 + 930/2401*T^26 + 
        1065/2401*T^25 + 65/343*T^24 - 370/2401*T^23 - 1013/2401*T^22 - 
        937/2401*T^21 - 202/2401*T^20 - 2145/2401*T^19 + 838/2401*T^18 - 
        1522/2401*T^17 + 515/2401*T^16 + 352/2401*T^15 + 977/2401*T^14 + 
        1002/2401*T^13 + 1261/2401*T^12 + 1403/2401*T^11 - 183/2401*T^10 - 
        33/343*T^9 - 1336/2401*T^8 - 748/2401*T^7 - 734/2401*T^6 + 125/2401*T^5 - 
        937/2401*T^4 - 67/343*T^3 + 20/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 2*X*Y^10 + 2*X*Y^8 + 4*X*Y^6 +
        4*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 2*X*Y + 2*X + Y^30 + 6*Y^29 + 5*Y^28
        + 5*Y^27 + 4*Y^26 + 3*Y^25 + 6*Y^24 + 5*Y^23 + 2*Y^22 + Y^21 + 4*Y^20 + 
        4*Y^19 + 6*Y^18 + 4*Y^17 + 4*Y^16 + 6*Y^14 + 5*Y^13 + 3*Y^12 + 6*Y^11 + 
        4*Y^10 + Y^9 + 5*Y^7 + 6*Y^5 + 4*Y^4 + Y^3 + Y^2 + 4*Y,
    -T^56 + 17/7*T^55 - 120/49*T^54 + 523/343*T^53 - 457/2401*T^52 - 2719/2401*T^51 
        + 2659/2401*T^50 + 1978/2401*T^49 - 6669/2401*T^48 + 6459/2401*T^47 - 
        3327/2401*T^46 + 58/343*T^45 + 2762/2401*T^44 - 4840/2401*T^43 + 
        3947/2401*T^42 - 43/49*T^41 + 803/2401*T^40 + 829/2401*T^39 - 314/343*T^38 +
        110/343*T^37 + 494/343*T^36 - 6616/2401*T^35 + 6089/2401*T^34 - 
        3996/2401*T^33 + 782/2401*T^32 + 2668/2401*T^31 - 2894/2401*T^30 + 
        1444/2401*T^29 - 1444/2401*T^27 + 2894/2401*T^26 - 2668/2401*T^25 - 
        782/2401*T^24 + 3996/2401*T^23 - 6089/2401*T^22 + 6616/2401*T^21 - 
        494/343*T^20 - 110/343*T^19 + 314/343*T^18 - 829/2401*T^17 - 803/2401*T^16 +
        43/49*T^15 - 3947/2401*T^14 + 4840/2401*T^13 - 2762/2401*T^12 - 58/343*T^11 
        + 3327/2401*T^10 - 6459/2401*T^9 + 6669/2401*T^8 - 1978/2401*T^7 - 
        2659/2401*T^6 + 2719/2401*T^5 + 457/2401*T^4 - 523/343*T^3 + 120/49*T^2 - 
        17/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 4*X*Y^8 +
        3*X*Y^5 + 2*X*Y^4 + 4*X*Y^2 + 3*X*Y + 4*X + 6*Y^30 + 3*Y^29 + 3*Y^28 + 
        5*Y^27 + 5*Y^26 + Y^25 + 3*Y^24 + 3*Y^21 + 4*Y^20 + 2*Y^19 + 3*Y^16 + 2*Y^15
        + 6*Y^14 + 6*Y^13 + 3*Y^12 + 3*Y^11 + 4*Y^10 + Y^9 + 4*Y^8 + 5*Y^7 + 4*Y^6 +
        Y^5 + 2*Y^4 + 2*Y^3 + 6*Y^2 + 5*Y + 1,
    -T^56 - 12/7*T^55 - 29/49*T^54 + 302/343*T^53 + 325/343*T^52 - 1003/2401*T^51 - 
        1152/2401*T^50 + 3226/2401*T^49 + 5809/2401*T^48 + 1249/2401*T^47 - 
        4418/2401*T^46 - 3006/2401*T^45 + 2239/2401*T^44 + 2825/2401*T^43 - 
        29/2401*T^42 + 731/2401*T^41 + 3672/2401*T^40 + 3363/2401*T^39 - 
        1860/2401*T^38 - 4272/2401*T^37 - 2154/2401*T^36 - 1469/2401*T^35 - 
        537/343*T^34 - 4129/2401*T^33 + 96/343*T^32 + 4097/2401*T^31 + 
        2129/2401*T^30 - 558/2401*T^29 + 558/2401*T^27 - 2129/2401*T^26 - 
        4097/2401*T^25 - 96/343*T^24 + 4129/2401*T^23 + 537/343*T^22 + 
        1469/2401*T^21 + 2154/2401*T^20 + 4272/2401*T^19 + 1860/2401*T^18 - 
        3363/2401*T^17 - 3672/2401*T^16 - 731/2401*T^15 + 29/2401*T^14 - 
        2825/2401*T^13 - 2239/2401*T^12 + 3006/2401*T^11 + 4418/2401*T^10 - 
        1249/2401*T^9 - 5809/2401*T^8 - 3226/2401*T^7 + 1152/2401*T^6 + 
        1003/2401*T^5 - 325/343*T^4 - 302/343*T^3 + 29/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        6*X*Y^8 + 3*X*Y^7 + X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + X*Y^3 + 2*X*Y^2 + 3*X*Y + X 
        + 2*Y^30 + 4*Y^29 + 2*Y^25 + Y^24 + 5*Y^23 + 2*Y^22 + 4*Y^21 + Y^20 + 5*Y^19
        + 3*Y^18 + 3*Y^17 + 4*Y^15 + 6*Y^14 + 4*Y^12 + 6*Y^11 + 3*Y^10 + 3*Y^8 + 
        6*Y^7 + 2*Y^4 + 4*Y^3 + 6*Y^2 + 4*Y + 6,
    T^56 - 10/7*T^55 + 39/49*T^54 - 4/7*T^53 + 3498/2401*T^52 - 2447/2401*T^51 - 
        214/343*T^50 + 1944/2401*T^49 + 283/2401*T^48 + 1220/2401*T^47 - 
        2910/2401*T^46 + 956/2401*T^45 + 981/2401*T^44 - 414/2401*T^43 - 5/343*T^42 
        - 538/2401*T^41 - 32/343*T^40 + 20/2401*T^39 + 748/2401*T^38 + 251/2401*T^37
        - 4/343*T^36 - 2915/2401*T^35 + 3448/2401*T^34 - 1716/2401*T^33 + 
        887/2401*T^32 - 981/2401*T^31 - 1026/2401*T^30 + 2447/2401*T^29 - 
        2598/2401*T^28 + 2447/2401*T^27 - 1026/2401*T^26 - 981/2401*T^25 + 
        887/2401*T^24 - 1716/2401*T^23 + 3448/2401*T^22 - 2915/2401*T^21 - 
        4/343*T^20 + 251/2401*T^19 + 748/2401*T^18 + 20/2401*T^17 - 32/343*T^16 - 
        538/2401*T^15 - 5/343*T^14 - 414/2401*T^13 + 981/2401*T^12 + 956/2401*T^11 -
        2910/2401*T^10 + 1220/2401*T^9 + 283/2401*T^8 + 1944/2401*T^7 - 214/343*T^6 
        - 2447/2401*T^5 + 3498/2401*T^4 - 4/7*T^3 + 39/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + X*Y^13 + X*Y^11 + 6*X*Y^9 + 3*X*Y^8 + 2*X*Y^7 + 
        X*Y^5 + X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 4*X + 3*Y^30 + 3*Y^29 + 6*Y^28 + 4*Y^27 
        + 2*Y^26 + 5*Y^25 + 2*Y^24 + 4*Y^23 + 6*Y^22 + 5*Y^21 + 4*Y^20 + 4*Y^17 + 
        3*Y^16 + Y^15 + Y^14 + 3*Y^13 + 5*Y^12 + 5*Y^11 + 2*Y^10 + 3*Y^9 + 3*Y^8 + 
        6*Y^7 + 6*Y^6 + 5*Y^5 + 6*Y^4 + 2*Y^3 + 4*Y^2 + 6*Y + 3,
    -T^56 + 18/7*T^55 - 151/49*T^54 + 948/343*T^53 - 6023/2401*T^52 + 745/343*T^51 -
        3001/2401*T^50 - 230/343*T^49 + 5665/2401*T^48 - 7286/2401*T^47 + 
        8270/2401*T^46 - 8101/2401*T^45 + 6953/2401*T^44 - 4861/2401*T^43 + 
        1793/2401*T^42 + 1370/2401*T^41 - 4877/2401*T^40 + 7522/2401*T^39 - 
        6886/2401*T^38 + 4940/2401*T^37 - 2875/2401*T^36 + 704/2401*T^35 + 
        2036/2401*T^34 - 5193/2401*T^33 + 900/343*T^32 - 5270/2401*T^31 + 
        625/343*T^30 - 2844/2401*T^29 + 2844/2401*T^27 - 625/343*T^26 + 
        5270/2401*T^25 - 900/343*T^24 + 5193/2401*T^23 - 2036/2401*T^22 - 
        704/2401*T^21 + 2875/2401*T^20 - 4940/2401*T^19 + 6886/2401*T^18 - 
        7522/2401*T^17 + 4877/2401*T^16 - 1370/2401*T^15 - 1793/2401*T^14 + 
        4861/2401*T^13 - 6953/2401*T^12 + 8101/2401*T^11 - 8270/2401*T^10 + 
        7286/2401*T^9 - 5665/2401*T^8 + 230/343*T^7 + 3001/2401*T^6 - 745/343*T^5 + 
        6023/2401*T^4 - 948/343*T^3 + 151/49*T^2 - 18/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^12 + 3*X*Y^11 + 5*X*Y^9 + X*Y^8 + X*Y^7 + 3*X*Y^5 + 
        4*X*Y^3 + 2*X*Y^2 + 2*X*Y + 2*X + 2*Y^30 + 3*Y^29 + 5*Y^28 + 2*Y^27 + 3*Y^26
        + 5*Y^25 + 5*Y^24 + Y^23 + 5*Y^22 + Y^21 + 5*Y^20 + 3*Y^19 + Y^17 + 2*Y^16 +
        3*Y^14 + 4*Y^13 + 6*Y^10 + 5*Y^9 + Y^8 + 3*Y^7 + Y^6 + Y^5 + 2*Y^4 + Y^3 + 
        5*Y^2 + Y + 3,
    T^56 + 3/7*T^55 - 19/49*T^54 + 88/343*T^53 - 795/2401*T^52 - 2171/2401*T^51 + 
        1471/2401*T^50 + 2399/2401*T^49 - 106/2401*T^48 + 236/2401*T^47 + 
        895/2401*T^46 - 2449/2401*T^45 - 400/343*T^44 + 646/2401*T^43 - 
        1129/2401*T^42 - 2230/2401*T^41 + 1485/2401*T^40 + 521/2401*T^39 - 
        1958/2401*T^38 - 15/2401*T^37 + 775/2401*T^36 - 2186/2401*T^35 - 
        621/2401*T^34 + 309/343*T^33 + 248/2401*T^32 + 362/2401*T^31 + 
        2320/2401*T^30 + 983/2401*T^29 - 202/2401*T^28 + 983/2401*T^27 + 
        2320/2401*T^26 + 362/2401*T^25 + 248/2401*T^24 + 309/343*T^23 - 
        621/2401*T^22 - 2186/2401*T^21 + 775/2401*T^20 - 15/2401*T^19 - 
        1958/2401*T^18 + 521/2401*T^17 + 1485/2401*T^16 - 2230/2401*T^15 - 
        1129/2401*T^14 + 646/2401*T^13 - 400/343*T^12 - 2449/2401*T^11 + 
        895/2401*T^10 + 236/2401*T^9 - 106/2401*T^8 + 2399/2401*T^7 + 1471/2401*T^6 
        - 2171/2401*T^5 - 795/2401*T^4 + 88/343*T^3 - 19/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 2*X*Y^13 + X*Y^12 + 6*X*Y^10 + 3*X*Y^9 + 5*X*Y^8 + 
        X*Y^7 + 2*X*Y^6 + X*Y^5 + 3*X*Y^3 + X*Y^2 + 4*X*Y + 6*X + Y^30 + 3*Y^29 + 
        2*Y^28 + 5*Y^27 + 2*Y^26 + 6*Y^25 + 6*Y^24 + Y^23 + 4*Y^21 + Y^20 + 5*Y^18 +
        2*Y^17 + 6*Y^16 + 5*Y^15 + 5*Y^14 + Y^13 + 2*Y^12 + 5*Y^11 + 6*Y^10 + 6*Y^9 
        + 2*Y^8 + 4*Y^7 + 2*Y^6 + 2*Y^4 + 4*Y^3 + 5*Y^2 + 6*Y + 6,
    -T^56 + 3/7*T^55 + 20/49*T^54 - 291/343*T^53 + 1541/2401*T^52 + 330/2401*T^51 - 
        2007/2401*T^50 - 13/343*T^49 - 863/2401*T^48 - 1523/2401*T^47 + 
        2201/2401*T^46 - 747/2401*T^45 - 643/2401*T^44 + 1858/2401*T^43 - 
        3292/2401*T^42 - 1086/2401*T^41 - 162/2401*T^40 - 950/2401*T^39 + 
        951/2401*T^38 + 2206/2401*T^37 - 1763/2401*T^36 - 624/2401*T^35 + 
        80/343*T^34 - 3848/2401*T^33 + 135/343*T^32 + 146/343*T^31 + 6/343*T^30 + 
        1924/2401*T^29 - 1924/2401*T^27 - 6/343*T^26 - 146/343*T^25 - 135/343*T^24 +
        3848/2401*T^23 - 80/343*T^22 + 624/2401*T^21 + 1763/2401*T^20 - 
        2206/2401*T^19 - 951/2401*T^18 + 950/2401*T^17 + 162/2401*T^16 + 
        1086/2401*T^15 + 3292/2401*T^14 - 1858/2401*T^13 + 643/2401*T^12 + 
        747/2401*T^11 - 2201/2401*T^10 + 1523/2401*T^9 + 863/2401*T^8 + 13/343*T^7 +
        2007/2401*T^6 - 330/2401*T^5 - 1541/2401*T^4 + 291/343*T^3 - 20/49*T^2 - 
        3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 
        + 3*X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 
        4*X*Y + 6*Y^30 + Y^29 + 3*Y^28 + Y^27 + 2*Y^26 + 2*Y^25 + 2*Y^24 + 2*Y^23 + 
        2*Y^22 + 3*Y^20 + 5*Y^19 + 4*Y^18 + 6*Y^17 + 6*Y^16 + 4*Y^15 + 5*Y^14 + Y^13
        + 3*Y^12 + 3*Y^10 + 2*Y^8 + 3*Y^7 + Y^6 + Y^5 + 3*Y^4 + 2*Y^2 + 5*Y + 3,
    -T^56 + 9/7*T^55 - 106/343*T^53 + 1553/2401*T^52 - 2171/2401*T^51 + 
        2216/2401*T^50 - 880/2401*T^49 - 3287/2401*T^48 + 1805/2401*T^47 + 
        191/343*T^46 - 780/2401*T^45 + 824/2401*T^44 - 337/343*T^43 + 1770/2401*T^42
        + 2370/2401*T^41 - 3235/2401*T^40 + 880/2401*T^39 + 363/2401*T^38 + 
        514/2401*T^37 + 125/343*T^36 - 3471/2401*T^35 - 52/2401*T^34 + 
        3037/2401*T^33 - 2103/2401*T^32 + 233/2401*T^31 + 211/2401*T^30 + 
        2154/2401*T^29 - 2154/2401*T^27 - 211/2401*T^26 - 233/2401*T^25 + 
        2103/2401*T^24 - 3037/2401*T^23 + 52/2401*T^22 + 3471/2401*T^21 - 
        125/343*T^20 - 514/2401*T^19 - 363/2401*T^18 - 880/2401*T^17 + 
        3235/2401*T^16 - 2370/2401*T^15 - 1770/2401*T^14 + 337/343*T^13 - 
        824/2401*T^12 + 780/2401*T^11 - 191/343*T^10 - 1805/2401*T^9 + 3287/2401*T^8
        + 880/2401*T^7 - 2216/2401*T^6 + 2171/2401*T^5 - 1553/2401*T^4 + 106/343*T^3
        - 9/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + X*Y^10 + X*Y^8 + X*Y^7 + 
        5*X*Y^6 + X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 4*X*Y + 2*X + 6*Y^30 + 
        4*Y^29 + Y^28 + 5*Y^27 + 4*Y^26 + 2*Y^25 + 4*Y^24 + 4*Y^23 + 3*Y^21 + 5*Y^20
        + 4*Y^18 + 6*Y^17 + 3*Y^16 + 6*Y^15 + 3*Y^14 + 2*Y^13 + 3*Y^12 + 2*Y^11 + 
        Y^10 + 3*Y^9 + 2*Y^8 + 2*Y^7 + 5*Y^6 + 5*Y^4 + 6*Y^3 + 6*Y^2 + 5*Y + 1,
    T^56 + 8/7*T^55 - 36/49*T^54 - 509/343*T^53 - 55/2401*T^52 + 317/343*T^51 + 
        712/2401*T^50 - 738/2401*T^49 - 223/343*T^48 - 591/2401*T^47 + 108/343*T^46 
        + 556/2401*T^45 - 209/2401*T^44 - 409/2401*T^43 + 207/2401*T^42 + 
        73/343*T^41 + 223/2401*T^40 - 526/2401*T^39 - 109/2401*T^38 + 1455/2401*T^37
        + 1838/2401*T^36 - 235/2401*T^35 - 2606/2401*T^34 - 1552/2401*T^33 + 
        1189/2401*T^32 + 2055/2401*T^31 + 830/2401*T^30 - 557/2401*T^29 - 
        138/343*T^28 - 557/2401*T^27 + 830/2401*T^26 + 2055/2401*T^25 + 
        1189/2401*T^24 - 1552/2401*T^23 - 2606/2401*T^22 - 235/2401*T^21 + 
        1838/2401*T^20 + 1455/2401*T^19 - 109/2401*T^18 - 526/2401*T^17 + 
        223/2401*T^16 + 73/343*T^15 + 207/2401*T^14 - 409/2401*T^13 - 209/2401*T^12 
        + 556/2401*T^11 + 108/343*T^10 - 591/2401*T^9 - 223/343*T^8 - 738/2401*T^7 +
        712/2401*T^6 + 317/343*T^5 - 55/2401*T^4 - 509/343*T^3 - 36/49*T^2 + 8/7*T +
        1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 2*X*Y^12 + 2*X*Y^10 + X*Y^9 + 3*X*Y^8 + 2*X*Y^7 + 
        X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + X*Y^3 + 2*X*Y^2 + 6*X*Y + 5*X + 5*Y^30 + 6*Y^28 
        + 3*Y^27 + 6*Y^26 + Y^25 + 4*Y^24 + 4*Y^23 + 3*Y^22 + 4*Y^20 + 5*Y^19 + 
        5*Y^18 + 2*Y^17 + Y^16 + Y^15 + 3*Y^14 + Y^13 + 6*Y^12 + 6*Y^11 + Y^10 + 
        5*Y^9 + 3*Y^8 + 2*Y^6 + 5*Y^5 + 3*Y^4 + 2*Y^3 + 3*Y^2 + Y + 5,
    -T^56 - 5/7*T^55 - 9/49*T^54 + 223/343*T^53 + 1084/2401*T^52 - 486/2401*T^51 - 
        1607/2401*T^50 - 1535/2401*T^49 - 281/2401*T^48 + 1572/2401*T^47 + 6/49*T^46
        + 185/2401*T^45 - 201/343*T^44 - 76/2401*T^43 + 1230/2401*T^42 + 
        1650/2401*T^41 + 15/343*T^40 - 900/2401*T^39 - 666/2401*T^38 + 724/2401*T^37
        + 1558/2401*T^36 + 1205/2401*T^35 - 817/2401*T^34 - 1366/2401*T^33 - 
        733/2401*T^32 + 818/2401*T^31 + 955/2401*T^30 + 23/49*T^29 - 23/49*T^27 - 
        955/2401*T^26 - 818/2401*T^25 + 733/2401*T^24 + 1366/2401*T^23 + 
        817/2401*T^22 - 1205/2401*T^21 - 1558/2401*T^20 - 724/2401*T^19 + 
        666/2401*T^18 + 900/2401*T^17 - 15/343*T^16 - 1650/2401*T^15 - 
        1230/2401*T^14 + 76/2401*T^13 + 201/343*T^12 - 185/2401*T^11 - 6/49*T^10 - 
        1572/2401*T^9 + 281/2401*T^8 + 1535/2401*T^7 + 1607/2401*T^6 + 486/2401*T^5 
        - 1084/2401*T^4 - 223/343*T^3 + 9/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 5*X*Y^13 + X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 3*X*Y^8 + 
        4*X*Y^6 + 2*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 4*X*Y + 6*X + 2*Y^30 + 5*Y^29 + 
        2*Y^28 + 4*Y^26 + 6*Y^25 + 2*Y^24 + 4*Y^23 + 3*Y^22 + 2*Y^21 + 6*Y^20 + 
        5*Y^19 + 3*Y^18 + Y^17 + 5*Y^16 + 4*Y^15 + 6*Y^14 + Y^13 + 3*Y^12 + 6*Y^11 +
        4*Y^9 + 4*Y^8 + 3*Y^7 + Y^6 + 3*Y^5 + 4*Y^3 + Y^2 + 3*Y + 2,
    T^56 - 6/7*T^55 + 8/49*T^54 + 475/343*T^53 - 2629/2401*T^52 - 1258/2401*T^51 + 
        4421/2401*T^50 - 3379/2401*T^49 - 1021/2401*T^48 + 2512/2401*T^47 - 
        2286/2401*T^46 + 44/2401*T^45 + 596/2401*T^44 - 2414/2401*T^43 + 
        1352/2401*T^42 + 8/343*T^41 - 2812/2401*T^40 + 1951/2401*T^39 + 
        1055/2401*T^38 - 375/343*T^37 + 1867/2401*T^36 + 1398/2401*T^35 - 
        348/343*T^34 + 1343/2401*T^33 + 1480/2401*T^32 - 2731/2401*T^31 + 
        1520/2401*T^30 + 1417/2401*T^29 - 2638/2401*T^28 + 1417/2401*T^27 + 
        1520/2401*T^26 - 2731/2401*T^25 + 1480/2401*T^24 + 1343/2401*T^23 - 
        348/343*T^22 + 1398/2401*T^21 + 1867/2401*T^20 - 375/343*T^19 + 
        1055/2401*T^18 + 1951/2401*T^17 - 2812/2401*T^16 + 8/343*T^15 + 
        1352/2401*T^14 - 2414/2401*T^13 + 596/2401*T^12 + 44/2401*T^11 - 
        2286/2401*T^10 + 2512/2401*T^9 - 1021/2401*T^8 - 3379/2401*T^7 + 
        4421/2401*T^6 - 1258/2401*T^5 - 2629/2401*T^4 + 475/343*T^3 + 8/49*T^2 - 
        6/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 5*X*Y^8 + 
        6*X*Y^7 + X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 5*X*Y + 5*X + 
        6*Y^30 + 4*Y^29 + 5*Y^28 + 2*Y^27 + 5*Y^26 + 6*Y^25 + 4*Y^24 + 6*Y^23 + Y^21
        + 5*Y^20 + 4*Y^17 + Y^16 + 2*Y^15 + 5*Y^14 + Y^13 + 3*Y^12 + 4*Y^11 + 6*Y^10
        + Y^9 + 5*Y^8 + 6*Y^7 + 2*Y^6 + Y^5 + 6*Y^4 + Y^3 + 2*Y^2 + 4*Y + 1,
    -T^56 + 6/7*T^55 + 3/49*T^54 + 13/343*T^53 + 85/343*T^52 - 2158/2401*T^51 + 
        3604/2401*T^50 - 3036/2401*T^49 + 1248/2401*T^48 - 480/2401*T^47 - 
        603/2401*T^46 + 2755/2401*T^45 - 2109/2401*T^44 + 1627/2401*T^43 - 
        1655/2401*T^42 + 795/2401*T^41 + 113/2401*T^40 - 22/49*T^39 + 443/2401*T^38 
        - 20/343*T^37 + 330/2401*T^36 - 229/2401*T^35 - 295/2401*T^34 + 40/2401*T^33
        + 36/2401*T^32 - 594/2401*T^31 + 521/2401*T^30 + 109/2401*T^29 - 
        109/2401*T^27 - 521/2401*T^26 + 594/2401*T^25 - 36/2401*T^24 - 40/2401*T^23 
        + 295/2401*T^22 + 229/2401*T^21 - 330/2401*T^20 + 20/343*T^19 - 
        443/2401*T^18 + 22/49*T^17 - 113/2401*T^16 - 795/2401*T^15 + 1655/2401*T^14 
        - 1627/2401*T^13 + 2109/2401*T^12 - 2755/2401*T^11 + 603/2401*T^10 + 
        480/2401*T^9 - 1248/2401*T^8 + 3036/2401*T^7 - 3604/2401*T^6 + 2158/2401*T^5
        - 85/343*T^4 - 13/343*T^3 - 3/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^13 + 5*X*Y^12 + X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 5*X*Y^7 + 
        4*X*Y^6 + X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 4*X + 6*Y^30 + 4*Y^29 + 4*Y^28 + 
        4*Y^27 + 4*Y^26 + 2*Y^25 + 2*Y^24 + 4*Y^23 + 4*Y^21 + 5*Y^20 + 6*Y^19 + 
        3*Y^18 + 5*Y^17 + 2*Y^16 + 5*Y^15 + 2*Y^14 + Y^13 + 2*Y^11 + 2*Y^10 + 6*Y^9 
        + 5*Y^8 + 3*Y^6 + 3*Y^5 + 6*Y^4 + 6*Y^3 + Y + 3,
    T^56 - 10/7*T^55 + 15/49*T^54 + 52/49*T^53 - 5555/2401*T^52 + 6323/2401*T^51 - 
        2812/2401*T^50 - 2400/2401*T^49 + 6394/2401*T^48 - 7363/2401*T^47 + 
        4476/2401*T^46 + 144/2401*T^45 - 4413/2401*T^44 + 5342/2401*T^43 - 
        3312/2401*T^42 + 2278/2401*T^41 - 692/2401*T^40 - 1278/2401*T^39 + 
        2507/2401*T^38 - 4785/2401*T^37 + 5315/2401*T^36 - 1942/2401*T^35 - 
        2288/2401*T^34 + 5571/2401*T^33 - 6830/2401*T^32 + 636/343*T^31 + 
        330/2401*T^30 - 804/343*T^29 + 7993/2401*T^28 - 804/343*T^27 + 330/2401*T^26
        + 636/343*T^25 - 6830/2401*T^24 + 5571/2401*T^23 - 2288/2401*T^22 - 
        1942/2401*T^21 + 5315/2401*T^20 - 4785/2401*T^19 + 2507/2401*T^18 - 
        1278/2401*T^17 - 692/2401*T^16 + 2278/2401*T^15 - 3312/2401*T^14 + 
        5342/2401*T^13 - 4413/2401*T^12 + 144/2401*T^11 + 4476/2401*T^10 - 
        7363/2401*T^9 + 6394/2401*T^8 - 2400/2401*T^7 - 2812/2401*T^6 + 
        6323/2401*T^5 - 5555/2401*T^4 + 52/49*T^3 + 15/49*T^2 - 10/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + X*Y^11 + X*Y^10 + X*Y^9 + 3*X*Y^8 + 6*X*Y^7
        + 3*X*Y^5 + 6*X*Y^4 + X*Y^3 + 3*X*Y + 6*X + 2*Y^30 + 4*Y^29 + 5*Y^27 + 
        4*Y^26 + Y^25 + 2*Y^24 + 5*Y^23 + Y^21 + 4*Y^20 + 3*Y^19 + Y^18 + 4*Y^17 + 
        6*Y^16 + 6*Y^15 + 3*Y^14 + 5*Y^13 + 2*Y^12 + 5*Y^11 + 2*Y^9 + 2*Y^8 + 6*Y^7 
        + Y^6 + 4*Y^5 + 2*Y^3 + 2*Y^2 + 2*Y + 3,
    T^56 + 3/7*T^55 - 23/49*T^54 - 102/343*T^53 - 233/2401*T^52 - 495/2401*T^51 - 
        2029/2401*T^50 - 29/49*T^49 - 397/2401*T^48 + 2853/2401*T^47 + 734/2401*T^46
        + 1089/2401*T^45 + 513/343*T^44 + 1774/2401*T^43 - 222/343*T^42 - 
        2882/2401*T^41 - 1577/2401*T^40 - 2187/2401*T^39 - 1836/2401*T^38 - 
        67/49*T^37 + 214/343*T^36 + 3924/2401*T^35 + 2921/2401*T^34 + 2885/2401*T^33
        + 2474/2401*T^32 + 44/343*T^31 - 2262/2401*T^30 - 2610/2401*T^29 - 
        4659/2401*T^28 - 2610/2401*T^27 - 2262/2401*T^26 + 44/343*T^25 + 
        2474/2401*T^24 + 2885/2401*T^23 + 2921/2401*T^22 + 3924/2401*T^21 + 
        214/343*T^20 - 67/49*T^19 - 1836/2401*T^18 - 2187/2401*T^17 - 1577/2401*T^16
        - 2882/2401*T^15 - 222/343*T^14 + 1774/2401*T^13 + 513/343*T^12 + 
        1089/2401*T^11 + 734/2401*T^10 + 2853/2401*T^9 - 397/2401*T^8 - 29/49*T^7 - 
        2029/2401*T^6 - 495/2401*T^5 - 233/2401*T^4 - 102/343*T^3 - 23/49*T^2 + 
        3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 2*X*Y^10 + 2*X*Y^9 + 5*X*Y^8 +
        4*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + X*Y + 2*X + 3*Y^30 + 5*Y^28 + 2*Y^27
        + Y^26 + 6*Y^25 + 4*Y^24 + 2*Y^23 + 2*Y^22 + 6*Y^21 + 3*Y^20 + 4*Y^19 + 
        4*Y^18 + 3*Y^17 + 2*Y^15 + 2*Y^14 + 3*Y^13 + 4*Y^12 + 3*Y^11 + 5*Y^10 + 
        2*Y^9 + Y^8 + 6*Y^6 + Y^5 + 2*Y^4 + 4*Y^3 + 4*Y^2 + 4,
    T^56 - 5/7*T^55 - 39/49*T^54 + 323/343*T^53 - 345/343*T^52 + 578/2401*T^51 + 
        321/343*T^50 - 1109/2401*T^49 + 197/2401*T^48 + 76/2401*T^47 - 
        1430/2401*T^46 + 712/2401*T^45 + 337/2401*T^44 - 907/2401*T^43 + 
        2376/2401*T^42 - 853/2401*T^41 - 639/2401*T^40 + 373/2401*T^39 - 
        332/343*T^38 + 13/49*T^37 + 1070/2401*T^36 + 621/2401*T^35 + 591/2401*T^34 +
        323/2401*T^33 - 1235/2401*T^32 - 1523/2401*T^31 + 440/2401*T^30 + 
        552/2401*T^29 + 109/343*T^28 + 552/2401*T^27 + 440/2401*T^26 - 
        1523/2401*T^25 - 1235/2401*T^24 + 323/2401*T^23 + 591/2401*T^22 + 
        621/2401*T^21 + 1070/2401*T^20 + 13/49*T^19 - 332/343*T^18 + 373/2401*T^17 -
        639/2401*T^16 - 853/2401*T^15 + 2376/2401*T^14 - 907/2401*T^13 + 
        337/2401*T^12 + 712/2401*T^11 - 1430/2401*T^10 + 76/2401*T^9 + 197/2401*T^8 
        - 1109/2401*T^7 + 321/343*T^6 + 578/2401*T^5 - 345/343*T^4 + 323/343*T^3 - 
        39/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 
        6*X*Y^7 + 4*X*Y^6 + 3*X*Y^4 + X*Y^3 + 6*X*Y + X + 3*Y^30 + 6*Y^29 + 4*Y^28 +
        2*Y^27 + 3*Y^26 + 6*Y^24 + 3*Y^23 + Y^22 + 6*Y^21 + 5*Y^20 + Y^18 + 3*Y^16 +
        4*Y^15 + 4*Y^14 + 2*Y^13 + 5*Y^11 + 6*Y^10 + 4*Y^9 + 6*Y^8 + 4*Y^6 + 6*Y^4 +
        Y^3 + 3*Y^2 + 5*Y + 6,
    -T^56 + 12/7*T^55 - 52/49*T^54 - 234/343*T^53 + 846/343*T^52 - 6439/2401*T^51 + 
        3566/2401*T^50 + 3019/2401*T^49 - 7409/2401*T^48 + 7237/2401*T^47 - 
        502/343*T^46 - 1658/2401*T^45 + 6036/2401*T^44 - 24/7*T^43 + 4757/2401*T^42 
        + 1662/2401*T^41 - 6925/2401*T^40 + 8425/2401*T^39 - 5045/2401*T^38 - 
        1142/2401*T^37 + 6737/2401*T^36 - 7779/2401*T^35 + 4933/2401*T^34 - 
        1095/2401*T^33 - 3628/2401*T^32 + 6617/2401*T^31 - 6897/2401*T^30 + 
        3932/2401*T^29 - 3932/2401*T^27 + 6897/2401*T^26 - 6617/2401*T^25 + 
        3628/2401*T^24 + 1095/2401*T^23 - 4933/2401*T^22 + 7779/2401*T^21 - 
        6737/2401*T^20 + 1142/2401*T^19 + 5045/2401*T^18 - 8425/2401*T^17 + 
        6925/2401*T^16 - 1662/2401*T^15 - 4757/2401*T^14 + 24/7*T^13 - 
        6036/2401*T^12 + 1658/2401*T^11 + 502/343*T^10 - 7237/2401*T^9 + 
        7409/2401*T^8 - 3019/2401*T^7 - 3566/2401*T^6 + 6439/2401*T^5 - 846/343*T^4 
        + 234/343*T^3 + 52/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 6*X*Y + 
        5*X + 6*Y^30 + 6*Y^28 + 4*Y^27 + 4*Y^26 + 6*Y^25 + 6*Y^24 + 5*Y^23 + 4*Y^22 
        + 4*Y^20 + 5*Y^18 + 6*Y^17 + Y^16 + 3*Y^15 + 6*Y^14 + 2*Y^13 + 6*Y^12 + Y^11
        + 5*Y^9 + Y^8 + 4*Y^6 + 5*Y^5 + 4*Y^4 + 5*Y^3 + Y^2 + 3*Y + 3,
    T^56 + 2*T^55 + 52/49*T^54 - 60/343*T^53 - 124/2401*T^52 + 873/2401*T^51 - 
        921/2401*T^50 - 5115/2401*T^49 - 1055/343*T^48 - 3952/2401*T^47 + 
        2283/2401*T^46 + 2633/2401*T^45 - 1922/2401*T^44 - 715/2401*T^43 + 
        5536/2401*T^42 + 946/343*T^41 - 109/2401*T^40 - 5423/2401*T^39 - 
        355/343*T^38 + 307/343*T^37 + 622/2401*T^36 - 3835/2401*T^35 - 
        2628/2401*T^34 + 492/343*T^33 + 5119/2401*T^32 - 184/2401*T^31 - 
        4157/2401*T^30 - 339/2401*T^29 + 524/343*T^28 - 339/2401*T^27 - 
        4157/2401*T^26 - 184/2401*T^25 + 5119/2401*T^24 + 492/343*T^23 - 
        2628/2401*T^22 - 3835/2401*T^21 + 622/2401*T^20 + 307/343*T^19 - 
        355/343*T^18 - 5423/2401*T^17 - 109/2401*T^16 + 946/343*T^15 + 
        5536/2401*T^14 - 715/2401*T^13 - 1922/2401*T^12 + 2633/2401*T^11 + 
        2283/2401*T^10 - 3952/2401*T^9 - 1055/343*T^8 - 5115/2401*T^7 - 921/2401*T^6
        + 873/2401*T^5 - 124/2401*T^4 - 60/343*T^3 + 52/49*T^2 + 2*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 
        + 5*X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + X*Y^2 + 3*X*Y 
        + 3*X + 2*Y^30 + 3*Y^29 + 4*Y^28 + 4*Y^27 + 2*Y^26 + 2*Y^25 + 4*Y^22 + 
        3*Y^21 + 6*Y^20 + 4*Y^19 + 2*Y^18 + Y^17 + 4*Y^16 + 6*Y^14 + 5*Y^13 + 4*Y^12
        + 6*Y^11 + 4*Y^10 + 6*Y^9 + 5*Y^8 + 4*Y^7 + 3*Y^5 + 4*Y^4 + 2*Y^3 + 6*Y^2 + 
        5*Y + 6,
    T^56 + 10/7*T^55 + 43/49*T^54 + 58/343*T^53 - 2117/2401*T^52 - 2158/2401*T^51 - 
        1525/2401*T^50 + 23/343*T^49 + 1116/2401*T^48 + 127/2401*T^47 - 
        478/2401*T^46 - 1391/2401*T^45 - 1171/2401*T^44 - 1228/2401*T^43 - 
        1709/2401*T^42 - 2036/2401*T^41 - 237/343*T^40 - 239/2401*T^39 + 
        1699/2401*T^38 + 2698/2401*T^37 + 1997/2401*T^36 + 108/343*T^35 - 
        974/2401*T^34 - 156/343*T^33 - 135/343*T^32 + 240/2401*T^31 + 1037/2401*T^30
        + 776/2401*T^29 + 1567/2401*T^28 + 776/2401*T^27 + 1037/2401*T^26 + 
        240/2401*T^25 - 135/343*T^24 - 156/343*T^23 - 974/2401*T^22 + 108/343*T^21 +
        1997/2401*T^20 + 2698/2401*T^19 + 1699/2401*T^18 - 239/2401*T^17 - 
        237/343*T^16 - 2036/2401*T^15 - 1709/2401*T^14 - 1228/2401*T^13 - 
        1171/2401*T^12 - 1391/2401*T^11 - 478/2401*T^10 + 127/2401*T^9 + 
        1116/2401*T^8 + 23/343*T^7 - 1525/2401*T^6 - 2158/2401*T^5 - 2117/2401*T^4 +
        58/343*T^3 + 43/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 6*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + X*Y^8 + 6*X*Y^4 + 
        4*X*Y^3 + X*Y^2 + 4*X*Y + 2*X + 3*Y^30 + 4*Y^29 + 4*Y^27 + 5*Y^26 + 3*Y^25 +
        Y^24 + 5*Y^23 + 6*Y^22 + 6*Y^20 + Y^19 + 4*Y^18 + 2*Y^17 + 4*Y^16 + 6*Y^15 +
        3*Y^14 + 5*Y^13 + 6*Y^12 + 4*Y^11 + 2*Y^10 + 3*Y^9 + 2*Y^8 + Y^7 + 5*Y^6 + 
        6*Y^5 + 4*Y^4 + 3*Y^3 + 4*Y^2 + 3*Y + 1,
    T^56 + 1/7*T^55 + 41/49*T^54 - 138/343*T^53 + 2/343*T^52 - 88/2401*T^51 + 
        23/343*T^50 - 419/2401*T^49 - 416/2401*T^48 + 656/2401*T^47 - 1844/2401*T^46
        + 67/343*T^45 - 2132/2401*T^44 + 108/343*T^43 + 9/2401*T^42 + 59/343*T^41 - 
        279/2401*T^40 + 964/2401*T^39 + 601/2401*T^38 + 622/2401*T^37 + 
        317/2401*T^36 - 891/2401*T^35 + 372/2401*T^34 - 169/2401*T^33 + 
        298/2401*T^32 + 278/2401*T^31 + 47/343*T^30 - 888/2401*T^29 + 244/2401*T^28 
        - 888/2401*T^27 + 47/343*T^26 + 278/2401*T^25 + 298/2401*T^24 - 
        169/2401*T^23 + 372/2401*T^22 - 891/2401*T^21 + 317/2401*T^20 + 
        622/2401*T^19 + 601/2401*T^18 + 964/2401*T^17 - 279/2401*T^16 + 59/343*T^15 
        + 9/2401*T^14 + 108/343*T^13 - 2132/2401*T^12 + 67/343*T^11 - 1844/2401*T^10
        + 656/2401*T^9 - 416/2401*T^8 - 419/2401*T^7 + 23/343*T^6 - 88/2401*T^5 + 
        2/343*T^4 - 138/343*T^3 + 41/49*T^2 + 1/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        6*X*Y^8 + 3*X*Y^7 + X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 6*X*Y + 
        6*X + 6*Y^30 + 3*Y^29 + 5*Y^28 + 5*Y^27 + 6*Y^25 + 6*Y^24 + 5*Y^23 + 3*Y^22 
        + 2*Y^20 + Y^18 + 6*Y^17 + 6*Y^16 + 4*Y^15 + 2*Y^14 + 3*Y^13 + 4*Y^12 + 
        4*Y^11 + 3*Y^8 + Y^7 + 3*Y^6 + 2*Y^4 + Y^3 + Y^2 + 6*Y + 5,
    T^56 + T^55 - 40/49*T^54 - 47/49*T^53 + 1068/2401*T^52 + 1182/2401*T^51 - 
        1055/2401*T^50 - 753/2401*T^49 + 317/2401*T^48 - 1328/2401*T^47 - 
        923/2401*T^46 + 1850/2401*T^45 + 1033/2401*T^44 - 194/343*T^43 - 
        942/2401*T^42 + 1006/2401*T^41 + 1790/2401*T^40 + 71/2401*T^39 - 
        545/2401*T^38 + 29/2401*T^37 - 1060/2401*T^36 - 1147/2401*T^35 + 
        768/2401*T^34 + 1394/2401*T^33 - 584/2401*T^32 - 1833/2401*T^31 - 
        93/2401*T^30 + 1233/2401*T^29 + 1083/2401*T^28 + 1233/2401*T^27 - 
        93/2401*T^26 - 1833/2401*T^25 - 584/2401*T^24 + 1394/2401*T^23 + 
        768/2401*T^22 - 1147/2401*T^21 - 1060/2401*T^20 + 29/2401*T^19 - 
        545/2401*T^18 + 71/2401*T^17 + 1790/2401*T^16 + 1006/2401*T^15 - 
        942/2401*T^14 - 194/343*T^13 + 1033/2401*T^12 + 1850/2401*T^11 - 
        923/2401*T^10 - 1328/2401*T^9 + 317/2401*T^8 - 753/2401*T^7 - 1055/2401*T^6 
        + 1182/2401*T^5 + 1068/2401*T^4 - 47/49*T^3 - 40/49*T^2 + T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + X*Y^12 + 2*X*Y^10 + 3*X*Y^9 + X*Y^8 + 
        6*X*Y^7 + X*Y^6 + 2*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 5*X*Y + 5*X + 4*Y^30 + 
        5*Y^29 + Y^28 + 2*Y^27 + 6*Y^26 + Y^25 + 3*Y^24 + 5*Y^22 + 2*Y^20 + 2*Y^18 +
        5*Y^16 + 3*Y^15 + 5*Y^14 + 2*Y^13 + Y^12 + 3*Y^10 + 4*Y^9 + 6*Y^8 + 6*Y^7 + 
        6*Y^6 + Y^5 + 4*Y + 1,
    -T^56 + 1/7*T^55 - 54/49*T^54 - 169/343*T^53 + 1717/2401*T^52 - 1774/2401*T^51 +
        3041/2401*T^50 + 9/2401*T^49 + 1/2401*T^48 + 1340/2401*T^47 - 2133/2401*T^46
        + 12/2401*T^45 - 1055/2401*T^44 - 354/2401*T^43 + 58/343*T^42 + 
        1971/2401*T^41 + 1951/2401*T^40 + 1682/2401*T^39 + 254/343*T^38 - 
        1873/2401*T^37 - 344/2401*T^36 - 2840/2401*T^35 - 772/2401*T^34 + 
        549/2401*T^33 + 253/2401*T^32 + 3218/2401*T^31 + 729/2401*T^30 + 
        1663/2401*T^29 - 1663/2401*T^27 - 729/2401*T^26 - 3218/2401*T^25 - 
        253/2401*T^24 - 549/2401*T^23 + 772/2401*T^22 + 2840/2401*T^21 + 
        344/2401*T^20 + 1873/2401*T^19 - 254/343*T^18 - 1682/2401*T^17 - 
        1951/2401*T^16 - 1971/2401*T^15 - 58/343*T^14 + 354/2401*T^13 + 
        1055/2401*T^12 - 12/2401*T^11 + 2133/2401*T^10 - 1340/2401*T^9 - 1/2401*T^8 
        - 9/2401*T^7 - 3041/2401*T^6 + 1774/2401*T^5 - 1717/2401*T^4 + 169/343*T^3 +
        54/49*T^2 - 1/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 3*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 + 
        X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 4*X*Y + 6*X + 
        5*Y^30 + 6*Y^28 + 3*Y^26 + 4*Y^24 + 6*Y^23 + Y^22 + 4*Y^21 + 4*Y^19 + 2*Y^18
        + 4*Y^17 + 5*Y^15 + 5*Y^13 + 5*Y^12 + 5*Y^11 + 5*Y^10 + 2*Y^8 + 2*Y^7 + 
        3*Y^6 + 6*Y^5 + Y^4 + 2*Y^3 + 5*Y^2 + 2*Y + 1,
    T^56 - T^55 + 40/49*T^54 - 222/343*T^53 + 1095/2401*T^52 + 26/2401*T^51 + 
        1503/2401*T^50 - 3233/2401*T^49 + 3278/2401*T^48 - 3511/2401*T^47 + 
        1914/2401*T^46 + 1/49*T^45 + 909/2401*T^44 - 1472/2401*T^43 + 2446/2401*T^42
        - 3433/2401*T^41 + 4056/2401*T^40 - 1759/2401*T^39 + 1289/2401*T^38 - 
        1521/2401*T^37 + 1731/2401*T^36 - 2979/2401*T^35 + 3382/2401*T^34 - 
        461/343*T^33 + 2867/2401*T^32 - 2167/2401*T^31 + 2189/2401*T^30 - 
        1462/2401*T^29 + 2473/2401*T^28 - 1462/2401*T^27 + 2189/2401*T^26 - 
        2167/2401*T^25 + 2867/2401*T^24 - 461/343*T^23 + 3382/2401*T^22 - 
        2979/2401*T^21 + 1731/2401*T^20 - 1521/2401*T^19 + 1289/2401*T^18 - 
        1759/2401*T^17 + 4056/2401*T^16 - 3433/2401*T^15 + 2446/2401*T^14 - 
        1472/2401*T^13 + 909/2401*T^12 + 1/49*T^11 + 1914/2401*T^10 - 3511/2401*T^9 
        + 3278/2401*T^8 - 3233/2401*T^7 + 1503/2401*T^6 + 26/2401*T^5 + 
        1095/2401*T^4 - 222/343*T^3 + 40/49*T^2 - T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 
        2*X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + X*Y^2 + 6*X*Y + 
        2*X + 2*Y^30 + 4*Y^29 + 5*Y^26 + 6*Y^25 + 6*Y^24 + 3*Y^23 + 2*Y^22 + 4*Y^21 
        + 3*Y^19 + Y^18 + 5*Y^17 + 6*Y^16 + 2*Y^15 + 3*Y^14 + 2*Y^13 + 6*Y^12 + 
        2*Y^10 + Y^9 + 4*Y^8 + Y^7 + 6*Y^4 + 4*Y^3 + Y^2 + 6,
    T^56 - 4/7*T^55 + 9/49*T^54 + 4/49*T^53 - 1144/2401*T^52 + 1773/2401*T^51 - 
        659/2401*T^50 - 149/343*T^49 - 730/2401*T^48 + 303/2401*T^47 + 271/2401*T^46
        + 1136/2401*T^45 - 1089/2401*T^44 - 258/2401*T^43 + 489/2401*T^42 + 
        478/2401*T^41 + 200/343*T^40 - 1514/2401*T^39 - 142/2401*T^38 - 
        1104/2401*T^37 + 86/343*T^36 + 186/2401*T^35 - 751/2401*T^34 - 790/2401*T^33
        - 594/2401*T^32 + 1331/2401*T^31 + 13/49*T^30 + 34/343*T^29 - 543/2401*T^28 
        + 34/343*T^27 + 13/49*T^26 + 1331/2401*T^25 - 594/2401*T^24 - 790/2401*T^23 
        - 751/2401*T^22 + 186/2401*T^21 + 86/343*T^20 - 1104/2401*T^19 - 
        142/2401*T^18 - 1514/2401*T^17 + 200/343*T^16 + 478/2401*T^15 + 
        489/2401*T^14 - 258/2401*T^13 - 1089/2401*T^12 + 1136/2401*T^11 + 
        271/2401*T^10 + 303/2401*T^9 - 730/2401*T^8 - 149/343*T^7 - 659/2401*T^6 + 
        1773/2401*T^5 - 1144/2401*T^4 + 4/49*T^3 + 9/49*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 5*X*Y^12 + 4*X*Y^11 + X*Y^10 + 5*X*Y^8 + X*Y^7 + X*Y^6
        + X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + X*Y^2 + 2*X*Y + 2*X + Y^30 + 4*Y^29 + Y^28 + 
        Y^27 + Y^26 + 6*Y^25 + 6*Y^24 + 6*Y^23 + 3*Y^22 + 4*Y^21 + 2*Y^20 + 4*Y^19 +
        4*Y^18 + 2*Y^17 + 5*Y^16 + 5*Y^15 + Y^14 + 5*Y^13 + 5*Y^12 + 3*Y^11 + 3*Y^9 
        + 4*Y^8 + 4*Y^7 + 3*Y^5 + 3*Y^4 + 3*Y^3 + 6*Y^2 + 6*Y + 3,
    T^56 + 4/7*T^55 - 11/49*T^54 - 142/343*T^53 - 2115/2401*T^52 + 256/2401*T^51 + 
        2586/2401*T^50 + 1858/2401*T^49 - 330/2401*T^48 - 2206/2401*T^47 - 
        2306/2401*T^46 + 166/343*T^45 + 1793/2401*T^44 + 540/2401*T^43 - 
        1494/2401*T^42 - 3030/2401*T^41 - 1520/2401*T^40 + 1000/2401*T^39 + 
        331/343*T^38 + 993/2401*T^37 - 1262/2401*T^36 - 1662/2401*T^35 - 
        369/2401*T^34 + 409/2401*T^33 + 916/2401*T^32 + 5/49*T^31 - 23/343*T^30 + 
        342/2401*T^29 + 752/2401*T^28 + 342/2401*T^27 - 23/343*T^26 + 5/49*T^25 + 
        916/2401*T^24 + 409/2401*T^23 - 369/2401*T^22 - 1662/2401*T^21 - 
        1262/2401*T^20 + 993/2401*T^19 + 331/343*T^18 + 1000/2401*T^17 - 
        1520/2401*T^16 - 3030/2401*T^15 - 1494/2401*T^14 + 540/2401*T^13 + 
        1793/2401*T^12 + 166/343*T^11 - 2306/2401*T^10 - 2206/2401*T^9 - 
        330/2401*T^8 + 1858/2401*T^7 + 2586/2401*T^6 + 256/2401*T^5 - 2115/2401*T^4 
        - 142/343*T^3 - 11/49*T^2 + 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 4*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + 6*X*Y^8 + 
        6*X*Y^7 + 6*X*Y^6 + X*Y^5 + 2*X*Y^3 + 3*X*Y^2 + X*Y + 2*Y^30 + 2*Y^29 + 
        5*Y^28 + 3*Y^27 + 4*Y^26 + 5*Y^25 + 5*Y^24 + 3*Y^23 + 3*Y^22 + 3*Y^21 + Y^20
        + 6*Y^19 + 3*Y^18 + 5*Y^17 + 6*Y^16 + 4*Y^15 + Y^14 + 5*Y^13 + 6*Y^12 + 
        5*Y^10 + 3*Y^9 + 5*Y^8 + Y^7 + 2*Y^6 + 3*Y^5 + 5*Y^4 + Y^2 + 3*Y + 5,
    T^56 + 1/7*T^55 - 81/49*T^54 - 60/49*T^53 + 1418/2401*T^52 + 2913/2401*T^51 + 
        1453/2401*T^50 + 18/343*T^49 - 1517/2401*T^48 - 16/49*T^47 - 645/2401*T^46 +
        1091/2401*T^45 + 2096/2401*T^44 - 935/2401*T^43 - 2475/2401*T^42 + 
        349/2401*T^41 + 2661/2401*T^40 + 227/2401*T^39 - 53/49*T^38 - 1467/2401*T^37
        + 1738/2401*T^36 + 1431/2401*T^35 - 661/2401*T^34 + 242/2401*T^33 + 
        26/343*T^32 - 1313/2401*T^31 - 792/2401*T^30 + 668/2401*T^29 + 216/343*T^28 
        + 668/2401*T^27 - 792/2401*T^26 - 1313/2401*T^25 + 26/343*T^24 + 
        242/2401*T^23 - 661/2401*T^22 + 1431/2401*T^21 + 1738/2401*T^20 - 
        1467/2401*T^19 - 53/49*T^18 + 227/2401*T^17 + 2661/2401*T^16 + 349/2401*T^15
        - 2475/2401*T^14 - 935/2401*T^13 + 2096/2401*T^12 + 1091/2401*T^11 - 
        645/2401*T^10 - 16/49*T^9 - 1517/2401*T^8 + 18/343*T^7 + 1453/2401*T^6 + 
        2913/2401*T^5 + 1418/2401*T^4 - 60/49*T^3 - 81/49*T^2 + 1/7*T + 1
*], [*
    X^3 + X*Y^14 + 3*X*Y^13 + X*Y^12 + 6*X*Y^10 + 6*X*Y^9 + X*Y^8 + 3*X*Y^7 + X*Y^6 
        + 6*X*Y^5 + 5*X*Y^4 + X*Y^3 + X*Y^2 + 4*X*Y + 5*X + 5*Y^30 + 2*Y^29 + Y^28 +
        6*Y^27 + Y^25 + 5*Y^24 + 5*Y^22 + 3*Y^21 + Y^19 + 2*Y^18 + 3*Y^17 + 3*Y^16 +
        Y^15 + 3*Y^14 + 5*Y^12 + 2*Y^10 + Y^9 + 3*Y^8 + 2*Y^7 + 3*Y^6 + Y^5 + 4*Y^3 
        + 5*Y^2 + 4*Y,
    -T^56 - 18/7*T^55 - 150/49*T^54 - 13/7*T^53 - 8/343*T^52 + 1174/2401*T^51 - 
        30/343*T^50 - 1581/2401*T^49 - 969/2401*T^48 + 9/49*T^47 + 899/2401*T^46 + 
        1874/2401*T^45 + 4345/2401*T^44 + 1047/343*T^43 + 1119/343*T^42 + 
        4591/2401*T^41 + 99/343*T^40 - 1908/2401*T^39 - 2525/2401*T^38 - 
        1340/2401*T^37 - 351/2401*T^36 - 116/2401*T^35 - 26/343*T^34 + 113/2401*T^33
        - 143/343*T^32 - 634/343*T^31 - 7120/2401*T^30 - 5812/2401*T^29 + 
        5812/2401*T^27 + 7120/2401*T^26 + 634/343*T^25 + 143/343*T^24 - 
        113/2401*T^23 + 26/343*T^22 + 116/2401*T^21 + 351/2401*T^20 + 1340/2401*T^19
        + 2525/2401*T^18 + 1908/2401*T^17 - 99/343*T^16 - 4591/2401*T^15 - 
        1119/343*T^14 - 1047/343*T^13 - 4345/2401*T^12 - 1874/2401*T^11 - 
        899/2401*T^10 - 9/49*T^9 + 969/2401*T^8 + 1581/2401*T^7 + 30/343*T^6 - 
        1174/2401*T^5 + 8/343*T^4 + 13/7*T^3 + 150/49*T^2 + 18/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^13 + 2*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 2*X*Y^8 + 6*X*Y^7 + 
        5*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 6*X*Y + 3*X + 6*Y^30 + 
        3*Y^29 + 4*Y^28 + Y^27 + 6*Y^26 + 5*Y^25 + 5*Y^24 + 5*Y^23 + Y^22 + 6*Y^21 +
        Y^20 + Y^19 + 2*Y^18 + 3*Y^17 + 3*Y^16 + Y^15 + Y^14 + 3*Y^13 + 4*Y^12 + 
        3*Y^11 + 5*Y^10 + Y^9 + 2*Y^8 + Y^7 + 2*Y^5 + Y^4 + 3*Y^3 + 4*Y^2 + Y + 1,
    T^56 - 5/7*T^55 + 2/49*T^54 - 134/343*T^53 + 71/2401*T^52 - 45/2401*T^51 - 
        229/2401*T^50 + 143/2401*T^49 + 1077/2401*T^48 + 197/2401*T^47 - 
        542/2401*T^46 - 363/2401*T^45 - 1116/2401*T^44 + 65/343*T^43 + 482/2401*T^42
        + 157/2401*T^41 + 415/2401*T^40 - 457/2401*T^39 + 751/2401*T^38 + 
        428/2401*T^37 - 1228/2401*T^36 + 174/2401*T^35 - 1115/2401*T^34 + 
        1356/2401*T^33 + 522/2401*T^32 - 62/2401*T^31 - 1028/2401*T^30 + 
        754/2401*T^29 - 925/2401*T^28 + 754/2401*T^27 - 1028/2401*T^26 - 
        62/2401*T^25 + 522/2401*T^24 + 1356/2401*T^23 - 1115/2401*T^22 + 
        174/2401*T^21 - 1228/2401*T^20 + 428/2401*T^19 + 751/2401*T^18 - 
        457/2401*T^17 + 415/2401*T^16 + 157/2401*T^15 + 482/2401*T^14 + 65/343*T^13 
        - 1116/2401*T^12 - 363/2401*T^11 - 542/2401*T^10 + 197/2401*T^9 + 
        1077/2401*T^8 + 143/2401*T^7 - 229/2401*T^6 - 45/2401*T^5 + 71/2401*T^4 - 
        134/343*T^3 + 2/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 3*X*Y^8 + 5*X*Y^7 +
        X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 2*X*Y^2 + 4*X*Y + X + 6*Y^30 + 3*Y^29 + 5*Y^28 +
        Y^26 + 5*Y^24 + 6*Y^23 + 5*Y^22 + Y^21 + 3*Y^20 + 4*Y^18 + 2*Y^17 + Y^16 + 
        6*Y^13 + Y^12 + 4*Y^11 + 6*Y^10 + Y^9 + 6*Y^8 + 5*Y^7 + 2*Y^6 + Y^4 + 5*Y^3 
        + 5*Y^2 + 3*Y,
    T^56 - 8/7*T^55 + 66/49*T^54 - 323/343*T^53 - 1479/2401*T^52 + 3257/2401*T^51 - 
        2935/2401*T^50 + 453/343*T^49 - 2432/2401*T^48 + 157/2401*T^47 - 
        170/343*T^46 - 226/343*T^45 + 3945/2401*T^44 - 4192/2401*T^43 + 
        3394/2401*T^42 - 1048/2401*T^41 - 367/343*T^40 + 4331/2401*T^39 - 
        2311/2401*T^38 + 1807/2401*T^37 - 86/343*T^36 + 737/2401*T^35 - 
        568/2401*T^34 - 137/2401*T^33 + 2414/2401*T^32 - 3009/2401*T^31 + 
        802/2401*T^30 + 701/2401*T^29 - 369/343*T^28 + 701/2401*T^27 + 802/2401*T^26
        - 3009/2401*T^25 + 2414/2401*T^24 - 137/2401*T^23 - 568/2401*T^22 + 
        737/2401*T^21 - 86/343*T^20 + 1807/2401*T^19 - 2311/2401*T^18 + 
        4331/2401*T^17 - 367/343*T^16 - 1048/2401*T^15 + 3394/2401*T^14 - 
        4192/2401*T^13 + 3945/2401*T^12 - 226/343*T^11 - 170/343*T^10 + 157/2401*T^9
        - 2432/2401*T^8 + 453/343*T^7 - 2935/2401*T^6 + 3257/2401*T^5 - 
        1479/2401*T^4 - 323/343*T^3 + 66/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        3*X*Y^8 + 6*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 4*X*Y + 6*X + 3*Y^30 + 6*Y^29 + 
        2*Y^28 + Y^27 + 2*Y^26 + Y^24 + Y^23 + 5*Y^21 + 3*Y^20 + Y^19 + 4*Y^18 + 
        2*Y^17 + 4*Y^16 + 5*Y^15 + 3*Y^14 + 5*Y^13 + 5*Y^12 + 4*Y^11 + 6*Y^10 + 
        5*Y^9 + Y^8 + 2*Y^7 + 2*Y^6 + 2*Y^5 + Y^4 + Y^3 + 2*Y^2 + 6*Y + 4,
    -T^56 + 1/7*T^55 - 17/49*T^54 + 3/49*T^53 + 17/2401*T^52 + 470/2401*T^51 - 
        106/343*T^50 + 1153/2401*T^49 - 167/2401*T^48 - 122/343*T^47 + 913/2401*T^46
        + 239/2401*T^45 + 61/343*T^44 + 123/343*T^43 + 163/343*T^42 - 771/2401*T^41 
        + 1395/2401*T^40 - 684/2401*T^39 - 325/2401*T^38 - 291/2401*T^37 + 
        464/2401*T^36 - 683/2401*T^35 + 1174/2401*T^34 - 926/2401*T^33 + 
        193/2401*T^32 - 659/2401*T^31 - 256/2401*T^30 - 590/2401*T^29 + 
        590/2401*T^27 + 256/2401*T^26 + 659/2401*T^25 - 193/2401*T^24 + 
        926/2401*T^23 - 1174/2401*T^22 + 683/2401*T^21 - 464/2401*T^20 + 
        291/2401*T^19 + 325/2401*T^18 + 684/2401*T^17 - 1395/2401*T^16 + 
        771/2401*T^15 - 163/343*T^14 - 123/343*T^13 - 61/343*T^12 - 239/2401*T^11 - 
        913/2401*T^10 + 122/343*T^9 + 167/2401*T^8 - 1153/2401*T^7 + 106/343*T^6 - 
        470/2401*T^5 - 17/2401*T^4 - 3/49*T^3 + 17/49*T^2 - 1/7*T + 1
*], [*
    X^3 + X*Y^14 + X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 + 
        4*X*Y^7 + X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 3*X*Y + X + Y^30 +
        3*Y^29 + 4*Y^28 + 6*Y^27 + Y^26 + 3*Y^24 + 6*Y^23 + 3*Y^22 + Y^21 + 3*Y^20 +
        2*Y^19 + 2*Y^18 + 4*Y^17 + 5*Y^16 + 2*Y^15 + 3*Y^14 + Y^13 + 2*Y^11 + 6*Y^9 
        + 2*Y^8 + 5*Y^7 + 6*Y^6 + 3*Y^5 + Y^4 + 2*Y^3 + 4*Y^2 + 6,
    -T^56 + 12/7*T^55 - 10/7*T^54 + 190/343*T^53 + 1354/2401*T^52 - 454/343*T^51 + 
        3715/2401*T^50 - 3289/2401*T^49 + 2899/2401*T^48 - 2777/2401*T^47 + 
        1588/2401*T^46 - 712/2401*T^45 - 396/2401*T^44 + 1212/2401*T^43 - 
        2502/2401*T^42 + 4932/2401*T^41 - 6420/2401*T^40 + 674/343*T^39 - 
        2216/2401*T^38 - 60/2401*T^37 + 1688/2401*T^36 - 2126/2401*T^35 + 
        310/343*T^34 - 2390/2401*T^33 + 3202/2401*T^32 - 4526/2401*T^31 + 
        4157/2401*T^30 - 2641/2401*T^29 + 2641/2401*T^27 - 4157/2401*T^26 + 
        4526/2401*T^25 - 3202/2401*T^24 + 2390/2401*T^23 - 310/343*T^22 + 
        2126/2401*T^21 - 1688/2401*T^20 + 60/2401*T^19 + 2216/2401*T^18 - 
        674/343*T^17 + 6420/2401*T^16 - 4932/2401*T^15 + 2502/2401*T^14 - 
        1212/2401*T^13 + 396/2401*T^12 + 712/2401*T^11 - 1588/2401*T^10 + 
        2777/2401*T^9 - 2899/2401*T^8 + 3289/2401*T^7 - 3715/2401*T^6 + 454/343*T^5 
        - 1354/2401*T^4 - 190/343*T^3 + 10/7*T^2 - 12/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + X*Y^11 + 6*X*Y^9 + 3*X*Y^8 + 2*X*Y^7 + 
        6*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 4*X*Y + 2*X + 2*Y^30 + 
        Y^28 + 5*Y^27 + 6*Y^26 + 2*Y^25 + 6*Y^24 + 4*Y^23 + 5*Y^22 + 2*Y^21 + 6*Y^20
        + 3*Y^19 + 2*Y^18 + 4*Y^17 + 5*Y^16 + 3*Y^14 + Y^11 + Y^10 + 5*Y^9 + 2*Y^8 +
        Y^7 + 4*Y^6 + 5*Y^5 + 6*Y^4 + 2*Y^3 + Y^2 + 6*Y + 4,
    T^56 - 1/7*T^55 - 52/49*T^54 + 139/343*T^53 + 68/343*T^52 - 1367/2401*T^51 - 
        762/2401*T^50 + 2152/2401*T^49 + 1003/2401*T^48 - 1227/2401*T^47 - 
        260/2401*T^46 + 2166/2401*T^45 - 170/343*T^44 - 3683/2401*T^43 + 
        1167/2401*T^42 + 9/7*T^41 - 443/2401*T^40 - 1794/2401*T^39 + 2099/2401*T^38 
        + 892/2401*T^37 - 2930/2401*T^36 - 747/2401*T^35 + 2041/2401*T^34 + 
        263/2401*T^33 - 671/2401*T^32 - 73/2401*T^31 + 2005/2401*T^30 + 
        100/2401*T^29 - 3974/2401*T^28 + 100/2401*T^27 + 2005/2401*T^26 - 
        73/2401*T^25 - 671/2401*T^24 + 263/2401*T^23 + 2041/2401*T^22 - 
        747/2401*T^21 - 2930/2401*T^20 + 892/2401*T^19 + 2099/2401*T^18 - 
        1794/2401*T^17 - 443/2401*T^16 + 9/7*T^15 + 1167/2401*T^14 - 3683/2401*T^13 
        - 170/343*T^12 + 2166/2401*T^11 - 260/2401*T^10 - 1227/2401*T^9 + 
        1003/2401*T^8 + 2152/2401*T^7 - 762/2401*T^6 - 1367/2401*T^5 + 68/343*T^4 + 
        139/343*T^3 - 52/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 4*X*Y^8 + 2*X*Y^7 +
        4*X*Y^6 + 6*X*Y^5 + X*Y^4 + X*Y^3 + 2*X*Y + 5*X + 3*Y^30 + 2*Y^29 + 3*Y^28 +
        6*Y^27 + 5*Y^26 + Y^25 + 5*Y^24 + 2*Y^22 + 3*Y^21 + 2*Y^20 + 6*Y^19 + 5*Y^18
        + 3*Y^17 + 3*Y^16 + 3*Y^15 + 6*Y^14 + 6*Y^13 + 3*Y^12 + 5*Y^11 + 5*Y^10 + 
        3*Y^9 + Y^8 + 4*Y^7 + 6*Y^6 + Y^5 + 6*Y^4 + 2*Y^3 + 6*Y^2 + 3*Y,
    -T^56 - 6/7*T^55 - 55/49*T^54 - 89/343*T^53 + 41/2401*T^52 - 310/2401*T^51 - 
        670/2401*T^50 - 955/2401*T^49 - 1472/2401*T^48 - 135/2401*T^47 - 
        66/2401*T^46 + 1067/2401*T^45 + 319/2401*T^44 - 751/2401*T^43 - 
        795/2401*T^42 - 719/2401*T^41 - 1013/2401*T^40 - 709/2401*T^39 - 
        1089/2401*T^38 - 120/2401*T^37 + 291/2401*T^36 - 65/2401*T^35 - 
        110/2401*T^34 - 68/2401*T^33 - 298/2401*T^32 + 503/2401*T^31 + 426/2401*T^30
        + 836/2401*T^29 - 836/2401*T^27 - 426/2401*T^26 - 503/2401*T^25 + 
        298/2401*T^24 + 68/2401*T^23 + 110/2401*T^22 + 65/2401*T^21 - 291/2401*T^20 
        + 120/2401*T^19 + 1089/2401*T^18 + 709/2401*T^17 + 1013/2401*T^16 + 
        719/2401*T^15 + 795/2401*T^14 + 751/2401*T^13 - 319/2401*T^12 - 
        1067/2401*T^11 + 66/2401*T^10 + 135/2401*T^9 + 1472/2401*T^8 + 955/2401*T^7 
        + 670/2401*T^6 + 310/2401*T^5 - 41/2401*T^4 + 89/343*T^3 + 55/49*T^2 + 6/7*T
        + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 
        5*X*Y^8 + 4*X*Y^7 + 5*X*Y^6 + X*Y^5 + 2*X*Y^3 + 4*X*Y^2 + 4*X*Y + 6*X + 
        3*Y^30 + Y^29 + 3*Y^28 + 6*Y^27 + 2*Y^25 + 5*Y^24 + 3*Y^22 + 6*Y^21 + Y^19 +
        6*Y^18 + Y^17 + 2*Y^16 + 6*Y^15 + 5*Y^14 + Y^13 + 4*Y^12 + 5*Y^11 + 4*Y^10 +
        Y^9 + 2*Y^8 + 3*Y^7 + Y^6 + 3*Y^5 + 3*Y^3 + 6*Y^2 + 3*Y + 5,
    -T^56 + 6/7*T^55 + 32/49*T^54 - 92/49*T^53 + 708/2401*T^52 + 4794/2401*T^51 - 
        495/343*T^50 - 1168/2401*T^49 + 47/49*T^48 + 155/2401*T^47 - 103/343*T^46 - 
        1097/2401*T^45 + 591/2401*T^44 + 594/2401*T^43 - 215/343*T^42 + 
        1280/2401*T^41 - 1020/2401*T^40 - 1004/2401*T^39 + 2476/2401*T^38 - 
        948/2401*T^37 - 2411/2401*T^36 + 2407/2401*T^35 + 746/2401*T^34 - 
        2068/2401*T^33 + 95/2401*T^32 + 1752/2401*T^31 - 92/2401*T^30 - 
        1485/2401*T^29 + 1485/2401*T^27 + 92/2401*T^26 - 1752/2401*T^25 - 
        95/2401*T^24 + 2068/2401*T^23 - 746/2401*T^22 - 2407/2401*T^21 + 
        2411/2401*T^20 + 948/2401*T^19 - 2476/2401*T^18 + 1004/2401*T^17 + 
        1020/2401*T^16 - 1280/2401*T^15 + 215/343*T^14 - 594/2401*T^13 - 
        591/2401*T^12 + 1097/2401*T^11 + 103/343*T^10 - 155/2401*T^9 - 47/49*T^8 + 
        1168/2401*T^7 + 495/343*T^6 - 4794/2401*T^5 - 708/2401*T^4 + 92/49*T^3 - 
        32/49*T^2 - 6/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + X*Y^12 + 5*X*Y^11 + 3*X*Y^9 + 3*X*Y^8 + 
        6*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 4*X*Y + Y^30 + 2*Y^29 + 5*Y^28 + 
        2*Y^27 + 4*Y^26 + 4*Y^25 + 6*Y^24 + 5*Y^23 + 3*Y^22 + 6*Y^21 + Y^20 + 5*Y^19
        + 5*Y^18 + 3*Y^17 + 5*Y^16 + 2*Y^15 + Y^14 + 5*Y^13 + 4*Y^11 + 3*Y^10 + 
        2*Y^9 + 4*Y^8 + 5*Y^7 + 5*Y^6 + 5*Y^5 + 2*Y^4 + Y^3 + 5*Y^2 + 2*Y + 3,
    T^56 - 20/7*T^55 + 157/49*T^54 - 597/343*T^53 + 851/2401*T^52 + 1602/2401*T^51 -
        127/49*T^50 + 1517/343*T^49 - 8524/2401*T^48 + 2766/2401*T^47 - 
        1150/2401*T^46 + 771/2401*T^45 + 4841/2401*T^44 - 9929/2401*T^43 + 
        1318/343*T^42 - 9819/2401*T^41 + 13540/2401*T^40 - 10362/2401*T^39 - 
        1555/2401*T^38 + 1401/343*T^37 - 10931/2401*T^36 + 14104/2401*T^35 - 
        17240/2401*T^34 + 10200/2401*T^33 + 2055/2401*T^32 - 6485/2401*T^31 + 
        6786/2401*T^30 - 12525/2401*T^29 + 17089/2401*T^28 - 12525/2401*T^27 + 
        6786/2401*T^26 - 6485/2401*T^25 + 2055/2401*T^24 + 10200/2401*T^23 - 
        17240/2401*T^22 + 14104/2401*T^21 - 10931/2401*T^20 + 1401/343*T^19 - 
        1555/2401*T^18 - 10362/2401*T^17 + 13540/2401*T^16 - 9819/2401*T^15 + 
        1318/343*T^14 - 9929/2401*T^13 + 4841/2401*T^12 + 771/2401*T^11 - 
        1150/2401*T^10 + 2766/2401*T^9 - 8524/2401*T^8 + 1517/343*T^7 - 127/49*T^6 +
        1602/2401*T^5 + 851/2401*T^4 - 597/343*T^3 + 157/49*T^2 - 20/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 
        + 4*X*Y^8 + 2*X*Y^6 + 4*X*Y^5 + X*Y^4 + 6*X*Y^3 + X*Y^2 + 6*Y^30 + 2*Y^29 + 
        4*Y^27 + 2*Y^26 + 6*Y^25 + 5*Y^24 + 6*Y^23 + 3*Y^22 + 5*Y^21 + Y^19 + 3*Y^18
        + 2*Y^17 + 3*Y^16 + Y^15 + 2*Y^14 + Y^13 + 5*Y^12 + 4*Y^11 + 3*Y^10 + 6*Y^9 
        + 4*Y^8 + Y^7 + 5*Y^6 + 2*Y^5 + 4*Y^4 + 6*Y^3 + Y + 5,
    -T^56 - 2/7*T^55 + 17/49*T^54 + 149/343*T^53 + 5/49*T^52 - 73/2401*T^51 + 
        927/2401*T^50 + 920/2401*T^49 - 597/2401*T^48 - 75/2401*T^47 + 
        1681/2401*T^46 + 1202/2401*T^45 - 746/2401*T^44 - 1440/2401*T^43 - 
        962/2401*T^42 - 692/2401*T^41 - 1943/2401*T^40 - 823/2401*T^39 + 
        466/2401*T^38 + 1191/2401*T^37 + 883/2401*T^36 + 75/2401*T^35 + 
        208/2401*T^34 - 60/2401*T^33 + 12/49*T^32 + 1496/2401*T^31 + 1933/2401*T^30 
        + 314/2401*T^29 - 314/2401*T^27 - 1933/2401*T^26 - 1496/2401*T^25 - 
        12/49*T^24 + 60/2401*T^23 - 208/2401*T^22 - 75/2401*T^21 - 883/2401*T^20 - 
        1191/2401*T^19 - 466/2401*T^18 + 823/2401*T^17 + 1943/2401*T^16 + 
        692/2401*T^15 + 962/2401*T^14 + 1440/2401*T^13 + 746/2401*T^12 - 
        1202/2401*T^11 - 1681/2401*T^10 + 75/2401*T^9 + 597/2401*T^8 - 920/2401*T^7 
        - 927/2401*T^6 + 73/2401*T^5 - 5/49*T^4 - 149/343*T^3 - 17/49*T^2 + 2/7*T + 
        1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 5*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 4*X*Y^7 +
        4*X*Y^6 + 3*X*Y^4 + 6*X*Y^2 + 5*X + 3*Y^30 + Y^28 + 6*Y^27 + Y^24 + 6*Y^23 +
        3*Y^21 + Y^20 + 4*Y^19 + 5*Y^18 + 4*Y^16 + 3*Y^15 + 5*Y^14 + Y^13 + 4*Y^12 +
        6*Y^11 + 5*Y^9 + 6*Y^8 + 3*Y^7 + 5*Y^6 + 3*Y^5 + 2*Y^4 + 6*Y^3 + 5*Y^2 + 5,
    T^56 - 10/7*T^55 + T^54 - 571/343*T^53 + 3000/2401*T^52 + 753/2401*T^51 - 
        3223/2401*T^50 + 885/343*T^49 - 7445/2401*T^48 + 7911/2401*T^47 - 
        7789/2401*T^46 + 3957/2401*T^45 - 927/2401*T^44 - 1587/2401*T^43 + 
        745/343*T^42 - 7568/2401*T^41 + 9089/2401*T^40 - 7094/2401*T^39 + 
        5690/2401*T^38 - 4881/2401*T^37 + 16/2401*T^36 + 2103/2401*T^35 - 
        2455/2401*T^34 + 3651/2401*T^33 - 422/343*T^32 + 2812/2401*T^31 - 
        1857/2401*T^30 + 1000/2401*T^29 - 1650/2401*T^28 + 1000/2401*T^27 - 
        1857/2401*T^26 + 2812/2401*T^25 - 422/343*T^24 + 3651/2401*T^23 - 
        2455/2401*T^22 + 2103/2401*T^21 + 16/2401*T^20 - 4881/2401*T^19 + 
        5690/2401*T^18 - 7094/2401*T^17 + 9089/2401*T^16 - 7568/2401*T^15 + 
        745/343*T^14 - 1587/2401*T^13 - 927/2401*T^12 + 3957/2401*T^11 - 
        7789/2401*T^10 + 7911/2401*T^9 - 7445/2401*T^8 + 885/343*T^7 - 3223/2401*T^6
        + 753/2401*T^5 + 3000/2401*T^4 - 571/343*T^3 + T^2 - 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + X*Y^10 + 3*X*Y^7 + 
        5*X*Y^6 + 2*X*Y^3 + X*Y^2 + X*Y + 6*X + 6*Y^30 + 3*Y^28 + 3*Y^26 + 6*Y^25 + 
        Y^24 + 3*Y^23 + 2*Y^22 + 5*Y^21 + 4*Y^20 + 3*Y^19 + 4*Y^18 + 2*Y^17 + 5*Y^16
        + 6*Y^15 + 3*Y^14 + 2*Y^13 + 6*Y^11 + 6*Y^10 + Y^9 + 3*Y^8 + 2*Y^7 + 5*Y^6 +
        4*Y^5 + 2*Y^4 + 5*Y^3 + 4*Y^2 + Y + 3,
    T^56 + 12/7*T^55 + 2*T^54 + 1003/343*T^53 + 1118/343*T^52 + 6710/2401*T^51 + 
        4828/2401*T^50 + 274/343*T^49 - 2305/2401*T^48 - 5496/2401*T^47 - 
        8538/2401*T^46 - 9972/2401*T^45 - 7967/2401*T^44 - 6364/2401*T^43 - 
        3511/2401*T^42 + 1576/2401*T^41 + 5358/2401*T^40 + 7395/2401*T^39 + 
        8938/2401*T^38 + 9116/2401*T^37 + 8339/2401*T^36 + 6592/2401*T^35 + 
        2914/2401*T^34 + 39/343*T^33 - 2074/2401*T^32 - 5914/2401*T^31 - 
        8231/2401*T^30 - 9059/2401*T^29 - 9700/2401*T^28 - 9059/2401*T^27 - 
        8231/2401*T^26 - 5914/2401*T^25 - 2074/2401*T^24 + 39/343*T^23 + 
        2914/2401*T^22 + 6592/2401*T^21 + 8339/2401*T^20 + 9116/2401*T^19 + 
        8938/2401*T^18 + 7395/2401*T^17 + 5358/2401*T^16 + 1576/2401*T^15 - 
        3511/2401*T^14 - 6364/2401*T^13 - 7967/2401*T^12 - 9972/2401*T^11 - 
        8538/2401*T^10 - 5496/2401*T^9 - 2305/2401*T^8 + 274/343*T^7 + 4828/2401*T^6
        + 6710/2401*T^5 + 1118/343*T^4 + 1003/343*T^3 + 2*T^2 + 12/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 
        X*Y^8 + 5*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 3*X*Y + 
        3*X + 4*Y^30 + 5*Y^29 + 3*Y^28 + 3*Y^27 + 2*Y^26 + Y^24 + 5*Y^23 + Y^22 + 
        Y^21 + 3*Y^20 + 5*Y^19 + 6*Y^17 + 6*Y^16 + Y^15 + 6*Y^14 + 4*Y^13 + 2*Y^12 +
        5*Y^11 + 3*Y^10 + 6*Y^9 + 4*Y^8 + 4*Y^6 + Y^5 + 4*Y^3 + 5*Y^2 + 4*Y + 5,
    T^56 + T^55 + 25/49*T^54 + 122/343*T^53 + 16/343*T^52 - 909/2401*T^51 - 
        897/2401*T^50 + 712/2401*T^49 - 48/2401*T^48 - 305/2401*T^47 + 118/2401*T^46
        + 834/2401*T^45 + 767/2401*T^44 + 204/2401*T^43 - 864/2401*T^42 - 
        1097/2401*T^41 - 1600/2401*T^40 - 1068/2401*T^39 - 585/2401*T^38 - 
        1759/2401*T^37 - 813/2401*T^36 + 488/2401*T^35 + 1046/2401*T^34 + 
        1282/2401*T^33 + 2206/2401*T^32 + 1268/2401*T^31 - 372/2401*T^30 + 
        85/2401*T^29 + 949/2401*T^28 + 85/2401*T^27 - 372/2401*T^26 + 1268/2401*T^25
        + 2206/2401*T^24 + 1282/2401*T^23 + 1046/2401*T^22 + 488/2401*T^21 - 
        813/2401*T^20 - 1759/2401*T^19 - 585/2401*T^18 - 1068/2401*T^17 - 
        1600/2401*T^16 - 1097/2401*T^15 - 864/2401*T^14 + 204/2401*T^13 + 
        767/2401*T^12 + 834/2401*T^11 + 118/2401*T^10 - 305/2401*T^9 - 48/2401*T^8 +
        712/2401*T^7 - 897/2401*T^6 - 909/2401*T^5 + 16/343*T^4 + 122/343*T^3 + 
        25/49*T^2 + T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 4*X*Y^9 
        + 6*X*Y^7 + 3*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + X*Y^2 + 6*X + Y^30 + 
        3*Y^29 + 4*Y^28 + Y^27 + Y^25 + Y^24 + 2*Y^23 + 6*Y^22 + Y^21 + 5*Y^17 + 
        4*Y^16 + 5*Y^15 + 6*Y^14 + 5*Y^13 + 4*Y^12 + Y^11 + 4*Y^10 + Y^9 + 6*Y^8 + 
        6*Y^7 + 2*Y^6 + 6*Y^4 + 2*Y^3 + 6*Y^2 + 5*Y,
    T^56 - 11/7*T^54 + 5/49*T^53 + 4443/2401*T^52 - 1383/2401*T^51 - 3487/2401*T^50 
        + 153/343*T^49 + 2641/2401*T^48 - 289/2401*T^47 - 1781/2401*T^46 - 
        1031/2401*T^45 + 429/2401*T^44 + 1926/2401*T^43 - 55/2401*T^42 - 
        2094/2401*T^41 + 5/2401*T^40 + 2166/2401*T^39 + 487/2401*T^38 - 
        1012/2401*T^37 - 2052/2401*T^36 - 192/2401*T^35 + 2927/2401*T^34 + 
        229/2401*T^33 - 3499/2401*T^32 + 5/2401*T^31 + 3764/2401*T^30 - 
        169/2401*T^29 - 3840/2401*T^28 - 169/2401*T^27 + 3764/2401*T^26 + 
        5/2401*T^25 - 3499/2401*T^24 + 229/2401*T^23 + 2927/2401*T^22 - 
        192/2401*T^21 - 2052/2401*T^20 - 1012/2401*T^19 + 487/2401*T^18 + 
        2166/2401*T^17 + 5/2401*T^16 - 2094/2401*T^15 - 55/2401*T^14 + 
        1926/2401*T^13 + 429/2401*T^12 - 1031/2401*T^11 - 1781/2401*T^10 - 
        289/2401*T^9 + 2641/2401*T^8 + 153/343*T^7 - 3487/2401*T^6 - 1383/2401*T^5 +
        4443/2401*T^4 + 5/49*T^3 - 11/7*T^2 + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + X*Y^10 + 5*X*Y^9 + 3*X*Y^8 + 4*X*Y^6 + 5*X*Y^5 + 
        2*X*Y^4 + 3*X*Y^2 + 6*X*Y + 2*X + 6*Y^30 + 4*Y^29 + 5*Y^28 + 6*Y^27 + 2*Y^25
        + 2*Y^24 + 5*Y^22 + 6*Y^21 + 4*Y^20 + 3*Y^19 + 2*Y^17 + 5*Y^16 + Y^15 + 
        2*Y^13 + 6*Y^12 + 2*Y^11 + 5*Y^10 + 4*Y^9 + 4*Y^8 + 3*Y^7 + 6*Y^6 + 4*Y^5 + 
        3*Y^4 + 4*Y^3 + 4*Y^2 + 1,
    T^56 + 2*T^55 + 82/49*T^54 - 222/343*T^53 - 857/343*T^52 - 3457/2401*T^51 + 
        1880/2401*T^50 + 3068/2401*T^49 - 836/2401*T^48 - 436/343*T^47 - 
        183/2401*T^46 + 3222/2401*T^45 + 1829/2401*T^44 - 1629/2401*T^43 - 
        348/343*T^42 + 1381/2401*T^41 + 3800/2401*T^40 + 800/2401*T^39 - 
        3882/2401*T^38 - 3063/2401*T^37 + 2718/2401*T^36 + 5333/2401*T^35 + 
        606/2401*T^34 - 5452/2401*T^33 - 4981/2401*T^32 - 141/2401*T^31 + 
        2784/2401*T^30 + 1194/2401*T^29 - 59/343*T^28 + 1194/2401*T^27 + 
        2784/2401*T^26 - 141/2401*T^25 - 4981/2401*T^24 - 5452/2401*T^23 + 
        606/2401*T^22 + 5333/2401*T^21 + 2718/2401*T^20 - 3063/2401*T^19 - 
        3882/2401*T^18 + 800/2401*T^17 + 3800/2401*T^16 + 1381/2401*T^15 - 
        348/343*T^14 - 1629/2401*T^13 + 1829/2401*T^12 + 3222/2401*T^11 - 
        183/2401*T^10 - 436/343*T^9 - 836/2401*T^8 + 3068/2401*T^7 + 1880/2401*T^6 -
        3457/2401*T^5 - 857/343*T^4 - 222/343*T^3 + 82/49*T^2 + 2*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 5*X*Y^10 + 6*X*Y^9 + 5*X*Y^7 +
        3*X*Y^6 + 6*X*Y^5 + 6*X*Y^3 + 4*X*Y^2 + 4*X*Y + 6*X + 2*Y^30 + 4*Y^28 + 
        2*Y^27 + 3*Y^26 + Y^24 + 3*Y^23 + 6*Y^22 + 5*Y^21 + 4*Y^20 + Y^19 + Y^18 + 
        5*Y^17 + 6*Y^16 + 4*Y^15 + 3*Y^14 + 2*Y^12 + 6*Y^11 + Y^10 + Y^9 + 4*Y^8 + 
        2*Y^7 + Y^5 + 2*Y^3 + 4*Y^2 + 4*Y,
    T^56 + 2/7*T^55 + 5/49*T^54 + 188/343*T^53 + 304/2401*T^52 + 1273/2401*T^51 - 
        17/49*T^50 + 1404/2401*T^49 - 565/2401*T^48 - 1766/2401*T^47 - 438/2401*T^46
        - 2148/2401*T^45 - 692/2401*T^44 - 3291/2401*T^43 - 305/2401*T^42 - 
        1196/2401*T^41 - 1937/2401*T^40 - 561/2401*T^39 - 475/2401*T^38 + 
        72/343*T^37 - 575/2401*T^36 + 2538/2401*T^35 - 804/2401*T^34 + 
        1209/2401*T^33 + 758/2401*T^32 + 916/2401*T^31 + 1929/2401*T^30 - 
        834/2401*T^29 + 2603/2401*T^28 - 834/2401*T^27 + 1929/2401*T^26 + 
        916/2401*T^25 + 758/2401*T^24 + 1209/2401*T^23 - 804/2401*T^22 + 
        2538/2401*T^21 - 575/2401*T^20 + 72/343*T^19 - 475/2401*T^18 - 561/2401*T^17
        - 1937/2401*T^16 - 1196/2401*T^15 - 305/2401*T^14 - 3291/2401*T^13 - 
        692/2401*T^12 - 2148/2401*T^11 - 438/2401*T^10 - 1766/2401*T^9 - 
        565/2401*T^8 + 1404/2401*T^7 - 17/49*T^6 + 1273/2401*T^5 + 304/2401*T^4 + 
        188/343*T^3 + 5/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 2*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 2*X*Y^6 + 
        3*X*Y^5 + 5*X*Y^3 + 5*X*Y + 6*X + 5*Y^30 + 2*Y^29 + 2*Y^28 + 6*Y^27 + 2*Y^26
        + Y^25 + 5*Y^24 + Y^23 + Y^21 + 4*Y^20 + 6*Y^18 + 4*Y^17 + 6*Y^15 + 6*Y^14 +
        Y^13 + 6*Y^12 + 5*Y^11 + 6*Y^10 + 6*Y^9 + 2*Y^8 + 3*Y^7 + Y^6 + 3*Y^4 + Y^3 
        + 5*Y^2 + 5*Y + 6,
    T^56 + 2/7*T^55 + 4/49*T^54 + 218/343*T^53 - 22/2401*T^52 - 115/343*T^51 - 
        255/2401*T^50 + 188/2401*T^49 - 1478/2401*T^48 + 46/2401*T^47 + 
        1207/2401*T^46 - 342/2401*T^45 + 1406/2401*T^44 + 1752/2401*T^43 + 
        222/2401*T^42 - 485/2401*T^41 - 524/2401*T^40 - 960/2401*T^39 - 
        771/2401*T^38 + 6/2401*T^37 - 478/2401*T^36 + 39/2401*T^35 + 897/2401*T^34 -
        205/2401*T^33 + 454/2401*T^32 + 1164/2401*T^31 - 656/2401*T^30 - 
        930/2401*T^29 + 278/2401*T^28 - 930/2401*T^27 - 656/2401*T^26 + 
        1164/2401*T^25 + 454/2401*T^24 - 205/2401*T^23 + 897/2401*T^22 + 
        39/2401*T^21 - 478/2401*T^20 + 6/2401*T^19 - 771/2401*T^18 - 960/2401*T^17 -
        524/2401*T^16 - 485/2401*T^15 + 222/2401*T^14 + 1752/2401*T^13 + 
        1406/2401*T^12 - 342/2401*T^11 + 1207/2401*T^10 + 46/2401*T^9 - 
        1478/2401*T^8 + 188/2401*T^7 - 255/2401*T^6 - 115/343*T^5 - 22/2401*T^4 + 
        218/343*T^3 + 4/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 6*X*Y^12 + 3*X*Y^11 + 6*X*Y^9 + 4*X*Y^8 + 5*X*Y^7 + 
        3*X*Y^6 + X*Y^5 + 6*X*Y^3 + 4*X*Y^2 + X*Y + 5*X + 4*Y^30 + 6*Y^29 + 2*Y^28 +
        6*Y^27 + Y^26 + 3*Y^25 + Y^24 + 6*Y^22 + 2*Y^21 + 6*Y^20 + 3*Y^19 + 2*Y^18 +
        Y^16 + 4*Y^14 + 2*Y^13 + 4*Y^11 + 3*Y^10 + 2*Y^9 + 2*Y^7 + 6*Y^6 + 2*Y^5 + 
        4*Y^4 + 5*Y^3 + 2*Y^2 + 4*Y + 1,
    -T^56 - 1/7*T^55 - 34/49*T^54 + 216/343*T^53 + 604/2401*T^52 + 1285/2401*T^51 + 
        109/2401*T^50 - 1860/2401*T^49 - 2286/2401*T^48 - 61/49*T^47 - 
        1965/2401*T^46 + 1138/2401*T^45 + 298/2401*T^44 + 1851/2401*T^43 - 
        1573/2401*T^42 - 1170/2401*T^41 - 2881/2401*T^40 - 1292/2401*T^39 - 
        20/2401*T^38 + 869/2401*T^37 + 715/2401*T^36 - 1369/2401*T^35 - 
        2778/2401*T^34 - 2297/2401*T^33 - 1034/2401*T^32 + 1843/2401*T^31 + 
        2182/2401*T^30 + 1870/2401*T^29 - 1870/2401*T^27 - 2182/2401*T^26 - 
        1843/2401*T^25 + 1034/2401*T^24 + 2297/2401*T^23 + 2778/2401*T^22 + 
        1369/2401*T^21 - 715/2401*T^20 - 869/2401*T^19 + 20/2401*T^18 + 
        1292/2401*T^17 + 2881/2401*T^16 + 1170/2401*T^15 + 1573/2401*T^14 - 
        1851/2401*T^13 - 298/2401*T^12 - 1138/2401*T^11 + 1965/2401*T^10 + 61/49*T^9
        + 2286/2401*T^8 + 1860/2401*T^7 - 109/2401*T^6 - 1285/2401*T^5 - 
        604/2401*T^4 - 216/343*T^3 + 34/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 
        + 3*X*Y^8 + 6*X*Y^7 + 6*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 2*X*Y + 4*X + 
        2*Y^30 + 6*Y^29 + 6*Y^28 + Y^27 + 3*Y^26 + 4*Y^25 + 5*Y^24 + Y^23 + 2*Y^22 +
        5*Y^21 + 2*Y^20 + 2*Y^19 + 2*Y^18 + 3*Y^17 + 2*Y^16 + 3*Y^15 + Y^14 + Y^12 +
        4*Y^11 + 4*Y^10 + Y^9 + Y^8 + 6*Y^6 + 6*Y^5 + Y^4 + 3*Y^3 + Y^2,
    -T^56 + T^55 - 109/343*T^53 + 1354/2401*T^52 - 1390/2401*T^51 - 601/2401*T^50 + 
        1075/2401*T^49 - 75/343*T^48 + 68/343*T^47 + 452/2401*T^46 - 1179/2401*T^45 
        + 1495/2401*T^44 - 313/343*T^43 + 558/2401*T^42 + 1076/2401*T^41 - 
        939/2401*T^40 + 307/2401*T^39 - 30/2401*T^38 + 346/2401*T^37 + 533/2401*T^36
        - 1243/2401*T^35 + 1263/2401*T^34 - 1228/2401*T^33 - 183/2401*T^32 + 
        1034/2401*T^31 - 454/2401*T^30 + 375/2401*T^29 - 375/2401*T^27 + 
        454/2401*T^26 - 1034/2401*T^25 + 183/2401*T^24 + 1228/2401*T^23 - 
        1263/2401*T^22 + 1243/2401*T^21 - 533/2401*T^20 - 346/2401*T^19 + 
        30/2401*T^18 - 307/2401*T^17 + 939/2401*T^16 - 1076/2401*T^15 - 
        558/2401*T^14 + 313/343*T^13 - 1495/2401*T^12 + 1179/2401*T^11 - 
        452/2401*T^10 - 68/343*T^9 + 75/343*T^8 - 1075/2401*T^7 + 601/2401*T^6 + 
        1390/2401*T^5 - 1354/2401*T^4 + 109/343*T^3 - T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 5*X*Y^10 + 4*X*Y^9 + 3*X*Y^7 +
        X*Y^6 + 4*X*Y^5 + X*Y^3 + 2*X*Y^2 + 6*X*Y + 3*X + 2*Y^30 + 6*Y^29 + 3*Y^28 +
        Y^27 + 6*Y^26 + Y^24 + 6*Y^23 + 4*Y^22 + 4*Y^21 + 2*Y^20 + Y^19 + 4*Y^18 + 
        2*Y^17 + 3*Y^15 + 5*Y^14 + 4*Y^13 + 4*Y^12 + 5*Y^11 + 2*Y^10 + 4*Y^9 + Y^8 +
        6*Y^7 + 4*Y^5 + 5*Y^4 + 3,
    T^56 + 1/7*T^55 - 24/49*T^54 - 134/343*T^53 - 2129/2401*T^52 + 40/343*T^51 - 
        332/2401*T^50 + 1063/2401*T^49 + 2869/2401*T^48 + 464/2401*T^47 + 
        256/2401*T^46 - 1488/2401*T^45 - 2774/2401*T^44 - 71/343*T^43 - 
        1303/2401*T^42 + 1886/2401*T^41 + 499/343*T^40 + 527/2401*T^39 + 
        95/2401*T^38 - 2353/2401*T^37 - 2551/2401*T^36 - 1276/2401*T^35 - 
        380/2401*T^34 + 2715/2401*T^33 + 3464/2401*T^32 + 1977/2401*T^31 - 
        306/2401*T^30 - 2388/2401*T^29 - 2588/2401*T^28 - 2388/2401*T^27 - 
        306/2401*T^26 + 1977/2401*T^25 + 3464/2401*T^24 + 2715/2401*T^23 - 
        380/2401*T^22 - 1276/2401*T^21 - 2551/2401*T^20 - 2353/2401*T^19 + 
        95/2401*T^18 + 527/2401*T^17 + 499/343*T^16 + 1886/2401*T^15 - 
        1303/2401*T^14 - 71/343*T^13 - 2774/2401*T^12 - 1488/2401*T^11 + 
        256/2401*T^10 + 464/2401*T^9 + 2869/2401*T^8 + 1063/2401*T^7 - 332/2401*T^6 
        + 40/343*T^5 - 2129/2401*T^4 - 134/343*T^3 - 24/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 3*X*Y^13 + X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 5*X*Y^8 + 
        6*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 4*X + Y^30 + 3*Y^29 + 6*Y^28 + 4*Y^27 + 2*Y^26
        + 4*Y^25 + 4*Y^24 + 6*Y^23 + Y^22 + 6*Y^21 + 3*Y^20 + 4*Y^19 + 2*Y^18 + 
        5*Y^17 + 6*Y^16 + 6*Y^15 + 3*Y^14 + 3*Y^13 + 5*Y^12 + 5*Y^11 + 6*Y^10 + Y^9 
        + Y^8 + 6*Y^7 + 2*Y^6 + 2*Y^5 + Y^4 + 6*Y^3 + Y^2 + 2*Y + 6,
    T^56 - 11/7*T^55 + 83/49*T^54 - 605/343*T^53 + 832/2401*T^52 + 3594/2401*T^51 - 
        6120/2401*T^50 + 7675/2401*T^49 - 932/343*T^48 + 2351/2401*T^47 + 
        187/343*T^46 - 3515/2401*T^45 + 4647/2401*T^44 - 3978/2401*T^43 + 
        1840/2401*T^42 - 17/2401*T^41 - 1544/2401*T^40 + 3958/2401*T^39 - 
        3942/2401*T^38 + 1395/2401*T^37 + 719/2401*T^36 - 4856/2401*T^35 + 
        1230/343*T^34 - 8065/2401*T^33 + 5419/2401*T^32 - 796/2401*T^31 - 
        846/343*T^30 + 1467/343*T^29 - 11534/2401*T^28 + 1467/343*T^27 - 
        846/343*T^26 - 796/2401*T^25 + 5419/2401*T^24 - 8065/2401*T^23 + 
        1230/343*T^22 - 4856/2401*T^21 + 719/2401*T^20 + 1395/2401*T^19 - 
        3942/2401*T^18 + 3958/2401*T^17 - 1544/2401*T^16 - 17/2401*T^15 + 
        1840/2401*T^14 - 3978/2401*T^13 + 4647/2401*T^12 - 3515/2401*T^11 + 
        187/343*T^10 + 2351/2401*T^9 - 932/343*T^8 + 7675/2401*T^7 - 6120/2401*T^6 +
        3594/2401*T^5 + 832/2401*T^4 - 605/343*T^3 + 83/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 2*X*Y^8 +
        5*X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 6*X*Y + X + Y^30
        + 6*Y^29 + Y^28 + 5*Y^27 + 4*Y^26 + 4*Y^25 + 3*Y^24 + Y^23 + 5*Y^22 + 2*Y^21
        + 4*Y^19 + 4*Y^18 + Y^17 + 5*Y^16 + 2*Y^15 + 5*Y^14 + 5*Y^13 + 2*Y^11 + 
        5*Y^10 + Y^9 + 2*Y^8 + 3*Y^7 + 5*Y^6 + 4*Y^5 + 5*Y^4 + 6*Y^3 + 2*Y^2 + Y,
    -T^56 + 1/7*T^55 + 5/7*T^54 + 241/343*T^53 - 954/2401*T^52 - 3319/2401*T^51 - 
        52/2401*T^50 - 141/2401*T^49 + 2076/2401*T^48 + 984/2401*T^47 - 
        2175/2401*T^46 + 45/2401*T^45 - 657/2401*T^44 - 55/343*T^43 - 988/2401*T^42 
        - 5/343*T^41 + 2985/2401*T^40 - 1520/2401*T^39 - 902/2401*T^38 - 
        1214/2401*T^37 - 801/2401*T^36 + 1122/2401*T^35 + 751/2401*T^34 + 
        142/2401*T^33 - 767/2401*T^32 - 626/2401*T^31 + 823/2401*T^30 - 
        785/2401*T^29 + 785/2401*T^27 - 823/2401*T^26 + 626/2401*T^25 + 
        767/2401*T^24 - 142/2401*T^23 - 751/2401*T^22 - 1122/2401*T^21 + 
        801/2401*T^20 + 1214/2401*T^19 + 902/2401*T^18 + 1520/2401*T^17 - 
        2985/2401*T^16 + 5/343*T^15 + 988/2401*T^14 + 55/343*T^13 + 657/2401*T^12 - 
        45/2401*T^11 + 2175/2401*T^10 - 984/2401*T^9 - 2076/2401*T^8 + 141/2401*T^7 
        + 52/2401*T^6 + 3319/2401*T^5 + 954/2401*T^4 - 241/343*T^3 - 5/7*T^2 - 1/7*T
        + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^13 + X*Y^12 + 2*X*Y^10 + 4*X*Y^9 + X*Y^8 + 2*X*Y^7 + 
        2*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + X*Y^2 + 4*X*Y + 4*Y^30 + 6*Y^29 + 
        3*Y^28 + 4*Y^27 + 3*Y^26 + 2*Y^25 + 6*Y^24 + 4*Y^23 + 2*Y^22 + 3*Y^21 + 
        5*Y^20 + 6*Y^19 + 4*Y^18 + 5*Y^17 + 2*Y^16 + 5*Y^14 + 3*Y^13 + 5*Y^12 + 
        3*Y^11 + 6*Y^10 + 3*Y^8 + 5*Y^7 + 6*Y^6 + 6*Y^5 + 6*Y^3 + 2*Y^2 + 2*Y + 3,
    -T^56 + 9/49*T^54 - 64/343*T^53 + 274/343*T^51 + 850/2401*T^50 + 488/2401*T^49 -
        374/2401*T^48 + 428/2401*T^47 - 1471/2401*T^46 - 970/2401*T^45 - 37/343*T^44
        + 377/2401*T^43 - 654/2401*T^42 + 1135/2401*T^41 + 674/2401*T^40 - 
        914/2401*T^39 + 661/2401*T^38 + 1349/2401*T^37 - 1734/2401*T^36 - 
        531/2401*T^35 + 127/343*T^34 - 396/2401*T^33 - 953/2401*T^32 + 138/2401*T^31
        + 631/2401*T^30 - 101/343*T^29 + 101/343*T^27 - 631/2401*T^26 - 
        138/2401*T^25 + 953/2401*T^24 + 396/2401*T^23 - 127/343*T^22 + 531/2401*T^21
        + 1734/2401*T^20 - 1349/2401*T^19 - 661/2401*T^18 + 914/2401*T^17 - 
        674/2401*T^16 - 1135/2401*T^15 + 654/2401*T^14 - 377/2401*T^13 + 37/343*T^12
        + 970/2401*T^11 + 1471/2401*T^10 - 428/2401*T^9 + 374/2401*T^8 - 
        488/2401*T^7 - 850/2401*T^6 - 274/343*T^5 + 64/343*T^3 - 9/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 3*X*Y^9 + X*Y^8 + 
        6*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 2*X*Y + 5*X + 
        2*Y^30 + 3*Y^29 + 2*Y^28 + 3*Y^27 + 4*Y^26 + Y^25 + 4*Y^24 + 3*Y^23 + 6*Y^22
        + 6*Y^21 + 2*Y^20 + Y^19 + 3*Y^18 + 4*Y^17 + 3*Y^16 + 4*Y^15 + 4*Y^14 + 
        5*Y^13 + 2*Y^12 + 4*Y^11 + 3*Y^10 + 6*Y^9 + Y^8 + 6*Y^7 + 5*Y^6 + 6*Y^5 + 
        Y^4 + 5*Y^3 + Y^2 + Y + 3,
    -T^56 - 8/49*T^54 - 6/49*T^53 + 2692/2401*T^52 + 148/343*T^51 + 188/343*T^50 - 
        3/49*T^49 - 1125/2401*T^48 + 159/2401*T^47 - 771/2401*T^46 - 50/343*T^45 + 
        377/2401*T^44 - 408/2401*T^43 - 234/2401*T^42 - 34/2401*T^41 + 669/2401*T^40
        + 78/343*T^39 + 41/2401*T^38 + 2/2401*T^37 - 458/2401*T^36 - 640/2401*T^35 -
        426/2401*T^34 - 268/2401*T^33 + 66/2401*T^32 + 589/2401*T^31 + 155/2401*T^30
        + 554/2401*T^29 - 554/2401*T^27 - 155/2401*T^26 - 589/2401*T^25 - 
        66/2401*T^24 + 268/2401*T^23 + 426/2401*T^22 + 640/2401*T^21 + 458/2401*T^20
        - 2/2401*T^19 - 41/2401*T^18 - 78/343*T^17 - 669/2401*T^16 + 34/2401*T^15 + 
        234/2401*T^14 + 408/2401*T^13 - 377/2401*T^12 + 50/343*T^11 + 771/2401*T^10 
        - 159/2401*T^9 + 1125/2401*T^8 + 3/49*T^7 - 188/343*T^6 - 148/343*T^5 - 
        2692/2401*T^4 + 6/49*T^3 + 8/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^14 + 4*X*Y^12 + X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 4*X*Y^8 + 3*X*Y^7 + 
        5*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 6*X*Y^2 + 3*X*Y + 6*X + 3*Y^30 + 2*Y^28 + 
        5*Y^27 + 5*Y^26 + 4*Y^25 + 3*Y^24 + 2*Y^23 + 5*Y^22 + 3*Y^21 + 5*Y^20 + 
        2*Y^19 + Y^18 + 3*Y^17 + 5*Y^15 + 3*Y^14 + 4*Y^13 + 2*Y^12 + 6*Y^11 + 3*Y^10
        + Y^9 + Y^8 + 5*Y^7 + 2*Y^6 + 5*Y^5 + 4*Y^4 + 6*Y^3 + 3*Y^2 + 1,
    T^56 - 24/7*T^55 + 283/49*T^54 - 2195/343*T^53 + 11700/2401*T^52 - 
        7137/2401*T^51 + 5182/2401*T^50 - 3837/2401*T^49 + 1182/2401*T^48 + 
        303/343*T^47 - 2782/2401*T^46 + 715/2401*T^45 - 507/2401*T^44 + 
        3736/2401*T^43 - 7202/2401*T^42 + 6107/2401*T^41 - 972/2401*T^40 - 
        2936/2401*T^39 + 3564/2401*T^38 - 2952/2401*T^37 + 3397/2401*T^36 - 
        3154/2401*T^35 + 109/2401*T^34 + 3257/2401*T^33 - 3706/2401*T^32 + 
        1345/2401*T^31 - 234/2401*T^30 + 2152/2401*T^29 - 3637/2401*T^28 + 
        2152/2401*T^27 - 234/2401*T^26 + 1345/2401*T^25 - 3706/2401*T^24 + 
        3257/2401*T^23 + 109/2401*T^22 - 3154/2401*T^21 + 3397/2401*T^20 - 
        2952/2401*T^19 + 3564/2401*T^18 - 2936/2401*T^17 - 972/2401*T^16 + 
        6107/2401*T^15 - 7202/2401*T^14 + 3736/2401*T^13 - 507/2401*T^12 + 
        715/2401*T^11 - 2782/2401*T^10 + 303/343*T^9 + 1182/2401*T^8 - 3837/2401*T^7
        + 5182/2401*T^6 - 7137/2401*T^5 + 11700/2401*T^4 - 2195/343*T^3 + 283/49*T^2
        - 24/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 3*X*Y^8 + 2*X*Y^7 + X*Y^6 + 
        X*Y^5 + 4*X*Y^4 + 6*X*Y^2 + 5*X*Y + 3*X + 3*Y^30 + 4*Y^29 + 5*Y^28 + 2*Y^27 
        + 2*Y^26 + 4*Y^25 + 3*Y^24 + 5*Y^23 + 6*Y^22 + 4*Y^21 + 5*Y^20 + 5*Y^19 + 
        4*Y^18 + 6*Y^17 + 2*Y^16 + 3*Y^15 + Y^14 + Y^13 + Y^12 + 2*Y^10 + Y^9 + 
        6*Y^8 + 2*Y^7 + 3*Y^5 + 6*Y^4 + 4*Y^3 + 2*Y^2 + Y + 4,
    -T^56 + 10/7*T^55 - 47/49*T^54 + 226/343*T^53 - 1802/2401*T^52 + 2306/2401*T^51 
        - 142/2401*T^50 + 87/2401*T^49 - 1436/2401*T^48 + 1786/2401*T^47 - 
        325/2401*T^46 - 1430/2401*T^45 + 577/2401*T^44 - 233/2401*T^43 + 
        993/2401*T^42 - 640/2401*T^41 - 370/2401*T^40 + 1270/2401*T^39 - 
        569/2401*T^38 - 90/343*T^37 + 254/2401*T^36 - 46/343*T^35 - 62/2401*T^34 + 
        90/2401*T^33 + 296/2401*T^32 - 526/2401*T^31 + 1061/2401*T^30 + 79/2401*T^29
        - 79/2401*T^27 - 1061/2401*T^26 + 526/2401*T^25 - 296/2401*T^24 - 
        90/2401*T^23 + 62/2401*T^22 + 46/343*T^21 - 254/2401*T^20 + 90/343*T^19 + 
        569/2401*T^18 - 1270/2401*T^17 + 370/2401*T^16 + 640/2401*T^15 - 
        993/2401*T^14 + 233/2401*T^13 - 577/2401*T^12 + 1430/2401*T^11 + 
        325/2401*T^10 - 1786/2401*T^9 + 1436/2401*T^8 - 87/2401*T^7 + 142/2401*T^6 -
        2306/2401*T^5 + 1802/2401*T^4 - 226/343*T^3 + 47/49*T^2 - 10/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + X*Y^12 + 4*X*Y^11 + 6*X*Y^9 + X*Y^8 + 4*X*Y^7 + 
        3*X*Y^6 + 5*X*Y^4 + 2*X*Y^2 + 4*X*Y + 6*X + 5*Y^30 + 5*Y^29 + 4*Y^27 + 
        2*Y^25 + 5*Y^24 + 2*Y^23 + 2*Y^21 + Y^20 + 6*Y^19 + Y^18 + 2*Y^17 + 3*Y^16 +
        2*Y^15 + 6*Y^14 + Y^11 + 3*Y^10 + 4*Y^9 + Y^8 + 2*Y^7 + 6*Y^5 + 6*Y^4 + Y^3 
        + 5*Y^2 + 3*Y,
    -T^56 - 10/7*T^55 - 12/49*T^54 + 474/343*T^53 + 3478/2401*T^52 - 1265/2401*T^51 
        - 2837/2401*T^50 + 81/343*T^49 + 2598/2401*T^48 + 374/2401*T^47 - 
        1969/2401*T^46 + 509/2401*T^45 + 3692/2401*T^44 + 2473/2401*T^43 - 
        559/2401*T^42 - 1144/2401*T^41 + 52/2401*T^40 - 1138/2401*T^39 - 
        2420/2401*T^38 - 827/2401*T^37 + 1731/2401*T^36 + 1237/2401*T^35 - 
        45/49*T^34 - 404/343*T^33 - 857/2401*T^32 + 261/2401*T^31 - 775/2401*T^30 - 
        1859/2401*T^29 + 1859/2401*T^27 + 775/2401*T^26 - 261/2401*T^25 + 
        857/2401*T^24 + 404/343*T^23 + 45/49*T^22 - 1237/2401*T^21 - 1731/2401*T^20 
        + 827/2401*T^19 + 2420/2401*T^18 + 1138/2401*T^17 - 52/2401*T^16 + 
        1144/2401*T^15 + 559/2401*T^14 - 2473/2401*T^13 - 3692/2401*T^12 - 
        509/2401*T^11 + 1969/2401*T^10 - 374/2401*T^9 - 2598/2401*T^8 - 81/343*T^7 +
        2837/2401*T^6 + 1265/2401*T^5 - 3478/2401*T^4 - 474/343*T^3 + 12/49*T^2 + 
        10/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 4*X*Y^13 + X*Y^12 + 2*X*Y^11 + 3*X*Y^8 + 6*X*Y^7 + X*Y^6 + 
        6*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 5*X*Y + 2*X + Y^30 + 5*Y^29 + 6*Y^28
        + Y^27 + Y^26 + 3*Y^25 + 5*Y^23 + 6*Y^22 + Y^21 + 4*Y^20 + Y^19 + 4*Y^18 + 
        5*Y^17 + Y^15 + 2*Y^14 + 5*Y^13 + 4*Y^12 + 6*Y^11 + 4*Y^9 + 3*Y^8 + 4*Y^7 + 
        6*Y^6 + 5*Y^5 + 6*Y^4 + 6*Y^3 + 3,
    T^56 + T^55 - 31/49*T^54 - 386/343*T^53 - 653/2401*T^52 + 33/49*T^51 + 
        83/343*T^50 - 656/2401*T^49 - 149/343*T^48 - 606/2401*T^47 + 111/2401*T^46 +
        578/2401*T^45 + 674/2401*T^44 - 955/2401*T^43 - 690/2401*T^42 + 
        1556/2401*T^41 + 164/343*T^40 - 1611/2401*T^39 - 2430/2401*T^38 - 
        705/2401*T^37 + 2747/2401*T^36 + 2299/2401*T^35 - 962/2401*T^34 - 
        1902/2401*T^33 + 314/2401*T^32 + 1395/2401*T^31 + 396/2401*T^30 - 
        205/2401*T^29 - 1133/2401*T^28 - 205/2401*T^27 + 396/2401*T^26 + 
        1395/2401*T^25 + 314/2401*T^24 - 1902/2401*T^23 - 962/2401*T^22 + 
        2299/2401*T^21 + 2747/2401*T^20 - 705/2401*T^19 - 2430/2401*T^18 - 
        1611/2401*T^17 + 164/343*T^16 + 1556/2401*T^15 - 690/2401*T^14 - 
        955/2401*T^13 + 674/2401*T^12 + 578/2401*T^11 + 111/2401*T^10 - 606/2401*T^9
        - 149/343*T^8 - 656/2401*T^7 + 83/343*T^6 + 33/49*T^5 - 653/2401*T^4 - 
        386/343*T^3 - 31/49*T^2 + T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 5*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + 5*X*Y^8 + 5*X*Y^7 + 
        6*X*Y^3 + 4*X*Y^2 + 6*X*Y + 4*X + 2*Y^30 + 5*Y^29 + 6*Y^27 + 3*Y^26 + 5*Y^24
        + Y^23 + 6*Y^21 + 5*Y^20 + Y^19 + 6*Y^17 + 4*Y^16 + 4*Y^15 + 6*Y^14 + 4*Y^13
        + 6*Y^12 + 5*Y^11 + 2*Y^10 + 2*Y^9 + 6*Y^8 + Y^7 + 2*Y^6 + 6*Y^4 + 6*Y^3 + Y
        + 4,
    T^56 - 4/7*T^55 + 6/49*T^54 + 2/343*T^53 - 1297/2401*T^52 - 472/2401*T^51 + 
        82/343*T^50 + 866/2401*T^49 - 167/2401*T^48 + 223/2401*T^47 - 1201/2401*T^46
        - 277/2401*T^45 + 74/343*T^44 - 288/2401*T^43 + 188/343*T^42 + 
        1027/2401*T^41 - 1823/2401*T^40 + 586/2401*T^39 - 472/2401*T^38 - 
        1054/2401*T^37 + 764/2401*T^36 + 1391/2401*T^35 - 61/343*T^34 - 
        1023/2401*T^33 + 257/2401*T^32 - 1319/2401*T^31 - 610/2401*T^30 + 
        1593/2401*T^29 + 212/2401*T^28 + 1593/2401*T^27 - 610/2401*T^26 - 
        1319/2401*T^25 + 257/2401*T^24 - 1023/2401*T^23 - 61/343*T^22 + 
        1391/2401*T^21 + 764/2401*T^20 - 1054/2401*T^19 - 472/2401*T^18 + 
        586/2401*T^17 - 1823/2401*T^16 + 1027/2401*T^15 + 188/343*T^14 - 
        288/2401*T^13 + 74/343*T^12 - 277/2401*T^11 - 1201/2401*T^10 + 223/2401*T^9 
        - 167/2401*T^8 + 866/2401*T^7 + 82/343*T^6 - 472/2401*T^5 - 1297/2401*T^4 + 
        2/343*T^3 + 6/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 5*X*Y^8 + 
        4*X*Y^7 + 6*X*Y^6 + 2*X*Y^5 + X*Y^4 + 6*X*Y^3 + 6*X*Y + 5*Y^30 + Y^29 + 
        2*Y^28 + 4*Y^26 + 3*Y^25 + Y^24 + Y^22 + 2*Y^20 + 5*Y^19 + 5*Y^18 + 3*Y^17 +
        6*Y^16 + 4*Y^14 + 4*Y^13 + 2*Y^12 + 3*Y^11 + 4*Y^9 + Y^8 + 4*Y^7 + 5*Y^6 + 
        2*Y^5 + 2*Y^4 + 3*Y^3 + Y^2 + 5*Y + 5,
    -T^56 + 4/7*T^55 - T^54 - 225/343*T^53 + 1159/2401*T^52 - 181/343*T^51 - 
        13/2401*T^50 + 26/49*T^49 - 279/2401*T^48 + 114/2401*T^47 + 1528/2401*T^46 -
        1738/2401*T^45 + 2272/2401*T^44 - 691/2401*T^43 - 169/2401*T^42 + 
        1307/2401*T^41 - 1018/2401*T^40 - 351/2401*T^39 + 736/2401*T^38 - 
        1315/2401*T^37 + 998/2401*T^36 + 499/2401*T^35 - 751/2401*T^34 + 
        2938/2401*T^33 - 744/2401*T^32 + 369/2401*T^31 + 2235/2401*T^30 - 
        1405/2401*T^29 + 1405/2401*T^27 - 2235/2401*T^26 - 369/2401*T^25 + 
        744/2401*T^24 - 2938/2401*T^23 + 751/2401*T^22 - 499/2401*T^21 - 
        998/2401*T^20 + 1315/2401*T^19 - 736/2401*T^18 + 351/2401*T^17 + 
        1018/2401*T^16 - 1307/2401*T^15 + 169/2401*T^14 + 691/2401*T^13 - 
        2272/2401*T^12 + 1738/2401*T^11 - 1528/2401*T^10 - 114/2401*T^9 + 
        279/2401*T^8 - 26/49*T^7 + 13/2401*T^6 + 181/343*T^5 - 1159/2401*T^4 + 
        225/343*T^3 + T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + X*Y^10 + 5*X*Y^9 + X*Y^8 + 3*X*Y^7 + 
        5*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 3*X*Y^2 + 5*X*Y + 3*X + 6*Y^30 + Y^29 + 6*Y^28
        + 5*Y^27 + 3*Y^26 + 4*Y^25 + 5*Y^24 + Y^23 + 4*Y^22 + 3*Y^21 + 4*Y^20 + 
        3*Y^19 + 3*Y^18 + 5*Y^17 + 6*Y^16 + 5*Y^14 + Y^13 + 4*Y^11 + 5*Y^10 + Y^7 + 
        4*Y^5 + 4*Y^4 + 3*Y^3 + 4*Y^2 + 5*Y + 1,
    T^56 - 3/7*T^55 - 29/49*T^54 + 58/343*T^53 + 857/2401*T^52 - 68/2401*T^51 - 
        1011/2401*T^50 + 41/2401*T^49 + 972/2401*T^48 + 409/2401*T^47 - 
        1132/2401*T^46 - 937/2401*T^45 + 4/343*T^44 + 198/2401*T^43 + 740/2401*T^42 
        - 181/343*T^41 - 180/2401*T^40 + 740/2401*T^39 + 503/2401*T^38 - 
        130/343*T^37 - 456/2401*T^36 + 689/2401*T^35 + 1562/2401*T^34 - 
        1683/2401*T^33 - 806/2401*T^32 + 862/2401*T^31 + 573/2401*T^30 + 
        50/2401*T^29 - 258/2401*T^28 + 50/2401*T^27 + 573/2401*T^26 + 862/2401*T^25 
        - 806/2401*T^24 - 1683/2401*T^23 + 1562/2401*T^22 + 689/2401*T^21 - 
        456/2401*T^20 - 130/343*T^19 + 503/2401*T^18 + 740/2401*T^17 - 180/2401*T^16
        - 181/343*T^15 + 740/2401*T^14 + 198/2401*T^13 + 4/343*T^12 - 937/2401*T^11 
        - 1132/2401*T^10 + 409/2401*T^9 + 972/2401*T^8 + 41/2401*T^7 - 1011/2401*T^6
        - 68/2401*T^5 + 857/2401*T^4 + 58/343*T^3 - 29/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 2*X*Y^8 
        + 5*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 2*X*Y + X + 6*Y^30 + 4*Y^29 + 
        4*Y^28 + Y^27 + 3*Y^26 + 6*Y^25 + 4*Y^22 + 2*Y^21 + Y^19 + Y^18 + 4*Y^17 + 
        5*Y^16 + 5*Y^15 + 6*Y^14 + 6*Y^13 + 2*Y^12 + 4*Y^11 + 5*Y^10 + 2*Y^8 + 4*Y^7
        + Y^5 + 2*Y^4 + 3*Y^3 + 2*Y^2 + 4*Y + 3,
    T^56 + 5/7*T^55 + 19/49*T^54 + 184/343*T^53 + 1146/2401*T^52 + 874/2401*T^51 + 
        1391/2401*T^50 + 260/343*T^49 + 415/2401*T^48 + 877/2401*T^47 - 
        513/2401*T^46 - 2336/2401*T^45 - 2089/2401*T^44 - 1214/2401*T^43 - 
        1965/2401*T^42 - 2469/2401*T^41 - 2487/2401*T^40 - 3981/2401*T^39 - 
        2823/2401*T^38 - 752/2401*T^37 - 330/2401*T^36 - 530/2401*T^35 + 
        1013/2401*T^34 + 935/2401*T^33 + 1312/2401*T^32 + 2215/2401*T^31 + 
        1976/2401*T^30 + 4331/2401*T^29 + 4934/2401*T^28 + 4331/2401*T^27 + 
        1976/2401*T^26 + 2215/2401*T^25 + 1312/2401*T^24 + 935/2401*T^23 + 
        1013/2401*T^22 - 530/2401*T^21 - 330/2401*T^20 - 752/2401*T^19 - 
        2823/2401*T^18 - 3981/2401*T^17 - 2487/2401*T^16 - 2469/2401*T^15 - 
        1965/2401*T^14 - 1214/2401*T^13 - 2089/2401*T^12 - 2336/2401*T^11 - 
        513/2401*T^10 + 877/2401*T^9 + 415/2401*T^8 + 260/343*T^7 + 1391/2401*T^6 + 
        874/2401*T^5 + 1146/2401*T^4 + 184/343*T^3 + 19/49*T^2 + 5/7*T + 1
*], [*
    X^3 + X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + X*Y^9 + X*Y^8 + X*Y^7
        + X*Y^6 + 6*X*Y^5 + 3*X*Y^3 + 3*X*Y + 4*X + 4*Y^30 + 5*Y^28 + 2*Y^27 + Y^26 
        + 2*Y^25 + 2*Y^24 + 3*Y^23 + Y^21 + 4*Y^20 + 6*Y^19 + 4*Y^18 + 6*Y^17 + Y^16
        + 3*Y^15 + 5*Y^14 + 5*Y^12 + 6*Y^11 + 2*Y^9 + 5*Y^8 + 6*Y^7 + 3*Y^6 + Y^5 + 
        6*Y^4 + 3*Y^3 + Y^2 + 2*Y + 6,
    -T^56 + T^55 - 6/7*T^54 + 244/343*T^53 - 610/2401*T^52 + 298/2401*T^51 - 
        1018/2401*T^50 + 146/2401*T^49 - 691/2401*T^48 + 2039/2401*T^47 - 
        1051/2401*T^46 + 629/2401*T^45 + 221/2401*T^44 - 978/2401*T^43 + 
        431/2401*T^42 - 334/2401*T^41 + 356/343*T^40 - 155/343*T^39 + 1424/2401*T^38
        - 2003/2401*T^37 + 106/343*T^36 - 202/343*T^35 + 1350/2401*T^34 - 
        76/2401*T^33 + 1712/2401*T^32 - 1804/2401*T^31 + 258/2401*T^30 - 
        813/2401*T^29 + 813/2401*T^27 - 258/2401*T^26 + 1804/2401*T^25 - 
        1712/2401*T^24 + 76/2401*T^23 - 1350/2401*T^22 + 202/343*T^21 - 106/343*T^20
        + 2003/2401*T^19 - 1424/2401*T^18 + 155/343*T^17 - 356/343*T^16 + 
        334/2401*T^15 - 431/2401*T^14 + 978/2401*T^13 - 221/2401*T^12 - 
        629/2401*T^11 + 1051/2401*T^10 - 2039/2401*T^9 + 691/2401*T^8 - 146/2401*T^7
        + 1018/2401*T^6 - 298/2401*T^5 + 610/2401*T^4 - 244/343*T^3 + 6/7*T^2 - T + 
        1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 3*X*Y^10 + 5*X*Y^9 + 5*X*Y^8 +
        3*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + X*Y^3 + 3*X*Y^2 + 6*X*Y + 5*Y^30 + 
        3*Y^29 + 3*Y^28 + 2*Y^27 + Y^26 + Y^25 + 4*Y^24 + 6*Y^23 + Y^22 + 5*Y^20 + 
        4*Y^18 + 4*Y^17 + 5*Y^15 + 4*Y^14 + Y^13 + 5*Y^12 + 6*Y^11 + 5*Y^10 + 2*Y^9 
        + Y^8 + 4*Y^7 + 4*Y^5 + 3*Y^4 + 3*Y^3 + 5*Y^2 + 2*Y + 5,
    T^56 - 4/7*T^55 - 68/49*T^54 + 388/343*T^53 + 2032/2401*T^52 - 1741/2401*T^51 - 
        410/343*T^50 + 265/343*T^49 + 2503/2401*T^48 - 2273/2401*T^47 - 
        745/2401*T^46 + 412/2401*T^45 + 1557/2401*T^44 - 181/2401*T^43 - 
        930/2401*T^42 + 153/2401*T^41 - 563/2401*T^40 + 293/343*T^39 - 184/2401*T^38
        - 2417/2401*T^37 + 144/2401*T^36 + 362/343*T^35 + 598/2401*T^34 - 
        3156/2401*T^33 - 9/2401*T^32 + 1760/2401*T^31 - 160/2401*T^30 - 
        272/2401*T^29 - 346/2401*T^28 - 272/2401*T^27 - 160/2401*T^26 + 
        1760/2401*T^25 - 9/2401*T^24 - 3156/2401*T^23 + 598/2401*T^22 + 362/343*T^21
        + 144/2401*T^20 - 2417/2401*T^19 - 184/2401*T^18 + 293/343*T^17 - 
        563/2401*T^16 + 153/2401*T^15 - 930/2401*T^14 - 181/2401*T^13 + 
        1557/2401*T^12 + 412/2401*T^11 - 745/2401*T^10 - 2273/2401*T^9 + 
        2503/2401*T^8 + 265/343*T^7 - 410/343*T^6 - 1741/2401*T^5 + 2032/2401*T^4 + 
        388/343*T^3 - 68/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 6*X*Y^7 
        + 6*X*Y^6 + X*Y^5 + X*Y^4 + 5*X*Y^2 + 3*X*Y + 3*X + 2*Y^30 + 5*Y^29 + 2*Y^28
        + 5*Y^26 + 2*Y^23 + 3*Y^22 + 5*Y^21 + 6*Y^20 + Y^19 + 6*Y^18 + 4*Y^17 + 
        3*Y^16 + 3*Y^15 + 5*Y^13 + 4*Y^12 + 5*Y^11 + 6*Y^10 + 6*Y^9 + 6*Y^8 + 5*Y^7 
        + 3*Y^6 + 3*Y^5 + 4*Y^4 + 4*Y^2 + Y + 4,
    -T^56 + 4/7*T^55 - 2/49*T^54 + 5/49*T^53 - 411/2401*T^52 - 11/2401*T^51 + 
        1361/2401*T^50 + 106/2401*T^49 - 421/2401*T^48 - 895/2401*T^47 + 
        1859/2401*T^46 + 2/49*T^45 - 677/2401*T^44 - 487/2401*T^43 + 701/2401*T^42 -
        156/2401*T^41 - 1110/2401*T^40 - 33/343*T^39 + 1149/2401*T^38 + 
        330/2401*T^37 - 606/2401*T^36 - 384/2401*T^35 + 958/2401*T^34 + 
        816/2401*T^33 - 121/2401*T^32 - 505/2401*T^31 + 552/2401*T^30 + 
        1178/2401*T^29 - 1178/2401*T^27 - 552/2401*T^26 + 505/2401*T^25 + 
        121/2401*T^24 - 816/2401*T^23 - 958/2401*T^22 + 384/2401*T^21 + 
        606/2401*T^20 - 330/2401*T^19 - 1149/2401*T^18 + 33/343*T^17 + 
        1110/2401*T^16 + 156/2401*T^15 - 701/2401*T^14 + 487/2401*T^13 + 
        677/2401*T^12 - 2/49*T^11 - 1859/2401*T^10 + 895/2401*T^9 + 421/2401*T^8 - 
        106/2401*T^7 - 1361/2401*T^6 + 11/2401*T^5 + 411/2401*T^4 - 5/49*T^3 + 
        2/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 6*X*Y^11 + 5*X*Y^9 + 5*X*Y^8 + 6*X*Y^7 + 
        3*X*Y^6 + 2*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 5*X*Y + 2*X + 4*Y^30 + 6*Y^29 + 
        5*Y^26 + 5*Y^25 + 6*Y^24 + Y^23 + Y^22 + 6*Y^21 + 6*Y^20 + 4*Y^19 + 5*Y^18 +
        4*Y^17 + 6*Y^15 + 2*Y^14 + 4*Y^12 + 3*Y^11 + Y^10 + Y^9 + Y^7 + 4*Y^6 + 
        3*Y^5 + 6*Y^4 + 4*Y^2 + 4,
    T^56 + 13/7*T^55 + 108/49*T^54 + 950/343*T^53 + 7584/2401*T^52 + 5592/2401*T^51 
        + 2085/2401*T^50 + 404/2401*T^49 - 1739/2401*T^48 - 569/343*T^47 - 
        4241/2401*T^46 - 3060/2401*T^45 - 2907/2401*T^44 - 2566/2401*T^43 - 
        652/2401*T^42 + 604/2401*T^41 + 873/2401*T^40 + 1166/2401*T^39 + 
        1892/2401*T^38 + 2406/2401*T^37 + 1968/2401*T^36 + 30/49*T^35 + 
        2626/2401*T^34 + 2448/2401*T^33 - 110/343*T^32 - 3792/2401*T^31 - 
        6199/2401*T^30 - 9446/2401*T^29 - 11526/2401*T^28 - 9446/2401*T^27 - 
        6199/2401*T^26 - 3792/2401*T^25 - 110/343*T^24 + 2448/2401*T^23 + 
        2626/2401*T^22 + 30/49*T^21 + 1968/2401*T^20 + 2406/2401*T^19 + 
        1892/2401*T^18 + 1166/2401*T^17 + 873/2401*T^16 + 604/2401*T^15 - 
        652/2401*T^14 - 2566/2401*T^13 - 2907/2401*T^12 - 3060/2401*T^11 - 
        4241/2401*T^10 - 569/343*T^9 - 1739/2401*T^8 + 404/2401*T^7 + 2085/2401*T^6 
        + 5592/2401*T^5 + 7584/2401*T^4 + 950/343*T^3 + 108/49*T^2 + 13/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 
        3*X*Y^8 + X*Y^7 + 5*X*Y^6 + 6*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 3*X*Y + 5*X + 
        6*Y^30 + Y^29 + 3*Y^28 + 5*Y^27 + 2*Y^26 + 5*Y^24 + 5*Y^23 + 4*Y^22 + 2*Y^21
        + 5*Y^19 + 3*Y^18 + 3*Y^17 + 4*Y^16 + 2*Y^14 + 2*Y^13 + 2*Y^12 + 4*Y^11 + 
        5*Y^10 + 4*Y^9 + Y^8 + Y^7 + 4*Y^6 + Y^5 + 5*Y^4 + 3*Y^2 + 4*Y + 2,
    -T^56 - T^55 + 34/49*T^54 + 540/343*T^53 + 505/2401*T^52 - 2216/2401*T^51 - 
        1311/2401*T^50 + 771/2401*T^49 + 1157/2401*T^48 - 115/343*T^47 - 
        1095/2401*T^46 - 185/2401*T^45 + 94/2401*T^44 + 641/2401*T^43 + 
        2810/2401*T^42 + 666/2401*T^41 - 4125/2401*T^40 - 461/343*T^39 + 
        3382/2401*T^38 + 5940/2401*T^37 + 275/2401*T^36 - 6138/2401*T^35 - 
        3195/2401*T^34 + 3084/2401*T^33 + 3873/2401*T^32 - 33/343*T^31 - 
        1616/2401*T^30 - 633/2401*T^29 + 633/2401*T^27 + 1616/2401*T^26 + 
        33/343*T^25 - 3873/2401*T^24 - 3084/2401*T^23 + 3195/2401*T^22 + 
        6138/2401*T^21 - 275/2401*T^20 - 5940/2401*T^19 - 3382/2401*T^18 + 
        461/343*T^17 + 4125/2401*T^16 - 666/2401*T^15 - 2810/2401*T^14 - 
        641/2401*T^13 - 94/2401*T^12 + 185/2401*T^11 + 1095/2401*T^10 + 115/343*T^9 
        - 1157/2401*T^8 - 771/2401*T^7 + 1311/2401*T^6 + 2216/2401*T^5 - 
        505/2401*T^4 - 540/343*T^3 - 34/49*T^2 + T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 
        2*X*Y^8 + 6*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + X*Y^3 + 4*X*Y^2 + 5*X*Y + 
        3*Y^30 + Y^29 + Y^28 + 4*Y^27 + 5*Y^26 + Y^25 + 3*Y^24 + 5*Y^23 + 3*Y^22 + 
        4*Y^20 + 5*Y^19 + 5*Y^18 + 4*Y^17 + 2*Y^16 + 2*Y^15 + 5*Y^14 + 4*Y^13 + 
        6*Y^12 + 3*Y^11 + 5*Y^10 + 4*Y^9 + 3*Y^8 + 4*Y^7 + Y^6 + 5*Y^5 + 6*Y^4 + 
        2*Y^3 + 5*Y^2 + 5,
    T^56 - 3/7*T^55 - 80/49*T^54 + 492/343*T^53 + 2234/2401*T^52 - 2495/2401*T^51 - 
        1012/2401*T^50 + 93/343*T^49 + 1293/2401*T^48 - 136/2401*T^47 + 
        214/2401*T^46 - 1136/2401*T^45 - 2588/2401*T^44 + 2067/2401*T^43 + 
        3706/2401*T^42 - 2449/2401*T^41 - 2902/2401*T^40 + 913/2401*T^39 + 
        752/2401*T^38 + 2398/2401*T^37 - 408/2401*T^36 - 5466/2401*T^35 + 
        47/343*T^34 + 835/343*T^33 + 30/2401*T^32 - 3984/2401*T^31 - 78/343*T^30 + 
        1329/2401*T^29 + 142/343*T^28 + 1329/2401*T^27 - 78/343*T^26 - 
        3984/2401*T^25 + 30/2401*T^24 + 835/343*T^23 + 47/343*T^22 - 5466/2401*T^21 
        - 408/2401*T^20 + 2398/2401*T^19 + 752/2401*T^18 + 913/2401*T^17 - 
        2902/2401*T^16 - 2449/2401*T^15 + 3706/2401*T^14 + 2067/2401*T^13 - 
        2588/2401*T^12 - 1136/2401*T^11 + 214/2401*T^10 - 136/2401*T^9 + 
        1293/2401*T^8 + 93/343*T^7 - 1012/2401*T^6 - 2495/2401*T^5 + 2234/2401*T^4 +
        492/343*T^3 - 80/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 5*X*Y^13 + X*Y^12 + 2*X*Y^11 + 3*X*Y^9 + 6*X*Y^8 + 4*X*Y^7 + 
        2*X*Y^6 + 5*X*Y^4 + X*Y^3 + 3*X*Y^2 + 2*X*Y + 4*X + 5*Y^30 + 5*Y^29 + Y^28 +
        Y^27 + 6*Y^26 + Y^24 + 4*Y^22 + 4*Y^21 + Y^20 + 6*Y^19 + 6*Y^18 + 2*Y^16 + 
        4*Y^15 + 2*Y^14 + 4*Y^12 + 5*Y^11 + 4*Y^10 + 2*Y^9 + 2*Y^7 + 3*Y^6 + 2*Y^5 +
        4*Y^4 + 6*Y^3 + 6*Y^2 + 3*Y + 3,
    T^56 + 2*T^55 + 34/49*T^54 - 685/343*T^53 - 9096/2401*T^52 - 4682/2401*T^51 + 
        5578/2401*T^50 + 8745/2401*T^49 + 3561/2401*T^48 - 466/343*T^47 - 
        6001/2401*T^46 - 2742/2401*T^45 + 237/2401*T^44 + 381/343*T^43 + 
        691/343*T^42 + 2640/2401*T^41 - 1618/2401*T^40 - 5613/2401*T^39 - 
        643/343*T^38 + 1781/2401*T^37 + 5070/2401*T^36 + 4385/2401*T^35 + 
        115/2401*T^34 - 3776/2401*T^33 - 3337/2401*T^32 - 2193/2401*T^31 + 
        652/2401*T^30 + 2745/2401*T^29 + 2277/2401*T^28 + 2745/2401*T^27 + 
        652/2401*T^26 - 2193/2401*T^25 - 3337/2401*T^24 - 3776/2401*T^23 + 
        115/2401*T^22 + 4385/2401*T^21 + 5070/2401*T^20 + 1781/2401*T^19 - 
        643/343*T^18 - 5613/2401*T^17 - 1618/2401*T^16 + 2640/2401*T^15 + 
        691/343*T^14 + 381/343*T^13 + 237/2401*T^12 - 2742/2401*T^11 - 
        6001/2401*T^10 - 466/343*T^9 + 3561/2401*T^8 + 8745/2401*T^7 + 5578/2401*T^6
        - 4682/2401*T^5 - 9096/2401*T^4 - 685/343*T^3 + 34/49*T^2 + 2*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 
        + X*Y^8 + 6*X*Y^7 + X*Y^3 + 2*X*Y^2 + X*Y + 4*X + 4*Y^30 + 2*Y^29 + Y^28 + 
        2*Y^27 + Y^26 + Y^25 + 3*Y^22 + 6*Y^21 + 5*Y^20 + 2*Y^19 + 5*Y^18 + 4*Y^17 +
        5*Y^16 + Y^15 + 4*Y^14 + 3*Y^13 + 5*Y^12 + 6*Y^11 + 4*Y^10 + 4*Y^9 + 3*Y^8 +
        6*Y^7 + 6*Y^6 + Y^5 + 6*Y^4 + 4*Y^2 + 3*Y,
    -T^56 - 8/7*T^55 - 22/49*T^54 + 40/49*T^53 + 2848/2401*T^52 + 2318/2401*T^51 + 
        115/343*T^50 - 482/2401*T^49 - 2314/2401*T^48 - 2291/2401*T^47 - 
        438/2401*T^46 + 1978/2401*T^45 + 1090/2401*T^44 - 1341/2401*T^43 - 
        3599/2401*T^42 - 401/343*T^41 - 921/2401*T^40 + 2003/2401*T^39 + 
        4428/2401*T^38 + 4429/2401*T^37 + 848/2401*T^36 - 1566/2401*T^35 - 
        2015/2401*T^34 - 1679/2401*T^33 - 341/343*T^32 - 2073/2401*T^31 - 
        239/2401*T^30 + 771/2401*T^29 - 771/2401*T^27 + 239/2401*T^26 + 
        2073/2401*T^25 + 341/343*T^24 + 1679/2401*T^23 + 2015/2401*T^22 + 
        1566/2401*T^21 - 848/2401*T^20 - 4429/2401*T^19 - 4428/2401*T^18 - 
        2003/2401*T^17 + 921/2401*T^16 + 401/343*T^15 + 3599/2401*T^14 + 
        1341/2401*T^13 - 1090/2401*T^12 - 1978/2401*T^11 + 438/2401*T^10 + 
        2291/2401*T^9 + 2314/2401*T^8 + 482/2401*T^7 - 115/343*T^6 - 2318/2401*T^5 -
        2848/2401*T^4 - 40/49*T^3 + 22/49*T^2 + 8/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 6*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 5*X*Y^8 + 
        X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 6*X*Y + X + 6*Y^30 + 2*Y^29 
        + 3*Y^28 + 5*Y^27 + 3*Y^26 + 3*Y^25 + Y^24 + 4*Y^23 + 5*Y^22 + Y^21 + 4*Y^20
        + 4*Y^18 + 5*Y^17 + 5*Y^16 + 5*Y^15 + Y^14 + 2*Y^13 + 3*Y^12 + 3*Y^11 + 
        2*Y^10 + 3*Y^9 + Y^8 + 3*Y^7 + 3*Y^6 + 6*Y^5 + 4*Y^4 + 6*Y^3 + 3*Y + 4,
    -T^56 + 5/7*T^55 + 30/49*T^54 - 177/343*T^53 - 893/2401*T^52 + 1119/2401*T^51 + 
        390/2401*T^50 - 127/2401*T^49 - 523/2401*T^48 - 22/2401*T^47 + 691/2401*T^46
        + 246/2401*T^45 - 607/2401*T^44 - 1151/2401*T^43 + 1328/2401*T^42 + 
        144/2401*T^41 - 453/2401*T^40 + 24/2401*T^39 - 726/2401*T^38 + 65/2401*T^37 
        + 1315/2401*T^36 - 635/2401*T^35 - 247/2401*T^34 - 51/343*T^33 + 
        103/2401*T^32 + 545/2401*T^31 - 22/2401*T^30 - 528/2401*T^29 + 528/2401*T^27
        + 22/2401*T^26 - 545/2401*T^25 - 103/2401*T^24 + 51/343*T^23 + 247/2401*T^22
        + 635/2401*T^21 - 1315/2401*T^20 - 65/2401*T^19 + 726/2401*T^18 - 
        24/2401*T^17 + 453/2401*T^16 - 144/2401*T^15 - 1328/2401*T^14 + 
        1151/2401*T^13 + 607/2401*T^12 - 246/2401*T^11 - 691/2401*T^10 + 22/2401*T^9
        + 523/2401*T^8 + 127/2401*T^7 - 390/2401*T^6 - 1119/2401*T^5 + 893/2401*T^4 
        + 177/343*T^3 - 30/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 4*X*Y^9 + X*Y^8 + 4*X*Y^7 + 
        3*X*Y^6 + 4*X*Y^5 + X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 6*X*Y + 4*Y^30 + 2*Y^28 + 
        4*Y^27 + 6*Y^26 + 6*Y^25 + 5*Y^24 + 5*Y^23 + 4*Y^22 + 4*Y^20 + 4*Y^19 + 
        5*Y^17 + 4*Y^15 + 4*Y^14 + 6*Y^13 + 6*Y^12 + 5*Y^11 + 4*Y^10 + 2*Y^9 + Y^8 +
        5*Y^7 + 2*Y^6 + 5*Y^3 + 5*Y^2 + 6*Y + 2,
    -T^56 - 10/7*T^55 - 10/7*T^54 - 191/343*T^53 + 1275/2401*T^52 + 2337/2401*T^51 +
        1381/2401*T^50 - 859/2401*T^49 - 1850/2401*T^48 - 709/2401*T^47 + 
        1231/2401*T^46 + 296/343*T^45 + 165/343*T^44 + 135/2401*T^43 - 795/2401*T^42
        + 225/2401*T^41 + 1944/2401*T^40 + 556/343*T^39 + 573/343*T^38 + 
        2824/2401*T^37 + 1549/2401*T^36 + 717/2401*T^35 + 96/343*T^34 + 
        340/2401*T^33 + 29/343*T^32 + 215/2401*T^31 + 33/2401*T^30 - 33/2401*T^26 - 
        215/2401*T^25 - 29/343*T^24 - 340/2401*T^23 - 96/343*T^22 - 717/2401*T^21 - 
        1549/2401*T^20 - 2824/2401*T^19 - 573/343*T^18 - 556/343*T^17 - 
        1944/2401*T^16 - 225/2401*T^15 + 795/2401*T^14 - 135/2401*T^13 - 
        165/343*T^12 - 296/343*T^11 - 1231/2401*T^10 + 709/2401*T^9 + 1850/2401*T^8 
        + 859/2401*T^7 - 1381/2401*T^6 - 2337/2401*T^5 - 1275/2401*T^4 + 191/343*T^3
        + 10/7*T^2 + 10/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 
        X*Y^8 + X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 3*X*Y + 
        2*X + 3*Y^30 + Y^29 + 4*Y^28 + 4*Y^27 + Y^26 + 2*Y^25 + 6*Y^23 + 5*Y^22 + 
        5*Y^21 + Y^18 + 4*Y^17 + Y^16 + 6*Y^15 + 4*Y^14 + 2*Y^13 + 6*Y^12 + 3*Y^10 +
        3*Y^9 + Y^7 + Y^6 + 5*Y^5 + 3*Y^3 + 3*Y^2 + 2*Y,
    T^56 - 3/7*T^55 - 12/49*T^54 + 37/49*T^53 - 1791/2401*T^52 - 892/2401*T^51 + 
        1699/2401*T^50 + 1160/2401*T^49 - 96/343*T^48 + 1534/2401*T^47 + 
        1545/2401*T^46 - 1741/2401*T^45 - 943/2401*T^44 + 1810/2401*T^43 - 
        1258/2401*T^42 - 341/2401*T^41 + 2073/2401*T^40 - 1058/2401*T^39 + 
        115/343*T^38 + 41/49*T^37 - 1672/2401*T^36 + 992/2401*T^35 + 934/2401*T^34 -
        2028/2401*T^33 + 32/343*T^32 + 1261/2401*T^31 - 692/2401*T^30 - 90/2401*T^29
        + 2994/2401*T^28 - 90/2401*T^27 - 692/2401*T^26 + 1261/2401*T^25 + 
        32/343*T^24 - 2028/2401*T^23 + 934/2401*T^22 + 992/2401*T^21 - 
        1672/2401*T^20 + 41/49*T^19 + 115/343*T^18 - 1058/2401*T^17 + 2073/2401*T^16
        - 341/2401*T^15 - 1258/2401*T^14 + 1810/2401*T^13 - 943/2401*T^12 - 
        1741/2401*T^11 + 1545/2401*T^10 + 1534/2401*T^9 - 96/343*T^8 + 1160/2401*T^7
        + 1699/2401*T^6 - 892/2401*T^5 - 1791/2401*T^4 + 37/49*T^3 - 12/49*T^2 - 
        3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 2*X*Y^8 + 4*X*Y^7 +
        4*X*Y^6 + X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + X + 4*Y^30 + Y^29 + 4*Y^28 + 3*Y^27 + 
        5*Y^26 + 4*Y^25 + 5*Y^24 + 6*Y^22 + 6*Y^21 + 2*Y^20 + 4*Y^19 + 6*Y^18 + 
        3*Y^17 + 5*Y^16 + 6*Y^15 + 3*Y^13 + 4*Y^12 + Y^8 + 2*Y^6 + 3*Y^5 + 2*Y^4 + 
        6*Y^3 + 5*Y^2 + 3*Y + 6,
    T^56 - 2/7*T^55 - 32/49*T^54 + 222/343*T^53 - 391/2401*T^52 - 446/2401*T^51 + 
        159/2401*T^50 - 1521/2401*T^49 + 47/2401*T^48 + 85/343*T^47 - 1388/2401*T^46
        - 241/2401*T^45 + 1737/2401*T^44 + 393/2401*T^43 - 145/2401*T^42 + 
        53/343*T^41 - 24/343*T^40 + 22/49*T^39 + 487/2401*T^38 - 978/2401*T^37 - 
        661/2401*T^36 + 549/2401*T^35 - 838/2401*T^34 - 1340/2401*T^33 + 
        118/343*T^32 - 823/2401*T^31 + 628/2401*T^30 + 1405/2401*T^29 - 
        1903/2401*T^28 + 1405/2401*T^27 + 628/2401*T^26 - 823/2401*T^25 + 
        118/343*T^24 - 1340/2401*T^23 - 838/2401*T^22 + 549/2401*T^21 - 
        661/2401*T^20 - 978/2401*T^19 + 487/2401*T^18 + 22/49*T^17 - 24/343*T^16 + 
        53/343*T^15 - 145/2401*T^14 + 393/2401*T^13 + 1737/2401*T^12 - 241/2401*T^11
        - 1388/2401*T^10 + 85/343*T^9 + 47/2401*T^8 - 1521/2401*T^7 + 159/2401*T^6 -
        446/2401*T^5 - 391/2401*T^4 + 222/343*T^3 - 32/49*T^2 - 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        3*X*Y^8 + 6*X*Y^7 + X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X + 4*Y^30 + 
        3*Y^29 + 4*Y^28 + Y^27 + 6*Y^26 + 3*Y^24 + 2*Y^23 + 2*Y^22 + 4*Y^21 + 4*Y^19
        + 4*Y^17 + 3*Y^16 + 3*Y^15 + 5*Y^14 + 5*Y^13 + 4*Y^12 + 3*Y^11 + 3*Y^10 + 
        4*Y^8 + 6*Y^7 + 6*Y^6 + 2*Y^5 + 3*Y^4 + Y^3 + 5*Y + 2,
    T^56 - 4/7*T^55 + 5/49*T^54 - 299/343*T^53 - 73/2401*T^52 - 32/343*T^51 + 
        101/2401*T^50 - 29/2401*T^49 + 1361/2401*T^48 - 646/2401*T^47 + 
        488/2401*T^46 - 1081/2401*T^45 + 89/2401*T^44 + 608/2401*T^43 - 82/343*T^42 
        + 1511/2401*T^41 + 4/2401*T^40 + 942/2401*T^39 + 187/2401*T^38 - 
        136/343*T^37 - 1194/2401*T^36 - 121/2401*T^35 - 523/2401*T^34 + 5/7*T^33 - 
        1356/2401*T^32 + 205/343*T^31 - 326/2401*T^30 + 22/2401*T^29 - 
        1074/2401*T^28 + 22/2401*T^27 - 326/2401*T^26 + 205/343*T^25 - 
        1356/2401*T^24 + 5/7*T^23 - 523/2401*T^22 - 121/2401*T^21 - 1194/2401*T^20 -
        136/343*T^19 + 187/2401*T^18 + 942/2401*T^17 + 4/2401*T^16 + 1511/2401*T^15 
        - 82/343*T^14 + 608/2401*T^13 + 89/2401*T^12 - 1081/2401*T^11 + 
        488/2401*T^10 - 646/2401*T^9 + 1361/2401*T^8 - 29/2401*T^7 + 101/2401*T^6 - 
        32/343*T^5 - 73/2401*T^4 - 299/343*T^3 + 5/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + X*Y^7 + 
        5*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + X*Y^2 + 6*X*Y + 3*X + 2*Y^30 + 
        3*Y^29 + Y^28 + 6*Y^27 + 2*Y^26 + 6*Y^25 + 3*Y^24 + 2*Y^23 + 6*Y^22 + 5*Y^21
        + Y^20 + 5*Y^19 + 4*Y^18 + 4*Y^17 + 6*Y^15 + 4*Y^13 + 2*Y^12 + 6*Y^11 + Y^10
        + 3*Y^7 + 2*Y^5 + Y^4 + 5*Y^3 + 4*Y^2 + Y + 2,
    T^56 + 1/7*T^55 - 26/49*T^54 + 48/49*T^53 - 1413/2401*T^52 - 2346/2401*T^51 + 
        739/2401*T^50 - 1819/2401*T^49 - 296/343*T^48 + 2329/2401*T^47 - 30/343*T^46
        - 92/343*T^45 + 3718/2401*T^44 - 137/2401*T^43 + 40/2401*T^42 + 
        2081/2401*T^41 - 1129/2401*T^40 - 1373/2401*T^39 + 520/2401*T^38 - 
        1924/2401*T^37 - 1195/2401*T^36 + 184/343*T^35 - 146/343*T^34 + 
        631/2401*T^33 + 178/343*T^32 - 1336/2401*T^31 + 1357/2401*T^30 + 
        1039/2401*T^29 - 2444/2401*T^28 + 1039/2401*T^27 + 1357/2401*T^26 - 
        1336/2401*T^25 + 178/343*T^24 + 631/2401*T^23 - 146/343*T^22 + 184/343*T^21 
        - 1195/2401*T^20 - 1924/2401*T^19 + 520/2401*T^18 - 1373/2401*T^17 - 
        1129/2401*T^16 + 2081/2401*T^15 + 40/2401*T^14 - 137/2401*T^13 + 
        3718/2401*T^12 - 92/343*T^11 - 30/343*T^10 + 2329/2401*T^9 - 296/343*T^8 - 
        1819/2401*T^7 + 739/2401*T^6 - 2346/2401*T^5 - 1413/2401*T^4 + 48/49*T^3 - 
        26/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 6*X*Y^12 + 6*X*Y^9 + 3*X*Y^7 + X*Y^6 + 5*X*Y^4 + 2*X*Y^3 + 
        5*X*Y^2 + 3*X*Y + X + 2*Y^30 + 3*Y^29 + 5*Y^28 + 5*Y^27 + Y^25 + Y^24 + 
        4*Y^23 + 5*Y^22 + 4*Y^21 + 6*Y^20 + 2*Y^19 + 3*Y^18 + 2*Y^17 + Y^16 + 5*Y^14
        + 6*Y^13 + Y^12 + 6*Y^11 + 4*Y^10 + 3*Y^9 + 3*Y^8 + 6*Y^7 + Y^5 + 6*Y^4 + 
        2*Y^3 + 4*Y^2 + 6*Y + 6,
    -T^56 + 8/7*T^55 + 27/49*T^54 - 523/343*T^53 + 2683/2401*T^52 - 146/343*T^51 - 
        314/2401*T^50 + 1935/2401*T^49 - 3331/2401*T^48 + 2467/2401*T^47 - 
        415/2401*T^46 - 1898/2401*T^45 + 3566/2401*T^44 - 3537/2401*T^43 + 
        43/2401*T^42 + 3653/2401*T^41 - 3595/2401*T^40 + 1422/2401*T^39 + 
        559/2401*T^38 - 1214/2401*T^37 + 2075/2401*T^36 - 2150/2401*T^35 + 
        15/49*T^34 - 80/2401*T^33 - 1480/2401*T^32 + 382/343*T^31 - 145/343*T^30 - 
        829/2401*T^29 + 829/2401*T^27 + 145/343*T^26 - 382/343*T^25 + 1480/2401*T^24
        + 80/2401*T^23 - 15/49*T^22 + 2150/2401*T^21 - 2075/2401*T^20 + 
        1214/2401*T^19 - 559/2401*T^18 - 1422/2401*T^17 + 3595/2401*T^16 - 
        3653/2401*T^15 - 43/2401*T^14 + 3537/2401*T^13 - 3566/2401*T^12 + 
        1898/2401*T^11 + 415/2401*T^10 - 2467/2401*T^9 + 3331/2401*T^8 - 
        1935/2401*T^7 + 314/2401*T^6 + 146/343*T^5 - 2683/2401*T^4 + 523/343*T^3 - 
        27/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 3*X*Y^6 + 3*X*Y^4 + 6*X*Y^3 + X*Y + 4*X + Y^30 + 4*Y^29 + 5*Y^28 +
        2*Y^25 + Y^24 + 4*Y^23 + 3*Y^22 + 6*Y^21 + 4*Y^20 + 2*Y^19 + 5*Y^18 + Y^17 +
        6*Y^16 + 3*Y^15 + 2*Y^14 + Y^12 + 6*Y^11 + 3*Y^9 + 2*Y^8 + Y^7 + 2*Y^5 + 
        3*Y^4 + 5*Y^2 + 3*Y + 3,
    T^56 - 23/49*T^54 + 393/343*T^53 + 2377/2401*T^52 - 1677/2401*T^51 + 
        1560/2401*T^50 + 3293/2401*T^49 - 433/2401*T^48 - 85/2401*T^47 + 
        3221/2401*T^46 + 488/2401*T^45 - 515/2401*T^44 + 295/343*T^43 + 
        1422/2401*T^42 - 83/2401*T^41 + 1079/2401*T^40 + 2106/2401*T^39 + 
        612/2401*T^38 + 324/2401*T^37 + 2042/2401*T^36 + 1241/2401*T^35 - 
        24/2401*T^34 + 940/2401*T^33 + 1677/2401*T^32 + 53/2401*T^31 + 544/2401*T^30
        + 596/2401*T^29 + 128/2401*T^28 + 596/2401*T^27 + 544/2401*T^26 + 
        53/2401*T^25 + 1677/2401*T^24 + 940/2401*T^23 - 24/2401*T^22 + 
        1241/2401*T^21 + 2042/2401*T^20 + 324/2401*T^19 + 612/2401*T^18 + 
        2106/2401*T^17 + 1079/2401*T^16 - 83/2401*T^15 + 1422/2401*T^14 + 
        295/343*T^13 - 515/2401*T^12 + 488/2401*T^11 + 3221/2401*T^10 - 85/2401*T^9 
        - 433/2401*T^8 + 3293/2401*T^7 + 1560/2401*T^6 - 1677/2401*T^5 + 
        2377/2401*T^4 + 393/343*T^3 - 23/49*T^2 + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^13 + 3*X*Y^12 + X*Y^11 + 6*X*Y^9 + 2*X*Y^7 + 2*X*Y^4 + 
        2*X*Y^3 + 3*X*Y^2 + X*Y + 4*X + 3*Y^30 + 5*Y^29 + 2*Y^28 + 5*Y^27 + 6*Y^26 +
        5*Y^25 + 6*Y^24 + 4*Y^23 + 4*Y^21 + Y^20 + 4*Y^19 + Y^16 + 6*Y^15 + 2*Y^14 +
        4*Y^13 + Y^12 + 6*Y^11 + Y^10 + 3*Y^9 + 6*Y^8 + 3*Y^7 + 3*Y^6 + 2*Y^4 + Y^3 
        + 5*Y^2 + 6*Y + 1,
    T^56 + 5/7*T^55 - 13/49*T^54 + 29/49*T^53 + 871/2401*T^52 - 3350/2401*T^51 - 
        517/343*T^50 - 394/2401*T^49 + 338/2401*T^48 - 1108/2401*T^47 - 71/343*T^46 
        + 3735/2401*T^45 + 2108/2401*T^44 - 2830/2401*T^43 + 8/49*T^42 + 
        3203/2401*T^41 - 1461/2401*T^40 - 2979/2401*T^39 + 1271/2401*T^38 + 
        956/2401*T^37 - 2613/2401*T^36 - 2955/2401*T^35 + 1649/2401*T^34 + 
        1542/2401*T^33 - 58/49*T^32 - 303/2401*T^31 + 3697/2401*T^30 + 
        1319/2401*T^29 - 1916/2401*T^28 + 1319/2401*T^27 + 3697/2401*T^26 - 
        303/2401*T^25 - 58/49*T^24 + 1542/2401*T^23 + 1649/2401*T^22 - 
        2955/2401*T^21 - 2613/2401*T^20 + 956/2401*T^19 + 1271/2401*T^18 - 
        2979/2401*T^17 - 1461/2401*T^16 + 3203/2401*T^15 + 8/49*T^14 - 
        2830/2401*T^13 + 2108/2401*T^12 + 3735/2401*T^11 - 71/343*T^10 - 
        1108/2401*T^9 + 338/2401*T^8 - 394/2401*T^7 - 517/343*T^6 - 3350/2401*T^5 + 
        871/2401*T^4 + 29/49*T^3 - 13/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        X*Y^8 + 6*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 5*X*Y + 
        2*X + 6*Y^30 + 3*Y^29 + 5*Y^28 + 2*Y^27 + 6*Y^26 + Y^25 + 6*Y^24 + 4*Y^23 + 
        2*Y^22 + 2*Y^21 + 6*Y^20 + 4*Y^19 + 3*Y^18 + 6*Y^17 + 6*Y^16 + 5*Y^15 + 
        2*Y^14 + 6*Y^13 + 5*Y^11 + 4*Y^10 + 5*Y^9 + Y^8 + 3*Y^7 + 6*Y^6 + 6*Y^5 + 
        2*Y^4 + Y^3 + 5*Y^2 + 3*Y + 6,
    -T^56 - 11/7*T^55 - 9/7*T^54 - 95/343*T^53 + 4/7*T^52 + 1359/2401*T^51 + 
        1021/2401*T^50 - 289/2401*T^49 - 215/2401*T^48 + 866/2401*T^47 + 
        2946/2401*T^46 + 2260/2401*T^45 + 148/2401*T^44 - 1170/2401*T^43 - 
        1168/2401*T^42 - 193/2401*T^41 - 206/2401*T^40 + 445/2401*T^39 - 
        195/2401*T^38 - 694/2401*T^37 - 1280/2401*T^36 - 522/2401*T^35 + 
        1810/2401*T^34 + 2356/2401*T^33 + 1885/2401*T^32 - 988/2401*T^31 - 
        349/343*T^30 - 2267/2401*T^29 + 2267/2401*T^27 + 349/343*T^26 + 
        988/2401*T^25 - 1885/2401*T^24 - 2356/2401*T^23 - 1810/2401*T^22 + 
        522/2401*T^21 + 1280/2401*T^20 + 694/2401*T^19 + 195/2401*T^18 - 
        445/2401*T^17 + 206/2401*T^16 + 193/2401*T^15 + 1168/2401*T^14 + 
        1170/2401*T^13 - 148/2401*T^12 - 2260/2401*T^11 - 2946/2401*T^10 - 
        866/2401*T^9 + 215/2401*T^8 + 289/2401*T^7 - 1021/2401*T^6 - 1359/2401*T^5 -
        4/7*T^4 + 95/343*T^3 + 9/7*T^2 + 11/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 5*X*Y^8 + 
        4*X*Y^7 + 5*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 4*X*Y + 5*X + 
        4*Y^30 + 2*Y^29 + 4*Y^27 + 4*Y^25 + 2*Y^23 + 6*Y^21 + 3*Y^19 + 6*Y^18 + 
        2*Y^17 + 3*Y^16 + Y^15 + Y^14 + 3*Y^13 + 3*Y^12 + 3*Y^11 + 5*Y^10 + 4*Y^9 + 
        6*Y^8 + 6*Y^7 + 6*Y^6 + 4*Y^5 + 3*Y^2 + 5*Y + 1,
    T^56 + 4/7*T^55 - 5/49*T^54 + 246/343*T^53 + 278/2401*T^52 - 2718/2401*T^51 - 
        1516/2401*T^50 - 494/2401*T^49 - 270/343*T^48 - 1181/2401*T^47 + 
        2022/2401*T^46 + 1179/2401*T^45 - 1035/2401*T^44 + 1899/2401*T^43 + 
        1492/2401*T^42 - 1321/2401*T^41 + 139/2401*T^40 + 62/2401*T^39 - 
        1671/2401*T^38 - 2285/2401*T^37 - 718/2401*T^36 - 858/2401*T^35 - 2/7*T^34 +
        1977/2401*T^33 + 1760/2401*T^32 + 513/2401*T^31 + 958/2401*T^30 + 
        34/343*T^29 - 192/343*T^28 + 34/343*T^27 + 958/2401*T^26 + 513/2401*T^25 + 
        1760/2401*T^24 + 1977/2401*T^23 - 2/7*T^22 - 858/2401*T^21 - 718/2401*T^20 -
        2285/2401*T^19 - 1671/2401*T^18 + 62/2401*T^17 + 139/2401*T^16 - 
        1321/2401*T^15 + 1492/2401*T^14 + 1899/2401*T^13 - 1035/2401*T^12 + 
        1179/2401*T^11 + 2022/2401*T^10 - 1181/2401*T^9 - 270/343*T^8 - 494/2401*T^7
        - 1516/2401*T^6 - 2718/2401*T^5 + 278/2401*T^4 + 246/343*T^3 - 5/49*T^2 + 
        4/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 3*X*Y^11 + 2*X*Y^10 + 4*X*Y^9 + 2*X*Y^7 + 
        5*X*Y^6 + 4*X*Y^3 + 5*X*Y^2 + X*Y + 6*X + 3*Y^30 + 2*Y^29 + 4*Y^28 + 5*Y^27 
        + 2*Y^26 + Y^24 + Y^22 + Y^21 + 6*Y^20 + 3*Y^19 + 2*Y^18 + Y^17 + 5*Y^16 + 
        5*Y^15 + 3*Y^14 + 5*Y^13 + Y^11 + 4*Y^10 + 4*Y^9 + 3*Y^8 + 2*Y^7 + Y^6 + 
        6*Y^5 + 3*Y^4 + 5*Y^3 + 5*Y^2 + 3*Y + 3,
    T^56 + 2/7*T^55 - 4/49*T^54 - 44/343*T^53 - 1097/2401*T^52 + 1576/2401*T^51 + 
        270/2401*T^50 - 1591/2401*T^49 + 271/2401*T^48 - 1143/2401*T^47 + 
        1324/2401*T^46 + 1443/2401*T^45 - 1605/2401*T^44 + 832/2401*T^43 - 
        141/343*T^42 - 618/2401*T^41 + 29/49*T^40 - 24/49*T^39 + 597/2401*T^38 - 
        90/343*T^37 - 1501/2401*T^36 + 184/343*T^35 + 248/2401*T^34 + 107/343*T^33 +
        473/2401*T^32 - 1544/2401*T^31 - 625/2401*T^30 + 272/2401*T^29 - 
        291/2401*T^28 + 272/2401*T^27 - 625/2401*T^26 - 1544/2401*T^25 + 
        473/2401*T^24 + 107/343*T^23 + 248/2401*T^22 + 184/343*T^21 - 1501/2401*T^20
        - 90/343*T^19 + 597/2401*T^18 - 24/49*T^17 + 29/49*T^16 - 618/2401*T^15 - 
        141/343*T^14 + 832/2401*T^13 - 1605/2401*T^12 + 1443/2401*T^11 + 
        1324/2401*T^10 - 1143/2401*T^9 + 271/2401*T^8 - 1591/2401*T^7 + 270/2401*T^6
        + 1576/2401*T^5 - 1097/2401*T^4 - 44/343*T^3 - 4/49*T^2 + 2/7*T + 1
*], [*
    X^3 + X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 5*X*Y^8 + 
        2*X*Y^7 + X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + X*Y + 5*Y^30 + 
        2*Y^29 + 3*Y^28 + 3*Y^25 + 6*Y^23 + 4*Y^22 + 6*Y^21 + 2*Y^20 + 4*Y^19 + 
        3*Y^18 + 4*Y^17 + 2*Y^16 + 2*Y^15 + 2*Y^14 + Y^13 + Y^12 + 6*Y^11 + 5*Y^10 +
        3*Y^8 + 6*Y^7 + 5*Y^6 + 6*Y^4 + 5*Y^3 + 5*Y^2 + 5,
    T^56 + 8/7*T^55 + 13/49*T^54 - 271/343*T^53 - 596/343*T^52 - 2209/2401*T^51 + 
        1515/2401*T^50 + 2644/2401*T^49 + 1216/2401*T^48 - 149/343*T^47 - 
        1173/2401*T^46 + 1664/2401*T^45 + 2781/2401*T^44 + 864/2401*T^43 - 
        2763/2401*T^42 - 4414/2401*T^41 - 173/343*T^40 + 1517/2401*T^39 + 
        2502/2401*T^38 + 723/2401*T^37 - 1742/2401*T^36 - 683/2401*T^35 + 
        869/2401*T^34 + 1196/2401*T^33 + 522/2401*T^32 - 1349/2401*T^31 - 
        1378/2401*T^30 + 135/2401*T^29 + 352/2401*T^28 + 135/2401*T^27 - 
        1378/2401*T^26 - 1349/2401*T^25 + 522/2401*T^24 + 1196/2401*T^23 + 
        869/2401*T^22 - 683/2401*T^21 - 1742/2401*T^20 + 723/2401*T^19 + 
        2502/2401*T^18 + 1517/2401*T^17 - 173/343*T^16 - 4414/2401*T^15 - 
        2763/2401*T^14 + 864/2401*T^13 + 2781/2401*T^12 + 1664/2401*T^11 - 
        1173/2401*T^10 - 149/343*T^9 + 1216/2401*T^8 + 2644/2401*T^7 + 1515/2401*T^6
        - 2209/2401*T^5 - 596/343*T^4 - 271/343*T^3 + 13/49*T^2 + 8/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^13 + 2*X*Y^12 + 4*X*Y^10 + X*Y^9 + X*Y^8 + 2*X*Y^7 + 
        6*X*Y^6 + 3*X*Y^5 + 5*X*Y^3 + 5*X*Y^2 + 2*X*Y + Y^30 + 4*Y^29 + 4*Y^28 + 
        6*Y^27 + 6*Y^25 + 3*Y^24 + 3*Y^23 + 3*Y^22 + 3*Y^20 + Y^19 + 2*Y^18 + 4*Y^17
        + 5*Y^16 + 2*Y^15 + 5*Y^14 + 4*Y^13 + Y^12 + 2*Y^11 + 2*Y^10 + 5*Y^9 + 6*Y^8
        + 4*Y^5 + 3*Y^4 + 5*Y^3 + 3*Y^2 + 6*Y + 5,
    -T^56 + 11/7*T^55 - T^54 + 33/49*T^53 - 302/2401*T^52 - 1074/2401*T^51 + 
        2087/2401*T^50 - 1705/2401*T^49 + 997/2401*T^48 - 1186/2401*T^47 + 
        99/343*T^46 + 37/343*T^45 - 1186/2401*T^44 + 1333/2401*T^43 - 1880/2401*T^42
        + 1762/2401*T^41 - 803/2401*T^40 - 171/2401*T^39 + 768/2401*T^38 + 
        150/2401*T^37 - 757/2401*T^36 + 471/2401*T^35 - 55/2401*T^34 - 173/2401*T^33
        + 797/2401*T^32 - 1674/2401*T^31 + 201/343*T^30 - 529/2401*T^29 + 
        529/2401*T^27 - 201/343*T^26 + 1674/2401*T^25 - 797/2401*T^24 + 
        173/2401*T^23 + 55/2401*T^22 - 471/2401*T^21 + 757/2401*T^20 - 150/2401*T^19
        - 768/2401*T^18 + 171/2401*T^17 + 803/2401*T^16 - 1762/2401*T^15 + 
        1880/2401*T^14 - 1333/2401*T^13 + 1186/2401*T^12 - 37/343*T^11 - 99/343*T^10
        + 1186/2401*T^9 - 997/2401*T^8 + 1705/2401*T^7 - 2087/2401*T^6 + 
        1074/2401*T^5 + 302/2401*T^4 - 33/49*T^3 + T^2 - 11/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + X*Y^13 + 5*X*Y^12 + X*Y^11 + 3*X*Y^10 + 4*X*Y^7 + 
        X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + X*Y^2 + 3*X + 5*Y^30 + 5*Y^28 + Y^27 +
        Y^26 + 6*Y^25 + 5*Y^24 + 4*Y^23 + 2*Y^22 + 5*Y^21 + 6*Y^20 + Y^19 + 4*Y^18 +
        Y^17 + 4*Y^15 + 4*Y^14 + 2*Y^13 + 2*Y^12 + Y^11 + Y^10 + 3*Y^9 + 4*Y^8 + 
        2*Y^7 + 5*Y^6 + 4*Y^5 + Y^4 + 6*Y^3 + Y^2 + Y + 3,
    -T^56 - 15/7*T^55 - 95/49*T^54 - 383/343*T^53 - 2389/2401*T^52 - 2273/2401*T^51 
        + 475/2401*T^50 + 3583/2401*T^49 + 5297/2401*T^48 + 6015/2401*T^47 + 
        6991/2401*T^46 + 141/49*T^45 + 4647/2401*T^44 + 958/2401*T^43 - 
        1366/2401*T^42 - 2479/2401*T^41 - 5335/2401*T^40 - 8761/2401*T^39 - 
        1192/343*T^38 - 5002/2401*T^37 - 2963/2401*T^36 - 209/343*T^35 + 
        1614/2401*T^34 + 4876/2401*T^33 + 5834/2401*T^32 + 5840/2401*T^31 + 
        5459/2401*T^30 + 3541/2401*T^29 - 3541/2401*T^27 - 5459/2401*T^26 - 
        5840/2401*T^25 - 5834/2401*T^24 - 4876/2401*T^23 - 1614/2401*T^22 + 
        209/343*T^21 + 2963/2401*T^20 + 5002/2401*T^19 + 1192/343*T^18 + 
        8761/2401*T^17 + 5335/2401*T^16 + 2479/2401*T^15 + 1366/2401*T^14 - 
        958/2401*T^13 - 4647/2401*T^12 - 141/49*T^11 - 6991/2401*T^10 - 
        6015/2401*T^9 - 5297/2401*T^8 - 3583/2401*T^7 - 475/2401*T^6 + 2273/2401*T^5
        + 2389/2401*T^4 + 383/343*T^3 + 95/49*T^2 + 15/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 4*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 +
        2*X*Y^7 + X*Y^6 + 5*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 6*X*Y + 4*X + 2*Y^30 + Y^29 
        + 6*Y^28 + 5*Y^27 + 5*Y^26 + 4*Y^25 + 6*Y^24 + 4*Y^23 + 6*Y^22 + 4*Y^21 + 
        2*Y^20 + 2*Y^19 + 4*Y^18 + 5*Y^17 + 4*Y^16 + Y^15 + 2*Y^14 + Y^13 + 6*Y^12 +
        2*Y^11 + 2*Y^10 + 3*Y^9 + 5*Y^8 + 4*Y^7 + Y^6 + 5*Y^5 + 4*Y^4 + 3*Y^3 + 
        6*Y^2 + 4,
    T^56 + 5/7*T^55 - 78/49*T^54 - 248/343*T^53 + 3069/2401*T^52 - 1289/2401*T^51 - 
        2872/2401*T^50 + 3092/2401*T^49 + 2200/2401*T^48 - 3719/2401*T^47 - 
        1075/2401*T^46 + 521/343*T^45 + 184/2401*T^44 - 227/343*T^43 + 
        1787/2401*T^42 - 194/2401*T^41 - 3191/2401*T^40 + 388/2401*T^39 + 
        293/343*T^38 - 36/343*T^37 + 779/2401*T^36 + 229/343*T^35 - 415/343*T^34 - 
        2928/2401*T^33 + 3599/2401*T^32 + 2495/2401*T^31 - 3319/2401*T^30 - 
        929/2401*T^29 + 2845/2401*T^28 - 929/2401*T^27 - 3319/2401*T^26 + 
        2495/2401*T^25 + 3599/2401*T^24 - 2928/2401*T^23 - 415/343*T^22 + 
        229/343*T^21 + 779/2401*T^20 - 36/343*T^19 + 293/343*T^18 + 388/2401*T^17 - 
        3191/2401*T^16 - 194/2401*T^15 + 1787/2401*T^14 - 227/343*T^13 + 
        184/2401*T^12 + 521/343*T^11 - 1075/2401*T^10 - 3719/2401*T^9 + 
        2200/2401*T^8 + 3092/2401*T^7 - 2872/2401*T^6 - 1289/2401*T^5 + 
        3069/2401*T^4 - 248/343*T^3 - 78/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        3*X*Y^8 + X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 2*X*Y + 
        5*X + Y^30 + 3*Y^29 + 2*Y^28 + 5*Y^27 + Y^26 + 5*Y^25 + 5*Y^24 + 2*Y^23 + 
        4*Y^22 + 2*Y^21 + 2*Y^19 + 5*Y^18 + 3*Y^17 + 6*Y^16 + 5*Y^14 + 3*Y^13 + Y^12
        + 2*Y^10 + 5*Y^9 + 4*Y^8 + 2*Y^7 + 5*Y^6 + 4*Y^4 + 4*Y^3 + 3*Y^2 + 2*Y + 2,
    -T^56 + 13/7*T^55 - 43/49*T^54 + 96/343*T^53 - 3005/2401*T^52 + 2615/2401*T^51 +
        90/343*T^50 - 1332/2401*T^49 - 387/2401*T^48 + 332/2401*T^47 + 
        1553/2401*T^46 - 2159/2401*T^45 + 555/2401*T^44 + 629/2401*T^43 + 
        869/2401*T^42 - 2461/2401*T^41 + 1005/2401*T^40 + 598/2401*T^39 + 
        1753/2401*T^38 - 3865/2401*T^37 + 2288/2401*T^36 - 712/2401*T^35 + 
        204/343*T^34 - 1259/2401*T^33 - 512/2401*T^32 + 1214/2401*T^31 - 
        132/2401*T^30 - 404/2401*T^29 + 404/2401*T^27 + 132/2401*T^26 - 
        1214/2401*T^25 + 512/2401*T^24 + 1259/2401*T^23 - 204/343*T^22 + 
        712/2401*T^21 - 2288/2401*T^20 + 3865/2401*T^19 - 1753/2401*T^18 - 
        598/2401*T^17 - 1005/2401*T^16 + 2461/2401*T^15 - 869/2401*T^14 - 
        629/2401*T^13 - 555/2401*T^12 + 2159/2401*T^11 - 1553/2401*T^10 - 
        332/2401*T^9 + 387/2401*T^8 + 1332/2401*T^7 - 90/343*T^6 - 2615/2401*T^5 + 
        3005/2401*T^4 - 96/343*T^3 + 43/49*T^2 - 13/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 2*X*Y^11 + 4*X*Y^10 + X*Y^8 + 3*X*Y^7 + 6*X*Y^6 + 
        2*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 3*X*Y + 3*X + 3*Y^30 + 3*Y^29 + 
        3*Y^27 + Y^26 + 3*Y^24 + 6*Y^23 + 2*Y^22 + 5*Y^21 + 6*Y^20 + 3*Y^19 + 2*Y^18
        + 4*Y^16 + Y^15 + 4*Y^14 + 6*Y^13 + 5*Y^12 + Y^11 + 4*Y^10 + 6*Y^9 + 5*Y^8 +
        5*Y^7 + 3*Y^6 + Y^5 + Y^4 + 4*Y^3 + 3*Y^2 + 4,
    -T^56 + 4/7*T^55 + 3/49*T^54 - 431/343*T^53 + 58/49*T^52 - 1987/2401*T^51 - 
        12/343*T^50 + 1887/2401*T^49 - 404/2401*T^48 + 558/2401*T^47 - 632/2401*T^46
        + 565/2401*T^45 + 1410/2401*T^44 - 1623/2401*T^43 - 265/2401*T^42 + 
        2561/2401*T^41 - 5361/2401*T^40 + 3776/2401*T^39 + 47/2401*T^38 - 
        4143/2401*T^37 + 2537/2401*T^36 - 3/7*T^35 + 786/2401*T^34 - 172/343*T^33 + 
        2012/2401*T^32 - 1763/2401*T^31 + 211/2401*T^30 + 1734/2401*T^29 - 
        1734/2401*T^27 - 211/2401*T^26 + 1763/2401*T^25 - 2012/2401*T^24 + 
        172/343*T^23 - 786/2401*T^22 + 3/7*T^21 - 2537/2401*T^20 + 4143/2401*T^19 - 
        47/2401*T^18 - 3776/2401*T^17 + 5361/2401*T^16 - 2561/2401*T^15 + 
        265/2401*T^14 + 1623/2401*T^13 - 1410/2401*T^12 - 565/2401*T^11 + 
        632/2401*T^10 - 558/2401*T^9 + 404/2401*T^8 - 1887/2401*T^7 + 12/343*T^6 + 
        1987/2401*T^5 - 58/49*T^4 + 431/343*T^3 - 3/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 4*X*Y^10 + 3*X*Y^9 + X*Y^8 + 
        3*X*Y^6 + 6*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 3*X*Y + 3*X + 3*Y^30 + 3*Y^29 + 
        5*Y^28 + 5*Y^27 + 4*Y^26 + Y^25 + 4*Y^24 + 6*Y^23 + 5*Y^22 + Y^21 + Y^18 + 
        6*Y^17 + 2*Y^16 + 2*Y^15 + 3*Y^14 + 3*Y^13 + 2*Y^12 + 3*Y^11 + 2*Y^10 + 
        2*Y^9 + 3*Y^8 + 5*Y^6 + 2*Y^5 + 2*Y^3 + 5*Y^2 + Y + 1,
    -T^56 + 8/7*T^55 - 24/49*T^54 + 82/343*T^53 + 1350/2401*T^52 - 1730/2401*T^51 - 
        1193/2401*T^50 + 1978/2401*T^49 - 1451/2401*T^48 + 393/2401*T^47 + 
        1601/2401*T^46 - 2258/2401*T^45 + 1581/2401*T^44 - 1016/2401*T^43 + 
        796/2401*T^42 - 106/2401*T^41 + 380/2401*T^40 - 964/2401*T^39 + 
        1642/2401*T^38 - 1312/2401*T^37 + 554/2401*T^36 + 1004/2401*T^35 - 
        839/2401*T^34 + 135/2401*T^33 + 985/2401*T^32 - 67/2401*T^31 - 
        1446/2401*T^30 + 66/343*T^29 - 66/343*T^27 + 1446/2401*T^26 + 67/2401*T^25 -
        985/2401*T^24 - 135/2401*T^23 + 839/2401*T^22 - 1004/2401*T^21 - 
        554/2401*T^20 + 1312/2401*T^19 - 1642/2401*T^18 + 964/2401*T^17 - 
        380/2401*T^16 + 106/2401*T^15 - 796/2401*T^14 + 1016/2401*T^13 - 
        1581/2401*T^12 + 2258/2401*T^11 - 1601/2401*T^10 - 393/2401*T^9 + 
        1451/2401*T^8 - 1978/2401*T^7 + 1193/2401*T^6 + 1730/2401*T^5 - 
        1350/2401*T^4 - 82/343*T^3 + 24/49*T^2 - 8/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 2*X*Y 
        + 6*X + 6*Y^30 + 4*Y^29 + 2*Y^28 + 3*Y^25 + 5*Y^24 + 5*Y^23 + 6*Y^21 + 
        2*Y^20 + 2*Y^19 + 4*Y^17 + 4*Y^16 + 3*Y^15 + Y^13 + 5*Y^12 + Y^11 + Y^10 + 
        6*Y^9 + 4*Y^8 + 6*Y^7 + 5*Y^6 + 3*Y^5 + 5*Y^4 + 3*Y^3 + 5*Y^2 + 6*Y + 1,
    -T^56 - 4/7*T^55 - 5/49*T^54 + 251/343*T^53 + 235/2401*T^52 - 159/2401*T^51 - 
        874/2401*T^50 - 65/343*T^49 + 878/2401*T^48 + 2195/2401*T^47 + 128/343*T^46 
        - 1527/2401*T^45 - 1804/2401*T^44 - 149/343*T^43 + 1123/2401*T^42 + 
        1779/2401*T^41 + 656/2401*T^40 - 2006/2401*T^39 - 365/343*T^38 - 
        1324/2401*T^37 + 2104/2401*T^36 + 1629/2401*T^35 + 842/2401*T^34 - 
        398/343*T^33 - 1501/2401*T^32 + 478/2401*T^31 + 2823/2401*T^30 + 
        1989/2401*T^29 - 1989/2401*T^27 - 2823/2401*T^26 - 478/2401*T^25 + 
        1501/2401*T^24 + 398/343*T^23 - 842/2401*T^22 - 1629/2401*T^21 - 
        2104/2401*T^20 + 1324/2401*T^19 + 365/343*T^18 + 2006/2401*T^17 - 
        656/2401*T^16 - 1779/2401*T^15 - 1123/2401*T^14 + 149/343*T^13 + 
        1804/2401*T^12 + 1527/2401*T^11 - 128/343*T^10 - 2195/2401*T^9 - 
        878/2401*T^8 + 65/343*T^7 + 874/2401*T^6 + 159/2401*T^5 - 235/2401*T^4 - 
        251/343*T^3 + 5/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 
        + 3*X*Y^8 + 6*X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 
        4*X*Y + 4*X + Y^30 + 2*Y^29 + 5*Y^28 + 4*Y^27 + 2*Y^24 + 2*Y^23 + 5*Y^22 + 
        6*Y^21 + 5*Y^19 + 3*Y^18 + 5*Y^17 + Y^16 + 5*Y^15 + 4*Y^14 + 4*Y^13 + 5*Y^11
        + 3*Y^10 + 4*Y^9 + Y^8 + 3*Y^7 + 4*Y^6 + 3*Y^5 + 4*Y^3 + 6*Y^2 + 2*Y + 4,
    -T^56 + 6/7*T^55 - 9/49*T^54 - 243/343*T^53 + 3847/2401*T^52 - 2134/2401*T^51 + 
        1021/2401*T^50 + 2215/2401*T^49 - 2950/2401*T^48 + 1350/2401*T^47 + 
        103/343*T^46 - 3433/2401*T^45 + 1634/2401*T^44 + 1455/2401*T^43 - 
        2175/2401*T^42 + 2109/2401*T^41 + 195/2401*T^40 - 1086/2401*T^39 - 
        8/343*T^38 + 200/2401*T^37 - 1763/2401*T^36 + 16/343*T^35 + 1219/2401*T^34 -
        2834/2401*T^33 + 409/343*T^32 + 492/2401*T^31 - 227/343*T^30 + 
        1837/2401*T^29 - 1837/2401*T^27 + 227/343*T^26 - 492/2401*T^25 - 
        409/343*T^24 + 2834/2401*T^23 - 1219/2401*T^22 - 16/343*T^21 + 
        1763/2401*T^20 - 200/2401*T^19 + 8/343*T^18 + 1086/2401*T^17 - 195/2401*T^16
        - 2109/2401*T^15 + 2175/2401*T^14 - 1455/2401*T^13 - 1634/2401*T^12 + 
        3433/2401*T^11 - 103/343*T^10 - 1350/2401*T^9 + 2950/2401*T^8 - 
        2215/2401*T^7 - 1021/2401*T^6 + 2134/2401*T^5 - 3847/2401*T^4 + 243/343*T^3 
        + 9/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 5*X*Y^7 + X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 5*X*Y + 
        5*Y^30 + 4*Y^28 + Y^27 + Y^26 + Y^25 + 3*Y^24 + 5*Y^23 + 2*Y^22 + Y^21 + 
        Y^20 + 6*Y^19 + 3*Y^17 + Y^16 + 5*Y^15 + 3*Y^13 + 3*Y^12 + Y^11 + 5*Y^10 + 
        2*Y^8 + 5*Y^7 + 6*Y^5 + Y^4 + 5*Y^3 + 4*Y^2 + 2*Y + 1,
    T^56 - 4/7*T^55 - 9/49*T^54 + 113/343*T^53 - 213/2401*T^52 - 1028/2401*T^51 + 
        76/343*T^50 - 108/343*T^49 + 129/2401*T^48 + 64/2401*T^47 - 403/2401*T^46 - 
        207/343*T^45 + 1336/2401*T^44 + 922/2401*T^43 - 2278/2401*T^42 + 
        761/2401*T^41 + 1206/2401*T^40 - 1707/2401*T^39 + 1157/2401*T^38 + 
        961/2401*T^37 - 901/2401*T^36 + 561/2401*T^35 + 292/2401*T^34 - 
        929/2401*T^33 - 43/343*T^32 + 2435/2401*T^31 - 283/343*T^30 - 550/2401*T^29 
        + 1522/2401*T^28 - 550/2401*T^27 - 283/343*T^26 + 2435/2401*T^25 - 
        43/343*T^24 - 929/2401*T^23 + 292/2401*T^22 + 561/2401*T^21 - 901/2401*T^20 
        + 961/2401*T^19 + 1157/2401*T^18 - 1707/2401*T^17 + 1206/2401*T^16 + 
        761/2401*T^15 - 2278/2401*T^14 + 922/2401*T^13 + 1336/2401*T^12 - 
        207/343*T^11 - 403/2401*T^10 + 64/2401*T^9 + 129/2401*T^8 - 108/343*T^7 + 
        76/343*T^6 - 1028/2401*T^5 - 213/2401*T^4 + 113/343*T^3 - 9/49*T^2 - 4/7*T +
        1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 6*X*Y^8 + 
        2*X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 5*X*Y + 4*Y^30 +
        4*Y^29 + 5*Y^28 + 3*Y^27 + 2*Y^26 + Y^25 + 4*Y^24 + 6*Y^23 + 5*Y^22 + 4*Y^21
        + 5*Y^20 + 6*Y^19 + Y^18 + 4*Y^17 + 5*Y^16 + 6*Y^15 + 2*Y^14 + 4*Y^13 + Y^12
        + 6*Y^11 + 3*Y^10 + 3*Y^9 + 2*Y^7 + Y^6 + Y^4 + 4*Y^3 + Y^2 + 3*Y + 2,
    T^56 + T^55 + 72/49*T^54 + 492/343*T^53 + 48/343*T^52 - 2514/2401*T^51 - 
        590/343*T^50 - 5590/2401*T^49 - 3097/2401*T^48 + 1335/2401*T^47 + 
        3282/2401*T^46 + 4988/2401*T^45 + 3205/2401*T^44 - 193/2401*T^43 - 
        4062/2401*T^42 - 4700/2401*T^41 - 5190/2401*T^40 - 1665/2401*T^39 + 
        150/343*T^38 + 376/343*T^37 + 3301/2401*T^36 + 1560/2401*T^35 - 
        492/2401*T^34 - 2166/2401*T^33 - 2381/2401*T^32 - 1821/2401*T^31 + 
        937/2401*T^30 + 1871/2401*T^29 + 3469/2401*T^28 + 1871/2401*T^27 + 
        937/2401*T^26 - 1821/2401*T^25 - 2381/2401*T^24 - 2166/2401*T^23 - 
        492/2401*T^22 + 1560/2401*T^21 + 3301/2401*T^20 + 376/343*T^19 + 
        150/343*T^18 - 1665/2401*T^17 - 5190/2401*T^16 - 4700/2401*T^15 - 
        4062/2401*T^14 - 193/2401*T^13 + 3205/2401*T^12 + 4988/2401*T^11 + 
        3282/2401*T^10 + 1335/2401*T^9 - 3097/2401*T^8 - 5590/2401*T^7 - 590/343*T^6
        - 2514/2401*T^5 + 48/343*T^4 + 492/343*T^3 + 72/49*T^2 + T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + 
        X*Y^8 + X*Y^7 + X*Y^6 + 5*X*Y^5 + X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 2*X*Y + 2*Y^30
        + 6*Y^29 + 6*Y^28 + 6*Y^26 + 5*Y^24 + 2*Y^23 + 4*Y^22 + 5*Y^21 + 4*Y^20 + 
        4*Y^18 + Y^17 + 5*Y^16 + Y^14 + 4*Y^13 + 5*Y^12 + 5*Y^10 + 5*Y^9 + 2*Y^8 + 
        4*Y^7 + 6*Y^6 + 4*Y^5 + 2*Y^4 + 3*Y^3 + 3,
    -T^56 - 3/7*T^55 + 48/49*T^54 + 438/343*T^53 + 815/2401*T^52 - 1768/2401*T^51 - 
        1922/2401*T^50 - 9/343*T^49 + 1101/2401*T^48 + 1016/2401*T^47 - 
        1256/2401*T^46 - 1965/2401*T^45 - 491/2401*T^44 + 1664/2401*T^43 + 
        310/343*T^42 + 124/343*T^41 - 349/2401*T^40 - 1051/2401*T^39 - 194/343*T^38 
        - 585/2401*T^37 + 404/2401*T^36 + 982/2401*T^35 - 29/2401*T^34 - 
        485/2401*T^33 - 395/2401*T^32 - 33/2401*T^31 + 793/2401*T^30 + 3/2401*T^29 -
        3/2401*T^27 - 793/2401*T^26 + 33/2401*T^25 + 395/2401*T^24 + 485/2401*T^23 +
        29/2401*T^22 - 982/2401*T^21 - 404/2401*T^20 + 585/2401*T^19 + 194/343*T^18 
        + 1051/2401*T^17 + 349/2401*T^16 - 124/343*T^15 - 310/343*T^14 - 
        1664/2401*T^13 + 491/2401*T^12 + 1965/2401*T^11 + 1256/2401*T^10 - 
        1016/2401*T^9 - 1101/2401*T^8 + 9/343*T^7 + 1922/2401*T^6 + 1768/2401*T^5 - 
        815/2401*T^4 - 438/343*T^3 - 48/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 5*X*Y^8 
        + 6*X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + 4*X*Y^3 + 4*X*Y^2 + 4*X*Y + 5*X + 2*Y^30 + 
        6*Y^29 + 4*Y^27 + 4*Y^25 + 4*Y^24 + 5*Y^22 + 2*Y^20 + 3*Y^19 + Y^17 + 4*Y^16
        + 4*Y^15 + 3*Y^14 + Y^12 + 4*Y^11 + 2*Y^10 + Y^9 + 3*Y^8 + 4*Y^7 + 3*Y^6 + 
        6*Y^5 + Y^4 + 6*Y^3 + 5*Y^2 + 3*Y + 1,
    T^56 - 10/7*T^55 - 18/49*T^54 + 218/343*T^53 + 23/49*T^52 - 1262/2401*T^51 + 
        1243/2401*T^50 + 1132/2401*T^49 - 1702/2401*T^48 - 2118/2401*T^47 + 
        788/2401*T^46 + 2532/2401*T^45 + 53/343*T^44 - 2295/2401*T^43 - 
        235/2401*T^42 + 1159/2401*T^41 - 736/2401*T^40 - 184/343*T^39 + 
        2602/2401*T^38 + 932/2401*T^37 - 914/2401*T^36 - 267/343*T^35 + 
        304/2401*T^34 + 107/2401*T^33 + 311/2401*T^32 - 226/2401*T^31 + 
        2010/2401*T^30 - 886/2401*T^29 - 27/49*T^28 - 886/2401*T^27 + 2010/2401*T^26
        - 226/2401*T^25 + 311/2401*T^24 + 107/2401*T^23 + 304/2401*T^22 - 
        267/343*T^21 - 914/2401*T^20 + 932/2401*T^19 + 2602/2401*T^18 - 184/343*T^17
        - 736/2401*T^16 + 1159/2401*T^15 - 235/2401*T^14 - 2295/2401*T^13 + 
        53/343*T^12 + 2532/2401*T^11 + 788/2401*T^10 - 2118/2401*T^9 - 1702/2401*T^8
        + 1132/2401*T^7 + 1243/2401*T^6 - 1262/2401*T^5 + 23/49*T^4 + 218/343*T^3 - 
        18/49*T^2 - 10/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + X*Y^9 + 2*X*Y^8 + 
        3*X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 3*X*Y + 5*X + 
        4*Y^30 + 3*Y^29 + 6*Y^28 + 5*Y^27 + 3*Y^26 + 3*Y^25 + 2*Y^24 + 6*Y^23 + 
        4*Y^22 + 4*Y^21 + 5*Y^20 + Y^19 + 3*Y^17 + 2*Y^16 + Y^15 + 4*Y^14 + 4*Y^13 +
        2*Y^12 + Y^11 + Y^10 + 2*Y^9 + 5*Y^8 + 6*Y^7 + 6*Y^6 + 2*Y^5 + 6*Y^4 + 6*Y^3
        + 3*Y^2 + 6*Y + 3,
    -T^56 - 5/7*T^55 + 15/49*T^54 + 312/343*T^53 + 519/2401*T^52 - 2196/2401*T^51 - 
        2280/2401*T^50 + 1264/2401*T^49 + 1703/2401*T^48 + 236/2401*T^47 - 
        480/2401*T^46 - 524/2401*T^45 + 766/2401*T^44 - 708/2401*T^43 - 
        402/2401*T^42 + 827/2401*T^41 + 1643/2401*T^40 + 436/2401*T^39 - 72/343*T^38
        - 974/2401*T^37 + 201/343*T^36 + 115/343*T^35 + 347/2401*T^34 - 
        165/2401*T^33 + 1378/2401*T^32 + 1262/2401*T^31 - 803/2401*T^30 - 
        1917/2401*T^29 + 1917/2401*T^27 + 803/2401*T^26 - 1262/2401*T^25 - 
        1378/2401*T^24 + 165/2401*T^23 - 347/2401*T^22 - 115/343*T^21 - 201/343*T^20
        + 974/2401*T^19 + 72/343*T^18 - 436/2401*T^17 - 1643/2401*T^16 - 
        827/2401*T^15 + 402/2401*T^14 + 708/2401*T^13 - 766/2401*T^12 + 
        524/2401*T^11 + 480/2401*T^10 - 236/2401*T^9 - 1703/2401*T^8 - 1264/2401*T^7
        + 2280/2401*T^6 + 2196/2401*T^5 - 519/2401*T^4 - 312/343*T^3 - 15/49*T^2 + 
        5/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 
        + 5*X*Y^8 + 2*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 3*X 
        + 5*Y^30 + 2*Y^28 + Y^27 + 5*Y^25 + 6*Y^24 + 3*Y^23 + 5*Y^22 + 2*Y^20 + 
        4*Y^19 + 2*Y^18 + 2*Y^17 + 4*Y^16 + 6*Y^15 + 2*Y^14 + 2*Y^12 + 3*Y^10 + 
        4*Y^9 + 6*Y^8 + 6*Y^7 + 3*Y^6 + 6*Y^5 + 5*Y^4 + Y^3 + 5*Y^2 + 2*Y,
    -T^56 - 3/7*T^55 + 45/49*T^54 - 30/343*T^53 - 1422/2401*T^52 + 1937/2401*T^51 + 
        2677/2401*T^50 + 10/2401*T^49 - 1607/2401*T^48 - 236/343*T^47 - 68/2401*T^46
        + 529/2401*T^45 - 2393/2401*T^44 - 142/343*T^43 + 3762/2401*T^42 + 
        1815/2401*T^41 - 803/2401*T^40 - 73/343*T^39 + 374/2401*T^38 + 366/2401*T^37
        - 1732/2401*T^36 - 2867/2401*T^35 + 66/343*T^34 + 2447/2401*T^33 - 
        111/2401*T^32 - 167/343*T^31 + 256/343*T^30 + 2083/2401*T^29 - 
        2083/2401*T^27 - 256/343*T^26 + 167/343*T^25 + 111/2401*T^24 - 
        2447/2401*T^23 - 66/343*T^22 + 2867/2401*T^21 + 1732/2401*T^20 - 
        366/2401*T^19 - 374/2401*T^18 + 73/343*T^17 + 803/2401*T^16 - 1815/2401*T^15
        - 3762/2401*T^14 + 142/343*T^13 + 2393/2401*T^12 - 529/2401*T^11 + 
        68/2401*T^10 + 236/343*T^9 + 1607/2401*T^8 - 10/2401*T^7 - 2677/2401*T^6 - 
        1937/2401*T^5 + 1422/2401*T^4 + 30/343*T^3 - 45/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 2*X*Y^12 + 4*X*Y^10 + 6*X*Y^9 + 2*X*Y^8 + 6*X*Y^7 + 
        X*Y^6 + X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 3*X*Y + Y^30 + 5*Y^29 + 4*Y^28
        + 3*Y^27 + 2*Y^26 + 4*Y^25 + Y^24 + 6*Y^23 + 6*Y^22 + 3*Y^21 + Y^20 + 6*Y^19
        + Y^17 + 4*Y^16 + 2*Y^15 + 4*Y^14 + 2*Y^13 + 5*Y^11 + 4*Y^10 + 5*Y^8 + 3*Y^7
        + 4*Y^6 + 4*Y^5 + 4*Y^4 + 5*Y^3 + Y^2 + 3*Y + 2,
    -T^56 - 6/7*T^55 + 11/49*T^54 - 50/343*T^53 - 62/49*T^52 - 1296/2401*T^51 + 
        2005/2401*T^50 + 837/2401*T^49 - 3586/2401*T^48 - 1822/2401*T^47 + 
        2416/2401*T^46 + 887/2401*T^45 - 2154/2401*T^44 - 103/343*T^43 + 
        2776/2401*T^42 + 2588/2401*T^41 - 2372/2401*T^40 - 1870/2401*T^39 + 
        2181/2401*T^38 + 187/343*T^37 - 373/343*T^36 - 2516/2401*T^35 + 
        769/2401*T^34 + 1340/2401*T^33 - 1926/2401*T^32 - 2577/2401*T^31 + 
        563/2401*T^30 + 1719/2401*T^29 - 1719/2401*T^27 - 563/2401*T^26 + 
        2577/2401*T^25 + 1926/2401*T^24 - 1340/2401*T^23 - 769/2401*T^22 + 
        2516/2401*T^21 + 373/343*T^20 - 187/343*T^19 - 2181/2401*T^18 + 
        1870/2401*T^17 + 2372/2401*T^16 - 2588/2401*T^15 - 2776/2401*T^14 + 
        103/343*T^13 + 2154/2401*T^12 - 887/2401*T^11 - 2416/2401*T^10 + 
        1822/2401*T^9 + 3586/2401*T^8 - 837/2401*T^7 - 2005/2401*T^6 + 1296/2401*T^5
        + 62/49*T^4 + 50/343*T^3 - 11/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        6*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 6*X*Y + 5*X + 
        Y^30 + 5*Y^29 + 2*Y^28 + 4*Y^27 + 2*Y^26 + 6*Y^25 + Y^24 + 4*Y^23 + 2*Y^22 +
        2*Y^21 + 4*Y^19 + 4*Y^18 + 4*Y^17 + Y^16 + 4*Y^15 + 3*Y^14 + 3*Y^13 + 3*Y^12
        + 2*Y^11 + 6*Y^10 + 2*Y^9 + 4*Y^8 + 4*Y^7 + 5*Y^6 + Y^5 + 3*Y^4 + 4*Y^3 + 
        Y^2 + 4*Y + 4,
    -T^56 + 4/7*T^55 + 8/49*T^54 - 211/343*T^53 + 1110/2401*T^52 + 547/2401*T^51 + 
        57/2401*T^50 + 1945/2401*T^49 - 145/343*T^48 - 103/2401*T^47 + 963/2401*T^46
        - 807/2401*T^45 - 358/2401*T^44 + 554/2401*T^43 - 246/2401*T^42 + 
        138/343*T^41 - 346/2401*T^40 - 313/2401*T^39 + 752/2401*T^38 - 19/49*T^37 - 
        439/2401*T^36 - 142/2401*T^35 - 151/343*T^34 + 232/2401*T^33 - 25/343*T^32 -
        902/2401*T^31 + 57/343*T^30 + 44/2401*T^29 - 44/2401*T^27 - 57/343*T^26 + 
        902/2401*T^25 + 25/343*T^24 - 232/2401*T^23 + 151/343*T^22 + 142/2401*T^21 +
        439/2401*T^20 + 19/49*T^19 - 752/2401*T^18 + 313/2401*T^17 + 346/2401*T^16 -
        138/343*T^15 + 246/2401*T^14 - 554/2401*T^13 + 358/2401*T^12 + 807/2401*T^11
        - 963/2401*T^10 + 103/2401*T^9 + 145/343*T^8 - 1945/2401*T^7 - 57/2401*T^6 -
        547/2401*T^5 - 1110/2401*T^4 + 211/343*T^3 - 8/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 
        + 6*X*Y^8 + 5*X*Y^7 + X*Y^6 + X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 5*X*Y + 6*X + 
        4*Y^30 + 3*Y^29 + 5*Y^28 + 3*Y^27 + 5*Y^26 + 4*Y^25 + 6*Y^24 + Y^23 + 5*Y^22
        + 3*Y^21 + 5*Y^20 + 2*Y^19 + 4*Y^18 + 6*Y^16 + 6*Y^15 + 3*Y^14 + 6*Y^13 + 
        2*Y^12 + Y^11 + 6*Y^10 + 3*Y^9 + 2*Y^8 + 2*Y^6 + 2*Y^5 + 6*Y^4 + 6*Y^3 + 
        6*Y^2 + 5*Y + 3,
    -T^56 - 15/49*T^54 - 127/343*T^53 - 16/2401*T^52 - 149/343*T^51 + 578/2401*T^50 
        - 31/343*T^49 + 32/2401*T^48 + 72/2401*T^47 - 20/343*T^46 - 358/2401*T^45 + 
        106/343*T^44 - 135/2401*T^43 - 429/2401*T^42 - 88/2401*T^41 - 139/2401*T^40 
        + 699/2401*T^39 - 1170/2401*T^38 + 419/2401*T^37 + 430/2401*T^36 - 
        375/2401*T^35 + 823/2401*T^34 - 1458/2401*T^33 + 675/2401*T^32 - 83/343*T^31
        - 989/2401*T^30 + 544/2401*T^29 - 544/2401*T^27 + 989/2401*T^26 + 
        83/343*T^25 - 675/2401*T^24 + 1458/2401*T^23 - 823/2401*T^22 + 375/2401*T^21
        - 430/2401*T^20 - 419/2401*T^19 + 1170/2401*T^18 - 699/2401*T^17 + 
        139/2401*T^16 + 88/2401*T^15 + 429/2401*T^14 + 135/2401*T^13 - 106/343*T^12 
        + 358/2401*T^11 + 20/343*T^10 - 72/2401*T^9 - 32/2401*T^8 + 31/343*T^7 - 
        578/2401*T^6 + 149/343*T^5 + 16/2401*T^4 + 127/343*T^3 + 15/49*T^2 + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 4*X*Y^9 + 5*X*Y^7 +
        4*X*Y^6 + 3*X*Y^5 + X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + X*Y + 5*X + 3*Y^30 + 6*Y^29 
        + 6*Y^28 + 5*Y^27 + 4*Y^26 + 5*Y^24 + 4*Y^23 + 5*Y^22 + 4*Y^21 + Y^20 + 
        3*Y^19 + 2*Y^18 + 6*Y^17 + 6*Y^16 + 5*Y^15 + 2*Y^13 + 4*Y^12 + 6*Y^11 + 
        2*Y^10 + 6*Y^9 + Y^8 + 3*Y^7 + Y^6 + 4*Y^5 + 5*Y^4 + 2*Y^3 + 4*Y^2 + 4,
    T^56 - 22/7*T^55 + 23/7*T^54 - 32/49*T^53 - 482/2401*T^52 - 533/343*T^51 + 
        4136/2401*T^50 - 1620/2401*T^49 + 3385/2401*T^48 - 4916/2401*T^47 + 
        2424/2401*T^46 - 1858/2401*T^45 + 2591/2401*T^44 + 606/2401*T^43 - 
        3501/2401*T^42 + 2151/2401*T^41 - 429/2401*T^40 - 68/2401*T^39 + 
        387/2401*T^38 + 335/2401*T^37 - 1269/2401*T^36 + 1082/2401*T^35 - 
        851/2401*T^34 - 199/2401*T^33 + 1738/2401*T^32 + 519/2401*T^31 - 65/49*T^30 
        - 1277/2401*T^29 + 5713/2401*T^28 - 1277/2401*T^27 - 65/49*T^26 + 
        519/2401*T^25 + 1738/2401*T^24 - 199/2401*T^23 - 851/2401*T^22 + 
        1082/2401*T^21 - 1269/2401*T^20 + 335/2401*T^19 + 387/2401*T^18 - 
        68/2401*T^17 - 429/2401*T^16 + 2151/2401*T^15 - 3501/2401*T^14 + 
        606/2401*T^13 + 2591/2401*T^12 - 1858/2401*T^11 + 2424/2401*T^10 - 
        4916/2401*T^9 + 3385/2401*T^8 - 1620/2401*T^7 + 4136/2401*T^6 - 533/343*T^5 
        - 482/2401*T^4 - 32/49*T^3 + 23/7*T^2 - 22/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 
        4*X*Y^8 + X*Y^7 + 5*X*Y^6 + X*Y^5 + 3*X*Y^4 + X*Y^3 + 6*X*Y^2 + 6*X + 4*Y^30
        + 6*Y^29 + 5*Y^28 + 5*Y^26 + 5*Y^24 + 5*Y^23 + Y^22 + 5*Y^21 + Y^19 + 6*Y^18
        + 5*Y^17 + 4*Y^16 + Y^15 + 6*Y^13 + 5*Y^12 + 4*Y^11 + Y^10 + 3*Y^9 + 3*Y^8 +
        4*Y^7 + 4*Y^6 + Y^4 + 2*Y^3 + 4*Y^2 + 3*Y,
    T^56 + 10/7*T^55 + 5/7*T^54 + 122/343*T^53 + 611/2401*T^52 + 6/49*T^51 + 
        1391/2401*T^50 + 358/2401*T^49 - 2180/2401*T^48 - 2516/2401*T^47 - 
        2172/2401*T^46 - 1614/2401*T^45 - 201/343*T^44 - 2208/2401*T^43 - 
        1801/2401*T^42 - 107/2401*T^41 + 659/2401*T^40 + 1810/2401*T^39 + 
        2270/2401*T^38 + 1180/2401*T^37 - 9/2401*T^36 + 18/343*T^35 + 1321/2401*T^34
        + 2486/2401*T^33 + 64/343*T^32 - 2621/2401*T^31 - 2545/2401*T^30 - 
        1058/2401*T^29 - 551/2401*T^28 - 1058/2401*T^27 - 2545/2401*T^26 - 
        2621/2401*T^25 + 64/343*T^24 + 2486/2401*T^23 + 1321/2401*T^22 + 18/343*T^21
        - 9/2401*T^20 + 1180/2401*T^19 + 2270/2401*T^18 + 1810/2401*T^17 + 
        659/2401*T^16 - 107/2401*T^15 - 1801/2401*T^14 - 2208/2401*T^13 - 
        201/343*T^12 - 1614/2401*T^11 - 2172/2401*T^10 - 2516/2401*T^9 - 
        2180/2401*T^8 + 358/2401*T^7 + 1391/2401*T^6 + 6/49*T^5 + 611/2401*T^4 + 
        122/343*T^3 + 5/7*T^2 + 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 4*X*Y^13 + X*Y^12 + 4*X*Y^11 + 2*X*Y^8 + X*Y^7 + 
        5*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 3*X*Y + 5*X + 6*Y^30 + 
        4*Y^29 + Y^28 + 6*Y^26 + 5*Y^25 + 5*Y^24 + 4*Y^23 + Y^22 + 5*Y^21 + Y^20 + 
        4*Y^17 + 6*Y^16 + Y^15 + 2*Y^13 + 5*Y^12 + 2*Y^10 + 4*Y^8 + 6*Y^7 + 3*Y^6 + 
        3*Y^5 + 2*Y^4 + 5*Y^3 + 3*Y^2 + 4*Y + 2,
    T^56 + 10/7*T^55 + 2/49*T^54 - 450/343*T^53 - 3481/2401*T^52 - 1054/2401*T^51 + 
        1726/2401*T^50 + 2770/2401*T^49 + 263/2401*T^48 - 1732/2401*T^47 - 
        683/2401*T^46 - 74/2401*T^45 - 587/2401*T^44 - 968/2401*T^43 - 111/2401*T^42
        + 561/2401*T^41 - 29/2401*T^40 - 869/2401*T^39 - 159/2401*T^38 + 
        1485/2401*T^37 + 1224/2401*T^36 - 893/2401*T^35 - 2496/2401*T^34 - 
        1385/2401*T^33 + 1425/2401*T^32 + 446/343*T^31 + 1697/2401*T^30 - 
        1083/2401*T^29 - 2220/2401*T^28 - 1083/2401*T^27 + 1697/2401*T^26 + 
        446/343*T^25 + 1425/2401*T^24 - 1385/2401*T^23 - 2496/2401*T^22 - 
        893/2401*T^21 + 1224/2401*T^20 + 1485/2401*T^19 - 159/2401*T^18 - 
        869/2401*T^17 - 29/2401*T^16 + 561/2401*T^15 - 111/2401*T^14 - 968/2401*T^13
        - 587/2401*T^12 - 74/2401*T^11 - 683/2401*T^10 - 1732/2401*T^9 + 
        263/2401*T^8 + 2770/2401*T^7 + 1726/2401*T^6 - 1054/2401*T^5 - 3481/2401*T^4
        - 450/343*T^3 + 2/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 
        + 4*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 6*X + 6*Y^30 +
        6*Y^29 + Y^27 + 6*Y^26 + 5*Y^25 + 5*Y^24 + 2*Y^23 + 5*Y^22 + 3*Y^21 + 6*Y^20
        + Y^18 + Y^17 + 6*Y^15 + 6*Y^14 + Y^12 + 3*Y^11 + 4*Y^8 + 5*Y^6 + 4*Y^5 + 
        3*Y^4 + 2*Y^3 + 6*Y^2 + 5*Y + 4,
    -T^56 - 6/7*T^55 - 2/7*T^54 + 83/343*T^53 - 37/2401*T^52 + 138/343*T^51 + 
        54/343*T^50 - 418/2401*T^49 + 215/2401*T^48 + 297/2401*T^47 - 495/2401*T^46 
        - 272/2401*T^45 - 55/343*T^44 - 1083/2401*T^43 - 282/2401*T^42 + 
        533/2401*T^41 + 375/2401*T^40 + 895/2401*T^39 + 2552/2401*T^38 + 
        661/2401*T^37 + 37/343*T^36 - 531/2401*T^35 - 244/2401*T^34 - 54/2401*T^33 +
        137/343*T^32 - 627/2401*T^31 - 946/2401*T^30 + 325/2401*T^29 - 325/2401*T^27
        + 946/2401*T^26 + 627/2401*T^25 - 137/343*T^24 + 54/2401*T^23 + 
        244/2401*T^22 + 531/2401*T^21 - 37/343*T^20 - 661/2401*T^19 - 2552/2401*T^18
        - 895/2401*T^17 - 375/2401*T^16 - 533/2401*T^15 + 282/2401*T^14 + 
        1083/2401*T^13 + 55/343*T^12 + 272/2401*T^11 + 495/2401*T^10 - 297/2401*T^9 
        - 215/2401*T^8 + 418/2401*T^7 - 54/343*T^6 - 138/343*T^5 + 37/2401*T^4 - 
        83/343*T^3 + 2/7*T^2 + 6/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + X*Y^11 + 6*X*Y^10 + 3*X*Y^8 + X*Y^7 + 
        6*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + X*Y^3 + 4*X*Y^2 + 6*Y^30 + 3*Y^29 + 4*Y^28 + 
        5*Y^27 + 3*Y^26 + Y^25 + 6*Y^24 + 3*Y^23 + 5*Y^22 + 2*Y^21 + 6*Y^19 + 3*Y^18
        + 3*Y^17 + 2*Y^16 + 2*Y^15 + 3*Y^13 + Y^12 + 6*Y^11 + Y^10 + 4*Y^9 + 4*Y^8 +
        4*Y^7 + 4*Y^6 + 6*Y^5 + 3*Y^4 + 2*Y^3 + 4,
    T^56 + T^55 + 50/49*T^54 + 365/343*T^53 + 2623/2401*T^52 + 2479/2401*T^51 + 
        23/49*T^50 - 921/2401*T^49 - 3436/2401*T^48 - 4815/2401*T^47 - 
        6047/2401*T^46 - 6999/2401*T^45 - 6189/2401*T^44 - 5199/2401*T^43 - 
        4735/2401*T^42 - 2042/2401*T^41 + 164/2401*T^40 + 2363/2401*T^39 + 
        4033/2401*T^38 + 4112/2401*T^37 + 3462/2401*T^36 + 556/343*T^35 + 
        3968/2401*T^34 + 335/343*T^33 + 864/2401*T^32 + 30/343*T^31 - 17/343*T^30 - 
        741/2401*T^29 - 331/2401*T^28 - 741/2401*T^27 - 17/343*T^26 + 30/343*T^25 + 
        864/2401*T^24 + 335/343*T^23 + 3968/2401*T^22 + 556/343*T^21 + 
        3462/2401*T^20 + 4112/2401*T^19 + 4033/2401*T^18 + 2363/2401*T^17 + 
        164/2401*T^16 - 2042/2401*T^15 - 4735/2401*T^14 - 5199/2401*T^13 - 
        6189/2401*T^12 - 6999/2401*T^11 - 6047/2401*T^10 - 4815/2401*T^9 - 
        3436/2401*T^8 - 921/2401*T^7 + 23/49*T^6 + 2479/2401*T^5 + 2623/2401*T^4 + 
        365/343*T^3 + 50/49*T^2 + T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 
        5*X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + X*Y^4 + 3*X*Y^3 + 6*X*Y + 6*X + 
        2*Y^30 + 3*Y^29 + 6*Y^28 + 5*Y^27 + 3*Y^25 + 6*Y^23 + Y^22 + 4*Y^21 + 6*Y^20
        + 4*Y^19 + 3*Y^18 + 3*Y^17 + Y^15 + 5*Y^14 + 3*Y^13 + 6*Y^12 + 2*Y^11 + 
        6*Y^10 + Y^9 + 6*Y^8 + 5*Y^7 + 2*Y^6 + Y^5 + 2*Y^4 + 3*Y^3 + 2*Y^2 + Y + 5,
    T^56 - 12/7*T^55 + 55/49*T^54 - 221/343*T^53 + 45/343*T^52 + 1217/2401*T^51 - 
        367/343*T^50 + 1896/2401*T^49 - 108/2401*T^48 - 199/2401*T^47 + 197/343*T^46
        - 3105/2401*T^45 + 1903/2401*T^44 + 526/2401*T^43 - 2133/2401*T^42 + 
        2942/2401*T^41 - 2514/2401*T^40 + 1804/2401*T^39 - 43/343*T^38 - 
        1104/2401*T^37 + 1627/2401*T^36 - 1714/2401*T^35 + 429/2401*T^34 + 
        605/2401*T^33 - 281/2401*T^32 + 3/49*T^31 - 500/2401*T^30 + 398/2401*T^29 - 
        23/343*T^28 + 398/2401*T^27 - 500/2401*T^26 + 3/49*T^25 - 281/2401*T^24 + 
        605/2401*T^23 + 429/2401*T^22 - 1714/2401*T^21 + 1627/2401*T^20 - 
        1104/2401*T^19 - 43/343*T^18 + 1804/2401*T^17 - 2514/2401*T^16 + 
        2942/2401*T^15 - 2133/2401*T^14 + 526/2401*T^13 + 1903/2401*T^12 - 
        3105/2401*T^11 + 197/343*T^10 - 199/2401*T^9 - 108/2401*T^8 + 1896/2401*T^7 
        - 367/343*T^6 + 1217/2401*T^5 + 45/343*T^4 - 221/343*T^3 + 55/49*T^2 - 
        12/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 3*X*Y^12 + X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 4*X*Y^7 + 
        X*Y^5 + 2*X*Y^3 + 3*X*Y^2 + 3*X + 6*Y^30 + 3*Y^29 + 4*Y^27 + 6*Y^26 + 3*Y^25
        + 6*Y^24 + Y^22 + 3*Y^20 + 5*Y^19 + 2*Y^18 + 4*Y^17 + 2*Y^16 + 6*Y^15 + 
        5*Y^14 + 6*Y^13 + 4*Y^8 + 5*Y^7 + 5*Y^5 + 3*Y^4 + 2*Y^3 + 6*Y^2 + 6,
    T^56 + 4/7*T^55 - 3/49*T^54 - 194/343*T^53 - 2995/2401*T^52 - 1520/2401*T^51 - 
        1681/2401*T^50 + 799/2401*T^49 + 1998/2401*T^48 + 241/343*T^47 + 
        1521/2401*T^46 - 1835/2401*T^45 - 1551/2401*T^44 - 2418/2401*T^43 - 
        618/2401*T^42 + 3718/2401*T^41 + 2921/2401*T^40 + 2941/2401*T^39 - 
        428/2401*T^38 - 2560/2401*T^37 - 3006/2401*T^36 - 3427/2401*T^35 + 
        32/2401*T^34 + 1196/2401*T^33 + 2925/2401*T^32 + 2432/2401*T^31 + 
        590/2401*T^30 - 1163/2401*T^29 - 3571/2401*T^28 - 1163/2401*T^27 + 
        590/2401*T^26 + 2432/2401*T^25 + 2925/2401*T^24 + 1196/2401*T^23 + 
        32/2401*T^22 - 3427/2401*T^21 - 3006/2401*T^20 - 2560/2401*T^19 - 
        428/2401*T^18 + 2941/2401*T^17 + 2921/2401*T^16 + 3718/2401*T^15 - 
        618/2401*T^14 - 2418/2401*T^13 - 1551/2401*T^12 - 1835/2401*T^11 + 
        1521/2401*T^10 + 241/343*T^9 + 1998/2401*T^8 + 799/2401*T^7 - 1681/2401*T^6 
        - 1520/2401*T^5 - 2995/2401*T^4 - 194/343*T^3 - 3/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 5*X*Y^8 
        + 3*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + X*Y^3 + 4*X*Y^2 + 6*X*Y + 3*X + Y^30 + 
        3*Y^29 + 3*Y^28 + 6*Y^27 + 4*Y^26 + 6*Y^25 + 2*Y^23 + Y^22 + 2*Y^21 + 3*Y^19
        + Y^18 + Y^17 + 4*Y^16 + 4*Y^15 + 2*Y^14 + 4*Y^13 + 6*Y^12 + 4*Y^11 + Y^10 +
        2*Y^9 + 3*Y^8 + 3*Y^7 + 5*Y^5 + 4*Y^3 + 4*Y^2 + 3*Y + 3,
    -T^56 + 78/49*T^54 - 68/343*T^53 - 1179/2401*T^52 - 1019/2401*T^51 - 
        2389/2401*T^50 + 1675/2401*T^49 + 1714/2401*T^48 - 367/2401*T^47 + 
        241/2401*T^46 - 857/2401*T^45 - 1156/2401*T^44 - 645/2401*T^43 + 
        374/2401*T^42 + 1942/2401*T^41 + 1924/2401*T^40 - 1283/2401*T^39 - 
        3616/2401*T^38 + 57/2401*T^37 + 2405/2401*T^36 + 1612/2401*T^35 + 
        613/2401*T^34 - 2249/2401*T^33 - 183/343*T^32 + 1483/2401*T^31 + 
        111/2401*T^30 + 594/2401*T^29 - 594/2401*T^27 - 111/2401*T^26 - 
        1483/2401*T^25 + 183/343*T^24 + 2249/2401*T^23 - 613/2401*T^22 - 
        1612/2401*T^21 - 2405/2401*T^20 - 57/2401*T^19 + 3616/2401*T^18 + 
        1283/2401*T^17 - 1924/2401*T^16 - 1942/2401*T^15 - 374/2401*T^14 + 
        645/2401*T^13 + 1156/2401*T^12 + 857/2401*T^11 - 241/2401*T^10 + 
        367/2401*T^9 - 1714/2401*T^8 - 1675/2401*T^7 + 2389/2401*T^6 + 1019/2401*T^5
        + 1179/2401*T^4 + 68/343*T^3 - 78/49*T^2 + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + X*Y^13 + 2*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 + 
        6*X*Y^7 + X*Y^6 + X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + X*Y^2 + 5*X*Y + 4*Y^30 + Y^29 
        + Y^27 + 5*Y^26 + 2*Y^25 + 6*Y^24 + 3*Y^22 + 4*Y^21 + 5*Y^20 + 5*Y^19 + 
        3*Y^18 + 2*Y^17 + 5*Y^16 + 6*Y^15 + 6*Y^14 + 2*Y^13 + 5*Y^12 + 6*Y^11 + 
        5*Y^10 + 5*Y^8 + Y^7 + 5*Y^6 + 6*Y^5 + 5*Y^4 + 2*Y^3 + Y^2 + 3*Y + 6,
    -T^56 - 6/7*T^55 - 1/7*T^54 - 220/343*T^53 - 382/343*T^52 - 284/343*T^51 + 
        13/343*T^50 + 395/2401*T^49 - 1376/2401*T^48 + 118/2401*T^47 + 610/2401*T^46
        + 19/2401*T^45 + 661/2401*T^44 + 296/2401*T^43 + 55/2401*T^42 + 
        1472/2401*T^41 + 1129/2401*T^40 + 226/343*T^39 + 262/343*T^38 + 
        1993/2401*T^37 + 335/343*T^36 + 2062/2401*T^35 + 1742/2401*T^34 + 
        100/343*T^33 + 227/2401*T^32 + 1287/2401*T^31 + 177/2401*T^30 - 
        1518/2401*T^29 + 1518/2401*T^27 - 177/2401*T^26 - 1287/2401*T^25 - 
        227/2401*T^24 - 100/343*T^23 - 1742/2401*T^22 - 2062/2401*T^21 - 
        335/343*T^20 - 1993/2401*T^19 - 262/343*T^18 - 226/343*T^17 - 1129/2401*T^16
        - 1472/2401*T^15 - 55/2401*T^14 - 296/2401*T^13 - 661/2401*T^12 - 
        19/2401*T^11 - 610/2401*T^10 - 118/2401*T^9 + 1376/2401*T^8 - 395/2401*T^7 -
        13/343*T^6 + 284/343*T^5 + 382/343*T^4 + 220/343*T^3 + 1/7*T^2 + 6/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 3*X*Y^13 + X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 + 
        4*X*Y^7 + 6*X*Y^5 + 5*X*Y^4 + 3*X*Y^2 + 2*X*Y + 6*X + 6*Y^30 + 4*Y^29 + 
        4*Y^28 + 3*Y^27 + 4*Y^26 + 3*Y^25 + Y^24 + Y^23 + Y^22 + 6*Y^21 + 6*Y^20 + 
        3*Y^19 + 2*Y^18 + Y^17 + Y^16 + 6*Y^15 + 4*Y^14 + 5*Y^12 + 2*Y^11 + 5*Y^9 + 
        6*Y^7 + 2*Y^6 + 2*Y^5 + 2*Y^4 + 4*Y^3 + Y^2 + 5*Y + 5,
    -T^56 - 12/7*T^55 - 16/7*T^54 - 750/343*T^53 - 3744/2401*T^52 - 627/2401*T^51 + 
        4444/2401*T^50 + 6542/2401*T^49 + 6865/2401*T^48 + 3541/2401*T^47 + 
        1031/2401*T^46 - 2921/2401*T^45 - 4093/2401*T^44 - 3057/2401*T^43 - 
        248/2401*T^42 + 2679/2401*T^41 + 2511/2401*T^40 + 2329/2401*T^39 - 
        171/2401*T^38 - 1291/2401*T^37 - 369/343*T^36 - 1710/2401*T^35 - 
        1327/2401*T^34 - 1277/2401*T^33 - 2048/2401*T^32 - 2986/2401*T^31 - 
        2787/2401*T^30 - 2057/2401*T^29 + 2057/2401*T^27 + 2787/2401*T^26 + 
        2986/2401*T^25 + 2048/2401*T^24 + 1277/2401*T^23 + 1327/2401*T^22 + 
        1710/2401*T^21 + 369/343*T^20 + 1291/2401*T^19 + 171/2401*T^18 - 
        2329/2401*T^17 - 2511/2401*T^16 - 2679/2401*T^15 + 248/2401*T^14 + 
        3057/2401*T^13 + 4093/2401*T^12 + 2921/2401*T^11 - 1031/2401*T^10 - 
        3541/2401*T^9 - 6865/2401*T^8 - 6542/2401*T^7 - 4444/2401*T^6 + 627/2401*T^5
        + 3744/2401*T^4 + 750/343*T^3 + 16/7*T^2 + 12/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + X*Y^12 + 5*X*Y^11 + 4*X*Y^9 + 2*X*Y^8 + X*Y^7 + 4*X*Y^6 + 
        6*X*Y^5 + X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + X + 3*Y^30 + 5*Y^29 + 4*Y^28 + 4*Y^27 
        + 2*Y^26 + 6*Y^25 + 5*Y^24 + 6*Y^23 + 5*Y^22 + 4*Y^21 + 6*Y^20 + 5*Y^19 + 
        4*Y^17 + 6*Y^16 + 4*Y^14 + Y^13 + 4*Y^12 + 4*Y^11 + 2*Y^10 + 4*Y^9 + 3*Y^7 +
        4*Y^6 + Y^5 + 3*Y^4 + 5*Y^3 + Y^2 + 6*Y,
    -T^56 + 4/7*T^55 + 13/49*T^54 - 480/343*T^53 + 3173/2401*T^52 - 1924/2401*T^51 -
        1910/2401*T^50 + 2025/2401*T^49 - 3419/2401*T^48 + 2579/2401*T^47 - 
        2010/2401*T^46 - 1790/2401*T^45 + 4016/2401*T^44 - 823/343*T^43 + 
        1051/2401*T^42 + 1339/2401*T^41 - 3786/2401*T^40 + 360/343*T^39 - 
        1763/2401*T^38 - 353/2401*T^37 - 8/49*T^36 - 2302/2401*T^35 + 351/343*T^34 -
        934/2401*T^33 - 1621/2401*T^32 + 951/2401*T^31 - 4/49*T^30 - 1088/2401*T^29 
        + 1088/2401*T^27 + 4/49*T^26 - 951/2401*T^25 + 1621/2401*T^24 + 
        934/2401*T^23 - 351/343*T^22 + 2302/2401*T^21 + 8/49*T^20 + 353/2401*T^19 + 
        1763/2401*T^18 - 360/343*T^17 + 3786/2401*T^16 - 1339/2401*T^15 - 
        1051/2401*T^14 + 823/343*T^13 - 4016/2401*T^12 + 1790/2401*T^11 + 
        2010/2401*T^10 - 2579/2401*T^9 + 3419/2401*T^8 - 2025/2401*T^7 + 
        1910/2401*T^6 + 1924/2401*T^5 - 3173/2401*T^4 + 480/343*T^3 - 13/49*T^2 - 
        4/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^13 + 3*X*Y^12 + 4*X*Y^10 + 4*X*Y^9 + 3*X*Y^8 + 2*X*Y^7 + 
        5*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 3*X*Y^2 + 4*X*Y + 3*X + 3*Y^30 + Y^28 + 2*Y^27
        + 3*Y^26 + 4*Y^24 + 6*Y^23 + 6*Y^22 + 6*Y^20 + 4*Y^19 + 2*Y^18 + Y^17 + 
        5*Y^16 + 3*Y^15 + 4*Y^14 + 3*Y^13 + 5*Y^12 + 3*Y^10 + 6*Y^9 + 6*Y^8 + 4*Y^7 
        + 4*Y^5 + 3*Y^4 + Y^3 + 4*Y^2 + 3,
    -T^56 - 2/7*T^55 + 34/49*T^54 - 80/343*T^53 + 2134/2401*T^52 + 1828/2401*T^51 - 
        1780/2401*T^50 - 1893/2401*T^49 - 753/2401*T^48 - 645/2401*T^47 + 
        444/2401*T^46 + 1128/2401*T^45 + 242/2401*T^44 + 2047/2401*T^43 - 
        884/2401*T^42 - 1312/2401*T^41 + 1611/2401*T^40 - 1108/2401*T^39 - 
        1497/2401*T^38 + 834/2401*T^37 - 110/2401*T^36 - 1038/2401*T^35 + 
        674/2401*T^34 + 1151/2401*T^33 + 1133/2401*T^32 - 829/2401*T^31 - 
        2174/2401*T^30 - 2/2401*T^29 + 2/2401*T^27 + 2174/2401*T^26 + 829/2401*T^25 
        - 1133/2401*T^24 - 1151/2401*T^23 - 674/2401*T^22 + 1038/2401*T^21 + 
        110/2401*T^20 - 834/2401*T^19 + 1497/2401*T^18 + 1108/2401*T^17 - 
        1611/2401*T^16 + 1312/2401*T^15 + 884/2401*T^14 - 2047/2401*T^13 - 
        242/2401*T^12 - 1128/2401*T^11 - 444/2401*T^10 + 645/2401*T^9 + 753/2401*T^8
        + 1893/2401*T^7 + 1780/2401*T^6 - 1828/2401*T^5 - 2134/2401*T^4 + 80/343*T^3
        - 34/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 
        + X*Y^8 + 2*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + X*Y + 4*Y^30 + 6*Y^29 + 
        2*Y^27 + 4*Y^26 + 5*Y^25 + 6*Y^24 + 4*Y^22 + 2*Y^21 + 3*Y^20 + 4*Y^18 + 
        2*Y^17 + 4*Y^16 + 6*Y^15 + 2*Y^14 + 6*Y^12 + 6*Y^11 + 5*Y^10 + 2*Y^8 + 2*Y^7
        + 5*Y^6 + 2*Y^5 + 6*Y^4 + 5*Y^3 + 2*Y^2 + 6*Y + 5,
    T^56 - 54/49*T^54 + 4/49*T^53 + 3511/2401*T^52 - 1108/2401*T^51 - 2879/2401*T^50
        + 1111/2401*T^49 + 2623/2401*T^48 - 2442/2401*T^47 - 1689/2401*T^46 + 
        361/343*T^45 + 250/2401*T^44 - 432/343*T^43 + 403/2401*T^42 + 2312/2401*T^41
        + 46/2401*T^40 - 1354/2401*T^39 + 6/49*T^38 + 169/343*T^37 + 62/2401*T^36 - 
        117/343*T^35 + 1013/2401*T^34 + 118/343*T^33 - 925/2401*T^32 - 347/2401*T^31
        + 1080/2401*T^30 - 251/2401*T^29 - 1899/2401*T^28 - 251/2401*T^27 + 
        1080/2401*T^26 - 347/2401*T^25 - 925/2401*T^24 + 118/343*T^23 + 
        1013/2401*T^22 - 117/343*T^21 + 62/2401*T^20 + 169/343*T^19 + 6/49*T^18 - 
        1354/2401*T^17 + 46/2401*T^16 + 2312/2401*T^15 + 403/2401*T^14 - 
        432/343*T^13 + 250/2401*T^12 + 361/343*T^11 - 1689/2401*T^10 - 2442/2401*T^9
        + 2623/2401*T^8 + 1111/2401*T^7 - 2879/2401*T^6 - 1108/2401*T^5 + 
        3511/2401*T^4 + 4/49*T^3 - 54/49*T^2 + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + X*Y^13 + X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^8 + 
        3*X*Y^7 + 4*X*Y^5 + 6*X*Y^3 + 5*X*Y^2 + 3*X*Y + 4*X + 2*Y^30 + 4*Y^29 + 
        5*Y^28 + 4*Y^26 + 5*Y^25 + 4*Y^24 + Y^23 + 6*Y^22 + 6*Y^21 + 3*Y^20 + 6*Y^19
        + 4*Y^18 + 2*Y^17 + 2*Y^16 + 4*Y^15 + 3*Y^13 + 2*Y^12 + 3*Y^11 + 5*Y^10 + 
        Y^9 + 3*Y^8 + 4*Y^7 + 2*Y^6 + 2*Y^5 + 4*Y^4 + Y^3 + 3*Y^2 + 3*Y + 6,
    T^56 - 8/7*T^55 + 3/7*T^54 + 258/343*T^53 - 3127/2401*T^52 + 1829/2401*T^51 + 
        855/2401*T^50 - 2209/2401*T^49 + 377/2401*T^48 + 1079/2401*T^47 - 
        1801/2401*T^46 + 1440/2401*T^45 - 156/343*T^44 + 1107/2401*T^43 - 
        1868/2401*T^42 + 507/2401*T^41 + 550/2401*T^40 - 1521/2401*T^39 + 
        1249/2401*T^38 + 90/2401*T^37 - 776/2401*T^36 + 19/49*T^35 + 95/2401*T^34 - 
        1144/2401*T^33 + 1399/2401*T^32 - 424/2401*T^31 + 75/343*T^30 - 
        617/2401*T^29 + 13/49*T^28 - 617/2401*T^27 + 75/343*T^26 - 424/2401*T^25 + 
        1399/2401*T^24 - 1144/2401*T^23 + 95/2401*T^22 + 19/49*T^21 - 776/2401*T^20 
        + 90/2401*T^19 + 1249/2401*T^18 - 1521/2401*T^17 + 550/2401*T^16 + 
        507/2401*T^15 - 1868/2401*T^14 + 1107/2401*T^13 - 156/343*T^12 + 
        1440/2401*T^11 - 1801/2401*T^10 + 1079/2401*T^9 + 377/2401*T^8 - 
        2209/2401*T^7 + 855/2401*T^6 + 1829/2401*T^5 - 3127/2401*T^4 + 258/343*T^3 +
        3/7*T^2 - 8/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 6*X*Y^13 + X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + X*Y^8 + 
        5*X*Y^7 + 5*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 6*X*Y + X + 
        4*Y^30 + 3*Y^29 + Y^28 + 2*Y^27 + 2*Y^25 + Y^24 + 3*Y^23 + 6*Y^22 + 4*Y^21 +
        6*Y^20 + 6*Y^19 + 3*Y^18 + 3*Y^17 + 6*Y^16 + 5*Y^15 + 6*Y^14 + 6*Y^13 + 
        5*Y^12 + Y^11 + 4*Y^10 + 5*Y^9 + 5*Y^7 + 5*Y^6 + 4*Y^5 + 2*Y^4 + 6*Y^3 + 
        3*Y^2 + Y,
    T^56 + T^55 - 40/49*T^54 - 5/343*T^53 + 1448/2401*T^52 - 1685/2401*T^51 - 
        1380/2401*T^50 - 1770/2401*T^49 + 1452/2401*T^48 + 3891/2401*T^47 - 
        1047/2401*T^46 + 1394/2401*T^45 + 2309/2401*T^44 - 2755/2401*T^43 + 
        276/2401*T^42 - 1886/2401*T^41 - 592/343*T^40 + 1448/2401*T^39 - 
        1468/2401*T^38 + 698/2401*T^37 + 4266/2401*T^36 - 2858/2401*T^35 + 
        267/2401*T^34 + 2400/2401*T^33 - 172/343*T^32 + 1592/2401*T^31 - 
        3083/2401*T^30 - 1917/2401*T^29 + 5619/2401*T^28 - 1917/2401*T^27 - 
        3083/2401*T^26 + 1592/2401*T^25 - 172/343*T^24 + 2400/2401*T^23 + 
        267/2401*T^22 - 2858/2401*T^21 + 4266/2401*T^20 + 698/2401*T^19 - 
        1468/2401*T^18 + 1448/2401*T^17 - 592/343*T^16 - 1886/2401*T^15 + 
        276/2401*T^14 - 2755/2401*T^13 + 2309/2401*T^12 + 1394/2401*T^11 - 
        1047/2401*T^10 + 3891/2401*T^9 + 1452/2401*T^8 - 1770/2401*T^7 - 
        1380/2401*T^6 - 1685/2401*T^5 + 1448/2401*T^4 - 5/343*T^3 - 40/49*T^2 + T + 
        1
*], [*
    X^3 + 4*X*Y^14 + X*Y^13 + X*Y^12 + X*Y^11 + X*Y^9 + X*Y^7 + X*Y^6 + 4*X*Y^5 + 
        4*X*Y^4 + 2*X*Y^3 + 4*X + 2*Y^30 + 6*Y^29 + 4*Y^28 + 6*Y^27 + 3*Y^26 + 
        3*Y^24 + 3*Y^23 + 3*Y^22 + 6*Y^21 + 4*Y^20 + 3*Y^19 + Y^18 + 4*Y^17 + Y^16 +
        Y^15 + 5*Y^14 + Y^12 + Y^11 + 5*Y^9 + 4*Y^8 + 4*Y^7 + 3*Y^6 + 2*Y^5 + Y^4 + 
        3*Y^3 + 5*Y^2 + 5*Y,
    T^56 + 4/7*T^55 - 6/49*T^54 + 117/343*T^53 + 1025/2401*T^52 - 891/2401*T^51 - 
        2965/2401*T^50 - 1102/2401*T^49 - 129/343*T^48 - 1696/2401*T^47 - 
        1327/2401*T^46 + 827/2401*T^45 + 2367/2401*T^44 + 391/2401*T^43 + 
        1157/2401*T^42 + 1413/2401*T^41 + 701/2401*T^40 - 492/2401*T^39 - 
        1307/2401*T^38 - 1/49*T^37 - 176/2401*T^36 - 1208/2401*T^35 - 1234/2401*T^34
        - 10/343*T^33 + 645/2401*T^32 + 155/2401*T^31 - 166/2401*T^30 + 
        342/2401*T^29 + 930/2401*T^28 + 342/2401*T^27 - 166/2401*T^26 + 
        155/2401*T^25 + 645/2401*T^24 - 10/343*T^23 - 1234/2401*T^22 - 
        1208/2401*T^21 - 176/2401*T^20 - 1/49*T^19 - 1307/2401*T^18 - 492/2401*T^17 
        + 701/2401*T^16 + 1413/2401*T^15 + 1157/2401*T^14 + 391/2401*T^13 + 
        2367/2401*T^12 + 827/2401*T^11 - 1327/2401*T^10 - 1696/2401*T^9 - 
        129/343*T^8 - 1102/2401*T^7 - 2965/2401*T^6 - 891/2401*T^5 + 1025/2401*T^4 +
        117/343*T^3 - 6/49*T^2 + 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^13 + 2*X*Y^12 + X*Y^9 + 6*X*Y^8 + 4*X*Y^7 + 6*X*Y^6 + 
        3*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 2*X*Y + 5*Y^30 + 4*Y^29 + 6*Y^28 + 
        3*Y^27 + Y^26 + 3*Y^25 + 4*Y^24 + Y^22 + 4*Y^21 + Y^19 + 2*Y^18 + 5*Y^17 + 
        5*Y^12 + Y^11 + 3*Y^9 + 2*Y^8 + 6*Y^7 + 5*Y^6 + 4*Y^5 + Y^4 + Y^2 + Y + 4,
    T^56 + 8/7*T^55 - 29/49*T^53 - 1901/2401*T^52 - 1775/2401*T^51 + 429/2401*T^50 +
        3078/2401*T^49 + 2553/2401*T^48 + 960/2401*T^47 - 1765/2401*T^46 - 
        2803/2401*T^45 - 1665/2401*T^44 + 1/7*T^43 + 1298/2401*T^42 + 1870/2401*T^41
        + 531/2401*T^40 - 3116/2401*T^39 - 2390/2401*T^38 + 19/2401*T^37 + 
        811/2401*T^36 + 1494/2401*T^35 + 1728/2401*T^34 - 689/2401*T^33 - 
        1915/2401*T^32 - 1578/2401*T^31 - 786/2401*T^30 + 869/2401*T^29 + 
        1368/2401*T^28 + 869/2401*T^27 - 786/2401*T^26 - 1578/2401*T^25 - 
        1915/2401*T^24 - 689/2401*T^23 + 1728/2401*T^22 + 1494/2401*T^21 + 
        811/2401*T^20 + 19/2401*T^19 - 2390/2401*T^18 - 3116/2401*T^17 + 
        531/2401*T^16 + 1870/2401*T^15 + 1298/2401*T^14 + 1/7*T^13 - 1665/2401*T^12 
        - 2803/2401*T^11 - 1765/2401*T^10 + 960/2401*T^9 + 2553/2401*T^8 + 
        3078/2401*T^7 + 429/2401*T^6 - 1775/2401*T^5 - 1901/2401*T^4 - 29/49*T^3 + 
        8/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 
        + 5*X*Y^8 + 3*X*Y^6 + X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + X*Y^2 + 5*X*Y + 6*X + 
        6*Y^30 + 6*Y^29 + 3*Y^27 + 3*Y^26 + 6*Y^25 + 2*Y^24 + 3*Y^23 + 6*Y^21 + 
        2*Y^20 + Y^18 + Y^16 + 5*Y^15 + 6*Y^14 + 4*Y^13 + 6*Y^12 + 6*Y^11 + 4*Y^10 +
        Y^9 + 3*Y^8 + 5*Y^6 + 2*Y^5 + Y^4 + 3*Y^3 + 5*Y + 1,
    T^56 - 30/49*T^54 + 8/343*T^53 + 375/2401*T^52 - 157/2401*T^51 - 110/343*T^50 - 
        785/2401*T^49 - 160/343*T^48 + 1634/2401*T^47 + 1495/2401*T^46 - 
        1360/2401*T^45 + 1510/2401*T^44 + 2064/2401*T^43 - 366/2401*T^42 - 
        514/2401*T^41 + 278/2401*T^40 - 1441/2401*T^39 - 114/2401*T^38 + 
        559/2401*T^37 - 1884/2401*T^36 + 769/2401*T^35 + 183/343*T^34 - 
        754/2401*T^33 - 179/343*T^32 + 2497/2401*T^31 + 1004/2401*T^30 - 32/49*T^29 
        + 166/2401*T^28 - 32/49*T^27 + 1004/2401*T^26 + 2497/2401*T^25 - 
        179/343*T^24 - 754/2401*T^23 + 183/343*T^22 + 769/2401*T^21 - 1884/2401*T^20
        + 559/2401*T^19 - 114/2401*T^18 - 1441/2401*T^17 + 278/2401*T^16 - 
        514/2401*T^15 - 366/2401*T^14 + 2064/2401*T^13 + 1510/2401*T^12 - 
        1360/2401*T^11 + 1495/2401*T^10 + 1634/2401*T^9 - 160/343*T^8 - 785/2401*T^7
        - 110/343*T^6 - 157/2401*T^5 + 375/2401*T^4 + 8/343*T^3 - 30/49*T^2 + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 +
        2*X*Y^7 + X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 3*X*Y + 5*X + 
        2*Y^30 + 4*Y^29 + 6*Y^28 + 6*Y^27 + 3*Y^26 + 6*Y^25 + 3*Y^24 + 6*Y^23 + 
        3*Y^22 + 3*Y^21 + 5*Y^20 + 4*Y^19 + Y^18 + Y^15 + 2*Y^14 + 6*Y^13 + 2*Y^12 +
        2*Y^11 + 5*Y^10 + 3*Y^9 + 2*Y^8 + 4*Y^6 + 4*Y^5 + 6*Y^4 + 4*Y^2 + 6*Y,
    T^56 + 5/7*T^55 + 6/7*T^54 - 43/343*T^53 + 54/2401*T^52 + 52/343*T^51 + 
        2367/2401*T^50 + 1854/2401*T^49 + 2045/2401*T^48 + 1284/2401*T^47 + 
        354/2401*T^46 + 1126/2401*T^45 - 584/2401*T^44 + 1398/2401*T^43 - 
        209/2401*T^42 + 2129/2401*T^41 + 29/2401*T^40 + 2339/2401*T^39 - 
        50/2401*T^38 + 1518/2401*T^37 - 514/2401*T^36 + 16/2401*T^35 + 521/2401*T^34
        + 229/2401*T^33 + 1375/2401*T^32 - 1255/2401*T^31 + 712/2401*T^30 - 
        2046/2401*T^29 + 991/2401*T^28 - 2046/2401*T^27 + 712/2401*T^26 - 
        1255/2401*T^25 + 1375/2401*T^24 + 229/2401*T^23 + 521/2401*T^22 + 
        16/2401*T^21 - 514/2401*T^20 + 1518/2401*T^19 - 50/2401*T^18 + 
        2339/2401*T^17 + 29/2401*T^16 + 2129/2401*T^15 - 209/2401*T^14 + 
        1398/2401*T^13 - 584/2401*T^12 + 1126/2401*T^11 + 354/2401*T^10 + 
        1284/2401*T^9 + 2045/2401*T^8 + 1854/2401*T^7 + 2367/2401*T^6 + 52/343*T^5 +
        54/2401*T^4 - 43/343*T^3 + 6/7*T^2 + 5/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        2*X*Y^8 + 3*X*Y^7 + 6*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + X*Y^2 + 5*X*Y + 5*X + 
        4*Y^30 + Y^29 + 2*Y^28 + 4*Y^27 + Y^26 + Y^25 + Y^24 + 5*Y^22 + 6*Y^21 + 
        3*Y^20 + 2*Y^18 + Y^17 + Y^16 + Y^15 + 2*Y^13 + Y^12 + Y^11 + 4*Y^10 + 2*Y^9
        + 5*Y^8 + 4*Y^7 + 5*Y^6 + Y^5 + 6*Y^4 + 3*Y^3 + Y^2 + 6*Y + 5,
    T^56 + 1/7*T^55 - 45/49*T^54 - 159/343*T^53 + 31/2401*T^52 - 351/2401*T^51 - 
        47/2401*T^50 + 732/2401*T^49 + 257/2401*T^48 + 95/2401*T^47 + 512/2401*T^46 
        + 624/2401*T^45 - 1084/2401*T^44 - 1335/2401*T^43 - 573/2401*T^42 + 
        1378/2401*T^41 + 1258/2401*T^40 - 227/2401*T^39 + 198/2401*T^38 - 
        433/2401*T^37 - 1121/2401*T^36 - 414/2401*T^35 + 370/2401*T^34 - 
        167/2401*T^33 - 500/2401*T^32 + 482/2401*T^31 + 1513/2401*T^30 + 
        260/2401*T^29 - 1543/2401*T^28 + 260/2401*T^27 + 1513/2401*T^26 + 
        482/2401*T^25 - 500/2401*T^24 - 167/2401*T^23 + 370/2401*T^22 - 
        414/2401*T^21 - 1121/2401*T^20 - 433/2401*T^19 + 198/2401*T^18 - 
        227/2401*T^17 + 1258/2401*T^16 + 1378/2401*T^15 - 573/2401*T^14 - 
        1335/2401*T^13 - 1084/2401*T^12 + 624/2401*T^11 + 512/2401*T^10 + 
        95/2401*T^9 + 257/2401*T^8 + 732/2401*T^7 - 47/2401*T^6 - 351/2401*T^5 + 
        31/2401*T^4 - 159/343*T^3 - 45/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 2*X*Y^8 +
        4*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + X*Y^2 + 5*X + 3*Y^30 + 
        3*Y^27 + 3*Y^26 + 2*Y^25 + 2*Y^23 + 3*Y^22 + 2*Y^21 + 3*Y^20 + 4*Y^19 + 
        4*Y^18 + 4*Y^17 + 6*Y^16 + 3*Y^15 + Y^14 + 4*Y^13 + Y^12 + 3*Y^10 + 5*Y^8 + 
        5*Y^7 + 3*Y^6 + Y^5 + 6*Y^4 + 5*Y^2 + Y + 2,
    T^56 - 10/7*T^55 + 58/49*T^54 - 39/49*T^53 + 41/49*T^52 - 832/2401*T^51 - 
        293/2401*T^50 + 1670/2401*T^49 - 1689/2401*T^48 + 300/343*T^47 - 
        2238/2401*T^46 + 110/343*T^45 + 1970/2401*T^44 - 4348/2401*T^43 + 
        5297/2401*T^42 - 5422/2401*T^41 + 5667/2401*T^40 - 638/343*T^39 + 
        1356/2401*T^38 + 1220/2401*T^37 - 2661/2401*T^36 + 67/49*T^35 - 
        3596/2401*T^34 + 2622/2401*T^33 - 961/2401*T^32 - 1481/2401*T^31 + 
        4574/2401*T^30 - 7045/2401*T^29 + 7393/2401*T^28 - 7045/2401*T^27 + 
        4574/2401*T^26 - 1481/2401*T^25 - 961/2401*T^24 + 2622/2401*T^23 - 
        3596/2401*T^22 + 67/49*T^21 - 2661/2401*T^20 + 1220/2401*T^19 + 
        1356/2401*T^18 - 638/343*T^17 + 5667/2401*T^16 - 5422/2401*T^15 + 
        5297/2401*T^14 - 4348/2401*T^13 + 1970/2401*T^12 + 110/343*T^11 - 
        2238/2401*T^10 + 300/343*T^9 - 1689/2401*T^8 + 1670/2401*T^7 - 293/2401*T^6 
        - 832/2401*T^5 + 41/49*T^4 - 39/49*T^3 + 58/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 3*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + 6*X*Y^8 +
        3*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 5*X*Y + 5*Y^30 +
        2*Y^28 + 2*Y^27 + 4*Y^26 + Y^25 + 3*Y^23 + 3*Y^22 + Y^21 + 4*Y^20 + 3*Y^19 +
        3*Y^17 + 4*Y^16 + 5*Y^15 + 5*Y^14 + 2*Y^13 + 2*Y^12 + 3*Y^11 + 5*Y^10 + 
        4*Y^9 + 5*Y^8 + 2*Y^7 + 2*Y^6 + Y^4 + 5*Y^3 + 3*Y^2 + 6,
    T^56 - 5/7*T^55 - 12/7*T^54 + 424/343*T^53 + 2199/2401*T^52 - 1136/2401*T^51 - 
        578/2401*T^50 + 480/2401*T^49 - 678/2401*T^48 - 1237/2401*T^47 + 
        3447/2401*T^46 - 214/2401*T^45 - 4117/2401*T^44 + 412/2401*T^43 + 
        3333/2401*T^42 + 1671/2401*T^41 - 4118/2401*T^40 - 67/343*T^39 + 
        3372/2401*T^38 - 348/343*T^37 - 156/2401*T^36 + 2957/2401*T^35 - 
        2174/2401*T^34 - 60/49*T^33 + 2839/2401*T^32 + 3176/2401*T^31 - 
        2848/2401*T^30 - 1539/2401*T^29 + 2873/2401*T^28 - 1539/2401*T^27 - 
        2848/2401*T^26 + 3176/2401*T^25 + 2839/2401*T^24 - 60/49*T^23 - 
        2174/2401*T^22 + 2957/2401*T^21 - 156/2401*T^20 - 348/343*T^19 + 
        3372/2401*T^18 - 67/343*T^17 - 4118/2401*T^16 + 1671/2401*T^15 + 
        3333/2401*T^14 + 412/2401*T^13 - 4117/2401*T^12 - 214/2401*T^11 + 
        3447/2401*T^10 - 1237/2401*T^9 - 678/2401*T^8 + 480/2401*T^7 - 578/2401*T^6 
        - 1136/2401*T^5 + 2199/2401*T^4 + 424/343*T^3 - 12/7*T^2 - 5/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 5*X*Y^12 + 2*X*Y^10 + 4*X*Y^8 + 2*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 
        3*X*Y^3 + X*Y^2 + 2*X*Y + 5*X + 3*Y^30 + 3*Y^28 + 3*Y^27 + 4*Y^26 + Y^25 + 
        5*Y^24 + 3*Y^23 + 6*Y^22 + 3*Y^21 + Y^20 + Y^19 + 6*Y^18 + 3*Y^17 + 6*Y^14 +
        6*Y^13 + 3*Y^12 + 4*Y^11 + Y^10 + 2*Y^9 + 4*Y^8 + Y^6 + 2*Y^5 + 2*Y^4 + Y^3 
        + 3*Y^2 + 2,
    -T^56 + 10/7*T^55 - 1/7*T^54 - 270/343*T^53 + 515/2401*T^52 - 81/2401*T^51 + 
        234/343*T^50 - 1174/2401*T^49 - 955/2401*T^48 - 162/2401*T^47 + 
        1454/2401*T^46 - 843/2401*T^45 + 830/2401*T^44 - 701/2401*T^43 - 
        1613/2401*T^42 + 3433/2401*T^41 - 1738/2401*T^40 - 811/2401*T^39 + 
        1998/2401*T^38 - 1471/2401*T^37 + 193/2401*T^36 - 767/2401*T^35 + 
        540/2401*T^34 + 2367/2401*T^33 - 2556/2401*T^32 - 957/2401*T^31 + 
        349/343*T^30 - 510/2401*T^29 + 510/2401*T^27 - 349/343*T^26 + 957/2401*T^25 
        + 2556/2401*T^24 - 2367/2401*T^23 - 540/2401*T^22 + 767/2401*T^21 - 
        193/2401*T^20 + 1471/2401*T^19 - 1998/2401*T^18 + 811/2401*T^17 + 
        1738/2401*T^16 - 3433/2401*T^15 + 1613/2401*T^14 + 701/2401*T^13 - 
        830/2401*T^12 + 843/2401*T^11 - 1454/2401*T^10 + 162/2401*T^9 + 955/2401*T^8
        + 1174/2401*T^7 - 234/343*T^6 + 81/2401*T^5 - 515/2401*T^4 + 270/343*T^3 + 
        1/7*T^2 - 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 
        + 4*X*Y^8 + 6*X*Y^7 + X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 4*X*Y 
        + 2*X + 2*Y^30 + 6*Y^29 + 6*Y^28 + Y^27 + Y^26 + 5*Y^25 + Y^23 + 6*Y^22 + 
        4*Y^21 + 6*Y^20 + 4*Y^18 + 3*Y^17 + Y^16 + 2*Y^15 + 4*Y^14 + 3*Y^13 + Y^12 +
        5*Y^11 + 3*Y^10 + 3*Y^8 + 4*Y^7 + 6*Y^5 + 2*Y^4 + 2*Y^3 + 4*Y^2 + 1,
    -T^56 - 6/7*T^55 + 1/49*T^54 + 270/343*T^53 + 1762/2401*T^52 + 718/2401*T^51 - 
        579/2401*T^50 - 51/343*T^49 - 419/2401*T^48 - 163/343*T^47 + 624/2401*T^46 +
        1563/2401*T^45 + 605/2401*T^44 - 192/2401*T^43 - 911/2401*T^42 - 
        1191/2401*T^41 + 442/2401*T^40 + 975/2401*T^39 + 522/2401*T^38 - 47/343*T^37
        - 1226/2401*T^36 - 116/343*T^35 + 97/343*T^34 + 800/2401*T^33 + 
        646/2401*T^32 + 240/2401*T^31 - 221/2401*T^30 - 107/2401*T^29 + 
        107/2401*T^27 + 221/2401*T^26 - 240/2401*T^25 - 646/2401*T^24 - 
        800/2401*T^23 - 97/343*T^22 + 116/343*T^21 + 1226/2401*T^20 + 47/343*T^19 - 
        522/2401*T^18 - 975/2401*T^17 - 442/2401*T^16 + 1191/2401*T^15 + 
        911/2401*T^14 + 192/2401*T^13 - 605/2401*T^12 - 1563/2401*T^11 - 
        624/2401*T^10 + 163/343*T^9 + 419/2401*T^8 + 51/343*T^7 + 579/2401*T^6 - 
        718/2401*T^5 - 1762/2401*T^4 - 270/343*T^3 - 1/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 6*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 + X*Y^7 + 
        5*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 2*X*Y + 6*X + 4*Y^30 + 3*Y^29 + 
        4*Y^28 + 3*Y^27 + 5*Y^26 + 5*Y^25 + 4*Y^24 + 2*Y^22 + 4*Y^21 + 4*Y^20 + 
        4*Y^18 + 3*Y^17 + 3*Y^16 + 3*Y^15 + 4*Y^14 + Y^13 + 5*Y^12 + 2*Y^11 + Y^10 +
        4*Y^9 + 3*Y^8 + Y^7 + 5*Y^6 + Y^5 + 3*Y^3 + 3*Y^2 + 5*Y + 2,
    T^56 + 2/7*T^55 - 5/7*T^54 + 94/343*T^53 + 87/343*T^52 - 650/2401*T^51 + 
        424/2401*T^50 + 2061/2401*T^49 + 1096/2401*T^48 - 1627/2401*T^47 - 
        247/2401*T^46 - 117/2401*T^45 - 1621/2401*T^44 + 39/2401*T^43 + 
        1506/2401*T^42 + 1293/2401*T^41 - 1429/2401*T^40 - 1697/2401*T^39 - 
        150/2401*T^38 - 802/2401*T^37 - 145/2401*T^36 + 95/343*T^35 + 108/343*T^34 +
        548/2401*T^33 - 1228/2401*T^32 - 1314/2401*T^31 - 62/2401*T^30 + 
        677/2401*T^29 + 451/2401*T^28 + 677/2401*T^27 - 62/2401*T^26 - 
        1314/2401*T^25 - 1228/2401*T^24 + 548/2401*T^23 + 108/343*T^22 + 95/343*T^21
        - 145/2401*T^20 - 802/2401*T^19 - 150/2401*T^18 - 1697/2401*T^17 - 
        1429/2401*T^16 + 1293/2401*T^15 + 1506/2401*T^14 + 39/2401*T^13 - 
        1621/2401*T^12 - 117/2401*T^11 - 247/2401*T^10 - 1627/2401*T^9 + 
        1096/2401*T^8 + 2061/2401*T^7 + 424/2401*T^6 - 650/2401*T^5 + 87/343*T^4 + 
        94/343*T^3 - 5/7*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 
        4*X*Y^7 + X*Y^6 + 6*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 2*X*Y + 4*X + Y^30 + 5*Y^28 
        + 5*Y^27 + 6*Y^26 + 3*Y^24 + 6*Y^23 + 5*Y^21 + 6*Y^20 + 5*Y^19 + 3*Y^18 + 
        6*Y^17 + Y^16 + Y^15 + 5*Y^14 + 3*Y^12 + Y^11 + Y^10 + 5*Y^9 + Y^8 + 5*Y^7 +
        Y^6 + 5*Y^5 + 5*Y^4 + Y^3 + 3*Y^2 + 6*Y + 3,
    T^56 - 2/7*T^55 - 48/49*T^54 - 22/343*T^53 + 262/343*T^52 + 768/2401*T^51 - 
        834/2401*T^50 - 701/2401*T^49 - 88/2401*T^48 - 548/2401*T^47 + 939/2401*T^46
        - 67/343*T^45 - 365/2401*T^44 + 1448/2401*T^43 - 114/2401*T^42 - 
        827/2401*T^41 + 132/2401*T^40 + 716/2401*T^39 - 570/2401*T^38 - 
        376/2401*T^37 + 426/2401*T^36 - 85/2401*T^35 - 30/2401*T^34 + 457/2401*T^33 
        - 1040/2401*T^32 - 773/2401*T^31 + 998/2401*T^30 + 339/2401*T^29 - 
        856/2401*T^28 + 339/2401*T^27 + 998/2401*T^26 - 773/2401*T^25 - 
        1040/2401*T^24 + 457/2401*T^23 - 30/2401*T^22 - 85/2401*T^21 + 426/2401*T^20
        - 376/2401*T^19 - 570/2401*T^18 + 716/2401*T^17 + 132/2401*T^16 - 
        827/2401*T^15 - 114/2401*T^14 + 1448/2401*T^13 - 365/2401*T^12 - 67/343*T^11
        + 939/2401*T^10 - 548/2401*T^9 - 88/2401*T^8 - 701/2401*T^7 - 834/2401*T^6 +
        768/2401*T^5 + 262/343*T^4 - 22/343*T^3 - 48/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 6*X*Y^12 + 6*X*Y^10 + 3*X*Y^9 + 5*X*Y^7 + 3*X*Y^6 + 
        4*X*Y^5 + 3*X*Y^4 + X*Y^3 + 4*X*Y^2 + 2*X*Y + 5*X + 5*Y^30 + Y^28 + Y^27 + 
        4*Y^26 + 4*Y^24 + 2*Y^23 + 5*Y^22 + Y^21 + 3*Y^20 + Y^19 + 4*Y^18 + Y^17 + 
        Y^16 + 6*Y^15 + 5*Y^14 + 5*Y^13 + 4*Y^12 + Y^11 + 5*Y^10 + Y^9 + 2*Y^8 + 
        4*Y^6 + 5*Y^5 + 2*Y^4 + 2*Y^3 + 1,
    -T^56 - 8/7*T^55 + 3/343*T^53 - 340/2401*T^52 + 1334/2401*T^51 + 2368/2401*T^50 
        + 711/2401*T^49 - 2134/2401*T^48 - 352/343*T^47 - 237/2401*T^46 - 
        192/343*T^45 - 2890/2401*T^44 + 331/2401*T^43 + 3116/2401*T^42 + 
        2336/2401*T^41 + 675/2401*T^40 + 510/2401*T^39 + 533/2401*T^38 - 
        2410/2401*T^37 - 4633/2401*T^36 - 2376/2401*T^35 - 192/2401*T^34 - 
        3/343*T^33 + 25/49*T^32 + 2209/2401*T^31 + 2005/2401*T^30 + 1310/2401*T^29 -
        1310/2401*T^27 - 2005/2401*T^26 - 2209/2401*T^25 - 25/49*T^24 + 3/343*T^23 +
        192/2401*T^22 + 2376/2401*T^21 + 4633/2401*T^20 + 2410/2401*T^19 - 
        533/2401*T^18 - 510/2401*T^17 - 675/2401*T^16 - 2336/2401*T^15 - 
        3116/2401*T^14 - 331/2401*T^13 + 2890/2401*T^12 + 192/343*T^11 + 
        237/2401*T^10 + 352/343*T^9 + 2134/2401*T^8 - 711/2401*T^7 - 2368/2401*T^6 -
        1334/2401*T^5 + 340/2401*T^4 - 3/343*T^3 + 8/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 
        4*X*Y^8 + 4*X*Y^7 + 5*X*Y^6 + 5*X*Y^4 + 5*X*Y^2 + 2*X*Y + 6*X + 2*Y^30 + 
        4*Y^29 + 4*Y^28 + 3*Y^27 + 3*Y^26 + 4*Y^25 + 6*Y^24 + Y^23 + 2*Y^22 + 5*Y^21
        + 5*Y^20 + 5*Y^19 + 2*Y^18 + 4*Y^17 + 3*Y^16 + 5*Y^15 + Y^14 + 5*Y^13 + 
        5*Y^12 + Y^11 + 6*Y^10 + Y^8 + Y^7 + 3*Y^6 + 2*Y^5 + 6*Y^3 + 2*Y^2 + 3*Y + 
        4,
    T^56 - 6/7*T^55 - 29/49*T^54 + 478/343*T^53 - 2357/2401*T^52 - 39/343*T^51 + 
        2937/2401*T^50 - 227/343*T^49 - 2627/2401*T^48 + 3058/2401*T^47 + 1/7*T^46 -
        3559/2401*T^45 + 3349/2401*T^44 + 251/2401*T^43 - 3823/2401*T^42 + 
        2260/2401*T^41 + 1391/2401*T^40 - 2566/2401*T^39 + 1506/2401*T^38 + 
        2295/2401*T^37 - 4337/2401*T^36 + 96/343*T^35 + 3890/2401*T^34 - 
        3810/2401*T^33 + 563/2401*T^32 + 2220/2401*T^31 - 431/343*T^30 - 
        223/2401*T^29 + 2477/2401*T^28 - 223/2401*T^27 - 431/343*T^26 + 
        2220/2401*T^25 + 563/2401*T^24 - 3810/2401*T^23 + 3890/2401*T^22 + 
        96/343*T^21 - 4337/2401*T^20 + 2295/2401*T^19 + 1506/2401*T^18 - 
        2566/2401*T^17 + 1391/2401*T^16 + 2260/2401*T^15 - 3823/2401*T^14 + 
        251/2401*T^13 + 3349/2401*T^12 - 3559/2401*T^11 + 1/7*T^10 + 3058/2401*T^9 -
        2627/2401*T^8 - 227/343*T^7 + 2937/2401*T^6 - 39/343*T^5 - 2357/2401*T^4 + 
        478/343*T^3 - 29/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 3*X*Y^9 + 5*X*Y^8 +
        2*X*Y^7 + 4*X*Y^6 + X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 6*X + 6*Y^30 + 
        Y^29 + 4*Y^28 + Y^27 + 6*Y^26 + 2*Y^25 + 5*Y^24 + 6*Y^23 + 2*Y^22 + 2*Y^21 +
        4*Y^20 + 5*Y^19 + 3*Y^17 + Y^16 + 3*Y^15 + 4*Y^14 + 2*Y^13 + 6*Y^12 + 3*Y^11
        + 6*Y^10 + 5*Y^9 + 6*Y^8 + 5*Y^6 + 5*Y^5 + 5*Y^4 + 3*Y^3 + 5*Y^2 + Y + 5,
    -T^56 - 1/7*T^55 - 25/49*T^54 + 121/343*T^53 + 13/49*T^52 - 908/2401*T^51 - 
        123/2401*T^50 + 4/49*T^49 - 41/2401*T^48 + 663/2401*T^47 - 796/2401*T^46 + 
        482/2401*T^45 + 1236/2401*T^44 + 846/2401*T^43 + 989/2401*T^42 + 
        166/2401*T^41 - 603/2401*T^40 + 51/343*T^39 - 883/2401*T^38 + 104/2401*T^37 
        + 772/2401*T^36 + 482/2401*T^35 + 1627/2401*T^34 - 645/2401*T^33 + 
        164/2401*T^32 - 156/2401*T^31 - 537/2401*T^30 + 351/2401*T^29 - 
        351/2401*T^27 + 537/2401*T^26 + 156/2401*T^25 - 164/2401*T^24 + 
        645/2401*T^23 - 1627/2401*T^22 - 482/2401*T^21 - 772/2401*T^20 - 
        104/2401*T^19 + 883/2401*T^18 - 51/343*T^17 + 603/2401*T^16 - 166/2401*T^15 
        - 989/2401*T^14 - 846/2401*T^13 - 1236/2401*T^12 - 482/2401*T^11 + 
        796/2401*T^10 - 663/2401*T^9 + 41/2401*T^8 - 4/49*T^7 + 123/2401*T^6 + 
        908/2401*T^5 - 13/49*T^4 - 121/343*T^3 + 25/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 
        4*X*Y^8 + 2*X*Y^7 + 4*X*Y^6 + 3*X*Y^4 + 3*X*Y^3 + X*Y + 2*X + 6*Y^30 + 
        4*Y^29 + 3*Y^28 + 6*Y^25 + 4*Y^24 + 4*Y^23 + 5*Y^22 + 5*Y^20 + 2*Y^19 + 
        3*Y^18 + 4*Y^17 + 4*Y^16 + 5*Y^15 + 5*Y^14 + 2*Y^13 + 5*Y^12 + 3*Y^11 + 
        5*Y^10 + 4*Y^9 + 3*Y^8 + Y^7 + 4*Y^6 + 6*Y^5 + Y^4 + 4*Y^3 + 3*Y^2 + 4*Y + 
        4,
    -T^56 - 1/7*T^55 + 79/49*T^54 + 46/343*T^53 - 2589/2401*T^52 - 383/2401*T^51 + 
        2466/2401*T^50 + 1075/2401*T^49 - 1395/2401*T^48 - 297/343*T^47 + 
        1116/2401*T^46 + 1640/2401*T^45 - 1817/2401*T^44 + 4/343*T^43 + 
        1478/2401*T^42 - 431/2401*T^41 - 1389/2401*T^40 + 1944/2401*T^39 - 
        554/2401*T^38 - 1423/2401*T^37 + 184/2401*T^36 - 943/2401*T^35 + 
        1117/2401*T^34 + 6/343*T^33 - 405/2401*T^32 + 213/2401*T^31 + 1465/2401*T^30
        - 746/2401*T^29 + 746/2401*T^27 - 1465/2401*T^26 - 213/2401*T^25 + 
        405/2401*T^24 - 6/343*T^23 - 1117/2401*T^22 + 943/2401*T^21 - 184/2401*T^20 
        + 1423/2401*T^19 + 554/2401*T^18 - 1944/2401*T^17 + 1389/2401*T^16 + 
        431/2401*T^15 - 1478/2401*T^14 - 4/343*T^13 + 1817/2401*T^12 - 
        1640/2401*T^11 - 1116/2401*T^10 + 297/343*T^9 + 1395/2401*T^8 - 
        1075/2401*T^7 - 2466/2401*T^6 + 383/2401*T^5 + 2589/2401*T^4 - 46/343*T^3 - 
        79/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 4*X*Y^8 + 
        6*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 5*X*Y^3 + 4*X*Y^2 + 6*X*Y + 3*X + 4*Y^30 + 
        6*Y^29 + 3*Y^28 + 3*Y^27 + 6*Y^26 + 5*Y^25 + 6*Y^24 + 6*Y^23 + 6*Y^22 + 
        2*Y^21 + 3*Y^20 + 4*Y^19 + 6*Y^18 + 5*Y^17 + 6*Y^16 + 6*Y^14 + 3*Y^13 + 
        6*Y^12 + 2*Y^11 + Y^10 + 3*Y^9 + 2*Y^8 + 3*Y^7 + 5*Y^5 + 5*Y^4 + 5*Y^3 + Y^2
        + 6,
    -T^56 - 16/7*T^55 - 104/49*T^54 - 37/49*T^53 + 2645/2401*T^52 + 5254/2401*T^51 +
        5501/2401*T^50 + 6403/2401*T^49 + 6469/2401*T^48 + 5828/2401*T^47 + 
        853/343*T^46 + 4131/2401*T^45 + 254/2401*T^44 - 4547/2401*T^43 - 
        9021/2401*T^42 - 11154/2401*T^41 - 12218/2401*T^40 - 11191/2401*T^39 - 
        7020/2401*T^38 - 2360/2401*T^37 + 39/49*T^36 + 4976/2401*T^35 + 
        7375/2401*T^34 + 9368/2401*T^33 + 8950/2401*T^32 + 8814/2401*T^31 + 
        9419/2401*T^30 + 6380/2401*T^29 - 6380/2401*T^27 - 9419/2401*T^26 - 
        8814/2401*T^25 - 8950/2401*T^24 - 9368/2401*T^23 - 7375/2401*T^22 - 
        4976/2401*T^21 - 39/49*T^20 + 2360/2401*T^19 + 7020/2401*T^18 + 
        11191/2401*T^17 + 12218/2401*T^16 + 11154/2401*T^15 + 9021/2401*T^14 + 
        4547/2401*T^13 - 254/2401*T^12 - 4131/2401*T^11 - 853/343*T^10 - 
        5828/2401*T^9 - 6469/2401*T^8 - 6403/2401*T^7 - 5501/2401*T^6 - 
        5254/2401*T^5 - 2645/2401*T^4 + 37/49*T^3 + 104/49*T^2 + 16/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 2*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 +
        4*X*Y^7 + X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 2*X*Y + 5*Y^30 + 
        4*Y^29 + 4*Y^28 + 6*Y^27 + 6*Y^26 + Y^25 + 2*Y^24 + 2*Y^23 + 6*Y^22 + 3*Y^21
        + Y^20 + 2*Y^19 + 4*Y^18 + 2*Y^16 + 6*Y^14 + 4*Y^13 + 6*Y^11 + 4*Y^10 + 
        5*Y^9 + 6*Y^8 + 6*Y^7 + 5*Y^6 + 2*Y^5 + 6*Y^4 + 6*Y^3 + 3*Y^2 + 4*Y + 5,
    T^56 - 12/7*T^55 + 2/49*T^54 + 621/343*T^53 - 633/343*T^52 + 3070/2401*T^51 + 
        711/2401*T^50 - 5235/2401*T^49 + 2516/2401*T^48 + 2434/2401*T^47 - 
        1678/2401*T^46 + 9/343*T^45 + 143/343*T^44 - 2795/2401*T^43 + 15/2401*T^42 +
        621/343*T^41 - 3083/2401*T^40 - 471/2401*T^39 + 3039/2401*T^38 - 
        4870/2401*T^37 + 1837/2401*T^36 + 3242/2401*T^35 - 547/343*T^34 + 
        1844/2401*T^33 + 246/2401*T^32 - 1788/2401*T^31 + 1234/2401*T^30 - 
        93/2401*T^29 - 96/2401*T^28 - 93/2401*T^27 + 1234/2401*T^26 - 1788/2401*T^25
        + 246/2401*T^24 + 1844/2401*T^23 - 547/343*T^22 + 3242/2401*T^21 + 
        1837/2401*T^20 - 4870/2401*T^19 + 3039/2401*T^18 - 471/2401*T^17 - 
        3083/2401*T^16 + 621/343*T^15 + 15/2401*T^14 - 2795/2401*T^13 + 143/343*T^12
        + 9/343*T^11 - 1678/2401*T^10 + 2434/2401*T^9 + 2516/2401*T^8 - 
        5235/2401*T^7 + 711/2401*T^6 + 3070/2401*T^5 - 633/343*T^4 + 621/343*T^3 + 
        2/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 
        + X*Y^8 + X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 2*X*Y + 
        4*X + Y^30 + Y^29 + 3*Y^28 + 3*Y^26 + 2*Y^25 + 3*Y^24 + 4*Y^23 + 6*Y^22 + 
        4*Y^21 + 5*Y^20 + 5*Y^19 + 3*Y^18 + 4*Y^17 + 4*Y^16 + Y^15 + Y^13 + 4*Y^12 +
        2*Y^10 + 6*Y^9 + 3*Y^8 + 2*Y^7 + 5*Y^6 + 2*Y^5 + Y^4 + 4*Y^3 + 4*Y^2 + 3*Y +
        3,
    T^56 + 4/7*T^55 + 19/49*T^54 - 204/343*T^53 - 477/2401*T^52 + 702/2401*T^51 + 
        218/343*T^50 + 591/2401*T^49 - 521/2401*T^48 - 2423/2401*T^47 - 191/343*T^46
        - 41/2401*T^45 + 1565/2401*T^44 - 375/2401*T^43 - 1930/2401*T^42 - 
        2675/2401*T^41 - 166/343*T^40 - 83/2401*T^39 + 755/2401*T^38 - 221/2401*T^37
        - 683/2401*T^36 - 1193/2401*T^35 + 86/343*T^34 + 772/2401*T^33 + 
        1179/2401*T^32 + 96/343*T^31 + 877/2401*T^30 + 397/2401*T^29 + 558/2401*T^28
        + 397/2401*T^27 + 877/2401*T^26 + 96/343*T^25 + 1179/2401*T^24 + 
        772/2401*T^23 + 86/343*T^22 - 1193/2401*T^21 - 683/2401*T^20 - 221/2401*T^19
        + 755/2401*T^18 - 83/2401*T^17 - 166/343*T^16 - 2675/2401*T^15 - 
        1930/2401*T^14 - 375/2401*T^13 + 1565/2401*T^12 - 41/2401*T^11 - 
        191/343*T^10 - 2423/2401*T^9 - 521/2401*T^8 + 591/2401*T^7 + 218/343*T^6 + 
        702/2401*T^5 - 477/2401*T^4 - 204/343*T^3 + 19/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + X*Y^13 + X*Y^12 + X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 
        X*Y^8 + 4*X*Y^7 + X*Y^5 + 4*X*Y^4 + X*Y^3 + 4*X*Y^2 + 3*X*Y + 3*X + 2*Y^30 +
        Y^29 + 3*Y^28 + 4*Y^27 + Y^26 + 5*Y^24 + 3*Y^23 + 3*Y^22 + 6*Y^21 + 4*Y^20 +
        Y^19 + 2*Y^18 + 4*Y^17 + 5*Y^14 + 6*Y^13 + Y^12 + 5*Y^11 + 2*Y^10 + 2*Y^8 + 
        3*Y^7 + 2*Y^6 + Y^5 + 2*Y^4 + 3*Y^3 + 6*Y^2 + 2*Y,
    T^56 + 5/7*T^55 - 2/7*T^54 + 307/343*T^53 - 1340/2401*T^52 - 4310/2401*T^51 + 
        857/2401*T^50 - 1597/2401*T^49 - 2084/2401*T^48 + 3615/2401*T^47 + 
        349/2401*T^46 - 1038/2401*T^45 + 2147/2401*T^44 - 926/2401*T^43 - 
        1032/2401*T^42 + 1389/2401*T^41 - 1546/2401*T^40 + 453/2401*T^39 + 
        1950/2401*T^38 - 1700/2401*T^37 + 1660/2401*T^36 + 1546/2401*T^35 - 
        474/343*T^34 + 116/2401*T^33 - 37/343*T^32 - 3652/2401*T^31 + 1776/2401*T^30
        + 53/49*T^29 - 1020/2401*T^28 + 53/49*T^27 + 1776/2401*T^26 - 3652/2401*T^25
        - 37/343*T^24 + 116/2401*T^23 - 474/343*T^22 + 1546/2401*T^21 + 
        1660/2401*T^20 - 1700/2401*T^19 + 1950/2401*T^18 + 453/2401*T^17 - 
        1546/2401*T^16 + 1389/2401*T^15 - 1032/2401*T^14 - 926/2401*T^13 + 
        2147/2401*T^12 - 1038/2401*T^11 + 349/2401*T^10 + 3615/2401*T^9 - 
        2084/2401*T^8 - 1597/2401*T^7 + 857/2401*T^6 - 4310/2401*T^5 - 1340/2401*T^4
        + 307/343*T^3 - 2/7*T^2 + 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + X*Y^9 + X*Y^8 + 
        4*X*Y^7 + 5*X*Y^4 + 5*X*Y^2 + 6*X*Y + 4*X + 5*Y^30 + 2*Y^29 + 4*Y^28 + 
        5*Y^27 + 2*Y^26 + 4*Y^25 + 6*Y^24 + 4*Y^22 + 4*Y^21 + 2*Y^20 + 3*Y^19 + Y^18
        + 2*Y^17 + 6*Y^16 + Y^15 + 3*Y^14 + 4*Y^13 + 5*Y^12 + 2*Y^11 + 4*Y^10 + 
        4*Y^9 + 5*Y^8 + 5*Y^7 + Y^6 + 6*Y^5 + 6*Y^4 + 5*Y^3 + 3*Y^2 + 6,
    T^56 - 4/7*T^55 + 3/49*T^54 - 115/343*T^53 - 1544/2401*T^52 + 3006/2401*T^51 - 
        109/2401*T^50 + 863/2401*T^49 - 858/2401*T^48 - 33/49*T^47 + 423/2401*T^46 +
        358/2401*T^45 + 1152/2401*T^44 - 1025/2401*T^43 + 25/49*T^42 - 781/2401*T^41
        - 86/2401*T^40 - 155/2401*T^39 - 1695/2401*T^38 + 961/2401*T^37 + 
        152/2401*T^36 + 1424/2401*T^35 - 1252/2401*T^34 - 38/343*T^33 - 
        1473/2401*T^32 + 890/2401*T^31 + 1173/2401*T^30 - 1501/2401*T^29 + 
        1089/2401*T^28 - 1501/2401*T^27 + 1173/2401*T^26 + 890/2401*T^25 - 
        1473/2401*T^24 - 38/343*T^23 - 1252/2401*T^22 + 1424/2401*T^21 + 
        152/2401*T^20 + 961/2401*T^19 - 1695/2401*T^18 - 155/2401*T^17 - 
        86/2401*T^16 - 781/2401*T^15 + 25/49*T^14 - 1025/2401*T^13 + 1152/2401*T^12 
        + 358/2401*T^11 + 423/2401*T^10 - 33/49*T^9 - 858/2401*T^8 + 863/2401*T^7 - 
        109/2401*T^6 + 3006/2401*T^5 - 1544/2401*T^4 - 115/343*T^3 + 3/49*T^2 - 
        4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 6*X*Y^7 + 5*X*Y^6 + 2*X*Y^3 + 6*X*Y^2 + 2*X*Y + 6*X + 5*Y^30 + 
        Y^29 + 3*Y^28 + 6*Y^27 + Y^25 + 6*Y^23 + 6*Y^22 + 4*Y^20 + 5*Y^18 + 5*Y^17 +
        2*Y^16 + 2*Y^14 + Y^13 + 4*Y^12 + Y^11 + 3*Y^10 + Y^9 + 6*Y^8 + 4*Y^7 + 
        2*Y^5 + 6*Y^4 + 4*Y^3 + 6*Y^2 + 6*Y + 2,
    -T^56 + 6/7*T^55 - 1/7*T^54 + 144/343*T^53 - 1822/2401*T^52 + 1700/2401*T^51 - 
        1045/2401*T^50 - 136/343*T^49 + 159/2401*T^48 + 212/343*T^47 + 753/2401*T^46
        - 1193/2401*T^45 + 41/343*T^44 - 114/2401*T^43 + 108/2401*T^42 - 
        776/2401*T^41 + 1016/2401*T^40 - 23/2401*T^39 + 141/2401*T^38 - 
        641/2401*T^37 + 9/49*T^36 + 459/2401*T^35 - 59/2401*T^34 - 173/2401*T^33 - 
        951/2401*T^32 + 1507/2401*T^31 - 302/2401*T^30 + 78/2401*T^29 - 78/2401*T^27
        + 302/2401*T^26 - 1507/2401*T^25 + 951/2401*T^24 + 173/2401*T^23 + 
        59/2401*T^22 - 459/2401*T^21 - 9/49*T^20 + 641/2401*T^19 - 141/2401*T^18 + 
        23/2401*T^17 - 1016/2401*T^16 + 776/2401*T^15 - 108/2401*T^14 + 
        114/2401*T^13 - 41/343*T^12 + 1193/2401*T^11 - 753/2401*T^10 - 212/343*T^9 -
        159/2401*T^8 + 136/343*T^7 + 1045/2401*T^6 - 1700/2401*T^5 + 1822/2401*T^4 -
        144/343*T^3 + 1/7*T^2 - 6/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        3*X*Y^8 + 4*X*Y^7 + 5*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 6*X*Y 
        + 3*X + 5*Y^30 + 3*Y^29 + Y^27 + 2*Y^26 + 6*Y^25 + 6*Y^24 + Y^23 + 5*Y^22 + 
        Y^21 + 2*Y^20 + 3*Y^19 + Y^18 + 5*Y^17 + 5*Y^16 + 2*Y^15 + 2*Y^14 + Y^13 + 
        5*Y^12 + 5*Y^11 + 5*Y^10 + 6*Y^8 + 3*Y^7 + Y^6 + Y^5 + 3*Y^4 + Y^3 + 4*Y + 
        1,
    T^56 + 3/7*T^55 - 20/49*T^54 - 71/343*T^53 - 2168/2401*T^52 - 1584/2401*T^51 - 
        1965/2401*T^50 - 1041/2401*T^49 + 1502/2401*T^48 + 229/2401*T^47 + 
        1777/2401*T^46 + 2678/2401*T^45 + 562/2401*T^44 + 730/2401*T^43 - 
        320/2401*T^42 - 1035/2401*T^41 - 1607/2401*T^40 - 1545/2401*T^39 + 
        436/2401*T^38 - 295/2401*T^37 + 206/343*T^36 + 2311/2401*T^35 + 
        365/2401*T^34 + 69/343*T^33 + 501/2401*T^32 + 388/2401*T^31 - 1600/2401*T^30
        - 1879/2401*T^29 - 492/2401*T^28 - 1879/2401*T^27 - 1600/2401*T^26 + 
        388/2401*T^25 + 501/2401*T^24 + 69/343*T^23 + 365/2401*T^22 + 2311/2401*T^21
        + 206/343*T^20 - 295/2401*T^19 + 436/2401*T^18 - 1545/2401*T^17 - 
        1607/2401*T^16 - 1035/2401*T^15 - 320/2401*T^14 + 730/2401*T^13 + 
        562/2401*T^12 + 2678/2401*T^11 + 1777/2401*T^10 + 229/2401*T^9 + 
        1502/2401*T^8 - 1041/2401*T^7 - 1965/2401*T^6 - 1584/2401*T^5 - 
        2168/2401*T^4 - 71/343*T^3 - 20/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 2*X*Y^12 + 3*X*Y^9 + 3*X*Y^8 + 6*X*Y^7 + 6*X*Y^6 + 
        5*X*Y^5 + 3*X*Y^3 + X*Y^2 + 6*X*Y + X + 4*Y^30 + 4*Y^29 + 3*Y^27 + 4*Y^26 + 
        5*Y^25 + Y^24 + 5*Y^23 + Y^21 + 4*Y^20 + 3*Y^19 + 3*Y^18 + 6*Y^17 + Y^15 + 
        3*Y^14 + 4*Y^13 + 6*Y^12 + 4*Y^11 + 6*Y^10 + 5*Y^9 + 4*Y^7 + 2*Y^6 + 2*Y^5 +
        4*Y^4 + 2*Y^3 + 5*Y^2 + Y + 6,
    T^56 - 1/7*T^55 - 12/7*T^54 + 64/343*T^53 + 2836/2401*T^52 - 212/343*T^51 + 
        1690/2401*T^50 + 1186/2401*T^49 - 5200/2401*T^48 - 101/2401*T^47 + 
        6000/2401*T^46 - 1793/2401*T^45 - 2847/2401*T^44 + 2557/2401*T^43 - 
        2207/2401*T^42 - 2207/2401*T^41 + 5580/2401*T^40 + 429/2401*T^39 - 
        4625/2401*T^38 + 1236/2401*T^37 + 333/2401*T^36 - 870/2401*T^35 + 
        2236/2401*T^34 + 278/2401*T^33 - 384/343*T^32 + 128/2401*T^31 + 
        664/2401*T^30 + 466/2401*T^29 + 5/343*T^28 + 466/2401*T^27 + 664/2401*T^26 +
        128/2401*T^25 - 384/343*T^24 + 278/2401*T^23 + 2236/2401*T^22 - 
        870/2401*T^21 + 333/2401*T^20 + 1236/2401*T^19 - 4625/2401*T^18 + 
        429/2401*T^17 + 5580/2401*T^16 - 2207/2401*T^15 - 2207/2401*T^14 + 
        2557/2401*T^13 - 2847/2401*T^12 - 1793/2401*T^11 + 6000/2401*T^10 - 
        101/2401*T^9 - 5200/2401*T^8 + 1186/2401*T^7 + 1690/2401*T^6 - 212/343*T^5 +
        2836/2401*T^4 + 64/343*T^3 - 12/7*T^2 - 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^13 + 4*X*Y^12 + X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 3*X*Y^8 + 
        X*Y^7 + 6*X*Y^6 + X*Y^5 + X*Y^4 + 3*X*Y^2 + 6*X*Y + 3*X + 5*Y^30 + 2*Y^29 + 
        Y^28 + 2*Y^26 + 4*Y^25 + 4*Y^24 + 3*Y^23 + Y^22 + Y^21 + 2*Y^20 + 2*Y^18 + 
        Y^17 + 4*Y^16 + 5*Y^15 + 3*Y^14 + Y^13 + Y^12 + 2*Y^11 + 5*Y^10 + 3*Y^9 + 
        4*Y^8 + Y^6 + 4*Y^3 + 2*Y + 1,
    -T^56 + 17/7*T^55 - 24/7*T^54 + 130/49*T^53 - 2011/2401*T^52 - 2460/2401*T^51 + 
        5528/2401*T^50 - 7445/2401*T^49 + 8257/2401*T^48 - 6236/2401*T^47 + 
        41/49*T^46 + 2529/2401*T^45 - 4261/2401*T^44 + 4351/2401*T^43 - 
        3804/2401*T^42 + 2955/2401*T^41 - 220/2401*T^40 - 2402/2401*T^39 + 
        2267/2401*T^38 + 1490/2401*T^37 - 4617/2401*T^36 + 699/343*T^35 - 
        296/343*T^34 + 1/2401*T^33 + 143/343*T^32 - 1517/2401*T^31 + 2859/2401*T^30 
        - 2608/2401*T^29 + 2608/2401*T^27 - 2859/2401*T^26 + 1517/2401*T^25 - 
        143/343*T^24 - 1/2401*T^23 + 296/343*T^22 - 699/343*T^21 + 4617/2401*T^20 - 
        1490/2401*T^19 - 2267/2401*T^18 + 2402/2401*T^17 + 220/2401*T^16 - 
        2955/2401*T^15 + 3804/2401*T^14 - 4351/2401*T^13 + 4261/2401*T^12 - 
        2529/2401*T^11 - 41/49*T^10 + 6236/2401*T^9 - 8257/2401*T^8 + 7445/2401*T^7 
        - 5528/2401*T^6 + 2460/2401*T^5 + 2011/2401*T^4 - 130/49*T^3 + 24/7*T^2 - 
        17/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 4*X*Y^12 + X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 5*X*Y^8 + 
        X*Y^7 + X*Y^6 + 6*X*Y^5 + X*Y^4 + 5*X*Y^2 + 6*X*Y + 3*X + 5*Y^30 + Y^29 + 
        Y^28 + 4*Y^27 + 3*Y^26 + 5*Y^25 + 4*Y^23 + 4*Y^20 + 3*Y^19 + 3*Y^18 + 2*Y^17
        + Y^16 + 3*Y^15 + 6*Y^14 + 6*Y^13 + 4*Y^12 + 6*Y^11 + 6*Y^10 + 6*Y^9 + 6*Y^8
        + 4*Y^7 + 3*Y^4 + 3*Y^3 + Y^2 + 4*Y + 3,
    -T^56 - T^55 + 53/49*T^54 + 489/343*T^53 + 236/2401*T^52 - 60/343*T^51 - 
        142/2401*T^50 - 328/2401*T^49 - 200/2401*T^48 - 82/343*T^47 - 1035/2401*T^46
        - 158/2401*T^45 + 1619/2401*T^44 - 3/2401*T^43 - 1646/2401*T^42 + 
        81/343*T^41 + 1884/2401*T^40 + 359/2401*T^39 - 624/2401*T^38 - 519/2401*T^37
        - 1173/2401*T^36 - 342/2401*T^35 + 905/2401*T^34 - 95/343*T^33 - 9/343*T^32 
        + 2484/2401*T^31 + 164/2401*T^30 - 2017/2401*T^29 + 2017/2401*T^27 - 
        164/2401*T^26 - 2484/2401*T^25 + 9/343*T^24 + 95/343*T^23 - 905/2401*T^22 + 
        342/2401*T^21 + 1173/2401*T^20 + 519/2401*T^19 + 624/2401*T^18 - 
        359/2401*T^17 - 1884/2401*T^16 - 81/343*T^15 + 1646/2401*T^14 + 3/2401*T^13 
        - 1619/2401*T^12 + 158/2401*T^11 + 1035/2401*T^10 + 82/343*T^9 + 
        200/2401*T^8 + 328/2401*T^7 + 142/2401*T^6 + 60/343*T^5 - 236/2401*T^4 - 
        489/343*T^3 - 53/49*T^2 + T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        4*X*Y^7 + 4*X*Y^6 + X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 2*Y^30 + 5*Y^29 + 
        5*Y^28 + 4*Y^27 + 6*Y^26 + 4*Y^25 + 2*Y^24 + 5*Y^23 + Y^22 + 4*Y^20 + 6*Y^19
        + 3*Y^17 + 3*Y^16 + 4*Y^15 + 5*Y^14 + 5*Y^13 + 2*Y^11 + Y^10 + 4*Y^9 + 2*Y^8
        + 4*Y^7 + 4*Y^6 + 3*Y^5 + 5*Y^4 + 2*Y^3 + Y^2 + 2,
    -T^56 - 10/7*T^55 - 3/49*T^54 + 173/343*T^53 - 792/2401*T^52 - 534/2401*T^51 + 
        2077/2401*T^50 + 848/2401*T^49 - 981/2401*T^48 + 438/2401*T^47 + 
        2293/2401*T^46 + 1285/2401*T^45 - 99/343*T^44 - 580/2401*T^43 + 9/49*T^42 - 
        158/2401*T^41 - 235/343*T^40 - 344/2401*T^39 + 566/2401*T^38 - 38/343*T^37 -
        531/2401*T^36 + 281/2401*T^35 + 789/2401*T^34 - 69/2401*T^33 - 831/2401*T^32
        - 956/2401*T^31 - 528/2401*T^30 - 157/2401*T^29 + 157/2401*T^27 + 
        528/2401*T^26 + 956/2401*T^25 + 831/2401*T^24 + 69/2401*T^23 - 789/2401*T^22
        - 281/2401*T^21 + 531/2401*T^20 + 38/343*T^19 - 566/2401*T^18 + 
        344/2401*T^17 + 235/343*T^16 + 158/2401*T^15 - 9/49*T^14 + 580/2401*T^13 + 
        99/343*T^12 - 1285/2401*T^11 - 2293/2401*T^10 - 438/2401*T^9 + 981/2401*T^8 
        - 848/2401*T^7 - 2077/2401*T^6 + 534/2401*T^5 + 792/2401*T^4 - 173/343*T^3 +
        3/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + X*Y^10 + 5*X*Y^9 + 
        4*X*Y^8 + 2*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + X*Y^3 + 2*X*Y^2 + 3*X*Y + 
        5*X + 2*Y^30 + Y^28 + 2*Y^27 + 6*Y^24 + 3*Y^21 + 2*Y^20 + 3*Y^18 + 6*Y^17 + 
        4*Y^16 + 2*Y^15 + 5*Y^14 + 6*Y^12 + Y^11 + 6*Y^9 + 5*Y^5 + 5*Y^4 + 3*Y^3 + 
        3*Y^2 + 4*Y,
    -T^56 - 4/7*T^55 + 5/7*T^54 + 220/343*T^53 + 222/2401*T^52 + 2344/2401*T^51 + 
        249/343*T^50 - 2518/2401*T^49 - 2605/2401*T^48 - 6/343*T^47 - 485/2401*T^46 
        - 1380/2401*T^45 + 649/2401*T^44 + 2283/2401*T^43 + 2239/2401*T^42 + 
        471/2401*T^41 + 440/2401*T^40 - 352/2401*T^39 - 2190/2401*T^38 - 
        2200/2401*T^37 + 36/343*T^36 + 199/343*T^35 + 211/2401*T^34 + 978/2401*T^33 
        + 899/2401*T^32 - 591/2401*T^31 - 544/2401*T^30 + 520/2401*T^29 - 
        520/2401*T^27 + 544/2401*T^26 + 591/2401*T^25 - 899/2401*T^24 - 
        978/2401*T^23 - 211/2401*T^22 - 199/343*T^21 - 36/343*T^20 + 2200/2401*T^19 
        + 2190/2401*T^18 + 352/2401*T^17 - 440/2401*T^16 - 471/2401*T^15 - 
        2239/2401*T^14 - 2283/2401*T^13 - 649/2401*T^12 + 1380/2401*T^11 + 
        485/2401*T^10 + 6/343*T^9 + 2605/2401*T^8 + 2518/2401*T^7 - 249/343*T^6 - 
        2344/2401*T^5 - 222/2401*T^4 - 220/343*T^3 - 5/7*T^2 + 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 3*X*Y^9 
        + 3*X*Y^7 + 5*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + X*Y + 5*X + 3*Y^30 + 
        6*Y^29 + Y^28 + 2*Y^27 + 3*Y^25 + 2*Y^24 + 4*Y^23 + 2*Y^22 + 3*Y^21 + 2*Y^20
        + 2*Y^19 + 3*Y^18 + 6*Y^16 + Y^15 + 2*Y^14 + 3*Y^12 + 6*Y^11 + 4*Y^10 + 
        2*Y^9 + 3*Y^8 + 6*Y^7 + 5*Y^5 + 4*Y^2 + 3*Y + 3,
    -T^56 + 10/7*T^55 - 4/49*T^54 - 510/343*T^53 + 1739/2401*T^52 + 2224/2401*T^51 -
        2126/2401*T^50 - 1401/2401*T^49 + 2964/2401*T^48 - 743/2401*T^47 - 
        2017/2401*T^46 + 913/2401*T^45 + 2398/2401*T^44 - 2453/2401*T^43 - 
        1710/2401*T^42 + 2953/2401*T^41 + 769/2401*T^40 - 3179/2401*T^39 + 
        64/343*T^38 + 58/49*T^37 - 2854/2401*T^36 - 124/2401*T^35 + 233/343*T^34 + 
        386/2401*T^33 - 2714/2401*T^32 + 165/343*T^31 + 2434/2401*T^30 - 
        429/343*T^29 + 429/343*T^27 - 2434/2401*T^26 - 165/343*T^25 + 2714/2401*T^24
        - 386/2401*T^23 - 233/343*T^22 + 124/2401*T^21 + 2854/2401*T^20 - 58/49*T^19
        - 64/343*T^18 + 3179/2401*T^17 - 769/2401*T^16 - 2953/2401*T^15 + 
        1710/2401*T^14 + 2453/2401*T^13 - 2398/2401*T^12 - 913/2401*T^11 + 
        2017/2401*T^10 + 743/2401*T^9 - 2964/2401*T^8 + 1401/2401*T^7 + 
        2126/2401*T^6 - 2224/2401*T^5 - 1739/2401*T^4 + 510/343*T^3 + 4/49*T^2 - 
        10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 
        + 6*X*Y^8 + 6*X*Y^7 + 3*X*Y^6 + X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 3*X*Y 
        + 2*X + Y^30 + Y^29 + 5*Y^28 + 6*Y^27 + Y^26 + Y^25 + 3*Y^24 + 5*Y^23 + 
        5*Y^22 + 2*Y^21 + 5*Y^20 + 6*Y^19 + 5*Y^17 + Y^16 + Y^15 + 4*Y^14 + 3*Y^13 +
        4*Y^12 + 6*Y^11 + 2*Y^10 + 3*Y^8 + 4*Y^7 + 5*Y^6 + Y^5 + 3*Y^4 + 5*Y^3 + Y^2
        + 5*Y + 6,
    -T^56 + 15/7*T^55 - 80/49*T^54 - 178/343*T^53 + 4807/2401*T^52 - 6808/2401*T^51 
        + 7087/2401*T^50 - 2946/2401*T^49 - 4120/2401*T^48 + 6843/2401*T^47 - 
        4433/2401*T^46 + 1404/2401*T^45 + 213/343*T^44 - 3869/2401*T^43 + 
        3520/2401*T^42 - 822/2401*T^41 - 1167/2401*T^40 + 3004/2401*T^39 - 
        5049/2401*T^38 + 4265/2401*T^37 - 664/2401*T^36 - 225/343*T^35 + 
        3630/2401*T^34 - 916/343*T^33 + 5304/2401*T^32 - 12/343*T^31 - 
        1325/2401*T^30 - 596/2401*T^29 + 596/2401*T^27 + 1325/2401*T^26 + 
        12/343*T^25 - 5304/2401*T^24 + 916/343*T^23 - 3630/2401*T^22 + 225/343*T^21 
        + 664/2401*T^20 - 4265/2401*T^19 + 5049/2401*T^18 - 3004/2401*T^17 + 
        1167/2401*T^16 + 822/2401*T^15 - 3520/2401*T^14 + 3869/2401*T^13 - 
        213/343*T^12 - 1404/2401*T^11 + 4433/2401*T^10 - 6843/2401*T^9 + 
        4120/2401*T^8 + 2946/2401*T^7 - 7087/2401*T^6 + 6808/2401*T^5 - 
        4807/2401*T^4 + 178/343*T^3 + 80/49*T^2 - 15/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 5*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 
        2*X*Y^4 + 5*X*Y^3 + 3*X*Y + 4*X + Y^30 + Y^28 + Y^27 + 4*Y^26 + Y^25 + 
        3*Y^24 + 2*Y^21 + 6*Y^20 + 6*Y^19 + 2*Y^18 + 3*Y^17 + 4*Y^16 + 2*Y^14 + 
        2*Y^13 + 6*Y^12 + Y^11 + 5*Y^10 + 4*Y^9 + 2*Y^8 + 5*Y^7 + 5*Y^6 + Y^5 + 
        4*Y^4 + 4*Y^3 + 3*Y^2 + 3*Y + 1,
    -T^56 + 6/7*T^55 + 27/49*T^54 - 25/343*T^53 - 663/2401*T^52 - 1733/2401*T^51 + 
        1348/2401*T^50 + 292/2401*T^49 + 281/2401*T^48 - 474/2401*T^47 - 2/2401*T^46
        - 1077/2401*T^45 + 1199/2401*T^44 + 515/2401*T^43 + 344/2401*T^42 - 
        86/343*T^41 - 1333/2401*T^40 + 767/2401*T^39 + 45/2401*T^38 + 237/2401*T^37 
        - 360/2401*T^36 + 813/2401*T^35 - 24/343*T^34 - 585/2401*T^33 + 
        402/2401*T^32 + 423/2401*T^31 + 43/343*T^30 - 1398/2401*T^29 + 
        1398/2401*T^27 - 43/343*T^26 - 423/2401*T^25 - 402/2401*T^24 + 585/2401*T^23
        + 24/343*T^22 - 813/2401*T^21 + 360/2401*T^20 - 237/2401*T^19 - 45/2401*T^18
        - 767/2401*T^17 + 1333/2401*T^16 + 86/343*T^15 - 344/2401*T^14 - 
        515/2401*T^13 - 1199/2401*T^12 + 1077/2401*T^11 + 2/2401*T^10 + 474/2401*T^9
        - 281/2401*T^8 - 292/2401*T^7 - 1348/2401*T^6 + 1733/2401*T^5 + 663/2401*T^4
        + 25/343*T^3 - 27/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 
        5*X*Y^8 + 5*X*Y^6 + 4*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 6*X*Y + 6*X + 4*Y^30 + 
        4*Y^28 + 4*Y^27 + 2*Y^26 + 5*Y^25 + 3*Y^24 + 3*Y^22 + 3*Y^21 + Y^20 + 3*Y^19
        + 5*Y^18 + 4*Y^17 + 3*Y^16 + Y^15 + 6*Y^14 + 3*Y^13 + 5*Y^12 + 3*Y^11 + 
        6*Y^10 + 6*Y^9 + 4*Y^8 + 2*Y^7 + 6*Y^6 + 4*Y^5 + 4*Y^4 + Y^3 + Y + 5,
    T^56 + 13/7*T^55 + 95/49*T^54 + 95/343*T^53 - 2606/2401*T^52 - 3273/2401*T^51 - 
        451/2401*T^50 + 652/2401*T^49 - 849/2401*T^48 - 3868/2401*T^47 - 
        341/343*T^46 + 2082/2401*T^45 + 4967/2401*T^44 + 1980/2401*T^43 - 
        2439/2401*T^42 - 4267/2401*T^41 - 1602/2401*T^40 + 149/2401*T^39 + 
        400/2401*T^38 - 1275/2401*T^37 - 398/2401*T^36 + 1209/2401*T^35 + 
        3428/2401*T^34 + 2644/2401*T^33 + 1252/2401*T^32 - 918/2401*T^31 - 
        1587/2401*T^30 - 3263/2401*T^29 - 3295/2401*T^28 - 3263/2401*T^27 - 
        1587/2401*T^26 - 918/2401*T^25 + 1252/2401*T^24 + 2644/2401*T^23 + 
        3428/2401*T^22 + 1209/2401*T^21 - 398/2401*T^20 - 1275/2401*T^19 + 
        400/2401*T^18 + 149/2401*T^17 - 1602/2401*T^16 - 4267/2401*T^15 - 
        2439/2401*T^14 + 1980/2401*T^13 + 4967/2401*T^12 + 2082/2401*T^11 - 
        341/343*T^10 - 3868/2401*T^9 - 849/2401*T^8 + 652/2401*T^7 - 451/2401*T^6 - 
        3273/2401*T^5 - 2606/2401*T^4 + 95/343*T^3 + 95/49*T^2 + 13/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 
        5*X*Y^8 + 6*X*Y^7 + X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + X*Y^2 + 6*X*Y + X + 2*Y^30 +
        6*Y^28 + Y^27 + 5*Y^26 + 5*Y^25 + 6*Y^24 + 2*Y^23 + 2*Y^22 + 5*Y^21 + 2*Y^20
        + 2*Y^19 + Y^18 + Y^17 + Y^15 + 6*Y^14 + 3*Y^13 + 5*Y^12 + 4*Y^11 + 5*Y^10 +
        2*Y^9 + 2*Y^8 + Y^7 + 6*Y^6 + 2*Y^5 + 3*Y^4 + Y^3 + 3*Y^2 + 4*Y,
    -T^56 - 2/7*T^55 + 30/49*T^54 + 344/343*T^53 - 388/2401*T^52 - 2456/2401*T^51 - 
        979/2401*T^50 - 839/2401*T^49 + 692/2401*T^48 + 302/2401*T^47 + 
        1602/2401*T^46 + 114/2401*T^45 - 906/2401*T^44 - 583/2401*T^43 - 
        832/2401*T^42 - 296/2401*T^41 - 181/2401*T^40 + 1742/2401*T^39 + 
        291/2401*T^38 - 22/2401*T^37 + 15/2401*T^36 + 722/2401*T^35 - 16/2401*T^34 -
        2056/2401*T^33 - 811/2401*T^32 + 186/2401*T^31 + 421/343*T^30 + 293/343*T^29
        - 293/343*T^27 - 421/343*T^26 - 186/2401*T^25 + 811/2401*T^24 + 
        2056/2401*T^23 + 16/2401*T^22 - 722/2401*T^21 - 15/2401*T^20 + 22/2401*T^19 
        - 291/2401*T^18 - 1742/2401*T^17 + 181/2401*T^16 + 296/2401*T^15 + 
        832/2401*T^14 + 583/2401*T^13 + 906/2401*T^12 - 114/2401*T^11 - 
        1602/2401*T^10 - 302/2401*T^9 - 692/2401*T^8 + 839/2401*T^7 + 979/2401*T^6 +
        2456/2401*T^5 + 388/2401*T^4 - 344/343*T^3 - 30/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 4*X*Y^11 + 6*X*Y^10 + 3*X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + 
        X*Y^4 + 3*X*Y^3 + 6*X*Y + 2*X + 6*Y^30 + Y^29 + 5*Y^28 + 3*Y^27 + 3*Y^26 + 
        4*Y^25 + Y^24 + 3*Y^23 + 6*Y^22 + 4*Y^21 + 4*Y^20 + 4*Y^19 + Y^18 + 6*Y^17 +
        5*Y^16 + 6*Y^13 + 5*Y^12 + 2*Y^11 + 4*Y^10 + 3*Y^8 + 6*Y^7 + 5*Y^6 + 5*Y^5 +
        5*Y^4 + Y^3 + 5*Y^2 + 2*Y + 6,
    -T^56 - 6/7*T^55 + 11/49*T^54 + 404/343*T^53 + 2945/2401*T^52 + 1357/2401*T^51 +
        768/2401*T^50 - 199/2401*T^49 - 2040/2401*T^48 - 2804/2401*T^47 - 
        1332/2401*T^46 - 1467/2401*T^45 - 36/343*T^44 + 632/2401*T^43 + 
        2056/2401*T^42 + 1881/2401*T^41 + 1111/2401*T^40 + 2/7*T^39 + 666/2401*T^38 
        + 32/343*T^37 - 1147/2401*T^36 - 937/2401*T^35 - 1965/2401*T^34 - 
        88/343*T^33 + 194/2401*T^32 + 1388/2401*T^31 + 137/2401*T^30 - 568/2401*T^29
        + 568/2401*T^27 - 137/2401*T^26 - 1388/2401*T^25 - 194/2401*T^24 + 
        88/343*T^23 + 1965/2401*T^22 + 937/2401*T^21 + 1147/2401*T^20 - 32/343*T^19 
        - 666/2401*T^18 - 2/7*T^17 - 1111/2401*T^16 - 1881/2401*T^15 - 
        2056/2401*T^14 - 632/2401*T^13 + 36/343*T^12 + 1467/2401*T^11 + 
        1332/2401*T^10 + 2804/2401*T^9 + 2040/2401*T^8 + 199/2401*T^7 - 768/2401*T^6
        - 1357/2401*T^5 - 2945/2401*T^4 - 404/343*T^3 - 11/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 4*X*Y^13 + X*Y^11 + 5*X*Y^10 + X*Y^9 + 4*X*Y^8 + 2*X*Y^7 + 2*X*Y^6 + 
        4*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 6*X*Y + 6*X + 3*Y^30 + 3*Y^28 + 
        2*Y^27 + 2*Y^26 + 4*Y^25 + 2*Y^24 + 4*Y^23 + 2*Y^22 + 4*Y^21 + 5*Y^20 + 
        3*Y^19 + 2*Y^18 + 6*Y^15 + 3*Y^13 + Y^11 + 4*Y^10 + 5*Y^9 + Y^8 + 4*Y^7 + 
        6*Y^6 + 6*Y^5 + 4*Y^4 + 2*Y^3 + 4*Y^2 + 4*Y + 2,
    -T^56 + 16/7*T^55 - 83/49*T^54 - 191/343*T^53 + 4301/2401*T^52 - 505/2401*T^51 -
        5102/2401*T^50 + 85/49*T^49 + 2382/2401*T^48 - 5177/2401*T^47 + 
        355/2401*T^46 + 3354/2401*T^45 - 103/343*T^44 - 2567/2401*T^43 + 
        1042/2401*T^42 + 3284/2401*T^41 - 3621/2401*T^40 - 535/2401*T^39 + 
        2561/2401*T^38 + 502/2401*T^37 - 2931/2401*T^36 + 327/2401*T^35 + 
        3040/2401*T^34 - 2836/2401*T^33 + 319/2401*T^32 + 179/343*T^31 + 
        124/2401*T^30 - 1446/2401*T^29 + 1446/2401*T^27 - 124/2401*T^26 - 
        179/343*T^25 - 319/2401*T^24 + 2836/2401*T^23 - 3040/2401*T^22 - 
        327/2401*T^21 + 2931/2401*T^20 - 502/2401*T^19 - 2561/2401*T^18 + 
        535/2401*T^17 + 3621/2401*T^16 - 3284/2401*T^15 - 1042/2401*T^14 + 
        2567/2401*T^13 + 103/343*T^12 - 3354/2401*T^11 - 355/2401*T^10 + 
        5177/2401*T^9 - 2382/2401*T^8 - 85/49*T^7 + 5102/2401*T^6 + 505/2401*T^5 - 
        4301/2401*T^4 + 191/343*T^3 + 83/49*T^2 - 16/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^13 + 6*X*Y^10 + 2*X*Y^8 + 6*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 
        2*X*Y^4 + 3*X*Y^2 + 2*X*Y + 3*Y^30 + Y^29 + Y^28 + 4*Y^27 + 2*Y^26 + 6*Y^24 
        + 4*Y^23 + 3*Y^22 + 6*Y^21 + 6*Y^18 + 2*Y^17 + 3*Y^16 + Y^15 + 2*Y^14 + 
        5*Y^13 + Y^12 + 4*Y^11 + 5*Y^10 + 2*Y^9 + 5*Y^8 + Y^7 + 5*Y^6 + 2*Y^5 + 
        4*Y^4 + 2*Y^3 + 4*Y^2 + 2*Y + 5,
    T^56 - 5/7*T^55 + 2/49*T^54 + 17/49*T^53 - 1444/2401*T^52 + 2760/2401*T^51 - 
        3419/2401*T^50 - 185/2401*T^49 + 2301/2401*T^48 - 2171/2401*T^47 + 
        1698/2401*T^46 - 1784/2401*T^45 - 248/2401*T^44 + 314/343*T^43 - 
        1818/2401*T^42 + 573/2401*T^41 + 495/2401*T^40 - 52/2401*T^39 + 
        524/2401*T^38 - 999/2401*T^37 - 45/2401*T^36 + 1125/2401*T^35 - 
        190/2401*T^34 - 615/2401*T^33 + 572/2401*T^32 + 27/2401*T^31 + 176/2401*T^30
        + 145/2401*T^29 - 199/343*T^28 + 145/2401*T^27 + 176/2401*T^26 + 
        27/2401*T^25 + 572/2401*T^24 - 615/2401*T^23 - 190/2401*T^22 + 
        1125/2401*T^21 - 45/2401*T^20 - 999/2401*T^19 + 524/2401*T^18 - 52/2401*T^17
        + 495/2401*T^16 + 573/2401*T^15 - 1818/2401*T^14 + 314/343*T^13 - 
        248/2401*T^12 - 1784/2401*T^11 + 1698/2401*T^10 - 2171/2401*T^9 + 
        2301/2401*T^8 - 185/2401*T^7 - 3419/2401*T^6 + 2760/2401*T^5 - 1444/2401*T^4
        + 17/49*T^3 + 2/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 
        3*X*Y^8 + X*Y^7 + 6*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 3*X*Y + 6*X + 
        5*Y^30 + 5*Y^29 + 2*Y^28 + 6*Y^26 + 4*Y^25 + 3*Y^24 + Y^23 + 5*Y^22 + 2*Y^21
        + 4*Y^20 + 3*Y^19 + 3*Y^18 + 6*Y^17 + Y^16 + Y^12 + 3*Y^11 + 5*Y^10 + 5*Y^8 
        + 4*Y^7 + Y^5 + Y^4 + 3*Y^3 + 4*Y^2 + 2*Y + 1,
    -T^56 + 27/49*T^54 + 305/343*T^53 + 787/2401*T^52 + 62/2401*T^51 + 216/2401*T^50
        - 2123/2401*T^49 - 2050/2401*T^48 - 1685/2401*T^47 + 601/2401*T^46 + 
        1486/2401*T^45 + 2983/2401*T^44 + 1845/2401*T^43 + 81/343*T^42 - 
        1699/2401*T^41 - 1434/2401*T^40 - 2480/2401*T^39 - 44/49*T^38 + 
        564/2401*T^37 + 2255/2401*T^36 + 2976/2401*T^35 + 429/2401*T^34 + 12/49*T^33
        - 101/2401*T^32 - 1639/2401*T^31 - 2666/2401*T^30 - 1636/2401*T^29 + 
        1636/2401*T^27 + 2666/2401*T^26 + 1639/2401*T^25 + 101/2401*T^24 - 
        12/49*T^23 - 429/2401*T^22 - 2976/2401*T^21 - 2255/2401*T^20 - 564/2401*T^19
        + 44/49*T^18 + 2480/2401*T^17 + 1434/2401*T^16 + 1699/2401*T^15 - 
        81/343*T^14 - 1845/2401*T^13 - 2983/2401*T^12 - 1486/2401*T^11 - 
        601/2401*T^10 + 1685/2401*T^9 + 2050/2401*T^8 + 2123/2401*T^7 - 216/2401*T^6
        - 62/2401*T^5 - 787/2401*T^4 - 305/343*T^3 - 27/49*T^2 + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 + 
        2*X*Y^7 + 6*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 5*X*Y + 6*X + 
        4*Y^30 + 6*Y^29 + 3*Y^28 + Y^27 + 5*Y^26 + 6*Y^25 + 6*Y^24 + 2*Y^23 + 6*Y^22
        + 5*Y^21 + 4*Y^20 + 4*Y^19 + 4*Y^18 + 4*Y^17 + Y^16 + 6*Y^15 + 4*Y^13 + 
        3*Y^12 + 6*Y^11 + 2*Y^10 + 4*Y^9 + Y^8 + 4*Y^6 + 4*Y^5 + 4*Y^4 + Y^3 + 5*Y^2
        + 6*Y + 1,
    T^56 + 5/7*T^55 + 9/49*T^54 - 346/343*T^53 - 3079/2401*T^52 - 3446/2401*T^51 - 
        1640/2401*T^50 + 44/343*T^49 + 2057/2401*T^48 + 435/343*T^47 + 
        3170/2401*T^46 + 2031/2401*T^45 + 206/2401*T^44 - 867/2401*T^43 - 
        275/343*T^42 - 939/2401*T^41 - 444/2401*T^40 - 673/2401*T^39 - 822/2401*T^38
        - 1241/2401*T^37 - 265/343*T^36 - 380/2401*T^35 + 2241/2401*T^34 + 
        3540/2401*T^33 + 2691/2401*T^32 + 1114/2401*T^31 - 1392/2401*T^30 - 
        2193/2401*T^29 - 400/343*T^28 - 2193/2401*T^27 - 1392/2401*T^26 + 
        1114/2401*T^25 + 2691/2401*T^24 + 3540/2401*T^23 + 2241/2401*T^22 - 
        380/2401*T^21 - 265/343*T^20 - 1241/2401*T^19 - 822/2401*T^18 - 
        673/2401*T^17 - 444/2401*T^16 - 939/2401*T^15 - 275/343*T^14 - 867/2401*T^13
        + 206/2401*T^12 + 2031/2401*T^11 + 3170/2401*T^10 + 435/343*T^9 + 
        2057/2401*T^8 + 44/343*T^7 - 1640/2401*T^6 - 3446/2401*T^5 - 3079/2401*T^4 -
        346/343*T^3 + 9/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + X*Y^11 + X*Y^10 + 3*X*Y^8 + 
        3*X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 2*X*Y + 6*X + 2*Y^30 + 
        Y^29 + 5*Y^28 + 2*Y^27 + 2*Y^26 + 6*Y^25 + 5*Y^24 + Y^22 + 6*Y^21 + 6*Y^20 +
        5*Y^19 + 2*Y^18 + 4*Y^17 + Y^14 + 3*Y^13 + 2*Y^12 + Y^11 + 2*Y^10 + Y^9 + 
        6*Y^8 + 2*Y^7 + 6*Y^6 + Y^5 + 5*Y^4 + 2*Y^3 + 6*Y^2 + 3*Y + 5,
    T^56 + 4/7*T^55 + 93/49*T^54 + 853/343*T^53 + 6000/2401*T^52 + 1359/343*T^51 + 
        9413/2401*T^50 + 10169/2401*T^49 + 11607/2401*T^48 + 11068/2401*T^47 + 
        12211/2401*T^46 + 11687/2401*T^45 + 11646/2401*T^44 + 12347/2401*T^43 + 
        9855/2401*T^42 + 11152/2401*T^41 + 1333/343*T^40 + 7211/2401*T^39 + 
        1087/343*T^38 + 4714/2401*T^37 + 3271/2401*T^36 + 1594/2401*T^35 - 
        409/2401*T^34 - 2362/2401*T^33 - 652/343*T^32 - 5645/2401*T^31 - 
        7404/2401*T^30 - 8471/2401*T^29 - 7599/2401*T^28 - 8471/2401*T^27 - 
        7404/2401*T^26 - 5645/2401*T^25 - 652/343*T^24 - 2362/2401*T^23 - 
        409/2401*T^22 + 1594/2401*T^21 + 3271/2401*T^20 + 4714/2401*T^19 + 
        1087/343*T^18 + 7211/2401*T^17 + 1333/343*T^16 + 11152/2401*T^15 + 
        9855/2401*T^14 + 12347/2401*T^13 + 11646/2401*T^12 + 11687/2401*T^11 + 
        12211/2401*T^10 + 11068/2401*T^9 + 11607/2401*T^8 + 10169/2401*T^7 + 
        9413/2401*T^6 + 1359/343*T^5 + 6000/2401*T^4 + 853/343*T^3 + 93/49*T^2 + 
        4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 
        + 6*X*Y^8 + 5*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + X*Y 
        + 2*X + 5*Y^30 + 3*Y^29 + 4*Y^28 + 4*Y^27 + 2*Y^26 + 4*Y^25 + 2*Y^24 + 
        5*Y^23 + 4*Y^22 + 2*Y^21 + 4*Y^20 + 4*Y^19 + Y^18 + 4*Y^17 + 6*Y^16 + 4*Y^15
        + 4*Y^14 + 6*Y^13 + 5*Y^12 + 3*Y^11 + 6*Y^10 + Y^9 + 4*Y^8 + 3*Y^6 + Y^5 + 
        Y^4 + 5*Y^3 + Y^2 + 5*Y + 6,
    T^56 + 2/7*T^55 - 65/49*T^54 - 138/343*T^53 + 1159/2401*T^52 + 1633/2401*T^51 + 
        125/343*T^50 - 2013/2401*T^49 - 1966/2401*T^48 + 192/343*T^47 + 
        1075/2401*T^46 - 107/343*T^45 - 96/343*T^44 - 355/2401*T^43 + 982/2401*T^42 
        + 1420/2401*T^41 - 2038/2401*T^40 - 1703/2401*T^39 + 1153/2401*T^38 + 
        1273/2401*T^37 + 680/2401*T^36 - 192/343*T^35 - 2067/2401*T^34 + 
        1706/2401*T^33 + 1870/2401*T^32 - 1900/2401*T^31 - 737/2401*T^30 + 
        986/2401*T^29 + 985/2401*T^28 + 986/2401*T^27 - 737/2401*T^26 - 
        1900/2401*T^25 + 1870/2401*T^24 + 1706/2401*T^23 - 2067/2401*T^22 - 
        192/343*T^21 + 680/2401*T^20 + 1273/2401*T^19 + 1153/2401*T^18 - 
        1703/2401*T^17 - 2038/2401*T^16 + 1420/2401*T^15 + 982/2401*T^14 - 
        355/2401*T^13 - 96/343*T^12 - 107/343*T^11 + 1075/2401*T^10 + 192/343*T^9 - 
        1966/2401*T^8 - 2013/2401*T^7 + 125/343*T^6 + 1633/2401*T^5 + 1159/2401*T^4 
        - 138/343*T^3 - 65/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 5*X*Y^13 + X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 6*X*Y^8 + 6*X*Y^7 + 
        3*X*Y^6 + 4*X*Y^5 + X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 6*X*Y + 5*X + 6*Y^30 + 
        5*Y^29 + Y^28 + 2*Y^27 + 5*Y^26 + 3*Y^25 + 3*Y^24 + 3*Y^23 + 4*Y^22 + 2*Y^21
        + 4*Y^20 + 6*Y^18 + Y^16 + Y^14 + Y^12 + 5*Y^11 + 2*Y^8 + 4*Y^7 + 5*Y^6 + 
        4*Y^5 + 6*Y^4 + Y^3 + 2*Y^2 + Y + 5,
    T^56 + 4/7*T^55 - 73/49*T^54 - 488/343*T^53 + 457/2401*T^52 + 2964/2401*T^51 + 
        2557/2401*T^50 + 107/2401*T^49 - 3546/2401*T^48 - 3712/2401*T^47 + 
        275/343*T^46 + 3939/2401*T^45 + 83/343*T^44 - 34/2401*T^43 - 703/2401*T^42 -
        2056/2401*T^41 - 2291/2401*T^40 + 38/343*T^39 + 513/343*T^38 + 
        2047/2401*T^37 - 811/2401*T^36 - 2490/2401*T^35 - 2585/2401*T^34 + 
        592/2401*T^33 + 3487/2401*T^32 + 349/343*T^31 - 1815/2401*T^30 - 
        2026/2401*T^29 + 666/2401*T^28 - 2026/2401*T^27 - 1815/2401*T^26 + 
        349/343*T^25 + 3487/2401*T^24 + 592/2401*T^23 - 2585/2401*T^22 - 
        2490/2401*T^21 - 811/2401*T^20 + 2047/2401*T^19 + 513/343*T^18 + 38/343*T^17
        - 2291/2401*T^16 - 2056/2401*T^15 - 703/2401*T^14 - 34/2401*T^13 + 
        83/343*T^12 + 3939/2401*T^11 + 275/343*T^10 - 3712/2401*T^9 - 3546/2401*T^8 
        + 107/2401*T^7 + 2557/2401*T^6 + 2964/2401*T^5 + 457/2401*T^4 - 488/343*T^3 
        - 73/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^10 + 2*X*Y^9 + 5*X*Y^7 +
        4*X*Y^6 + X*Y^5 + X*Y^4 + 4*X*Y^2 + 5*X*Y + 5*X + Y^30 + 3*Y^27 + 5*Y^26 + 
        2*Y^25 + 3*Y^24 + 5*Y^23 + 2*Y^22 + 4*Y^21 + Y^20 + Y^19 + 4*Y^17 + 2*Y^16 +
        2*Y^15 + 5*Y^14 + 4*Y^13 + 3*Y^12 + 4*Y^10 + 2*Y^9 + 2*Y^8 + 4*Y^7 + 2*Y^6 +
        3*Y^5 + 6*Y^4 + Y^3 + 2*Y^2,
    T^56 - 10/7*T^55 + 544/343*T^53 - 3433/2401*T^52 - 1635/2401*T^51 + 
        5228/2401*T^50 - 2859/2401*T^49 - 2760/2401*T^48 + 5728/2401*T^47 - 
        1961/2401*T^46 - 4189/2401*T^45 + 4957/2401*T^44 - 57/343*T^43 - 
        4716/2401*T^42 + 4234/2401*T^41 + 212/343*T^40 - 5588/2401*T^39 + 
        3170/2401*T^38 + 3088/2401*T^37 - 5342/2401*T^36 + 1635/2401*T^35 + 
        403/343*T^34 - 458/343*T^33 - 44/343*T^32 + 3338/2401*T^31 - 2242/2401*T^30 
        - 129/343*T^29 + 2167/2401*T^28 - 129/343*T^27 - 2242/2401*T^26 + 
        3338/2401*T^25 - 44/343*T^24 - 458/343*T^23 + 403/343*T^22 + 1635/2401*T^21 
        - 5342/2401*T^20 + 3088/2401*T^19 + 3170/2401*T^18 - 5588/2401*T^17 + 
        212/343*T^16 + 4234/2401*T^15 - 4716/2401*T^14 - 57/343*T^13 + 
        4957/2401*T^12 - 4189/2401*T^11 - 1961/2401*T^10 + 5728/2401*T^9 - 
        2760/2401*T^8 - 2859/2401*T^7 + 5228/2401*T^6 - 1635/2401*T^5 - 
        3433/2401*T^4 + 544/343*T^3 - 10/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 3*X*Y^10 + 2*X*Y^9 + 6*X*Y^8 +
        6*X*Y^6 + X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 6*X*Y + X + Y^30 + 2*Y^29 + 
        6*Y^28 + 6*Y^26 + 3*Y^25 + 3*Y^24 + 6*Y^23 + Y^22 + 5*Y^21 + 3*Y^20 + 2*Y^19
        + Y^18 + 2*Y^16 + 4*Y^15 + 6*Y^14 + 5*Y^13 + 3*Y^12 + 3*Y^11 + 6*Y^10 + Y^9 
        + 5*Y^8 + 5*Y^7 + 5*Y^2 + 1,
    T^56 + 30/49*T^54 + 54/343*T^53 + 41/343*T^52 - 953/2401*T^51 - 964/2401*T^50 + 
        418/2401*T^49 - 151/343*T^48 + 134/343*T^47 - 177/2401*T^46 + 40/2401*T^45 -
        1383/2401*T^44 + 562/2401*T^43 - 2122/2401*T^42 - 1433/2401*T^41 - 
        1227/2401*T^40 - 58/2401*T^39 - 53/343*T^38 - 269/2401*T^37 + 1650/2401*T^36
        - 422/2401*T^35 + 538/2401*T^34 + 319/2401*T^33 - 33/343*T^32 + 40/2401*T^31
        + 1840/2401*T^30 + 1331/2401*T^29 + 510/2401*T^28 + 1331/2401*T^27 + 
        1840/2401*T^26 + 40/2401*T^25 - 33/343*T^24 + 319/2401*T^23 + 538/2401*T^22 
        - 422/2401*T^21 + 1650/2401*T^20 - 269/2401*T^19 - 53/343*T^18 - 
        58/2401*T^17 - 1227/2401*T^16 - 1433/2401*T^15 - 2122/2401*T^14 + 
        562/2401*T^13 - 1383/2401*T^12 + 40/2401*T^11 - 177/2401*T^10 + 134/343*T^9 
        - 151/343*T^8 + 418/2401*T^7 - 964/2401*T^6 - 953/2401*T^5 + 41/343*T^4 + 
        54/343*T^3 + 30/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 4*X*Y^8 
        + 5*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 6*X*Y + 4*X + 
        2*Y^30 + 4*Y^29 + 3*Y^28 + 6*Y^27 + Y^26 + 2*Y^24 + 6*Y^23 + 3*Y^21 + 5*Y^20
        + Y^19 + 4*Y^18 + 3*Y^17 + Y^16 + Y^15 + 3*Y^14 + 6*Y^13 + 3*Y^12 + 2*Y^11 +
        6*Y^10 + 5*Y^9 + Y^7 + 3*Y^6 + 2*Y^4 + 4*Y^3 + 4*Y^2 + 4*Y + 1,
    T^56 - 8/7*T^55 + 8/49*T^54 + 547/343*T^53 - 755/343*T^52 + 1592/2401*T^51 + 
        528/343*T^50 - 4723/2401*T^49 + 1574/2401*T^48 + 1588/2401*T^47 - 
        2340/2401*T^46 + 1556/2401*T^45 - 841/2401*T^44 + 514/2401*T^43 + 
        1081/2401*T^42 - 1682/2401*T^41 + 1494/2401*T^40 + 921/2401*T^39 - 
        2747/2401*T^38 + 1811/2401*T^37 + 150/2401*T^36 - 3506/2401*T^35 + 
        3324/2401*T^34 - 464/2401*T^33 - 3135/2401*T^32 + 3582/2401*T^31 - 
        1305/2401*T^30 - 1950/2401*T^29 + 565/343*T^28 - 1950/2401*T^27 - 
        1305/2401*T^26 + 3582/2401*T^25 - 3135/2401*T^24 - 464/2401*T^23 + 
        3324/2401*T^22 - 3506/2401*T^21 + 150/2401*T^20 + 1811/2401*T^19 - 
        2747/2401*T^18 + 921/2401*T^17 + 1494/2401*T^16 - 1682/2401*T^15 + 
        1081/2401*T^14 + 514/2401*T^13 - 841/2401*T^12 + 1556/2401*T^11 - 
        2340/2401*T^10 + 1588/2401*T^9 + 1574/2401*T^8 - 4723/2401*T^7 + 528/343*T^6
        + 1592/2401*T^5 - 755/343*T^4 + 547/343*T^3 + 8/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 4*X*Y^6 + 
        4*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 6*X + 5*Y^30 + 3*Y^28 + 5*Y^26 + 
        3*Y^25 + 6*Y^24 + 2*Y^23 + 6*Y^22 + 6*Y^20 + Y^19 + 2*Y^18 + 3*Y^15 + 2*Y^14
        + 6*Y^13 + 5*Y^12 + 2*Y^11 + Y^10 + 5*Y^9 + 4*Y^8 + 2*Y^6 + 2*Y^5 + 2*Y^3 + 
        2*Y^2 + 6*Y + 3,
    -T^56 - 11/7*T^55 - 69/49*T^54 - 260/343*T^53 + 80/2401*T^52 + 823/2401*T^51 + 
        1321/2401*T^50 + 13/2401*T^49 - 2301/2401*T^48 - 4304/2401*T^47 - 
        4320/2401*T^46 - 2260/2401*T^45 - 1607/2401*T^44 - 269/2401*T^43 + 
        1471/2401*T^42 + 2657/2401*T^41 + 2341/2401*T^40 + 696/2401*T^39 - 
        80/2401*T^38 - 1107/2401*T^37 - 1973/2401*T^36 - 1977/2401*T^35 + 
        232/2401*T^34 + 327/343*T^33 + 1767/2401*T^32 + 1490/2401*T^31 + 
        1616/2401*T^30 + 1467/2401*T^29 - 1467/2401*T^27 - 1616/2401*T^26 - 
        1490/2401*T^25 - 1767/2401*T^24 - 327/343*T^23 - 232/2401*T^22 + 
        1977/2401*T^21 + 1973/2401*T^20 + 1107/2401*T^19 + 80/2401*T^18 - 
        696/2401*T^17 - 2341/2401*T^16 - 2657/2401*T^15 - 1471/2401*T^14 + 
        269/2401*T^13 + 1607/2401*T^12 + 2260/2401*T^11 + 4320/2401*T^10 + 
        4304/2401*T^9 + 2301/2401*T^8 - 13/2401*T^7 - 1321/2401*T^6 - 823/2401*T^5 -
        80/2401*T^4 + 260/343*T^3 + 69/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 3*X*Y^3 + 4*X*Y^2 + 3*X*Y + 5*Y^30 + 
        3*Y^29 + 3*Y^28 + 3*Y^27 + 3*Y^26 + 3*Y^25 + 4*Y^24 + 6*Y^23 + 6*Y^22 + 
        6*Y^21 + 6*Y^20 + 4*Y^19 + 4*Y^18 + 3*Y^17 + 2*Y^16 + 2*Y^15 + 2*Y^14 + 
        2*Y^13 + 3*Y^12 + 6*Y^10 + 6*Y^9 + 5*Y^8 + 3*Y^7 + 3*Y^6 + 3*Y^5 + Y^4 + Y^3
        + 6*Y^2 + 3*Y + 1,
    T^56 - T^55 - 1/49*T^54 + 58/343*T^53 - 690/2401*T^52 + 628/343*T^51 - 
        4743/2401*T^50 + 1011/2401*T^49 + 110/2401*T^48 - 673/2401*T^47 + 
        3193/2401*T^46 - 4050/2401*T^45 + 3322/2401*T^44 - 2579/2401*T^43 + 
        396/2401*T^42 + 1681/2401*T^41 - 3560/2401*T^40 + 5581/2401*T^39 - 
        4528/2401*T^38 + 1094/2401*T^37 + 873/2401*T^36 - 3460/2401*T^35 + 
        5419/2401*T^34 - 492/343*T^33 + 271/343*T^32 - 624/2401*T^31 - 
        2213/2401*T^30 + 3382/2401*T^29 - 2532/2401*T^28 + 3382/2401*T^27 - 
        2213/2401*T^26 - 624/2401*T^25 + 271/343*T^24 - 492/343*T^23 + 
        5419/2401*T^22 - 3460/2401*T^21 + 873/2401*T^20 + 1094/2401*T^19 - 
        4528/2401*T^18 + 5581/2401*T^17 - 3560/2401*T^16 + 1681/2401*T^15 + 
        396/2401*T^14 - 2579/2401*T^13 + 3322/2401*T^12 - 4050/2401*T^11 + 
        3193/2401*T^10 - 673/2401*T^9 + 110/2401*T^8 + 1011/2401*T^7 - 4743/2401*T^6
        + 628/343*T^5 - 690/2401*T^4 + 58/343*T^3 - 1/49*T^2 - T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 4*X*Y^9 + 2*X*Y^8 + 3*X*Y^7 + 
        5*X*Y^6 + 3*X*Y^5 + X*Y^4 + X*Y^3 + 2*X*Y^2 + 6*X*Y + 3*X + 6*Y^30 + Y^29 + 
        4*Y^28 + 4*Y^27 + 6*Y^26 + 2*Y^24 + 6*Y^23 + Y^22 + 6*Y^21 + 6*Y^20 + 2*Y^19
        + Y^18 + 5*Y^17 + 2*Y^16 + Y^15 + Y^14 + 5*Y^13 + 2*Y^12 + 5*Y^11 + 6*Y^10 +
        3*Y^9 + 5*Y^8 + 2*Y^7 + Y^6 + 3*Y^4 + Y^2 + 6*Y + 5,
    T^56 + 10/7*T^55 + 10/49*T^54 - 146/343*T^53 - 514/2401*T^52 - 191/2401*T^51 - 
        883/2401*T^50 - 825/2401*T^49 + 162/343*T^48 + 1802/2401*T^47 + 
        1097/2401*T^46 + 631/2401*T^45 + 73/2401*T^44 - 1038/2401*T^43 - 
        1742/2401*T^42 - 1998/2401*T^41 - 1906/2401*T^40 - 13/2401*T^39 + 
        1402/2401*T^38 + 1175/2401*T^37 + 354/2401*T^36 - 101/2401*T^35 - 
        534/2401*T^34 - 1097/2401*T^33 - 414/2401*T^32 - 551/2401*T^31 - 
        358/2401*T^30 + 1131/2401*T^29 + 230/343*T^28 + 1131/2401*T^27 - 
        358/2401*T^26 - 551/2401*T^25 - 414/2401*T^24 - 1097/2401*T^23 - 
        534/2401*T^22 - 101/2401*T^21 + 354/2401*T^20 + 1175/2401*T^19 + 
        1402/2401*T^18 - 13/2401*T^17 - 1906/2401*T^16 - 1998/2401*T^15 - 
        1742/2401*T^14 - 1038/2401*T^13 + 73/2401*T^12 + 631/2401*T^11 + 
        1097/2401*T^10 + 1802/2401*T^9 + 162/343*T^8 - 825/2401*T^7 - 883/2401*T^6 -
        191/2401*T^5 - 514/2401*T^4 - 146/343*T^3 + 10/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + X*Y^12 + X*Y^10 + 2*X*Y^9 + X*Y^8 + 
        6*X*Y^7 + 5*X*Y^6 + X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 4*X*Y + 5*X + 
        2*Y^30 + 3*Y^28 + 2*Y^27 + 5*Y^26 + 4*Y^24 + 4*Y^23 + 4*Y^22 + 6*Y^20 + 
        2*Y^18 + 2*Y^16 + 6*Y^15 + 2*Y^14 + 3*Y^12 + 5*Y^11 + 3*Y^9 + 2*Y^8 + Y^7 + 
        6*Y^6 + 5*Y^5 + 5*Y^4 + 6*Y^3 + Y^2 + Y + 1,
    T^56 - 10/7*T^55 + 41/49*T^54 - 80/343*T^53 - 9/49*T^52 + 1412/2401*T^51 - 
        3789/2401*T^50 + 5203/2401*T^49 - 668/343*T^48 + 2144/2401*T^47 - 
        1174/2401*T^46 + 783/2401*T^45 + 463/2401*T^44 - 2265/2401*T^43 + 
        3936/2401*T^42 - 423/343*T^41 + 1989/2401*T^40 - 1782/2401*T^39 + 
        1147/2401*T^38 - 650/2401*T^37 + 732/2401*T^36 + 26/343*T^35 + 31/343*T^34 -
        669/2401*T^33 + 12/2401*T^32 + 1108/2401*T^31 - 2320/2401*T^30 + 
        1497/2401*T^29 - 141/343*T^28 + 1497/2401*T^27 - 2320/2401*T^26 + 
        1108/2401*T^25 + 12/2401*T^24 - 669/2401*T^23 + 31/343*T^22 + 26/343*T^21 + 
        732/2401*T^20 - 650/2401*T^19 + 1147/2401*T^18 - 1782/2401*T^17 + 
        1989/2401*T^16 - 423/343*T^15 + 3936/2401*T^14 - 2265/2401*T^13 + 
        463/2401*T^12 + 783/2401*T^11 - 1174/2401*T^10 + 2144/2401*T^9 - 668/343*T^8
        + 5203/2401*T^7 - 3789/2401*T^6 + 1412/2401*T^5 - 9/49*T^4 - 80/343*T^3 + 
        41/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 +
        2*X*Y^7 + 6*X*Y^6 + X*Y^5 + 3*X*Y^4 + 3*X*Y^2 + 2*X*Y + 5*X + Y^30 + 2*Y^29 
        + 6*Y^28 + 3*Y^27 + 3*Y^26 + 6*Y^24 + 3*Y^23 + 3*Y^22 + 2*Y^21 + 5*Y^20 + 
        5*Y^19 + 5*Y^18 + Y^17 + 2*Y^16 + 6*Y^15 + 3*Y^14 + 4*Y^12 + 4*Y^11 + 2*Y^10
        + 3*Y^9 + 5*Y^8 + Y^7 + Y^5 + 6*Y^4 + 5*Y^3 + 3*Y^2 + 3,
    T^56 - 3/7*T^55 - 29/49*T^54 + 130/343*T^53 - 489/2401*T^52 + 230/2401*T^51 + 
        1487/2401*T^50 + 450/2401*T^49 - 701/2401*T^48 - 892/2401*T^47 - 
        52/2401*T^46 + 1186/2401*T^45 + 48/343*T^44 - 773/2401*T^43 + 1031/2401*T^42
        - 409/2401*T^41 - 731/2401*T^40 + 22/2401*T^39 - 92/343*T^38 + 471/2401*T^37
        + 443/2401*T^36 - 600/2401*T^35 + 761/2401*T^34 - 362/2401*T^33 - 
        1945/2401*T^32 + 1026/2401*T^31 - 183/2401*T^30 - 150/343*T^29 + 
        1495/2401*T^28 - 150/343*T^27 - 183/2401*T^26 + 1026/2401*T^25 - 
        1945/2401*T^24 - 362/2401*T^23 + 761/2401*T^22 - 600/2401*T^21 + 
        443/2401*T^20 + 471/2401*T^19 - 92/343*T^18 + 22/2401*T^17 - 731/2401*T^16 -
        409/2401*T^15 + 1031/2401*T^14 - 773/2401*T^13 + 48/343*T^12 + 
        1186/2401*T^11 - 52/2401*T^10 - 892/2401*T^9 - 701/2401*T^8 + 450/2401*T^7 +
        1487/2401*T^6 + 230/2401*T^5 - 489/2401*T^4 + 130/343*T^3 - 29/49*T^2 - 
        3/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 4*X*Y^13 + 5*X*Y^11 + 5*X*Y^10 + X*Y^9 + 2*X*Y^8 + 3*X*Y^7 + 
        5*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 4*X*Y + 3*X + 5*Y^30 + 6*Y^29 + 
        5*Y^28 + 6*Y^27 + 3*Y^26 + 3*Y^25 + 4*Y^24 + Y^23 + 6*Y^22 + 4*Y^20 + 3*Y^19
        + 3*Y^17 + 6*Y^16 + Y^14 + 2*Y^13 + 5*Y^12 + 2*Y^11 + 5*Y^10 + Y^9 + 4*Y^8 +
        3*Y^6 + 4*Y^5 + 6*Y^4 + 4*Y^3 + 3*Y^2 + 5*Y + 3,
    -T^56 + 1/7*T^55 + 57/49*T^54 - 62/343*T^53 + 45/343*T^52 - 573/2401*T^51 + 
        131/2401*T^50 + 1829/2401*T^49 - 1412/2401*T^48 - 806/2401*T^47 + 
        841/2401*T^46 + 281/2401*T^45 - 71/343*T^44 - 1636/2401*T^43 - 622/2401*T^42
        + 251/2401*T^41 + 216/343*T^40 + 123/2401*T^39 - 141/343*T^38 + 
        1355/2401*T^37 + 706/2401*T^36 + 243/2401*T^35 - 157/2401*T^34 - 
        2773/2401*T^33 + 464/2401*T^32 + 2616/2401*T^31 - 1518/2401*T^30 - 
        1208/2401*T^29 + 1208/2401*T^27 + 1518/2401*T^26 - 2616/2401*T^25 - 
        464/2401*T^24 + 2773/2401*T^23 + 157/2401*T^22 - 243/2401*T^21 - 
        706/2401*T^20 - 1355/2401*T^19 + 141/343*T^18 - 123/2401*T^17 - 216/343*T^16
        - 251/2401*T^15 + 622/2401*T^14 + 1636/2401*T^13 + 71/343*T^12 - 
        281/2401*T^11 - 841/2401*T^10 + 806/2401*T^9 + 1412/2401*T^8 - 1829/2401*T^7
        - 131/2401*T^6 + 573/2401*T^5 - 45/343*T^4 + 62/343*T^3 - 57/49*T^2 - 1/7*T 
        + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 
        4*X*Y^8 + 6*X*Y^6 + X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 5*X*Y + 6*X + 
        4*Y^30 + 5*Y^29 + Y^27 + 3*Y^26 + 5*Y^25 + 6*Y^24 + 4*Y^23 + 3*Y^22 + 5*Y^21
        + 5*Y^20 + 5*Y^19 + 2*Y^18 + 3*Y^17 + 2*Y^16 + 2*Y^15 + 5*Y^14 + 4*Y^13 + 
        4*Y^11 + 3*Y^10 + Y^9 + 2*Y^8 + 3*Y^7 + 4*Y^6 + Y^5 + Y^4 + 3*Y^3 + 4*Y^2 + 
        3*Y + 2,
    T^56 - 1/7*T^55 - 80/49*T^54 - 108/343*T^53 + 2007/2401*T^52 + 327/343*T^51 + 
        583/2401*T^50 - 2871/2401*T^49 - 2140/2401*T^48 + 1846/2401*T^47 + 
        2574/2401*T^46 + 475/2401*T^45 - 285/343*T^44 - 188/2401*T^43 - 106/343*T^42
        - 345/2401*T^41 + 1398/2401*T^40 + 235/343*T^39 - 1039/2401*T^38 - 
        2669/2401*T^37 - 494/2401*T^36 + 2108/2401*T^35 + 2409/2401*T^34 - 
        118/2401*T^33 - 2370/2401*T^32 - 730/2401*T^31 + 1423/2401*T^30 - 
        283/2401*T^29 - 54/2401*T^28 - 283/2401*T^27 + 1423/2401*T^26 - 
        730/2401*T^25 - 2370/2401*T^24 - 118/2401*T^23 + 2409/2401*T^22 + 
        2108/2401*T^21 - 494/2401*T^20 - 2669/2401*T^19 - 1039/2401*T^18 + 
        235/343*T^17 + 1398/2401*T^16 - 345/2401*T^15 - 106/343*T^14 - 188/2401*T^13
        - 285/343*T^12 + 475/2401*T^11 + 2574/2401*T^10 + 1846/2401*T^9 - 
        2140/2401*T^8 - 2871/2401*T^7 + 583/2401*T^6 + 327/343*T^5 + 2007/2401*T^4 -
        108/343*T^3 - 80/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 5*X*Y^7 + 5*X*Y^6 + X*Y^5 + 2*X*Y^4 + X*Y^3 + 5*X*Y + 2*X + 3*Y^30
        + 2*Y^29 + 6*Y^27 + 3*Y^25 + Y^24 + 2*Y^23 + 4*Y^22 + 3*Y^21 + 6*Y^20 + 
        2*Y^18 + 5*Y^17 + Y^14 + Y^13 + Y^12 + 6*Y^9 + 5*Y^8 + 2*Y^7 + 2*Y^6 + 6*Y^5
        + 5*Y^4 + 4*Y^3 + Y + 1,
    T^56 - 4/7*T^55 + 9/49*T^54 + 249/343*T^53 - 240/343*T^52 + 606/2401*T^51 - 
        915/2401*T^50 + 24/2401*T^49 - 807/2401*T^48 - 1352/2401*T^47 + 
        1073/2401*T^46 - 1605/2401*T^45 + 674/2401*T^44 + 402/2401*T^43 - 
        689/2401*T^42 + 1387/2401*T^41 - 1230/2401*T^40 + 1038/2401*T^39 + 
        242/2401*T^38 - 765/2401*T^37 + 565/2401*T^36 + 169/2401*T^35 + 31/2401*T^34
        - 356/2401*T^33 + 571/2401*T^32 - 331/2401*T^31 + 33/2401*T^30 + 
        442/2401*T^29 - 519/2401*T^28 + 442/2401*T^27 + 33/2401*T^26 - 331/2401*T^25
        + 571/2401*T^24 - 356/2401*T^23 + 31/2401*T^22 + 169/2401*T^21 + 
        565/2401*T^20 - 765/2401*T^19 + 242/2401*T^18 + 1038/2401*T^17 - 
        1230/2401*T^16 + 1387/2401*T^15 - 689/2401*T^14 + 402/2401*T^13 + 
        674/2401*T^12 - 1605/2401*T^11 + 1073/2401*T^10 - 1352/2401*T^9 - 
        807/2401*T^8 + 24/2401*T^7 - 915/2401*T^6 + 606/2401*T^5 - 240/343*T^4 + 
        249/343*T^3 + 9/49*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 3*X*Y^12 + 2*X*Y^9 + 4*X*Y^8 + 4*X*Y^7 + 4*X*Y^6 + 
        5*X*Y^5 + 2*X*Y^3 + 5*X*Y^2 + 6*X*Y + 3*X + Y^30 + 6*Y^29 + Y^28 + 3*Y^26 + 
        4*Y^24 + Y^23 + 2*Y^22 + 2*Y^21 + 2*Y^20 + 2*Y^19 + Y^16 + 2*Y^15 + 3*Y^14 +
        4*Y^13 + 4*Y^12 + 3*Y^11 + 4*Y^10 + 4*Y^9 + Y^8 + Y^7 + 4*Y^5 + 5*Y^4 + 
        3*Y^3 + Y^2 + 3*Y + 1,
    T^56 - 3/7*T^55 + 1/7*T^54 + 100/343*T^53 - 1081/2401*T^52 + 1959/2401*T^51 + 
        792/2401*T^50 - 1229/2401*T^49 + 1412/2401*T^48 - 1495/2401*T^47 - 
        1549/2401*T^46 + 41/49*T^45 - 2012/2401*T^44 + 1306/2401*T^43 - 
        358/2401*T^42 - 2334/2401*T^41 + 962/2401*T^40 - 142/343*T^39 + 
        157/2401*T^38 + 1655/2401*T^37 - 1732/2401*T^36 + 149/343*T^35 + 
        108/2401*T^34 - 1231/2401*T^33 + 2579/2401*T^32 - 130/343*T^31 + 
        75/2401*T^30 + 1845/2401*T^29 - 1600/2401*T^28 + 1845/2401*T^27 + 
        75/2401*T^26 - 130/343*T^25 + 2579/2401*T^24 - 1231/2401*T^23 + 
        108/2401*T^22 + 149/343*T^21 - 1732/2401*T^20 + 1655/2401*T^19 + 
        157/2401*T^18 - 142/343*T^17 + 962/2401*T^16 - 2334/2401*T^15 - 
        358/2401*T^14 + 1306/2401*T^13 - 2012/2401*T^12 + 41/49*T^11 - 
        1549/2401*T^10 - 1495/2401*T^9 + 1412/2401*T^8 - 1229/2401*T^7 + 
        792/2401*T^6 + 1959/2401*T^5 - 1081/2401*T^4 + 100/343*T^3 + 1/7*T^2 - 3/7*T
        + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 + 
        3*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 3*X*Y + 5*X + 4*Y^30 + 
        5*Y^29 + 2*Y^28 + 3*Y^27 + 3*Y^26 + Y^25 + 2*Y^24 + 2*Y^23 + 6*Y^22 + 6*Y^21
        + 4*Y^20 + 4*Y^18 + Y^17 + 5*Y^16 + 5*Y^14 + Y^13 + 2*Y^12 + 3*Y^11 + 2*Y^10
        + Y^9 + 2*Y^8 + 2*Y^7 + 6*Y^5 + Y^4 + 6*Y^3 + 2*Y + 3,
    -T^56 - 11/7*T^55 - 54/49*T^54 + 8/343*T^53 + 1845/2401*T^52 + 1951/2401*T^51 + 
        2830/2401*T^50 + 2899/2401*T^49 + 405/343*T^48 + 1368/2401*T^47 - 
        393/2401*T^46 - 138/2401*T^45 - 761/2401*T^44 - 1762/2401*T^43 - 
        1964/2401*T^42 - 1184/2401*T^41 - 79/2401*T^40 - 221/2401*T^39 + 1/343*T^38 
        - 309/2401*T^37 - 15/49*T^36 - 99/343*T^35 - 958/2401*T^34 + 4/2401*T^33 + 
        1549/2401*T^32 + 1794/2401*T^31 + 2330/2401*T^30 + 1667/2401*T^29 - 
        1667/2401*T^27 - 2330/2401*T^26 - 1794/2401*T^25 - 1549/2401*T^24 - 
        4/2401*T^23 + 958/2401*T^22 + 99/343*T^21 + 15/49*T^20 + 309/2401*T^19 - 
        1/343*T^18 + 221/2401*T^17 + 79/2401*T^16 + 1184/2401*T^15 + 1964/2401*T^14 
        + 1762/2401*T^13 + 761/2401*T^12 + 138/2401*T^11 + 393/2401*T^10 - 
        1368/2401*T^9 - 405/343*T^8 - 2899/2401*T^7 - 2830/2401*T^6 - 1951/2401*T^5 
        - 1845/2401*T^4 - 8/343*T^3 + 54/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 
        X*Y^7 + X*Y^6 + X*Y^4 + 2*X*Y^3 + X*Y^2 + 6*X + 4*Y^30 + 3*Y^28 + 6*Y^26 + 
        2*Y^25 + 5*Y^24 + 2*Y^23 + 5*Y^22 + 3*Y^21 + 5*Y^20 + 3*Y^19 + 2*Y^18 + 
        5*Y^17 + 2*Y^16 + 4*Y^15 + 3*Y^14 + 3*Y^13 + Y^12 + 4*Y^11 + 6*Y^10 + 3*Y^8 
        + 6*Y^7 + 3*Y^6 + 6*Y^5 + Y^4 + 6*Y^3 + 5*Y^2 + Y,
    -T^56 - 2/7*T^55 - 39/49*T^54 - 61/49*T^53 - 1251/2401*T^52 - 5232/2401*T^51 - 
        1566/2401*T^50 - 3330/2401*T^49 - 5151/2401*T^48 - 1949/2401*T^47 - 
        697/343*T^46 - 2945/2401*T^45 - 3023/2401*T^44 - 4990/2401*T^43 - 
        2668/2401*T^42 - 2861/2401*T^41 - 4128/2401*T^40 - 307/343*T^39 - 
        3579/2401*T^38 - 2725/2401*T^37 - 698/2401*T^36 - 4171/2401*T^35 - 
        387/2401*T^34 - 1095/2401*T^33 - 2197/2401*T^32 + 1034/2401*T^31 - 
        453/343*T^30 + 195/343*T^29 - 195/343*T^27 + 453/343*T^26 - 1034/2401*T^25 +
        2197/2401*T^24 + 1095/2401*T^23 + 387/2401*T^22 + 4171/2401*T^21 + 
        698/2401*T^20 + 2725/2401*T^19 + 3579/2401*T^18 + 307/343*T^17 + 
        4128/2401*T^16 + 2861/2401*T^15 + 2668/2401*T^14 + 4990/2401*T^13 + 
        3023/2401*T^12 + 2945/2401*T^11 + 697/343*T^10 + 1949/2401*T^9 + 
        5151/2401*T^8 + 3330/2401*T^7 + 1566/2401*T^6 + 5232/2401*T^5 + 
        1251/2401*T^4 + 61/49*T^3 + 39/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 2*X*Y^10 + X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 
        4*X*Y^4 + 4*X*Y^3 + X*Y^2 + 5*X*Y + 3*X + 4*Y^30 + 3*Y^27 + 3*Y^26 + 6*Y^24 
        + 4*Y^23 + Y^22 + 2*Y^21 + 5*Y^20 + 2*Y^19 + 3*Y^17 + 3*Y^15 + 2*Y^14 + 
        6*Y^13 + 2*Y^12 + 5*Y^11 + 5*Y^10 + 5*Y^8 + 3*Y^7 + Y^6 + 6*Y^5 + 2*Y^4 + 
        4*Y^3 + 5*Y^2 + 2*Y + 6,
    T^56 + 8/7*T^55 + 4/7*T^54 - 15/343*T^53 - 654/2401*T^52 - 1361/2401*T^51 - 
        67/343*T^50 + 591/2401*T^49 + 432/2401*T^48 + 1908/2401*T^47 + 
        2582/2401*T^46 + 992/2401*T^45 - 697/2401*T^44 - 485/2401*T^43 - 
        650/2401*T^42 - 682/2401*T^41 + 748/2401*T^40 + 989/2401*T^39 + 106/343*T^38
        + 1332/2401*T^37 + 2007/2401*T^36 + 379/2401*T^35 - 785/2401*T^34 - 
        667/2401*T^33 - 186/343*T^32 - 274/2401*T^31 + 1636/2401*T^30 + 390/343*T^29
        + 1492/2401*T^28 + 390/343*T^27 + 1636/2401*T^26 - 274/2401*T^25 - 
        186/343*T^24 - 667/2401*T^23 - 785/2401*T^22 + 379/2401*T^21 + 
        2007/2401*T^20 + 1332/2401*T^19 + 106/343*T^18 + 989/2401*T^17 + 
        748/2401*T^16 - 682/2401*T^15 - 650/2401*T^14 - 485/2401*T^13 - 
        697/2401*T^12 + 992/2401*T^11 + 2582/2401*T^10 + 1908/2401*T^9 + 
        432/2401*T^8 + 591/2401*T^7 - 67/343*T^6 - 1361/2401*T^5 - 654/2401*T^4 - 
        15/343*T^3 + 4/7*T^2 + 8/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 +
        6*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 3*X*Y + 3*X + 2*Y^30 + 
        5*Y^28 + 4*Y^27 + 4*Y^25 + 5*Y^24 + Y^23 + 5*Y^22 + 3*Y^21 + 5*Y^20 + Y^19 +
        3*Y^18 + 2*Y^17 + 5*Y^16 + 6*Y^14 + 5*Y^13 + 3*Y^12 + Y^11 + 2*Y^10 + 4*Y^9 
        + 6*Y^8 + 3*Y^7 + 2*Y^6 + 4*Y^5 + 6*Y^4 + 6*Y^3 + 6*Y^2 + 5*Y,
    -T^56 + 4/7*T^55 + 58/49*T^54 - 67/49*T^53 - 1698/2401*T^52 + 2414/2401*T^51 + 
        1660/2401*T^50 - 2816/2401*T^49 - 1026/2401*T^48 + 1873/2401*T^47 - 
        696/2401*T^46 - 477/2401*T^45 - 51/2401*T^44 + 142/2401*T^43 + 13/49*T^42 - 
        176/2401*T^41 - 753/2401*T^40 - 185/2401*T^39 + 950/2401*T^38 + 26/2401*T^37
        - 1774/2401*T^36 + 562/2401*T^35 + 1128/2401*T^34 - 583/2401*T^33 + 
        72/2401*T^32 - 698/2401*T^31 + 66/343*T^30 + 396/2401*T^29 - 396/2401*T^27 -
        66/343*T^26 + 698/2401*T^25 - 72/2401*T^24 + 583/2401*T^23 - 1128/2401*T^22 
        - 562/2401*T^21 + 1774/2401*T^20 - 26/2401*T^19 - 950/2401*T^18 + 
        185/2401*T^17 + 753/2401*T^16 + 176/2401*T^15 - 13/49*T^14 - 142/2401*T^13 +
        51/2401*T^12 + 477/2401*T^11 + 696/2401*T^10 - 1873/2401*T^9 + 1026/2401*T^8
        + 2816/2401*T^7 - 1660/2401*T^6 - 2414/2401*T^5 + 1698/2401*T^4 + 67/49*T^3 
        - 58/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + X*Y^10 + X*Y^9 + 
        3*X*Y^8 + 5*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + X*Y^2 + X*Y + 4*X + 3*Y^30 + 5*Y^29 
        + 5*Y^28 + Y^27 + Y^26 + 3*Y^25 + 5*Y^24 + 5*Y^23 + 2*Y^22 + 3*Y^20 + 2*Y^19
        + 2*Y^18 + 2*Y^17 + 3*Y^16 + 3*Y^15 + 4*Y^14 + Y^11 + 2*Y^10 + 3*Y^9 + 3*Y^8
        + 6*Y^7 + 6*Y^6 + Y^4 + 3*Y^3 + 6*Y + 1,
    T^56 + 10/7*T^55 + 30/49*T^54 + 36/343*T^53 - 340/2401*T^52 - 627/2401*T^51 - 
        92/2401*T^50 + 506/2401*T^49 - 327/2401*T^48 - 806/2401*T^47 - 
        1538/2401*T^46 - 2028/2401*T^45 - 1082/2401*T^44 - 162/343*T^43 - 
        1772/2401*T^42 - 914/2401*T^41 + 101/2401*T^40 + 536/2401*T^39 + 
        176/2401*T^38 - 496/2401*T^37 - 15/49*T^36 - 129/343*T^35 - 33/343*T^34 + 
        676/2401*T^33 + 1529/2401*T^32 + 1513/2401*T^31 + 1242/2401*T^30 + 
        1255/2401*T^29 + 1060/2401*T^28 + 1255/2401*T^27 + 1242/2401*T^26 + 
        1513/2401*T^25 + 1529/2401*T^24 + 676/2401*T^23 - 33/343*T^22 - 129/343*T^21
        - 15/49*T^20 - 496/2401*T^19 + 176/2401*T^18 + 536/2401*T^17 + 101/2401*T^16
        - 914/2401*T^15 - 1772/2401*T^14 - 162/343*T^13 - 1082/2401*T^12 - 
        2028/2401*T^11 - 1538/2401*T^10 - 806/2401*T^9 - 327/2401*T^8 + 506/2401*T^7
        - 92/2401*T^6 - 627/2401*T^5 - 340/2401*T^4 + 36/343*T^3 + 30/49*T^2 + 
        10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + X*Y^10 + X*Y^9 + 
        2*X*Y^8 + 4*X*Y^7 + X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 4*X*Y + 
        6*X + 5*Y^30 + Y^29 + 2*Y^27 + 4*Y^26 + 6*Y^24 + 5*Y^23 + 5*Y^21 + 6*Y^20 + 
        3*Y^19 + 4*Y^18 + 3*Y^16 + 6*Y^15 + Y^14 + Y^13 + Y^12 + 6*Y^11 + 3*Y^10 + 
        4*Y^8 + 4*Y^7 + Y^6 + 2*Y^5 + 6*Y^4 + 5*Y^3 + 6*Y^2 + 5*Y + 2,
    -T^56 + 1/7*T^55 + 3/49*T^54 - 190/343*T^53 - 1233/2401*T^52 - 710/2401*T^51 + 
        4/2401*T^50 - 264/2401*T^49 + 1352/2401*T^48 - 607/2401*T^47 + 299/2401*T^46
        + 2216/2401*T^45 + 1444/2401*T^44 + 1324/2401*T^43 + 739/2401*T^42 + 
        52/343*T^41 + 1325/2401*T^40 + 1485/2401*T^39 + 83/2401*T^38 - 237/343*T^37 
        + 4/49*T^36 + 323/2401*T^35 - 1044/2401*T^34 + 39/343*T^33 - 200/343*T^32 - 
        535/2401*T^31 - 732/2401*T^30 + 1025/2401*T^29 - 1025/2401*T^27 + 
        732/2401*T^26 + 535/2401*T^25 + 200/343*T^24 - 39/343*T^23 + 1044/2401*T^22 
        - 323/2401*T^21 - 4/49*T^20 + 237/343*T^19 - 83/2401*T^18 - 1485/2401*T^17 -
        1325/2401*T^16 - 52/343*T^15 - 739/2401*T^14 - 1324/2401*T^13 - 
        1444/2401*T^12 - 2216/2401*T^11 - 299/2401*T^10 + 607/2401*T^9 - 
        1352/2401*T^8 + 264/2401*T^7 - 4/2401*T^6 + 710/2401*T^5 + 1233/2401*T^4 + 
        190/343*T^3 - 3/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + X*Y^3 + 6*X*Y^2 + X*Y + 
        5*X + 6*Y^30 + 4*Y^29 + Y^28 + 6*Y^27 + 5*Y^26 + 4*Y^24 + 3*Y^23 + 4*Y^22 + 
        6*Y^21 + 6*Y^18 + 3*Y^17 + 3*Y^16 + 2*Y^15 + 2*Y^14 + 6*Y^13 + 2*Y^12 + 
        5*Y^11 + 6*Y^9 + 5*Y^8 + 4*Y^7 + 5*Y^6 + 5*Y^5 + 5*Y^3 + 6*Y^2 + 5*Y + 2,
    T^56 + 5/7*T^55 - 45/49*T^54 - 474/343*T^53 - 1467/2401*T^52 + 3456/2401*T^51 + 
        3293/2401*T^50 - 883/2401*T^49 - 2217/2401*T^48 - 2/7*T^47 + 1845/2401*T^46 
        - 54/2401*T^45 - 4078/2401*T^44 - 2197/2401*T^43 + 2155/2401*T^42 + 
        3144/2401*T^41 + 460/2401*T^40 - 3420/2401*T^39 - 857/2401*T^38 + 
        2227/2401*T^37 - 324/2401*T^36 - 2452/2401*T^35 - 1457/2401*T^34 + 
        407/343*T^33 + 495/343*T^32 - 585/2401*T^31 - 2010/2401*T^30 + 215/2401*T^29
        + 302/343*T^28 + 215/2401*T^27 - 2010/2401*T^26 - 585/2401*T^25 + 
        495/343*T^24 + 407/343*T^23 - 1457/2401*T^22 - 2452/2401*T^21 - 
        324/2401*T^20 + 2227/2401*T^19 - 857/2401*T^18 - 3420/2401*T^17 + 
        460/2401*T^16 + 3144/2401*T^15 + 2155/2401*T^14 - 2197/2401*T^13 - 
        4078/2401*T^12 - 54/2401*T^11 + 1845/2401*T^10 - 2/7*T^9 - 2217/2401*T^8 - 
        883/2401*T^7 + 3293/2401*T^6 + 3456/2401*T^5 - 1467/2401*T^4 - 474/343*T^3 -
        45/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 3*X*Y^13 + X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 5*X*Y^8 + 3*X*Y^6 + 
        5*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 2*X*Y + 4*X + Y^30 + 2*Y^27 + 6*Y^26 + 5*Y^25 
        + 6*Y^24 + 6*Y^23 + 6*Y^22 + 6*Y^21 + Y^20 + 3*Y^18 + 4*Y^17 + 2*Y^16 + 
        6*Y^15 + 2*Y^14 + 4*Y^13 + 2*Y^12 + 5*Y^11 + Y^10 + 2*Y^9 + Y^8 + 6*Y^7 + 
        4*Y^6 + 4*Y^5 + 3*Y^4 + 5*Y^3 + Y^2 + 3*Y + 4,
    -T^56 + 10/7*T^55 - 22/49*T^54 + 184/343*T^53 - 725/2401*T^52 - 3387/2401*T^51 +
        5133/2401*T^50 - 4056/2401*T^49 + 2411/2401*T^48 - 827/2401*T^47 - 4/49*T^46
        + 510/343*T^45 - 5056/2401*T^44 + 2782/2401*T^43 - 3093/2401*T^42 + 
        400/343*T^41 + 342/2401*T^40 - 1434/2401*T^39 + 1828/2401*T^38 - 
        516/343*T^37 + 4244/2401*T^36 - 3170/2401*T^35 + 1328/2401*T^34 + 
        20/343*T^33 - 2525/2401*T^32 + 5730/2401*T^31 - 783/343*T^30 + 
        2125/2401*T^29 - 2125/2401*T^27 + 783/343*T^26 - 5730/2401*T^25 + 
        2525/2401*T^24 - 20/343*T^23 - 1328/2401*T^22 + 3170/2401*T^21 - 
        4244/2401*T^20 + 516/343*T^19 - 1828/2401*T^18 + 1434/2401*T^17 - 
        342/2401*T^16 - 400/343*T^15 + 3093/2401*T^14 - 2782/2401*T^13 + 
        5056/2401*T^12 - 510/343*T^11 + 4/49*T^10 + 827/2401*T^9 - 2411/2401*T^8 + 
        4056/2401*T^7 - 5133/2401*T^6 + 3387/2401*T^5 + 725/2401*T^4 - 184/343*T^3 +
        22/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 5*X*Y^11 + 2*X*Y^9 + 2*X*Y^8 + 6*X*Y^7 + 
        4*X*Y^6 + 6*X*Y^5 + 2*X*Y^3 + 3*X*Y^2 + 2*X*Y + 3*X + 3*Y^30 + 4*Y^29 + 
        4*Y^28 + 2*Y^27 + 6*Y^26 + 5*Y^25 + 5*Y^24 + 5*Y^23 + 3*Y^22 + 3*Y^19 + 
        5*Y^18 + 4*Y^17 + 3*Y^16 + Y^15 + 6*Y^14 + Y^13 + 3*Y^11 + 5*Y^10 + 2*Y^9 + 
        6*Y^8 + 4*Y^7 + 4*Y^5 + Y^4 + 3*Y^3 + 4*Y + 5,
    T^56 - 2/7*T^55 - 18/49*T^54 - 15/49*T^53 + 93/2401*T^52 + 715/2401*T^51 + 
        192/2401*T^50 - 10/2401*T^49 - 727/2401*T^48 - 74/343*T^47 - 117/2401*T^46 +
        793/2401*T^45 - 890/2401*T^44 - 276/2401*T^43 - 173/2401*T^42 + 48/2401*T^41
        + 811/2401*T^40 - 1310/2401*T^39 + 1033/2401*T^38 - 776/2401*T^37 + 
        668/2401*T^36 - 933/2401*T^35 + 1312/2401*T^34 + 1114/2401*T^33 - 
        403/2401*T^32 - 927/2401*T^31 - 669/2401*T^30 + 1044/2401*T^29 + 
        192/2401*T^28 + 1044/2401*T^27 - 669/2401*T^26 - 927/2401*T^25 - 
        403/2401*T^24 + 1114/2401*T^23 + 1312/2401*T^22 - 933/2401*T^21 + 
        668/2401*T^20 - 776/2401*T^19 + 1033/2401*T^18 - 1310/2401*T^17 + 
        811/2401*T^16 + 48/2401*T^15 - 173/2401*T^14 - 276/2401*T^13 - 890/2401*T^12
        + 793/2401*T^11 - 117/2401*T^10 - 74/343*T^9 - 727/2401*T^8 - 10/2401*T^7 + 
        192/2401*T^6 + 715/2401*T^5 + 93/2401*T^4 - 15/49*T^3 - 18/49*T^2 - 2/7*T + 
        1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^13 + 3*X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + 4*X*Y^8 + 2*X*Y^6 +
        6*X*Y^5 + 3*X*Y^4 + 6*X*Y^2 + 3*X + 3*Y^30 + 5*Y^29 + Y^28 + 6*Y^27 + 5*Y^26
        + 6*Y^25 + Y^24 + 6*Y^22 + 5*Y^21 + 4*Y^20 + 4*Y^19 + 4*Y^17 + 5*Y^16 + Y^15
        + 6*Y^14 + 2*Y^13 + Y^12 + 3*Y^11 + 3*Y^10 + 2*Y^8 + 2*Y^7 + 5*Y^6 + Y^5 + 
        2*Y^2 + 5,
    -T^56 + 2*T^55 - 18/7*T^54 + 116/49*T^53 - 3845/2401*T^52 + 110/343*T^51 + 
        358/343*T^50 - 5337/2401*T^49 + 7773/2401*T^48 - 1107/343*T^47 + 
        7006/2401*T^46 - 4311/2401*T^45 + 881/2401*T^44 + 1609/2401*T^43 - 
        3415/2401*T^42 + 4570/2401*T^41 - 5165/2401*T^40 + 5609/2401*T^39 - 
        5840/2401*T^38 + 5370/2401*T^37 - 4240/2401*T^36 + 2137/2401*T^35 + 
        916/2401*T^34 - 3684/2401*T^33 + 6557/2401*T^32 - 8145/2401*T^31 + 
        7523/2401*T^30 - 4752/2401*T^29 + 4752/2401*T^27 - 7523/2401*T^26 + 
        8145/2401*T^25 - 6557/2401*T^24 + 3684/2401*T^23 - 916/2401*T^22 - 
        2137/2401*T^21 + 4240/2401*T^20 - 5370/2401*T^19 + 5840/2401*T^18 - 
        5609/2401*T^17 + 5165/2401*T^16 - 4570/2401*T^15 + 3415/2401*T^14 - 
        1609/2401*T^13 - 881/2401*T^12 + 4311/2401*T^11 - 7006/2401*T^10 + 
        1107/343*T^9 - 7773/2401*T^8 + 5337/2401*T^7 - 358/343*T^6 - 110/343*T^5 + 
        3845/2401*T^4 - 116/49*T^3 + 18/7*T^2 - 2*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 
        + 4*X*Y^7 + 3*X*Y^6 + X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 6*X*Y + X + Y^30
        + 2*Y^29 + 6*Y^28 + 4*Y^27 + 5*Y^25 + 4*Y^24 + Y^23 + 5*Y^22 + Y^21 + Y^20 +
        2*Y^19 + 4*Y^17 + 4*Y^16 + 3*Y^15 + 5*Y^14 + 2*Y^13 + 2*Y^12 + 3*Y^11 + Y^10
        + 6*Y^9 + 3*Y^8 + Y^7 + 6*Y^6 + 6*Y^5 + 5*Y^4 + 5*Y^3 + 2*Y^2 + 5*Y + 4,
    T^56 - 8/7*T^55 - 52/49*T^54 + 629/343*T^53 - 218/2401*T^52 - 1818/2401*T^51 - 
        342/2401*T^50 + 338/2401*T^49 + 1144/2401*T^48 - 1686/2401*T^47 + 
        1812/2401*T^46 + 846/2401*T^45 - 3694/2401*T^44 + 2179/2401*T^43 - 
        302/2401*T^42 - 221/2401*T^41 + 1665/2401*T^40 - 1863/2401*T^39 - 
        73/2401*T^38 - 626/2401*T^37 + 2284/2401*T^36 + 2164/2401*T^35 - 
        4054/2401*T^34 - 1247/2401*T^33 + 2400/2401*T^32 + 1206/2401*T^31 - 
        1006/2401*T^30 - 1030/2401*T^29 + 1264/2401*T^28 - 1030/2401*T^27 - 
        1006/2401*T^26 + 1206/2401*T^25 + 2400/2401*T^24 - 1247/2401*T^23 - 
        4054/2401*T^22 + 2164/2401*T^21 + 2284/2401*T^20 - 626/2401*T^19 - 
        73/2401*T^18 - 1863/2401*T^17 + 1665/2401*T^16 - 221/2401*T^15 - 
        302/2401*T^14 + 2179/2401*T^13 - 3694/2401*T^12 + 846/2401*T^11 + 
        1812/2401*T^10 - 1686/2401*T^9 + 1144/2401*T^8 + 338/2401*T^7 - 342/2401*T^6
        - 1818/2401*T^5 - 218/2401*T^4 + 629/343*T^3 - 52/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 6*X*Y^9 + 5*X*Y^8 +
        3*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 5*X*Y^3 + 2*X*Y^2 + 5*X + 5*Y^30 + Y^29 + Y^24
        + Y^22 + 5*Y^21 + 4*Y^20 + 4*Y^19 + 5*Y^18 + 2*Y^17 + 5*Y^16 + Y^15 + Y^14 +
        4*Y^13 + 3*Y^12 + Y^11 + 5*Y^10 + 4*Y^9 + Y^8 + 5*Y^7 + 3*Y^6 + 6*Y^4 + 
        4*Y^3 + 4*Y^2 + 6*Y + 4,
    T^56 - 15/7*T^55 + 51/49*T^54 - 107/343*T^53 + 3364/2401*T^52 + 1354/2401*T^51 -
        7447/2401*T^50 + 1837/2401*T^49 + 815/2401*T^48 + 3956/2401*T^47 + 
        1024/2401*T^46 - 7003/2401*T^45 + 1034/2401*T^44 + 2028/2401*T^43 + 
        2459/2401*T^42 - 1420/2401*T^41 - 3947/2401*T^40 + 2493/2401*T^39 + 
        2278/2401*T^38 + 866/2401*T^37 - 4119/2401*T^36 - 292/343*T^35 + 
        3380/2401*T^34 + 2413/2401*T^33 + 703/2401*T^32 - 3359/2401*T^31 - 
        4168/2401*T^30 + 599/343*T^29 + 689/2401*T^28 + 599/343*T^27 - 
        4168/2401*T^26 - 3359/2401*T^25 + 703/2401*T^24 + 2413/2401*T^23 + 
        3380/2401*T^22 - 292/343*T^21 - 4119/2401*T^20 + 866/2401*T^19 + 
        2278/2401*T^18 + 2493/2401*T^17 - 3947/2401*T^16 - 1420/2401*T^15 + 
        2459/2401*T^14 + 2028/2401*T^13 + 1034/2401*T^12 - 7003/2401*T^11 + 
        1024/2401*T^10 + 3956/2401*T^9 + 815/2401*T^8 + 1837/2401*T^7 - 
        7447/2401*T^6 + 1354/2401*T^5 + 3364/2401*T^4 - 107/343*T^3 + 51/49*T^2 - 
        15/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 
        4*X*Y^8 + 3*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 4*X*Y + 5*Y^30 +
        4*Y^29 + 2*Y^28 + Y^27 + 5*Y^26 + 6*Y^24 + 3*Y^23 + 4*Y^22 + 2*Y^21 + 2*Y^20
        + 3*Y^19 + 4*Y^18 + 6*Y^17 + 2*Y^16 + 3*Y^15 + 2*Y^14 + 3*Y^13 + 4*Y^12 + 
        5*Y^11 + 2*Y^10 + 5*Y^9 + 5*Y^7 + 4*Y^6 + Y^5 + 6*Y^4 + 6*Y^3 + 6*Y + 2,
    -T^56 - 9/7*T^55 - 22/49*T^54 + 1/7*T^53 - 321/2401*T^52 - 1531/2401*T^51 - 
        1696/2401*T^50 - 1186/2401*T^49 - 706/2401*T^48 + 715/2401*T^47 + 
        2572/2401*T^46 + 1317/2401*T^45 - 438/2401*T^44 - 1217/2401*T^43 - 
        738/2401*T^42 + 197/2401*T^41 + 120/2401*T^40 - 5/343*T^39 + 341/2401*T^38 -
        528/2401*T^37 - 1187/2401*T^36 - 720/2401*T^35 + 782/2401*T^34 + 
        1824/2401*T^33 + 213/343*T^32 + 545/2401*T^31 - 61/2401*T^30 - 573/2401*T^29
        + 573/2401*T^27 + 61/2401*T^26 - 545/2401*T^25 - 213/343*T^24 - 
        1824/2401*T^23 - 782/2401*T^22 + 720/2401*T^21 + 1187/2401*T^20 + 
        528/2401*T^19 - 341/2401*T^18 + 5/343*T^17 - 120/2401*T^16 - 197/2401*T^15 +
        738/2401*T^14 + 1217/2401*T^13 + 438/2401*T^12 - 1317/2401*T^11 - 
        2572/2401*T^10 - 715/2401*T^9 + 706/2401*T^8 + 1186/2401*T^7 + 1696/2401*T^6
        + 1531/2401*T^5 + 321/2401*T^4 - 1/7*T^3 + 22/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + X*Y^12 + 2*X*Y^11 + X*Y^9 + 4*X*Y^8 + 
        2*X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 6*X*Y + 3*X + Y^30
        + 4*Y^29 + 2*Y^27 + Y^26 + 3*Y^25 + 4*Y^24 + 4*Y^23 + 4*Y^22 + 5*Y^21 + 
        5*Y^20 + Y^19 + 3*Y^18 + 2*Y^17 + 5*Y^16 + 5*Y^15 + 5*Y^11 + Y^10 + 4*Y^9 + 
        6*Y^8 + 5*Y^6 + 2*Y^5 + 5*Y^4 + Y^3 + 4*Y^2 + 2*Y + 3,
    T^56 - 1/7*T^55 + 58/49*T^54 + 211/343*T^53 + 2559/2401*T^52 + 1921/2401*T^51 + 
        2223/2401*T^50 + 2645/2401*T^49 + 1620/2401*T^48 + 1458/2401*T^47 + 
        1394/2401*T^46 + 4/343*T^45 + 1105/2401*T^44 - 1291/2401*T^43 + 
        747/2401*T^42 - 920/2401*T^41 - 542/2401*T^40 - 117/2401*T^39 - 
        649/2401*T^38 + 705/2401*T^37 - 1217/2401*T^36 + 682/2401*T^35 - 
        964/2401*T^34 + 471/2401*T^33 - 275/343*T^32 - 2/2401*T^31 - 270/343*T^30 - 
        153/343*T^29 - 2358/2401*T^28 - 153/343*T^27 - 270/343*T^26 - 2/2401*T^25 - 
        275/343*T^24 + 471/2401*T^23 - 964/2401*T^22 + 682/2401*T^21 - 
        1217/2401*T^20 + 705/2401*T^19 - 649/2401*T^18 - 117/2401*T^17 - 
        542/2401*T^16 - 920/2401*T^15 + 747/2401*T^14 - 1291/2401*T^13 + 
        1105/2401*T^12 + 4/343*T^11 + 1394/2401*T^10 + 1458/2401*T^9 + 1620/2401*T^8
        + 2645/2401*T^7 + 2223/2401*T^6 + 1921/2401*T^5 + 2559/2401*T^4 + 
        211/343*T^3 + 58/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 +
        X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + X*Y^3 + 2*X*Y + 3*Y^30 + 6*Y^29 + 
        2*Y^28 + 5*Y^27 + 3*Y^26 + 5*Y^25 + 6*Y^24 + Y^23 + 3*Y^22 + 3*Y^21 + Y^19 +
        3*Y^17 + Y^16 + 4*Y^14 + 6*Y^13 + 5*Y^12 + 5*Y^11 + 6*Y^9 + 2*Y^8 + 5*Y^7 + 
        4*Y^6 + 5*Y^5 + 2*Y^4 + 2*Y^3 + Y^2 + Y + 5,
    T^56 - 10/7*T^55 - 3/7*T^54 + 213/343*T^53 + 253/2401*T^52 + 3768/2401*T^51 - 
        3716/2401*T^50 - 958/2401*T^49 + 1676/2401*T^48 - 1154/2401*T^47 + 
        436/2401*T^46 - 533/2401*T^45 + 1921/2401*T^44 - 667/2401*T^43 + 
        556/2401*T^42 - 1395/2401*T^41 - 1118/2401*T^40 + 421/343*T^39 - 
        3594/2401*T^38 + 475/343*T^37 + 792/2401*T^36 - 4149/2401*T^35 + 
        2193/2401*T^34 - 268/2401*T^33 + 1594/2401*T^32 - 46/2401*T^31 - 
        3826/2401*T^30 + 1069/2401*T^29 + 2923/2401*T^28 + 1069/2401*T^27 - 
        3826/2401*T^26 - 46/2401*T^25 + 1594/2401*T^24 - 268/2401*T^23 + 
        2193/2401*T^22 - 4149/2401*T^21 + 792/2401*T^20 + 475/343*T^19 - 
        3594/2401*T^18 + 421/343*T^17 - 1118/2401*T^16 - 1395/2401*T^15 + 
        556/2401*T^14 - 667/2401*T^13 + 1921/2401*T^12 - 533/2401*T^11 + 
        436/2401*T^10 - 1154/2401*T^9 + 1676/2401*T^8 - 958/2401*T^7 - 3716/2401*T^6
        + 3768/2401*T^5 + 253/2401*T^4 + 213/343*T^3 - 3/7*T^2 - 10/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 
        5*X*Y^8 + X*Y^7 + X*Y^6 + 5*X*Y^5 + 4*X*Y^3 + 4*X*Y^2 + X*Y + 6*X + 3*Y^30 +
        4*Y^29 + 2*Y^28 + Y^27 + 6*Y^26 + 4*Y^25 + 2*Y^24 + 2*Y^23 + 2*Y^22 + 6*Y^21
        + 3*Y^20 + 6*Y^19 + Y^18 + Y^17 + 3*Y^16 + Y^15 + 6*Y^14 + 6*Y^13 + 3*Y^11 +
        4*Y^9 + 2*Y^7 + 5*Y^6 + 4*Y^4 + 6*Y^3 + 5*Y^2 + 5*Y + 3,
    T^56 - 3/7*T^55 - 32/49*T^54 + 8/343*T^53 + 484/2401*T^52 + 116/343*T^51 - 
        209/2401*T^50 + 407/2401*T^49 - 474/2401*T^48 - 412/2401*T^47 - 
        818/2401*T^46 + 698/2401*T^45 - 117/343*T^44 - 8/2401*T^43 + 53/343*T^42 - 
        640/2401*T^41 - 746/2401*T^40 + 915/2401*T^39 - 860/2401*T^38 - 103/343*T^37
        + 981/2401*T^36 + 628/2401*T^35 + 669/2401*T^34 - 1382/2401*T^33 + 
        173/2401*T^32 + 27/343*T^31 - 250/2401*T^30 + 61/343*T^29 + 1571/2401*T^28 +
        61/343*T^27 - 250/2401*T^26 + 27/343*T^25 + 173/2401*T^24 - 1382/2401*T^23 +
        669/2401*T^22 + 628/2401*T^21 + 981/2401*T^20 - 103/343*T^19 - 860/2401*T^18
        + 915/2401*T^17 - 746/2401*T^16 - 640/2401*T^15 + 53/343*T^14 - 8/2401*T^13 
        - 117/343*T^12 + 698/2401*T^11 - 818/2401*T^10 - 412/2401*T^9 - 474/2401*T^8
        + 407/2401*T^7 - 209/2401*T^6 + 116/343*T^5 + 484/2401*T^4 + 8/343*T^3 - 
        32/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        6*X*Y^8 + 3*X*Y^7 + 3*X*Y^6 + 4*X*Y^5 + 3*X*Y^3 + X*Y^2 + 5*X*Y + 3*X + 
        2*Y^30 + 3*Y^29 + 6*Y^28 + 6*Y^27 + 5*Y^26 + 3*Y^24 + 5*Y^23 + 3*Y^21 + Y^20
        + 4*Y^19 + 4*Y^18 + 2*Y^17 + 5*Y^16 + 4*Y^15 + Y^14 + 6*Y^13 + 4*Y^12 + 
        4*Y^11 + 6*Y^10 + 2*Y^9 + 6*Y^8 + 3*Y^7 + 3*Y^6 + 4*Y^5 + 6*Y^4 + Y^3 + 
        6*Y^2 + 3*Y + 3,
    T^56 + T^55 + 10/49*T^54 + 22/343*T^53 + 110/343*T^52 + 1804/2401*T^51 + 
        107/2401*T^50 - 81/2401*T^49 + 1076/2401*T^48 + 587/2401*T^47 + 
        353/2401*T^46 + 780/2401*T^45 + 268/343*T^44 + 1252/2401*T^43 + 183/343*T^42
        + 1951/2401*T^41 + 436/2401*T^40 - 11/343*T^39 + 835/2401*T^38 + 
        2629/2401*T^37 + 703/2401*T^36 - 1479/2401*T^35 + 284/2401*T^34 + 
        487/2401*T^33 + 101/2401*T^32 + 114/2401*T^31 + 1167/2401*T^30 + 
        1238/2401*T^29 - 191/2401*T^28 + 1238/2401*T^27 + 1167/2401*T^26 + 
        114/2401*T^25 + 101/2401*T^24 + 487/2401*T^23 + 284/2401*T^22 - 
        1479/2401*T^21 + 703/2401*T^20 + 2629/2401*T^19 + 835/2401*T^18 - 
        11/343*T^17 + 436/2401*T^16 + 1951/2401*T^15 + 183/343*T^14 + 1252/2401*T^13
        + 268/343*T^12 + 780/2401*T^11 + 353/2401*T^10 + 587/2401*T^9 + 
        1076/2401*T^8 - 81/2401*T^7 + 107/2401*T^6 + 1804/2401*T^5 + 110/343*T^4 + 
        22/343*T^3 + 10/49*T^2 + T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + X*Y^10 + 5*X*Y^9 + 
        5*X*Y^8 + 6*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 5*X*Y + 3*Y^30 +
        4*Y^29 + 4*Y^28 + 5*Y^27 + Y^26 + Y^25 + 5*Y^23 + 5*Y^22 + 4*Y^21 + 5*Y^19 +
        4*Y^18 + 6*Y^15 + 4*Y^14 + 6*Y^13 + Y^12 + 3*Y^11 + 5*Y^9 + Y^6 + 5*Y^5 + 
        6*Y^4 + Y^3 + 6*Y + 4,
    -T^56 - 3/7*T^55 + 26/49*T^54 + 19/343*T^53 - 102/343*T^52 + 1915/2401*T^51 - 
        571/2401*T^50 - 206/343*T^49 - 706/2401*T^48 - 1909/2401*T^47 - 17/49*T^46 +
        1469/2401*T^45 - 1264/2401*T^44 + 47/343*T^43 + 2180/2401*T^42 - 
        2211/2401*T^41 - 2383/2401*T^40 + 67/343*T^39 - 1118/2401*T^38 + 
        207/2401*T^37 + 1578/2401*T^36 - 1859/2401*T^35 + 291/2401*T^34 + 
        1289/2401*T^33 - 2133/2401*T^32 - 325/2401*T^31 + 1549/2401*T^30 - 
        2383/2401*T^29 + 2383/2401*T^27 - 1549/2401*T^26 + 325/2401*T^25 + 
        2133/2401*T^24 - 1289/2401*T^23 - 291/2401*T^22 + 1859/2401*T^21 - 
        1578/2401*T^20 - 207/2401*T^19 + 1118/2401*T^18 - 67/343*T^17 + 
        2383/2401*T^16 + 2211/2401*T^15 - 2180/2401*T^14 - 47/343*T^13 + 
        1264/2401*T^12 - 1469/2401*T^11 + 17/49*T^10 + 1909/2401*T^9 + 706/2401*T^8 
        + 206/343*T^7 + 571/2401*T^6 - 1915/2401*T^5 + 102/343*T^4 - 19/343*T^3 - 
        26/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + 6*X*Y^8 
        + 2*X*Y^7 + 5*X*Y^4 + 4*X*Y^3 + X*Y^2 + 5*X + 4*Y^30 + 6*Y^29 + 2*Y^27 + 
        4*Y^26 + 4*Y^25 + 2*Y^24 + 2*Y^23 + 5*Y^22 + 6*Y^21 + 4*Y^20 + 3*Y^19 + 
        2*Y^18 + Y^17 + 5*Y^16 + Y^15 + 5*Y^13 + 6*Y^12 + 4*Y^10 + 3*Y^9 + 2*Y^8 + 
        2*Y^7 + 5*Y^6 + 6*Y^5 + Y^4 + 6*Y^3 + Y^2 + 2*Y + 3,
    -T^56 - 18/7*T^55 - 157/49*T^54 - 782/343*T^53 + 620/2401*T^52 + 5853/2401*T^51 
        + 7548/2401*T^50 + 7209/2401*T^49 + 4561/2401*T^48 + 204/2401*T^47 - 
        4600/2401*T^46 - 8733/2401*T^45 - 9565/2401*T^44 - 6609/2401*T^43 - 
        1919/2401*T^42 + 352/343*T^41 + 4640/2401*T^40 + 3820/2401*T^39 + 
        2357/2401*T^38 + 2291/2401*T^37 + 3688/2401*T^36 + 4561/2401*T^35 + 
        1976/2401*T^34 - 4005/2401*T^33 - 9587/2401*T^32 - 10981/2401*T^31 - 
        8185/2401*T^30 - 3686/2401*T^29 + 3686/2401*T^27 + 8185/2401*T^26 + 
        10981/2401*T^25 + 9587/2401*T^24 + 4005/2401*T^23 - 1976/2401*T^22 - 
        4561/2401*T^21 - 3688/2401*T^20 - 2291/2401*T^19 - 2357/2401*T^18 - 
        3820/2401*T^17 - 4640/2401*T^16 - 352/343*T^15 + 1919/2401*T^14 + 
        6609/2401*T^13 + 9565/2401*T^12 + 8733/2401*T^11 + 4600/2401*T^10 - 
        204/2401*T^9 - 4561/2401*T^8 - 7209/2401*T^7 - 7548/2401*T^6 - 5853/2401*T^5
        - 620/2401*T^4 + 782/343*T^3 + 157/49*T^2 + 18/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 6*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 3*X*Y^7 +
        X*Y^6 + 6*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 2*X*Y + 5*X + 2*Y^30 + 6*Y^29 + 3*Y^28
        + 4*Y^27 + 6*Y^26 + Y^24 + 5*Y^23 + Y^22 + 4*Y^21 + 4*Y^20 + 6*Y^19 + 4*Y^18
        + 3*Y^17 + 6*Y^16 + 5*Y^15 + 5*Y^14 + 5*Y^13 + Y^12 + 4*Y^11 + Y^10 + Y^9 + 
        2*Y^8 + 4*Y^7 + 6*Y^5 + Y^4 + 2*Y^3 + 5*Y + 2,
    -T^56 + 4/7*T^55 - 1/7*T^54 + 151/343*T^53 - 75/2401*T^52 - 1/7*T^51 + 
        1009/2401*T^50 - 1923/2401*T^49 + 225/343*T^48 - 1035/2401*T^47 + 
        566/2401*T^46 + 461/2401*T^45 - 362/2401*T^44 + 1213/2401*T^43 - 
        831/2401*T^42 + 598/2401*T^41 + 72/2401*T^40 - 638/2401*T^39 + 171/2401*T^38
        - 335/2401*T^37 - 51/2401*T^36 - 265/2401*T^35 + 219/2401*T^34 + 
        589/2401*T^33 + 274/2401*T^32 + 40/2401*T^31 - 387/2401*T^30 - 
        1083/2401*T^29 + 1083/2401*T^27 + 387/2401*T^26 - 40/2401*T^25 - 
        274/2401*T^24 - 589/2401*T^23 - 219/2401*T^22 + 265/2401*T^21 + 51/2401*T^20
        + 335/2401*T^19 - 171/2401*T^18 + 638/2401*T^17 - 72/2401*T^16 - 
        598/2401*T^15 + 831/2401*T^14 - 1213/2401*T^13 + 362/2401*T^12 - 
        461/2401*T^11 - 566/2401*T^10 + 1035/2401*T^9 - 225/343*T^8 + 1923/2401*T^7 
        - 1009/2401*T^6 + 1/7*T^5 + 75/2401*T^4 - 151/343*T^3 + 1/7*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 +
        4*X*Y^7 + 3*X*Y^6 + X*Y^5 + 2*X*Y^4 + 4*X*Y^2 + 3*X*Y + 3*Y^30 + 2*Y^29 + 
        Y^27 + Y^25 + 6*Y^24 + 2*Y^23 + Y^22 + 6*Y^21 + 4*Y^20 + 2*Y^19 + 4*Y^16 + 
        3*Y^14 + 6*Y^13 + Y^11 + 3*Y^10 + 3*Y^9 + 2*Y^7 + 5*Y^6 + 2*Y^5 + 4*Y^4 + 
        2*Y^2 + 4*Y + 1,
    -T^56 + 5/7*T^55 + 6/7*T^54 - 130/343*T^53 - 80/2401*T^52 - 904/2401*T^51 - 
        667/2401*T^50 + 59/49*T^49 + 326/2401*T^48 - 269/343*T^47 - 142/343*T^46 - 
        1153/2401*T^45 + 1725/2401*T^44 + 2651/2401*T^43 - 429/2401*T^42 - 
        2872/2401*T^41 - 200/343*T^40 + 376/2401*T^39 + 277/343*T^38 + 
        1985/2401*T^37 - 755/2401*T^36 - 2791/2401*T^35 - 867/2401*T^34 + 
        2577/2401*T^33 + 2396/2401*T^32 - 138/2401*T^31 - 2180/2401*T^30 - 
        2278/2401*T^29 + 2278/2401*T^27 + 2180/2401*T^26 + 138/2401*T^25 - 
        2396/2401*T^24 - 2577/2401*T^23 + 867/2401*T^22 + 2791/2401*T^21 + 
        755/2401*T^20 - 1985/2401*T^19 - 277/343*T^18 - 376/2401*T^17 + 200/343*T^16
        + 2872/2401*T^15 + 429/2401*T^14 - 2651/2401*T^13 - 1725/2401*T^12 + 
        1153/2401*T^11 + 142/343*T^10 + 269/343*T^9 - 326/2401*T^8 - 59/49*T^7 + 
        667/2401*T^6 + 904/2401*T^5 + 80/2401*T^4 + 130/343*T^3 - 6/7*T^2 - 5/7*T + 
        1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 4*X*Y^9 + X*Y^8 + 
        3*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + X*Y^3 + 3*X*Y^2 + 3*X*Y + X + 4*Y^30
        + 2*Y^29 + 5*Y^27 + 4*Y^26 + Y^25 + 5*Y^24 + 4*Y^23 + 3*Y^22 + 2*Y^20 + Y^19
        + Y^18 + 4*Y^15 + Y^14 + 6*Y^13 + Y^12 + 4*Y^11 + 6*Y^8 + 2*Y^7 + 5*Y^6 + 
        6*Y^5 + 4*Y^4 + 3*Y^3 + 4*Y + 3,
    -T^56 - 6/7*T^55 - 64/49*T^54 - 128/343*T^53 - 2571/2401*T^52 - 1399/2401*T^51 -
        23/343*T^50 + 781/2401*T^49 + 185/343*T^48 - 1371/2401*T^47 + 37/49*T^46 - 
        96/2401*T^45 + 3109/2401*T^44 - 1145/2401*T^43 + 1616/2401*T^42 + 
        613/2401*T^41 + 2328/2401*T^40 + 899/2401*T^39 - 1136/2401*T^38 + 
        934/2401*T^37 - 951/2401*T^36 + 1102/2401*T^35 - 3631/2401*T^34 + 
        89/2401*T^33 - 2070/2401*T^32 + 1019/2401*T^31 - 1776/2401*T^30 - 
        460/2401*T^29 + 460/2401*T^27 + 1776/2401*T^26 - 1019/2401*T^25 + 
        2070/2401*T^24 - 89/2401*T^23 + 3631/2401*T^22 - 1102/2401*T^21 + 
        951/2401*T^20 - 934/2401*T^19 + 1136/2401*T^18 - 899/2401*T^17 - 
        2328/2401*T^16 - 613/2401*T^15 - 1616/2401*T^14 + 1145/2401*T^13 - 
        3109/2401*T^12 + 96/2401*T^11 - 37/49*T^10 + 1371/2401*T^9 - 185/343*T^8 - 
        781/2401*T^7 + 23/343*T^6 + 1399/2401*T^5 + 2571/2401*T^4 + 128/343*T^3 + 
        64/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + X*Y^13 + X*Y^12 + 3*X*Y^11 + 2*X*Y^9 + X*Y^8 + 
        3*X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 2*X*Y + 3*X + 
        5*Y^30 + Y^29 + Y^28 + 5*Y^27 + 4*Y^26 + Y^25 + 5*Y^24 + 4*Y^23 + 2*Y^22 + 
        2*Y^21 + 2*Y^20 + Y^19 + Y^17 + 2*Y^16 + 2*Y^15 + 6*Y^14 + 4*Y^13 + 6*Y^12 +
        3*Y^11 + 6*Y^10 + 3*Y^8 + 3*Y^7 + 4*Y^5 + 4*Y^4 + 3*Y^3 + 4*Y^2 + Y + 4,
    -T^56 - 2/7*T^55 + 81/49*T^54 + 209/343*T^53 - 410/343*T^52 - 2033/2401*T^51 + 
        1061/2401*T^50 + 2116/2401*T^49 + 47/343*T^48 - 1914/2401*T^47 - 
        1191/2401*T^46 + 2382/2401*T^45 + 1985/2401*T^44 - 3454/2401*T^43 - 
        3309/2401*T^42 + 2487/2401*T^41 + 3184/2401*T^40 - 640/2401*T^39 - 
        1905/2401*T^38 - 319/2401*T^37 + 718/2401*T^36 + 590/2401*T^35 + 
        129/2401*T^34 - 1075/2401*T^33 - 388/2401*T^32 + 1208/2401*T^31 + 
        25/2401*T^30 - 1138/2401*T^29 + 1138/2401*T^27 - 25/2401*T^26 - 
        1208/2401*T^25 + 388/2401*T^24 + 1075/2401*T^23 - 129/2401*T^22 - 
        590/2401*T^21 - 718/2401*T^20 + 319/2401*T^19 + 1905/2401*T^18 + 
        640/2401*T^17 - 3184/2401*T^16 - 2487/2401*T^15 + 3309/2401*T^14 + 
        3454/2401*T^13 - 1985/2401*T^12 - 2382/2401*T^11 + 1191/2401*T^10 + 
        1914/2401*T^9 - 47/343*T^8 - 2116/2401*T^7 - 1061/2401*T^6 + 2033/2401*T^5 +
        410/343*T^4 - 209/343*T^3 - 81/49*T^2 + 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 6*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + X*Y^9 + 5*X*Y^8 + 
        3*X*Y^7 + 3*X*Y^5 + 6*X*Y^3 + 2*X*Y^2 + 2*X*Y + 2*X + 4*Y^30 + 4*Y^29 + Y^28
        + Y^27 + Y^26 + 3*Y^25 + 4*Y^24 + 6*Y^23 + 5*Y^22 + 3*Y^21 + 2*Y^20 + 2*Y^19
        + Y^18 + 4*Y^17 + 3*Y^16 + Y^15 + 2*Y^14 + 6*Y^13 + 5*Y^12 + Y^11 + 4*Y^10 +
        4*Y^9 + 3*Y^7 + 3*Y^6 + 2*Y^5 + 3*Y^3 + 6*Y^2 + 2*Y,
    -T^56 - 10/7*T^55 - 10/49*T^54 + 38/49*T^53 + 2899/2401*T^52 - 131/2401*T^51 - 
        4065/2401*T^50 - 3436/2401*T^49 + 144/2401*T^48 + 3779/2401*T^47 + 
        414/343*T^46 - 816/2401*T^45 - 2689/2401*T^44 - 25/49*T^43 + 2705/2401*T^42 
        + 4054/2401*T^41 + 177/343*T^40 - 1747/2401*T^39 - 2133/2401*T^38 + 
        459/2401*T^37 + 3828/2401*T^36 + 3257/2401*T^35 + 411/2401*T^34 - 
        1095/2401*T^33 - 150/343*T^32 + 783/2401*T^31 + 1996/2401*T^30 + 
        272/343*T^29 - 272/343*T^27 - 1996/2401*T^26 - 783/2401*T^25 + 150/343*T^24 
        + 1095/2401*T^23 - 411/2401*T^22 - 3257/2401*T^21 - 3828/2401*T^20 - 
        459/2401*T^19 + 2133/2401*T^18 + 1747/2401*T^17 - 177/343*T^16 - 
        4054/2401*T^15 - 2705/2401*T^14 + 25/49*T^13 + 2689/2401*T^12 + 
        816/2401*T^11 - 414/343*T^10 - 3779/2401*T^9 - 144/2401*T^8 + 3436/2401*T^7 
        + 4065/2401*T^6 + 131/2401*T^5 - 2899/2401*T^4 - 38/49*T^3 + 10/49*T^2 + 
        10/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 6*X*Y^12 + X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 4*X*Y^8 + 
        X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + 2*X*Y^3 + 4*X*Y^2 + 4*X + Y^30 + 4*Y^29 + 4*Y^28
        + 6*Y^27 + 5*Y^26 + 2*Y^25 + 2*Y^24 + 3*Y^23 + 4*Y^22 + 3*Y^21 + 5*Y^20 + 
        5*Y^19 + Y^18 + 5*Y^17 + 2*Y^16 + 6*Y^15 + 4*Y^14 + Y^13 + 4*Y^12 + 4*Y^11 +
        3*Y^10 + Y^8 + 2*Y^7 + 4*Y^6 + 3*Y^5 + 6*Y^4 + 2*Y^3 + 2*Y^2 + 4*Y + 3,
    T^56 - 5/7*T^55 - 40/49*T^54 + 192/343*T^53 + 820/2401*T^52 - 391/2401*T^51 - 
        1200/2401*T^50 + 501/2401*T^49 + 554/2401*T^48 + 209/2401*T^47 - 
        1431/2401*T^46 - 590/2401*T^45 + 2326/2401*T^44 + 218/2401*T^43 - 
        477/2401*T^42 - 288/343*T^41 + 627/2401*T^40 + 2608/2401*T^39 - 
        1593/2401*T^38 - 953/2401*T^37 + 12/49*T^36 + 606/2401*T^35 + 90/343*T^34 - 
        911/2401*T^33 - 20/49*T^32 + 1093/2401*T^31 + 1235/2401*T^30 - 706/2401*T^29
        - 1350/2401*T^28 - 706/2401*T^27 + 1235/2401*T^26 + 1093/2401*T^25 - 
        20/49*T^24 - 911/2401*T^23 + 90/343*T^22 + 606/2401*T^21 + 12/49*T^20 - 
        953/2401*T^19 - 1593/2401*T^18 + 2608/2401*T^17 + 627/2401*T^16 - 
        288/343*T^15 - 477/2401*T^14 + 218/2401*T^13 + 2326/2401*T^12 - 
        590/2401*T^11 - 1431/2401*T^10 + 209/2401*T^9 + 554/2401*T^8 + 501/2401*T^7 
        - 1200/2401*T^6 - 391/2401*T^5 + 820/2401*T^4 + 192/343*T^3 - 40/49*T^2 - 
        5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 
        + 4*X*Y^8 + 6*X*Y^6 + 6*X*Y^4 + X*Y^2 + 3*X*Y + 6*X + 2*Y^30 + Y^28 + 2*Y^27
        + 4*Y^26 + 3*Y^25 + 5*Y^24 + 4*Y^23 + 5*Y^22 + 5*Y^21 + 2*Y^20 + 3*Y^19 + 
        6*Y^18 + 6*Y^17 + 6*Y^16 + Y^15 + 2*Y^14 + 6*Y^13 + Y^12 + 5*Y^10 + 6*Y^9 + 
        4*Y^8 + 3*Y^6 + 3*Y^5 + 2*Y^3 + 6*Y^2 + 2,
    -T^56 - 4/7*T^55 + 64/49*T^54 + 295/343*T^53 - 346/343*T^52 + 44/2401*T^51 + 
        283/343*T^50 - 2055/2401*T^49 - 2813/2401*T^48 + 2862/2401*T^47 + 
        1633/2401*T^46 - 1737/2401*T^45 + 753/2401*T^44 + 1952/2401*T^43 - 
        306/343*T^42 - 1916/2401*T^41 + 1586/2401*T^40 + 1285/2401*T^39 - 
        755/2401*T^38 + 1623/2401*T^37 + 1436/2401*T^36 - 1782/2401*T^35 - 
        1408/2401*T^34 + 1118/2401*T^33 + 393/2401*T^32 - 677/2401*T^31 + 
        213/2401*T^30 + 950/2401*T^29 - 950/2401*T^27 - 213/2401*T^26 + 
        677/2401*T^25 - 393/2401*T^24 - 1118/2401*T^23 + 1408/2401*T^22 + 
        1782/2401*T^21 - 1436/2401*T^20 - 1623/2401*T^19 + 755/2401*T^18 - 
        1285/2401*T^17 - 1586/2401*T^16 + 1916/2401*T^15 + 306/343*T^14 - 
        1952/2401*T^13 - 753/2401*T^12 + 1737/2401*T^11 - 1633/2401*T^10 - 
        2862/2401*T^9 + 2813/2401*T^8 + 2055/2401*T^7 - 283/343*T^6 - 44/2401*T^5 + 
        346/343*T^4 - 295/343*T^3 - 64/49*T^2 + 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 6*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 
        6*X*Y^7 + 5*X*Y^6 + 6*X*Y^4 + X*Y^3 + 5*X*Y^2 + 5*X*Y + X + 5*Y^30 + 6*Y^29 
        + 3*Y^27 + 3*Y^26 + Y^25 + 3*Y^24 + 2*Y^23 + 2*Y^22 + 6*Y^21 + 2*Y^20 + 
        2*Y^19 + 4*Y^18 + 3*Y^17 + 3*Y^16 + 2*Y^14 + 3*Y^13 + 5*Y^12 + 5*Y^11 + 
        3*Y^9 + 6*Y^8 + 4*Y^7 + 6*Y^6 + Y^5 + 5*Y^4 + 6*Y^3 + 6*Y^2 + 3*Y + 1,
    -T^56 - 9/7*T^55 - 17/49*T^54 - 61/343*T^53 + 1153/2401*T^52 + 89/343*T^51 - 
        1658/2401*T^50 - 313/2401*T^49 - 248/2401*T^48 + 1296/2401*T^47 + 
        4710/2401*T^46 + 3230/2401*T^45 + 2503/2401*T^44 + 1210/2401*T^43 - 
        1318/2401*T^42 + 1730/2401*T^41 + 2224/2401*T^40 + 974/2401*T^39 + 
        1170/2401*T^38 - 3408/2401*T^37 - 4111/2401*T^36 - 2731/2401*T^35 - 
        3358/2401*T^34 + 178/2401*T^33 - 1390/2401*T^32 - 3369/2401*T^31 - 
        1329/2401*T^30 - 3266/2401*T^29 + 3266/2401*T^27 + 1329/2401*T^26 + 
        3369/2401*T^25 + 1390/2401*T^24 - 178/2401*T^23 + 3358/2401*T^22 + 
        2731/2401*T^21 + 4111/2401*T^20 + 3408/2401*T^19 - 1170/2401*T^18 - 
        974/2401*T^17 - 2224/2401*T^16 - 1730/2401*T^15 + 1318/2401*T^14 - 
        1210/2401*T^13 - 2503/2401*T^12 - 3230/2401*T^11 - 4710/2401*T^10 - 
        1296/2401*T^9 + 248/2401*T^8 + 313/2401*T^7 + 1658/2401*T^6 - 89/343*T^5 - 
        1153/2401*T^4 + 61/343*T^3 + 17/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + X*Y^9 + 6*X*Y^8 + 
        3*X*Y^7 + 5*X*Y^6 + 3*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 5*X*Y + X + 5*Y^30 + 
        5*Y^29 + 5*Y^28 + Y^27 + 5*Y^26 + 5*Y^24 + 5*Y^22 + 6*Y^19 + 4*Y^18 + 3*Y^14
        + Y^13 + 2*Y^12 + 4*Y^11 + 2*Y^10 + 6*Y^8 + 4*Y^7 + 3*Y^6 + 2*Y^5 + 5*Y^4 + 
        3*Y^3 + 5*Y^2 + 6*Y + 1,
    -T^56 - T^55 + 27/49*T^54 + 613/343*T^53 + 2438/2401*T^52 - 1447/2401*T^51 - 
        260/343*T^50 - 2041/2401*T^49 - 2109/2401*T^48 + 64/2401*T^47 + 556/343*T^46
        + 3386/2401*T^45 - 1136/2401*T^44 - 2456/2401*T^43 - 1095/2401*T^42 - 
        649/2401*T^41 - 367/2401*T^40 + 1447/2401*T^39 + 2080/2401*T^38 - 
        1178/2401*T^37 - 2201/2401*T^36 + 40/2401*T^35 + 1465/2401*T^34 + 
        1086/2401*T^33 + 17/49*T^32 + 740/2401*T^31 - 2468/2401*T^30 - 
        3597/2401*T^29 + 3597/2401*T^27 + 2468/2401*T^26 - 740/2401*T^25 - 
        17/49*T^24 - 1086/2401*T^23 - 1465/2401*T^22 - 40/2401*T^21 + 2201/2401*T^20
        + 1178/2401*T^19 - 2080/2401*T^18 - 1447/2401*T^17 + 367/2401*T^16 + 
        649/2401*T^15 + 1095/2401*T^14 + 2456/2401*T^13 + 1136/2401*T^12 - 
        3386/2401*T^11 - 556/343*T^10 - 64/2401*T^9 + 2109/2401*T^8 + 2041/2401*T^7 
        + 260/343*T^6 + 1447/2401*T^5 - 2438/2401*T^4 - 613/343*T^3 - 27/49*T^2 + T 
        + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 2*X*Y^8 + 
        X*Y^7 + X*Y^4 + 6*X*Y^3 + X*Y^2 + 6*X*Y + 5*X + 5*Y^30 + 4*Y^29 + 5*Y^28 + 
        4*Y^27 + 4*Y^26 + Y^24 + Y^23 + 6*Y^22 + 3*Y^20 + 6*Y^19 + 3*Y^18 + 2*Y^17 +
        Y^16 + 3*Y^14 + 2*Y^13 + 5*Y^12 + 3*Y^11 + 2*Y^10 + 3*Y^8 + 2*Y^7 + 3*Y^6 + 
        5*Y^5 + 3*Y^4 + 3*Y^3 + Y^2 + Y + 5,
    T^56 + 6/7*T^55 - 3/7*T^54 - 313/343*T^53 - 1006/2401*T^52 - 1004/2401*T^51 - 
        471/2401*T^50 + 419/2401*T^49 + 1907/2401*T^48 + 2857/2401*T^47 + 
        850/2401*T^46 - 2574/2401*T^45 - 2361/2401*T^44 - 2/343*T^43 + 640/2401*T^42
        - 879/2401*T^41 + 396/2401*T^40 + 2370/2401*T^39 + 593/2401*T^38 - 
        922/2401*T^37 + 458/2401*T^36 + 1445/2401*T^35 + 891/2401*T^34 - 
        1349/2401*T^33 - 3147/2401*T^32 - 661/2401*T^31 + 1952/2401*T^30 + 
        1065/2401*T^29 - 204/2401*T^28 + 1065/2401*T^27 + 1952/2401*T^26 - 
        661/2401*T^25 - 3147/2401*T^24 - 1349/2401*T^23 + 891/2401*T^22 + 
        1445/2401*T^21 + 458/2401*T^20 - 922/2401*T^19 + 593/2401*T^18 + 
        2370/2401*T^17 + 396/2401*T^16 - 879/2401*T^15 + 640/2401*T^14 - 2/343*T^13 
        - 2361/2401*T^12 - 2574/2401*T^11 + 850/2401*T^10 + 2857/2401*T^9 + 
        1907/2401*T^8 + 419/2401*T^7 - 471/2401*T^6 - 1004/2401*T^5 - 1006/2401*T^4 
        - 313/343*T^3 - 3/7*T^2 + 6/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 + 
        3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + X*Y^3 + 5*X*Y + 6*X + 6*Y^30 + 6*Y^29 + 2*Y^28
        + 5*Y^27 + 4*Y^26 + 3*Y^24 + 2*Y^22 + 4*Y^21 + 2*Y^20 + 4*Y^19 + 2*Y^18 + 
        5*Y^17 + 6*Y^16 + 5*Y^15 + Y^14 + 5*Y^13 + 5*Y^12 + 2*Y^11 + Y^10 + 4*Y^9 + 
        Y^7 + 5*Y^4 + 5*Y^3 + 5*Y + 2,
    T^56 - 2/7*T^55 - 11/49*T^54 + 80/343*T^53 + 524/2401*T^52 + 920/2401*T^51 - 
        2222/2401*T^50 + 1264/2401*T^49 - 853/2401*T^48 + 97/343*T^47 - 
        543/2401*T^46 - 1319/2401*T^45 + 19/49*T^44 - 748/2401*T^43 + 692/2401*T^42 
        - 2425/2401*T^41 + 1356/2401*T^40 - 366/2401*T^39 - 1000/2401*T^38 - 
        256/2401*T^37 - 761/2401*T^36 + 2024/2401*T^35 - 1192/2401*T^34 + 
        703/2401*T^33 - 524/2401*T^32 + 781/2401*T^31 + 4/7*T^30 - 159/343*T^29 + 
        761/2401*T^28 - 159/343*T^27 + 4/7*T^26 + 781/2401*T^25 - 524/2401*T^24 + 
        703/2401*T^23 - 1192/2401*T^22 + 2024/2401*T^21 - 761/2401*T^20 - 
        256/2401*T^19 - 1000/2401*T^18 - 366/2401*T^17 + 1356/2401*T^16 - 
        2425/2401*T^15 + 692/2401*T^14 - 748/2401*T^13 + 19/49*T^12 - 1319/2401*T^11
        - 543/2401*T^10 + 97/343*T^9 - 853/2401*T^8 + 1264/2401*T^7 - 2222/2401*T^6 
        + 920/2401*T^5 + 524/2401*T^4 + 80/343*T^3 - 11/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + X*Y^10 + 4*X*Y^9 + 
        4*X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 3*X*Y 
        + 6*X + 3*Y^30 + 3*Y^29 + 4*Y^28 + 2*Y^27 + 4*Y^26 + 5*Y^25 + 5*Y^24 + 
        2*Y^23 + 4*Y^22 + Y^19 + 3*Y^18 + 2*Y^17 + 4*Y^16 + 2*Y^15 + 2*Y^14 + 6*Y^13
        + 6*Y^11 + 5*Y^10 + 4*Y^6 + 6*Y^5 + 2*Y^3 + Y^2 + 5*Y + 4,
    T^56 - 1/7*T^55 - 51/49*T^54 - 468/343*T^53 + 536/2401*T^52 + 1745/2401*T^51 + 
        3086/2401*T^50 + 1945/2401*T^49 + 401/2401*T^48 - 2894/2401*T^47 - 
        3566/2401*T^46 - 1991/2401*T^45 + 1474/2401*T^44 + 3109/2401*T^43 + 
        2696/2401*T^42 + 103/2401*T^41 - 1748/2401*T^40 - 2248/2401*T^39 - 
        1207/2401*T^38 - 232/2401*T^37 + 2491/2401*T^36 + 2446/2401*T^35 + 
        1110/2401*T^34 - 1836/2401*T^33 - 2276/2401*T^32 - 426/343*T^31 - 
        132/2401*T^30 + 212/343*T^29 + 4407/2401*T^28 + 212/343*T^27 - 132/2401*T^26
        - 426/343*T^25 - 2276/2401*T^24 - 1836/2401*T^23 + 1110/2401*T^22 + 
        2446/2401*T^21 + 2491/2401*T^20 - 232/2401*T^19 - 1207/2401*T^18 - 
        2248/2401*T^17 - 1748/2401*T^16 + 103/2401*T^15 + 2696/2401*T^14 + 
        3109/2401*T^13 + 1474/2401*T^12 - 1991/2401*T^11 - 3566/2401*T^10 - 
        2894/2401*T^9 + 401/2401*T^8 + 1945/2401*T^7 + 3086/2401*T^6 + 1745/2401*T^5
        + 536/2401*T^4 - 468/343*T^3 - 51/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 2*X*Y^12 + 6*X*Y^10 + 3*X*Y^9 + 3*X*Y^7 + 6*X*Y^6 + 
        5*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + X*Y^2 + X*Y + 6*Y^30 + 3*Y^29 + 6*Y^28 + 
        3*Y^27 + 4*Y^26 + 2*Y^25 + 2*Y^24 + Y^23 + 5*Y^22 + 3*Y^21 + 6*Y^20 + 5*Y^19
        + 3*Y^18 + 5*Y^17 + Y^16 + 6*Y^15 + 2*Y^14 + 5*Y^13 + 3*Y^12 + Y^11 + 5*Y^9 
        + 3*Y^7 + 5*Y^6 + 3*Y^5 + 4*Y^4 + 2*Y^3 + 3*Y^2 + 5*Y + 6,
    T^56 + 3/7*T^55 - 12/49*T^54 - 444/343*T^53 - 3786/2401*T^52 + 429/2401*T^51 + 
        390/343*T^50 + 3298/2401*T^49 + 143/2401*T^48 - 2083/2401*T^47 - 
        1863/2401*T^46 + 100/343*T^45 + 240/343*T^44 + 841/2401*T^43 - 
        2119/2401*T^42 - 338/343*T^41 - 222/2401*T^40 + 1861/2401*T^39 + 
        3950/2401*T^38 - 27/343*T^37 - 1527/2401*T^36 - 2406/2401*T^35 - 
        837/2401*T^34 + 1846/2401*T^33 + 29/49*T^32 + 1222/2401*T^31 - 489/2401*T^30
        - 1058/2401*T^29 - 1531/2401*T^28 - 1058/2401*T^27 - 489/2401*T^26 + 
        1222/2401*T^25 + 29/49*T^24 + 1846/2401*T^23 - 837/2401*T^22 - 
        2406/2401*T^21 - 1527/2401*T^20 - 27/343*T^19 + 3950/2401*T^18 + 
        1861/2401*T^17 - 222/2401*T^16 - 338/343*T^15 - 2119/2401*T^14 + 
        841/2401*T^13 + 240/343*T^12 + 100/343*T^11 - 1863/2401*T^10 - 2083/2401*T^9
        + 143/2401*T^8 + 3298/2401*T^7 + 390/343*T^6 + 429/2401*T^5 - 3786/2401*T^4 
        - 444/343*T^3 - 12/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 4*X*Y^11 + X*Y^10 + 3*X*Y^9 + 3*X*Y^7 + 
        5*X*Y^6 + 4*X*Y^5 + 6*X*Y^3 + 2*X*Y^2 + 2*X*Y + 3*X + 6*Y^30 + Y^28 + Y^27 +
        Y^26 + 2*Y^25 + 6*Y^23 + 4*Y^22 + 2*Y^21 + 3*Y^20 + 6*Y^19 + 3*Y^18 + 4*Y^17
        + 2*Y^16 + 5*Y^14 + 6*Y^13 + 6*Y^12 + 4*Y^11 + 6*Y^10 + Y^9 + 4*Y^8 + 6*Y^7 
        + 5*Y^5 + 5*Y^4 + 3*Y^3 + 3*Y^2 + 2,
    -T^56 - 1/7*T^55 - 11/49*T^54 + 153/343*T^53 - 955/2401*T^52 + 248/2401*T^51 - 
        844/2401*T^50 + 824/2401*T^49 - 513/2401*T^48 - 5/2401*T^47 - 349/2401*T^46 
        + 820/2401*T^45 + 30/343*T^44 + 205/2401*T^43 + 909/2401*T^42 + 
        1058/2401*T^41 + 26/343*T^40 - 454/2401*T^39 - 110/2401*T^38 + 645/2401*T^37
        - 31/2401*T^36 - 485/2401*T^35 - 1356/2401*T^34 - 104/2401*T^33 - 
        170/2401*T^32 - 55/2401*T^31 + 170/2401*T^30 + 436/2401*T^29 - 436/2401*T^27
        - 170/2401*T^26 + 55/2401*T^25 + 170/2401*T^24 + 104/2401*T^23 + 
        1356/2401*T^22 + 485/2401*T^21 + 31/2401*T^20 - 645/2401*T^19 + 
        110/2401*T^18 + 454/2401*T^17 - 26/343*T^16 - 1058/2401*T^15 - 909/2401*T^14
        - 205/2401*T^13 - 30/343*T^12 - 820/2401*T^11 + 349/2401*T^10 + 5/2401*T^9 +
        513/2401*T^8 - 824/2401*T^7 + 844/2401*T^6 - 248/2401*T^5 + 955/2401*T^4 - 
        153/343*T^3 + 11/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 2*X*Y^10 + 6*X*Y^9 + 5*X*Y^8 +
        4*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + 5*X*Y + 4*X + 
        4*Y^30 + 3*Y^28 + Y^27 + 4*Y^26 + 3*Y^25 + 5*Y^24 + Y^22 + 3*Y^21 + 3*Y^20 +
        5*Y^19 + 2*Y^18 + 4*Y^17 + 4*Y^16 + 2*Y^15 + 4*Y^14 + Y^13 + 6*Y^12 + 2*Y^11
        + 6*Y^10 + 5*Y^9 + 4*Y^8 + Y^7 + 4*Y^6 + 3*Y^5 + 6*Y^4 + 6*Y^3 + Y^2 + 6*Y +
        3,
    -T^56 - 5/7*T^55 + 78/49*T^54 + 55/49*T^53 - 3571/2401*T^52 - 267/343*T^51 + 
        2736/2401*T^50 - 96/2401*T^49 - 2124/2401*T^48 + 2196/2401*T^47 + 
        1382/2401*T^46 - 2538/2401*T^45 - 69/2401*T^44 + 307/343*T^43 + 
        467/2401*T^42 - 233/2401*T^41 - 331/2401*T^40 - 1147/2401*T^39 + 
        128/2401*T^38 + 1899/2401*T^37 + 46/343*T^36 - 703/2401*T^35 + 454/2401*T^34
        - 228/2401*T^33 - 604/2401*T^32 + 1126/2401*T^31 + 179/2401*T^30 - 
        1952/2401*T^29 + 1952/2401*T^27 - 179/2401*T^26 - 1126/2401*T^25 + 
        604/2401*T^24 + 228/2401*T^23 - 454/2401*T^22 + 703/2401*T^21 - 46/343*T^20 
        - 1899/2401*T^19 - 128/2401*T^18 + 1147/2401*T^17 + 331/2401*T^16 + 
        233/2401*T^15 - 467/2401*T^14 - 307/343*T^13 + 69/2401*T^12 + 2538/2401*T^11
        - 1382/2401*T^10 - 2196/2401*T^9 + 2124/2401*T^8 + 96/2401*T^7 - 
        2736/2401*T^6 + 267/343*T^5 + 3571/2401*T^4 - 55/49*T^3 - 78/49*T^2 + 5/7*T 
        + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 4*X*Y^8 + 
        4*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 6*X*Y + 5*Y^30 +
        6*Y^29 + 2*Y^28 + 6*Y^27 + 6*Y^26 + 3*Y^25 + Y^24 + 6*Y^23 + 6*Y^22 + Y^21 +
        6*Y^20 + 4*Y^18 + 4*Y^17 + 2*Y^14 + 2*Y^13 + 6*Y^11 + 5*Y^10 + Y^9 + Y^8 + 
        4*Y^7 + 3*Y^6 + 6*Y^5 + 3*Y^4 + Y^3 + 4*Y^2 + 4*Y + 1,
    -T^56 + 3/7*T^55 + 27/49*T^54 - 131/343*T^53 + 1450/2401*T^52 - 1748/2401*T^51 +
        549/2401*T^50 - 10/343*T^49 + 526/2401*T^48 + 1773/2401*T^47 - 
        1166/2401*T^46 + 963/2401*T^45 - 2454/2401*T^44 + 724/2401*T^43 + 
        1037/2401*T^42 - 146/343*T^41 + 2000/2401*T^40 - 1936/2401*T^39 + 
        745/2401*T^38 + 408/2401*T^37 - 804/2401*T^36 + 1335/2401*T^35 - 
        823/2401*T^34 - 318/2401*T^33 - 710/2401*T^32 - 68/2401*T^31 + 698/2401*T^30
        - 1292/2401*T^29 + 1292/2401*T^27 - 698/2401*T^26 + 68/2401*T^25 + 
        710/2401*T^24 + 318/2401*T^23 + 823/2401*T^22 - 1335/2401*T^21 + 
        804/2401*T^20 - 408/2401*T^19 - 745/2401*T^18 + 1936/2401*T^17 - 
        2000/2401*T^16 + 146/343*T^15 - 1037/2401*T^14 - 724/2401*T^13 + 
        2454/2401*T^12 - 963/2401*T^11 + 1166/2401*T^10 - 1773/2401*T^9 - 
        526/2401*T^8 + 10/343*T^7 - 549/2401*T^6 + 1748/2401*T^5 - 1450/2401*T^4 + 
        131/343*T^3 - 27/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^13 + 3*X*Y^12 + 6*X*Y^9 + 6*X*Y^8 + X*Y^7 + 2*X*Y^5 + 
        3*X*Y^4 + 6*X*Y^2 + 5*X*Y + 6*X + 4*Y^30 + 6*Y^29 + Y^28 + 4*Y^27 + 6*Y^25 +
        3*Y^24 + 5*Y^23 + 4*Y^22 + 4*Y^21 + 5*Y^20 + 4*Y^18 + 5*Y^16 + 2*Y^15 + 
        6*Y^14 + 2*Y^13 + 5*Y^11 + 3*Y^10 + Y^9 + 4*Y^8 + 2*Y^7 + Y^6 + 4*Y^5 + 
        3*Y^4 + Y^3 + 5*Y^2 + 3*Y,
    -T^56 - 4/7*T^55 + 51/49*T^54 + 431/343*T^53 - 515/2401*T^52 - 3352/2401*T^51 - 
        2939/2401*T^50 + 1753/2401*T^49 + 2962/2401*T^48 - 1720/2401*T^47 - 
        2437/2401*T^46 + 1513/2401*T^45 + 2764/2401*T^44 + 124/2401*T^43 - 
        2638/2401*T^42 - 2992/2401*T^41 + 1424/2401*T^40 + 4148/2401*T^39 + 
        446/2401*T^38 - 2287/2401*T^37 - 153/343*T^36 + 1102/2401*T^35 + 
        2188/2401*T^34 + 466/2401*T^33 - 3022/2401*T^32 - 1194/2401*T^31 + 
        2500/2401*T^30 + 2708/2401*T^29 - 2708/2401*T^27 - 2500/2401*T^26 + 
        1194/2401*T^25 + 3022/2401*T^24 - 466/2401*T^23 - 2188/2401*T^22 - 
        1102/2401*T^21 + 153/343*T^20 + 2287/2401*T^19 - 446/2401*T^18 - 
        4148/2401*T^17 - 1424/2401*T^16 + 2992/2401*T^15 + 2638/2401*T^14 - 
        124/2401*T^13 - 2764/2401*T^12 - 1513/2401*T^11 + 2437/2401*T^10 + 
        1720/2401*T^9 - 2962/2401*T^8 - 1753/2401*T^7 + 2939/2401*T^6 + 
        3352/2401*T^5 + 515/2401*T^4 - 431/343*T^3 - 51/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + X*Y^8 + 3*X*Y^7 + 
        2*X*Y^6 + 2*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 2*X*Y + X + 2*Y^30 + 2*Y^28 + 4*Y^27
        + Y^26 + 5*Y^25 + 3*Y^22 + 2*Y^21 + 4*Y^19 + 6*Y^18 + 4*Y^17 + 5*Y^16 + 
        6*Y^15 + 6*Y^13 + 3*Y^12 + Y^11 + 3*Y^9 + Y^8 + 5*Y^7 + Y^6 + 5*Y^5 + 5*Y^4 
        + 6*Y^3 + 5*Y^2 + 2*Y + 6,
    -T^56 + 9/7*T^55 - 38/49*T^54 + 40/343*T^53 - 523/2401*T^52 + 1034/2401*T^51 - 
        850/2401*T^50 + 1796/2401*T^49 - 1492/2401*T^48 + 1124/2401*T^47 - 
        170/2401*T^46 + 585/2401*T^45 + 685/2401*T^44 - 165/343*T^43 + 278/2401*T^42
        + 8/343*T^41 + 312/2401*T^40 - 845/2401*T^39 + 571/2401*T^38 - 
        1317/2401*T^37 + 1184/2401*T^36 - 1404/2401*T^35 + 1336/2401*T^34 - 
        821/2401*T^33 + 73/2401*T^32 - 293/2401*T^31 + 1158/2401*T^30 - 18/49*T^29 +
        18/49*T^27 - 1158/2401*T^26 + 293/2401*T^25 - 73/2401*T^24 + 821/2401*T^23 -
        1336/2401*T^22 + 1404/2401*T^21 - 1184/2401*T^20 + 1317/2401*T^19 - 
        571/2401*T^18 + 845/2401*T^17 - 312/2401*T^16 - 8/343*T^15 - 278/2401*T^14 +
        165/343*T^13 - 685/2401*T^12 - 585/2401*T^11 + 170/2401*T^10 - 1124/2401*T^9
        + 1492/2401*T^8 - 1796/2401*T^7 + 850/2401*T^6 - 1034/2401*T^5 + 
        523/2401*T^4 - 40/343*T^3 + 38/49*T^2 - 9/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + X*Y^13 + X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + X*Y^8 + 
        3*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + X*Y^2 + 2*X*Y + 5*X + 
        4*Y^30 + 5*Y^29 + Y^27 + 5*Y^25 + 2*Y^24 + 5*Y^22 + 4*Y^20 + 2*Y^17 + Y^16 +
        4*Y^15 + 3*Y^14 + 5*Y^12 + Y^11 + 6*Y^10 + Y^9 + 6*Y^8 + 2*Y^7 + 3*Y^6 + 
        6*Y^5 + 3*Y^4 + 5*Y^3 + 2*Y^2 + 5*Y + 2,
    T^56 + 12/7*T^55 + 71/49*T^54 + 43/49*T^53 - 296/2401*T^52 - 845/2401*T^51 + 
        1560/2401*T^50 + 2718/2401*T^49 + 836/2401*T^48 - 1560/2401*T^47 - 
        3424/2401*T^46 - 44/49*T^45 + 1427/2401*T^44 + 2711/2401*T^43 + 
        1413/2401*T^42 - 1131/2401*T^41 - 1565/2401*T^40 + 1419/2401*T^39 + 
        652/343*T^38 + 737/343*T^37 + 3295/2401*T^36 + 501/2401*T^35 - 130/343*T^34 
        + 873/2401*T^33 + 1894/2401*T^32 + 654/2401*T^31 - 53/343*T^30 - 
        2512/2401*T^29 - 3873/2401*T^28 - 2512/2401*T^27 - 53/343*T^26 + 
        654/2401*T^25 + 1894/2401*T^24 + 873/2401*T^23 - 130/343*T^22 + 
        501/2401*T^21 + 3295/2401*T^20 + 737/343*T^19 + 652/343*T^18 + 
        1419/2401*T^17 - 1565/2401*T^16 - 1131/2401*T^15 + 1413/2401*T^14 + 
        2711/2401*T^13 + 1427/2401*T^12 - 44/49*T^11 - 3424/2401*T^10 - 
        1560/2401*T^9 + 836/2401*T^8 + 2718/2401*T^7 + 1560/2401*T^6 - 845/2401*T^5 
        - 296/2401*T^4 + 43/49*T^3 + 71/49*T^2 + 12/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 3*X*Y^10 + 6*X*Y^9 + X*Y^7 + 
        2*X*Y^6 + 5*X*Y^5 + X*Y^2 + 3*X*Y + X + 2*Y^30 + 3*Y^28 + 6*Y^27 + 5*Y^26 + 
        4*Y^25 + 4*Y^24 + 4*Y^23 + 5*Y^22 + 6*Y^21 + Y^20 + 4*Y^19 + 3*Y^18 + 6*Y^17
        + 4*Y^16 + Y^15 + 6*Y^14 + 4*Y^13 + 2*Y^12 + Y^11 + 6*Y^10 + 2*Y^8 + 2*Y^7 +
        Y^6 + 6*Y^5 + Y^4 + 4*Y^3 + 6*Y^2 + 6,
    T^56 - 9/7*T^55 + 45/49*T^54 + 61/343*T^53 - 2371/2401*T^52 + 3268/2401*T^51 - 
        1881/2401*T^50 + 333/2401*T^49 + 1046/2401*T^48 - 1049/2401*T^47 + 
        1003/2401*T^46 + 199/2401*T^45 - 530/2401*T^44 + 548/2401*T^43 + 
        93/2401*T^42 - 1072/2401*T^41 + 1175/2401*T^40 - 1070/2401*T^39 - 
        603/2401*T^38 + 2118/2401*T^37 - 3182/2401*T^36 + 1840/2401*T^35 + 
        681/2401*T^34 - 3148/2401*T^33 + 3069/2401*T^32 - 1719/2401*T^31 - 
        702/2401*T^30 + 1331/2401*T^29 - 2070/2401*T^28 + 1331/2401*T^27 - 
        702/2401*T^26 - 1719/2401*T^25 + 3069/2401*T^24 - 3148/2401*T^23 + 
        681/2401*T^22 + 1840/2401*T^21 - 3182/2401*T^20 + 2118/2401*T^19 - 
        603/2401*T^18 - 1070/2401*T^17 + 1175/2401*T^16 - 1072/2401*T^15 + 
        93/2401*T^14 + 548/2401*T^13 - 530/2401*T^12 + 199/2401*T^11 + 
        1003/2401*T^10 - 1049/2401*T^9 + 1046/2401*T^8 + 333/2401*T^7 - 
        1881/2401*T^6 + 3268/2401*T^5 - 2371/2401*T^4 + 61/343*T^3 + 45/49*T^2 - 
        9/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 6*X*Y^9 + 2*X*Y^7 + 
        3*X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 5*X*Y + 5*X + Y^30 + 
        3*Y^29 + 6*Y^28 + 2*Y^27 + Y^26 + 5*Y^25 + 2*Y^23 + 2*Y^22 + 6*Y^21 + 3*Y^20
        + 6*Y^19 + 3*Y^18 + Y^17 + 2*Y^16 + 2*Y^15 + Y^14 + 6*Y^13 + 3*Y^12 + 3*Y^11
        + Y^10 + 6*Y^9 + 5*Y^7 + 5*Y^6 + 5*Y^5 + 2*Y^4 + 2*Y^3 + 3*Y,
    T^56 + 2/7*T^55 - 71/49*T^54 + 191/343*T^53 + 275/343*T^52 - 794/2401*T^51 + 
        67/343*T^50 - 3328/2401*T^49 - 139/2401*T^48 + 363/343*T^47 - 324/343*T^46 +
        613/2401*T^45 - 39/2401*T^44 - 1013/2401*T^43 + 1511/2401*T^42 - 
        1385/2401*T^41 + 103/343*T^40 + 793/2401*T^39 - 2028/2401*T^38 + 67/343*T^37
        - 323/2401*T^36 + 411/2401*T^35 + 615/2401*T^34 - 1002/2401*T^33 + 
        913/2401*T^32 - 551/2401*T^31 + 823/2401*T^30 + 1279/2401*T^29 - 
        1992/2401*T^28 + 1279/2401*T^27 + 823/2401*T^26 - 551/2401*T^25 + 
        913/2401*T^24 - 1002/2401*T^23 + 615/2401*T^22 + 411/2401*T^21 - 
        323/2401*T^20 + 67/343*T^19 - 2028/2401*T^18 + 793/2401*T^17 + 103/343*T^16 
        - 1385/2401*T^15 + 1511/2401*T^14 - 1013/2401*T^13 - 39/2401*T^12 + 
        613/2401*T^11 - 324/343*T^10 + 363/343*T^9 - 139/2401*T^8 - 3328/2401*T^7 + 
        67/343*T^6 - 794/2401*T^5 + 275/343*T^4 + 191/343*T^3 - 71/49*T^2 + 2/7*T + 
        1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 4*X*Y^9 + 
        6*X*Y^8 + X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 4*X*Y + X + 6*Y^30
        + Y^29 + 2*Y^28 + 6*Y^27 + 2*Y^26 + 4*Y^24 + 6*Y^23 + 3*Y^22 + 4*Y^21 + 
        2*Y^20 + 6*Y^19 + 4*Y^18 + 4*Y^17 + 6*Y^16 + 3*Y^14 + Y^13 + 6*Y^12 + 3*Y^11
        + 6*Y^10 + 2*Y^9 + 3*Y^8 + Y^7 + 3*Y^6 + 6*Y^5 + 5*Y^4 + 6*Y^3 + 6*Y^2 + 6*Y
        + 6,
    -T^56 - 5/7*T^55 + 64/49*T^54 + 286/343*T^53 - 2440/2401*T^52 - 1667/2401*T^51 +
        139/343*T^50 - 16/343*T^49 - 491/2401*T^48 + 702/2401*T^47 + 1893/2401*T^46 
        - 577/2401*T^45 - 3162/2401*T^44 + 137/2401*T^43 + 2546/2401*T^42 - 
        67/343*T^41 - 2390/2401*T^40 + 1333/2401*T^39 + 1878/2401*T^38 - 
        1803/2401*T^37 - 48/49*T^36 + 212/343*T^35 + 1229/2401*T^34 - 2011/2401*T^33
        + 855/2401*T^32 + 432/343*T^31 - 1118/2401*T^30 - 3753/2401*T^29 + 
        3753/2401*T^27 + 1118/2401*T^26 - 432/343*T^25 - 855/2401*T^24 + 
        2011/2401*T^23 - 1229/2401*T^22 - 212/343*T^21 + 48/49*T^20 + 1803/2401*T^19
        - 1878/2401*T^18 - 1333/2401*T^17 + 2390/2401*T^16 + 67/343*T^15 - 
        2546/2401*T^14 - 137/2401*T^13 + 3162/2401*T^12 + 577/2401*T^11 - 
        1893/2401*T^10 - 702/2401*T^9 + 491/2401*T^8 + 16/343*T^7 - 139/343*T^6 + 
        1667/2401*T^5 + 2440/2401*T^4 - 286/343*T^3 - 64/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + X*Y^8 + 4*X*Y^7 + 
        6*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 6*X*Y + X + 5*Y^30 + 4*Y^29 + 4*Y^27
        + 6*Y^26 + 5*Y^25 + 3*Y^24 + 6*Y^23 + 6*Y^22 + Y^21 + 4*Y^20 + 4*Y^19 + Y^18
        + Y^17 + 5*Y^16 + Y^15 + 2*Y^14 + 4*Y^13 + 2*Y^12 + 5*Y^11 + 3*Y^10 + Y^9 + 
        4*Y^8 + 6*Y^7 + 2*Y^6 + 2*Y^5 + 2*Y^4 + Y^3 + 3*Y^2 + 5*Y + 6,
    T^56 - 3/7*T^55 + 32/49*T^54 - 20/343*T^53 + 204/2401*T^52 + 267/2401*T^51 - 
        227/2401*T^50 + 405/2401*T^49 - 2010/2401*T^48 - 32/343*T^47 - 591/2401*T^46
        - 256/343*T^45 - 411/2401*T^44 - 764/2401*T^43 - 171/2401*T^42 - 
        96/2401*T^41 + 681/2401*T^40 + 940/2401*T^39 + 1097/2401*T^38 + 
        2627/2401*T^37 + 1140/2401*T^36 + 1100/2401*T^35 + 283/2401*T^34 + 
        694/2401*T^33 - 563/2401*T^32 - 453/2401*T^31 - 204/343*T^30 - 870/2401*T^29
        - 2360/2401*T^28 - 870/2401*T^27 - 204/343*T^26 - 453/2401*T^25 - 
        563/2401*T^24 + 694/2401*T^23 + 283/2401*T^22 + 1100/2401*T^21 + 
        1140/2401*T^20 + 2627/2401*T^19 + 1097/2401*T^18 + 940/2401*T^17 + 
        681/2401*T^16 - 96/2401*T^15 - 171/2401*T^14 - 764/2401*T^13 - 411/2401*T^12
        - 256/343*T^11 - 591/2401*T^10 - 32/343*T^9 - 2010/2401*T^8 + 405/2401*T^7 -
        227/2401*T^6 + 267/2401*T^5 + 204/2401*T^4 - 20/343*T^3 + 32/49*T^2 - 3/7*T 
        + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + X*Y^8 + 4*X*Y^7 + 
        X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 2*X*Y + 3*X + 5*Y^30 + 
        4*Y^29 + 4*Y^28 + 5*Y^27 + 5*Y^26 + 5*Y^25 + 2*Y^24 + Y^23 + Y^22 + 4*Y^20 +
        Y^19 + 2*Y^18 + 4*Y^17 + 2*Y^16 + 4*Y^15 + 2*Y^14 + Y^13 + 3*Y^10 + 3*Y^8 + 
        6*Y^7 + 2*Y^6 + 3*Y^5 + 4*Y^2 + 6,
    T^56 - 4/7*T^55 - 24/49*T^54 + 334/343*T^53 + 545/2401*T^52 - 947/2401*T^51 - 
        1025/2401*T^50 + 1469/2401*T^49 - 410/2401*T^48 + 194/2401*T^47 + 
        1579/2401*T^46 - 771/2401*T^45 - 2085/2401*T^44 + 2005/2401*T^43 + 
        2638/2401*T^42 - 2696/2401*T^41 - 305/343*T^40 + 1574/2401*T^39 + 
        1689/2401*T^38 - 1114/2401*T^37 - 243/2401*T^36 + 571/2401*T^35 - 
        713/2401*T^34 + 1070/2401*T^33 + 1503/2401*T^32 - 5/49*T^31 - 2092/2401*T^30
        - 76/2401*T^29 + 3148/2401*T^28 - 76/2401*T^27 - 2092/2401*T^26 - 5/49*T^25 
        + 1503/2401*T^24 + 1070/2401*T^23 - 713/2401*T^22 + 571/2401*T^21 - 
        243/2401*T^20 - 1114/2401*T^19 + 1689/2401*T^18 + 1574/2401*T^17 - 
        305/343*T^16 - 2696/2401*T^15 + 2638/2401*T^14 + 2005/2401*T^13 - 
        2085/2401*T^12 - 771/2401*T^11 + 1579/2401*T^10 + 194/2401*T^9 - 
        410/2401*T^8 + 1469/2401*T^7 - 1025/2401*T^6 - 947/2401*T^5 + 545/2401*T^4 +
        334/343*T^3 - 24/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 
        5*X*Y^8 + X*Y^7 + 2*X*Y^5 + 4*X*Y^2 + X + 2*Y^30 + 3*Y^29 + 3*Y^28 + 5*Y^27 
        + 6*Y^26 + 3*Y^25 + 5*Y^24 + 5*Y^23 + 6*Y^22 + 3*Y^20 + Y^19 + 5*Y^18 + 
        3*Y^16 + 4*Y^15 + 4*Y^14 + 6*Y^13 + 4*Y^12 + 5*Y^11 + Y^10 + 5*Y^9 + 3*Y^8 +
        2*Y^7 + 6*Y^6 + 6*Y^5 + 2*Y^4 + 5*Y^3 + 5*Y + 3,
    -T^56 - 3/7*T^55 + 26/49*T^54 + 484/343*T^53 + 517/2401*T^52 - 1593/2401*T^51 - 
        1054/2401*T^50 + 715/2401*T^49 + 137/2401*T^48 - 1027/2401*T^47 + 
        44/343*T^46 - 473/2401*T^45 - 132/343*T^44 - 757/2401*T^43 + 2813/2401*T^42 
        + 2022/2401*T^41 - 466/2401*T^40 - 1558/2401*T^39 - 26/2401*T^38 + 
        555/2401*T^37 - 1080/2401*T^36 - 1433/2401*T^35 - 565/2401*T^34 + 
        1125/2401*T^33 + 845/2401*T^32 + 1151/2401*T^31 + 488/2401*T^30 + 
        20/343*T^29 - 20/343*T^27 - 488/2401*T^26 - 1151/2401*T^25 - 845/2401*T^24 -
        1125/2401*T^23 + 565/2401*T^22 + 1433/2401*T^21 + 1080/2401*T^20 - 
        555/2401*T^19 + 26/2401*T^18 + 1558/2401*T^17 + 466/2401*T^16 - 
        2022/2401*T^15 - 2813/2401*T^14 + 757/2401*T^13 + 132/343*T^12 + 
        473/2401*T^11 - 44/343*T^10 + 1027/2401*T^9 - 137/2401*T^8 - 715/2401*T^7 + 
        1054/2401*T^6 + 1593/2401*T^5 - 517/2401*T^4 - 484/343*T^3 - 26/49*T^2 + 
        3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 
        + 6*X*Y^8 + X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + X*Y + 2*X + 
        6*Y^30 + 3*Y^28 + 3*Y^27 + 2*Y^26 + 3*Y^25 + 4*Y^23 + 6*Y^22 + Y^20 + 2*Y^19
        + 5*Y^18 + 2*Y^17 + 2*Y^16 + Y^15 + 4*Y^14 + 3*Y^13 + 2*Y^12 + 2*Y^11 + 
        3*Y^10 + 6*Y^9 + 5*Y^8 + 5*Y^7 + 6*Y^6 + 2*Y^4 + 4*Y^3 + Y^2 + 3,
    T^56 + 3/7*T^55 - 5/49*T^54 - 227/343*T^53 - 817/2401*T^52 - 1784/2401*T^51 - 
        2612/2401*T^50 - 1156/2401*T^49 + 950/2401*T^48 + 1423/2401*T^47 + 
        282/2401*T^46 + 1583/2401*T^45 + 1398/2401*T^44 + 741/2401*T^43 - 
        163/2401*T^42 + 864/2401*T^41 - 64/2401*T^40 + 164/2401*T^39 - 57/2401*T^38 
        - 2/49*T^37 - 34/49*T^36 - 1346/2401*T^35 - 597/2401*T^34 - 641/2401*T^33 - 
        73/343*T^32 + 2/49*T^31 + 1920/2401*T^30 + 408/2401*T^29 + 179/2401*T^28 + 
        408/2401*T^27 + 1920/2401*T^26 + 2/49*T^25 - 73/343*T^24 - 641/2401*T^23 - 
        597/2401*T^22 - 1346/2401*T^21 - 34/49*T^20 - 2/49*T^19 - 57/2401*T^18 + 
        164/2401*T^17 - 64/2401*T^16 + 864/2401*T^15 - 163/2401*T^14 + 741/2401*T^13
        + 1398/2401*T^12 + 1583/2401*T^11 + 282/2401*T^10 + 1423/2401*T^9 + 
        950/2401*T^8 - 1156/2401*T^7 - 2612/2401*T^6 - 1784/2401*T^5 - 817/2401*T^4 
        - 227/343*T^3 - 5/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + X*Y^11 + 6*X*Y^9 + 4*X*Y^8 + 4*X*Y^7 + 
        5*X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + X*Y^3 + 4*X*Y^2 + X*Y + 3*X + 6*Y^30 + 6*Y^29 
        + 3*Y^28 + 5*Y^27 + 6*Y^26 + 5*Y^25 + 6*Y^23 + 5*Y^22 + Y^19 + 5*Y^18 + 
        6*Y^17 + 3*Y^16 + 4*Y^15 + 5*Y^14 + 2*Y^13 + 4*Y^12 + 6*Y^11 + Y^9 + 4*Y^8 +
        4*Y^7 + Y^6 + 5*Y^5 + 6*Y^4 + Y^3 + 3*Y^2 + 5*Y + 5,
    T^56 + 5/7*T^55 + 26/49*T^54 + 40/49*T^53 + 939/2401*T^52 + 1949/2401*T^51 + 
        396/343*T^50 + 1935/2401*T^49 + 109/343*T^48 + 1192/2401*T^47 + 19/49*T^46 -
        214/2401*T^45 + 612/2401*T^44 - 666/2401*T^43 - 1941/2401*T^42 - 
        1489/2401*T^41 - 1832/2401*T^40 - 338/343*T^39 - 1824/2401*T^38 - 
        1342/2401*T^37 - 3005/2401*T^36 - 2057/2401*T^35 - 80/343*T^34 - 
        901/2401*T^33 + 86/2401*T^32 + 488/2401*T^31 - 785/2401*T^30 + 156/2401*T^29
        + 1062/2401*T^28 + 156/2401*T^27 - 785/2401*T^26 + 488/2401*T^25 + 
        86/2401*T^24 - 901/2401*T^23 - 80/343*T^22 - 2057/2401*T^21 - 3005/2401*T^20
        - 1342/2401*T^19 - 1824/2401*T^18 - 338/343*T^17 - 1832/2401*T^16 - 
        1489/2401*T^15 - 1941/2401*T^14 - 666/2401*T^13 + 612/2401*T^12 - 
        214/2401*T^11 + 19/49*T^10 + 1192/2401*T^9 + 109/343*T^8 + 1935/2401*T^7 + 
        396/343*T^6 + 1949/2401*T^5 + 939/2401*T^4 + 40/49*T^3 + 26/49*T^2 + 5/7*T +
        1
*], [*
    X^3 + 2*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + X*Y^9 + 2*X*Y^7 + 
        2*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 4*X*Y + 5*X + 2*Y^30 + 
        6*Y^29 + 2*Y^28 + 5*Y^27 + Y^26 + 2*Y^24 + Y^23 + 2*Y^22 + 3*Y^21 + 3*Y^20 +
        6*Y^19 + Y^18 + 6*Y^17 + 3*Y^16 + 4*Y^15 + 5*Y^14 + 4*Y^13 + 5*Y^11 + 4*Y^10
        + 6*Y^9 + 5*Y^8 + Y^7 + 6*Y^6 + 2*Y^5 + 3*Y^4 + Y^3 + 6*Y^2 + 6*Y,
    T^56 - 13/7*T^55 + 68/49*T^54 + 19/343*T^53 - 1740/2401*T^52 + 2105/2401*T^51 - 
        2623/2401*T^50 + 2535/2401*T^49 - 39/343*T^48 - 2977/2401*T^47 + 
        5410/2401*T^46 - 730/343*T^45 + 2686/2401*T^44 + 244/343*T^43 - 
        6012/2401*T^42 + 6402/2401*T^41 - 2453/2401*T^40 - 1891/2401*T^39 + 
        4084/2401*T^38 - 5721/2401*T^37 + 5674/2401*T^36 - 2626/2401*T^35 - 
        2377/2401*T^34 + 6191/2401*T^33 - 6844/2401*T^32 + 4019/2401*T^31 + 
        272/2401*T^30 - 579/343*T^29 + 5314/2401*T^28 - 579/343*T^27 + 272/2401*T^26
        + 4019/2401*T^25 - 6844/2401*T^24 + 6191/2401*T^23 - 2377/2401*T^22 - 
        2626/2401*T^21 + 5674/2401*T^20 - 5721/2401*T^19 + 4084/2401*T^18 - 
        1891/2401*T^17 - 2453/2401*T^16 + 6402/2401*T^15 - 6012/2401*T^14 + 
        244/343*T^13 + 2686/2401*T^12 - 730/343*T^11 + 5410/2401*T^10 - 
        2977/2401*T^9 - 39/343*T^8 + 2535/2401*T^7 - 2623/2401*T^6 + 2105/2401*T^5 -
        1740/2401*T^4 + 19/343*T^3 + 68/49*T^2 - 13/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 4*X*Y^11 + X*Y^10 + 4*X*Y^9 + 5*X*Y^8 + 
        3*X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + X*Y^3 + 3*X*Y^2 + 3*X*Y + 2*Y^30 + 
        5*Y^29 + 2*Y^28 + Y^27 + 5*Y^26 + 5*Y^25 + 6*Y^24 + 2*Y^23 + 3*Y^22 + 6*Y^21
        + 2*Y^20 + Y^19 + 2*Y^17 + Y^16 + 2*Y^15 + 2*Y^14 + 3*Y^13 + 5*Y^12 + 5*Y^11
        + Y^10 + 6*Y^7 + Y^6 + 6*Y^5 + Y^4 + 6*Y^3 + 2*Y^2 + 4*Y + 4,
    -T^56 + 1/7*T^55 + 73/49*T^54 + 52/343*T^53 - 1611/2401*T^52 + 360/2401*T^51 - 
        1079/2401*T^50 + 331/2401*T^49 + 1192/2401*T^48 - 2089/2401*T^47 - 
        626/2401*T^46 + 912/2401*T^45 - 473/2401*T^44 + 286/2401*T^43 + 
        1571/2401*T^42 - 239/2401*T^41 - 135/343*T^40 - 167/2401*T^39 + 
        368/2401*T^38 + 839/2401*T^37 + 1431/2401*T^36 - 1758/2401*T^35 - 
        2755/2401*T^34 + 228/343*T^33 + 1861/2401*T^32 - 698/2401*T^31 - 
        592/2401*T^30 - 1019/2401*T^29 + 1019/2401*T^27 + 592/2401*T^26 + 
        698/2401*T^25 - 1861/2401*T^24 - 228/343*T^23 + 2755/2401*T^22 + 
        1758/2401*T^21 - 1431/2401*T^20 - 839/2401*T^19 - 368/2401*T^18 + 
        167/2401*T^17 + 135/343*T^16 + 239/2401*T^15 - 1571/2401*T^14 - 
        286/2401*T^13 + 473/2401*T^12 - 912/2401*T^11 + 626/2401*T^10 + 
        2089/2401*T^9 - 1192/2401*T^8 - 331/2401*T^7 + 1079/2401*T^6 - 360/2401*T^5 
        + 1611/2401*T^4 - 52/343*T^3 - 73/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 6*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 + 3*X*Y^7 + 
        4*X*Y^6 + 5*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 3*X*Y + 2*X + 6*Y^30 + Y^29 + Y^27 +
        3*Y^26 + 6*Y^25 + 2*Y^24 + 5*Y^22 + Y^20 + 3*Y^19 + 5*Y^18 + 2*Y^17 + 3*Y^16
        + 4*Y^14 + Y^13 + 6*Y^10 + Y^9 + 3*Y^8 + 6*Y^7 + 5*Y^6 + 3*Y^5 + 3*Y^4 + 
        6*Y^3 + 4*Y^2 + 2*Y + 1,
    -T^56 - 20/7*T^55 - 153/49*T^54 - 249/343*T^53 + 5864/2401*T^52 + 9088/2401*T^51
        + 5778/2401*T^50 - 1957/2401*T^49 - 8451/2401*T^48 - 1089/343*T^47 + 
        3/49*T^46 + 1153/343*T^45 + 9893/2401*T^44 + 5112/2401*T^43 - 2647/2401*T^42
        - 8217/2401*T^41 - 6740/2401*T^40 + 164/2401*T^39 + 5840/2401*T^38 + 
        6436/2401*T^37 + 2605/2401*T^36 - 2473/2401*T^35 - 5081/2401*T^34 - 
        3842/2401*T^33 - 95/343*T^32 + 2626/2401*T^31 + 5104/2401*T^30 + 
        4544/2401*T^29 - 4544/2401*T^27 - 5104/2401*T^26 - 2626/2401*T^25 + 
        95/343*T^24 + 3842/2401*T^23 + 5081/2401*T^22 + 2473/2401*T^21 - 
        2605/2401*T^20 - 6436/2401*T^19 - 5840/2401*T^18 - 164/2401*T^17 + 
        6740/2401*T^16 + 8217/2401*T^15 + 2647/2401*T^14 - 5112/2401*T^13 - 
        9893/2401*T^12 - 1153/343*T^11 - 3/49*T^10 + 1089/343*T^9 + 8451/2401*T^8 + 
        1957/2401*T^7 - 5778/2401*T^6 - 9088/2401*T^5 - 5864/2401*T^4 + 249/343*T^3 
        + 153/49*T^2 + 20/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^12 + X*Y^11 + 4*X*Y^10 + X*Y^9 + 6*X*Y^8 + 5*X*Y^5 + 
        5*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 3*X*Y + 5*X + 2*Y^30 + 4*Y^29 + Y^28 + 6*Y^27 
        + Y^25 + 5*Y^24 + 2*Y^23 + 4*Y^20 + 3*Y^18 + Y^17 + 4*Y^16 + 4*Y^14 + 5*Y^13
        + 3*Y^12 + 5*Y^11 + 5*Y^10 + 6*Y^9 + 5*Y^8 + 4*Y^7 + Y^6 + 3*Y^5 + 5*Y^4 + 
        Y^3 + 5*Y^2 + 2*Y + 3,
    -T^56 - 13/7*T^55 - 16/49*T^54 + 696/343*T^53 + 852/343*T^52 + 76/49*T^51 - 
        423/2401*T^50 - 5296/2401*T^49 - 6417/2401*T^48 - 2609/2401*T^47 + 
        320/343*T^46 + 4653/2401*T^45 + 3128/2401*T^44 - 1061/2401*T^43 - 
        3524/2401*T^42 - 1948/2401*T^41 + 1343/2401*T^40 + 537/343*T^39 + 
        4208/2401*T^38 + 1720/2401*T^37 - 2683/2401*T^36 - 5255/2401*T^35 - 
        4240/2401*T^34 - 1269/2401*T^33 + 2099/2401*T^32 + 4266/2401*T^31 + 
        3771/2401*T^30 + 1716/2401*T^29 - 1716/2401*T^27 - 3771/2401*T^26 - 
        4266/2401*T^25 - 2099/2401*T^24 + 1269/2401*T^23 + 4240/2401*T^22 + 
        5255/2401*T^21 + 2683/2401*T^20 - 1720/2401*T^19 - 4208/2401*T^18 - 
        537/343*T^17 - 1343/2401*T^16 + 1948/2401*T^15 + 3524/2401*T^14 + 
        1061/2401*T^13 - 3128/2401*T^12 - 4653/2401*T^11 - 320/343*T^10 + 
        2609/2401*T^9 + 6417/2401*T^8 + 5296/2401*T^7 + 423/2401*T^6 - 76/49*T^5 - 
        852/343*T^4 - 696/343*T^3 + 16/49*T^2 + 13/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 5*X*Y^10 + 4*X*Y^9 + 3*X*Y^7 +
        2*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + X*Y^3 + X*Y^2 + 3*X*Y + X + 6*Y^30 + Y^29 + 
        6*Y^28 + 4*Y^27 + Y^26 + 6*Y^25 + Y^24 + 6*Y^23 + Y^22 + 3*Y^21 + 3*Y^20 + 
        Y^19 + 3*Y^18 + 5*Y^17 + 4*Y^15 + 4*Y^14 + Y^13 + 4*Y^12 + 2*Y^11 + 6*Y^10 +
        3*Y^9 + 5*Y^8 + 2*Y^7 + 4*Y^6 + 4*Y^5 + 2*Y^4 + 4*Y^3 + 5*Y^2 + 5*Y + 4,
    T^56 - 15/7*T^55 + 142/49*T^54 - 1030/343*T^53 + 3263/2401*T^52 + 2595/2401*T^51
        - 7974/2401*T^50 + 1562/343*T^49 - 8641/2401*T^48 + 3146/2401*T^47 + 
        3305/2401*T^46 - 8079/2401*T^45 + 7204/2401*T^44 - 2524/2401*T^43 - 
        3468/2401*T^42 + 1263/343*T^41 - 9152/2401*T^40 + 4653/2401*T^39 + 
        2101/2401*T^38 - 8950/2401*T^37 + 10631/2401*T^36 - 6432/2401*T^35 - 
        181/343*T^34 + 8741/2401*T^33 - 11325/2401*T^32 + 1077/343*T^31 + 
        65/343*T^30 - 8334/2401*T^29 + 11724/2401*T^28 - 8334/2401*T^27 + 
        65/343*T^26 + 1077/343*T^25 - 11325/2401*T^24 + 8741/2401*T^23 - 
        181/343*T^22 - 6432/2401*T^21 + 10631/2401*T^20 - 8950/2401*T^19 + 
        2101/2401*T^18 + 4653/2401*T^17 - 9152/2401*T^16 + 1263/343*T^15 - 
        3468/2401*T^14 - 2524/2401*T^13 + 7204/2401*T^12 - 8079/2401*T^11 + 
        3305/2401*T^10 + 3146/2401*T^9 - 8641/2401*T^8 + 1562/343*T^7 - 
        7974/2401*T^6 + 2595/2401*T^5 + 3263/2401*T^4 - 1030/343*T^3 + 142/49*T^2 - 
        15/7*T + 1
*], [*
    X^3 + 2*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 2*X*Y^8 + 4*X*Y^6 + 4*X*Y^3 + 
        X*Y^2 + 3*X + 6*Y^30 + 3*Y^29 + 2*Y^28 + 5*Y^27 + 2*Y^26 + 5*Y^25 + 5*Y^24 +
        5*Y^23 + 5*Y^22 + 2*Y^20 + 2*Y^19 + Y^18 + 4*Y^17 + 3*Y^16 + 5*Y^15 + Y^14 +
        3*Y^13 + 5*Y^11 + 4*Y^8 + 5*Y^7 + 4*Y^6 + 3*Y^5 + 6*Y^4 + Y^3 + 5*Y^2 + 6*Y 
        + 1,
    -T^56 + 2/7*T^55 + 12/49*T^54 - 50/343*T^53 + 871/2401*T^52 + 1123/2401*T^51 - 
        505/2401*T^50 - 159/343*T^49 + 642/2401*T^48 + 1494/2401*T^47 - 
        1135/2401*T^46 - 159/2401*T^45 + 591/2401*T^44 - 1410/2401*T^43 - 
        51/343*T^42 + 1303/2401*T^41 + 144/2401*T^40 - 678/2401*T^39 + 422/2401*T^38
        + 318/2401*T^37 - 1765/2401*T^36 + 222/2401*T^35 + 1104/2401*T^34 + 
        26/343*T^33 - 144/2401*T^32 + 30/49*T^31 + 680/2401*T^30 - 1264/2401*T^29 + 
        1264/2401*T^27 - 680/2401*T^26 - 30/49*T^25 + 144/2401*T^24 - 26/343*T^23 - 
        1104/2401*T^22 - 222/2401*T^21 + 1765/2401*T^20 - 318/2401*T^19 - 
        422/2401*T^18 + 678/2401*T^17 - 144/2401*T^16 - 1303/2401*T^15 + 51/343*T^14
        + 1410/2401*T^13 - 591/2401*T^12 + 159/2401*T^11 + 1135/2401*T^10 - 
        1494/2401*T^9 - 642/2401*T^8 + 159/343*T^7 + 505/2401*T^6 - 1123/2401*T^5 - 
        871/2401*T^4 + 50/343*T^3 - 12/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 5*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 +
        5*X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 2*X + 6*Y^30 + 
        5*Y^29 + 5*Y^28 + 2*Y^27 + 4*Y^26 + 4*Y^25 + 6*Y^24 + 3*Y^23 + 4*Y^21 + 
        2*Y^19 + 4*Y^18 + 4*Y^16 + 5*Y^15 + 5*Y^14 + 3*Y^13 + 4*Y^12 + 5*Y^11 + 
        3*Y^10 + 3*Y^9 + 3*Y^8 + 6*Y^7 + 4*Y^6 + 2*Y^5 + 2*Y^4 + 4*Y^3 + Y^2 + 6*Y +
        4,
    T^56 - 5/7*T^55 + 5/7*T^54 - 68/343*T^53 - 928/2401*T^52 + 2782/2401*T^51 - 
        3851/2401*T^50 + 2259/2401*T^49 - 584/2401*T^48 - 2907/2401*T^47 + 
        4213/2401*T^46 - 4066/2401*T^45 + 52/2401*T^44 + 61/49*T^43 - 824/343*T^42 +
        6578/2401*T^41 - 4416/2401*T^40 - 939/2401*T^39 + 4835/2401*T^38 - 
        7194/2401*T^37 + 5637/2401*T^36 - 1595/2401*T^35 - 3492/2401*T^34 + 
        6929/2401*T^33 - 6191/2401*T^32 + 3558/2401*T^31 + 1923/2401*T^30 - 
        6303/2401*T^29 + 9333/2401*T^28 - 6303/2401*T^27 + 1923/2401*T^26 + 
        3558/2401*T^25 - 6191/2401*T^24 + 6929/2401*T^23 - 3492/2401*T^22 - 
        1595/2401*T^21 + 5637/2401*T^20 - 7194/2401*T^19 + 4835/2401*T^18 - 
        939/2401*T^17 - 4416/2401*T^16 + 6578/2401*T^15 - 824/343*T^14 + 61/49*T^13 
        + 52/2401*T^12 - 4066/2401*T^11 + 4213/2401*T^10 - 2907/2401*T^9 - 
        584/2401*T^8 + 2259/2401*T^7 - 3851/2401*T^6 + 2782/2401*T^5 - 928/2401*T^4 
        - 68/343*T^3 + 5/7*T^2 - 5/7*T + 1
*], [*
    X^3 + 3*X*Y^13 + 5*X*Y^12 + 3*X*Y^10 + 5*X*Y^9 + X*Y^8 + 2*X*Y^5 + 2*X*Y^4 + 
        6*X*Y^3 + X*Y^2 + 5*X*Y + 2*Y^30 + 4*Y^28 + 4*Y^27 + 6*Y^26 + 6*Y^25 + Y^24 
        + 6*Y^23 + 5*Y^22 + 2*Y^21 + 4*Y^20 + Y^19 + 5*Y^18 + 4*Y^17 + 2*Y^16 + Y^15
        + 5*Y^14 + 3*Y^13 + 5*Y^12 + 3*Y^11 + 6*Y^10 + Y^8 + 6*Y^7 + 4*Y^5 + 3*Y^3 +
        4*Y^2 + 5*Y + 6,
    T^56 + 9/7*T^55 + 50/49*T^54 + 251/343*T^53 + 370/343*T^52 + 2536/2401*T^51 + 
        916/2401*T^50 - 86/2401*T^49 - 333/2401*T^48 - 388/2401*T^47 - 
        2810/2401*T^46 - 4981/2401*T^45 - 687/343*T^44 - 2692/2401*T^43 - 
        2868/2401*T^42 - 4253/2401*T^41 - 492/343*T^40 - 2518/2401*T^39 - 
        2152/2401*T^38 - 2907/2401*T^37 - 1151/2401*T^36 + 694/2401*T^35 + 
        1746/2401*T^34 + 1394/2401*T^33 + 1503/2401*T^32 + 3037/2401*T^31 + 
        4364/2401*T^30 + 4885/2401*T^29 + 4260/2401*T^28 + 4885/2401*T^27 + 
        4364/2401*T^26 + 3037/2401*T^25 + 1503/2401*T^24 + 1394/2401*T^23 + 
        1746/2401*T^22 + 694/2401*T^21 - 1151/2401*T^20 - 2907/2401*T^19 - 
        2152/2401*T^18 - 2518/2401*T^17 - 492/343*T^16 - 4253/2401*T^15 - 
        2868/2401*T^14 - 2692/2401*T^13 - 687/343*T^12 - 4981/2401*T^11 - 
        2810/2401*T^10 - 388/2401*T^9 - 333/2401*T^8 - 86/2401*T^7 + 916/2401*T^6 + 
        2536/2401*T^5 + 370/343*T^4 + 251/343*T^3 + 50/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 5*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 + 
        6*X*Y^7 + X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 6*X*Y^2 + X*Y + X + 3*Y^30 + 2*Y^29 + 
        Y^28 + 2*Y^27 + 6*Y^26 + 2*Y^25 + Y^24 + 5*Y^23 + 5*Y^22 + 4*Y^21 + Y^20 + 
        5*Y^19 + Y^18 + Y^17 + Y^16 + 3*Y^15 + Y^14 + Y^13 + 4*Y^12 + 5*Y^10 + 3*Y^8
        + Y^7 + 6*Y^6 + 6*Y^5 + 5*Y^4 + 3*Y^3 + Y,
    T^56 - 1/7*T^55 - 50/49*T^54 + 9/49*T^53 + 216/2401*T^52 - 494/2401*T^51 + 
        1067/2401*T^50 + 1551/2401*T^49 - 242/343*T^48 - 1415/2401*T^47 + 
        1027/2401*T^46 + 510/2401*T^45 - 86/2401*T^44 - 290/2401*T^43 - 
        398/2401*T^42 + 256/2401*T^41 - 590/2401*T^40 - 3/2401*T^39 + 964/2401*T^38 
        - 1202/2401*T^37 - 1352/2401*T^36 + 1263/2401*T^35 + 219/343*T^34 - 
        988/2401*T^33 + 74/2401*T^32 + 713/2401*T^31 - 1181/2401*T^30 + 1/2401*T^29 
        + 954/2401*T^28 + 1/2401*T^27 - 1181/2401*T^26 + 713/2401*T^25 + 
        74/2401*T^24 - 988/2401*T^23 + 219/343*T^22 + 1263/2401*T^21 - 
        1352/2401*T^20 - 1202/2401*T^19 + 964/2401*T^18 - 3/2401*T^17 - 
        590/2401*T^16 + 256/2401*T^15 - 398/2401*T^14 - 290/2401*T^13 - 86/2401*T^12
        + 510/2401*T^11 + 1027/2401*T^10 - 1415/2401*T^9 - 242/343*T^8 + 
        1551/2401*T^7 + 1067/2401*T^6 - 494/2401*T^5 + 216/2401*T^4 + 9/49*T^3 - 
        50/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 4*X*Y^9 + 6*X*Y^8 + 
        6*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + X*Y^2 + X + 3*Y^30 + 
        5*Y^29 + 5*Y^28 + 5*Y^27 + 4*Y^26 + 4*Y^25 + 5*Y^24 + 2*Y^22 + 6*Y^21 + 
        2*Y^20 + 5*Y^19 + 6*Y^18 + 5*Y^17 + 2*Y^16 + 5*Y^15 + 6*Y^14 + 6*Y^12 + 
        2*Y^11 + 2*Y^9 + Y^8 + 3*Y^7 + 6*Y^6 + Y^5 + 2*Y^2 + 4*Y,
    -T^56 - 1/7*T^55 + 5/7*T^54 + 229/343*T^53 - 835/2401*T^52 - 38/343*T^51 + 
        85/2401*T^50 + 281/2401*T^49 - 40/2401*T^48 - 876/2401*T^47 - 279/2401*T^46 
        + 178/2401*T^45 + 813/2401*T^44 - 151/2401*T^43 + 579/2401*T^42 - 
        352/2401*T^41 + 351/2401*T^40 + 723/2401*T^39 + 36/2401*T^38 - 
        2076/2401*T^37 - 391/2401*T^36 + 1751/2401*T^35 + 768/2401*T^34 - 
        256/2401*T^33 - 528/2401*T^32 + 153/2401*T^31 - 45/2401*T^30 + 171/2401*T^29
        - 171/2401*T^27 + 45/2401*T^26 - 153/2401*T^25 + 528/2401*T^24 + 
        256/2401*T^23 - 768/2401*T^22 - 1751/2401*T^21 + 391/2401*T^20 + 
        2076/2401*T^19 - 36/2401*T^18 - 723/2401*T^17 - 351/2401*T^16 + 
        352/2401*T^15 - 579/2401*T^14 + 151/2401*T^13 - 813/2401*T^12 - 
        178/2401*T^11 + 279/2401*T^10 + 876/2401*T^9 + 40/2401*T^8 - 281/2401*T^7 - 
        85/2401*T^6 + 38/343*T^5 + 835/2401*T^4 - 229/343*T^3 - 5/7*T^2 + 1/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^10 + 4*X*Y^9 + X*Y^8 + 
        4*X*Y^6 + 4*X*Y^5 + 4*X*Y^3 + 6*X*Y^2 + 2*X*Y + 5*X + 5*Y^30 + Y^29 + 3*Y^28
        + 6*Y^26 + 6*Y^25 + 4*Y^24 + 2*Y^23 + 2*Y^21 + 3*Y^19 + 4*Y^18 + Y^17 + 
        4*Y^16 + 4*Y^14 + 5*Y^13 + 5*Y^12 + 2*Y^11 + Y^9 + 2*Y^8 + Y^7 + 2*Y^6 + 
        2*Y^5 + 3*Y^4 + 5*Y^3 + 6*Y^2 + 3*Y + 6,
    -T^56 - 4/7*T^55 + 34/49*T^54 - 101/343*T^53 - 3447/2401*T^52 - 508/2401*T^51 + 
        3845/2401*T^50 + 176/2401*T^49 - 3606/2401*T^48 - 10/343*T^47 + 
        4688/2401*T^46 + 12/49*T^45 - 4045/2401*T^44 + 618/2401*T^43 + 
        3018/2401*T^42 - 544/2401*T^41 - 3993/2401*T^40 + 436/2401*T^39 + 
        2005/2401*T^38 - 2543/2401*T^37 - 2251/2401*T^36 + 1872/2401*T^35 + 
        1766/2401*T^34 - 2683/2401*T^33 - 607/2401*T^32 + 3095/2401*T^31 + 
        1060/2401*T^30 - 3726/2401*T^29 + 3726/2401*T^27 - 1060/2401*T^26 - 
        3095/2401*T^25 + 607/2401*T^24 + 2683/2401*T^23 - 1766/2401*T^22 - 
        1872/2401*T^21 + 2251/2401*T^20 + 2543/2401*T^19 - 2005/2401*T^18 - 
        436/2401*T^17 + 3993/2401*T^16 + 544/2401*T^15 - 3018/2401*T^14 - 
        618/2401*T^13 + 4045/2401*T^12 - 12/49*T^11 - 4688/2401*T^10 + 10/343*T^9 + 
        3606/2401*T^8 - 176/2401*T^7 - 3845/2401*T^6 + 508/2401*T^5 + 3447/2401*T^4 
        + 101/343*T^3 - 34/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 5*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 +
        X*Y^7 + 4*X*Y^6 + 5*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 2*X*Y + 5*X + 5*Y^30 + 
        4*Y^29 + 5*Y^28 + 2*Y^27 + Y^25 + Y^23 + Y^21 + 4*Y^20 + 2*Y^19 + 4*Y^18 + 
        3*Y^17 + 5*Y^16 + 2*Y^15 + 6*Y^14 + 2*Y^13 + 5*Y^12 + 3*Y^11 + 3*Y^10 + 
        4*Y^8 + 4*Y^6 + 5*Y^5 + 2*Y^4 + 3*Y^3 + 2*Y,
    T^56 - 4/7*T^55 + 67/49*T^54 - 306/343*T^53 + 2411/2401*T^52 - 22/2401*T^51 + 
        1301/2401*T^50 - 36/343*T^49 - 317/2401*T^48 + 208/2401*T^47 - 771/2401*T^46
        + 2204/2401*T^45 - 2864/2401*T^44 + 2621/2401*T^43 - 4058/2401*T^42 + 
        4191/2401*T^41 - 4027/2401*T^40 + 3372/2401*T^39 - 4050/2401*T^38 + 
        1566/2401*T^37 - 1595/2401*T^36 + 436/2401*T^35 + 33/343*T^34 - 37/49*T^33 +
        1994/2401*T^32 - 73/49*T^31 + 650/343*T^30 - 5420/2401*T^29 + 5423/2401*T^28
        - 5420/2401*T^27 + 650/343*T^26 - 73/49*T^25 + 1994/2401*T^24 - 37/49*T^23 +
        33/343*T^22 + 436/2401*T^21 - 1595/2401*T^20 + 1566/2401*T^19 - 
        4050/2401*T^18 + 3372/2401*T^17 - 4027/2401*T^16 + 4191/2401*T^15 - 
        4058/2401*T^14 + 2621/2401*T^13 - 2864/2401*T^12 + 2204/2401*T^11 - 
        771/2401*T^10 + 208/2401*T^9 - 317/2401*T^8 - 36/343*T^7 + 1301/2401*T^6 - 
        22/2401*T^5 + 2411/2401*T^4 - 306/343*T^3 + 67/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 
        + 4*X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 
        6*X*Y + 3*X + 4*Y^30 + Y^29 + 5*Y^28 + 2*Y^27 + 4*Y^24 + 2*Y^22 + 4*Y^21 + 
        Y^20 + 5*Y^19 + 4*Y^18 + 3*Y^17 + 5*Y^16 + Y^15 + 4*Y^14 + 4*Y^13 + 3*Y^12 +
        Y^11 + 4*Y^10 + Y^9 + 6*Y^8 + 5*Y^7 + 6*Y^6 + Y^5 + 5*Y^4 + Y^3 + 2*Y^2 + 
        3*Y + 3,
    -T^56 - 12/7*T^55 - 61/49*T^54 - 170/343*T^53 - 19/49*T^52 - 2159/2401*T^51 - 
        2979/2401*T^50 - 3401/2401*T^49 - 6/7*T^48 + 942/2401*T^47 + 482/343*T^46 + 
        2113/2401*T^45 + 404/2401*T^44 + 941/2401*T^43 + 1963/2401*T^42 + 
        2588/2401*T^41 + 3421/2401*T^40 + 3807/2401*T^39 + 2395/2401*T^38 + 
        949/2401*T^37 + 1146/2401*T^36 + 2790/2401*T^35 + 3529/2401*T^34 + 
        2542/2401*T^33 + 1884/2401*T^32 + 36/49*T^31 + 1212/2401*T^30 + 125/343*T^29
        - 125/343*T^27 - 1212/2401*T^26 - 36/49*T^25 - 1884/2401*T^24 - 
        2542/2401*T^23 - 3529/2401*T^22 - 2790/2401*T^21 - 1146/2401*T^20 - 
        949/2401*T^19 - 2395/2401*T^18 - 3807/2401*T^17 - 3421/2401*T^16 - 
        2588/2401*T^15 - 1963/2401*T^14 - 941/2401*T^13 - 404/2401*T^12 - 
        2113/2401*T^11 - 482/343*T^10 - 942/2401*T^9 + 6/7*T^8 + 3401/2401*T^7 + 
        2979/2401*T^6 + 2159/2401*T^5 + 19/49*T^4 + 170/343*T^3 + 61/49*T^2 + 12/7*T
        + 1
*], [*
    X^3 + 2*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + X*Y^8 + 6*X*Y^7 + 
        5*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 2*X*Y + 6*X + 4*Y^30 + 
        2*Y^29 + 6*Y^28 + Y^25 + 5*Y^24 + 4*Y^23 + 3*Y^22 + 5*Y^20 + 6*Y^19 + 5*Y^18
        + 2*Y^17 + 2*Y^16 + 6*Y^15 + 4*Y^14 + 2*Y^13 + 4*Y^10 + 3*Y^9 + Y^8 + 5*Y^4 
        + 6*Y^3 + 2*Y^2 + Y + 6,
    -T^56 - 19/7*T^55 - 129/49*T^54 - 283/343*T^53 + 1328/2401*T^52 + 3931/2401*T^51
        + 956/343*T^50 + 4546/2401*T^49 - 1586/2401*T^48 - 4086/2401*T^47 - 
        3656/2401*T^46 - 4113/2401*T^45 - 1628/2401*T^44 + 613/343*T^43 + 
        5598/2401*T^42 + 2409/2401*T^41 + 702/2401*T^40 - 80/343*T^39 - 
        1416/2401*T^38 + 1299/2401*T^37 + 4663/2401*T^36 + 3978/2401*T^35 + 
        2425/2401*T^34 + 2530/2401*T^33 + 106/343*T^32 - 2462/2401*T^31 - 
        400/343*T^30 - 750/2401*T^29 + 750/2401*T^27 + 400/343*T^26 + 2462/2401*T^25
        - 106/343*T^24 - 2530/2401*T^23 - 2425/2401*T^22 - 3978/2401*T^21 - 
        4663/2401*T^20 - 1299/2401*T^19 + 1416/2401*T^18 + 80/343*T^17 - 
        702/2401*T^16 - 2409/2401*T^15 - 5598/2401*T^14 - 613/343*T^13 + 
        1628/2401*T^12 + 4113/2401*T^11 + 3656/2401*T^10 + 4086/2401*T^9 + 
        1586/2401*T^8 - 4546/2401*T^7 - 956/343*T^6 - 3931/2401*T^5 - 1328/2401*T^4 
        + 283/343*T^3 + 129/49*T^2 + 19/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^12 + X*Y^10 + 5*X*Y^9 + 5*X*Y^7 + 4*X*Y^3 + 2*X*Y^2 + 
        6*X*Y + 4*X + 6*Y^30 + 2*Y^29 + 4*Y^28 + 3*Y^27 + Y^26 + 4*Y^25 + 4*Y^24 + 
        Y^23 + 5*Y^21 + Y^20 + Y^19 + 2*Y^17 + Y^16 + 4*Y^15 + 5*Y^14 + 5*Y^13 + 
        5*Y^12 + 5*Y^11 + 4*Y^9 + 6*Y^8 + Y^7 + 2*Y^6 + 5*Y^5 + Y^4 + 4*Y^3 + 4*Y^2 
        + 2*Y + 3,
    T^56 + 2/7*T^55 - 12/49*T^54 - 17/49*T^53 + 454/2401*T^52 - 796/2401*T^51 - 
        1626/2401*T^50 - 556/2401*T^49 + 290/2401*T^48 + 2/343*T^47 - 211/2401*T^46 
        + 22/2401*T^45 + 1037/2401*T^44 + 1270/2401*T^43 + 831/2401*T^42 - 
        939/2401*T^41 - 465/2401*T^40 + 58/2401*T^39 - 597/2401*T^38 - 
        1175/2401*T^37 - 736/2401*T^36 + 1642/2401*T^35 - 130/2401*T^34 + 
        17/2401*T^33 - 94/2401*T^32 + 649/2401*T^31 - 500/2401*T^30 - 187/2401*T^29 
        + 188/2401*T^28 - 187/2401*T^27 - 500/2401*T^26 + 649/2401*T^25 - 
        94/2401*T^24 + 17/2401*T^23 - 130/2401*T^22 + 1642/2401*T^21 - 736/2401*T^20
        - 1175/2401*T^19 - 597/2401*T^18 + 58/2401*T^17 - 465/2401*T^16 - 
        939/2401*T^15 + 831/2401*T^14 + 1270/2401*T^13 + 1037/2401*T^12 + 
        22/2401*T^11 - 211/2401*T^10 + 2/343*T^9 + 290/2401*T^8 - 556/2401*T^7 - 
        1626/2401*T^6 - 796/2401*T^5 + 454/2401*T^4 - 17/49*T^3 - 12/49*T^2 + 2/7*T 
        + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + X*Y^10 + 6*X*Y^9 + 
        X*Y^8 + 3*X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 2*X*Y + 
        X + Y^30 + 3*Y^29 + 3*Y^28 + 2*Y^27 + 3*Y^26 + 2*Y^25 + 5*Y^24 + 5*Y^21 + 
        2*Y^20 + Y^19 + 3*Y^18 + 5*Y^17 + 4*Y^15 + 3*Y^14 + 3*Y^12 + 6*Y^11 + 6*Y^10
        + Y^9 + 6*Y^8 + 2*Y^7 + 4*Y^6 + 6*Y^5 + 4*Y^2 + Y + 3,
    -T^56 - 4/7*T^55 + 6/7*T^54 + 314/343*T^53 + 2208/2401*T^52 + 26/2401*T^51 - 
        549/2401*T^50 - 377/2401*T^49 - 1670/2401*T^48 - 132/343*T^47 - 
        1390/2401*T^46 + 349/2401*T^45 + 1947/2401*T^44 + 109/343*T^43 - 
        635/2401*T^42 - 705/2401*T^41 + 264/2401*T^40 + 611/2401*T^39 + 
        1201/2401*T^38 - 123/343*T^37 - 1233/2401*T^36 + 303/2401*T^35 - 
        139/2401*T^34 - 334/2401*T^33 - 998/2401*T^32 + 471/2401*T^31 + 
        2097/2401*T^30 + 929/2401*T^29 - 929/2401*T^27 - 2097/2401*T^26 - 
        471/2401*T^25 + 998/2401*T^24 + 334/2401*T^23 + 139/2401*T^22 - 
        303/2401*T^21 + 1233/2401*T^20 + 123/343*T^19 - 1201/2401*T^18 - 
        611/2401*T^17 - 264/2401*T^16 + 705/2401*T^15 + 635/2401*T^14 - 109/343*T^13
        - 1947/2401*T^12 - 349/2401*T^11 + 1390/2401*T^10 + 132/343*T^9 + 
        1670/2401*T^8 + 377/2401*T^7 + 549/2401*T^6 - 26/2401*T^5 - 2208/2401*T^4 - 
        314/343*T^3 - 6/7*T^2 + 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 
        4*X*Y^8 + X*Y^7 + 5*X*Y^6 + X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 5*X*Y + 
        6*X + 3*Y^30 + 4*Y^29 + 4*Y^28 + 5*Y^27 + 5*Y^26 + 2*Y^23 + 6*Y^22 + Y^21 + 
        5*Y^19 + 2*Y^17 + Y^16 + 5*Y^15 + 2*Y^14 + 3*Y^13 + 5*Y^11 + 6*Y^10 + Y^9 + 
        3*Y^8 + 5*Y^7 + 6*Y^6 + 2*Y^5 + 4*Y^3,
    T^56 - 11/7*T^55 + 69/49*T^54 - 440/343*T^53 + 362/343*T^52 - 2031/2401*T^51 - 
        20/2401*T^50 + 46/343*T^49 - 765/2401*T^48 + 1826/2401*T^47 - 429/343*T^46 +
        3753/2401*T^45 - 2215/2401*T^44 + 1357/2401*T^43 + 270/2401*T^42 - 
        227/2401*T^41 - 976/2401*T^40 + 1650/2401*T^39 - 2087/2401*T^38 + 
        1601/2401*T^37 - 2288/2401*T^36 + 1487/2401*T^35 - 1010/2401*T^34 + 
        68/343*T^33 + 293/2401*T^32 - 1356/2401*T^31 + 3151/2401*T^30 - 
        3744/2401*T^29 + 4246/2401*T^28 - 3744/2401*T^27 + 3151/2401*T^26 - 
        1356/2401*T^25 + 293/2401*T^24 + 68/343*T^23 - 1010/2401*T^22 + 
        1487/2401*T^21 - 2288/2401*T^20 + 1601/2401*T^19 - 2087/2401*T^18 + 
        1650/2401*T^17 - 976/2401*T^16 - 227/2401*T^15 + 270/2401*T^14 + 
        1357/2401*T^13 - 2215/2401*T^12 + 3753/2401*T^11 - 429/343*T^10 + 
        1826/2401*T^9 - 765/2401*T^8 + 46/343*T^7 - 20/2401*T^6 - 2031/2401*T^5 + 
        362/343*T^4 - 440/343*T^3 + 69/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 6*X*Y^13 + 3*X*Y^11 + 2*X*Y^10 + 5*X*Y^8 + 5*X*Y^6 + 
        3*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 6*X*Y + 2*X + Y^30 + 2*Y^29 + 4*Y^28 + Y^27 + 
        Y^26 + Y^25 + Y^24 + 6*Y^23 + 6*Y^21 + 6*Y^20 + 4*Y^19 + Y^18 + 4*Y^17 + 
        5*Y^16 + 3*Y^15 + 5*Y^14 + 5*Y^12 + 5*Y^10 + 6*Y^9 + 2*Y^8 + Y^6 + Y^5 + 
        5*Y^3 + 2*Y^2 + 4*Y,
    T^56 - 3/7*T^55 - 6/49*T^54 - 2/49*T^53 + 456/2401*T^52 + 1551/2401*T^51 + 
        290/2401*T^50 + 673/2401*T^49 - 739/2401*T^48 - 878/2401*T^47 + 
        1622/2401*T^46 + 711/2401*T^45 + 522/2401*T^44 + 282/2401*T^43 - 
        281/343*T^42 + 1115/2401*T^41 - 439/2401*T^40 + 255/343*T^39 + 37/2401*T^38 
        - 954/2401*T^37 - 139/343*T^36 - 856/2401*T^35 + 911/2401*T^34 + 
        123/2401*T^33 - 15/343*T^32 - 1194/2401*T^31 - 1615/2401*T^30 - 
        559/2401*T^29 + 1251/2401*T^28 - 559/2401*T^27 - 1615/2401*T^26 - 
        1194/2401*T^25 - 15/343*T^24 + 123/2401*T^23 + 911/2401*T^22 - 856/2401*T^21
        - 139/343*T^20 - 954/2401*T^19 + 37/2401*T^18 + 255/343*T^17 - 439/2401*T^16
        + 1115/2401*T^15 - 281/343*T^14 + 282/2401*T^13 + 522/2401*T^12 + 
        711/2401*T^11 + 1622/2401*T^10 - 878/2401*T^9 - 739/2401*T^8 + 673/2401*T^7 
        + 290/2401*T^6 + 1551/2401*T^5 + 456/2401*T^4 - 2/49*T^3 - 6/49*T^2 - 3/7*T 
        + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + X*Y^13 + X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 
        4*X*Y^8 + 4*X*Y^7 + 6*X*Y^6 + X*Y^5 + X*Y^4 + 4*X*Y^3 + 4*X*Y + 4*X + 6*Y^30
        + 4*Y^28 + 3*Y^27 + Y^26 + Y^24 + 2*Y^23 + 4*Y^22 + 5*Y^21 + 5*Y^20 + 5*Y^19
        + 4*Y^18 + 3*Y^17 + 2*Y^16 + 6*Y^15 + Y^14 + 4*Y^13 + Y^12 + Y^11 + 4*Y^10 +
        Y^9 + 5*Y^8 + 2*Y^7 + 2*Y^5 + 5*Y^4 + 5*Y^3 + 2*Y^2 + 6*Y + 1,
    -T^56 + 4/7*T^55 + 33/49*T^54 - 83/343*T^53 - 127/343*T^52 - 1108/2401*T^51 + 
        636/2401*T^50 + 2038/2401*T^49 - 365/2401*T^48 - 347/343*T^47 + 
        2109/2401*T^46 - 142/2401*T^45 - 995/2401*T^44 + 1445/2401*T^43 - 
        895/2401*T^42 + 646/2401*T^41 + 1126/2401*T^40 - 1496/2401*T^39 - 
        717/2401*T^38 + 2276/2401*T^37 - 778/2401*T^36 + 43/343*T^35 - 177/2401*T^34
        - 2369/2401*T^33 + 2444/2401*T^32 + 1636/2401*T^31 - 325/343*T^30 - 
        720/2401*T^29 + 720/2401*T^27 + 325/343*T^26 - 1636/2401*T^25 - 
        2444/2401*T^24 + 2369/2401*T^23 + 177/2401*T^22 - 43/343*T^21 + 
        778/2401*T^20 - 2276/2401*T^19 + 717/2401*T^18 + 1496/2401*T^17 - 
        1126/2401*T^16 - 646/2401*T^15 + 895/2401*T^14 - 1445/2401*T^13 + 
        995/2401*T^12 + 142/2401*T^11 - 2109/2401*T^10 + 347/343*T^9 + 365/2401*T^8 
        - 2038/2401*T^7 - 636/2401*T^6 + 1108/2401*T^5 + 127/343*T^4 + 83/343*T^3 - 
        33/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 2*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 4*X*Y^2 + 2*X*Y + 2*X + 
        5*Y^30 + Y^29 + 4*Y^28 + 6*Y^27 + 3*Y^26 + 6*Y^25 + 3*Y^24 + 2*Y^23 + 6*Y^21
        + Y^19 + Y^17 + 4*Y^15 + 2*Y^14 + 3*Y^13 + Y^12 + 6*Y^11 + 4*Y^10 + 3*Y^9 + 
        6*Y^8 + 2*Y^7 + 5*Y^6 + 5*Y^5 + 4*Y^3 + Y^2 + 2*Y,
    -T^56 - 1/7*T^55 + 59/49*T^54 + 61/49*T^53 - 393/2401*T^52 - 4016/2401*T^51 - 
        171/343*T^50 + 130/343*T^49 + 2014/2401*T^48 + 34/2401*T^47 - 760/2401*T^46 
        + 503/2401*T^45 + 416/2401*T^44 - 549/2401*T^43 - 247/343*T^42 + 
        256/2401*T^41 + 1264/2401*T^40 + 2096/2401*T^39 + 48/2401*T^38 - 
        1731/2401*T^37 - 2489/2401*T^36 - 463/2401*T^35 + 3237/2401*T^34 + 
        1584/2401*T^33 - 306/2401*T^32 - 2784/2401*T^31 - 111/2401*T^30 + 
        94/343*T^29 - 94/343*T^27 + 111/2401*T^26 + 2784/2401*T^25 + 306/2401*T^24 -
        1584/2401*T^23 - 3237/2401*T^22 + 463/2401*T^21 + 2489/2401*T^20 + 
        1731/2401*T^19 - 48/2401*T^18 - 2096/2401*T^17 - 1264/2401*T^16 - 
        256/2401*T^15 + 247/343*T^14 + 549/2401*T^13 - 416/2401*T^12 - 503/2401*T^11
        + 760/2401*T^10 - 34/2401*T^9 - 2014/2401*T^8 - 130/343*T^7 + 171/343*T^6 + 
        4016/2401*T^5 + 393/2401*T^4 - 61/49*T^3 - 59/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + X*Y^13 + 6*X*Y^12 + X*Y^10 + 4*X*Y^9 + 6*X*Y^7 + 
        2*X*Y^6 + 5*X*Y^5 + 4*X*Y + 6*X + 4*Y^30 + 3*Y^29 + 5*Y^28 + 5*Y^27 + 2*Y^26
        + 6*Y^24 + Y^23 + Y^22 + Y^21 + 5*Y^19 + 2*Y^18 + 4*Y^17 + 5*Y^15 + 2*Y^14 +
        4*Y^12 + 2*Y^10 + 4*Y^9 + Y^8 + 5*Y^5 + 2*Y^4 + Y^3 + Y^2 + 6*Y + 1,
    T^56 - 1/7*T^55 + 3/7*T^54 + 86/343*T^53 + 1019/2401*T^52 - 885/2401*T^51 - 
        125/343*T^50 - 3/49*T^49 - 1696/2401*T^48 - 127/2401*T^47 - 2141/2401*T^46 -
        127/2401*T^45 - 1313/2401*T^44 + 426/2401*T^43 - 1023/2401*T^42 - 
        402/2401*T^41 + 1328/2401*T^40 + 912/2401*T^39 + 223/343*T^38 + 
        393/2401*T^37 + 2476/2401*T^36 + 410/2401*T^35 + 1063/2401*T^34 + 
        89/2401*T^33 - 11/49*T^32 - 787/2401*T^31 - 1306/2401*T^30 - 572/2401*T^29 -
        2683/2401*T^28 - 572/2401*T^27 - 1306/2401*T^26 - 787/2401*T^25 - 11/49*T^24
        + 89/2401*T^23 + 1063/2401*T^22 + 410/2401*T^21 + 2476/2401*T^20 + 
        393/2401*T^19 + 223/343*T^18 + 912/2401*T^17 + 1328/2401*T^16 - 
        402/2401*T^15 - 1023/2401*T^14 + 426/2401*T^13 - 1313/2401*T^12 - 
        127/2401*T^11 - 2141/2401*T^10 - 127/2401*T^9 - 1696/2401*T^8 - 3/49*T^7 - 
        125/343*T^6 - 885/2401*T^5 + 1019/2401*T^4 + 86/343*T^3 + 3/7*T^2 - 1/7*T + 
        1
*], [*
    X^3 + 6*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + X*Y^10 + 2*X*Y^9 + 4*X*Y^8 + 
        3*X*Y^7 + 3*X*Y^4 + 4*X*Y^3 + X*Y^2 + 4*X*Y + 4*X + 5*Y^30 + 6*Y^29 + 2*Y^28
        + 4*Y^27 + Y^25 + 3*Y^24 + 5*Y^23 + 4*Y^22 + 2*Y^21 + 2*Y^20 + 2*Y^19 + 
        4*Y^18 + 2*Y^17 + 4*Y^16 + 6*Y^15 + 3*Y^14 + 2*Y^11 + 4*Y^10 + 3*Y^9 + 6*Y^8
        + 5*Y^6 + 5*Y^5 + 5*Y^4 + 5*Y^3 + 4*Y^2 + 4*Y,
    -T^56 - 6/7*T^55 + 55/49*T^54 + 263/343*T^53 - 1242/2401*T^52 - 198/2401*T^51 - 
        1062/2401*T^50 - 1077/2401*T^49 + 1979/2401*T^48 + 997/2401*T^47 - 
        223/2401*T^46 + 933/2401*T^45 - 566/2401*T^44 - 585/2401*T^43 + 104/343*T^42
        - 1368/2401*T^41 - 75/343*T^40 + 2229/2401*T^39 + 701/2401*T^38 - 
        599/2401*T^37 - 650/2401*T^36 - 1396/2401*T^35 + 1226/2401*T^34 + 
        2080/2401*T^33 - 1007/2401*T^32 + 549/2401*T^31 + 1270/2401*T^30 - 
        2651/2401*T^29 + 2651/2401*T^27 - 1270/2401*T^26 - 549/2401*T^25 + 
        1007/2401*T^24 - 2080/2401*T^23 - 1226/2401*T^22 + 1396/2401*T^21 + 
        650/2401*T^20 + 599/2401*T^19 - 701/2401*T^18 - 2229/2401*T^17 + 75/343*T^16
        + 1368/2401*T^15 - 104/343*T^14 + 585/2401*T^13 + 566/2401*T^12 - 
        933/2401*T^11 + 223/2401*T^10 - 997/2401*T^9 - 1979/2401*T^8 + 1077/2401*T^7
        + 1062/2401*T^6 + 198/2401*T^5 + 1242/2401*T^4 - 263/343*T^3 - 55/49*T^2 + 
        6/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 +
        3*X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + X*Y + 5*X + 5*Y^30 + 
        5*Y^29 + 2*Y^28 + 3*Y^27 + 2*Y^26 + 4*Y^25 + 2*Y^24 + Y^23 + 6*Y^22 + 3*Y^21
        + 3*Y^20 + 5*Y^19 + 3*Y^18 + 2*Y^17 + 3*Y^16 + 4*Y^15 + Y^14 + 5*Y^12 + 
        6*Y^11 + 4*Y^10 + 4*Y^9 + 6*Y^8 + 2*Y^7 + 4*Y^6 + Y^5 + 2*Y^4 + 3*Y^3 + 
        5*Y^2 + 4,
    -T^56 + T^55 - 13/49*T^54 - 278/343*T^53 + 293/2401*T^52 - 249/343*T^51 + 
        668/2401*T^50 - 20/49*T^49 - 1891/2401*T^48 - 204/343*T^47 - 769/2401*T^46 +
        1072/2401*T^45 - 400/343*T^44 - 2319/2401*T^43 + 445/2401*T^42 - 
        2253/2401*T^41 + 1116/2401*T^40 - 2104/2401*T^39 - 2830/2401*T^38 + 
        467/2401*T^37 + 794/2401*T^36 - 1277/2401*T^35 - 1746/2401*T^34 - 
        880/2401*T^33 + 45/343*T^32 + 781/2401*T^31 - 50/2401*T^30 - 2075/2401*T^29 
        + 2075/2401*T^27 + 50/2401*T^26 - 781/2401*T^25 - 45/343*T^24 + 
        880/2401*T^23 + 1746/2401*T^22 + 1277/2401*T^21 - 794/2401*T^20 - 
        467/2401*T^19 + 2830/2401*T^18 + 2104/2401*T^17 - 1116/2401*T^16 + 
        2253/2401*T^15 - 445/2401*T^14 + 2319/2401*T^13 + 400/343*T^12 - 
        1072/2401*T^11 + 769/2401*T^10 + 204/343*T^9 + 1891/2401*T^8 + 20/49*T^7 - 
        668/2401*T^6 + 249/343*T^5 - 293/2401*T^4 + 278/343*T^3 + 13/49*T^2 - T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 
        2*X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 3*X + 
        5*Y^30 + 4*Y^29 + 3*Y^27 + 5*Y^26 + 3*Y^25 + Y^24 + 3*Y^23 + Y^22 + 3*Y^21 +
        Y^20 + 3*Y^19 + 6*Y^18 + 3*Y^15 + 3*Y^14 + 6*Y^13 + Y^12 + 6*Y^11 + 2*Y^10 +
        6*Y^9 + 5*Y^8 + 5*Y^7 + 5*Y^6 + 2*Y^5 + 6*Y^4 + Y^3 + 6*Y^2 + 3*Y + 3,
    T^56 + 10/7*T^55 + 71/49*T^54 + 773/343*T^53 + 4247/2401*T^52 + 160/343*T^51 - 
        384/2401*T^50 - 3327/2401*T^49 - 4684/2401*T^48 - 4101/2401*T^47 - 
        402/343*T^46 - 389/2401*T^45 + 1313/2401*T^44 + 4020/2401*T^43 + 
        4763/2401*T^42 + 3534/2401*T^41 + 3403/2401*T^40 + 1458/2401*T^39 - 
        683/2401*T^38 - 1716/2401*T^37 - 471/343*T^36 - 312/343*T^35 - 
        1665/2401*T^34 - 1776/2401*T^33 + 37/343*T^32 + 102/343*T^31 + 764/2401*T^30
        + 1275/2401*T^29 + 162/343*T^28 + 1275/2401*T^27 + 764/2401*T^26 + 
        102/343*T^25 + 37/343*T^24 - 1776/2401*T^23 - 1665/2401*T^22 - 312/343*T^21 
        - 471/343*T^20 - 1716/2401*T^19 - 683/2401*T^18 + 1458/2401*T^17 + 
        3403/2401*T^16 + 3534/2401*T^15 + 4763/2401*T^14 + 4020/2401*T^13 + 
        1313/2401*T^12 - 389/2401*T^11 - 402/343*T^10 - 4101/2401*T^9 - 
        4684/2401*T^8 - 3327/2401*T^7 - 384/2401*T^6 + 160/343*T^5 + 4247/2401*T^4 +
        773/343*T^3 + 71/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 4*X*Y^9 
        + 6*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + X*Y^2 + 3*X*Y + 2*X + 4*Y^30 + 6*Y^29 + 
        4*Y^28 + 4*Y^27 + 4*Y^26 + 6*Y^25 + 3*Y^23 + 6*Y^22 + 4*Y^21 + 5*Y^20 + 
        6*Y^19 + 4*Y^18 + 2*Y^17 + 4*Y^15 + Y^14 + 3*Y^13 + 5*Y^11 + 5*Y^10 + 2*Y^8 
        + 5*Y^7 + 2*Y^6 + 2*Y^5 + 3*Y^4 + 5*Y^3 + 4*Y^2 + Y + 6,
    T^56 - 11/7*T^55 + 62/49*T^54 + 38/343*T^53 - 2816/2401*T^52 + 1976/2401*T^51 - 
        474/2401*T^50 + 928/2401*T^49 - 368/343*T^48 + 2609/2401*T^47 - 
        1181/2401*T^46 - 1702/2401*T^45 + 1559/2401*T^44 - 102/2401*T^43 - 
        1731/2401*T^42 + 1009/2401*T^41 - 65/343*T^40 + 752/2401*T^39 - 
        2087/2401*T^38 + 1943/2401*T^37 - 628/2401*T^36 - 155/2401*T^35 - 
        220/2401*T^34 + 52/2401*T^33 + 1861/2401*T^32 - 2640/2401*T^31 + 
        431/343*T^30 - 1178/2401*T^29 + 618/2401*T^28 - 1178/2401*T^27 + 
        431/343*T^26 - 2640/2401*T^25 + 1861/2401*T^24 + 52/2401*T^23 - 
        220/2401*T^22 - 155/2401*T^21 - 628/2401*T^20 + 1943/2401*T^19 - 
        2087/2401*T^18 + 752/2401*T^17 - 65/343*T^16 + 1009/2401*T^15 - 
        1731/2401*T^14 - 102/2401*T^13 + 1559/2401*T^12 - 1702/2401*T^11 - 
        1181/2401*T^10 + 2609/2401*T^9 - 368/343*T^8 + 928/2401*T^7 - 474/2401*T^6 +
        1976/2401*T^5 - 2816/2401*T^4 + 38/343*T^3 + 62/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 5*X*Y^8 +
        2*X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + X*Y^4 + 6*X*Y^3 + X*Y + 5*X + 4*Y^30 + 6*Y^28 
        + 4*Y^27 + Y^26 + 5*Y^25 + 4*Y^24 + 6*Y^23 + 4*Y^22 + Y^20 + 5*Y^18 + 3*Y^17
        + 3*Y^16 + 5*Y^15 + Y^13 + 3*Y^12 + 5*Y^10 + Y^9 + 4*Y^8 + 5*Y^7 + 5*Y^6 + 
        Y^5 + 5*Y^4 + Y^2 + 3*Y + 2,
    -T^56 - 5/7*T^55 - 36/49*T^54 - 50/49*T^53 - 1965/2401*T^52 - 1630/2401*T^51 - 
        30/2401*T^50 + 1408/2401*T^49 + 2183/2401*T^48 + 2526/2401*T^47 + 
        2514/2401*T^46 + 416/343*T^45 + 3597/2401*T^44 + 2385/2401*T^43 + 
        796/2401*T^42 + 396/2401*T^41 - 8/343*T^40 + 37/2401*T^39 - 1146/2401*T^38 -
        779/2401*T^37 - 1441/2401*T^36 - 879/2401*T^35 + 83/343*T^34 - 
        1200/2401*T^33 - 1671/2401*T^32 - 1231/2401*T^31 - 694/2401*T^30 + 
        46/2401*T^29 - 46/2401*T^27 + 694/2401*T^26 + 1231/2401*T^25 + 
        1671/2401*T^24 + 1200/2401*T^23 - 83/343*T^22 + 879/2401*T^21 + 
        1441/2401*T^20 + 779/2401*T^19 + 1146/2401*T^18 - 37/2401*T^17 + 8/343*T^16 
        - 396/2401*T^15 - 796/2401*T^14 - 2385/2401*T^13 - 3597/2401*T^12 - 
        416/343*T^11 - 2514/2401*T^10 - 2526/2401*T^9 - 2183/2401*T^8 - 
        1408/2401*T^7 + 30/2401*T^6 + 1630/2401*T^5 + 1965/2401*T^4 + 50/49*T^3 + 
        36/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 4*X*Y^10 + 2*X*Y^9 + 6*X*Y^8 +
        X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + X*Y^2 + X*Y + 2*X + 4*Y^30 + 2*Y^29 + 5*Y^28 + 
        4*Y^26 + Y^25 + 5*Y^24 + 3*Y^23 + Y^22 + 2*Y^21 + 3*Y^19 + 5*Y^18 + 5*Y^17 +
        Y^16 + 3*Y^15 + Y^13 + 3*Y^12 + 2*Y^11 + Y^8 + Y^7 + 6*Y^6 + 6*Y^4 + 6*Y^3 +
        2*Y^2 + 2*Y + 4,
    -T^56 - 6/7*T^55 + 22/49*T^54 + 177/343*T^53 + 265/2401*T^52 - 290/2401*T^51 + 
        661/2401*T^50 + 1045/2401*T^49 + 530/2401*T^48 - 698/2401*T^47 - 
        137/2401*T^46 + 1378/2401*T^45 - 209/2401*T^44 - 361/2401*T^43 + 
        1307/2401*T^42 + 348/2401*T^41 - 1399/2401*T^40 - 207/343*T^39 - 
        279/2401*T^38 + 1340/2401*T^37 + 247/2401*T^36 - 1934/2401*T^35 - 
        604/2401*T^34 + 1538/2401*T^33 + 856/2401*T^32 - 831/2401*T^31 + 
        89/2401*T^30 + 528/2401*T^29 - 528/2401*T^27 - 89/2401*T^26 + 831/2401*T^25 
        - 856/2401*T^24 - 1538/2401*T^23 + 604/2401*T^22 + 1934/2401*T^21 - 
        247/2401*T^20 - 1340/2401*T^19 + 279/2401*T^18 + 207/343*T^17 + 
        1399/2401*T^16 - 348/2401*T^15 - 1307/2401*T^14 + 361/2401*T^13 + 
        209/2401*T^12 - 1378/2401*T^11 + 137/2401*T^10 + 698/2401*T^9 - 530/2401*T^8
        - 1045/2401*T^7 - 661/2401*T^6 + 290/2401*T^5 - 265/2401*T^4 - 177/343*T^3 -
        22/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + X*Y^13 + 2*X*Y^12 + X*Y^11 + X*Y^10 + 3*X*Y^9 + 
        6*X*Y^8 + X*Y^7 + 2*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + X*Y + 4*X + Y^30 +
        2*Y^29 + 4*Y^27 + 2*Y^26 + Y^25 + 6*Y^24 + Y^23 + 5*Y^22 + 4*Y^21 + 6*Y^20 +
        3*Y^19 + 4*Y^16 + 2*Y^15 + 6*Y^14 + Y^13 + Y^12 + Y^11 + 6*Y^9 + 2*Y^8 + Y^7
        + Y^6 + Y^5 + 2*Y^4 + 2*Y^2 + 5*Y + 6,
    -T^56 + 10/7*T^55 + 27/49*T^54 - 467/343*T^53 + 240/2401*T^52 + 869/2401*T^51 + 
        227/2401*T^50 - 1068/2401*T^49 + 871/2401*T^48 - 1117/2401*T^47 + 
        1696/2401*T^46 - 157/2401*T^45 - 2442/2401*T^44 + 341/343*T^43 + 6/343*T^42 
        - 1585/2401*T^41 - 5/2401*T^40 + 2427/2401*T^39 - 122/343*T^38 - 
        1492/2401*T^37 - 2/343*T^36 + 726/2401*T^35 + 1108/2401*T^34 - 694/2401*T^33
        - 1024/2401*T^32 + 2/49*T^31 + 895/2401*T^30 + 40/2401*T^29 - 40/2401*T^27 -
        895/2401*T^26 - 2/49*T^25 + 1024/2401*T^24 + 694/2401*T^23 - 1108/2401*T^22 
        - 726/2401*T^21 + 2/343*T^20 + 1492/2401*T^19 + 122/343*T^18 - 
        2427/2401*T^17 + 5/2401*T^16 + 1585/2401*T^15 - 6/343*T^14 - 341/343*T^13 + 
        2442/2401*T^12 + 157/2401*T^11 - 1696/2401*T^10 + 1117/2401*T^9 - 
        871/2401*T^8 + 1068/2401*T^7 - 227/2401*T^6 - 869/2401*T^5 - 240/2401*T^4 + 
        467/343*T^3 - 27/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 
        6*X*Y^8 + 3*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 6*X*Y 
        + 2*X + 2*Y^30 + 4*Y^29 + 5*Y^28 + 2*Y^26 + 3*Y^25 + 6*Y^24 + 5*Y^23 + Y^22 
        + 2*Y^21 + Y^20 + 2*Y^19 + 4*Y^18 + Y^17 + 3*Y^16 + 4*Y^15 + 2*Y^14 + 5*Y^13
        + Y^12 + 5*Y^11 + Y^9 + 5*Y^7 + 4*Y^6 + 5*Y^4 + 6*Y^3 + 3*Y^2 + 1,
    -T^56 - 11/7*T^55 - 85/49*T^54 - 92/343*T^53 + 1367/2401*T^52 + 1846/2401*T^51 -
        850/2401*T^50 - 2218/2401*T^49 - 2603/2401*T^48 - 3231/2401*T^47 - 
        2033/2401*T^46 - 538/2401*T^45 + 1977/2401*T^44 + 81/343*T^43 - 
        1509/2401*T^42 - 4153/2401*T^41 - 2763/2401*T^40 - 1156/2401*T^39 + 
        541/2401*T^38 + 627/2401*T^37 + 967/2401*T^36 - 1335/2401*T^35 - 8/7*T^34 - 
        4433/2401*T^33 - 1424/2401*T^32 + 1805/2401*T^31 + 4913/2401*T^30 + 
        3425/2401*T^29 - 3425/2401*T^27 - 4913/2401*T^26 - 1805/2401*T^25 + 
        1424/2401*T^24 + 4433/2401*T^23 + 8/7*T^22 + 1335/2401*T^21 - 967/2401*T^20 
        - 627/2401*T^19 - 541/2401*T^18 + 1156/2401*T^17 + 2763/2401*T^16 + 
        4153/2401*T^15 + 1509/2401*T^14 - 81/343*T^13 - 1977/2401*T^12 + 
        538/2401*T^11 + 2033/2401*T^10 + 3231/2401*T^9 + 2603/2401*T^8 + 
        2218/2401*T^7 + 850/2401*T^6 - 1846/2401*T^5 - 1367/2401*T^4 + 92/343*T^3 + 
        85/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 5*X*Y^9 + 5*X*Y^8 +
        3*X*Y^7 + 2*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 2*X*Y + 3*X + 
        6*Y^30 + 3*Y^29 + Y^28 + Y^27 + 4*Y^26 + 5*Y^24 + Y^23 + 5*Y^22 + 3*Y^21 + 
        Y^19 + Y^18 + Y^17 + Y^16 + Y^15 + 5*Y^14 + 4*Y^13 + Y^12 + 5*Y^11 + 5*Y^10 
        + 4*Y^9 + 2*Y^8 + 6*Y^7 + 4*Y^6 + 5*Y^5 + 4*Y^4 + 6*Y^3 + 4*Y^2 + 5,
    -T^56 - 16/7*T^55 - 95/49*T^54 + 25/343*T^53 + 2410/2401*T^52 - 1117/2401*T^51 -
        5247/2401*T^50 - 4236/2401*T^49 - 801/2401*T^48 - 99/343*T^47 - 
        3588/2401*T^46 - 4168/2401*T^45 - 1003/2401*T^44 + 1426/2401*T^43 - 
        113/2401*T^42 - 3513/2401*T^41 - 3961/2401*T^40 - 1073/2401*T^39 + 
        2055/2401*T^38 + 18/49*T^37 - 2909/2401*T^36 - 3207/2401*T^35 + 25/343*T^34 
        + 450/2401*T^33 - 55/49*T^32 - 3221/2401*T^31 + 1147/2401*T^30 + 
        3459/2401*T^29 - 3459/2401*T^27 - 1147/2401*T^26 + 3221/2401*T^25 + 
        55/49*T^24 - 450/2401*T^23 - 25/343*T^22 + 3207/2401*T^21 + 2909/2401*T^20 -
        18/49*T^19 - 2055/2401*T^18 + 1073/2401*T^17 + 3961/2401*T^16 + 
        3513/2401*T^15 + 113/2401*T^14 - 1426/2401*T^13 + 1003/2401*T^12 + 
        4168/2401*T^11 + 3588/2401*T^10 + 99/343*T^9 + 801/2401*T^8 + 4236/2401*T^7 
        + 5247/2401*T^6 + 1117/2401*T^5 - 2410/2401*T^4 - 25/343*T^3 + 95/49*T^2 + 
        16/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + X*Y^13 + 5*X*Y^12 + 2*X*Y^10 + 2*X*Y^9 + 5*X*Y^8 + 
        3*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + X*Y^2 + 5*X*Y + 6*X + 
        6*Y^30 + 3*Y^29 + 5*Y^28 + 4*Y^27 + 4*Y^26 + 6*Y^25 + 2*Y^24 + 5*Y^22 + 
        6*Y^21 + 6*Y^20 + 4*Y^19 + 4*Y^18 + 3*Y^16 + 2*Y^14 + 3*Y^13 + 5*Y^12 + Y^10
        + Y^9 + 2*Y^8 + 3*Y^7 + Y^6 + 3*Y^4 + Y^3 + 2*Y,
    T^56 + 6/7*T^55 + 18/49*T^54 + 487/343*T^53 + 2218/2401*T^52 + 759/2401*T^51 - 
        234/2401*T^50 - 1222/2401*T^49 - 1838/2401*T^48 - 3896/2401*T^47 - 
        2824/2401*T^46 - 1178/2401*T^45 - 3/2401*T^44 + 502/2401*T^43 + 
        2880/2401*T^42 + 4174/2401*T^41 + 2511/2401*T^40 + 3152/2401*T^39 + 
        712/2401*T^38 - 383/2401*T^37 - 2210/2401*T^36 - 4598/2401*T^35 - 
        1671/2401*T^34 - 349/343*T^33 - 1917/2401*T^32 + 1356/2401*T^31 + 
        3323/2401*T^30 + 4358/2401*T^29 + 540/343*T^28 + 4358/2401*T^27 + 
        3323/2401*T^26 + 1356/2401*T^25 - 1917/2401*T^24 - 349/343*T^23 - 
        1671/2401*T^22 - 4598/2401*T^21 - 2210/2401*T^20 - 383/2401*T^19 + 
        712/2401*T^18 + 3152/2401*T^17 + 2511/2401*T^16 + 4174/2401*T^15 + 
        2880/2401*T^14 + 502/2401*T^13 - 3/2401*T^12 - 1178/2401*T^11 - 
        2824/2401*T^10 - 3896/2401*T^9 - 1838/2401*T^8 - 1222/2401*T^7 - 
        234/2401*T^6 + 759/2401*T^5 + 2218/2401*T^4 + 487/343*T^3 + 18/49*T^2 + 
        6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + X*Y^13 + 6*X*Y^12 + X*Y^11 + X*Y^10 + 2*X*Y^9 + 
        5*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 5*X*Y + X + 
        6*Y^30 + 2*Y^29 + 2*Y^28 + 2*Y^27 + 4*Y^26 + 4*Y^25 + 3*Y^24 + 2*Y^23 + 
        6*Y^22 + 4*Y^21 + Y^20 + 2*Y^19 + 6*Y^18 + 4*Y^17 + 2*Y^16 + 2*Y^14 + 3*Y^13
        + 6*Y^10 + 5*Y^8 + Y^7 + 2*Y^6 + 3*Y^3 + 4*Y^2 + 2*Y,
    T^56 + 2/7*T^55 - 55/49*T^54 - 205/343*T^53 + 3539/2401*T^52 + 15/49*T^51 - 
        3001/2401*T^50 - 2074/2401*T^49 + 299/343*T^48 + 2655/2401*T^47 - 
        1093/2401*T^46 - 3093/2401*T^45 + 622/2401*T^44 + 2825/2401*T^43 - 
        1573/2401*T^42 - 1730/2401*T^41 + 1186/2401*T^40 + 1124/2401*T^39 - 
        1548/2401*T^38 - 71/2401*T^37 + 408/2401*T^36 - 12/343*T^35 - 656/2401*T^34 
        + 929/2401*T^33 + 1726/2401*T^32 - 102/2401*T^31 - 1856/2401*T^30 - 
        205/2401*T^29 + 1943/2401*T^28 - 205/2401*T^27 - 1856/2401*T^26 - 
        102/2401*T^25 + 1726/2401*T^24 + 929/2401*T^23 - 656/2401*T^22 - 12/343*T^21
        + 408/2401*T^20 - 71/2401*T^19 - 1548/2401*T^18 + 1124/2401*T^17 + 
        1186/2401*T^16 - 1730/2401*T^15 - 1573/2401*T^14 + 2825/2401*T^13 + 
        622/2401*T^12 - 3093/2401*T^11 - 1093/2401*T^10 + 2655/2401*T^9 + 
        299/343*T^8 - 2074/2401*T^7 - 3001/2401*T^6 + 15/49*T^5 + 3539/2401*T^4 - 
        205/343*T^3 - 55/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + X*Y^10 + 3*X*Y^8 + 5*X*Y^7 + 
        3*X*Y^6 + X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + X*Y^2 + X*Y + 6*X + 6*Y^30 + 2*Y^28 + 
        4*Y^27 + Y^26 + 2*Y^25 + 4*Y^24 + Y^23 + 4*Y^22 + 2*Y^21 + 6*Y^19 + 5*Y^18 +
        4*Y^17 + 4*Y^16 + 3*Y^15 + Y^14 + 3*Y^13 + 6*Y^12 + 3*Y^11 + 6*Y^10 + 3*Y^8 
        + 4*Y^7 + 6*Y^6 + 2*Y^5 + 4*Y^4 + 2*Y^3 + 6*Y^2 + 3*Y,
    T^56 + T^55 + 12/49*T^54 + 144/343*T^53 - 358/2401*T^52 - 2412/2401*T^51 - 
        1681/2401*T^50 - 96/343*T^49 - 831/2401*T^48 - 801/2401*T^47 + 373/2401*T^46
        + 352/2401*T^45 - 1045/2401*T^44 - 463/2401*T^43 - 32/343*T^42 - 
        150/2401*T^41 + 101/343*T^40 + 225/343*T^39 + 248/343*T^38 + 43/343*T^37 - 
        767/2401*T^36 - 447/2401*T^35 - 1270/2401*T^34 - 776/2401*T^33 + 
        402/2401*T^32 + 66/2401*T^31 + 2/2401*T^30 + 409/2401*T^29 + 752/2401*T^28 +
        409/2401*T^27 + 2/2401*T^26 + 66/2401*T^25 + 402/2401*T^24 - 776/2401*T^23 -
        1270/2401*T^22 - 447/2401*T^21 - 767/2401*T^20 + 43/343*T^19 + 248/343*T^18 
        + 225/343*T^17 + 101/343*T^16 - 150/2401*T^15 - 32/343*T^14 - 463/2401*T^13 
        - 1045/2401*T^12 + 352/2401*T^11 + 373/2401*T^10 - 801/2401*T^9 - 
        831/2401*T^8 - 96/343*T^7 - 1681/2401*T^6 - 2412/2401*T^5 - 358/2401*T^4 + 
        144/343*T^3 + 12/49*T^2 + T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 6*X*Y^12 + X*Y^11 + 3*X*Y^10 + X*Y^9 + 4*X*Y^8 + 
        6*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 3*X*Y + X + 
        2*Y^30 + Y^29 + 2*Y^28 + 5*Y^27 + 4*Y^26 + 4*Y^24 + 5*Y^23 + 5*Y^22 + 3*Y^21
        + 5*Y^20 + Y^19 + 5*Y^18 + 3*Y^17 + 2*Y^15 + 5*Y^12 + 6*Y^11 + 6*Y^10 + 
        2*Y^9 + 2*Y^8 + 6*Y^6 + 2*Y^5 + 5*Y^3 + Y^2 + 6*Y + 4,
    -T^56 + 18/7*T^55 - 181/49*T^54 + 1117/343*T^53 - 4385/2401*T^52 + 
        3301/2401*T^51 - 5857/2401*T^50 + 9922/2401*T^49 - 10081/2401*T^48 + 
        5214/2401*T^47 + 246/343*T^46 - 5459/2401*T^45 + 2889/2401*T^44 + 
        3421/2401*T^43 - 1076/343*T^42 + 4908/2401*T^41 + 300/343*T^40 - 
        6212/2401*T^39 + 2763/2401*T^38 + 4565/2401*T^37 - 8200/2401*T^36 + 
        4587/2401*T^35 + 3881/2401*T^34 - 9837/2401*T^33 + 9113/2401*T^32 - 
        2400/2401*T^31 - 4093/2401*T^30 + 4931/2401*T^29 - 4931/2401*T^27 + 
        4093/2401*T^26 + 2400/2401*T^25 - 9113/2401*T^24 + 9837/2401*T^23 - 
        3881/2401*T^22 - 4587/2401*T^21 + 8200/2401*T^20 - 4565/2401*T^19 - 
        2763/2401*T^18 + 6212/2401*T^17 - 300/343*T^16 - 4908/2401*T^15 + 
        1076/343*T^14 - 3421/2401*T^13 - 2889/2401*T^12 + 5459/2401*T^11 - 
        246/343*T^10 - 5214/2401*T^9 + 10081/2401*T^8 - 9922/2401*T^7 + 
        5857/2401*T^6 - 3301/2401*T^5 + 4385/2401*T^4 - 1117/343*T^3 + 181/49*T^2 - 
        18/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 
        2*X*Y^8 + 5*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 6*X*Y^2 + X*Y + 6*X + 
        5*Y^30 + 4*Y^27 + 3*Y^26 + 5*Y^25 + Y^24 + 6*Y^23 + 6*Y^21 + 4*Y^19 + 3*Y^18
        + 5*Y^17 + 5*Y^16 + 3*Y^15 + Y^14 + 6*Y^12 + 2*Y^10 + 4*Y^9 + 6*Y^8 + 3*Y^7 
        + 5*Y^5 + 4*Y^3 + 2*Y^2 + 6*Y + 5,
    -T^56 - 5/7*T^55 + 54/49*T^54 + 67/343*T^53 - 242/343*T^52 + 3671/2401*T^51 + 
        3404/2401*T^50 - 2715/2401*T^49 - 1294/2401*T^48 + 209/343*T^47 - 
        337/343*T^46 - 2818/2401*T^45 + 236/343*T^44 + 1266/2401*T^43 - 
        180/2401*T^42 + 211/343*T^41 + 1556/2401*T^40 - 187/2401*T^39 - 
        1520/2401*T^38 - 33/49*T^37 - 23/343*T^36 - 902/2401*T^35 - 1586/2401*T^34 +
        1094/2401*T^33 + 2207/2401*T^32 + 212/2401*T^31 + 491/2401*T^30 + 
        1528/2401*T^29 - 1528/2401*T^27 - 491/2401*T^26 - 212/2401*T^25 - 
        2207/2401*T^24 - 1094/2401*T^23 + 1586/2401*T^22 + 902/2401*T^21 + 
        23/343*T^20 + 33/49*T^19 + 1520/2401*T^18 + 187/2401*T^17 - 1556/2401*T^16 -
        211/343*T^15 + 180/2401*T^14 - 1266/2401*T^13 - 236/343*T^12 + 
        2818/2401*T^11 + 337/343*T^10 - 209/343*T^9 + 1294/2401*T^8 + 2715/2401*T^7 
        - 3404/2401*T^6 - 3671/2401*T^5 + 242/343*T^4 - 67/343*T^3 - 54/49*T^2 + 
        5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 3*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 2*X*Y^8 +
        4*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 3*X + Y^30 + 
        4*Y^28 + 5*Y^27 + 2*Y^25 + 4*Y^24 + 6*Y^23 + Y^22 + 2*Y^21 + 4*Y^20 + 2*Y^19
        + 3*Y^18 + 4*Y^17 + 2*Y^16 + Y^15 + Y^14 + 4*Y^13 + Y^12 + Y^11 + 5*Y^10 + 
        3*Y^9 + 5*Y^8 + 6*Y^6 + 2*Y^5 + 6*Y^4 + 6*Y^3 + Y^2 + 3,
    -T^56 + T^55 + 45/49*T^54 - 713/343*T^53 + 1040/2401*T^52 + 461/343*T^51 - 
        3312/2401*T^50 + 646/2401*T^49 + 2927/2401*T^48 - 4255/2401*T^47 + 
        20/2401*T^46 + 768/343*T^45 - 2781/2401*T^44 - 2801/2401*T^43 + 
        3309/2401*T^42 - 744/2401*T^41 - 1731/2401*T^40 + 2509/2401*T^39 - 
        319/2401*T^38 - 1378/2401*T^37 + 766/2401*T^36 - 949/2401*T^35 + 
        1275/2401*T^34 + 1586/2401*T^33 - 3278/2401*T^32 - 246/2401*T^31 + 
        2645/2401*T^30 - 578/2401*T^29 + 578/2401*T^27 - 2645/2401*T^26 + 
        246/2401*T^25 + 3278/2401*T^24 - 1586/2401*T^23 - 1275/2401*T^22 + 
        949/2401*T^21 - 766/2401*T^20 + 1378/2401*T^19 + 319/2401*T^18 - 
        2509/2401*T^17 + 1731/2401*T^16 + 744/2401*T^15 - 3309/2401*T^14 + 
        2801/2401*T^13 + 2781/2401*T^12 - 768/343*T^11 - 20/2401*T^10 + 
        4255/2401*T^9 - 2927/2401*T^8 - 646/2401*T^7 + 3312/2401*T^6 - 461/343*T^5 -
        1040/2401*T^4 + 713/343*T^3 - 45/49*T^2 - T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 5*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 5*X*Y^8 +
        X*Y^7 + X*Y^6 + 5*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 3*X*Y + 3*Y^30 + 3*Y^29 + 
        3*Y^28 + 6*Y^26 + 4*Y^25 + 6*Y^24 + 3*Y^23 + Y^22 + 4*Y^21 + 6*Y^20 + 4*Y^19
        + 4*Y^18 + 2*Y^17 + 6*Y^16 + 5*Y^15 + 4*Y^12 + 5*Y^11 + 6*Y^10 + 4*Y^9 + 
        5*Y^8 + 6*Y^7 + 3*Y^6 + 2*Y^5 + Y^4 + 5*Y^2 + 4*Y + 3,
    T^56 - 9/7*T^55 + 72/49*T^54 - 240/343*T^53 + 923/2401*T^52 + 534/2401*T^51 - 
        3002/2401*T^50 + 6509/2401*T^49 - 8703/2401*T^48 + 7841/2401*T^47 - 
        6099/2401*T^46 + 2958/2401*T^45 + 12/49*T^44 - 5577/2401*T^43 + 
        9273/2401*T^42 - 11712/2401*T^41 + 10449/2401*T^40 - 7976/2401*T^39 + 
        4013/2401*T^38 + 550/2401*T^37 - 786/343*T^36 + 9596/2401*T^35 - 
        11204/2401*T^34 + 8664/2401*T^33 - 678/343*T^32 + 1069/2401*T^31 + 
        3631/2401*T^30 - 153/49*T^29 + 9960/2401*T^28 - 153/49*T^27 + 3631/2401*T^26
        + 1069/2401*T^25 - 678/343*T^24 + 8664/2401*T^23 - 11204/2401*T^22 + 
        9596/2401*T^21 - 786/343*T^20 + 550/2401*T^19 + 4013/2401*T^18 - 
        7976/2401*T^17 + 10449/2401*T^16 - 11712/2401*T^15 + 9273/2401*T^14 - 
        5577/2401*T^13 + 12/49*T^12 + 2958/2401*T^11 - 6099/2401*T^10 + 
        7841/2401*T^9 - 8703/2401*T^8 + 6509/2401*T^7 - 3002/2401*T^6 + 534/2401*T^5
        + 923/2401*T^4 - 240/343*T^3 + 72/49*T^2 - 9/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + X*Y^10 + X*Y^9 + 
        X*Y^8 + 3*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 2*X*Y + 
        4*X + 6*Y^30 + Y^29 + Y^28 + 4*Y^27 + 4*Y^26 + 4*Y^25 + 2*Y^24 + 4*Y^22 + 
        3*Y^21 + 6*Y^20 + 6*Y^18 + 6*Y^17 + 4*Y^16 + 5*Y^15 + Y^14 + 5*Y^11 + 6*Y^9 
        + Y^8 + 4*Y^7 + Y^6 + 4*Y^4 + Y^3 + 2*Y^2 + 1,
    T^56 + 8/7*T^55 - 36/49*T^54 - 383/343*T^53 - 325/343*T^52 - 605/343*T^51 + 
        1234/2401*T^50 + 4568/2401*T^49 - 922/2401*T^48 + 158/343*T^47 + 
        3379/2401*T^46 - 1128/2401*T^45 + 1949/2401*T^44 + 1074/2401*T^43 - 
        6285/2401*T^42 - 2073/2401*T^41 + 1338/2401*T^40 - 1896/2401*T^39 + 
        2069/2401*T^38 + 1782/2401*T^37 - 3279/2401*T^36 + 1077/2401*T^35 + 
        4203/2401*T^34 + 265/2401*T^33 + 673/2401*T^32 + 758/2401*T^31 - 
        2862/2401*T^30 - 1752/2401*T^29 + 1100/2401*T^28 - 1752/2401*T^27 - 
        2862/2401*T^26 + 758/2401*T^25 + 673/2401*T^24 + 265/2401*T^23 + 
        4203/2401*T^22 + 1077/2401*T^21 - 3279/2401*T^20 + 1782/2401*T^19 + 
        2069/2401*T^18 - 1896/2401*T^17 + 1338/2401*T^16 - 2073/2401*T^15 - 
        6285/2401*T^14 + 1074/2401*T^13 + 1949/2401*T^12 - 1128/2401*T^11 + 
        3379/2401*T^10 + 158/343*T^9 - 922/2401*T^8 + 4568/2401*T^7 + 1234/2401*T^6 
        - 605/343*T^5 - 325/343*T^4 - 383/343*T^3 - 36/49*T^2 + 8/7*T + 1
*], [*
    X^3 + X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + X*Y^10 + 5*X*Y^9 + 3*X*Y^8 + 
        4*X*Y^7 + 4*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 2*X*Y + 4*X + 5*Y^30 + 
        2*Y^29 + 5*Y^28 + 3*Y^27 + 2*Y^26 + 6*Y^25 + Y^24 + 2*Y^23 + 3*Y^21 + 3*Y^20
        + Y^18 + 2*Y^17 + 6*Y^16 + 2*Y^15 + 6*Y^14 + 6*Y^13 + 4*Y^11 + 4*Y^10 + Y^9 
        + 5*Y^8 + 3*Y^7 + Y^6 + Y^5 + 4*Y^4 + 5*Y^2 + 3*Y,
    -T^56 + 2/7*T^55 + 13/7*T^54 + 183/343*T^53 - 2906/2401*T^52 - 578/343*T^51 - 
        1475/2401*T^50 + 2819/2401*T^49 + 687/343*T^48 + 846/2401*T^47 - 
        3464/2401*T^46 - 3254/2401*T^45 - 156/2401*T^44 + 1248/2401*T^43 + 
        2827/2401*T^42 + 1308/2401*T^41 - 1159/2401*T^40 - 1707/2401*T^39 - 
        1835/2401*T^38 + 775/2401*T^37 + 1773/2401*T^36 + 134/2401*T^35 - 
        71/2401*T^34 - 68/2401*T^33 - 990/2401*T^32 + 1167/2401*T^31 - 297/2401*T^30
        - 1354/2401*T^29 + 1354/2401*T^27 + 297/2401*T^26 - 1167/2401*T^25 + 
        990/2401*T^24 + 68/2401*T^23 + 71/2401*T^22 - 134/2401*T^21 - 1773/2401*T^20
        - 775/2401*T^19 + 1835/2401*T^18 + 1707/2401*T^17 + 1159/2401*T^16 - 
        1308/2401*T^15 - 2827/2401*T^14 - 1248/2401*T^13 + 156/2401*T^12 + 
        3254/2401*T^11 + 3464/2401*T^10 - 846/2401*T^9 - 687/343*T^8 - 2819/2401*T^7
        + 1475/2401*T^6 + 578/343*T^5 + 2906/2401*T^4 - 183/343*T^3 - 13/7*T^2 - 
        2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 4*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 6*X*Y + Y^30 + 
        3*Y^29 + Y^27 + 5*Y^26 + 4*Y^25 + 5*Y^24 + 4*Y^23 + 2*Y^22 + Y^20 + 4*Y^19 +
        6*Y^18 + Y^16 + Y^15 + 4*Y^13 + 3*Y^12 + Y^10 + 3*Y^9 + 3*Y^7 + 5*Y^6 + Y^5 
        + 3*Y^4 + 5*Y^3 + 6*Y^2 + 4*Y + 4,
    T^56 - 8/7*T^55 + 29/49*T^54 - 103/343*T^53 + 138/2401*T^52 + 34/2401*T^51 - 
        925/2401*T^50 + 529/2401*T^49 - 1140/2401*T^48 + 1768/2401*T^47 - 
        2243/2401*T^46 + 1770/2401*T^45 - 169/2401*T^44 - 45/343*T^43 + 
        459/2401*T^42 - 408/2401*T^41 + 433/2401*T^40 - 26/2401*T^39 + 166/2401*T^38
        - 592/2401*T^37 + 120/2401*T^36 + 111/2401*T^35 + 172/2401*T^34 + 
        286/2401*T^33 - 664/2401*T^32 + 76/2401*T^31 - 45/2401*T^30 + 223/2401*T^29 
        - 166/2401*T^28 + 223/2401*T^27 - 45/2401*T^26 + 76/2401*T^25 - 
        664/2401*T^24 + 286/2401*T^23 + 172/2401*T^22 + 111/2401*T^21 + 
        120/2401*T^20 - 592/2401*T^19 + 166/2401*T^18 - 26/2401*T^17 + 433/2401*T^16
        - 408/2401*T^15 + 459/2401*T^14 - 45/343*T^13 - 169/2401*T^12 + 
        1770/2401*T^11 - 2243/2401*T^10 + 1768/2401*T^9 - 1140/2401*T^8 + 
        529/2401*T^7 - 925/2401*T^6 + 34/2401*T^5 + 138/2401*T^4 - 103/343*T^3 + 
        29/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 3*X*Y^9 + X*Y^6 + 
        4*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 4*X*Y + X + 3*Y^30 + 3*Y^29 + 4*Y^28
        + 4*Y^27 + 4*Y^26 + 2*Y^25 + 4*Y^24 + 6*Y^23 + 6*Y^22 + 6*Y^21 + Y^20 + 
        5*Y^18 + 4*Y^17 + 4*Y^16 + Y^14 + 6*Y^13 + 6*Y^12 + 4*Y^11 + 4*Y^9 + 5*Y^8 +
        Y^7 + 2*Y^6 + 3*Y^5 + 4*Y^4 + 2*Y^3 + 6*Y^2 + 6*Y + 1,
    T^56 + 5/7*T^55 + 48/49*T^54 + 365/343*T^53 + 1255/2401*T^52 + 3925/2401*T^51 + 
        2915/2401*T^50 + 424/343*T^49 + 4146/2401*T^48 + 1648/2401*T^47 + 
        2875/2401*T^46 + 1670/2401*T^45 + 948/2401*T^44 + 1522/2401*T^43 - 
        533/2401*T^42 + 520/2401*T^41 - 205/2401*T^40 - 1154/2401*T^39 - 
        1648/2401*T^38 - 3357/2401*T^37 - 2756/2401*T^36 - 2846/2401*T^35 - 
        3093/2401*T^34 - 2586/2401*T^33 - 537/343*T^32 - 3266/2401*T^31 - 
        3433/2401*T^30 - 3350/2401*T^29 - 2602/2401*T^28 - 3350/2401*T^27 - 
        3433/2401*T^26 - 3266/2401*T^25 - 537/343*T^24 - 2586/2401*T^23 - 
        3093/2401*T^22 - 2846/2401*T^21 - 2756/2401*T^20 - 3357/2401*T^19 - 
        1648/2401*T^18 - 1154/2401*T^17 - 205/2401*T^16 + 520/2401*T^15 - 
        533/2401*T^14 + 1522/2401*T^13 + 948/2401*T^12 + 1670/2401*T^11 + 
        2875/2401*T^10 + 1648/2401*T^9 + 4146/2401*T^8 + 424/343*T^7 + 2915/2401*T^6
        + 3925/2401*T^5 + 1255/2401*T^4 + 365/343*T^3 + 48/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 5*X*Y^10 + 6*X*Y^9 + 4*X*Y^8 +
        X*Y^7 + 6*X*Y^6 + 2*X*Y^4 + 2*X*Y^3 + 3*X*Y + 4*X + 2*Y^30 + 2*Y^28 + 5*Y^27
        + 6*Y^26 + 5*Y^25 + Y^23 + 3*Y^22 + 5*Y^21 + 4*Y^20 + 2*Y^19 + 6*Y^18 + Y^17
        + Y^16 + 5*Y^15 + 5*Y^14 + Y^13 + 6*Y^12 + 4*Y^11 + Y^10 + Y^9 + 3*Y^8 + 
        4*Y^7 + Y^6 + Y^5 + 4*Y^4 + Y^2 + 3*Y + 4,
    T^56 - 11/7*T^55 - 4/49*T^54 + 919/343*T^53 - 6708/2401*T^52 + 477/2401*T^51 + 
        4667/2401*T^50 - 5819/2401*T^49 + 4071/2401*T^48 + 18/343*T^47 - 
        5709/2401*T^46 + 5721/2401*T^45 - 13/343*T^44 - 3978/2401*T^43 + 
        369/343*T^42 - 948/2401*T^41 + 857/2401*T^40 + 1261/2401*T^39 - 
        4071/2401*T^38 + 2830/2401*T^37 + 1271/2401*T^36 - 2613/2401*T^35 + 
        2115/2401*T^34 - 2172/2401*T^33 + 258/2401*T^32 + 4243/2401*T^31 - 
        4533/2401*T^30 - 1909/2401*T^29 + 916/343*T^28 - 1909/2401*T^27 - 
        4533/2401*T^26 + 4243/2401*T^25 + 258/2401*T^24 - 2172/2401*T^23 + 
        2115/2401*T^22 - 2613/2401*T^21 + 1271/2401*T^20 + 2830/2401*T^19 - 
        4071/2401*T^18 + 1261/2401*T^17 + 857/2401*T^16 - 948/2401*T^15 + 
        369/343*T^14 - 3978/2401*T^13 - 13/343*T^12 + 5721/2401*T^11 - 
        5709/2401*T^10 + 18/343*T^9 + 4071/2401*T^8 - 5819/2401*T^7 + 4667/2401*T^6 
        + 477/2401*T^5 - 6708/2401*T^4 + 919/343*T^3 - 4/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 
        6*X*Y^8 + 5*X*Y^4 + 3*X*Y^3 + 4*X*Y + 3*X + 2*Y^30 + 2*Y^28 + 6*Y^27 + 
        4*Y^26 + 5*Y^25 + 5*Y^24 + 4*Y^22 + 5*Y^20 + 6*Y^19 + Y^18 + 5*Y^17 + Y^16 +
        Y^15 + 2*Y^14 + 6*Y^13 + 3*Y^12 + 6*Y^11 + 5*Y^9 + 4*Y^8 + Y^7 + 6*Y^6 + 
        2*Y^5 + 6*Y^4 + 5*Y^3 + 6*Y^2 + 5*Y + 6,
    -T^56 - 11/7*T^55 - 2/7*T^54 + 219/343*T^53 - 127/343*T^52 - 1587/2401*T^51 + 
        1551/2401*T^50 + 2820/2401*T^49 + 880/2401*T^48 + 2/2401*T^47 - 67/2401*T^46
        - 1248/2401*T^45 - 1637/2401*T^44 - 601/2401*T^43 + 55/2401*T^42 - 
        317/2401*T^41 - 710/2401*T^40 + 135/2401*T^39 + 1648/2401*T^38 + 
        1326/2401*T^37 - 419/2401*T^36 - 90/2401*T^35 + 109/343*T^34 - 167/2401*T^33
        - 1821/2401*T^32 - 1616/2401*T^31 - 94/343*T^30 - 185/2401*T^29 + 
        185/2401*T^27 + 94/343*T^26 + 1616/2401*T^25 + 1821/2401*T^24 + 
        167/2401*T^23 - 109/343*T^22 + 90/2401*T^21 + 419/2401*T^20 - 1326/2401*T^19
        - 1648/2401*T^18 - 135/2401*T^17 + 710/2401*T^16 + 317/2401*T^15 - 
        55/2401*T^14 + 601/2401*T^13 + 1637/2401*T^12 + 1248/2401*T^11 + 
        67/2401*T^10 - 2/2401*T^9 - 880/2401*T^8 - 2820/2401*T^7 - 1551/2401*T^6 + 
        1587/2401*T^5 + 127/343*T^4 - 219/343*T^3 + 2/7*T^2 + 11/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + X*Y^11 + 5*X*Y^10 + X*Y^9 + 3*X*Y^8 + 
        5*X*Y^7 + 6*X*Y^6 + 5*X*Y^5 + X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + X*Y + X + 2*Y^30 +
        5*Y^29 + 6*Y^28 + Y^27 + 6*Y^26 + 6*Y^25 + 2*Y^23 + 2*Y^22 + 6*Y^21 + 3*Y^18
        + 5*Y^17 + 3*Y^16 + 5*Y^15 + 6*Y^14 + 3*Y^13 + 3*Y^12 + Y^11 + 5*Y^10 + 
        2*Y^9 + 4*Y^8 + 5*Y^7 + 5*Y^6 + 6*Y^5 + Y^4 + 3*Y^3 + 6*Y^2 + 4*Y + 3,
    T^56 - 5/7*T^55 - 6/7*T^54 + 39/343*T^53 + 1901/2401*T^52 + 755/2401*T^51 - 
        400/2401*T^50 - 1202/2401*T^49 - 1307/2401*T^48 + 2222/2401*T^47 - 
        173/343*T^46 + 1249/2401*T^45 + 1244/2401*T^44 - 1110/2401*T^43 - 
        2734/2401*T^42 + 656/2401*T^41 + 2984/2401*T^40 - 649/2401*T^39 + 
        33/343*T^38 - 2530/2401*T^37 + 771/2401*T^36 + 12/343*T^35 + 557/2401*T^34 +
        1201/2401*T^33 + 156/343*T^32 - 271/343*T^31 - 4122/2401*T^30 + 
        2531/2401*T^29 + 2407/2401*T^28 + 2531/2401*T^27 - 4122/2401*T^26 - 
        271/343*T^25 + 156/343*T^24 + 1201/2401*T^23 + 557/2401*T^22 + 12/343*T^21 +
        771/2401*T^20 - 2530/2401*T^19 + 33/343*T^18 - 649/2401*T^17 + 
        2984/2401*T^16 + 656/2401*T^15 - 2734/2401*T^14 - 1110/2401*T^13 + 
        1244/2401*T^12 + 1249/2401*T^11 - 173/343*T^10 + 2222/2401*T^9 - 
        1307/2401*T^8 - 1202/2401*T^7 - 400/2401*T^6 + 755/2401*T^5 + 1901/2401*T^4 
        + 39/343*T^3 - 6/7*T^2 - 5/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 4*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 6*X*Y^8 + X*Y^7 + 
        4*X*Y^5 + 5*X*Y^4 + X*Y^2 + 3*X*Y + 2*X + Y^30 + 4*Y^29 + 2*Y^28 + 2*Y^27 + 
        2*Y^25 + 6*Y^24 + 6*Y^23 + 2*Y^22 + 6*Y^19 + 4*Y^18 + Y^17 + 3*Y^16 + 2*Y^15
        + 6*Y^14 + 3*Y^13 + 2*Y^12 + 6*Y^10 + 2*Y^9 + 4*Y^8 + Y^7 + 6*Y^5 + 6*Y^4 + 
        6*Y^3 + 6*Y^2 + 4*Y,
    T^56 - 1/7*T^55 - 11/49*T^54 + 39/49*T^53 - 818/2401*T^52 - 102/2401*T^51 + 
        1945/2401*T^50 + 240/2401*T^49 - 1241/2401*T^48 + 97/2401*T^47 + 
        111/2401*T^46 - 571/2401*T^45 + 859/2401*T^44 - 325/2401*T^43 - 
        1360/2401*T^42 - 736/2401*T^41 - 599/2401*T^40 - 52/343*T^39 + 62/2401*T^38 
        + 1145/2401*T^37 - 790/2401*T^36 - 705/2401*T^35 + 100/343*T^34 + 
        230/2401*T^33 + 736/2401*T^32 + 284/2401*T^31 + 1380/2401*T^30 + 
        1347/2401*T^29 - 694/2401*T^28 + 1347/2401*T^27 + 1380/2401*T^26 + 
        284/2401*T^25 + 736/2401*T^24 + 230/2401*T^23 + 100/343*T^22 - 705/2401*T^21
        - 790/2401*T^20 + 1145/2401*T^19 + 62/2401*T^18 - 52/343*T^17 - 
        599/2401*T^16 - 736/2401*T^15 - 1360/2401*T^14 - 325/2401*T^13 + 
        859/2401*T^12 - 571/2401*T^11 + 111/2401*T^10 + 97/2401*T^9 - 1241/2401*T^8 
        + 240/2401*T^7 + 1945/2401*T^6 - 102/2401*T^5 - 818/2401*T^4 + 39/49*T^3 - 
        11/49*T^2 - 1/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + X*Y^3 + 2*X*Y^2 + 4*X*Y + 
        5*X + 3*Y^30 + Y^29 + 2*Y^28 + 4*Y^27 + 3*Y^25 + 5*Y^24 + 4*Y^23 + 3*Y^22 + 
        5*Y^21 + 3*Y^20 + 6*Y^19 + 6*Y^18 + 2*Y^17 + Y^16 + Y^15 + Y^14 + 3*Y^13 + 
        2*Y^12 + 4*Y^11 + Y^10 + 4*Y^9 + Y^8 + Y^7 + Y^5 + 5*Y^4 + 3*Y^3 + 5*Y^2 + 
        2*Y + 6,
    -T^56 + 4/7*T^55 - 12/49*T^54 - 74/343*T^53 + 682/2401*T^52 + 1492/2401*T^51 + 
        457/2401*T^50 - 2262/2401*T^49 + 839/2401*T^48 + 214/2401*T^47 - 
        1553/2401*T^46 - 1121/2401*T^45 + 2174/2401*T^44 + 564/2401*T^43 - 
        1529/2401*T^42 - 213/2401*T^41 + 2370/2401*T^40 - 823/2401*T^39 - 
        2007/2401*T^38 + 1094/2401*T^37 + 1828/2401*T^36 - 1741/2401*T^35 - 
        1755/2401*T^34 + 1810/2401*T^33 + 1768/2401*T^32 - 3238/2401*T^31 + 
        115/343*T^30 + 2034/2401*T^29 - 2034/2401*T^27 - 115/343*T^26 + 
        3238/2401*T^25 - 1768/2401*T^24 - 1810/2401*T^23 + 1755/2401*T^22 + 
        1741/2401*T^21 - 1828/2401*T^20 - 1094/2401*T^19 + 2007/2401*T^18 + 
        823/2401*T^17 - 2370/2401*T^16 + 213/2401*T^15 + 1529/2401*T^14 - 
        564/2401*T^13 - 2174/2401*T^12 + 1121/2401*T^11 + 1553/2401*T^10 - 
        214/2401*T^9 - 839/2401*T^8 + 2262/2401*T^7 - 457/2401*T^6 - 1492/2401*T^5 -
        682/2401*T^4 + 74/343*T^3 + 12/49*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 
        6*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 5*X*Y + X + 
        5*Y^30 + 5*Y^29 + 4*Y^28 + 4*Y^27 + 5*Y^26 + 4*Y^25 + 4*Y^24 + 6*Y^23 + 
        2*Y^22 + 6*Y^21 + 6*Y^20 + 6*Y^19 + 3*Y^18 + 4*Y^16 + 6*Y^15 + 6*Y^14 + 
        2*Y^13 + 3*Y^12 + 5*Y^9 + 3*Y^8 + 3*Y^6 + 5*Y^5 + 6*Y^4 + 2*Y^3 + 2*Y^2 + Y,
    T^56 + 3/7*T^55 - 73/49*T^54 - 137/343*T^53 + 3860/2401*T^52 + 1072/2401*T^51 - 
        3967/2401*T^50 - 1226/2401*T^49 + 2344/2401*T^48 + 52/343*T^47 - 
        1786/2401*T^46 - 149/2401*T^45 + 1301/2401*T^44 + 1482/2401*T^43 + 
        426/2401*T^42 - 2376/2401*T^41 - 146/343*T^40 + 4059/2401*T^39 + 
        2536/2401*T^38 - 5729/2401*T^37 - 600/343*T^36 + 3950/2401*T^35 + 
        3851/2401*T^34 - 457/343*T^33 - 4013/2401*T^32 + 1961/2401*T^31 + 
        2853/2401*T^30 - 188/2401*T^29 - 1796/2401*T^28 - 188/2401*T^27 + 
        2853/2401*T^26 + 1961/2401*T^25 - 4013/2401*T^24 - 457/343*T^23 + 
        3851/2401*T^22 + 3950/2401*T^21 - 600/343*T^20 - 5729/2401*T^19 + 
        2536/2401*T^18 + 4059/2401*T^17 - 146/343*T^16 - 2376/2401*T^15 + 
        426/2401*T^14 + 1482/2401*T^13 + 1301/2401*T^12 - 149/2401*T^11 - 
        1786/2401*T^10 + 52/343*T^9 + 2344/2401*T^8 - 1226/2401*T^7 - 3967/2401*T^6 
        + 1072/2401*T^5 + 3860/2401*T^4 - 137/343*T^3 - 73/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 4*X*Y^9 + 5*X*Y^7 +
        4*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 4*X*Y + 6*X + 4*Y^30 + 6*Y^29 + 
        5*Y^28 + 3*Y^27 + 4*Y^26 + Y^25 + 6*Y^24 + 2*Y^23 + 3*Y^22 + Y^21 + 4*Y^19 +
        6*Y^18 + 2*Y^16 + 4*Y^15 + 3*Y^14 + 5*Y^13 + 2*Y^12 + 4*Y^11 + 3*Y^10 + 
        4*Y^6 + Y^5 + 2*Y^3 + 2*Y^2 + 2*Y + 4,
    T^56 - 5/7*T^55 - 6/7*T^54 + 503/343*T^53 + 5/343*T^52 - 2451/2401*T^51 + 
        968/2401*T^50 + 498/2401*T^49 - 1088/2401*T^48 + 591/2401*T^47 - 
        51/2401*T^46 - 151/343*T^45 + 412/2401*T^44 + 62/343*T^43 - 118/343*T^42 - 
        37/2401*T^41 + 127/343*T^40 - 306/2401*T^39 - 484/2401*T^38 + 1650/2401*T^37
        - 1479/2401*T^36 - 578/2401*T^35 + 494/343*T^34 - 1597/2401*T^33 - 
        345/343*T^32 + 2316/2401*T^31 + 801/2401*T^30 - 1044/2401*T^29 - 
        676/2401*T^28 - 1044/2401*T^27 + 801/2401*T^26 + 2316/2401*T^25 - 
        345/343*T^24 - 1597/2401*T^23 + 494/343*T^22 - 578/2401*T^21 - 
        1479/2401*T^20 + 1650/2401*T^19 - 484/2401*T^18 - 306/2401*T^17 + 
        127/343*T^16 - 37/2401*T^15 - 118/343*T^14 + 62/343*T^13 + 412/2401*T^12 - 
        151/343*T^11 - 51/2401*T^10 + 591/2401*T^9 - 1088/2401*T^8 + 498/2401*T^7 + 
        968/2401*T^6 - 2451/2401*T^5 + 5/343*T^4 + 503/343*T^3 - 6/7*T^2 - 5/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 4*X*Y^8 + 
        2*X*Y^6 + X*Y^5 + 2*X*Y^4 + 3*X*Y^2 + 3*X*Y + X + 4*Y^30 + Y^29 + 5*Y^28 + 
        6*Y^27 + Y^26 + 5*Y^24 + 6*Y^23 + 3*Y^22 + 6*Y^21 + 5*Y^20 + 2*Y^19 + 5*Y^18
        + 4*Y^17 + 4*Y^15 + 6*Y^14 + 4*Y^13 + 6*Y^12 + 2*Y^10 + 2*Y^9 + Y^8 + 6*Y^7 
        + 5*Y^4 + Y^3 + Y^2 + Y + 6,
    -T^56 - 1/7*T^55 + 15/49*T^54 - 5/343*T^53 - 142/343*T^52 - 1118/2401*T^51 + 
        271/2401*T^50 - 1054/2401*T^49 - 1175/2401*T^48 - 8/2401*T^47 + 
        1103/2401*T^46 + 892/2401*T^45 + 9/2401*T^44 - 6/49*T^43 - 34/2401*T^42 + 
        559/2401*T^41 + 874/2401*T^40 + 901/2401*T^39 + 879/2401*T^38 + 
        1867/2401*T^37 + 29/49*T^36 + 38/343*T^35 - 120/2401*T^34 + 607/2401*T^33 + 
        23/49*T^32 + 1255/2401*T^31 + 432/2401*T^30 + 695/2401*T^29 - 695/2401*T^27 
        - 432/2401*T^26 - 1255/2401*T^25 - 23/49*T^24 - 607/2401*T^23 + 
        120/2401*T^22 - 38/343*T^21 - 29/49*T^20 - 1867/2401*T^19 - 879/2401*T^18 - 
        901/2401*T^17 - 874/2401*T^16 - 559/2401*T^15 + 34/2401*T^14 + 6/49*T^13 - 
        9/2401*T^12 - 892/2401*T^11 - 1103/2401*T^10 + 8/2401*T^9 + 1175/2401*T^8 + 
        1054/2401*T^7 - 271/2401*T^6 + 1118/2401*T^5 + 142/343*T^4 + 5/343*T^3 - 
        15/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 3*X*Y^9 + X*Y^8 + 6*X*Y^7 + 
        2*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + X*Y + 2*X + 5*Y^30 + 
        4*Y^27 + 5*Y^25 + 3*Y^24 + Y^23 + 4*Y^22 + 2*Y^20 + 3*Y^19 + 3*Y^18 + 6*Y^16
        + 2*Y^15 + 6*Y^14 + Y^12 + 3*Y^11 + 4*Y^9 + 3*Y^8 + 6*Y^7 + 2*Y^6 + 5*Y^4 + 
        2*Y^3 + 6*Y^2 + 4*Y + 1,
    -T^56 - 8/7*T^55 - 18/49*T^54 - 89/343*T^53 + 391/2401*T^52 - 1184/2401*T^51 - 
        1661/2401*T^50 + 330/2401*T^49 + 1325/2401*T^48 + 271/343*T^47 - 
        209/2401*T^46 - 2538/2401*T^45 - 116/343*T^44 + 2081/2401*T^43 + 
        1723/2401*T^42 + 1563/2401*T^41 - 919/2401*T^40 - 2112/2401*T^39 + 
        1087/2401*T^38 + 568/2401*T^37 + 438/2401*T^36 - 1609/2401*T^35 - 
        3062/2401*T^34 + 604/2401*T^33 + 1709/2401*T^32 + 1562/2401*T^31 - 
        214/2401*T^30 - 279/343*T^29 + 279/343*T^27 + 214/2401*T^26 - 1562/2401*T^25
        - 1709/2401*T^24 - 604/2401*T^23 + 3062/2401*T^22 + 1609/2401*T^21 - 
        438/2401*T^20 - 568/2401*T^19 - 1087/2401*T^18 + 2112/2401*T^17 + 
        919/2401*T^16 - 1563/2401*T^15 - 1723/2401*T^14 - 2081/2401*T^13 + 
        116/343*T^12 + 2538/2401*T^11 + 209/2401*T^10 - 271/343*T^9 - 1325/2401*T^8 
        - 330/2401*T^7 + 1661/2401*T^6 + 1184/2401*T^5 - 391/2401*T^4 + 89/343*T^3 +
        18/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^13 + X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 
        2*X*Y^7 + X*Y^6 + X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + X*Y^2 + X*Y + 4*X + 4*Y^30 + 
        5*Y^29 + Y^28 + Y^27 + 4*Y^26 + 3*Y^25 + 5*Y^24 + 3*Y^23 + 6*Y^22 + 5*Y^21 +
        3*Y^19 + 4*Y^18 + 6*Y^17 + 3*Y^16 + 4*Y^15 + Y^14 + 5*Y^13 + 6*Y^12 + 5*Y^10
        + 6*Y^9 + Y^7 + 4*Y^6 + 4*Y^5 + Y^4 + 6*Y^3 + Y^2 + Y + 6,
    -T^56 + 1/7*T^55 - 3/7*T^54 + 16/49*T^53 + 152/2401*T^52 + 230/2401*T^51 + 
        62/2401*T^50 + 1727/2401*T^49 + 400/2401*T^48 + 816/2401*T^47 + 
        1041/2401*T^46 + 488/2401*T^45 + 237/2401*T^44 - 489/2401*T^43 - 
        332/2401*T^42 - 710/2401*T^41 + 1480/2401*T^40 - 1257/2401*T^39 - 
        174/2401*T^38 - 1248/2401*T^37 + 389/2401*T^36 - 1541/2401*T^35 + 
        565/2401*T^34 - 1646/2401*T^33 + 474/2401*T^32 - 303/2401*T^31 - 
        1243/2401*T^30 - 860/2401*T^29 + 860/2401*T^27 + 1243/2401*T^26 + 
        303/2401*T^25 - 474/2401*T^24 + 1646/2401*T^23 - 565/2401*T^22 + 
        1541/2401*T^21 - 389/2401*T^20 + 1248/2401*T^19 + 174/2401*T^18 + 
        1257/2401*T^17 - 1480/2401*T^16 + 710/2401*T^15 + 332/2401*T^14 + 
        489/2401*T^13 - 237/2401*T^12 - 488/2401*T^11 - 1041/2401*T^10 - 
        816/2401*T^9 - 400/2401*T^8 - 1727/2401*T^7 - 62/2401*T^6 - 230/2401*T^5 - 
        152/2401*T^4 - 16/49*T^3 + 3/7*T^2 - 1/7*T + 1
*], [*
    X^3 + 6*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 5*X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 
        X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 3*X*Y + 5*X + 3*Y^30 + 5*Y^29 + Y^28 +
        4*Y^27 + 3*Y^26 + 5*Y^25 + Y^24 + 2*Y^23 + 6*Y^22 + Y^21 + 4*Y^20 + 3*Y^19 +
        3*Y^18 + Y^17 + 4*Y^16 + 6*Y^15 + Y^14 + Y^13 + Y^12 + 5*Y^11 + 2*Y^10 + Y^8
        + 5*Y^6 + 2*Y^5 + 6*Y^3 + 4*Y^2 + 1,
    -T^56 + 16/7*T^55 - 79/49*T^54 - 460/343*T^53 + 8110/2401*T^52 - 4565/2401*T^51 
        - 4052/2401*T^50 + 8703/2401*T^49 - 5487/2401*T^48 - 2242/2401*T^47 + 
        7510/2401*T^46 - 5626/2401*T^45 - 1409/2401*T^44 + 7057/2401*T^43 - 
        932/343*T^42 + 496/2401*T^41 + 5293/2401*T^40 - 6663/2401*T^39 + 
        2917/2401*T^38 + 3085/2401*T^37 - 6003/2401*T^36 + 3044/2401*T^35 + 
        2461/2401*T^34 - 97/49*T^33 + 358/343*T^32 + 828/2401*T^31 - 2034/2401*T^30 
        + 1487/2401*T^29 - 1487/2401*T^27 + 2034/2401*T^26 - 828/2401*T^25 - 
        358/343*T^24 + 97/49*T^23 - 2461/2401*T^22 - 3044/2401*T^21 + 6003/2401*T^20
        - 3085/2401*T^19 - 2917/2401*T^18 + 6663/2401*T^17 - 5293/2401*T^16 - 
        496/2401*T^15 + 932/343*T^14 - 7057/2401*T^13 + 1409/2401*T^12 + 
        5626/2401*T^11 - 7510/2401*T^10 + 2242/2401*T^9 + 5487/2401*T^8 - 
        8703/2401*T^7 + 4052/2401*T^6 + 4565/2401*T^5 - 8110/2401*T^4 + 460/343*T^3 
        + 79/49*T^2 - 16/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 
        2*X*Y^7 + X*Y^6 + 2*X*Y^5 + X*Y^4 + 3*X*Y^3 + X*Y^2 + 5*X*Y + 3*X + Y^30 + 
        6*Y^29 + 6*Y^28 + 4*Y^27 + 3*Y^26 + 3*Y^25 + 6*Y^24 + 2*Y^23 + 6*Y^22 + 
        6*Y^21 + 4*Y^19 + 4*Y^18 + 3*Y^17 + 5*Y^16 + 4*Y^15 + 5*Y^14 + Y^13 + 5*Y^12
        + 3*Y^11 + 3*Y^10 + 3*Y^9 + 6*Y^6 + 4*Y^5 + 4*Y^4 + Y^3 + 3*Y^2 + 4*Y + 3,
    T^56 + T^55 + 1/7*T^54 + 53/343*T^53 + 185/2401*T^52 + 1807/2401*T^51 + 
        15/49*T^50 - 748/2401*T^49 + 900/2401*T^48 + 51/343*T^47 + 1143/2401*T^46 + 
        703/2401*T^45 + 181/2401*T^44 + 1601/2401*T^43 + 128/2401*T^42 - 
        288/2401*T^41 + 117/2401*T^40 + 522/2401*T^39 + 54/343*T^38 - 1196/2401*T^37
        - 1005/2401*T^36 + 156/2401*T^35 + 559/2401*T^34 - 332/2401*T^33 - 
        32/49*T^32 - 64/343*T^31 + 670/2401*T^30 - 514/2401*T^29 - 1429/2401*T^28 - 
        514/2401*T^27 + 670/2401*T^26 - 64/343*T^25 - 32/49*T^24 - 332/2401*T^23 + 
        559/2401*T^22 + 156/2401*T^21 - 1005/2401*T^20 - 1196/2401*T^19 + 
        54/343*T^18 + 522/2401*T^17 + 117/2401*T^16 - 288/2401*T^15 + 128/2401*T^14 
        + 1601/2401*T^13 + 181/2401*T^12 + 703/2401*T^11 + 1143/2401*T^10 + 
        51/343*T^9 + 900/2401*T^8 - 748/2401*T^7 + 15/49*T^6 + 1807/2401*T^5 + 
        185/2401*T^4 + 53/343*T^3 + 1/7*T^2 + T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + X*Y^9 + 6*X*Y^8 + X*Y^7 + 
        4*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + X*Y^2 + 3*X*Y + 2*X + 2*Y^30 + 
        2*Y^29 + 3*Y^28 + 6*Y^27 + 5*Y^25 + 3*Y^24 + 4*Y^23 + 2*Y^22 + 6*Y^21 + 
        5*Y^20 + 4*Y^19 + Y^18 + 4*Y^16 + 5*Y^14 + Y^13 + 5*Y^11 + Y^10 + Y^9 + 
        3*Y^8 + 2*Y^7 + Y^6 + 2*Y^5 + 2*Y^3 + 5*Y^2 + 4*Y,
    -T^56 + 1/7*T^55 + 47/49*T^54 + 24/49*T^53 - 263/343*T^52 - 101/343*T^51 - 
        9/2401*T^50 + 2811/2401*T^49 - 1031/2401*T^48 - 3118/2401*T^47 - 
        955/2401*T^46 + 2571/2401*T^45 + 188/343*T^44 - 2/49*T^43 - 2486/2401*T^42 -
        1206/2401*T^41 + 442/343*T^40 + 1028/2401*T^39 - 1683/2401*T^38 - 
        1675/2401*T^37 + 414/2401*T^36 + 1228/2401*T^35 + 1730/2401*T^34 - 
        195/343*T^33 - 865/2401*T^32 - 755/2401*T^31 + 199/2401*T^30 + 
        1187/2401*T^29 - 1187/2401*T^27 - 199/2401*T^26 + 755/2401*T^25 + 
        865/2401*T^24 + 195/343*T^23 - 1730/2401*T^22 - 1228/2401*T^21 - 
        414/2401*T^20 + 1675/2401*T^19 + 1683/2401*T^18 - 1028/2401*T^17 - 
        442/343*T^16 + 1206/2401*T^15 + 2486/2401*T^14 + 2/49*T^13 - 188/343*T^12 - 
        2571/2401*T^11 + 955/2401*T^10 + 3118/2401*T^9 + 1031/2401*T^8 - 
        2811/2401*T^7 + 9/2401*T^6 + 101/343*T^5 + 263/343*T^4 - 24/49*T^3 - 
        47/49*T^2 - 1/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 4*X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + X*Y^3 + 2*X*Y^2 + 3*X*Y + 
        4*X + 6*Y^30 + 6*Y^29 + 4*Y^28 + 2*Y^27 + 3*Y^26 + Y^24 + 5*Y^23 + 5*Y^19 + 
        4*Y^18 + 5*Y^17 + Y^16 + 2*Y^15 + Y^14 + Y^13 + 2*Y^11 + 4*Y^10 + Y^9 + 
        5*Y^8 + 6*Y^6 + 6*Y^5 + 2*Y^4 + 6*Y^2 + 3*Y + 3,
    T^56 + 2/7*T^55 - 44/49*T^54 - 277/343*T^53 + 814/2401*T^52 + 2238/2401*T^51 - 
        654/2401*T^50 - 1389/2401*T^49 - 199/2401*T^48 - 61/343*T^47 - 6/343*T^46 + 
        482/2401*T^45 + 458/2401*T^44 - 1233/2401*T^43 - 171/2401*T^42 + 
        1283/2401*T^41 - 120/2401*T^40 - 360/2401*T^39 - 109/2401*T^38 + 
        149/343*T^37 - 1083/2401*T^36 - 1338/2401*T^35 + 286/343*T^34 + 
        1457/2401*T^33 - 1013/2401*T^32 - 1707/2401*T^31 - 86/2401*T^30 + 
        1207/2401*T^29 - 74/2401*T^28 + 1207/2401*T^27 - 86/2401*T^26 - 
        1707/2401*T^25 - 1013/2401*T^24 + 1457/2401*T^23 + 286/343*T^22 - 
        1338/2401*T^21 - 1083/2401*T^20 + 149/343*T^19 - 109/2401*T^18 - 
        360/2401*T^17 - 120/2401*T^16 + 1283/2401*T^15 - 171/2401*T^14 - 
        1233/2401*T^13 + 458/2401*T^12 + 482/2401*T^11 - 6/343*T^10 - 61/343*T^9 - 
        199/2401*T^8 - 1389/2401*T^7 - 654/2401*T^6 + 2238/2401*T^5 + 814/2401*T^4 -
        277/343*T^3 - 44/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 6*X*Y^6 + 2*X*Y^5 + X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + X*Y + 2*X + 3*Y^30
        + 5*Y^29 + 5*Y^27 + 2*Y^26 + Y^25 + 6*Y^24 + 6*Y^23 + 5*Y^22 + 4*Y^21 + 
        2*Y^19 + 4*Y^17 + Y^16 + Y^15 + 5*Y^14 + 4*Y^13 + Y^11 + 2*Y^10 + 4*Y^8 + 
        3*Y^7 + 6*Y^6 + 5*Y^5 + 5*Y^4 + 4*Y^3 + 2*Y^2,
    -T^56 - 6/7*T^55 - 1/7*T^54 + 32/49*T^53 + 51/2401*T^52 - 535/2401*T^51 + 
        339/2401*T^50 + 1324/2401*T^49 + 1275/2401*T^48 + 1117/2401*T^47 + 
        1150/2401*T^46 + 13/49*T^45 - 811/2401*T^44 - 1672/2401*T^43 + 208/2401*T^42
        + 585/2401*T^41 - 211/2401*T^40 - 2389/2401*T^39 - 107/2401*T^38 + 
        785/2401*T^37 + 17/49*T^36 - 866/2401*T^35 + 102/2401*T^34 - 316/2401*T^33 -
        1335/2401*T^32 - 1502/2401*T^31 + 290/2401*T^30 + 131/343*T^29 - 
        131/343*T^27 - 290/2401*T^26 + 1502/2401*T^25 + 1335/2401*T^24 + 
        316/2401*T^23 - 102/2401*T^22 + 866/2401*T^21 - 17/49*T^20 - 785/2401*T^19 +
        107/2401*T^18 + 2389/2401*T^17 + 211/2401*T^16 - 585/2401*T^15 - 
        208/2401*T^14 + 1672/2401*T^13 + 811/2401*T^12 - 13/49*T^11 - 1150/2401*T^10
        - 1117/2401*T^9 - 1275/2401*T^8 - 1324/2401*T^7 - 339/2401*T^6 + 
        535/2401*T^5 - 51/2401*T^4 - 32/49*T^3 + 1/7*T^2 + 6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + X*Y^11 + 2*X*Y^10 + 6*X*Y^9 + 
        4*X*Y^8 + 4*X*Y^7 + X*Y^6 + X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + X*Y^2 + 6*X*Y + 2*X 
        + 6*Y^30 + Y^29 + 3*Y^24 + 4*Y^22 + 5*Y^20 + 5*Y^19 + Y^18 + 4*Y^17 + 6*Y^15
        + Y^14 + 6*Y^13 + 3*Y^12 + 5*Y^11 + 6*Y^10 + 2*Y^9 + Y^8 + 5*Y^7 + 3*Y^6 + 
        Y^5 + 6*Y^4 + Y^3 + Y^2 + 4,
    -T^56 + 2/7*T^55 + 8/49*T^54 + 95/343*T^53 + 485/2401*T^52 - 376/2401*T^51 + 
        1898/2401*T^50 - 1655/2401*T^49 + 164/2401*T^48 + 369/2401*T^47 + 
        95/343*T^46 - 187/2401*T^45 - 690/2401*T^44 - 419/2401*T^43 - 131/2401*T^42 
        - 38/2401*T^41 - 594/2401*T^40 + 445/2401*T^39 - 768/2401*T^38 + 
        948/2401*T^37 - 99/2401*T^36 - 276/2401*T^35 + 540/2401*T^34 + 262/2401*T^33
        + 81/2401*T^32 + 101/2401*T^31 - 13/343*T^30 + 821/2401*T^29 - 821/2401*T^27
        + 13/343*T^26 - 101/2401*T^25 - 81/2401*T^24 - 262/2401*T^23 - 540/2401*T^22
        + 276/2401*T^21 + 99/2401*T^20 - 948/2401*T^19 + 768/2401*T^18 - 
        445/2401*T^17 + 594/2401*T^16 + 38/2401*T^15 + 131/2401*T^14 + 419/2401*T^13
        + 690/2401*T^12 + 187/2401*T^11 - 95/343*T^10 - 369/2401*T^9 - 164/2401*T^8 
        + 1655/2401*T^7 - 1898/2401*T^6 + 376/2401*T^5 - 485/2401*T^4 - 95/343*T^3 -
        8/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 4*X*Y^8 + 6*X*Y^7 + 
        3*X*Y^6 + X*Y^5 + 5*X*Y^4 + X*Y^3 + X*Y^2 + 4*X*Y + 3*X + 5*Y^30 + 4*Y^29 + 
        4*Y^28 + 2*Y^26 + 3*Y^23 + 4*Y^22 + Y^21 + Y^20 + 5*Y^18 + 2*Y^17 + 3*Y^16 +
        5*Y^15 + Y^14 + 4*Y^13 + 2*Y^12 + 2*Y^11 + 5*Y^10 + 3*Y^9 + 6*Y^8 + Y^7 + 
        4*Y^6 + 2*Y^5 + Y^4 + 4*Y^3 + 6*Y^2 + 2*Y + 1,
    -T^56 + 5/7*T^55 + 32/49*T^54 - 344/343*T^53 + 771/2401*T^52 - 593/2401*T^51 + 
        1429/2401*T^50 + 1090/2401*T^49 - 2220/2401*T^48 + 921/2401*T^47 - 
        363/2401*T^46 - 87/343*T^45 + 1692/2401*T^44 - 898/2401*T^43 - 
        1058/2401*T^42 + 1532/2401*T^41 - 402/2401*T^40 + 801/2401*T^39 - 
        418/2401*T^38 - 159/343*T^37 + 1660/2401*T^36 - 348/2401*T^35 - 
        1234/2401*T^34 + 1163/2401*T^33 + 391/2401*T^32 - 1105/2401*T^31 + 
        1420/2401*T^30 - 634/2401*T^29 + 634/2401*T^27 - 1420/2401*T^26 + 
        1105/2401*T^25 - 391/2401*T^24 - 1163/2401*T^23 + 1234/2401*T^22 + 
        348/2401*T^21 - 1660/2401*T^20 + 159/343*T^19 + 418/2401*T^18 - 
        801/2401*T^17 + 402/2401*T^16 - 1532/2401*T^15 + 1058/2401*T^14 + 
        898/2401*T^13 - 1692/2401*T^12 + 87/343*T^11 + 363/2401*T^10 - 921/2401*T^9 
        + 2220/2401*T^8 - 1090/2401*T^7 - 1429/2401*T^6 + 593/2401*T^5 - 
        771/2401*T^4 + 344/343*T^3 - 32/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 2*X*Y^9 
        + 5*X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 6*X*Y 
        + 5*X + Y^30 + 6*Y^29 + 3*Y^28 + 4*Y^27 + 2*Y^26 + Y^25 + 4*Y^24 + Y^23 + 
        Y^22 + Y^21 + Y^19 + 3*Y^18 + 5*Y^17 + 5*Y^16 + 2*Y^15 + 6*Y^14 + 6*Y^13 + 
        3*Y^12 + 6*Y^11 + 2*Y^10 + Y^9 + Y^8 + 3*Y^7 + 5*Y^6 + 6*Y^5 + 4*Y^4 + 6*Y^3
        + 2*Y^2 + 5*Y + 3,
    -T^56 - 4/7*T^55 + 5/49*T^54 + 24/49*T^53 - 458/2401*T^52 + 48/343*T^51 + 
        15/2401*T^50 - 101/2401*T^49 - 1228/2401*T^48 - 855/2401*T^47 - 
        851/2401*T^46 + 303/2401*T^45 + 489/2401*T^44 + 1003/2401*T^43 + 
        425/2401*T^42 - 149/2401*T^41 - 873/2401*T^40 - 940/2401*T^39 - 
        769/2401*T^38 + 362/2401*T^37 + 1495/2401*T^36 + 271/2401*T^35 - 
        688/2401*T^34 + 510/2401*T^33 + 1115/2401*T^32 - 482/2401*T^31 - 
        692/2401*T^30 - 47/343*T^29 + 47/343*T^27 + 692/2401*T^26 + 482/2401*T^25 - 
        1115/2401*T^24 - 510/2401*T^23 + 688/2401*T^22 - 271/2401*T^21 - 
        1495/2401*T^20 - 362/2401*T^19 + 769/2401*T^18 + 940/2401*T^17 + 
        873/2401*T^16 + 149/2401*T^15 - 425/2401*T^14 - 1003/2401*T^13 - 
        489/2401*T^12 - 303/2401*T^11 + 851/2401*T^10 + 855/2401*T^9 + 1228/2401*T^8
        + 101/2401*T^7 - 15/2401*T^6 - 48/343*T^5 + 458/2401*T^4 - 24/49*T^3 - 
        5/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 5*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + X*Y^10 + X*Y^9 + 4*X*Y^8 + 3*X*Y^7 + 
        6*X*Y^6 + 6*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 3*X*Y + 2*Y^30 + Y^29 + 
        4*Y^28 + 4*Y^27 + Y^26 + 3*Y^25 + 6*Y^24 + 3*Y^23 + 5*Y^21 + 3*Y^20 + 5*Y^19
        + Y^18 + 6*Y^17 + Y^15 + 5*Y^13 + Y^12 + 3*Y^11 + 2*Y^10 + 5*Y^9 + 3*Y^8 + 
        5*Y^7 + Y^6 + 5*Y^5 + 4*Y^4 + 3*Y^3 + 4*Y^2 + 6*Y + 1,
    T^56 - 13/7*T^55 + T^54 + 158/343*T^53 - 2900/2401*T^52 + 283/343*T^51 - 
        1798/2401*T^50 + 3727/2401*T^49 - 4601/2401*T^48 + 2372/2401*T^47 + 
        1390/2401*T^46 - 53/49*T^45 + 1821/2401*T^44 - 2411/2401*T^43 + 95/49*T^42 -
        751/343*T^41 + 366/343*T^40 + 123/343*T^39 - 2111/2401*T^38 + 2076/2401*T^37
        - 3567/2401*T^36 + 5346/2401*T^35 - 4315/2401*T^34 + 1151/2401*T^33 + 
        1000/2401*T^32 - 566/2401*T^31 + 743/2401*T^30 - 3252/2401*T^29 + 
        4843/2401*T^28 - 3252/2401*T^27 + 743/2401*T^26 - 566/2401*T^25 + 
        1000/2401*T^24 + 1151/2401*T^23 - 4315/2401*T^22 + 5346/2401*T^21 - 
        3567/2401*T^20 + 2076/2401*T^19 - 2111/2401*T^18 + 123/343*T^17 + 
        366/343*T^16 - 751/343*T^15 + 95/49*T^14 - 2411/2401*T^13 + 1821/2401*T^12 -
        53/49*T^11 + 1390/2401*T^10 + 2372/2401*T^9 - 4601/2401*T^8 + 3727/2401*T^7 
        - 1798/2401*T^6 + 283/343*T^5 - 2900/2401*T^4 + 158/343*T^3 + T^2 - 13/7*T +
        1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 5*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 4*X*Y^8 + 3*X*Y^7 +
        5*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + X*Y^3 + 2*X*Y^2 + 3*X*Y + 3*X + 4*Y^30 + 
        4*Y^29 + 2*Y^28 + 2*Y^27 + 3*Y^26 + 3*Y^25 + 5*Y^23 + 6*Y^22 + 6*Y^21 + 
        5*Y^19 + 3*Y^18 + Y^17 + 6*Y^16 + 5*Y^15 + 4*Y^12 + 2*Y^11 + Y^10 + Y^9 + 
        Y^8 + Y^7 + 6*Y^6 + 6*Y^4 + Y^3 + 6*Y^2 + 3*Y + 1,
    -T^56 - 3/7*T^55 - 9/49*T^54 - 100/343*T^53 - 545/2401*T^52 + 2570/2401*T^51 + 
        1969/2401*T^50 - 1252/2401*T^49 + 445/2401*T^48 + 311/343*T^47 + 
        62/2401*T^46 - 1146/2401*T^45 + 1940/2401*T^44 + 46/2401*T^43 - 
        2619/2401*T^42 - 1175/2401*T^41 + 1292/2401*T^40 - 3/2401*T^39 - 22/49*T^38 
        + 751/2401*T^37 + 111/2401*T^36 - 486/2401*T^35 + 22/343*T^34 + 
        2475/2401*T^33 + 167/343*T^32 + 816/2401*T^31 - 459/2401*T^30 + 
        436/2401*T^29 - 436/2401*T^27 + 459/2401*T^26 - 816/2401*T^25 - 167/343*T^24
        - 2475/2401*T^23 - 22/343*T^22 + 486/2401*T^21 - 111/2401*T^20 - 
        751/2401*T^19 + 22/49*T^18 + 3/2401*T^17 - 1292/2401*T^16 + 1175/2401*T^15 +
        2619/2401*T^14 - 46/2401*T^13 - 1940/2401*T^12 + 1146/2401*T^11 - 
        62/2401*T^10 - 311/343*T^9 - 445/2401*T^8 + 1252/2401*T^7 - 1969/2401*T^6 - 
        2570/2401*T^5 + 545/2401*T^4 + 100/343*T^3 + 9/49*T^2 + 3/7*T + 1
*], [*
    X^3 + X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + X*Y^9 + 2*X*Y^8 + 6*X*Y^7 + X*Y^5 + 6*X*Y^4
        + 5*X*Y^3 + 5*X + 5*Y^30 + 5*Y^29 + 3*Y^28 + 6*Y^27 + 3*Y^26 + 3*Y^25 + Y^24
        + 6*Y^23 + 6*Y^22 + 5*Y^21 + Y^20 + 2*Y^19 + 6*Y^18 + 5*Y^17 + 3*Y^16 + Y^15
        + 5*Y^14 + 3*Y^13 + 5*Y^12 + 4*Y^11 + 2*Y^10 + 6*Y^9 + 2*Y^7 + 3*Y^6 + 2*Y^5
        + 3*Y^4 + 3*Y^3 + 3*Y^2 + 6*Y + 5,
    -T^56 + 3/7*T^55 + T^54 - 11/49*T^53 - 4/7*T^52 - 291/2401*T^51 + 2888/2401*T^50
        + 44/343*T^49 - 2211/2401*T^48 - 2253/2401*T^47 + 4079/2401*T^46 + 
        2568/2401*T^45 - 4931/2401*T^44 - 2487/2401*T^43 + 2846/2401*T^42 + 
        3900/2401*T^41 - 2671/2401*T^40 - 4394/2401*T^39 + 2148/2401*T^38 + 
        4748/2401*T^37 - 2208/2401*T^36 - 5140/2401*T^35 + 2105/2401*T^34 + 
        5038/2401*T^33 - 513/2401*T^32 - 5017/2401*T^31 - 445/2401*T^30 + 
        724/343*T^29 - 724/343*T^27 + 445/2401*T^26 + 5017/2401*T^25 + 513/2401*T^24
        - 5038/2401*T^23 - 2105/2401*T^22 + 5140/2401*T^21 + 2208/2401*T^20 - 
        4748/2401*T^19 - 2148/2401*T^18 + 4394/2401*T^17 + 2671/2401*T^16 - 
        3900/2401*T^15 - 2846/2401*T^14 + 2487/2401*T^13 + 4931/2401*T^12 - 
        2568/2401*T^11 - 4079/2401*T^10 + 2253/2401*T^9 + 2211/2401*T^8 - 44/343*T^7
        - 2888/2401*T^6 + 291/2401*T^5 + 4/7*T^4 + 11/49*T^3 - T^2 - 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 2*X*Y^12 + X*Y^11 + X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 
        4*X*Y^7 + 2*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 3*X*Y + 4*X + 6*Y^30 + 5*Y^29 + 
        3*Y^27 + 5*Y^26 + 4*Y^25 + 6*Y^24 + 3*Y^23 + 5*Y^22 + 4*Y^20 + 4*Y^18 + 
        5*Y^17 + Y^16 + 5*Y^15 + Y^14 + 4*Y^13 + 3*Y^12 + 6*Y^11 + 3*Y^10 + 3*Y^7 + 
        5*Y^6 + 3*Y^5 + Y^4 + 5*Y^3 + 2*Y^2 + 5*Y,
    T^56 + 2/7*T^55 - 34/49*T^54 - 169/343*T^53 - 464/2401*T^52 - 44/343*T^51 - 
        766/2401*T^50 + 1804/2401*T^49 + 1493/2401*T^48 - 991/2401*T^47 - 
        1236/2401*T^46 + 796/2401*T^45 + 82/343*T^44 - 866/2401*T^43 - 25/343*T^42 +
        537/2401*T^41 - 69/2401*T^40 - 733/2401*T^39 + 57/343*T^38 + 1709/2401*T^37 
        + 92/2401*T^36 - 488/2401*T^35 + 479/2401*T^34 - 148/2401*T^33 - 5/7*T^32 - 
        1117/2401*T^31 + 1314/2401*T^30 + 722/2401*T^29 - 481/2401*T^28 + 
        722/2401*T^27 + 1314/2401*T^26 - 1117/2401*T^25 - 5/7*T^24 - 148/2401*T^23 +
        479/2401*T^22 - 488/2401*T^21 + 92/2401*T^20 + 1709/2401*T^19 + 57/343*T^18 
        - 733/2401*T^17 - 69/2401*T^16 + 537/2401*T^15 - 25/343*T^14 - 866/2401*T^13
        + 82/343*T^12 + 796/2401*T^11 - 1236/2401*T^10 - 991/2401*T^9 + 
        1493/2401*T^8 + 1804/2401*T^7 - 766/2401*T^6 - 44/343*T^5 - 464/2401*T^4 - 
        169/343*T^3 - 34/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        X*Y^8 + 2*X*Y^7 + X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 5*X*Y^2 + 2*X*Y + 6*X + 5*Y^30
        + 5*Y^29 + 2*Y^28 + 5*Y^27 + 3*Y^26 + 6*Y^25 + Y^24 + 5*Y^23 + 5*Y^20 + Y^19
        + 5*Y^18 + 5*Y^17 + 6*Y^16 + 5*Y^15 + 3*Y^14 + Y^13 + 5*Y^12 + 3*Y^11 + Y^9 
        + 2*Y^8 + 3*Y^7 + Y^6 + 4*Y^5 + 5*Y^4 + 6*Y^3 + 2*Y^2 + Y,
    -T^56 - 6/7*T^55 + 1/49*T^54 + 146/343*T^53 + 32/49*T^52 + 89/2401*T^51 + 
        1040/2401*T^50 + 1850/2401*T^49 - 58/2401*T^48 - 197/343*T^47 - 
        1553/2401*T^46 - 110/343*T^45 + 533/2401*T^44 + 711/2401*T^43 + 
        101/2401*T^42 + 160/343*T^41 + 495/2401*T^40 - 320/2401*T^39 - 73/2401*T^38 
        - 701/2401*T^37 + 32/2401*T^36 - 410/2401*T^35 - 1550/2401*T^34 - 
        67/2401*T^33 + 1298/2401*T^32 + 1214/2401*T^31 + 179/343*T^30 - 
        649/2401*T^29 + 649/2401*T^27 - 179/343*T^26 - 1214/2401*T^25 - 
        1298/2401*T^24 + 67/2401*T^23 + 1550/2401*T^22 + 410/2401*T^21 - 
        32/2401*T^20 + 701/2401*T^19 + 73/2401*T^18 + 320/2401*T^17 - 495/2401*T^16 
        - 160/343*T^15 - 101/2401*T^14 - 711/2401*T^13 - 533/2401*T^12 + 
        110/343*T^11 + 1553/2401*T^10 + 197/343*T^9 + 58/2401*T^8 - 1850/2401*T^7 - 
        1040/2401*T^6 - 89/2401*T^5 - 32/49*T^4 - 146/343*T^3 - 1/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 5*X*Y^8 
        + 5*X*Y^7 + X*Y^6 + 3*X*Y^5 + 3*X*Y^3 + 4*X*Y^2 + 6*X*Y + 4*Y^30 + 2*Y^29 + 
        4*Y^28 + 2*Y^27 + 5*Y^25 + 5*Y^24 + 2*Y^23 + 3*Y^22 + 6*Y^18 + Y^17 + 6*Y^16
        + 5*Y^14 + 6*Y^13 + 6*Y^11 + 2*Y^10 + 3*Y^9 + Y^8 + 2*Y^6 + 4*Y^5 + 4*Y^3 + 
        3*Y^2 + 5,
    -T^56 - 3/7*T^55 - 37/49*T^54 - 307/343*T^53 - 1495/2401*T^52 + 922/2401*T^51 + 
        75/343*T^50 + 782/2401*T^49 + 1865/2401*T^48 + 1349/2401*T^47 - 
        330/2401*T^46 - 132/2401*T^45 - 114/2401*T^44 - 1072/2401*T^43 - 
        1221/2401*T^42 + 185/343*T^41 - 404/2401*T^40 - 25/343*T^39 - 256/2401*T^38 
        - 321/2401*T^37 - 2337/2401*T^36 - 155/343*T^35 + 130/2401*T^34 + 
        59/343*T^33 + 166/343*T^32 + 2556/2401*T^31 + 2593/2401*T^30 + 268/2401*T^29
        - 268/2401*T^27 - 2593/2401*T^26 - 2556/2401*T^25 - 166/343*T^24 - 
        59/343*T^23 - 130/2401*T^22 + 155/343*T^21 + 2337/2401*T^20 + 321/2401*T^19 
        + 256/2401*T^18 + 25/343*T^17 + 404/2401*T^16 - 185/343*T^15 + 
        1221/2401*T^14 + 1072/2401*T^13 + 114/2401*T^12 + 132/2401*T^11 + 
        330/2401*T^10 - 1349/2401*T^9 - 1865/2401*T^8 - 782/2401*T^7 - 75/343*T^6 - 
        922/2401*T^5 + 1495/2401*T^4 + 307/343*T^3 + 37/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + X*Y^10 + 6*X*Y^9 + 
        2*X*Y^8 + 5*X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + X*Y^3 + 3*X*Y^2 + X*Y + 
        6*X + Y^30 + 3*Y^29 + 6*Y^28 + 3*Y^27 + 2*Y^26 + 2*Y^25 + 5*Y^24 + 6*Y^23 + 
        2*Y^21 + 4*Y^19 + Y^18 + 4*Y^15 + 4*Y^14 + 3*Y^13 + 3*Y^12 + 5*Y^11 + 4*Y^10
        + 2*Y^9 + Y^8 + 2*Y^6 + Y^5 + 4*Y^4 + 2*Y^3 + 3*Y^2 + 4*Y + 2,
    -T^56 + 5/7*T^55 - 1/49*T^54 - 540/343*T^53 + 2228/2401*T^52 + 1566/2401*T^51 - 
        3313/2401*T^50 - 33/2401*T^49 + 600/343*T^48 - 2232/2401*T^47 - 
        2021/2401*T^46 + 64/49*T^45 + 2188/2401*T^44 - 629/343*T^43 + 503/2401*T^42 
        + 5365/2401*T^41 - 3802/2401*T^40 - 1934/2401*T^39 + 4268/2401*T^38 - 
        712/2401*T^37 - 3554/2401*T^36 + 2010/2401*T^35 + 848/2401*T^34 - 
        1557/2401*T^33 - 1368/2401*T^32 + 1569/2401*T^31 + 493/2401*T^30 - 
        1998/2401*T^29 + 1998/2401*T^27 - 493/2401*T^26 - 1569/2401*T^25 + 
        1368/2401*T^24 + 1557/2401*T^23 - 848/2401*T^22 - 2010/2401*T^21 + 
        3554/2401*T^20 + 712/2401*T^19 - 4268/2401*T^18 + 1934/2401*T^17 + 
        3802/2401*T^16 - 5365/2401*T^15 - 503/2401*T^14 + 629/343*T^13 - 
        2188/2401*T^12 - 64/49*T^11 + 2021/2401*T^10 + 2232/2401*T^9 - 600/343*T^8 +
        33/2401*T^7 + 3313/2401*T^6 - 1566/2401*T^5 - 2228/2401*T^4 + 540/343*T^3 + 
        1/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 
        X*Y^8 + 2*X*Y^7 + 3*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 4*X*Y + 5*X + 
        6*Y^30 + 5*Y^29 + 5*Y^27 + 6*Y^26 + 2*Y^25 + 4*Y^24 + 4*Y^23 + 4*Y^22 + 
        4*Y^20 + 3*Y^18 + 2*Y^17 + 3*Y^16 + Y^15 + 6*Y^13 + 6*Y^12 + Y^11 + 5*Y^10 +
        Y^8 + 2*Y^7 + Y^6 + 6*Y^5 + 3*Y^4 + Y^3 + Y^2 + Y + 3,
    T^56 + 2*T^55 + 72/49*T^54 - 81/343*T^53 - 3945/2401*T^52 - 3251/2401*T^51 - 
        1114/2401*T^50 - 1153/2401*T^49 - 1378/2401*T^48 + 1447/2401*T^47 + 
        5394/2401*T^46 + 5141/2401*T^45 + 582/2401*T^44 - 2977/2401*T^43 - 
        1891/2401*T^42 + 1058/2401*T^41 + 879/2401*T^40 - 1669/2401*T^39 - 
        282/343*T^38 - 435/2401*T^37 - 2/343*T^36 - 194/343*T^35 - 1669/2401*T^34 + 
        20/49*T^33 + 3170/2401*T^32 + 1615/2401*T^31 - 163/343*T^30 - 2599/2401*T^29
        - 2963/2401*T^28 - 2599/2401*T^27 - 163/343*T^26 + 1615/2401*T^25 + 
        3170/2401*T^24 + 20/49*T^23 - 1669/2401*T^22 - 194/343*T^21 - 2/343*T^20 - 
        435/2401*T^19 - 282/343*T^18 - 1669/2401*T^17 + 879/2401*T^16 + 
        1058/2401*T^15 - 1891/2401*T^14 - 2977/2401*T^13 + 582/2401*T^12 + 
        5141/2401*T^11 + 5394/2401*T^10 + 1447/2401*T^9 - 1378/2401*T^8 - 
        1153/2401*T^7 - 1114/2401*T^6 - 3251/2401*T^5 - 3945/2401*T^4 - 81/343*T^3 +
        72/49*T^2 + 2*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 3*X*Y^8 
        + 6*X*Y^7 + 3*X*Y^6 + X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + X*Y^2 + 3*X*Y + 4*X + 
        4*Y^30 + 4*Y^29 + 6*Y^28 + 5*Y^27 + 2*Y^26 + 4*Y^24 + 3*Y^23 + 3*Y^22 + 
        3*Y^21 + Y^20 + 5*Y^19 + 3*Y^18 + 6*Y^16 + 6*Y^15 + 4*Y^13 + 2*Y^11 + 2*Y^9 
        + 4*Y^8 + 4*Y^7 + 2*Y^6 + 4*Y^4 + 6*Y^3 + 4*Y^2 + 6,
    T^56 + 8/7*T^55 + 48/49*T^54 + 30/49*T^53 + 414/2401*T^52 - 517/2401*T^51 - 
        825/2401*T^50 - 696/2401*T^49 - 1184/2401*T^48 - 218/343*T^47 - 16/343*T^46 
        + 271/2401*T^45 + 297/2401*T^44 - 1069/2401*T^43 - 1289/2401*T^42 - 
        510/2401*T^41 + 1198/2401*T^40 + 2600/2401*T^39 + 2489/2401*T^38 + 
        2018/2401*T^37 + 1679/2401*T^36 + 615/2401*T^35 + 484/2401*T^34 - 
        429/2401*T^33 - 1037/2401*T^32 - 1388/2401*T^31 - 487/2401*T^30 + 
        197/2401*T^29 - 439/2401*T^28 + 197/2401*T^27 - 487/2401*T^26 - 
        1388/2401*T^25 - 1037/2401*T^24 - 429/2401*T^23 + 484/2401*T^22 + 
        615/2401*T^21 + 1679/2401*T^20 + 2018/2401*T^19 + 2489/2401*T^18 + 
        2600/2401*T^17 + 1198/2401*T^16 - 510/2401*T^15 - 1289/2401*T^14 - 
        1069/2401*T^13 + 297/2401*T^12 + 271/2401*T^11 - 16/343*T^10 - 218/343*T^9 -
        1184/2401*T^8 - 696/2401*T^7 - 825/2401*T^6 - 517/2401*T^5 + 414/2401*T^4 + 
        30/49*T^3 + 48/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 
        2*X*Y^8 + 3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 5*X*Y + 2*X + Y^30 + 
        5*Y^29 + 4*Y^27 + Y^26 + 3*Y^25 + 4*Y^24 + 2*Y^23 + 6*Y^22 + Y^21 + 6*Y^19 +
        Y^17 + 5*Y^16 + 3*Y^15 + 4*Y^14 + 6*Y^13 + 6*Y^12 + 2*Y^10 + 5*Y^9 + 6*Y^8 +
        Y^7 + 5*Y^6 + 6*Y^5 + Y^4 + 4*Y^3 + 3*Y^2 + 6*Y + 6,
    -T^56 + 10/7*T^55 + 1/49*T^54 - 517/343*T^53 + 1663/2401*T^52 + 166/343*T^51 + 
        342/2401*T^50 - 2346/2401*T^49 + 194/2401*T^48 + 3037/2401*T^47 - 
        2454/2401*T^46 - 248/2401*T^45 + 1683/2401*T^44 - 1219/2401*T^43 + 8/49*T^42
        - 27/2401*T^41 - 431/2401*T^40 + 715/2401*T^39 + 454/2401*T^38 - 
        181/343*T^37 - 89/2401*T^36 + 412/2401*T^35 + 1243/2401*T^34 - 
        1210/2401*T^33 - 907/2401*T^32 + 1584/2401*T^31 - 44/343*T^30 - 
        573/2401*T^29 + 573/2401*T^27 + 44/343*T^26 - 1584/2401*T^25 + 907/2401*T^24
        + 1210/2401*T^23 - 1243/2401*T^22 - 412/2401*T^21 + 89/2401*T^20 + 
        181/343*T^19 - 454/2401*T^18 - 715/2401*T^17 + 431/2401*T^16 + 27/2401*T^15 
        - 8/49*T^14 + 1219/2401*T^13 - 1683/2401*T^12 + 248/2401*T^11 + 
        2454/2401*T^10 - 3037/2401*T^9 - 194/2401*T^8 + 2346/2401*T^7 - 342/2401*T^6
        - 166/343*T^5 - 1663/2401*T^4 + 517/343*T^3 - 1/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + X*Y^11 + 3*X*Y^10 + 5*X*Y^8 + 
        5*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + X*Y + 5*X + 
        6*Y^30 + 5*Y^29 + Y^28 + 5*Y^27 + 5*Y^26 + 6*Y^25 + 3*Y^23 + 6*Y^22 + 5*Y^20
        + 6*Y^19 + 5*Y^18 + 5*Y^17 + 4*Y^15 + 2*Y^13 + 6*Y^12 + 2*Y^11 + 5*Y^10 + 
        2*Y^8 + 2*Y^7 + 3*Y^6 + 3*Y^5 + 6*Y^4 + Y^2 + 5*Y + 2,
    T^56 - 17/49*T^54 - 335/343*T^53 - 1660/2401*T^52 + 676/2401*T^51 + 
        1892/2401*T^50 + 773/2401*T^49 - 1332/2401*T^48 + 177/2401*T^47 - 
        283/2401*T^46 + 1789/2401*T^45 + 583/2401*T^44 - 950/2401*T^43 - 
        347/343*T^42 + 173/2401*T^41 + 32/2401*T^40 + 306/343*T^39 - 67/2401*T^38 - 
        36/49*T^37 - 2305/2401*T^36 + 535/2401*T^35 + 2553/2401*T^34 + 
        2225/2401*T^33 + 1136/2401*T^32 - 2834/2401*T^31 - 579/2401*T^30 - 
        590/2401*T^29 + 1832/2401*T^28 - 590/2401*T^27 - 579/2401*T^26 - 
        2834/2401*T^25 + 1136/2401*T^24 + 2225/2401*T^23 + 2553/2401*T^22 + 
        535/2401*T^21 - 2305/2401*T^20 - 36/49*T^19 - 67/2401*T^18 + 306/343*T^17 + 
        32/2401*T^16 + 173/2401*T^15 - 347/343*T^14 - 950/2401*T^13 + 583/2401*T^12 
        + 1789/2401*T^11 - 283/2401*T^10 + 177/2401*T^9 - 1332/2401*T^8 + 
        773/2401*T^7 + 1892/2401*T^6 + 676/2401*T^5 - 1660/2401*T^4 - 335/343*T^3 - 
        17/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 6*X*Y^7 + 5*X*Y^6 + X*Y^5 + 6*X*Y^4 + X*Y^3 + X*Y^2 + X*Y + 6*X + 
        6*Y^30 + 5*Y^29 + Y^27 + 2*Y^26 + 5*Y^25 + 5*Y^24 + 3*Y^23 + 4*Y^22 + 5*Y^21
        + 5*Y^19 + 4*Y^18 + 6*Y^17 + 5*Y^16 + 5*Y^15 + 5*Y^14 + 3*Y^13 + 6*Y^12 + 
        3*Y^11 + 5*Y^10 + Y^9 + 2*Y^8 + 5*Y^6 + 4*Y^5 + 2*Y^4 + Y^2 + 5*Y + 3,
    T^56 + 10/7*T^55 + 24/49*T^54 + 11/49*T^53 + 709/2401*T^52 + 103/343*T^51 - 
        240/2401*T^50 - 1019/2401*T^49 - 53/2401*T^48 - 900/2401*T^47 - 
        1586/2401*T^46 - 593/2401*T^45 - 67/343*T^44 - 646/2401*T^43 - 
        1131/2401*T^42 - 1283/2401*T^41 - 673/2401*T^40 + 225/2401*T^39 + 
        268/2401*T^38 + 227/2401*T^37 + 1119/2401*T^36 + 94/2401*T^35 - 
        405/2401*T^34 - 57/343*T^33 - 1327/2401*T^32 + 79/2401*T^31 + 48/343*T^30 - 
        443/2401*T^29 - 170/2401*T^28 - 443/2401*T^27 + 48/343*T^26 + 79/2401*T^25 -
        1327/2401*T^24 - 57/343*T^23 - 405/2401*T^22 + 94/2401*T^21 + 1119/2401*T^20
        + 227/2401*T^19 + 268/2401*T^18 + 225/2401*T^17 - 673/2401*T^16 - 
        1283/2401*T^15 - 1131/2401*T^14 - 646/2401*T^13 - 67/343*T^12 - 
        593/2401*T^11 - 1586/2401*T^10 - 900/2401*T^9 - 53/2401*T^8 - 1019/2401*T^7 
        - 240/2401*T^6 + 103/343*T^5 + 709/2401*T^4 + 11/49*T^3 + 24/49*T^2 + 10/7*T
        + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 
        2*X*Y^8 + 3*X*Y^7 + X*Y^6 + 5*X*Y^5 + X*Y^4 + 5*X*Y^2 + X*Y + X + 5*Y^30 + 
        5*Y^28 + Y^26 + 5*Y^23 + 4*Y^21 + 2*Y^20 + Y^18 + 4*Y^16 + 3*Y^15 + Y^14 + 
        4*Y^13 + 5*Y^12 + 6*Y^11 + 5*Y^8 + Y^7 + 6*Y^6 + 5*Y^5 + 4*Y^4 + 3*Y^2 + Y +
        3,
    T^56 - 1/7*T^55 - 51/49*T^54 + 79/343*T^53 + 127/343*T^52 - 58/2401*T^51 - 
        1208/2401*T^50 + 600/2401*T^49 + 202/343*T^48 + 445/2401*T^47 - 
        125/2401*T^46 - 367/2401*T^45 - 345/2401*T^44 + 24/343*T^43 + 130/2401*T^42 
        - 349/2401*T^41 + 165/2401*T^40 - 201/2401*T^39 + 34/2401*T^38 + 
        547/2401*T^37 + 26/343*T^36 - 2/7*T^35 - 127/2401*T^34 + 1096/2401*T^33 - 
        636/2401*T^32 - 589/2401*T^31 + 486/2401*T^30 - 222/2401*T^29 - 
        109/2401*T^28 - 222/2401*T^27 + 486/2401*T^26 - 589/2401*T^25 - 
        636/2401*T^24 + 1096/2401*T^23 - 127/2401*T^22 - 2/7*T^21 + 26/343*T^20 + 
        547/2401*T^19 + 34/2401*T^18 - 201/2401*T^17 + 165/2401*T^16 - 349/2401*T^15
        + 130/2401*T^14 + 24/343*T^13 - 345/2401*T^12 - 367/2401*T^11 - 
        125/2401*T^10 + 445/2401*T^9 + 202/343*T^8 + 600/2401*T^7 - 1208/2401*T^6 - 
        58/2401*T^5 + 127/343*T^4 + 79/343*T^3 - 51/49*T^2 - 1/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 
        X*Y^8 + 6*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 5*X*Y + 
        2*X + 2*Y^30 + 3*Y^29 + 5*Y^28 + Y^26 + 5*Y^24 + 3*Y^23 + 5*Y^22 + Y^20 + 
        4*Y^19 + 2*Y^18 + 6*Y^17 + 5*Y^16 + 2*Y^15 + 5*Y^14 + 4*Y^13 + 5*Y^12 + 
        6*Y^11 + 2*Y^10 + 3*Y^9 + 6*Y^8 + 4*Y^7 + 4*Y^6 + Y^5 + 6*Y^2 + Y,
    T^56 + 1/7*T^55 - 6/7*T^54 - 75/343*T^53 - 501/2401*T^52 - 558/2401*T^51 + 
        257/343*T^50 - 1559/2401*T^49 + 127/2401*T^48 + 1413/2401*T^47 - 
        324/343*T^46 + 9/49*T^45 + 2290/2401*T^44 - 1048/2401*T^43 + 914/2401*T^42 -
        958/2401*T^41 - 785/2401*T^40 + 2143/2401*T^39 - 1763/2401*T^38 - 
        739/2401*T^37 + 190/343*T^36 - 1516/2401*T^35 + 2043/2401*T^34 + 
        829/2401*T^33 - 2558/2401*T^32 + 2227/2401*T^31 - 1367/2401*T^30 - 
        1718/2401*T^29 + 3242/2401*T^28 - 1718/2401*T^27 - 1367/2401*T^26 + 
        2227/2401*T^25 - 2558/2401*T^24 + 829/2401*T^23 + 2043/2401*T^22 - 
        1516/2401*T^21 + 190/343*T^20 - 739/2401*T^19 - 1763/2401*T^18 + 
        2143/2401*T^17 - 785/2401*T^16 - 958/2401*T^15 + 914/2401*T^14 - 
        1048/2401*T^13 + 2290/2401*T^12 + 9/49*T^11 - 324/343*T^10 + 1413/2401*T^9 +
        127/2401*T^8 - 1559/2401*T^7 + 257/343*T^6 - 558/2401*T^5 - 501/2401*T^4 - 
        75/343*T^3 - 6/7*T^2 + 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 5*X*Y^8 + 6*X*Y^7 +
        5*X*Y^3 + 5*X*Y^2 + 4*X*Y + 4*X + 5*Y^30 + 4*Y^29 + Y^27 + 4*Y^26 + 6*Y^25 +
        3*Y^24 + 6*Y^23 + 5*Y^22 + 4*Y^20 + 2*Y^19 + 4*Y^18 + 3*Y^17 + 2*Y^16 + 
        6*Y^15 + 5*Y^14 + 3*Y^13 + 3*Y^12 + 2*Y^10 + 4*Y^9 + Y^7 + Y^6 + 2*Y^2 + Y +
        3,
    -T^56 - 2/7*T^55 + 15/49*T^54 + 89/343*T^53 + 1343/2401*T^52 + 453/2401*T^51 + 
        1175/2401*T^50 - 495/2401*T^49 - 848/2401*T^48 + 57/2401*T^47 - 
        272/2401*T^46 - 313/2401*T^45 + 639/2401*T^44 + 652/2401*T^43 + 
        1038/2401*T^42 - 811/2401*T^41 - 58/343*T^40 - 418/2401*T^39 - 
        1243/2401*T^38 + 1087/2401*T^37 + 82/343*T^36 + 678/2401*T^35 - 106/343*T^34
        + 754/2401*T^33 + 381/2401*T^32 - 1685/2401*T^31 - 129/343*T^30 - 
        55/2401*T^29 + 55/2401*T^27 + 129/343*T^26 + 1685/2401*T^25 - 381/2401*T^24 
        - 754/2401*T^23 + 106/343*T^22 - 678/2401*T^21 - 82/343*T^20 - 
        1087/2401*T^19 + 1243/2401*T^18 + 418/2401*T^17 + 58/343*T^16 + 
        811/2401*T^15 - 1038/2401*T^14 - 652/2401*T^13 - 639/2401*T^12 + 
        313/2401*T^11 + 272/2401*T^10 - 57/2401*T^9 + 848/2401*T^8 + 495/2401*T^7 - 
        1175/2401*T^6 - 453/2401*T^5 - 1343/2401*T^4 - 89/343*T^3 - 15/49*T^2 + 
        2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + X*Y^7 + 4*X*Y^6 + 
        6*X*Y^5 + X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 4*X*Y + 3*X + 2*Y^30 + 4*Y^28 + 4*Y^27
        + 4*Y^26 + 5*Y^25 + 4*Y^23 + Y^21 + 3*Y^20 + 2*Y^19 + 2*Y^18 + Y^17 + Y^16 +
        6*Y^15 + 4*Y^14 + 6*Y^13 + 2*Y^12 + 5*Y^11 + 3*Y^10 + 3*Y^9 + 6*Y^8 + Y^7 + 
        3*Y^6 + 5*Y^5 + 5*Y^4 + 3*Y^3 + 3*Y^2 + Y + 2,
    T^56 + T^55 - 31/49*T^54 - 244/343*T^53 - 128/2401*T^52 + 442/2401*T^51 + 
        1678/2401*T^50 + 1823/2401*T^49 - 2488/2401*T^48 - 2540/2401*T^47 + 
        208/343*T^46 + 1035/2401*T^45 + 206/343*T^44 + 831/2401*T^43 - 
        3440/2401*T^42 - 2731/2401*T^41 + 312/343*T^40 + 1194/2401*T^39 - 
        92/2401*T^38 - 27/343*T^37 - 3378/2401*T^36 - 947/2401*T^35 + 4021/2401*T^34
        + 1892/2401*T^33 - 1004/2401*T^32 - 1223/2401*T^31 - 2785/2401*T^30 + 
        115/343*T^29 + 5490/2401*T^28 + 115/343*T^27 - 2785/2401*T^26 - 
        1223/2401*T^25 - 1004/2401*T^24 + 1892/2401*T^23 + 4021/2401*T^22 - 
        947/2401*T^21 - 3378/2401*T^20 - 27/343*T^19 - 92/2401*T^18 + 1194/2401*T^17
        + 312/343*T^16 - 2731/2401*T^15 - 3440/2401*T^14 + 831/2401*T^13 + 
        206/343*T^12 + 1035/2401*T^11 + 208/343*T^10 - 2540/2401*T^9 - 2488/2401*T^8
        + 1823/2401*T^7 + 1678/2401*T^6 + 442/2401*T^5 - 128/2401*T^4 - 244/343*T^3 
        - 31/49*T^2 + T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 4*X*Y^8 + 2*X*Y^7 + 3*X*Y^6 + 
        3*X*Y^5 + 5*X*Y^4 + X*Y^3 + X*Y^2 + 3*X + 3*Y^30 + 3*Y^29 + 4*Y^28 + Y^27 + 
        4*Y^26 + 4*Y^24 + 6*Y^23 + 5*Y^20 + 2*Y^19 + 6*Y^18 + 6*Y^17 + 3*Y^16 + 
        6*Y^14 + 2*Y^13 + 6*Y^11 + 2*Y^10 + 5*Y^9 + 3*Y^8 + 5*Y^6 + 4*Y^5 + 4*Y^3 + 
        6*Y + 4,
    -T^56 + 10/7*T^55 + 2/7*T^54 - 537/343*T^53 + 2522/2401*T^52 + 780/2401*T^51 - 
        2636/2401*T^50 + 1716/2401*T^49 + 456/2401*T^48 - 1809/2401*T^47 + 
        234/343*T^46 - 569/2401*T^45 - 975/2401*T^44 + 404/2401*T^43 + 
        1851/2401*T^42 - 1815/2401*T^41 + 214/2401*T^40 + 1968/2401*T^39 - 
        2290/2401*T^38 - 123/343*T^37 + 2585/2401*T^36 - 662/2401*T^35 - 
        1600/2401*T^34 + 40/49*T^33 - 1430/2401*T^32 + 463/2401*T^31 + 
        1401/2401*T^30 - 2024/2401*T^29 + 2024/2401*T^27 - 1401/2401*T^26 - 
        463/2401*T^25 + 1430/2401*T^24 - 40/49*T^23 + 1600/2401*T^22 + 662/2401*T^21
        - 2585/2401*T^20 + 123/343*T^19 + 2290/2401*T^18 - 1968/2401*T^17 - 
        214/2401*T^16 + 1815/2401*T^15 - 1851/2401*T^14 - 404/2401*T^13 + 
        975/2401*T^12 + 569/2401*T^11 - 234/343*T^10 + 1809/2401*T^9 - 456/2401*T^8 
        - 1716/2401*T^7 + 2636/2401*T^6 - 780/2401*T^5 - 2522/2401*T^4 + 537/343*T^3
        - 2/7*T^2 - 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + X*Y^11 + X*Y^10 + 6*X*Y^9 + 
        3*X*Y^8 + 3*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 5*X*Y^3 + 2*X + Y^30 + 5*Y^29 + 
        4*Y^28 + 6*Y^27 + Y^26 + 4*Y^25 + Y^24 + 2*Y^23 + Y^22 + 2*Y^21 + 5*Y^20 + 
        Y^19 + 5*Y^18 + 5*Y^17 + 2*Y^16 + 6*Y^15 + 5*Y^14 + 6*Y^13 + Y^12 + Y^11 + 
        4*Y^10 + 3*Y^9 + Y^8 + 2*Y^7 + 6*Y^6 + 6*Y^4 + 2*Y^3 + Y^2 + 6*Y,
    T^56 - 4/7*T^55 - 6/7*T^54 + 135/343*T^53 + 2106/2401*T^52 - 129/343*T^51 - 
        995/2401*T^50 + 372/2401*T^49 + 1067/2401*T^48 + 10/343*T^47 - 106/343*T^46 
        - 223/2401*T^45 + 1839/2401*T^44 - 10/343*T^43 - 2984/2401*T^42 + 
        269/2401*T^41 + 2556/2401*T^40 + 556/2401*T^39 - 1305/2401*T^38 + 
        165/2401*T^37 - 373/2401*T^36 + 711/2401*T^35 + 8/49*T^34 + 383/2401*T^33 - 
        717/2401*T^32 + 50/2401*T^31 - 510/2401*T^30 + 400/2401*T^29 + 
        1416/2401*T^28 + 400/2401*T^27 - 510/2401*T^26 + 50/2401*T^25 - 
        717/2401*T^24 + 383/2401*T^23 + 8/49*T^22 + 711/2401*T^21 - 373/2401*T^20 + 
        165/2401*T^19 - 1305/2401*T^18 + 556/2401*T^17 + 2556/2401*T^16 + 
        269/2401*T^15 - 2984/2401*T^14 - 10/343*T^13 + 1839/2401*T^12 - 
        223/2401*T^11 - 106/343*T^10 + 10/343*T^9 + 1067/2401*T^8 + 372/2401*T^7 - 
        995/2401*T^6 - 129/343*T^5 + 2106/2401*T^4 + 135/343*T^3 - 6/7*T^2 - 4/7*T +
        1
*], [*
    X^3 + 3*X*Y^15 + X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 + 
        6*X*Y^6 + 3*X*Y^4 + 6*X*Y^3 + 4*X + 3*Y^30 + 5*Y^29 + 5*Y^28 + 5*Y^27 + 
        2*Y^24 + 3*Y^23 + 6*Y^21 + 3*Y^20 + 4*Y^19 + 6*Y^18 + 5*Y^17 + 6*Y^16 + 
        6*Y^15 + 2*Y^14 + 5*Y^12 + Y^11 + 2*Y^10 + 5*Y^9 + 4*Y^8 + 3*Y^7 + 3*Y^6 + 
        3*Y^4 + 3*Y^3 + Y^2 + 2*Y + 1,
    T^56 - 6/7*T^55 - 4/7*T^54 + 659/343*T^53 - 2075/2401*T^52 - 2159/2401*T^51 + 
        2248/2401*T^50 + 946/2401*T^49 - 619/2401*T^48 - 4166/2401*T^47 + 
        3816/2401*T^46 + 2389/2401*T^45 - 7412/2401*T^44 + 2130/2401*T^43 + 
        3925/2401*T^42 - 4203/2401*T^41 - 1931/2401*T^40 + 3012/2401*T^39 + 
        198/343*T^38 - 4820/2401*T^37 - 802/2401*T^36 + 6896/2401*T^35 - 
        2950/2401*T^34 - 6164/2401*T^33 + 6941/2401*T^32 + 3572/2401*T^31 - 
        6869/2401*T^30 - 120/2401*T^29 + 7146/2401*T^28 - 120/2401*T^27 - 
        6869/2401*T^26 + 3572/2401*T^25 + 6941/2401*T^24 - 6164/2401*T^23 - 
        2950/2401*T^22 + 6896/2401*T^21 - 802/2401*T^20 - 4820/2401*T^19 + 
        198/343*T^18 + 3012/2401*T^17 - 1931/2401*T^16 - 4203/2401*T^15 + 
        3925/2401*T^14 + 2130/2401*T^13 - 7412/2401*T^12 + 2389/2401*T^11 + 
        3816/2401*T^10 - 4166/2401*T^9 - 619/2401*T^8 + 946/2401*T^7 + 2248/2401*T^6
        - 2159/2401*T^5 - 2075/2401*T^4 + 659/343*T^3 - 4/7*T^2 - 6/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        3*X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + X*Y^5 + 4*X*Y^4 + X*Y^3 + 2*X*Y + 5*Y^30 + 
        3*Y^29 + Y^28 + Y^27 + 2*Y^26 + Y^25 + 3*Y^24 + Y^23 + Y^22 + 5*Y^21 + 
        5*Y^20 + Y^19 + Y^18 + 6*Y^17 + Y^16 + 4*Y^15 + 5*Y^14 + Y^13 + 3*Y^12 + 
        Y^11 + 2*Y^10 + 2*Y^9 + 2*Y^8 + 2*Y^6 + Y^5 + 2*Y^4 + 3*Y^3 + 6*Y^2 + 3,
    T^56 + 1/7*T^55 - 83/49*T^54 - 27/49*T^53 + 3341/2401*T^52 + 408/2401*T^51 - 
        3876/2401*T^50 + 1412/2401*T^49 + 635/343*T^48 - 2514/2401*T^47 - 
        4278/2401*T^46 + 2673/2401*T^45 + 600/343*T^44 - 2480/2401*T^43 - 
        2020/2401*T^42 + 59/49*T^41 + 274/2401*T^40 - 2509/2401*T^39 + 466/2401*T^38
        + 337/343*T^37 - 1777/2401*T^36 - 2823/2401*T^35 + 2316/2401*T^34 + 
        1093/2401*T^33 - 3492/2401*T^32 - 360/2401*T^31 + 4492/2401*T^30 + 
        722/2401*T^29 - 4490/2401*T^28 + 722/2401*T^27 + 4492/2401*T^26 - 
        360/2401*T^25 - 3492/2401*T^24 + 1093/2401*T^23 + 2316/2401*T^22 - 
        2823/2401*T^21 - 1777/2401*T^20 + 337/343*T^19 + 466/2401*T^18 - 
        2509/2401*T^17 + 274/2401*T^16 + 59/49*T^15 - 2020/2401*T^14 - 
        2480/2401*T^13 + 600/343*T^12 + 2673/2401*T^11 - 4278/2401*T^10 - 
        2514/2401*T^9 + 635/343*T^8 + 1412/2401*T^7 - 3876/2401*T^6 + 408/2401*T^5 +
        3341/2401*T^4 - 27/49*T^3 - 83/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 6*X*Y^13 + X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 
        2*X*Y^8 + 3*X*Y^7 + 6*X*Y^5 + 6*X*Y^4 + 2*X*Y^2 + 3*X + Y^30 + 2*Y^29 + Y^28
        + 4*Y^27 + 2*Y^26 + 5*Y^24 + 6*Y^23 + Y^22 + 4*Y^21 + 4*Y^19 + Y^18 + 2*Y^17
        + Y^16 + 4*Y^14 + 6*Y^13 + 4*Y^12 + 4*Y^11 + 5*Y^10 + 5*Y^9 + 5*Y^7 + 2*Y^6 
        + 3*Y^5 + 4*Y^4 + Y^2 + 3*Y + 2,
    T^56 - 1/7*T^55 + 3/49*T^54 + 67/343*T^53 + 253/343*T^52 + 1929/2401*T^51 + 
        330/2401*T^50 - 160/2401*T^49 + 146/2401*T^48 + 1321/2401*T^47 + 
        603/2401*T^46 - 391/2401*T^45 - 734/2401*T^44 + 290/2401*T^43 + 
        326/2401*T^42 + 635/2401*T^41 - 375/2401*T^40 - 144/2401*T^39 + 
        481/2401*T^38 + 1206/2401*T^37 + 1647/2401*T^36 - 355/2401*T^35 - 
        667/2401*T^34 + 141/343*T^33 + 842/2401*T^32 + 52/2401*T^31 - 993/2401*T^30 
        + 120/2401*T^29 - 582/2401*T^28 + 120/2401*T^27 - 993/2401*T^26 + 
        52/2401*T^25 + 842/2401*T^24 + 141/343*T^23 - 667/2401*T^22 - 355/2401*T^21 
        + 1647/2401*T^20 + 1206/2401*T^19 + 481/2401*T^18 - 144/2401*T^17 - 
        375/2401*T^16 + 635/2401*T^15 + 326/2401*T^14 + 290/2401*T^13 - 
        734/2401*T^12 - 391/2401*T^11 + 603/2401*T^10 + 1321/2401*T^9 + 146/2401*T^8
        - 160/2401*T^7 + 330/2401*T^6 + 1929/2401*T^5 + 253/343*T^4 + 67/343*T^3 + 
        3/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 5*X*Y^12 + 2*X*Y^11 + 2*X*Y^9 + 6*X*Y^8 + 5*X*Y^7 + 
        6*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 6*X*Y + 6*X + 2*Y^30 + 
        3*Y^29 + 4*Y^28 + 2*Y^26 + 5*Y^25 + 6*Y^23 + 2*Y^22 + Y^21 + Y^20 + 5*Y^19 +
        5*Y^17 + 4*Y^16 + Y^15 + Y^14 + Y^12 + 4*Y^11 + Y^9 + 6*Y^8 + 3*Y^7 + 3*Y^6 
        + 3*Y^5 + 5*Y^4 + 6*Y^3 + Y^2 + 2*Y + 6,
    -T^56 + 5/7*T^55 - 11/49*T^54 - 22/343*T^53 + 662/2401*T^52 - 578/2401*T^51 - 
        211/2401*T^50 + 177/2401*T^49 + 828/2401*T^48 - 18/2401*T^47 - 142/2401*T^46
        - 1656/2401*T^45 + 1010/2401*T^44 - 806/2401*T^43 + 239/2401*T^42 - 
        709/2401*T^41 - 282/2401*T^40 + 853/2401*T^39 - 1243/2401*T^38 + 
        1805/2401*T^37 + 243/2401*T^36 - 1485/2401*T^35 + 111/2401*T^34 + 
        408/2401*T^33 + 341/2401*T^32 + 352/2401*T^31 - 1794/2401*T^30 + 25/343*T^29
        - 25/343*T^27 + 1794/2401*T^26 - 352/2401*T^25 - 341/2401*T^24 - 
        408/2401*T^23 - 111/2401*T^22 + 1485/2401*T^21 - 243/2401*T^20 - 
        1805/2401*T^19 + 1243/2401*T^18 - 853/2401*T^17 + 282/2401*T^16 + 
        709/2401*T^15 - 239/2401*T^14 + 806/2401*T^13 - 1010/2401*T^12 + 
        1656/2401*T^11 + 142/2401*T^10 + 18/2401*T^9 - 828/2401*T^8 - 177/2401*T^7 +
        211/2401*T^6 + 578/2401*T^5 - 662/2401*T^4 + 22/343*T^3 + 11/49*T^2 - 5/7*T 
        + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 
        3*X*Y^8 + 3*X*Y^7 + 4*X*Y^6 + 5*X*Y^4 + X*Y^3 + 2*X*Y^2 + 5*X*Y + 5*X + 
        3*Y^30 + Y^29 + 2*Y^28 + 3*Y^27 + 3*Y^26 + 4*Y^25 + 3*Y^24 + 5*Y^23 + 5*Y^22
        + 6*Y^21 + 5*Y^20 + Y^19 + Y^18 + 6*Y^17 + 6*Y^16 + Y^15 + 4*Y^14 + 2*Y^12 +
        6*Y^10 + 6*Y^9 + Y^8 + 4*Y^6 + 3*Y^5 + 4*Y^4 + 5*Y^3 + 2*Y^2 + 5*Y + 1,
    T^56 - 9/7*T^55 + T^54 + 5/343*T^53 + 177/2401*T^52 - 585/2401*T^51 + 
        1248/2401*T^50 - 1793/2401*T^49 + 929/2401*T^48 + 165/343*T^47 - 
        354/343*T^46 + 9/2401*T^45 + 2462/2401*T^44 - 3450/2401*T^43 + 
        1206/2401*T^42 + 1082/2401*T^41 - 3013/2401*T^40 + 1570/2401*T^39 + 
        1013/2401*T^38 - 2985/2401*T^37 + 2232/2401*T^36 + 601/2401*T^35 - 
        2514/2401*T^34 + 860/2401*T^33 + 3172/2401*T^32 - 4660/2401*T^31 + 
        1990/2401*T^30 + 1644/2401*T^29 - 3244/2401*T^28 + 1644/2401*T^27 + 
        1990/2401*T^26 - 4660/2401*T^25 + 3172/2401*T^24 + 860/2401*T^23 - 
        2514/2401*T^22 + 601/2401*T^21 + 2232/2401*T^20 - 2985/2401*T^19 + 
        1013/2401*T^18 + 1570/2401*T^17 - 3013/2401*T^16 + 1082/2401*T^15 + 
        1206/2401*T^14 - 3450/2401*T^13 + 2462/2401*T^12 + 9/2401*T^11 - 
        354/343*T^10 + 165/343*T^9 + 929/2401*T^8 - 1793/2401*T^7 + 1248/2401*T^6 - 
        585/2401*T^5 + 177/2401*T^4 + 5/343*T^3 + T^2 - 9/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 6*X*Y^7 + 
        2*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 4*X*Y^3 + X*Y^2 + X*Y + 6*X + 6*Y^30 + 2*Y^29 
        + 6*Y^28 + 3*Y^27 + 4*Y^25 + 2*Y^24 + 5*Y^23 + 4*Y^22 + 2*Y^21 + 5*Y^18 + 
        2*Y^17 + Y^16 + 5*Y^15 + 5*Y^14 + 5*Y^13 + 5*Y^12 + 4*Y^11 + 4*Y^10 + 2*Y^8 
        + 6*Y^7 + 6*Y^6 + 3*Y^4 + 6*Y^3 + 2*Y^2 + 6*Y + 6,
    T^56 + 2/7*T^55 + 2/7*T^54 + 9/49*T^53 + 536/2401*T^52 + 331/2401*T^51 + 
        208/2401*T^50 - 131/2401*T^49 + 244/2401*T^48 + 765/2401*T^47 - 
        901/2401*T^46 - 1055/2401*T^45 - 1429/2401*T^44 - 782/2401*T^43 - 
        1467/2401*T^42 - 473/2401*T^41 - 1196/2401*T^40 - 55/343*T^39 - 
        475/2401*T^38 - 1707/2401*T^37 - 156/2401*T^36 + 408/2401*T^35 + 
        153/2401*T^34 + 202/2401*T^33 + 311/2401*T^32 + 891/2401*T^31 + 
        1178/2401*T^30 + 746/2401*T^29 + 264/2401*T^28 + 746/2401*T^27 + 
        1178/2401*T^26 + 891/2401*T^25 + 311/2401*T^24 + 202/2401*T^23 + 
        153/2401*T^22 + 408/2401*T^21 - 156/2401*T^20 - 1707/2401*T^19 - 
        475/2401*T^18 - 55/343*T^17 - 1196/2401*T^16 - 473/2401*T^15 - 
        1467/2401*T^14 - 782/2401*T^13 - 1429/2401*T^12 - 1055/2401*T^11 - 
        901/2401*T^10 + 765/2401*T^9 + 244/2401*T^8 - 131/2401*T^7 + 208/2401*T^6 + 
        331/2401*T^5 + 536/2401*T^4 + 9/49*T^3 + 2/7*T^2 + 2/7*T + 1
*], [*
    X^3 + 4*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 5*X*Y^8 + 4*X*Y^7 + X*Y^6 + 
        5*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 5*X*Y + 2*X + Y^30 + 4*Y^28 + 6*Y^27
        + 4*Y^26 + Y^25 + 3*Y^24 + Y^23 + 4*Y^22 + 2*Y^21 + Y^20 + 6*Y^19 + 3*Y^18 +
        3*Y^17 + Y^15 + 5*Y^14 + 3*Y^13 + 6*Y^12 + 2*Y^11 + 5*Y^10 + Y^9 + 2*Y^8 + 
        5*Y^7 + 6*Y^6 + 2*Y^5 + 2*Y^4 + 6*Y^3 + 6*Y^2 + 6*Y + 3,
    -T^56 - 2/7*T^55 + 57/49*T^54 + 222/343*T^53 - 1461/2401*T^52 - 443/343*T^51 + 
        1137/2401*T^50 + 1836/2401*T^49 - 712/2401*T^48 + 278/2401*T^47 + 
        972/2401*T^46 - 571/2401*T^45 - 1611/2401*T^44 + 304/2401*T^43 + 
        2309/2401*T^42 - 577/2401*T^41 - 2460/2401*T^40 + 1913/2401*T^39 + 
        1987/2401*T^38 - 1623/2401*T^37 - 1935/2401*T^36 + 815/2401*T^35 + 
        257/343*T^34 - 1133/2401*T^33 + 268/2401*T^32 + 2424/2401*T^31 - 
        824/2401*T^30 - 3048/2401*T^29 + 3048/2401*T^27 + 824/2401*T^26 - 
        2424/2401*T^25 - 268/2401*T^24 + 1133/2401*T^23 - 257/343*T^22 - 
        815/2401*T^21 + 1935/2401*T^20 + 1623/2401*T^19 - 1987/2401*T^18 - 
        1913/2401*T^17 + 2460/2401*T^16 + 577/2401*T^15 - 2309/2401*T^14 - 
        304/2401*T^13 + 1611/2401*T^12 + 571/2401*T^11 - 972/2401*T^10 - 
        278/2401*T^9 + 712/2401*T^8 - 1836/2401*T^7 - 1137/2401*T^6 + 443/343*T^5 + 
        1461/2401*T^4 - 222/343*T^3 - 57/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 2*X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + X*Y^2 + X*Y + 
        5*X + 4*Y^30 + 4*Y^29 + 3*Y^28 + 6*Y^27 + Y^26 + 6*Y^24 + 4*Y^23 + 4*Y^22 + 
        4*Y^20 + Y^18 + 4*Y^17 + Y^16 + 4*Y^15 + 6*Y^13 + Y^12 + 4*Y^11 + 2*Y^10 + 
        3*Y^9 + 6*Y^7 + Y^6 + 3*Y^5 + 3*Y^4 + 2*Y^3 + 5*Y^2 + 2*Y + 2,
    T^56 + 1/7*T^55 + 59/49*T^54 + 47/49*T^53 + 2559/2401*T^52 + 3783/2401*T^51 + 
        2440/2401*T^50 + 444/343*T^49 + 1952/2401*T^48 + 1944/2401*T^47 + 
        1565/2401*T^46 + 1205/2401*T^45 + 257/343*T^44 + 871/2401*T^43 + 
        345/343*T^42 + 50/49*T^41 + 2886/2401*T^40 + 3722/2401*T^39 + 3708/2401*T^38
        + 4292/2401*T^37 + 3601/2401*T^36 + 4246/2401*T^35 + 465/343*T^34 + 
        530/343*T^33 + 2997/2401*T^32 + 2545/2401*T^31 + 3100/2401*T^30 + 
        2347/2401*T^29 + 3224/2401*T^28 + 2347/2401*T^27 + 3100/2401*T^26 + 
        2545/2401*T^25 + 2997/2401*T^24 + 530/343*T^23 + 465/343*T^22 + 
        4246/2401*T^21 + 3601/2401*T^20 + 4292/2401*T^19 + 3708/2401*T^18 + 
        3722/2401*T^17 + 2886/2401*T^16 + 50/49*T^15 + 345/343*T^14 + 871/2401*T^13 
        + 257/343*T^12 + 1205/2401*T^11 + 1565/2401*T^10 + 1944/2401*T^9 + 
        1952/2401*T^8 + 444/343*T^7 + 2440/2401*T^6 + 3783/2401*T^5 + 2559/2401*T^4 
        + 47/49*T^3 + 59/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 +
        X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 3*X*Y^3 + 6*X*Y^2 + X*Y + 3*X + 2*Y^30 + 3*Y^29 
        + 2*Y^28 + 2*Y^27 + 4*Y^26 + 2*Y^25 + 4*Y^24 + Y^23 + 3*Y^22 + 4*Y^21 + 
        3*Y^20 + 6*Y^19 + Y^18 + 4*Y^17 + 2*Y^16 + Y^15 + Y^14 + 6*Y^13 + 2*Y^12 + 
        2*Y^11 + 3*Y^9 + 3*Y^8 + 3*Y^7 + 3*Y^6 + 4*Y^5 + Y^4 + 3*Y^2 + Y + 2,
    T^56 - 2/7*T^55 - 24/49*T^54 + 19/49*T^53 + 489/2401*T^52 - 876/2401*T^51 - 
        1301/2401*T^50 + 478/2401*T^49 + 1366/2401*T^48 - 2232/2401*T^47 + 
        319/2401*T^46 + 2041/2401*T^45 - 1075/2401*T^44 - 426/2401*T^43 + 
        26/343*T^42 - 305/2401*T^41 + 919/2401*T^40 - 1777/2401*T^39 + 146/2401*T^38
        + 181/343*T^37 - 1089/2401*T^36 + 323/2401*T^35 + 521/2401*T^34 - 
        29/343*T^33 + 982/2401*T^32 - 1529/2401*T^31 + 1081/2401*T^30 + 
        397/2401*T^29 - 2320/2401*T^28 + 397/2401*T^27 + 1081/2401*T^26 - 
        1529/2401*T^25 + 982/2401*T^24 - 29/343*T^23 + 521/2401*T^22 + 323/2401*T^21
        - 1089/2401*T^20 + 181/343*T^19 + 146/2401*T^18 - 1777/2401*T^17 + 
        919/2401*T^16 - 305/2401*T^15 + 26/343*T^14 - 426/2401*T^13 - 1075/2401*T^12
        + 2041/2401*T^11 + 319/2401*T^10 - 2232/2401*T^9 + 1366/2401*T^8 + 
        478/2401*T^7 - 1301/2401*T^6 - 876/2401*T^5 + 489/2401*T^4 + 19/49*T^3 - 
        24/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 5*X*Y^10 + 2*X*Y^9 + X*Y^8 + 
        4*X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 2*X*Y + 6*Y^30 + 2*Y^29 + 
        4*Y^28 + Y^27 + 5*Y^26 + 3*Y^24 + 3*Y^23 + 5*Y^22 + 4*Y^21 + Y^20 + Y^19 + 
        4*Y^18 + 5*Y^17 + 6*Y^16 + 3*Y^15 + 4*Y^14 + 3*Y^13 + 5*Y^12 + 5*Y^10 + 
        3*Y^8 + 6*Y^7 + 2*Y^6 + Y^5 + Y^4 + 3*Y^3 + 5*Y^2 + 4*Y + 1,
    -T^56 - T^55 + 20/49*T^54 + 820/343*T^53 + 3828/2401*T^52 - 713/2401*T^51 - 
        3383/2401*T^50 - 1084/2401*T^49 - 90/2401*T^48 - 1583/2401*T^47 - 
        2466/2401*T^46 - 36/2401*T^45 + 2168/2401*T^44 + 289/343*T^43 + 205/343*T^42
        - 132/343*T^41 - 3106/2401*T^40 - 3226/2401*T^39 + 2375/2401*T^38 + 
        769/343*T^37 + 3450/2401*T^36 - 3211/2401*T^35 - 3475/2401*T^34 + 
        88/2401*T^33 + 2979/2401*T^32 - 477/2401*T^31 - 3505/2401*T^30 - 
        3337/2401*T^29 + 3337/2401*T^27 + 3505/2401*T^26 + 477/2401*T^25 - 
        2979/2401*T^24 - 88/2401*T^23 + 3475/2401*T^22 + 3211/2401*T^21 - 
        3450/2401*T^20 - 769/343*T^19 - 2375/2401*T^18 + 3226/2401*T^17 + 
        3106/2401*T^16 + 132/343*T^15 - 205/343*T^14 - 289/343*T^13 - 2168/2401*T^12
        + 36/2401*T^11 + 2466/2401*T^10 + 1583/2401*T^9 + 90/2401*T^8 + 
        1084/2401*T^7 + 3383/2401*T^6 + 713/2401*T^5 - 3828/2401*T^4 - 820/343*T^3 -
        20/49*T^2 + T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + X*Y^8 + 
        X*Y^7 + 2*X*Y^6 + X*Y^5 + X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 6*X*Y + X + 3*Y^30 + 
        Y^28 + 3*Y^27 + 6*Y^26 + 5*Y^25 + 3*Y^24 + 2*Y^23 + 4*Y^22 + 3*Y^20 + Y^19 +
        6*Y^18 + 2*Y^17 + 2*Y^16 + 5*Y^15 + 3*Y^14 + Y^13 + 6*Y^12 + 5*Y^11 + 4*Y^10
        + 2*Y^9 + 2*Y^8 + 6*Y^6 + Y^5 + 5*Y^4 + Y^3 + 2*Y + 1,
    T^56 + T^55 + 110/49*T^54 + 99/49*T^53 + 4917/2401*T^52 + 4121/2401*T^51 + 
        2083/2401*T^50 + 1577/2401*T^49 + 155/2401*T^48 - 1200/2401*T^47 - 
        493/2401*T^46 - 5027/2401*T^45 - 453/343*T^44 - 7459/2401*T^43 - 
        984/343*T^42 - 7474/2401*T^41 - 8058/2401*T^40 - 956/343*T^39 - 
        6242/2401*T^38 - 4867/2401*T^37 - 1811/2401*T^36 - 1559/2401*T^35 + 
        3492/2401*T^34 + 2081/2401*T^33 + 5690/2401*T^32 + 5319/2401*T^31 + 
        6588/2401*T^30 + 7103/2401*T^29 + 7144/2401*T^28 + 7103/2401*T^27 + 
        6588/2401*T^26 + 5319/2401*T^25 + 5690/2401*T^24 + 2081/2401*T^23 + 
        3492/2401*T^22 - 1559/2401*T^21 - 1811/2401*T^20 - 4867/2401*T^19 - 
        6242/2401*T^18 - 956/343*T^17 - 8058/2401*T^16 - 7474/2401*T^15 - 
        984/343*T^14 - 7459/2401*T^13 - 453/343*T^12 - 5027/2401*T^11 - 
        493/2401*T^10 - 1200/2401*T^9 + 155/2401*T^8 + 1577/2401*T^7 + 2083/2401*T^6
        + 4121/2401*T^5 + 4917/2401*T^4 + 99/49*T^3 + 110/49*T^2 + T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 5*X*Y^8 +
        3*X*Y^6 + 2*X*Y^5 + X*Y^4 + X*Y^3 + 3*X*Y^2 + 6*X*Y + X + 6*Y^30 + 6*Y^29 + 
        5*Y^27 + Y^25 + Y^24 + Y^23 + 4*Y^22 + 5*Y^21 + 2*Y^20 + 3*Y^19 + 5*Y^18 + 
        3*Y^17 + 2*Y^16 + 2*Y^15 + 2*Y^14 + 3*Y^12 + 4*Y^11 + Y^9 + 3*Y^8 + 5*Y^7 + 
        6*Y^6 + 5*Y^5 + 5*Y^4 + 6*Y^2 + 2*Y + 4,
    T^56 - 3/7*T^55 - 36/49*T^54 + 110/343*T^53 + 2963/2401*T^52 - 2943/2401*T^51 - 
        1282/2401*T^50 + 1681/2401*T^49 + 920/2401*T^48 - 3620/2401*T^47 + 
        82/343*T^46 + 3981/2401*T^45 - 53/2401*T^44 - 5174/2401*T^43 + 
        1614/2401*T^42 + 4401/2401*T^41 - 2011/2401*T^40 - 3420/2401*T^39 + 
        2446/2401*T^38 + 1490/2401*T^37 - 2995/2401*T^36 - 459/2401*T^35 + 
        2521/2401*T^34 + 939/2401*T^33 - 3305/2401*T^32 + 457/2401*T^31 + 
        1649/2401*T^30 + 153/343*T^29 - 3322/2401*T^28 + 153/343*T^27 + 
        1649/2401*T^26 + 457/2401*T^25 - 3305/2401*T^24 + 939/2401*T^23 + 
        2521/2401*T^22 - 459/2401*T^21 - 2995/2401*T^20 + 1490/2401*T^19 + 
        2446/2401*T^18 - 3420/2401*T^17 - 2011/2401*T^16 + 4401/2401*T^15 + 
        1614/2401*T^14 - 5174/2401*T^13 - 53/2401*T^12 + 3981/2401*T^11 + 
        82/343*T^10 - 3620/2401*T^9 + 920/2401*T^8 + 1681/2401*T^7 - 1282/2401*T^6 -
        2943/2401*T^5 + 2963/2401*T^4 + 110/343*T^3 - 36/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + X*Y^10 + 3*X*Y^9 + 3*X*Y^8 + 
        6*X*Y^7 + X*Y^5 + 3*X*Y^4 + X*Y^3 + 4*X*Y^2 + 2*X*Y + X + Y^30 + 2*Y^29 + 
        6*Y^28 + 2*Y^27 + 2*Y^26 + 2*Y^25 + 5*Y^24 + 5*Y^23 + 6*Y^22 + Y^21 + 4*Y^20
        + 4*Y^19 + 6*Y^18 + 5*Y^17 + 5*Y^16 + 3*Y^15 + Y^14 + 5*Y^13 + 3*Y^11 + 
        5*Y^9 + 5*Y^7 + 3*Y^6 + 3*Y^5 + 6*Y^3 + 2*Y^2 + 3*Y + 4,
    -T^56 + T^55 - 6/7*T^54 + 351/343*T^53 - 1170/2401*T^52 + 936/2401*T^51 - 
        1887/2401*T^50 + 1808/2401*T^49 - 1898/2401*T^48 + 2132/2401*T^47 - 
        494/2401*T^46 - 1602/2401*T^45 + 1858/2401*T^44 - 1285/2401*T^43 + 3/7*T^42 
        - 939/2401*T^41 + 800/2401*T^40 - 41/49*T^39 + 1983/2401*T^38 - 
        1488/2401*T^37 + 1371/2401*T^36 - 1020/2401*T^35 - 481/2401*T^34 + 
        543/2401*T^33 + 471/2401*T^32 + 258/2401*T^31 - 150/2401*T^30 + 
        304/2401*T^29 - 304/2401*T^27 + 150/2401*T^26 - 258/2401*T^25 - 
        471/2401*T^24 - 543/2401*T^23 + 481/2401*T^22 + 1020/2401*T^21 - 
        1371/2401*T^20 + 1488/2401*T^19 - 1983/2401*T^18 + 41/49*T^17 - 
        800/2401*T^16 + 939/2401*T^15 - 3/7*T^14 + 1285/2401*T^13 - 1858/2401*T^12 +
        1602/2401*T^11 + 494/2401*T^10 - 2132/2401*T^9 + 1898/2401*T^8 - 
        1808/2401*T^7 + 1887/2401*T^6 - 936/2401*T^5 + 1170/2401*T^4 - 351/343*T^3 +
        6/7*T^2 - T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + 5*X*Y^8 + 3*X*Y^7 + 
        6*X*Y^6 + X*Y^4 + 5*X*Y^3 + 4*X*Y + 4*Y^30 + 5*Y^29 + 2*Y^27 + 5*Y^26 + 
        3*Y^25 + 3*Y^24 + 5*Y^23 + Y^22 + 2*Y^20 + 3*Y^19 + Y^17 + Y^16 + 6*Y^15 + 
        5*Y^14 + 3*Y^13 + 6*Y^12 + 6*Y^11 + 4*Y^10 + 2*Y^9 + 5*Y^8 + 2*Y^7 + 2*Y^6 +
        Y^5 + 3*Y^4 + 3*Y^3 + Y^2 + 3*Y + 3,
    -T^56 + 5/7*T^55 + 19/49*T^54 + 8/49*T^53 - 80/2401*T^52 + 687/2401*T^51 - 
        1803/2401*T^50 - 1654/2401*T^49 + 2055/2401*T^48 + 492/2401*T^47 + 
        302/2401*T^46 - 61/343*T^45 - 34/343*T^44 - 617/2401*T^43 - 1151/2401*T^42 +
        1347/2401*T^41 + 832/2401*T^40 + 19/49*T^39 - 1440/2401*T^38 - 642/2401*T^37
        - 697/2401*T^36 - 316/2401*T^35 + 1069/2401*T^34 + 1440/2401*T^33 + 
        1506/2401*T^32 - 2006/2401*T^31 - 155/343*T^30 - 410/2401*T^29 + 
        410/2401*T^27 + 155/343*T^26 + 2006/2401*T^25 - 1506/2401*T^24 - 
        1440/2401*T^23 - 1069/2401*T^22 + 316/2401*T^21 + 697/2401*T^20 + 
        642/2401*T^19 + 1440/2401*T^18 - 19/49*T^17 - 832/2401*T^16 - 1347/2401*T^15
        + 1151/2401*T^14 + 617/2401*T^13 + 34/343*T^12 + 61/343*T^11 - 302/2401*T^10
        - 492/2401*T^9 - 2055/2401*T^8 + 1654/2401*T^7 + 1803/2401*T^6 - 
        687/2401*T^5 + 80/2401*T^4 - 8/49*T^3 - 19/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + X*Y^12 + X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        6*X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 3*X*Y + 2*X + 
        5*Y^30 + 3*Y^29 + 3*Y^28 + 4*Y^27 + 5*Y^26 + 6*Y^25 + 4*Y^22 + 2*Y^20 + 
        6*Y^19 + 6*Y^18 + 3*Y^17 + 5*Y^16 + Y^15 + 6*Y^14 + Y^13 + 4*Y^12 + 2*Y^11 +
        3*Y^10 + 5*Y^9 + 3*Y^8 + Y^7 + 2*Y^6 + 6*Y^5 + 4*Y^4 + Y^3 + 4*Y^2,
    -T^56 + 1/7*T^55 + 87/49*T^54 - 221/343*T^53 - 561/343*T^52 + 2266/2401*T^51 + 
        538/343*T^50 - 51/49*T^49 - 466/343*T^48 + 2547/2401*T^47 + 2054/2401*T^46 -
        2054/2401*T^45 - 724/2401*T^44 + 816/2401*T^43 + 365/2401*T^42 + 
        52/2401*T^41 - 647/2401*T^40 + 223/2401*T^39 + 431/2401*T^38 + 
        1084/2401*T^37 - 593/2401*T^36 - 1690/2401*T^35 + 2150/2401*T^34 - 
        96/2401*T^33 - 2395/2401*T^32 + 1817/2401*T^31 + 1242/2401*T^30 - 
        1588/2401*T^29 + 1588/2401*T^27 - 1242/2401*T^26 - 1817/2401*T^25 + 
        2395/2401*T^24 + 96/2401*T^23 - 2150/2401*T^22 + 1690/2401*T^21 + 
        593/2401*T^20 - 1084/2401*T^19 - 431/2401*T^18 - 223/2401*T^17 + 
        647/2401*T^16 - 52/2401*T^15 - 365/2401*T^14 - 816/2401*T^13 + 724/2401*T^12
        + 2054/2401*T^11 - 2054/2401*T^10 - 2547/2401*T^9 + 466/343*T^8 + 51/49*T^7 
        - 538/343*T^6 - 2266/2401*T^5 + 561/343*T^4 + 221/343*T^3 - 87/49*T^2 - 
        1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 2*X*Y^8 + 
        4*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 6*X*Y + 2*X + 6*Y^30 + Y^29 + 6*Y^28 + 2*Y^27 
        + 3*Y^26 + Y^24 + 3*Y^21 + Y^20 + 2*Y^19 + 2*Y^18 + 4*Y^16 + 4*Y^15 + 5*Y^14
        + 6*Y^13 + Y^12 + 4*Y^11 + Y^10 + 5*Y^9 + Y^8 + Y^7 + 3*Y^6 + Y^5 + 5*Y^4 + 
        6*Y^3 + 4*Y^2 + 3*Y + 4,
    -T^56 - T^55 - 1/49*T^54 - 108/343*T^53 - 883/2401*T^52 - 48/2401*T^51 - 
        398/2401*T^50 - 325/2401*T^49 + 580/2401*T^48 + 1717/2401*T^47 - 
        1107/2401*T^46 - 3653/2401*T^45 - 1086/2401*T^44 + 230/2401*T^43 + 
        249/2401*T^42 + 526/2401*T^41 - 5/2401*T^40 + 244/2401*T^39 + 1395/2401*T^38
        + 2635/2401*T^37 + 1944/2401*T^36 - 799/2401*T^35 - 1089/2401*T^34 + 
        669/2401*T^33 + 1427/2401*T^32 + 88/343*T^31 - 703/2401*T^30 - 
        1013/2401*T^29 + 1013/2401*T^27 + 703/2401*T^26 - 88/343*T^25 - 
        1427/2401*T^24 - 669/2401*T^23 + 1089/2401*T^22 + 799/2401*T^21 - 
        1944/2401*T^20 - 2635/2401*T^19 - 1395/2401*T^18 - 244/2401*T^17 + 
        5/2401*T^16 - 526/2401*T^15 - 249/2401*T^14 - 230/2401*T^13 + 1086/2401*T^12
        + 3653/2401*T^11 + 1107/2401*T^10 - 1717/2401*T^9 - 580/2401*T^8 + 
        325/2401*T^7 + 398/2401*T^6 + 48/2401*T^5 + 883/2401*T^4 + 108/343*T^3 + 
        1/49*T^2 + T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 5*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 +
        5*X*Y^7 + 3*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 5*X*Y + 3*X + 
        Y^30 + 4*Y^29 + 5*Y^27 + Y^26 + 5*Y^25 + 4*Y^24 + 5*Y^23 + 2*Y^22 + 6*Y^21 +
        Y^20 + 4*Y^18 + 3*Y^17 + 2*Y^16 + 3*Y^15 + 3*Y^14 + 6*Y^13 + 4*Y^12 + 5*Y^11
        + Y^9 + 6*Y^7 + 2*Y^6 + 5*Y^5 + 4*Y^4 + 4*Y^3 + 6*Y^2 + 3*Y + 3,
    T^56 - T^55 + 62/49*T^54 - 442/343*T^53 + 2038/2401*T^52 - 2187/2401*T^51 + 
        1517/2401*T^50 - 1175/2401*T^49 + 470/2401*T^48 - 2008/2401*T^47 + 
        1224/2401*T^46 - 2424/2401*T^45 + 2734/2401*T^44 - 1845/2401*T^43 + 
        367/343*T^42 - 291/343*T^41 + 1443/2401*T^40 - 164/343*T^39 + 951/2401*T^38 
        + 20/2401*T^37 - 288/2401*T^36 + 1073/2401*T^35 - 2622/2401*T^34 + 
        2474/2401*T^33 - 2346/2401*T^32 + 1924/2401*T^31 - 705/2401*T^30 + 
        543/2401*T^29 - 134/2401*T^28 + 543/2401*T^27 - 705/2401*T^26 + 
        1924/2401*T^25 - 2346/2401*T^24 + 2474/2401*T^23 - 2622/2401*T^22 + 
        1073/2401*T^21 - 288/2401*T^20 + 20/2401*T^19 + 951/2401*T^18 - 164/343*T^17
        + 1443/2401*T^16 - 291/343*T^15 + 367/343*T^14 - 1845/2401*T^13 + 
        2734/2401*T^12 - 2424/2401*T^11 + 1224/2401*T^10 - 2008/2401*T^9 + 
        470/2401*T^8 - 1175/2401*T^7 + 1517/2401*T^6 - 2187/2401*T^5 + 2038/2401*T^4
        - 442/343*T^3 + 62/49*T^2 - T + 1
*], [*
    X^3 + 6*X*Y^14 + 3*X*Y^13 + 3*X*Y^12 + X*Y^11 + 4*X*Y^10 + X*Y^9 + 6*X*Y^7 + 
        3*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 4*X*Y + X + 4*Y^30 + 
        2*Y^29 + 2*Y^28 + 5*Y^27 + Y^26 + 5*Y^25 + 5*Y^24 + Y^23 + Y^22 + 3*Y^21 + 
        5*Y^20 + 2*Y^19 + 6*Y^18 + 5*Y^17 + 4*Y^16 + 2*Y^15 + 4*Y^14 + 2*Y^13 + 
        2*Y^12 + Y^11 + 6*Y^10 + 5*Y^9 + Y^8 + 5*Y^7 + Y^6 + 5*Y^5 + Y^4 + 3*Y^3 + 
        Y^2 + 1,
    T^56 + T^55 + 4/49*T^54 - 72/343*T^53 + 187/343*T^52 + 2462/2401*T^51 - 
        213/2401*T^50 - 1937/2401*T^49 - 726/2401*T^48 + 383/2401*T^47 - 
        1965/2401*T^46 - 2669/2401*T^45 - 1571/2401*T^44 - 100/343*T^43 - 
        808/2401*T^42 - 1420/2401*T^41 - 1090/2401*T^40 - 582/2401*T^39 + 
        177/2401*T^38 - 26/343*T^37 + 148/2401*T^36 + 102/2401*T^35 + 1202/2401*T^34
        + 683/2401*T^33 - 367/2401*T^32 + 165/343*T^31 + 1646/2401*T^30 + 
        1198/2401*T^29 + 223/2401*T^28 + 1198/2401*T^27 + 1646/2401*T^26 + 
        165/343*T^25 - 367/2401*T^24 + 683/2401*T^23 + 1202/2401*T^22 + 
        102/2401*T^21 + 148/2401*T^20 - 26/343*T^19 + 177/2401*T^18 - 582/2401*T^17 
        - 1090/2401*T^16 - 1420/2401*T^15 - 808/2401*T^14 - 100/343*T^13 - 
        1571/2401*T^12 - 2669/2401*T^11 - 1965/2401*T^10 + 383/2401*T^9 - 
        726/2401*T^8 - 1937/2401*T^7 - 213/2401*T^6 + 2462/2401*T^5 + 187/343*T^4 - 
        72/343*T^3 + 4/49*T^2 + T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 
        X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 3*X*Y + 
        3*X + 5*Y^30 + 3*Y^29 + 6*Y^28 + 4*Y^27 + Y^24 + 3*Y^23 + 6*Y^22 + Y^21 + 
        Y^20 + 3*Y^19 + 6*Y^18 + Y^17 + 6*Y^16 + 3*Y^15 + Y^14 + Y^13 + 5*Y^12 + 
        Y^10 + 3*Y^9 + 3*Y^7 + Y^5 + 6*Y^4 + 3*Y^3 + 6*Y^2 + 4*Y + 3,
    T^56 + 13/7*T^55 + 65/49*T^54 + 132/343*T^53 - 1091/2401*T^52 - 326/343*T^51 - 
        2343/2401*T^50 - 349/2401*T^49 + 3335/2401*T^48 + 5105/2401*T^47 + 
        2064/2401*T^46 - 1406/2401*T^45 - 2062/2401*T^44 - 979/2401*T^43 + 
        736/2401*T^42 + 302/343*T^41 + 2657/2401*T^40 + 1153/2401*T^39 - 
        1338/2401*T^38 - 458/343*T^37 - 2335/2401*T^36 + 65/343*T^35 + 
        1619/2401*T^34 + 435/2401*T^33 - 1070/2401*T^32 - 1689/2401*T^31 - 
        748/2401*T^30 - 558/2401*T^29 - 1472/2401*T^28 - 558/2401*T^27 - 
        748/2401*T^26 - 1689/2401*T^25 - 1070/2401*T^24 + 435/2401*T^23 + 
        1619/2401*T^22 + 65/343*T^21 - 2335/2401*T^20 - 458/343*T^19 - 
        1338/2401*T^18 + 1153/2401*T^17 + 2657/2401*T^16 + 302/343*T^15 + 
        736/2401*T^14 - 979/2401*T^13 - 2062/2401*T^12 - 1406/2401*T^11 + 
        2064/2401*T^10 + 5105/2401*T^9 + 3335/2401*T^8 - 349/2401*T^7 - 
        2343/2401*T^6 - 326/343*T^5 - 1091/2401*T^4 + 132/343*T^3 + 65/49*T^2 + 
        13/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 
        + 2*X*Y^8 + 4*X*Y^7 + 2*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + X*Y 
        + 2*Y^30 + 2*Y^27 + 6*Y^26 + 5*Y^25 + 6*Y^24 + 2*Y^23 + 4*Y^22 + 3*Y^21 + 
        4*Y^20 + 5*Y^19 + Y^18 + 6*Y^17 + 2*Y^16 + 2*Y^15 + Y^14 + 4*Y^13 + 6*Y^12 +
        5*Y^10 + 3*Y^9 + 6*Y^8 + 2*Y^7 + 4*Y^5 + 6*Y^4 + 6*Y^3 + 3*Y^2 + 4*Y + 4,
    -T^56 - 10/7*T^55 - 12/49*T^54 + 219/343*T^53 + 2476/2401*T^52 + 3281/2401*T^51 
        + 1594/2401*T^50 - 2374/2401*T^49 - 3459/2401*T^48 - 1228/2401*T^47 + 
        64/343*T^46 + 436/2401*T^45 + 99/343*T^44 + 333/2401*T^43 - 1100/2401*T^42 -
        957/2401*T^41 + 1212/2401*T^40 + 1384/2401*T^39 + 128/2401*T^38 - 
        281/2401*T^37 - 745/2401*T^36 - 327/2401*T^35 + 298/2401*T^34 + 
        587/2401*T^33 + 8/343*T^32 - 1311/2401*T^31 - 2087/2401*T^30 - 
        1312/2401*T^29 + 1312/2401*T^27 + 2087/2401*T^26 + 1311/2401*T^25 - 
        8/343*T^24 - 587/2401*T^23 - 298/2401*T^22 + 327/2401*T^21 + 745/2401*T^20 +
        281/2401*T^19 - 128/2401*T^18 - 1384/2401*T^17 - 1212/2401*T^16 + 
        957/2401*T^15 + 1100/2401*T^14 - 333/2401*T^13 - 99/343*T^12 - 436/2401*T^11
        - 64/343*T^10 + 1228/2401*T^9 + 3459/2401*T^8 + 2374/2401*T^7 - 
        1594/2401*T^6 - 3281/2401*T^5 - 2476/2401*T^4 - 219/343*T^3 + 12/49*T^2 + 
        10/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + X*Y^13 + X*Y^12 + 5*X*Y^11 + 3*X*Y^10 + 6*X*Y^8 + 
        X*Y^7 + 6*X*Y^6 + X*Y^5 + 3*X*Y^4 + 6*X*Y^2 + 4*X*Y + 5*X + 5*Y^30 + 5*Y^29 
        + 6*Y^28 + 4*Y^27 + 4*Y^26 + 3*Y^25 + 2*Y^24 + 6*Y^23 + 2*Y^22 + 2*Y^21 + 
        4*Y^20 + 6*Y^19 + 4*Y^18 + 5*Y^17 + 3*Y^16 + Y^15 + 6*Y^14 + 5*Y^13 + Y^11 +
        3*Y^10 + Y^9 + 5*Y^8 + 2*Y^7 + Y^6 + Y^5 + 5*Y^4 + 6*Y^3 + 6*Y^2 + 6*Y + 2,
    T^56 - T^55 - 3/49*T^54 + 379/343*T^53 - 1559/2401*T^52 - 1405/2401*T^51 + 
        267/343*T^50 - 244/2401*T^49 - 292/343*T^48 + 156/343*T^47 + 374/2401*T^46 -
        466/2401*T^45 - 249/2401*T^44 + 31/2401*T^43 + 747/2401*T^42 - 699/2401*T^41
        + 374/2401*T^40 - 194/2401*T^39 - 675/2401*T^38 + 708/2401*T^37 + 
        68/2401*T^36 - 1061/2401*T^35 - 547/2401*T^34 + 2862/2401*T^33 - 
        1052/2401*T^32 - 3082/2401*T^31 + 3383/2401*T^30 + 1356/2401*T^29 - 
        4105/2401*T^28 + 1356/2401*T^27 + 3383/2401*T^26 - 3082/2401*T^25 - 
        1052/2401*T^24 + 2862/2401*T^23 - 547/2401*T^22 - 1061/2401*T^21 + 
        68/2401*T^20 + 708/2401*T^19 - 675/2401*T^18 - 194/2401*T^17 + 374/2401*T^16
        - 699/2401*T^15 + 747/2401*T^14 + 31/2401*T^13 - 249/2401*T^12 - 
        466/2401*T^11 + 374/2401*T^10 + 156/343*T^9 - 292/343*T^8 - 244/2401*T^7 + 
        267/343*T^6 - 1405/2401*T^5 - 1559/2401*T^4 + 379/343*T^3 - 3/49*T^2 - T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 
        + 4*X*Y^8 + 6*X*Y^7 + 6*X*Y^5 + 6*X*Y^4 + X*Y^3 + 4*X*Y^2 + X + 3*Y^30 + 
        6*Y^29 + 3*Y^28 + 4*Y^27 + 6*Y^26 + Y^25 + 2*Y^24 + Y^23 + 5*Y^22 + 6*Y^21 +
        2*Y^20 + 3*Y^19 + 6*Y^18 + Y^17 + 4*Y^16 + Y^15 + 3*Y^14 + 5*Y^13 + 6*Y^11 +
        4*Y^10 + 6*Y^9 + 3*Y^8 + Y^7 + 4*Y^6 + 3*Y^5 + 2*Y^4 + 5*Y^2 + 2*Y + 1,
    -T^56 + 1/7*T^55 + 22/49*T^54 - 95/343*T^53 - 293/2401*T^52 - 1044/2401*T^51 - 
        356/2401*T^50 + 1013/2401*T^49 - 1819/2401*T^48 + 1797/2401*T^47 + 
        158/2401*T^46 - 2176/2401*T^45 + 32/49*T^44 + 486/2401*T^43 - 1640/2401*T^42
        + 17/49*T^41 - 256/2401*T^40 + 955/2401*T^39 - 558/2401*T^38 - 
        1625/2401*T^37 + 2292/2401*T^36 + 193/2401*T^35 - 1934/2401*T^34 + 
        2249/2401*T^33 + 383/2401*T^32 - 1248/2401*T^31 + 832/2401*T^30 + 
        99/343*T^29 - 99/343*T^27 - 832/2401*T^26 + 1248/2401*T^25 - 383/2401*T^24 -
        2249/2401*T^23 + 1934/2401*T^22 - 193/2401*T^21 - 2292/2401*T^20 + 
        1625/2401*T^19 + 558/2401*T^18 - 955/2401*T^17 + 256/2401*T^16 - 17/49*T^15 
        + 1640/2401*T^14 - 486/2401*T^13 - 32/49*T^12 + 2176/2401*T^11 - 
        158/2401*T^10 - 1797/2401*T^9 + 1819/2401*T^8 - 1013/2401*T^7 + 356/2401*T^6
        + 1044/2401*T^5 + 293/2401*T^4 + 95/343*T^3 - 22/49*T^2 - 1/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + X*Y^12 + X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 
        2*X*Y^7 + X*Y^3 + 4*X*Y^2 + 6*Y^30 + 2*Y^29 + 4*Y^28 + 4*Y^27 + Y^25 + 
        6*Y^24 + 2*Y^23 + 6*Y^22 + 2*Y^21 + 3*Y^19 + Y^18 + 5*Y^17 + 4*Y^16 + 6*Y^15
        + Y^14 + 3*Y^12 + 3*Y^11 + Y^10 + 5*Y^9 + 6*Y^7 + 6*Y^6 + 2*Y^5 + 4*Y^4 + 
        6*Y^3 + Y^2 + 2*Y + 1,
    T^56 - 6/7*T^55 + 6/7*T^54 - 90/343*T^53 - 473/2401*T^52 + 1620/2401*T^51 - 
        1986/2401*T^50 + 1992/2401*T^49 - 1627/2401*T^48 + 10/2401*T^47 + 
        1632/2401*T^46 - 3936/2401*T^45 + 4388/2401*T^44 - 3982/2401*T^43 + 
        1216/2401*T^42 + 2340/2401*T^41 - 4806/2401*T^40 + 5338/2401*T^39 - 
        737/343*T^38 + 2026/2401*T^37 + 631/2401*T^36 - 2690/2401*T^35 + 
        696/343*T^34 - 5393/2401*T^33 + 562/343*T^32 - 739/2401*T^31 - 
        2782/2401*T^30 + 6288/2401*T^29 - 7601/2401*T^28 + 6288/2401*T^27 - 
        2782/2401*T^26 - 739/2401*T^25 + 562/343*T^24 - 5393/2401*T^23 + 
        696/343*T^22 - 2690/2401*T^21 + 631/2401*T^20 + 2026/2401*T^19 - 
        737/343*T^18 + 5338/2401*T^17 - 4806/2401*T^16 + 2340/2401*T^15 + 
        1216/2401*T^14 - 3982/2401*T^13 + 4388/2401*T^12 - 3936/2401*T^11 + 
        1632/2401*T^10 + 10/2401*T^9 - 1627/2401*T^8 + 1992/2401*T^7 - 1986/2401*T^6
        + 1620/2401*T^5 - 473/2401*T^4 - 90/343*T^3 + 6/7*T^2 - 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 2*X*Y^9 + 6*X*Y^7 + 2*X*Y^6 + 
        5*X*Y^5 + 2*X*Y^3 + 4*X*Y^2 + 5*X*Y + 2*X + 4*Y^30 + 4*Y^28 + Y^27 + 6*Y^26 
        + 5*Y^25 + 3*Y^24 + Y^23 + Y^22 + 6*Y^20 + 3*Y^19 + 4*Y^18 + 5*Y^17 + Y^16 +
        4*Y^15 + 2*Y^14 + Y^13 + 5*Y^12 + 5*Y^10 + 5*Y^9 + 4*Y^8 + 4*Y^7 + 2*Y^5 + 
        6*Y^4 + 5*Y^3 + Y^2 + 2*Y + 1,
    -T^56 + 1/7*T^55 + 88/49*T^54 - 159/343*T^53 - 3971/2401*T^52 + 1874/2401*T^51 +
        2215/2401*T^50 - 2139/2401*T^49 - 1503/2401*T^48 + 2139/2401*T^47 + 
        1755/2401*T^46 - 1702/2401*T^45 - 1119/2401*T^44 + 2199/2401*T^43 + 
        176/2401*T^42 - 2969/2401*T^41 + 247/2401*T^40 + 2501/2401*T^39 + 4/49*T^38 
        - 1105/2401*T^37 + 29/343*T^36 + 229/2401*T^35 - 1124/2401*T^34 - 
        41/343*T^33 + 538/2401*T^32 + 29/343*T^31 + 292/2401*T^30 - 36/343*T^29 + 
        36/343*T^27 - 292/2401*T^26 - 29/343*T^25 - 538/2401*T^24 + 41/343*T^23 + 
        1124/2401*T^22 - 229/2401*T^21 - 29/343*T^20 + 1105/2401*T^19 - 4/49*T^18 - 
        2501/2401*T^17 - 247/2401*T^16 + 2969/2401*T^15 - 176/2401*T^14 - 
        2199/2401*T^13 + 1119/2401*T^12 + 1702/2401*T^11 - 1755/2401*T^10 - 
        2139/2401*T^9 + 1503/2401*T^8 + 2139/2401*T^7 - 2215/2401*T^6 - 
        1874/2401*T^5 + 3971/2401*T^4 + 159/343*T^3 - 88/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 
        + 6*X*Y^8 + 3*X*Y^7 + 5*X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 2*X + 5*Y^30 +
        Y^29 + Y^27 + Y^26 + 5*Y^25 + 2*Y^24 + Y^23 + 3*Y^21 + 6*Y^20 + 6*Y^19 + 
        3*Y^18 + Y^17 + 3*Y^16 + 5*Y^15 + 4*Y^13 + 5*Y^12 + Y^11 + 5*Y^10 + Y^9 + 
        Y^7 + 5*Y^6 + Y^4 + 2*Y^3 + 4*Y^2,
    -T^56 + 3/7*T^55 + 68/49*T^54 - 183/343*T^53 - 2990/2401*T^52 + 1244/2401*T^51 +
        366/343*T^50 + 8/343*T^49 - 3093/2401*T^48 - 1203/2401*T^47 + 4775/2401*T^46
        - 143/2401*T^45 - 507/343*T^44 - 388/2401*T^43 + 556/343*T^42 + 
        451/2401*T^41 - 4402/2401*T^40 - 722/2401*T^39 + 4157/2401*T^38 + 
        899/2401*T^37 - 3361/2401*T^36 - 919/2401*T^35 + 958/2401*T^34 + 
        524/343*T^33 - 2239/2401*T^32 - 2085/2401*T^31 + 225/343*T^30 + 
        1455/2401*T^29 - 1455/2401*T^27 - 225/343*T^26 + 2085/2401*T^25 + 
        2239/2401*T^24 - 524/343*T^23 - 958/2401*T^22 + 919/2401*T^21 + 
        3361/2401*T^20 - 899/2401*T^19 - 4157/2401*T^18 + 722/2401*T^17 + 
        4402/2401*T^16 - 451/2401*T^15 - 556/343*T^14 + 388/2401*T^13 + 507/343*T^12
        + 143/2401*T^11 - 4775/2401*T^10 + 1203/2401*T^9 + 3093/2401*T^8 - 8/343*T^7
        - 366/343*T^6 - 1244/2401*T^5 + 2990/2401*T^4 + 183/343*T^3 - 68/49*T^2 - 
        3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 2*X*Y^12 + X*Y^11 + X*Y^10 + 6*X*Y^9 + 2*X*Y^8 + 
        X*Y^7 + 4*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + X*Y^3 + 2*X*Y^2 + 6*X*Y + 5*X + 6*Y^30
        + 2*Y^27 + 4*Y^23 + 6*Y^22 + 2*Y^21 + 5*Y^20 + 4*Y^19 + 6*Y^16 + 6*Y^14 + 
        3*Y^13 + 3*Y^12 + 2*Y^11 + 6*Y^9 + 6*Y^8 + 6*Y^7 + 2*Y^6 + 2*Y^5 + Y^4 + 
        5*Y^3 + 3*Y^2 + 5*Y + 3,
    T^56 + 13/7*T^55 + 73/49*T^54 + 321/343*T^53 - 1017/2401*T^52 - 4065/2401*T^51 -
        3516/2401*T^50 - 3943/2401*T^49 - 2682/2401*T^48 + 1312/2401*T^47 + 
        1984/2401*T^46 + 2518/2401*T^45 + 1807/2401*T^44 - 421/343*T^43 - 
        4486/2401*T^42 - 4321/2401*T^41 - 4434/2401*T^40 - 16/49*T^39 + 
        1332/2401*T^38 + 1390/2401*T^37 + 348/343*T^36 + 835/2401*T^35 - 
        1335/2401*T^34 - 1296/2401*T^33 - 151/343*T^32 + 510/2401*T^31 + 
        3074/2401*T^30 + 4476/2401*T^29 + 4650/2401*T^28 + 4476/2401*T^27 + 
        3074/2401*T^26 + 510/2401*T^25 - 151/343*T^24 - 1296/2401*T^23 - 
        1335/2401*T^22 + 835/2401*T^21 + 348/343*T^20 + 1390/2401*T^19 + 
        1332/2401*T^18 - 16/49*T^17 - 4434/2401*T^16 - 4321/2401*T^15 - 
        4486/2401*T^14 - 421/343*T^13 + 1807/2401*T^12 + 2518/2401*T^11 + 
        1984/2401*T^10 + 1312/2401*T^9 - 2682/2401*T^8 - 3943/2401*T^7 - 
        3516/2401*T^6 - 4065/2401*T^5 - 1017/2401*T^4 + 321/343*T^3 + 73/49*T^2 + 
        13/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + X*Y^13 + 2*X*Y^12 + 3*X*Y^10 + 2*X*Y^9 + X*Y^7 + 
        5*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + X*Y^2 + 2*X*Y + 6*X + 2*Y^30 + 
        6*Y^29 + Y^28 + Y^27 + Y^26 + 2*Y^25 + 5*Y^24 + 4*Y^23 + 5*Y^22 + 3*Y^21 + 
        5*Y^20 + 6*Y^19 + 3*Y^18 + 3*Y^15 + 5*Y^14 + 4*Y^13 + 5*Y^12 + 3*Y^11 + Y^10
        + 2*Y^9 + Y^8 + Y^7 + 4*Y^6 + 6*Y^5 + 3*Y^4 + 6*Y^3 + 2*Y^2 + 3*Y + 5,
    T^56 + 5/7*T^55 - 47/49*T^54 - 65/49*T^53 - 908/2401*T^52 + 487/2401*T^51 - 
        12/2401*T^50 - 345/2401*T^49 + 857/2401*T^48 + 186/343*T^47 + 368/2401*T^46 
        + 500/2401*T^45 + 915/2401*T^44 + 271/2401*T^43 - 1392/2401*T^42 - 
        633/2401*T^41 + 845/2401*T^40 + 72/2401*T^39 - 970/2401*T^38 - 
        1213/2401*T^37 - 1984/2401*T^36 + 79/2401*T^35 + 2904/2401*T^34 + 
        2414/2401*T^33 + 914/2401*T^32 - 1210/2401*T^31 - 1683/2401*T^30 - 
        419/2401*T^29 + 442/2401*T^28 - 419/2401*T^27 - 1683/2401*T^26 - 
        1210/2401*T^25 + 914/2401*T^24 + 2414/2401*T^23 + 2904/2401*T^22 + 
        79/2401*T^21 - 1984/2401*T^20 - 1213/2401*T^19 - 970/2401*T^18 + 
        72/2401*T^17 + 845/2401*T^16 - 633/2401*T^15 - 1392/2401*T^14 + 
        271/2401*T^13 + 915/2401*T^12 + 500/2401*T^11 + 368/2401*T^10 + 186/343*T^9 
        + 857/2401*T^8 - 345/2401*T^7 - 12/2401*T^6 + 487/2401*T^5 - 908/2401*T^4 - 
        65/49*T^3 - 47/49*T^2 + 5/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 2*X*Y^9 + 
        X*Y^8 + 3*X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + X*Y + 
        5*X + 5*Y^30 + 5*Y^28 + 4*Y^27 + 6*Y^23 + Y^22 + Y^21 + Y^20 + 3*Y^19 + 
        4*Y^18 + 6*Y^17 + Y^16 + 3*Y^15 + 6*Y^14 + 6*Y^13 + 4*Y^12 + 2*Y^11 + 5*Y^10
        + 6*Y^9 + 3*Y^8 + Y^6 + 4*Y^5 + 3*Y^3 + 3*Y^2 + Y + 3,
    -T^56 - 8/7*T^55 + 22/49*T^54 + 94/343*T^53 - 1831/2401*T^52 + 1091/2401*T^51 + 
        3344/2401*T^50 + 27/2401*T^49 - 2670/2401*T^48 - 85/2401*T^47 + 
        667/2401*T^46 - 1606/2401*T^45 + 1121/2401*T^44 + 1980/2401*T^43 - 
        1524/2401*T^42 - 86/2401*T^41 + 37/49*T^40 - 16/343*T^39 - 326/2401*T^38 + 
        2152/2401*T^37 + 2038/2401*T^36 - 103/343*T^35 - 1032/2401*T^34 - 
        722/2401*T^33 - 1259/2401*T^32 + 975/2401*T^31 + 1422/2401*T^30 - 
        1006/2401*T^29 + 1006/2401*T^27 - 1422/2401*T^26 - 975/2401*T^25 + 
        1259/2401*T^24 + 722/2401*T^23 + 1032/2401*T^22 + 103/343*T^21 - 
        2038/2401*T^20 - 2152/2401*T^19 + 326/2401*T^18 + 16/343*T^17 - 37/49*T^16 +
        86/2401*T^15 + 1524/2401*T^14 - 1980/2401*T^13 - 1121/2401*T^12 + 
        1606/2401*T^11 - 667/2401*T^10 + 85/2401*T^9 + 2670/2401*T^8 - 27/2401*T^7 -
        3344/2401*T^6 - 1091/2401*T^5 + 1831/2401*T^4 - 94/343*T^3 - 22/49*T^2 + 
        8/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 3*X*Y^9 + 
        5*X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 2*X*Y^2 + 2*X*Y + 
        6*X + 4*Y^30 + Y^29 + 6*Y^28 + 2*Y^27 + 3*Y^26 + 3*Y^25 + 6*Y^23 + 2*Y^22 + 
        2*Y^21 + 4*Y^20 + Y^19 + 6*Y^18 + 2*Y^17 + Y^16 + Y^15 + 4*Y^13 + 4*Y^12 + 
        5*Y^10 + 4*Y^9 + 4*Y^8 + 3*Y^7 + 5*Y^6 + 2*Y^4 + Y^3 + 2*Y^2 + 3*Y + 4,
    -T^56 + 3/7*T^55 + 26/49*T^54 + 103/343*T^53 - 1431/2401*T^52 - 274/2401*T^51 + 
        1291/2401*T^50 + 222/2401*T^49 - 1072/2401*T^48 - 942/2401*T^47 + 
        1219/2401*T^46 + 1243/2401*T^45 + 187/2401*T^44 - 1919/2401*T^43 + 
        789/2401*T^42 + 110/2401*T^41 + 346/2401*T^40 - 402/2401*T^39 + 
        275/2401*T^38 - 264/2401*T^37 + 104/343*T^36 - 345/2401*T^35 - 760/2401*T^34
        - 1707/2401*T^33 + 1308/2401*T^32 + 722/2401*T^31 + 64/2401*T^30 - 
        993/2401*T^29 + 993/2401*T^27 - 64/2401*T^26 - 722/2401*T^25 - 
        1308/2401*T^24 + 1707/2401*T^23 + 760/2401*T^22 + 345/2401*T^21 - 
        104/343*T^20 + 264/2401*T^19 - 275/2401*T^18 + 402/2401*T^17 - 346/2401*T^16
        - 110/2401*T^15 - 789/2401*T^14 + 1919/2401*T^13 - 187/2401*T^12 - 
        1243/2401*T^11 - 1219/2401*T^10 + 942/2401*T^9 + 1072/2401*T^8 - 
        222/2401*T^7 - 1291/2401*T^6 + 274/2401*T^5 + 1431/2401*T^4 - 103/343*T^3 - 
        26/49*T^2 - 3/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 
        6*X*Y^7 + X*Y^6 + X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 2*X*Y + 2*X + 4*Y^30
        + 3*Y^29 + 6*Y^28 + 3*Y^27 + 6*Y^26 + 2*Y^25 + 4*Y^24 + 5*Y^22 + 3*Y^21 + 
        4*Y^20 + Y^19 + Y^18 + 2*Y^17 + 2*Y^15 + 3*Y^13 + 2*Y^12 + 6*Y^11 + 4*Y^10 +
        4*Y^8 + Y^7 + 6*Y^6 + 5*Y^5 + 6*Y^4 + Y^3 + 4*Y + 6,
    -T^56 - 10/7*T^55 - 72/49*T^54 - 93/49*T^53 - 2238/2401*T^52 + 61/343*T^51 + 
        2083/2401*T^50 + 5176/2401*T^49 + 6849/2401*T^48 + 116/49*T^47 + 
        5039/2401*T^46 + 2981/2401*T^45 - 145/343*T^44 - 557/343*T^43 - 874/343*T^42
        - 1114/343*T^41 - 7192/2401*T^40 - 4335/2401*T^39 - 289/343*T^38 + 
        449/2401*T^37 + 3532/2401*T^36 + 4063/2401*T^35 + 3582/2401*T^34 + 
        3965/2401*T^33 + 2599/2401*T^32 + 1999/2401*T^31 + 2005/2401*T^30 + 
        43/343*T^29 - 43/343*T^27 - 2005/2401*T^26 - 1999/2401*T^25 - 2599/2401*T^24
        - 3965/2401*T^23 - 3582/2401*T^22 - 4063/2401*T^21 - 3532/2401*T^20 - 
        449/2401*T^19 + 289/343*T^18 + 4335/2401*T^17 + 7192/2401*T^16 + 
        1114/343*T^15 + 874/343*T^14 + 557/343*T^13 + 145/343*T^12 - 2981/2401*T^11 
        - 5039/2401*T^10 - 116/49*T^9 - 6849/2401*T^8 - 5176/2401*T^7 - 
        2083/2401*T^6 - 61/343*T^5 + 2238/2401*T^4 + 93/49*T^3 + 72/49*T^2 + 10/7*T 
        + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 
        X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + X*Y^5 + 5*X*Y^4 + 4*X*Y^3 + X*Y^2 + 5*X*Y + 4*X 
        + 5*Y^30 + 3*Y^29 + 2*Y^28 + 4*Y^27 + 5*Y^26 + Y^25 + 4*Y^24 + Y^23 + 6*Y^22
        + 3*Y^21 + 3*Y^19 + Y^18 + Y^17 + 4*Y^15 + 5*Y^14 + 3*Y^13 + 2*Y^10 + Y^9 + 
        2*Y^8 + Y^6 + 3*Y^5 + 4*Y^4 + Y^3 + 5*Y^2 + 6*Y + 4,
    T^56 + 3/7*T^55 - 9/49*T^54 + 325/343*T^53 + 1131/2401*T^52 + 1005/2401*T^51 - 
        1045/2401*T^50 - 510/2401*T^49 + 234/343*T^48 - 1471/2401*T^47 - 
        958/2401*T^46 + 327/2401*T^45 + 1670/2401*T^44 + 325/2401*T^43 - 
        593/2401*T^42 + 221/343*T^41 + 47/343*T^40 - 1545/2401*T^39 - 1431/2401*T^38
        + 8/2401*T^37 - 661/2401*T^36 - 1684/2401*T^35 - 733/2401*T^34 + 
        772/2401*T^33 - 643/2401*T^32 - 542/2401*T^31 + 129/2401*T^30 - 
        753/2401*T^29 - 16/2401*T^28 - 753/2401*T^27 + 129/2401*T^26 - 542/2401*T^25
        - 643/2401*T^24 + 772/2401*T^23 - 733/2401*T^22 - 1684/2401*T^21 - 
        661/2401*T^20 + 8/2401*T^19 - 1431/2401*T^18 - 1545/2401*T^17 + 47/343*T^16 
        + 221/343*T^15 - 593/2401*T^14 + 325/2401*T^13 + 1670/2401*T^12 + 
        327/2401*T^11 - 958/2401*T^10 - 1471/2401*T^9 + 234/343*T^8 - 510/2401*T^7 -
        1045/2401*T^6 + 1005/2401*T^5 + 1131/2401*T^4 + 325/343*T^3 - 9/49*T^2 + 
        3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + X*Y^9 + 
        2*X*Y^8 + 3*X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 4*X*Y 
        + 5*X + Y^30 + 6*Y^28 + 2*Y^27 + Y^26 + 2*Y^25 + 3*Y^24 + Y^23 + 5*Y^22 + 
        4*Y^20 + 5*Y^19 + 6*Y^18 + 4*Y^17 + 4*Y^16 + 5*Y^15 + Y^14 + 3*Y^13 + Y^11 +
        5*Y^10 + 2*Y^9 + 4*Y^8 + 4*Y^7 + 4*Y^5 + 4*Y^4 + 2*Y^3 + 4*Y + 1,
    -T^56 - 8/7*T^55 + 8/49*T^54 + 183/343*T^53 + 1195/2401*T^52 + 1969/2401*T^51 + 
        774/2401*T^50 - 1564/2401*T^49 - 1618/2401*T^48 - 114/343*T^47 - 10/343*T^46
        + 180/2401*T^45 + 4/49*T^44 - 152/2401*T^43 - 522/2401*T^42 + 227/2401*T^41 
        + 548/2401*T^40 + 880/2401*T^39 + 75/2401*T^38 - 1272/2401*T^37 - 
        999/2401*T^36 - 202/2401*T^35 + 32/2401*T^34 + 848/2401*T^33 + 884/2401*T^32
        + 5/49*T^31 - 190/2401*T^30 - 1451/2401*T^29 + 1451/2401*T^27 + 
        190/2401*T^26 - 5/49*T^25 - 884/2401*T^24 - 848/2401*T^23 - 32/2401*T^22 + 
        202/2401*T^21 + 999/2401*T^20 + 1272/2401*T^19 - 75/2401*T^18 - 
        880/2401*T^17 - 548/2401*T^16 - 227/2401*T^15 + 522/2401*T^14 + 
        152/2401*T^13 - 4/49*T^12 - 180/2401*T^11 + 10/343*T^10 + 114/343*T^9 + 
        1618/2401*T^8 + 1564/2401*T^7 - 774/2401*T^6 - 1969/2401*T^5 - 1195/2401*T^4
        - 183/343*T^3 - 8/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 2*X*Y^12 + 2*X*Y^11 + 3*X*Y^9 + 4*X*Y^6 + 6*X*Y^5 + 
        2*X*Y^4 + 6*X*Y^3 + X*Y^2 + X*Y + 5*X + 5*Y^30 + 3*Y^29 + 3*Y^27 + 2*Y^25 + 
        Y^24 + 5*Y^23 + 4*Y^22 + 2*Y^21 + 5*Y^20 + 5*Y^19 + 5*Y^18 + 5*Y^17 + 6*Y^15
        + 3*Y^14 + 4*Y^12 + 4*Y^11 + 4*Y^10 + 2*Y^9 + Y^8 + 5*Y^7 + Y^6 + 2*Y^4 + 
        3*Y^3 + 3*Y^2 + 6*Y + 2,
    T^56 + 2/7*T^55 + 1/49*T^54 - 142/343*T^53 - 2459/2401*T^52 - 1333/2401*T^51 - 
        1770/2401*T^50 - 313/2401*T^49 + 2435/2401*T^48 + 1614/2401*T^47 + 
        2855/2401*T^46 + 1661/2401*T^45 - 451/2401*T^44 - 1202/2401*T^43 - 
        3047/2401*T^42 - 305/343*T^41 - 289/2401*T^40 + 488/2401*T^39 + 
        1177/2401*T^38 + 348/343*T^37 + 851/2401*T^36 + 283/2401*T^35 - 180/343*T^34
        - 2449/2401*T^33 - 263/2401*T^32 - 869/2401*T^31 - 187/2401*T^30 + 
        2267/2401*T^29 + 212/2401*T^28 + 2267/2401*T^27 - 187/2401*T^26 - 
        869/2401*T^25 - 263/2401*T^24 - 2449/2401*T^23 - 180/343*T^22 + 
        283/2401*T^21 + 851/2401*T^20 + 348/343*T^19 + 1177/2401*T^18 + 
        488/2401*T^17 - 289/2401*T^16 - 305/343*T^15 - 3047/2401*T^14 - 
        1202/2401*T^13 - 451/2401*T^12 + 1661/2401*T^11 + 2855/2401*T^10 + 
        1614/2401*T^9 + 2435/2401*T^8 - 313/2401*T^7 - 1770/2401*T^6 - 1333/2401*T^5
        - 2459/2401*T^4 - 142/343*T^3 + 1/49*T^2 + 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 6*X*Y^8 + 
        2*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + X + 2*Y^30 + 
        4*Y^29 + 5*Y^28 + 4*Y^27 + 4*Y^26 + 3*Y^25 + 6*Y^24 + 2*Y^23 + 4*Y^22 + 
        2*Y^21 + 4*Y^20 + 3*Y^19 + Y^18 + 3*Y^17 + 5*Y^16 + 6*Y^15 + 4*Y^14 + 5*Y^13
        + 5*Y^12 + 4*Y^10 + 2*Y^8 + 6*Y^7 + 2*Y^6 + 3*Y^5 + Y^4 + Y^3 + 3*Y^2 + 5*Y 
        + 3,
    -T^56 + T^55 + 1/49*T^54 - 265/343*T^53 + 1917/2401*T^52 + 803/2401*T^51 - 
        2528/2401*T^50 + 786/2401*T^49 + 1319/2401*T^48 - 2028/2401*T^47 + 
        969/2401*T^46 - 74/2401*T^45 + 249/343*T^44 - 710/2401*T^43 - 1429/2401*T^42
        + 330/343*T^41 - 1523/2401*T^40 - 1283/2401*T^39 + 1595/2401*T^38 - 
        29/2401*T^37 - 1510/2401*T^36 + 1293/2401*T^35 + 100/2401*T^34 - 3/343*T^33 
        - 705/2401*T^32 - 613/2401*T^31 + 209/343*T^30 - 1255/2401*T^29 + 
        1255/2401*T^27 - 209/343*T^26 + 613/2401*T^25 + 705/2401*T^24 + 3/343*T^23 -
        100/2401*T^22 - 1293/2401*T^21 + 1510/2401*T^20 + 29/2401*T^19 - 
        1595/2401*T^18 + 1283/2401*T^17 + 1523/2401*T^16 - 330/343*T^15 + 
        1429/2401*T^14 + 710/2401*T^13 - 249/343*T^12 + 74/2401*T^11 - 969/2401*T^10
        + 2028/2401*T^9 - 1319/2401*T^8 - 786/2401*T^7 + 2528/2401*T^6 - 
        803/2401*T^5 - 1917/2401*T^4 + 265/343*T^3 - 1/49*T^2 - T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + X*Y^12 + X*Y^11 + 5*X*Y^10 + 6*X*Y^9 + 
        5*X*Y^8 + 4*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + X*Y + Y^30 + 
        4*Y^29 + 3*Y^28 + Y^27 + Y^26 + 3*Y^25 + 2*Y^23 + 6*Y^22 + 4*Y^21 + 3*Y^20 +
        Y^19 + 4*Y^17 + 5*Y^16 + Y^15 + 4*Y^14 + Y^13 + 5*Y^12 + 4*Y^11 + 3*Y^10 + 
        6*Y^9 + 6*Y^8 + 3*Y^7 + Y^5 + 2*Y^3 + 4*Y^2 + 3*Y + 6,
    T^56 + 6/7*T^55 - 9/49*T^54 + 137/343*T^53 + 1513/2401*T^52 + 106/2401*T^51 - 
        89/2401*T^50 - 128/2401*T^49 + 337/2401*T^48 + 2062/2401*T^47 + 
        1308/2401*T^46 - 433/2401*T^45 + 284/2401*T^44 - 106/343*T^43 - 
        1804/2401*T^42 - 1150/2401*T^41 - 1552/2401*T^40 - 363/2401*T^39 + 
        73/2401*T^38 + 83/2401*T^37 + 1144/2401*T^36 - 445/2401*T^35 - 
        2762/2401*T^34 - 1241/2401*T^33 - 101/2401*T^32 - 314/343*T^31 - 
        585/2401*T^30 + 1360/2401*T^29 + 99/343*T^28 + 1360/2401*T^27 - 
        585/2401*T^26 - 314/343*T^25 - 101/2401*T^24 - 1241/2401*T^23 - 
        2762/2401*T^22 - 445/2401*T^21 + 1144/2401*T^20 + 83/2401*T^19 + 
        73/2401*T^18 - 363/2401*T^17 - 1552/2401*T^16 - 1150/2401*T^15 - 
        1804/2401*T^14 - 106/343*T^13 + 284/2401*T^12 - 433/2401*T^11 + 
        1308/2401*T^10 + 2062/2401*T^9 + 337/2401*T^8 - 128/2401*T^7 - 89/2401*T^6 +
        106/2401*T^5 + 1513/2401*T^4 + 137/343*T^3 - 9/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 3*X*Y^13 + X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + X*Y^8 + 6*X*Y^7 + 
        2*X*Y^6 + 3*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + 2*X*Y + X + 4*Y^30 + 
        5*Y^29 + 6*Y^28 + 4*Y^27 + 4*Y^26 + 2*Y^25 + Y^24 + 2*Y^23 + 6*Y^22 + 2*Y^21
        + Y^20 + Y^18 + 2*Y^17 + Y^16 + 2*Y^15 + 2*Y^14 + 5*Y^13 + 5*Y^12 + 6*Y^11 +
        3*Y^10 + Y^9 + 6*Y^8 + 4*Y^6 + 2*Y^5 + 4*Y^4 + 2*Y^3 + Y^2 + 4*Y,
    T^56 + 2/7*T^55 - 5/49*T^54 + 69/49*T^53 + 313/343*T^52 + 956/2401*T^51 + 
        4140/2401*T^50 + 626/2401*T^49 + 317/2401*T^48 + 4654/2401*T^47 + 
        107/2401*T^46 + 334/2401*T^45 + 835/2401*T^44 - 1354/2401*T^43 + 
        284/2401*T^42 + 5/49*T^41 - 2895/2401*T^40 - 1177/2401*T^39 - 2916/2401*T^38
        - 1189/2401*T^37 - 745/2401*T^36 - 4407/2401*T^35 - 942/2401*T^34 - 
        479/2401*T^33 - 2183/2401*T^32 + 417/2401*T^31 - 395/2401*T^30 - 
        1577/2401*T^29 + 2349/2401*T^28 - 1577/2401*T^27 - 395/2401*T^26 + 
        417/2401*T^25 - 2183/2401*T^24 - 479/2401*T^23 - 942/2401*T^22 - 
        4407/2401*T^21 - 745/2401*T^20 - 1189/2401*T^19 - 2916/2401*T^18 - 
        1177/2401*T^17 - 2895/2401*T^16 + 5/49*T^15 + 284/2401*T^14 - 1354/2401*T^13
        + 835/2401*T^12 + 334/2401*T^11 + 107/2401*T^10 + 4654/2401*T^9 + 
        317/2401*T^8 + 626/2401*T^7 + 4140/2401*T^6 + 956/2401*T^5 + 313/343*T^4 + 
        69/49*T^3 - 5/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + X*Y^13 + X*Y^12 + 2*X*Y^10 + 5*X*Y^8 + 5*X*Y^7 + X*Y^6
        + 4*X*Y^4 + X*Y^3 + X*Y + 3*X + 3*Y^30 + 2*Y^29 + 6*Y^28 + 2*Y^27 + 5*Y^26 +
        Y^25 + 3*Y^24 + 5*Y^23 + Y^21 + 2*Y^20 + Y^19 + Y^18 + 3*Y^17 + Y^16 + 
        6*Y^15 + Y^14 + 5*Y^13 + 3*Y^12 + Y^11 + 6*Y^10 + 4*Y^9 + 6*Y^7 + 6*Y^6 + 
        3*Y^4 + Y^3 + 6*Y^2 + 4*Y + 4,
    T^56 - 25/7*T^55 + 324/49*T^54 - 2763/343*T^53 + 15373/2401*T^52 - 
        5578/2401*T^51 - 3701/2401*T^50 + 1084/343*T^49 - 6679/2401*T^48 + 
        741/343*T^47 - 6875/2401*T^46 + 10823/2401*T^45 - 11317/2401*T^44 + 
        764/343*T^43 + 3300/2401*T^42 - 8004/2401*T^41 + 5584/2401*T^40 + 
        675/2401*T^39 - 4981/2401*T^38 + 5065/2401*T^37 - 2635/2401*T^36 + 
        832/2401*T^35 - 1100/2401*T^34 + 1809/2401*T^33 - 141/343*T^32 - 
        926/2401*T^31 + 2179/2401*T^30 - 1910/2401*T^29 + 1334/2401*T^28 - 
        1910/2401*T^27 + 2179/2401*T^26 - 926/2401*T^25 - 141/343*T^24 + 
        1809/2401*T^23 - 1100/2401*T^22 + 832/2401*T^21 - 2635/2401*T^20 + 
        5065/2401*T^19 - 4981/2401*T^18 + 675/2401*T^17 + 5584/2401*T^16 - 
        8004/2401*T^15 + 3300/2401*T^14 + 764/343*T^13 - 11317/2401*T^12 + 
        10823/2401*T^11 - 6875/2401*T^10 + 741/343*T^9 - 6679/2401*T^8 + 
        1084/343*T^7 - 3701/2401*T^6 - 5578/2401*T^5 + 15373/2401*T^4 - 2763/343*T^3
        + 324/49*T^2 - 25/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 3*X*Y^11 + 4*X*Y^9 + 2*X*Y^7 + 5*X*Y^6 + 
        2*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 3*X + 3*Y^30 + 6*Y^29 + Y^27 + 
        2*Y^26 + 3*Y^25 + 5*Y^24 + 3*Y^22 + 4*Y^20 + 4*Y^18 + Y^16 + Y^15 + 6*Y^14 +
        Y^13 + 5*Y^9 + Y^7 + 6*Y^6 + 3*Y^5 + 5*Y^4 + 5*Y^2 + 3*Y + 2,
    -T^56 + 10/7*T^55 + 52/49*T^54 - 2*T^53 - 3253/2401*T^52 + 4916/2401*T^51 + 
        558/343*T^50 - 3925/2401*T^49 - 772/343*T^48 + 4055/2401*T^47 + 
        5391/2401*T^46 - 4495/2401*T^45 - 1972/2401*T^44 + 1609/2401*T^43 + 
        800/2401*T^42 - 309/2401*T^41 + 278/2401*T^40 - 443/2401*T^39 + 
        201/2401*T^38 - 2327/2401*T^37 + 2782/2401*T^36 + 2979/2401*T^35 - 
        3520/2401*T^34 - 4457/2401*T^33 + 2629/2401*T^32 + 6564/2401*T^31 - 
        459/2401*T^30 - 9363/2401*T^29 + 9363/2401*T^27 + 459/2401*T^26 - 
        6564/2401*T^25 - 2629/2401*T^24 + 4457/2401*T^23 + 3520/2401*T^22 - 
        2979/2401*T^21 - 2782/2401*T^20 + 2327/2401*T^19 - 201/2401*T^18 + 
        443/2401*T^17 - 278/2401*T^16 + 309/2401*T^15 - 800/2401*T^14 - 
        1609/2401*T^13 + 1972/2401*T^12 + 4495/2401*T^11 - 5391/2401*T^10 - 
        4055/2401*T^9 + 772/343*T^8 + 3925/2401*T^7 - 558/343*T^6 - 4916/2401*T^5 + 
        3253/2401*T^4 + 2*T^3 - 52/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 
        + 2*X*Y^8 + 5*X*Y^7 + 2*X*Y^6 + 5*X*Y^4 + X*Y^3 + 6*X*Y^2 + 4*X*Y + 5*X + 
        3*Y^30 + 5*Y^29 + 3*Y^28 + 6*Y^27 + 5*Y^26 + 6*Y^25 + Y^24 + 2*Y^23 + 2*Y^22
        + Y^21 + 2*Y^20 + Y^19 + Y^18 + Y^17 + 5*Y^16 + 5*Y^14 + 3*Y^12 + 3*Y^11 + 
        2*Y^10 + 3*Y^9 + Y^8 + 3*Y^7 + 6*Y^5 + 2*Y^4 + Y^2 + 2,
    -T^56 + 15/7*T^55 - 185/49*T^54 + 1591/343*T^53 - 14130/2401*T^52 + 
        16067/2401*T^51 - 16649/2401*T^50 + 306/49*T^49 - 11890/2401*T^48 + 
        8340/2401*T^47 - 3091/2401*T^46 - 1612/2401*T^45 + 5835/2401*T^44 - 
        7783/2401*T^43 + 9816/2401*T^42 - 9579/2401*T^41 + 7629/2401*T^40 - 
        3757/2401*T^39 + 263/2401*T^38 + 3422/2401*T^37 - 7386/2401*T^36 + 
        10977/2401*T^35 - 12857/2401*T^34 + 13459/2401*T^33 - 13406/2401*T^32 + 
        11873/2401*T^31 - 8814/2401*T^30 + 4296/2401*T^29 - 4296/2401*T^27 + 
        8814/2401*T^26 - 11873/2401*T^25 + 13406/2401*T^24 - 13459/2401*T^23 + 
        12857/2401*T^22 - 10977/2401*T^21 + 7386/2401*T^20 - 3422/2401*T^19 - 
        263/2401*T^18 + 3757/2401*T^17 - 7629/2401*T^16 + 9579/2401*T^15 - 
        9816/2401*T^14 + 7783/2401*T^13 - 5835/2401*T^12 + 1612/2401*T^11 + 
        3091/2401*T^10 - 8340/2401*T^9 + 11890/2401*T^8 - 306/49*T^7 + 
        16649/2401*T^6 - 16067/2401*T^5 + 14130/2401*T^4 - 1591/343*T^3 + 185/49*T^2
        - 15/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + 2*X*Y^12 + 5*X*Y^11 + X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 2*X*Y^7 + 
        5*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + X*Y^2 + X*Y + 3*X + 4*Y^30 + 4*Y^29 + Y^28 + 
        4*Y^27 + 5*Y^26 + 4*Y^24 + 2*Y^23 + 6*Y^22 + 5*Y^20 + 6*Y^19 + 6*Y^18 + Y^17
        + 3*Y^14 + 3*Y^13 + 3*Y^12 + 3*Y^11 + 5*Y^10 + 4*Y^9 + 6*Y^8 + 6*Y^6 + 2*Y^4
        + 6*Y^3 + 6*Y^2 + Y + 1,
    T^56 - 1/7*T^55 - 23/49*T^54 + 150/343*T^53 - 3020/2401*T^52 - 99/343*T^51 + 
        802/2401*T^50 - 33/49*T^49 + 262/2401*T^48 + 718/2401*T^47 - 842/2401*T^46 +
        1847/2401*T^45 + 1318/2401*T^44 + 845/2401*T^43 + 1416/2401*T^42 - 
        1580/2401*T^41 - 171/2401*T^40 + 282/2401*T^39 - 877/2401*T^38 + 
        345/2401*T^37 + 166/2401*T^36 - 2585/2401*T^35 + 19/343*T^34 - 296/2401*T^33
        - 1460/2401*T^32 + 2487/2401*T^31 + 353/2401*T^30 - 67/343*T^29 + 
        1374/2401*T^28 - 67/343*T^27 + 353/2401*T^26 + 2487/2401*T^25 - 
        1460/2401*T^24 - 296/2401*T^23 + 19/343*T^22 - 2585/2401*T^21 + 
        166/2401*T^20 + 345/2401*T^19 - 877/2401*T^18 + 282/2401*T^17 - 
        171/2401*T^16 - 1580/2401*T^15 + 1416/2401*T^14 + 845/2401*T^13 + 
        1318/2401*T^12 + 1847/2401*T^11 - 842/2401*T^10 + 718/2401*T^9 + 
        262/2401*T^8 - 33/49*T^7 + 802/2401*T^6 - 99/343*T^5 - 3020/2401*T^4 + 
        150/343*T^3 - 23/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + X*Y^12 + X*Y^11 + 2*X*Y^10 + 3*X*Y^9 + 3*X*Y^8 + 
        X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 5*X*Y + 2*X + 2*Y^30 + 
        5*Y^29 + 5*Y^28 + 3*Y^26 + Y^25 + 5*Y^24 + 6*Y^23 + Y^22 + 4*Y^20 + 3*Y^19 +
        Y^18 + 2*Y^17 + 3*Y^16 + Y^15 + 4*Y^14 + 5*Y^13 + 6*Y^11 + 2*Y^10 + 5*Y^9 + 
        3*Y^8 + 6*Y^7 + 6*Y^6 + 5*Y^5 + 6*Y^4 + 5*Y^3 + 5*Y^2 + 4*Y,
    -T^56 + 1/7*T^55 + 19/49*T^54 - 2/343*T^53 + 386/2401*T^52 + 145/343*T^51 - 
        473/2401*T^50 - 1413/2401*T^49 + 1681/2401*T^48 + 575/2401*T^47 - 
        575/2401*T^46 + 740/2401*T^45 + 488/2401*T^44 - 1413/2401*T^43 - 41/343*T^42
        + 1084/2401*T^41 - 1733/2401*T^40 + 146/343*T^39 + 772/2401*T^38 - 
        624/2401*T^37 - 534/2401*T^36 + 162/2401*T^35 - 356/2401*T^34 - 
        662/2401*T^33 + 2201/2401*T^32 - 618/2401*T^31 - 745/2401*T^30 + 
        619/2401*T^29 - 619/2401*T^27 + 745/2401*T^26 + 618/2401*T^25 - 
        2201/2401*T^24 + 662/2401*T^23 + 356/2401*T^22 - 162/2401*T^21 + 
        534/2401*T^20 + 624/2401*T^19 - 772/2401*T^18 - 146/343*T^17 + 
        1733/2401*T^16 - 1084/2401*T^15 + 41/343*T^14 + 1413/2401*T^13 - 
        488/2401*T^12 - 740/2401*T^11 + 575/2401*T^10 - 575/2401*T^9 - 1681/2401*T^8
        + 1413/2401*T^7 + 473/2401*T^6 - 145/343*T^5 - 386/2401*T^4 + 2/343*T^3 - 
        19/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + X*Y^13 + X*Y^12 + 2*X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 
        3*X*Y^8 + 6*X*Y^6 + 4*X*Y^5 + 3*X*Y^3 + 6*X*Y^2 + 4*X*Y + Y^30 + Y^29 + 
        3*Y^28 + 4*Y^27 + 6*Y^26 + 5*Y^25 + 2*Y^24 + 5*Y^23 + 6*Y^22 + 5*Y^20 + 
        3*Y^19 + 6*Y^18 + Y^17 + 4*Y^15 + Y^14 + 4*Y^13 + 2*Y^12 + 6*Y^11 + 3*Y^10 +
        6*Y^9 + 4*Y^8 + 5*Y^7 + 4*Y^4 + 2*Y^3 + 3*Y^2 + 1,
    T^56 - 16/7*T^55 + 163/49*T^54 - 1690/343*T^53 + 15756/2401*T^52 - 2649/343*T^51
        + 19813/2401*T^50 - 20528/2401*T^49 + 19611/2401*T^48 - 345/49*T^47 + 
        13927/2401*T^46 - 11058/2401*T^45 + 8618/2401*T^44 - 7583/2401*T^43 + 
        8038/2401*T^42 - 9482/2401*T^41 + 12086/2401*T^40 - 2192/343*T^39 + 
        2610/343*T^38 - 19812/2401*T^37 + 20381/2401*T^36 - 19701/2401*T^35 + 
        16824/2401*T^34 - 1786/343*T^33 + 8738/2401*T^32 - 727/343*T^31 + 
        1084/2401*T^30 + 809/2401*T^29 - 956/2401*T^28 + 809/2401*T^27 + 
        1084/2401*T^26 - 727/343*T^25 + 8738/2401*T^24 - 1786/343*T^23 + 
        16824/2401*T^22 - 19701/2401*T^21 + 20381/2401*T^20 - 19812/2401*T^19 + 
        2610/343*T^18 - 2192/343*T^17 + 12086/2401*T^16 - 9482/2401*T^15 + 
        8038/2401*T^14 - 7583/2401*T^13 + 8618/2401*T^12 - 11058/2401*T^11 + 
        13927/2401*T^10 - 345/49*T^9 + 19611/2401*T^8 - 20528/2401*T^7 + 
        19813/2401*T^6 - 2649/343*T^5 + 15756/2401*T^4 - 1690/343*T^3 + 163/49*T^2 -
        16/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 
        + 4*X*Y^8 + 5*X*Y^7 + X*Y^6 + 4*X*Y^5 + X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + X*Y + 
        3*X + 2*Y^30 + 3*Y^29 + 6*Y^28 + Y^27 + Y^26 + Y^25 + 4*Y^24 + 6*Y^23 + Y^22
        + 2*Y^21 + 4*Y^20 + 6*Y^19 + 5*Y^18 + 3*Y^16 + Y^15 + 6*Y^14 + 6*Y^13 + 
        4*Y^11 + Y^10 + 3*Y^9 + 3*Y^8 + 2*Y^7 + 5*Y^5 + Y^3 + 6*Y^2 + 6*Y + 1,
    -T^56 - 8/7*T^55 - 12/49*T^54 - 96/343*T^53 - 278/343*T^52 - 3095/2401*T^51 - 
        2682/2401*T^50 + 80/343*T^49 + 116/2401*T^48 - 376/343*T^47 - 1385/2401*T^46
        + 1402/2401*T^45 + 2053/2401*T^44 + 1114/2401*T^43 - 323/2401*T^42 - 
        195/2401*T^41 + 2626/2401*T^40 + 2286/2401*T^39 + 211/343*T^38 + 
        1098/2401*T^37 - 143/2401*T^36 + 16/49*T^35 + 310/343*T^34 + 528/2401*T^33 -
        1511/2401*T^32 - 2054/2401*T^31 + 961/2401*T^30 + 2556/2401*T^29 - 
        2556/2401*T^27 - 961/2401*T^26 + 2054/2401*T^25 + 1511/2401*T^24 - 
        528/2401*T^23 - 310/343*T^22 - 16/49*T^21 + 143/2401*T^20 - 1098/2401*T^19 -
        211/343*T^18 - 2286/2401*T^17 - 2626/2401*T^16 + 195/2401*T^15 + 
        323/2401*T^14 - 1114/2401*T^13 - 2053/2401*T^12 - 1402/2401*T^11 + 
        1385/2401*T^10 + 376/343*T^9 - 116/2401*T^8 - 80/343*T^7 + 2682/2401*T^6 + 
        3095/2401*T^5 + 278/343*T^4 + 96/343*T^3 + 12/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 4*X*Y^9 + 2*X*Y^8 + 
        5*X*Y^7 + 2*X*Y^6 + X*Y^5 + 4*X*Y^3 + X*Y^2 + 5*X*Y + 2*X + 3*Y^30 + 6*Y^29 
        + 6*Y^28 + 6*Y^27 + 4*Y^26 + 6*Y^25 + 3*Y^24 + 4*Y^23 + 3*Y^21 + 5*Y^20 + 
        Y^18 + 5*Y^17 + Y^16 + 6*Y^15 + 6*Y^12 + Y^11 + 6*Y^10 + 3*Y^9 + 6*Y^8 + 
        4*Y^7 + 2*Y^6 + Y^3 + 5*Y^2 + 3*Y + 4,
    T^56 - 15/7*T^55 + 86/49*T^54 - 1/343*T^53 - 3835/2401*T^52 + 3789/2401*T^51 - 
        2265/2401*T^50 + 892/2401*T^49 + 30/2401*T^48 + 74/343*T^47 - 1756/2401*T^46
        + 1903/2401*T^45 + 78/2401*T^44 - 52/49*T^43 + 5098/2401*T^42 - 
        6025/2401*T^41 + 2795/2401*T^40 + 3198/2401*T^39 - 1006/343*T^38 + 
        5419/2401*T^37 - 608/2401*T^36 - 3499/2401*T^35 + 3265/2401*T^34 + 
        1058/2401*T^33 - 5006/2401*T^32 + 3105/2401*T^31 + 41/49*T^30 - 
        4538/2401*T^29 + 5053/2401*T^28 - 4538/2401*T^27 + 41/49*T^26 + 
        3105/2401*T^25 - 5006/2401*T^24 + 1058/2401*T^23 + 3265/2401*T^22 - 
        3499/2401*T^21 - 608/2401*T^20 + 5419/2401*T^19 - 1006/343*T^18 + 
        3198/2401*T^17 + 2795/2401*T^16 - 6025/2401*T^15 + 5098/2401*T^14 - 
        52/49*T^13 + 78/2401*T^12 + 1903/2401*T^11 - 1756/2401*T^10 + 74/343*T^9 + 
        30/2401*T^8 + 892/2401*T^7 - 2265/2401*T^6 + 3789/2401*T^5 - 3835/2401*T^4 -
        1/343*T^3 + 86/49*T^2 - 15/7*T + 1
*], [*
    X^3 + 3*X*Y^13 + 2*X*Y^12 + 6*X*Y^10 + 3*X*Y^9 + 6*X*Y^8 + 6*X*Y^7 + 4*X*Y^6 + 
        2*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 2*X*Y^2 + 5*X*Y + 2*X + 2*Y^30 + 2*Y^28 + Y^27
        + 3*Y^26 + 5*Y^25 + 2*Y^24 + 6*Y^23 + Y^22 + 2*Y^21 + Y^20 + 4*Y^19 + 5*Y^18
        + 6*Y^17 + 3*Y^16 + 2*Y^15 + 3*Y^14 + 6*Y^13 + 4*Y^11 + 3*Y^10 + 3*Y^9 + 
        6*Y^8 + 2*Y^7 + 2*Y^6 + 2*Y^5 + 4*Y^4 + 3*Y^2 + 3*Y + 4,
    -T^56 - 8/7*T^55 + 10/49*T^54 + 2/7*T^53 - 54/2401*T^52 + 750/2401*T^51 + 
        110/2401*T^50 - 2540/2401*T^49 - 2539/2401*T^48 - 688/2401*T^47 - 
        654/2401*T^46 + 19/2401*T^45 + 1320/2401*T^44 + 1233/2401*T^43 - 
        1305/2401*T^42 - 3295/2401*T^41 - 1262/2401*T^40 + 104/2401*T^39 - 
        155/2401*T^38 + 1580/2401*T^37 + 2008/2401*T^36 - 1599/2401*T^35 - 
        2851/2401*T^34 - 507/2401*T^33 - 173/2401*T^32 + 97/2401*T^31 + 
        2495/2401*T^30 + 2533/2401*T^29 - 2533/2401*T^27 - 2495/2401*T^26 - 
        97/2401*T^25 + 173/2401*T^24 + 507/2401*T^23 + 2851/2401*T^22 + 
        1599/2401*T^21 - 2008/2401*T^20 - 1580/2401*T^19 + 155/2401*T^18 - 
        104/2401*T^17 + 1262/2401*T^16 + 3295/2401*T^15 + 1305/2401*T^14 - 
        1233/2401*T^13 - 1320/2401*T^12 - 19/2401*T^11 + 654/2401*T^10 + 
        688/2401*T^9 + 2539/2401*T^8 + 2540/2401*T^7 - 110/2401*T^6 - 750/2401*T^5 +
        54/2401*T^4 - 2/7*T^3 - 10/49*T^2 + 8/7*T + 1
*], [*
    X^3 + X*Y^14 + X*Y^12 + 4*X*Y^10 + 5*X*Y^8 + 5*X*Y^7 + 2*X*Y^5 + 4*X*Y^4 + 
        6*X*Y^3 + 4*X*Y^2 + 6*X*Y + X + 4*Y^30 + 5*Y^29 + 2*Y^27 + 6*Y^26 + Y^25 + 
        Y^24 + 6*Y^23 + Y^22 + 2*Y^21 + 5*Y^20 + 2*Y^19 + 3*Y^18 + 3*Y^16 + 6*Y^15 +
        4*Y^14 + 2*Y^13 + 3*Y^12 + Y^11 + 5*Y^10 + 5*Y^9 + 4*Y^8 + Y^7 + 6*Y^4 + Y^2
        + 3*Y + 3,
    T^56 + 2*T^55 + 60/49*T^54 + 41/343*T^53 - 142/343*T^52 - 2619/2401*T^51 - 
        2757/2401*T^50 - 201/2401*T^49 + 1605/2401*T^48 + 961/2401*T^47 + 
        251/2401*T^46 - 397/2401*T^45 - 1748/2401*T^44 - 1672/2401*T^43 - 
        261/2401*T^42 + 13/2401*T^41 + 976/2401*T^40 + 1633/2401*T^39 - 73/343*T^38 
        - 268/2401*T^37 + 1689/2401*T^36 + 170/2401*T^35 - 188/343*T^34 - 
        75/343*T^33 - 128/343*T^32 - 705/2401*T^31 + 1126/2401*T^30 + 213/343*T^29 +
        19/49*T^28 + 213/343*T^27 + 1126/2401*T^26 - 705/2401*T^25 - 128/343*T^24 - 
        75/343*T^23 - 188/343*T^22 + 170/2401*T^21 + 1689/2401*T^20 - 268/2401*T^19 
        - 73/343*T^18 + 1633/2401*T^17 + 976/2401*T^16 + 13/2401*T^15 - 
        261/2401*T^14 - 1672/2401*T^13 - 1748/2401*T^12 - 397/2401*T^11 + 
        251/2401*T^10 + 961/2401*T^9 + 1605/2401*T^8 - 201/2401*T^7 - 2757/2401*T^6 
        - 2619/2401*T^5 - 142/343*T^4 + 41/343*T^3 + 60/49*T^2 + 2*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + X*Y^13 + 6*X*Y^12 + X*Y^10 + 4*X*Y^9 + 5*X*Y^8 + 
        4*X*Y^7 + 2*X*Y^5 + 3*X*Y^4 + X*Y^3 + 5*X*Y^2 + 5*X*Y + 2*X + 2*Y^30 + 
        2*Y^29 + 3*Y^28 + 2*Y^26 + 2*Y^25 + 3*Y^24 + 4*Y^23 + 6*Y^21 + 5*Y^19 + 
        5*Y^17 + 4*Y^16 + 3*Y^15 + 4*Y^14 + 2*Y^13 + 4*Y^12 + 4*Y^11 + 5*Y^10 + 
        3*Y^9 + Y^8 + 4*Y^6 + 4*Y^5 + Y^4 + 6*Y + 1,
    T^56 + 2/7*T^55 + 5/49*T^54 + 354/343*T^53 + 417/2401*T^52 + 305/2401*T^51 - 
        1595/2401*T^50 - 1135/2401*T^49 - 1551/2401*T^48 - 3516/2401*T^47 - 
        1597/2401*T^46 - 2258/2401*T^45 - 1389/2401*T^44 + 695/2401*T^43 + 
        807/2401*T^42 + 1059/2401*T^41 + 2006/2401*T^40 + 2066/2401*T^39 + 
        1363/2401*T^38 + 258/2401*T^37 + 323/2401*T^36 - 859/2401*T^35 - 
        1958/2401*T^34 + 249/2401*T^33 - 223/343*T^32 - 360/2401*T^31 + 
        1392/2401*T^30 + 44/343*T^29 + 1467/2401*T^28 + 44/343*T^27 + 1392/2401*T^26
        - 360/2401*T^25 - 223/343*T^24 + 249/2401*T^23 - 1958/2401*T^22 - 
        859/2401*T^21 + 323/2401*T^20 + 258/2401*T^19 + 1363/2401*T^18 + 
        2066/2401*T^17 + 2006/2401*T^16 + 1059/2401*T^15 + 807/2401*T^14 + 
        695/2401*T^13 - 1389/2401*T^12 - 2258/2401*T^11 - 1597/2401*T^10 - 
        3516/2401*T^9 - 1551/2401*T^8 - 1135/2401*T^7 - 1595/2401*T^6 + 305/2401*T^5
        + 417/2401*T^4 + 354/343*T^3 + 5/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 3*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 + 5*X*Y^8 +
        3*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 4*X*Y^3 + 6*X*Y^2 + 6*X*Y + 2*X + Y^30 + 
        2*Y^29 + 6*Y^27 + 3*Y^26 + 4*Y^24 + 4*Y^23 + 2*Y^22 + 4*Y^21 + 6*Y^19 + 
        5*Y^18 + 3*Y^17 + 4*Y^16 + 2*Y^15 + 2*Y^13 + Y^12 + 3*Y^11 + 3*Y^10 + Y^9 + 
        4*Y^8 + 5*Y^7 + 3*Y^6 + Y^5 + 6*Y^4 + 6*Y^3 + 2*Y^2 + 6*Y,
    T^56 + 10/7*T^55 - 26/49*T^54 - 925/343*T^53 - 4345/2401*T^52 + 2587/2401*T^51 +
        5797/2401*T^50 + 4617/2401*T^49 + 169/2401*T^48 - 4945/2401*T^47 - 
        5732/2401*T^46 - 247/2401*T^45 + 5127/2401*T^44 + 4975/2401*T^43 - 
        310/2401*T^42 - 5317/2401*T^41 - 4107/2401*T^40 + 1180/2401*T^39 + 
        4761/2401*T^38 + 2871/2401*T^37 - 1807/2401*T^36 - 3849/2401*T^35 - 
        677/2401*T^34 + 2318/2401*T^33 + 999/2401*T^32 + 90/2401*T^31 + 158/343*T^30
        - 521/2401*T^29 - 2619/2401*T^28 - 521/2401*T^27 + 158/343*T^26 + 
        90/2401*T^25 + 999/2401*T^24 + 2318/2401*T^23 - 677/2401*T^22 - 
        3849/2401*T^21 - 1807/2401*T^20 + 2871/2401*T^19 + 4761/2401*T^18 + 
        1180/2401*T^17 - 4107/2401*T^16 - 5317/2401*T^15 - 310/2401*T^14 + 
        4975/2401*T^13 + 5127/2401*T^12 - 247/2401*T^11 - 5732/2401*T^10 - 
        4945/2401*T^9 + 169/2401*T^8 + 4617/2401*T^7 + 5797/2401*T^6 + 2587/2401*T^5
        - 4345/2401*T^4 - 925/343*T^3 - 26/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + X*Y^11 + 4*X*Y^9 + 3*X*Y^8 + 
        2*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 2*X*Y^2 + 3*X*Y + 4*Y^30 + 2*Y^29 + 5*Y^28 + 
        5*Y^27 + 3*Y^26 + 3*Y^25 + 3*Y^24 + 3*Y^23 + 6*Y^22 + 4*Y^21 + 3*Y^20 + 
        3*Y^18 + 2*Y^17 + 2*Y^16 + 4*Y^15 + Y^14 + Y^13 + 5*Y^12 + 3*Y^10 + 6*Y^9 + 
        Y^8 + 3*Y^7 + 2*Y^6 + 6*Y^5 + 6*Y^4 + 6*Y^3 + Y^2 + 3*Y + 4,
    T^56 + 10/7*T^55 + 68/49*T^54 + 104/343*T^53 - 1163/2401*T^52 - 2021/2401*T^51 -
        3585/2401*T^50 - 3487/2401*T^49 - 4145/2401*T^48 - 3477/2401*T^47 - 
        2859/2401*T^46 - 66/343*T^45 + 291/343*T^44 + 3153/2401*T^43 + 
        5389/2401*T^42 + 5875/2401*T^41 + 4656/2401*T^40 + 125/343*T^39 - 
        1514/2401*T^38 - 2335/2401*T^37 - 5132/2401*T^36 - 5837/2401*T^35 - 
        5541/2401*T^34 - 3230/2401*T^33 - 180/343*T^32 + 1480/2401*T^31 + 
        4981/2401*T^30 + 5020/2401*T^29 + 5386/2401*T^28 + 5020/2401*T^27 + 
        4981/2401*T^26 + 1480/2401*T^25 - 180/343*T^24 - 3230/2401*T^23 - 
        5541/2401*T^22 - 5837/2401*T^21 - 5132/2401*T^20 - 2335/2401*T^19 - 
        1514/2401*T^18 + 125/343*T^17 + 4656/2401*T^16 + 5875/2401*T^15 + 
        5389/2401*T^14 + 3153/2401*T^13 + 291/343*T^12 - 66/343*T^11 - 
        2859/2401*T^10 - 3477/2401*T^9 - 4145/2401*T^8 - 3487/2401*T^7 - 
        3585/2401*T^6 - 2021/2401*T^5 - 1163/2401*T^4 + 104/343*T^3 + 68/49*T^2 + 
        10/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + X*Y^13 + 5*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 + 
        2*X*Y^7 + 2*X*Y^6 + 6*X*Y^5 + 5*X*Y^3 + X*Y^2 + 6*X*Y + 6*X + 6*Y^30 + 
        3*Y^29 + 3*Y^28 + 5*Y^27 + Y^26 + 5*Y^24 + 6*Y^23 + 5*Y^21 + 2*Y^20 + Y^18 +
        Y^17 + Y^16 + Y^15 + 2*Y^14 + 6*Y^13 + 4*Y^12 + Y^11 + 3*Y^10 + 6*Y^9 + 
        6*Y^8 + 2*Y^7 + 4*Y^6 + 5*Y^5 + 5*Y^4 + 5*Y^3 + 6*Y^2 + 4*Y + 4,
    T^56 + T^55 + 58/49*T^54 + 48/49*T^53 + 2315/2401*T^52 + 894/2401*T^51 - 
        177/2401*T^50 - 1411/2401*T^49 - 1607/2401*T^48 - 2462/2401*T^47 - 
        389/343*T^46 - 2661/2401*T^45 - 53/49*T^44 - 1434/2401*T^43 - 1280/2401*T^42
        + 572/2401*T^41 + 1158/2401*T^40 + 3007/2401*T^39 + 76/49*T^38 + 
        4605/2401*T^37 + 4308/2401*T^36 + 3965/2401*T^35 + 2151/2401*T^34 + 
        680/2401*T^33 - 1553/2401*T^32 - 2797/2401*T^31 - 517/343*T^30 - 
        4303/2401*T^29 - 3341/2401*T^28 - 4303/2401*T^27 - 517/343*T^26 - 
        2797/2401*T^25 - 1553/2401*T^24 + 680/2401*T^23 + 2151/2401*T^22 + 
        3965/2401*T^21 + 4308/2401*T^20 + 4605/2401*T^19 + 76/49*T^18 + 
        3007/2401*T^17 + 1158/2401*T^16 + 572/2401*T^15 - 1280/2401*T^14 - 
        1434/2401*T^13 - 53/49*T^12 - 2661/2401*T^11 - 389/343*T^10 - 2462/2401*T^9 
        - 1607/2401*T^8 - 1411/2401*T^7 - 177/2401*T^6 + 894/2401*T^5 + 
        2315/2401*T^4 + 48/49*T^3 + 58/49*T^2 + T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + X*Y^9 + 2*X*Y^7 + 
        3*X*Y^6 + 2*X*Y^5 + 3*X*Y^4 + 2*X*Y^2 + 6*X + 4*Y^30 + Y^29 + 4*Y^28 + 
        2*Y^27 + 3*Y^26 + 3*Y^25 + 6*Y^24 + 5*Y^23 + 2*Y^22 + 6*Y^20 + 3*Y^19 + Y^18
        + 2*Y^16 + 5*Y^15 + 3*Y^14 + 4*Y^13 + 3*Y^9 + 3*Y^8 + 3*Y^7 + 4*Y^6 + 6*Y^5 
        + 5*Y^4 + Y^3 + 3*Y^2 + 6*Y + 5,
    -T^56 - 2/7*T^55 + 23/49*T^54 - 30/343*T^53 + 1409/2401*T^52 - 13/2401*T^51 - 
        621/2401*T^50 + 2200/2401*T^49 - 1562/2401*T^48 + 41/2401*T^47 + 
        1275/2401*T^46 - 2283/2401*T^45 + 1531/2401*T^44 - 351/2401*T^43 - 
        1836/2401*T^42 + 3096/2401*T^41 - 108/343*T^40 - 153/2401*T^39 + 
        1170/2401*T^38 - 349/343*T^37 + 1466/2401*T^36 + 1101/2401*T^35 - 
        1712/2401*T^34 + 1615/2401*T^33 + 135/2401*T^32 + 261/2401*T^31 + 
        298/343*T^30 - 244/343*T^29 + 244/343*T^27 - 298/343*T^26 - 261/2401*T^25 - 
        135/2401*T^24 - 1615/2401*T^23 + 1712/2401*T^22 - 1101/2401*T^21 - 
        1466/2401*T^20 + 349/343*T^19 - 1170/2401*T^18 + 153/2401*T^17 + 
        108/343*T^16 - 3096/2401*T^15 + 1836/2401*T^14 + 351/2401*T^13 - 
        1531/2401*T^12 + 2283/2401*T^11 - 1275/2401*T^10 - 41/2401*T^9 + 
        1562/2401*T^8 - 2200/2401*T^7 + 621/2401*T^6 + 13/2401*T^5 - 1409/2401*T^4 +
        30/343*T^3 - 23/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + X*Y^13 + 2*X*Y^12 + X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 3*X*Y^8 + 
        3*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 6*X*Y + 2*X + 4*Y^30 + 2*Y^29 + 
        4*Y^28 + 5*Y^27 + Y^25 + 5*Y^23 + Y^22 + 3*Y^21 + 2*Y^20 + 2*Y^18 + 3*Y^17 +
        2*Y^16 + 5*Y^15 + 4*Y^14 + 6*Y^13 + 3*Y^12 + 5*Y^11 + 6*Y^10 + Y^9 + 2*Y^8 +
        Y^7 + 2*Y^6 + 5*Y^5 + 4*Y^4 + 2*Y^3 + 5*Y^2 + 3*Y,
    -T^56 + 2/7*T^54 + 300/343*T^53 + 886/2401*T^52 + 393/2401*T^51 - 639/2401*T^50 
        - 488/2401*T^49 - 1476/2401*T^48 - 860/2401*T^47 - 741/2401*T^46 + 
        971/2401*T^45 + 2179/2401*T^44 + 1473/2401*T^43 + 656/2401*T^42 - 
        376/2401*T^41 - 1419/2401*T^40 - 1560/2401*T^39 - 1083/2401*T^38 - 
        617/2401*T^37 + 1525/2401*T^36 + 25/49*T^35 + 937/2401*T^34 + 187/2401*T^33 
        - 10/2401*T^32 - 941/2401*T^31 - 1562/2401*T^30 - 594/2401*T^29 + 
        594/2401*T^27 + 1562/2401*T^26 + 941/2401*T^25 + 10/2401*T^24 - 
        187/2401*T^23 - 937/2401*T^22 - 25/49*T^21 - 1525/2401*T^20 + 617/2401*T^19 
        + 1083/2401*T^18 + 1560/2401*T^17 + 1419/2401*T^16 + 376/2401*T^15 - 
        656/2401*T^14 - 1473/2401*T^13 - 2179/2401*T^12 - 971/2401*T^11 + 
        741/2401*T^10 + 860/2401*T^9 + 1476/2401*T^8 + 488/2401*T^7 + 639/2401*T^6 -
        393/2401*T^5 - 886/2401*T^4 - 300/343*T^3 - 2/7*T^2 + 1
*], [*
    X^3 + 2*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 2*X*Y^9 + 3*X*Y^8 +
        3*X*Y^7 + X*Y^6 + 6*X*Y^5 + X*Y^4 + 3*X*Y^2 + 6*X*Y + 2*Y^30 + 2*Y^29 + 
        4*Y^28 + 4*Y^27 + 6*Y^26 + 3*Y^25 + 4*Y^24 + 3*Y^23 + 3*Y^22 + 3*Y^21 + 
        3*Y^20 + 3*Y^19 + 3*Y^17 + 3*Y^16 + Y^15 + 4*Y^14 + 5*Y^13 + 4*Y^12 + 4*Y^10
        + 4*Y^9 + 2*Y^7 + 3*Y^6 + 5*Y^5 + 5*Y^3 + 4*Y^2 + 5*Y + 4,
    T^56 + 2/7*T^55 - 48/49*T^54 - 124/343*T^53 + 223/343*T^52 + 1312/2401*T^51 - 
        2167/2401*T^50 - 20/2401*T^49 + 2287/2401*T^48 - 115/343*T^47 - 
        2032/2401*T^46 + 501/2401*T^45 + 1626/2401*T^44 + 199/2401*T^43 - 
        267/2401*T^42 + 270/2401*T^41 + 793/2401*T^40 - 477/2401*T^39 - 
        1248/2401*T^38 - 16/2401*T^37 + 1081/2401*T^36 + 1167/2401*T^35 - 
        766/2401*T^34 - 1122/2401*T^33 + 1240/2401*T^32 - 373/2401*T^31 - 
        255/343*T^30 + 626/2401*T^29 + 1585/2401*T^28 + 626/2401*T^27 - 255/343*T^26
        - 373/2401*T^25 + 1240/2401*T^24 - 1122/2401*T^23 - 766/2401*T^22 + 
        1167/2401*T^21 + 1081/2401*T^20 - 16/2401*T^19 - 1248/2401*T^18 - 
        477/2401*T^17 + 793/2401*T^16 + 270/2401*T^15 - 267/2401*T^14 + 
        199/2401*T^13 + 1626/2401*T^12 + 501/2401*T^11 - 2032/2401*T^10 - 
        115/343*T^9 + 2287/2401*T^8 - 20/2401*T^7 - 2167/2401*T^6 + 1312/2401*T^5 + 
        223/343*T^4 - 124/343*T^3 - 48/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^13 + X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 2*X*Y^7 + 
        6*X*Y^5 + 4*X*Y^4 + 3*X*Y^2 + 5*X*Y + 4*X + 4*Y^30 + 4*Y^29 + 2*Y^28 + 
        6*Y^27 + 6*Y^26 + 5*Y^25 + 3*Y^24 + 3*Y^23 + 5*Y^22 + 5*Y^21 + 5*Y^20 + Y^19
        + 3*Y^18 + 3*Y^17 + 6*Y^15 + 2*Y^14 + 5*Y^13 + 4*Y^10 + Y^9 + 3*Y^8 + 2*Y^7 
        + 6*Y^5 + 4*Y^4 + Y,
    -T^56 - 10/7*T^55 - 29/49*T^54 - 18/49*T^53 + 281/2401*T^52 + 2019/2401*T^51 + 
        2054/2401*T^50 + 2162/2401*T^49 + 909/2401*T^48 + 402/2401*T^47 + 
        1688/2401*T^46 + 2021/2401*T^45 + 2752/2401*T^44 + 1716/2401*T^43 + 
        232/2401*T^42 - 739/2401*T^41 - 2829/2401*T^40 - 478/343*T^39 - 
        2512/2401*T^38 - 1467/2401*T^37 - 54/2401*T^36 - 151/2401*T^35 - 
        397/2401*T^34 - 373/2401*T^33 + 431/2401*T^32 + 832/2401*T^31 + 88/343*T^30 
        + 1516/2401*T^29 - 1516/2401*T^27 - 88/343*T^26 - 832/2401*T^25 - 
        431/2401*T^24 + 373/2401*T^23 + 397/2401*T^22 + 151/2401*T^21 + 54/2401*T^20
        + 1467/2401*T^19 + 2512/2401*T^18 + 478/343*T^17 + 2829/2401*T^16 + 
        739/2401*T^15 - 232/2401*T^14 - 1716/2401*T^13 - 2752/2401*T^12 - 
        2021/2401*T^11 - 1688/2401*T^10 - 402/2401*T^9 - 909/2401*T^8 - 
        2162/2401*T^7 - 2054/2401*T^6 - 2019/2401*T^5 - 281/2401*T^4 + 18/49*T^3 + 
        29/49*T^2 + 10/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        5*X*Y^8 + 4*X*Y^7 + X*Y^6 + X*Y^5 + 6*X*Y^4 + X*Y^3 + 3*X*Y + 3*X + 4*Y^30 +
        6*Y^29 + 5*Y^27 + 3*Y^26 + 5*Y^25 + 5*Y^24 + 3*Y^23 + 3*Y^22 + 2*Y^21 + 
        3*Y^19 + 2*Y^18 + 3*Y^17 + 2*Y^16 + 6*Y^15 + Y^14 + 4*Y^12 + 5*Y^11 + 3*Y^9 
        + 2*Y^8 + 6*Y^7 + 3*Y^6 + 3*Y^5 + 2*Y^4 + 2*Y^3 + 4*Y^2 + Y + 2,
    -T^56 + 1/49*T^54 + 13/49*T^53 + 768/2401*T^52 - 974/2401*T^51 + 764/2401*T^50 +
        907/2401*T^49 + 905/2401*T^48 + 1047/2401*T^47 - 1088/2401*T^46 + 
        247/2401*T^45 + 13/343*T^44 + 117/2401*T^43 + 1012/2401*T^42 - 
        1108/2401*T^41 - 344/2401*T^40 + 222/2401*T^39 - 177/2401*T^38 + 10/49*T^37 
        - 68/2401*T^36 - 137/343*T^35 - 288/2401*T^34 - 767/2401*T^33 - 
        219/2401*T^32 + 66/2401*T^31 - 95/343*T^30 - 11/2401*T^29 + 11/2401*T^27 + 
        95/343*T^26 - 66/2401*T^25 + 219/2401*T^24 + 767/2401*T^23 + 288/2401*T^22 +
        137/343*T^21 + 68/2401*T^20 - 10/49*T^19 + 177/2401*T^18 - 222/2401*T^17 + 
        344/2401*T^16 + 1108/2401*T^15 - 1012/2401*T^14 - 117/2401*T^13 - 
        13/343*T^12 - 247/2401*T^11 + 1088/2401*T^10 - 1047/2401*T^9 - 905/2401*T^8 
        - 907/2401*T^7 - 764/2401*T^6 + 974/2401*T^5 - 768/2401*T^4 - 13/49*T^3 - 
        1/49*T^2 + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + X*Y^10 + 3*X*Y^9 + 
        6*X*Y^8 + 6*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 4*X + 4*Y^30 + Y^28 + 
        5*Y^27 + Y^25 + 2*Y^23 + 3*Y^21 + Y^20 + Y^19 + 4*Y^18 + 4*Y^17 + Y^16 + 
        Y^15 + 5*Y^14 + 5*Y^13 + 3*Y^12 + 3*Y^10 + 5*Y^9 + Y^8 + 5*Y^7 + 6*Y^6 + Y^5
        + 3*Y^4 + 6*Y^3 + 5*Y^2 + 6*Y + 4,
    -T^56 - 3/7*T^55 - 3/49*T^54 - 141/343*T^53 + 1297/2401*T^52 + 1689/2401*T^51 - 
        397/2401*T^50 - 201/2401*T^49 + 157/2401*T^48 - 797/2401*T^47 - 
        502/2401*T^46 + 775/2401*T^45 + 1796/2401*T^44 + 296/2401*T^43 - 
        32/2401*T^42 + 95/343*T^41 - 785/2401*T^40 - 549/2401*T^39 + 209/343*T^38 - 
        16/2401*T^37 - 135/2401*T^36 + 393/2401*T^35 - 474/2401*T^34 - 704/2401*T^33
        - 78/343*T^32 - 390/2401*T^31 - 1/7*T^30 + 4/343*T^29 - 4/343*T^27 + 
        1/7*T^26 + 390/2401*T^25 + 78/343*T^24 + 704/2401*T^23 + 474/2401*T^22 - 
        393/2401*T^21 + 135/2401*T^20 + 16/2401*T^19 - 209/343*T^18 + 549/2401*T^17 
        + 785/2401*T^16 - 95/343*T^15 + 32/2401*T^14 - 296/2401*T^13 - 
        1796/2401*T^12 - 775/2401*T^11 + 502/2401*T^10 + 797/2401*T^9 - 157/2401*T^8
        + 201/2401*T^7 + 397/2401*T^6 - 1689/2401*T^5 - 1297/2401*T^4 + 141/343*T^3 
        + 3/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 6*X*Y^10 + 3*X*Y^9 + 5*X*Y^8 + 4*X*Y^7 + 6*X*Y^6 + 
        5*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 5*X*Y + 5*X + 3*Y^30 + 6*Y^29 + 
        5*Y^28 + 5*Y^27 + 2*Y^26 + 3*Y^25 + 4*Y^24 + 2*Y^23 + 5*Y^22 + 3*Y^21 + 
        4*Y^20 + 6*Y^19 + 5*Y^18 + 4*Y^15 + 4*Y^14 + 3*Y^13 + Y^12 + 2*Y^11 + 5*Y^10
        + 4*Y^9 + 2*Y^8 + 4*Y^6 + 2*Y^4 + 2*Y^3 + 2*Y + 5,
    T^56 - 2*T^55 + 58/49*T^54 + 334/343*T^53 - 5945/2401*T^52 + 2077/2401*T^51 + 
        4437/2401*T^50 - 4245/2401*T^49 - 3154/2401*T^48 + 9157/2401*T^47 - 
        4086/2401*T^46 - 1038/343*T^45 + 11555/2401*T^44 - 3252/2401*T^43 - 
        8892/2401*T^42 + 201/49*T^41 + 232/343*T^40 - 10450/2401*T^39 + 
        5655/2401*T^38 + 7328/2401*T^37 - 12791/2401*T^36 + 3585/2401*T^35 + 
        9153/2401*T^34 - 10242/2401*T^33 - 121/343*T^32 + 10723/2401*T^31 - 
        7395/2401*T^30 - 5448/2401*T^29 + 12506/2401*T^28 - 5448/2401*T^27 - 
        7395/2401*T^26 + 10723/2401*T^25 - 121/343*T^24 - 10242/2401*T^23 + 
        9153/2401*T^22 + 3585/2401*T^21 - 12791/2401*T^20 + 7328/2401*T^19 + 
        5655/2401*T^18 - 10450/2401*T^17 + 232/343*T^16 + 201/49*T^15 - 
        8892/2401*T^14 - 3252/2401*T^13 + 11555/2401*T^12 - 1038/343*T^11 - 
        4086/2401*T^10 + 9157/2401*T^9 - 3154/2401*T^8 - 4245/2401*T^7 + 
        4437/2401*T^6 + 2077/2401*T^5 - 5945/2401*T^4 + 334/343*T^3 + 58/49*T^2 - 
        2*T + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + 4*X*Y^9 
        + 3*X*Y^8 + 4*X*Y^7 + 6*X*Y^6 + 2*X*Y^5 + X*Y^4 + 5*X*Y^2 + X*Y + 2*X + 
        2*Y^30 + 3*Y^29 + 3*Y^28 + 6*Y^27 + 2*Y^26 + 6*Y^24 + 3*Y^23 + 4*Y^22 + 
        2*Y^21 + Y^20 + 5*Y^19 + 5*Y^18 + 3*Y^17 + 6*Y^16 + 3*Y^15 + 6*Y^14 + 6*Y^13
        + 2*Y^10 + 6*Y^9 + 2*Y^8 + 5*Y^7 + 2*Y^6 + 5*Y^5 + 4*Y^4 + 2*Y^3 + 3*Y^2 + 
        3*Y + 3,
    -T^56 - 10/7*T^55 - 39/49*T^54 + 22/343*T^53 + 59/343*T^52 - 1444/2401*T^51 - 
        1439/2401*T^50 - 226/343*T^49 + 34/2401*T^48 + 1515/2401*T^47 + 
        118/2401*T^46 - 2537/2401*T^45 - 2788/2401*T^44 + 6/343*T^43 + 
        1970/2401*T^42 + 2007/2401*T^41 + 242/343*T^40 + 151/343*T^39 + 
        106/2401*T^38 + 639/2401*T^37 + 125/343*T^36 + 219/2401*T^35 - 467/2401*T^34
        - 83/2401*T^33 + 740/2401*T^32 + 639/2401*T^31 + 190/343*T^30 + 
        1142/2401*T^29 - 1142/2401*T^27 - 190/343*T^26 - 639/2401*T^25 - 
        740/2401*T^24 + 83/2401*T^23 + 467/2401*T^22 - 219/2401*T^21 - 125/343*T^20 
        - 639/2401*T^19 - 106/2401*T^18 - 151/343*T^17 - 242/343*T^16 - 
        2007/2401*T^15 - 1970/2401*T^14 - 6/343*T^13 + 2788/2401*T^12 + 
        2537/2401*T^11 - 118/2401*T^10 - 1515/2401*T^9 - 34/2401*T^8 + 226/343*T^7 +
        1439/2401*T^6 + 1444/2401*T^5 - 59/343*T^4 - 22/343*T^3 + 39/49*T^2 + 10/7*T
        + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 
        3*X*Y^8 + 4*X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + 6*X*Y^4 + 3*X*Y^2 + 6*X*Y + 2*X + 
        Y^30 + 5*Y^29 + 5*Y^28 + 2*Y^27 + 2*Y^26 + Y^25 + Y^24 + 5*Y^23 + 3*Y^22 + 
        2*Y^21 + 5*Y^19 + 2*Y^18 + 5*Y^17 + 3*Y^16 + 5*Y^15 + 2*Y^14 + 4*Y^13 + Y^12
        + Y^11 + 6*Y^10 + 4*Y^9 + Y^8 + 6*Y^7 + 3*Y^6 + 4*Y^5 + 6*Y^4 + 5*Y^3 + 
        4*Y^2 + 4*Y + 1,
    -T^56 + T^55 - 57/49*T^54 + 54/49*T^53 - 2127/2401*T^52 + 1098/2401*T^51 + 
        533/2401*T^50 + 23/2401*T^49 + 596/2401*T^48 + 936/2401*T^47 - 702/2401*T^46
        + 1535/2401*T^45 - 1982/2401*T^44 + 913/2401*T^43 - 33/343*T^42 - 
        962/2401*T^41 + 873/2401*T^40 - 113/343*T^39 + 998/2401*T^38 - 101/343*T^37 
        - 158/2401*T^36 + 215/2401*T^35 + 489/2401*T^34 - 1565/2401*T^33 + 
        1273/2401*T^32 - 2544/2401*T^31 + 1857/2401*T^30 - 195/343*T^29 + 
        195/343*T^27 - 1857/2401*T^26 + 2544/2401*T^25 - 1273/2401*T^24 + 
        1565/2401*T^23 - 489/2401*T^22 - 215/2401*T^21 + 158/2401*T^20 + 
        101/343*T^19 - 998/2401*T^18 + 113/343*T^17 - 873/2401*T^16 + 962/2401*T^15 
        + 33/343*T^14 - 913/2401*T^13 + 1982/2401*T^12 - 1535/2401*T^11 + 
        702/2401*T^10 - 936/2401*T^9 - 596/2401*T^8 - 23/2401*T^7 - 533/2401*T^6 - 
        1098/2401*T^5 + 2127/2401*T^4 - 54/49*T^3 + 57/49*T^2 - T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 5*X*Y^12 + X*Y^11 + 3*X*Y^10 + 4*X*Y^9 + 2*X*Y^8 + 
        6*X*Y^7 + 3*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 4*X + Y^30 + 
        3*Y^29 + 6*Y^27 + 2*Y^26 + 6*Y^25 + Y^24 + 6*Y^23 + 2*Y^22 + 3*Y^20 + Y^19 +
        Y^18 + 6*Y^17 + 2*Y^16 + Y^15 + 4*Y^14 + 2*Y^13 + 2*Y^12 + 2*Y^10 + 4*Y^8 + 
        4*Y^6 + 6*Y^5 + 5*Y^4 + 2*Y^3 + 3*Y^2 + 6*Y + 3,
    T^56 - 17/7*T^55 + 143/49*T^54 - 897/343*T^53 + 543/343*T^52 - 503/2401*T^51 - 
        45/49*T^50 + 4292/2401*T^49 - 4961/2401*T^48 + 4456/2401*T^47 - 
        4226/2401*T^46 + 3477/2401*T^45 - 1364/2401*T^44 - 339/2401*T^43 + 
        346/343*T^42 - 565/343*T^41 + 2851/2401*T^40 - 576/2401*T^39 - 209/2401*T^38
        - 460/2401*T^37 + 2132/2401*T^36 - 3604/2401*T^35 + 516/343*T^34 - 
        2245/2401*T^33 - 184/2401*T^32 + 284/343*T^31 - 2236/2401*T^30 + 
        2748/2401*T^29 - 3120/2401*T^28 + 2748/2401*T^27 - 2236/2401*T^26 + 
        284/343*T^25 - 184/2401*T^24 - 2245/2401*T^23 + 516/343*T^22 - 
        3604/2401*T^21 + 2132/2401*T^20 - 460/2401*T^19 - 209/2401*T^18 - 
        576/2401*T^17 + 2851/2401*T^16 - 565/343*T^15 + 346/343*T^14 - 339/2401*T^13
        - 1364/2401*T^12 + 3477/2401*T^11 - 4226/2401*T^10 + 4456/2401*T^9 - 
        4961/2401*T^8 + 4292/2401*T^7 - 45/49*T^6 - 503/2401*T^5 + 543/343*T^4 - 
        897/343*T^3 + 143/49*T^2 - 17/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 +
        X*Y^7 + X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 3*X*Y + 4*Y^30 + 4*Y^29 + 2*Y^27 + 
        3*Y^26 + 4*Y^25 + 3*Y^24 + 3*Y^23 + 5*Y^22 + 3*Y^20 + Y^19 + 5*Y^18 + Y^17 +
        Y^16 + 6*Y^14 + 4*Y^13 + 6*Y^12 + 5*Y^11 + 5*Y^10 + 3*Y^9 + 5*Y^8 + 2*Y^7 + 
        6*Y^6 + 3*Y^5 + 5*Y^4 + 3*Y^2 + Y + 1,
    -T^56 + 4/7*T^55 + 4/49*T^54 - 9/49*T^53 - 260/2401*T^52 + 2076/2401*T^51 + 
        171/2401*T^50 - 17/2401*T^49 - 1228/2401*T^48 + 2319/2401*T^47 - 93/343*T^46
        - 395/2401*T^45 - 368/2401*T^44 + 94/2401*T^43 - 934/2401*T^42 - 
        108/2401*T^41 + 809/2401*T^40 - 906/2401*T^39 + 272/2401*T^38 + 
        774/2401*T^37 - 2/7*T^36 - 93/343*T^35 + 1431/2401*T^34 - 6/49*T^33 + 
        215/2401*T^32 - 678/2401*T^31 - 240/2401*T^30 - 422/2401*T^29 + 
        422/2401*T^27 + 240/2401*T^26 + 678/2401*T^25 - 215/2401*T^24 + 6/49*T^23 - 
        1431/2401*T^22 + 93/343*T^21 + 2/7*T^20 - 774/2401*T^19 - 272/2401*T^18 + 
        906/2401*T^17 - 809/2401*T^16 + 108/2401*T^15 + 934/2401*T^14 - 94/2401*T^13
        + 368/2401*T^12 + 395/2401*T^11 + 93/343*T^10 - 2319/2401*T^9 + 
        1228/2401*T^8 + 17/2401*T^7 - 171/2401*T^6 - 2076/2401*T^5 + 260/2401*T^4 + 
        9/49*T^3 - 4/49*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + X*Y^10 + 5*X*Y^9 + 3*X*Y^8 + 
        2*X*Y^6 + 3*X*Y^5 + X*Y^4 + 6*X*Y^2 + 5*X + 3*Y^30 + 2*Y^29 + Y^28 + 4*Y^27 
        + 2*Y^26 + 4*Y^22 + 6*Y^21 + 2*Y^20 + 6*Y^19 + 2*Y^18 + Y^17 + 5*Y^16 + 
        2*Y^15 + 2*Y^14 + 5*Y^13 + 5*Y^12 + 5*Y^10 + 2*Y^9 + 2*Y^8 + 6*Y^7 + 3*Y^6 +
        3*Y^4 + 6*Y^3 + 2*Y^2 + 2*Y,
    T^56 - 2/7*T^55 - 25/49*T^54 - 45/49*T^53 + 1483/2401*T^52 - 562/2401*T^51 + 
        471/2401*T^50 - 526/2401*T^49 + 1201/2401*T^48 + 794/2401*T^47 + 
        433/2401*T^46 - 1867/2401*T^45 - 414/2401*T^44 + 2031/2401*T^43 + 
        29/2401*T^42 - 234/343*T^41 - 1345/2401*T^40 + 2622/2401*T^39 + 
        219/2401*T^38 - 681/2401*T^37 - 1718/2401*T^36 + 501/2401*T^35 + 
        1276/2401*T^34 - 71/2401*T^33 - 750/2401*T^32 + 22/343*T^31 + 2099/2401*T^30
        - 726/2401*T^29 - 2159/2401*T^28 - 726/2401*T^27 + 2099/2401*T^26 + 
        22/343*T^25 - 750/2401*T^24 - 71/2401*T^23 + 1276/2401*T^22 + 501/2401*T^21 
        - 1718/2401*T^20 - 681/2401*T^19 + 219/2401*T^18 + 2622/2401*T^17 - 
        1345/2401*T^16 - 234/343*T^15 + 29/2401*T^14 + 2031/2401*T^13 - 
        414/2401*T^12 - 1867/2401*T^11 + 433/2401*T^10 + 794/2401*T^9 + 
        1201/2401*T^8 - 526/2401*T^7 + 471/2401*T^6 - 562/2401*T^5 + 1483/2401*T^4 -
        45/49*T^3 - 25/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + X*Y^9 + 2*X*Y^8 + 
        4*X*Y^6 + 4*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + X*Y^2 + X + 4*Y^30 + 3*Y^29 + Y^28 +
        5*Y^27 + 3*Y^26 + 4*Y^25 + 6*Y^24 + 3*Y^23 + 6*Y^21 + 3*Y^20 + 5*Y^19 + Y^18
        + 4*Y^17 + Y^16 + Y^15 + 6*Y^14 + 6*Y^13 + 2*Y^11 + 3*Y^10 + 3*Y^9 + 5*Y^8 +
        5*Y^7 + 2*Y^6 + 5*Y^5 + 2*Y^4 + 4*Y^3 + Y + 1,
    T^56 + 8/7*T^55 - 2/49*T^54 - 208/343*T^53 - 1920/2401*T^52 - 37/49*T^51 - 
        1042/2401*T^50 - 1220/2401*T^49 - 16/49*T^48 + 1613/2401*T^47 + 
        2851/2401*T^46 + 2386/2401*T^45 + 1647/2401*T^44 + 464/2401*T^43 - 
        391/2401*T^42 - 268/343*T^41 - 2735/2401*T^40 - 1779/2401*T^39 - 
        1818/2401*T^38 - 1222/2401*T^37 + 190/343*T^36 + 3046/2401*T^35 + 
        2929/2401*T^34 + 1385/2401*T^33 - 220/2401*T^32 + 202/2401*T^31 - 
        69/343*T^30 - 2362/2401*T^29 - 3029/2401*T^28 - 2362/2401*T^27 - 69/343*T^26
        + 202/2401*T^25 - 220/2401*T^24 + 1385/2401*T^23 + 2929/2401*T^22 + 
        3046/2401*T^21 + 190/343*T^20 - 1222/2401*T^19 - 1818/2401*T^18 - 
        1779/2401*T^17 - 2735/2401*T^16 - 268/343*T^15 - 391/2401*T^14 + 
        464/2401*T^13 + 1647/2401*T^12 + 2386/2401*T^11 + 2851/2401*T^10 + 
        1613/2401*T^9 - 16/49*T^8 - 1220/2401*T^7 - 1042/2401*T^6 - 37/49*T^5 - 
        1920/2401*T^4 - 208/343*T^3 - 2/49*T^2 + 8/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 
        + 2*X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 6*X*Y^4 + X*Y^3 + 5*X*Y + X + 6*Y^30 + 
        5*Y^29 + 5*Y^28 + 3*Y^27 + 2*Y^26 + 4*Y^25 + 2*Y^24 + 3*Y^23 + 5*Y^22 + 
        3*Y^21 + Y^20 + Y^19 + Y^18 + 4*Y^17 + 2*Y^16 + 5*Y^15 + Y^14 + Y^13 + 
        2*Y^11 + 2*Y^10 + 2*Y^9 + 4*Y^7 + 2*Y^6 + 4*Y^5 + 2*Y^4 + 6*Y^3 + 6*Y^2 + 
        3*Y + 6,
    -T^56 - 6/7*T^55 + 20/49*T^54 + 356/343*T^53 + 1065/2401*T^52 + 124/2401*T^51 + 
        1845/2401*T^50 + 937/2401*T^49 - 1242/2401*T^48 - 1759/2401*T^47 - 
        526/2401*T^46 - 487/2401*T^45 - 282/343*T^44 - 165/2401*T^43 + 37/49*T^42 + 
        213/343*T^41 + 915/2401*T^40 + 606/2401*T^39 + 118/343*T^38 - 1448/2401*T^37
        - 1879/2401*T^36 - 1054/2401*T^35 - 114/2401*T^34 - 109/2401*T^33 - 
        65/2401*T^32 + 314/343*T^31 + 1599/2401*T^30 + 475/2401*T^29 - 475/2401*T^27
        - 1599/2401*T^26 - 314/343*T^25 + 65/2401*T^24 + 109/2401*T^23 + 
        114/2401*T^22 + 1054/2401*T^21 + 1879/2401*T^20 + 1448/2401*T^19 - 
        118/343*T^18 - 606/2401*T^17 - 915/2401*T^16 - 213/343*T^15 - 37/49*T^14 + 
        165/2401*T^13 + 282/343*T^12 + 487/2401*T^11 + 526/2401*T^10 + 1759/2401*T^9
        + 1242/2401*T^8 - 937/2401*T^7 - 1845/2401*T^6 - 124/2401*T^5 - 
        1065/2401*T^4 - 356/343*T^3 - 20/49*T^2 + 6/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 
        4*X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + X*Y^5 + X*Y^4 + 6*X*Y^3 + X*Y + 2*X + 2*Y^30 +
        3*Y^28 + 2*Y^25 + 6*Y^24 + 4*Y^23 + 5*Y^21 + 2*Y^20 + 6*Y^19 + Y^18 + Y^17 +
        4*Y^16 + 3*Y^15 + 5*Y^14 + 3*Y^13 + 2*Y^12 + 5*Y^11 + 2*Y^9 + 4*Y^8 + Y^7 + 
        3*Y^6 + 4*Y^5 + 6*Y^4 + Y^3 + 2*Y^2 + 5*Y,
    -T^56 + 1/7*T^55 + 39/49*T^54 + 61/343*T^53 - 1021/2401*T^52 - 972/2401*T^51 + 
        2346/2401*T^50 + 370/2401*T^49 - 124/343*T^48 - 102/343*T^47 + 487/2401*T^46
        + 839/2401*T^45 - 1357/2401*T^44 - 10/2401*T^43 + 1237/2401*T^42 - 
        737/2401*T^41 - 1467/2401*T^40 + 274/2401*T^39 + 982/2401*T^38 - 
        726/2401*T^37 - 1199/2401*T^36 + 758/2401*T^35 + 1896/2401*T^34 - 
        402/2401*T^33 - 283/2401*T^32 - 464/2401*T^31 + 1355/2401*T^30 + 
        400/2401*T^29 - 400/2401*T^27 - 1355/2401*T^26 + 464/2401*T^25 + 
        283/2401*T^24 + 402/2401*T^23 - 1896/2401*T^22 - 758/2401*T^21 + 
        1199/2401*T^20 + 726/2401*T^19 - 982/2401*T^18 - 274/2401*T^17 + 
        1467/2401*T^16 + 737/2401*T^15 - 1237/2401*T^14 + 10/2401*T^13 + 
        1357/2401*T^12 - 839/2401*T^11 - 487/2401*T^10 + 102/343*T^9 + 124/343*T^8 -
        370/2401*T^7 - 2346/2401*T^6 + 972/2401*T^5 + 1021/2401*T^4 - 61/343*T^3 - 
        39/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^13 + 3*X*Y^12 + X*Y^11 + 3*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 + 
        X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 6*X*Y^2 + X*Y + 6*X + 5*Y^30
        + 4*Y^29 + 2*Y^28 + Y^27 + 4*Y^26 + Y^25 + 5*Y^24 + Y^23 + Y^22 + Y^21 + 
        6*Y^20 + 6*Y^19 + Y^18 + 3*Y^17 + 3*Y^16 + 4*Y^14 + 6*Y^13 + 5*Y^11 + 3*Y^10
        + 2*Y^9 + Y^8 + 3*Y^7 + Y^6 + 6*Y^4 + 4*Y^3 + Y^2 + Y + 6,
    -T^56 + 57/49*T^54 - 179/343*T^53 - 1955/2401*T^52 + 484/2401*T^51 + 
        2239/2401*T^50 - 501/2401*T^49 - 2560/2401*T^48 + 831/2401*T^47 + 
        1790/2401*T^46 - 738/2401*T^45 - 1277/2401*T^44 + 185/343*T^43 + 
        1483/2401*T^42 - 662/2401*T^41 - 93/343*T^40 + 137/343*T^39 + 180/343*T^38 -
        111/2401*T^37 - 160/343*T^36 + 1326/2401*T^35 + 860/2401*T^34 - 
        627/2401*T^33 + 737/2401*T^32 + 141/2401*T^31 + 69/343*T^30 - 907/2401*T^29 
        + 907/2401*T^27 - 69/343*T^26 - 141/2401*T^25 - 737/2401*T^24 + 
        627/2401*T^23 - 860/2401*T^22 - 1326/2401*T^21 + 160/343*T^20 + 
        111/2401*T^19 - 180/343*T^18 - 137/343*T^17 + 93/343*T^16 + 662/2401*T^15 - 
        1483/2401*T^14 - 185/343*T^13 + 1277/2401*T^12 + 738/2401*T^11 - 
        1790/2401*T^10 - 831/2401*T^9 + 2560/2401*T^8 + 501/2401*T^7 - 2239/2401*T^6
        - 484/2401*T^5 + 1955/2401*T^4 + 179/343*T^3 - 57/49*T^2 + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + 6*X*Y^11 + 5*X*Y^10 + 5*X*Y^8 + 2*X*Y^7 +
        2*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + X*Y^2 + 6*X*Y + 5*X + Y^30 + Y^29 + 
        6*Y^28 + 4*Y^27 + 5*Y^26 + 6*Y^25 + 5*Y^23 + 5*Y^22 + 4*Y^20 + 6*Y^19 + Y^18
        + 2*Y^17 + 4*Y^16 + 4*Y^15 + 5*Y^14 + 3*Y^13 + 3*Y^12 + 6*Y^11 + 3*Y^9 + 
        2*Y^8 + Y^7 + 6*Y^5 + Y^4 + 2*Y^3 + 6*Y^2 + 3*Y + 5,
    T^56 - 5/7*T^55 + 18/49*T^54 + 1/49*T^53 - 1091/2401*T^52 + 1973/2401*T^51 - 
        25/49*T^50 + 2115/2401*T^49 - 83/2401*T^48 - 39/2401*T^47 + 411/2401*T^46 + 
        3/343*T^45 + 346/2401*T^44 - 416/2401*T^43 + 1424/2401*T^42 - 813/2401*T^41 
        + 681/2401*T^40 + 317/2401*T^39 - 104/343*T^38 + 512/2401*T^37 - 
        921/2401*T^36 - 50/2401*T^35 + 158/2401*T^34 - 1198/2401*T^33 + 
        261/2401*T^32 - 6/343*T^31 - 969/2401*T^30 + 247/2401*T^29 - 1172/2401*T^28 
        + 247/2401*T^27 - 969/2401*T^26 - 6/343*T^25 + 261/2401*T^24 - 
        1198/2401*T^23 + 158/2401*T^22 - 50/2401*T^21 - 921/2401*T^20 + 
        512/2401*T^19 - 104/343*T^18 + 317/2401*T^17 + 681/2401*T^16 - 813/2401*T^15
        + 1424/2401*T^14 - 416/2401*T^13 + 346/2401*T^12 + 3/343*T^11 + 
        411/2401*T^10 - 39/2401*T^9 - 83/2401*T^8 + 2115/2401*T^7 - 25/49*T^6 + 
        1973/2401*T^5 - 1091/2401*T^4 + 1/49*T^3 + 18/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 4*X*Y^10 + 4*X*Y^9 + X*Y^8 + 
        4*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 5*X + 3*Y^30 + 4*Y^29 + 
        2*Y^28 + 4*Y^27 + Y^25 + 4*Y^24 + 2*Y^23 + 4*Y^22 + Y^20 + Y^19 + 4*Y^18 + 
        2*Y^17 + Y^15 + Y^13 + Y^12 + 3*Y^11 + 3*Y^10 + Y^9 + 5*Y^8 + 6*Y^7 + 5*Y^6 
        + 4*Y^5 + Y^4 + 5*Y^2 + 6*Y + 6,
    T^56 - 1/49*T^54 - 211/343*T^53 - 2076/2401*T^52 + 705/2401*T^51 - 92/2401*T^50 
        + 1858/2401*T^49 + 362/2401*T^48 - 520/2401*T^47 + 1044/2401*T^46 - 
        138/343*T^45 + 233/343*T^44 - 26/49*T^43 - 648/2401*T^42 - 4/49*T^41 - 
        767/2401*T^40 + 2130/2401*T^39 - 934/2401*T^38 + 1033/2401*T^37 + 
        132/2401*T^36 + 110/2401*T^35 + 2146/2401*T^34 - 4/7*T^33 + 27/343*T^32 - 
        1361/2401*T^31 - 1259/2401*T^30 + 2322/2401*T^29 - 60/2401*T^28 + 
        2322/2401*T^27 - 1259/2401*T^26 - 1361/2401*T^25 + 27/343*T^24 - 4/7*T^23 + 
        2146/2401*T^22 + 110/2401*T^21 + 132/2401*T^20 + 1033/2401*T^19 - 
        934/2401*T^18 + 2130/2401*T^17 - 767/2401*T^16 - 4/49*T^15 - 648/2401*T^14 -
        26/49*T^13 + 233/343*T^12 - 138/343*T^11 + 1044/2401*T^10 - 520/2401*T^9 + 
        362/2401*T^8 + 1858/2401*T^7 - 92/2401*T^6 + 705/2401*T^5 - 2076/2401*T^4 - 
        211/343*T^3 - 1/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 
        4*X*Y^8 + 4*X*Y^7 + 6*X*Y^6 + X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 2*X + 
        5*Y^30 + 5*Y^29 + 5*Y^28 + 2*Y^27 + 4*Y^26 + 5*Y^25 + 5*Y^24 + 3*Y^22 + 
        2*Y^21 + 6*Y^20 + 5*Y^19 + Y^18 + 5*Y^17 + 3*Y^16 + 3*Y^15 + 6*Y^14 + 3*Y^13
        + 4*Y^12 + 6*Y^10 + 5*Y^9 + 2*Y^8 + 3*Y^7 + 6*Y^6 + 4*Y^5 + 3*Y^2 + 3*Y + 1,
    -T^56 + 6/7*T^55 - 4/7*T^54 + 1/49*T^53 + 729/2401*T^52 - 2932/2401*T^51 + 
        4394/2401*T^50 - 2508/2401*T^49 + 1975/2401*T^48 - 290/2401*T^47 - 
        1632/2401*T^46 + 3411/2401*T^45 - 2575/2401*T^44 + 1609/2401*T^43 - 
        1650/2401*T^42 + 67/2401*T^41 + 804/2401*T^40 - 880/2401*T^39 + 178/343*T^38
        - 738/2401*T^37 - 74/343*T^36 + 825/2401*T^35 - 193/2401*T^34 + 46/2401*T^33
        + 57/343*T^32 - 2390/2401*T^31 + 2383/2401*T^30 - 1054/2401*T^29 + 
        1054/2401*T^27 - 2383/2401*T^26 + 2390/2401*T^25 - 57/343*T^24 - 
        46/2401*T^23 + 193/2401*T^22 - 825/2401*T^21 + 74/343*T^20 + 738/2401*T^19 -
        178/343*T^18 + 880/2401*T^17 - 804/2401*T^16 - 67/2401*T^15 + 1650/2401*T^14
        - 1609/2401*T^13 + 2575/2401*T^12 - 3411/2401*T^11 + 1632/2401*T^10 + 
        290/2401*T^9 - 1975/2401*T^8 + 2508/2401*T^7 - 4394/2401*T^6 + 2932/2401*T^5
        - 729/2401*T^4 - 1/49*T^3 + 4/7*T^2 - 6/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 5*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 5*X*Y^7 + 4*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 4*X*Y + 6*Y^30 +
        Y^29 + 5*Y^28 + 4*Y^27 + 4*Y^26 + 3*Y^25 + 6*Y^24 + 6*Y^23 + Y^22 + Y^21 + 
        Y^20 + 4*Y^18 + 3*Y^17 + Y^16 + 6*Y^14 + Y^13 + 3*Y^12 + Y^11 + 3*Y^10 + 
        5*Y^8 + 6*Y^7 + 3*Y^5 + 4*Y^4 + Y^3 + 6*Y^2 + 3*Y + 6,
    T^56 + 10/7*T^55 + 51/49*T^54 + 296/343*T^53 - 206/2401*T^52 - 1325/2401*T^51 - 
        645/2401*T^50 - 1284/2401*T^49 - 1193/2401*T^48 - 894/2401*T^47 - 
        1222/2401*T^46 - 477/2401*T^45 + 362/2401*T^44 + 583/2401*T^43 + 
        292/2401*T^42 + 1412/2401*T^41 + 1948/2401*T^40 + 663/2401*T^39 - 
        292/2401*T^38 - 1322/2401*T^37 - 2273/2401*T^36 - 1395/2401*T^35 - 
        852/2401*T^34 - 1083/2401*T^33 - 559/2401*T^32 - 10/2401*T^31 + 
        908/2401*T^30 + 2131/2401*T^29 + 438/343*T^28 + 2131/2401*T^27 + 
        908/2401*T^26 - 10/2401*T^25 - 559/2401*T^24 - 1083/2401*T^23 - 
        852/2401*T^22 - 1395/2401*T^21 - 2273/2401*T^20 - 1322/2401*T^19 - 
        292/2401*T^18 + 663/2401*T^17 + 1948/2401*T^16 + 1412/2401*T^15 + 
        292/2401*T^14 + 583/2401*T^13 + 362/2401*T^12 - 477/2401*T^11 - 
        1222/2401*T^10 - 894/2401*T^9 - 1193/2401*T^8 - 1284/2401*T^7 - 645/2401*T^6
        - 1325/2401*T^5 - 206/2401*T^4 + 296/343*T^3 + 51/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + X*Y^10 + 2*X*Y^8 + 
        5*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 5*X*Y^2 + X*Y + 2*X + 3*Y^30 + 
        3*Y^29 + Y^28 + 5*Y^27 + 6*Y^26 + Y^24 + 5*Y^23 + 5*Y^22 + 4*Y^20 + 6*Y^19 +
        6*Y^18 + 6*Y^17 + 5*Y^16 + 4*Y^15 + Y^13 + 5*Y^12 + Y^11 + 2*Y^10 + 2*Y^9 + 
        2*Y^8 + 2*Y^7 + 2*Y^6 + Y^5 + 6*Y^3 + 3*Y^2 + 5*Y + 4,
    -T^56 + T^55 - 60/49*T^54 + 638/343*T^53 - 564/343*T^52 + 38/49*T^51 - 
        2586/2401*T^50 + 352/2401*T^49 + 3096/2401*T^48 - 2930/2401*T^47 + 
        589/343*T^46 - 5093/2401*T^45 + 3837/2401*T^44 - 1606/2401*T^43 + 
        34/343*T^42 + 3125/2401*T^41 - 4805/2401*T^40 + 6430/2401*T^39 - 
        900/343*T^38 + 4687/2401*T^37 - 2521/2401*T^36 + 158/2401*T^35 + 
        4415/2401*T^34 - 6282/2401*T^33 + 6648/2401*T^32 - 7531/2401*T^31 + 
        6365/2401*T^30 - 2176/2401*T^29 + 2176/2401*T^27 - 6365/2401*T^26 + 
        7531/2401*T^25 - 6648/2401*T^24 + 6282/2401*T^23 - 4415/2401*T^22 - 
        158/2401*T^21 + 2521/2401*T^20 - 4687/2401*T^19 + 900/343*T^18 - 
        6430/2401*T^17 + 4805/2401*T^16 - 3125/2401*T^15 - 34/343*T^14 + 
        1606/2401*T^13 - 3837/2401*T^12 + 5093/2401*T^11 - 589/343*T^10 + 
        2930/2401*T^9 - 3096/2401*T^8 - 352/2401*T^7 + 2586/2401*T^6 - 38/49*T^5 + 
        564/343*T^4 - 638/343*T^3 + 60/49*T^2 - T + 1
*], [*
    X^3 + 2*X*Y^14 + 5*X*Y^12 + 5*X*Y^10 + 6*X*Y^9 + 4*X*Y^8 + 5*X*Y^7 + X*Y^5 + 
        4*X*Y^4 + X*Y^3 + 4*X*Y^2 + 3*X*Y + 6*X + Y^30 + 4*Y^29 + 3*Y^28 + Y^26 + 
        3*Y^25 + 3*Y^24 + Y^23 + Y^22 + 2*Y^21 + 3*Y^19 + 5*Y^18 + Y^17 + 6*Y^16 + 
        2*Y^15 + 6*Y^13 + 4*Y^12 + Y^11 + 2*Y^9 + 4*Y^8 + Y^7 + Y^6 + 3*Y^5 + 3*Y^4 
        + 4*Y^3 + 6*Y^2 + 3*Y + 1,
    -T^56 + 18/7*T^55 - 24/7*T^54 + 1336/343*T^53 - 9022/2401*T^52 + 6571/2401*T^51 
        - 3306/2401*T^50 + 1/343*T^49 + 2193/2401*T^48 - 2102/2401*T^47 + 
        192/2401*T^46 + 1944/2401*T^45 - 2038/2401*T^44 - 260/2401*T^43 + 
        3126/2401*T^42 - 6445/2401*T^41 + 9165/2401*T^40 - 9682/2401*T^39 + 
        7817/2401*T^38 - 4696/2401*T^37 + 313/343*T^36 - 1297/2401*T^35 + 
        2599/2401*T^34 - 5079/2401*T^33 + 7037/2401*T^32 - 8417/2401*T^31 + 
        8306/2401*T^30 - 5018/2401*T^29 + 5018/2401*T^27 - 8306/2401*T^26 + 
        8417/2401*T^25 - 7037/2401*T^24 + 5079/2401*T^23 - 2599/2401*T^22 + 
        1297/2401*T^21 - 313/343*T^20 + 4696/2401*T^19 - 7817/2401*T^18 + 
        9682/2401*T^17 - 9165/2401*T^16 + 6445/2401*T^15 - 3126/2401*T^14 + 
        260/2401*T^13 + 2038/2401*T^12 - 1944/2401*T^11 - 192/2401*T^10 + 
        2102/2401*T^9 - 2193/2401*T^8 - 1/343*T^7 + 3306/2401*T^6 - 6571/2401*T^5 + 
        9022/2401*T^4 - 1336/343*T^3 + 24/7*T^2 - 18/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + X*Y^13 + 2*X*Y^11 + 3*X*Y^9 + X*Y^8 + 5*X*Y^7 + 
        X*Y^6 + X*Y^3 + 4*X*Y^2 + 4*X*Y + X + 4*Y^30 + 6*Y^29 + 3*Y^28 + 4*Y^27 + 
        5*Y^26 + 4*Y^25 + 5*Y^24 + 3*Y^23 + 2*Y^22 + 3*Y^21 + 4*Y^20 + 3*Y^19 + 
        4*Y^16 + 3*Y^15 + 5*Y^12 + 2*Y^11 + 3*Y^10 + 5*Y^9 + Y^8 + 5*Y^7 + 2*Y^6 + 
        Y^5 + 2*Y^4 + 6*Y^3 + 5*Y^2 + Y + 4,
    -T^56 - 13/7*T^55 - 61/49*T^54 - 5/49*T^53 + 1184/2401*T^52 + 2799/2401*T^51 + 
        3756/2401*T^50 + 2536/2401*T^49 + 1199/2401*T^48 - 246/2401*T^47 - 
        1607/2401*T^46 - 2211/2401*T^45 - 1601/2401*T^44 - 1587/2401*T^43 - 
        1168/2401*T^42 - 24/2401*T^41 + 1167/2401*T^40 + 1807/2401*T^39 + 
        905/2401*T^38 - 692/2401*T^37 - 2721/2401*T^36 - 3449/2401*T^35 - 
        2138/2401*T^34 + 202/2401*T^33 + 1574/2401*T^32 + 2843/2401*T^31 + 
        3146/2401*T^30 + 1844/2401*T^29 - 1844/2401*T^27 - 3146/2401*T^26 - 
        2843/2401*T^25 - 1574/2401*T^24 - 202/2401*T^23 + 2138/2401*T^22 + 
        3449/2401*T^21 + 2721/2401*T^20 + 692/2401*T^19 - 905/2401*T^18 - 
        1807/2401*T^17 - 1167/2401*T^16 + 24/2401*T^15 + 1168/2401*T^14 + 
        1587/2401*T^13 + 1601/2401*T^12 + 2211/2401*T^11 + 1607/2401*T^10 + 
        246/2401*T^9 - 1199/2401*T^8 - 2536/2401*T^7 - 3756/2401*T^6 - 2799/2401*T^5
        - 1184/2401*T^4 + 5/49*T^3 + 61/49*T^2 + 13/7*T + 1
*], [*
    X^3 + X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        5*X*Y^7 + 5*X*Y^6 + X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 6*X*Y + X + 4*Y^30
        + Y^29 + Y^28 + 3*Y^27 + 2*Y^26 + Y^25 + 5*Y^24 + 5*Y^23 + 5*Y^22 + 4*Y^21 +
        3*Y^20 + 2*Y^19 + 4*Y^18 + 3*Y^17 + 4*Y^16 + 6*Y^14 + 5*Y^13 + 4*Y^12 + 
        2*Y^11 + 4*Y^10 + 5*Y^9 + 3*Y^8 + 4*Y^7 + 5*Y^6 + 6*Y^5 + 6*Y^4 + 3*Y^3 + Y 
        + 4,
    -T^56 - 2/7*T^55 + 1/7*T^54 - 166/343*T^53 - 317/343*T^52 + 964/2401*T^51 - 
        382/2401*T^50 - 397/2401*T^49 + 1063/2401*T^48 + 193/2401*T^47 - 
        330/2401*T^46 + 22/49*T^45 + 122/2401*T^44 - 730/2401*T^43 - 243/2401*T^42 -
        78/2401*T^41 - 947/2401*T^40 - 207/2401*T^39 + 633/2401*T^38 - 130/2401*T^37
        - 3/7*T^36 + 1411/2401*T^35 + 1325/2401*T^34 - 108/2401*T^33 + 131/343*T^32 
        + 509/2401*T^31 - 284/2401*T^30 + 1262/2401*T^29 - 1262/2401*T^27 + 
        284/2401*T^26 - 509/2401*T^25 - 131/343*T^24 + 108/2401*T^23 - 
        1325/2401*T^22 - 1411/2401*T^21 + 3/7*T^20 + 130/2401*T^19 - 633/2401*T^18 +
        207/2401*T^17 + 947/2401*T^16 + 78/2401*T^15 + 243/2401*T^14 + 730/2401*T^13
        - 122/2401*T^12 - 22/49*T^11 + 330/2401*T^10 - 193/2401*T^9 - 1063/2401*T^8 
        + 397/2401*T^7 + 382/2401*T^6 - 964/2401*T^5 + 317/343*T^4 + 166/343*T^3 - 
        1/7*T^2 + 2/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^13 + X*Y^12 + 5*X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 3*X*Y^6 + 
        X*Y^5 + 6*X*Y^3 + 2*X*Y^2 + 4*X*Y + Y^30 + 6*Y^29 + 4*Y^28 + 6*Y^25 + 5*Y^24
        + 6*Y^22 + 6*Y^21 + 3*Y^20 + 4*Y^19 + 6*Y^18 + 6*Y^16 + 4*Y^15 + 6*Y^14 + 
        6*Y^12 + 4*Y^11 + 4*Y^10 + 6*Y^9 + 3*Y^8 + 6*Y^7 + 6*Y^6 + 4*Y^4 + 5*Y^3 + 
        6*Y^2 + 5*Y + 1,
    -T^56 + 13/7*T^55 - 60/49*T^54 + 360/343*T^53 - 2043/2401*T^52 - 388/2401*T^51 -
        773/2401*T^50 + 569/2401*T^49 + 3284/2401*T^48 - 1875/2401*T^47 + 
        123/343*T^46 - T^45 - 631/2401*T^44 + 18/49*T^43 + 1649/2401*T^42 + 
        221/343*T^41 - 2222/2401*T^40 - 319/2401*T^39 - 767/2401*T^38 - 
        1166/2401*T^37 + 3203/2401*T^36 + 355/2401*T^35 + 157/2401*T^34 - 
        3420/2401*T^33 + 1842/2401*T^32 - 2341/2401*T^31 + 2537/2401*T^30 + 
        997/2401*T^29 - 997/2401*T^27 - 2537/2401*T^26 + 2341/2401*T^25 - 
        1842/2401*T^24 + 3420/2401*T^23 - 157/2401*T^22 - 355/2401*T^21 - 
        3203/2401*T^20 + 1166/2401*T^19 + 767/2401*T^18 + 319/2401*T^17 + 
        2222/2401*T^16 - 221/343*T^15 - 1649/2401*T^14 - 18/49*T^13 + 631/2401*T^12 
        + T^11 - 123/343*T^10 + 1875/2401*T^9 - 3284/2401*T^8 - 569/2401*T^7 + 
        773/2401*T^6 + 388/2401*T^5 + 2043/2401*T^4 - 360/343*T^3 + 60/49*T^2 - 
        13/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + 4*X*Y^12 + X*Y^11 + 2*X*Y^10 + 2*X*Y^9 + 6*X*Y^8 + 
        2*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 3*X*Y + 5*X + 
        Y^30 + Y^29 + 5*Y^28 + 6*Y^27 + 3*Y^26 + 6*Y^25 + 4*Y^23 + 3*Y^21 + 4*Y^20 +
        3*Y^19 + 6*Y^17 + 5*Y^16 + 3*Y^15 + 6*Y^14 + 2*Y^12 + 3*Y^11 + 4*Y^10 + 
        5*Y^9 + 4*Y^8 + 6*Y^7 + 6*Y^6 + 6*Y^5 + 4*Y^4 + 5*Y^3 + 2*Y^2 + 5*Y + 6,
    T^56 - 3/7*T^55 - 9/7*T^54 + 289/343*T^53 - 45/343*T^52 - 1892/2401*T^51 + 
        3224/2401*T^50 + 359/2401*T^49 - 2425/2401*T^48 + 2418/2401*T^47 - 
        1383/2401*T^46 - 2279/2401*T^45 + 2512/2401*T^44 - 54/343*T^43 - 
        1058/2401*T^42 + 1440/2401*T^41 + 800/2401*T^40 - 1366/2401*T^39 - 
        1055/2401*T^38 + 1684/2401*T^37 - 684/2401*T^36 - 1516/2401*T^35 + 
        2501/2401*T^34 - 1643/2401*T^33 - 1283/2401*T^32 + 5276/2401*T^31 - 
        2754/2401*T^30 - 3083/2401*T^29 + 5265/2401*T^28 - 3083/2401*T^27 - 
        2754/2401*T^26 + 5276/2401*T^25 - 1283/2401*T^24 - 1643/2401*T^23 + 
        2501/2401*T^22 - 1516/2401*T^21 - 684/2401*T^20 + 1684/2401*T^19 - 
        1055/2401*T^18 - 1366/2401*T^17 + 800/2401*T^16 + 1440/2401*T^15 - 
        1058/2401*T^14 - 54/343*T^13 + 2512/2401*T^12 - 2279/2401*T^11 - 
        1383/2401*T^10 + 2418/2401*T^9 - 2425/2401*T^8 + 359/2401*T^7 + 
        3224/2401*T^6 - 1892/2401*T^5 - 45/343*T^4 + 289/343*T^3 - 9/7*T^2 - 3/7*T +
        1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 
        + 4*X*Y^8 + 3*X*Y^7 + 6*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 
        5*X*Y + 4*X + 3*Y^30 + 6*Y^29 + 2*Y^28 + 3*Y^27 + 3*Y^26 + 6*Y^25 + 6*Y^24 +
        2*Y^23 + 5*Y^22 + 6*Y^21 + 5*Y^20 + 6*Y^19 + Y^17 + 6*Y^16 + 5*Y^15 + Y^14 +
        5*Y^13 + 3*Y^12 + 5*Y^11 + 4*Y^10 + 6*Y^9 + 5*Y^8 + 5*Y^6 + 3*Y^5 + 6*Y^4 + 
        6*Y^3 + 4*Y^2 + Y,
    -T^56 - 2/49*T^54 - 368/343*T^53 + 354/2401*T^52 + 1101/2401*T^51 - 
        1928/2401*T^50 + 1627/2401*T^49 + 962/2401*T^48 - 1681/2401*T^47 + 
        1215/2401*T^46 + 64/2401*T^45 - 2096/2401*T^44 + 2431/2401*T^43 - 
        144/343*T^42 - 1215/2401*T^41 + 2725/2401*T^40 - 141/343*T^39 - 
        877/2401*T^38 + 345/343*T^37 - 306/343*T^36 + 500/2401*T^35 + 1529/2401*T^34
        - 2097/2401*T^33 + 1780/2401*T^32 + 1234/2401*T^31 - 2085/2401*T^30 + 
        2762/2401*T^29 - 2762/2401*T^27 + 2085/2401*T^26 - 1234/2401*T^25 - 
        1780/2401*T^24 + 2097/2401*T^23 - 1529/2401*T^22 - 500/2401*T^21 + 
        306/343*T^20 - 345/343*T^19 + 877/2401*T^18 + 141/343*T^17 - 2725/2401*T^16 
        + 1215/2401*T^15 + 144/343*T^14 - 2431/2401*T^13 + 2096/2401*T^12 - 
        64/2401*T^11 - 1215/2401*T^10 + 1681/2401*T^9 - 962/2401*T^8 - 1627/2401*T^7
        + 1928/2401*T^6 - 1101/2401*T^5 - 354/2401*T^4 + 368/343*T^3 + 2/49*T^2 + 1
*], [*
    X^3 + 5*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + 6*X*Y^10 + 3*X*Y^9 + 5*X*Y^8 + 3*X*Y^7 + 
        X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + X*Y^2 + 4*X*Y + 4*X + 6*Y^30 + 6*Y^29 
        + 2*Y^28 + 3*Y^26 + 3*Y^25 + 5*Y^24 + 3*Y^22 + 5*Y^21 + 2*Y^20 + 5*Y^18 + 
        2*Y^17 + 5*Y^16 + 5*Y^15 + 6*Y^14 + 3*Y^13 + 3*Y^12 + 5*Y^11 + 2*Y^10 + 
        3*Y^9 + 2*Y^8 + 5*Y^7 + Y^5 + Y^4 + 5*Y^3 + 4*Y^2 + 4*Y + 6,
    -T^56 - 3/7*T^55 + 43/49*T^54 + 184/343*T^53 - 258/2401*T^52 - 1592/2401*T^51 - 
        3394/2401*T^50 - 1656/2401*T^49 + 2636/2401*T^48 + 2095/2401*T^47 - 
        1934/2401*T^46 - 348/343*T^45 - 13/2401*T^44 + 739/2401*T^43 + 
        1899/2401*T^42 - 786/2401*T^41 - 4800/2401*T^40 - 43/49*T^39 + 
        4337/2401*T^38 + 4218/2401*T^37 - 233/2401*T^36 - 3127/2401*T^35 - 
        4285/2401*T^34 - 541/2401*T^33 + 4393/2401*T^32 + 2475/2401*T^31 - 
        1770/2401*T^30 - 2484/2401*T^29 + 2484/2401*T^27 + 1770/2401*T^26 - 
        2475/2401*T^25 - 4393/2401*T^24 + 541/2401*T^23 + 4285/2401*T^22 + 
        3127/2401*T^21 + 233/2401*T^20 - 4218/2401*T^19 - 4337/2401*T^18 + 
        43/49*T^17 + 4800/2401*T^16 + 786/2401*T^15 - 1899/2401*T^14 - 739/2401*T^13
        + 13/2401*T^12 + 348/343*T^11 + 1934/2401*T^10 - 2095/2401*T^9 - 
        2636/2401*T^8 + 1656/2401*T^7 + 3394/2401*T^6 + 1592/2401*T^5 + 258/2401*T^4
        - 184/343*T^3 - 43/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 
        + 2*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 2*X*Y + 3*Y^30
        + 6*Y^29 + 5*Y^28 + 6*Y^27 + 6*Y^26 + 2*Y^25 + 4*Y^24 + 2*Y^23 + 4*Y^22 + 
        6*Y^20 + 5*Y^19 + Y^16 + Y^14 + 6*Y^13 + 6*Y^12 + Y^11 + 3*Y^10 + 6*Y^9 + 
        6*Y^8 + 3*Y^6 + 2*Y^5 + 4*Y^4 + 3*Y^3 + 3*Y^2 + 5*Y + 3,
    T^56 - 18/7*T^55 + 178/49*T^54 - 1394/343*T^53 + 1535/343*T^52 - 12200/2401*T^51
        + 12130/2401*T^50 - 10499/2401*T^49 + 9056/2401*T^48 - 8336/2401*T^47 + 
        6700/2401*T^46 - 654/343*T^45 + 414/343*T^44 - 1864/2401*T^43 + 
        456/2401*T^42 + 1852/2401*T^41 - 2985/2401*T^40 + 429/343*T^39 - 
        2958/2401*T^38 + 3124/2401*T^37 - 310/343*T^36 + 859/2401*T^35 + 3/2401*T^34
        - 5/343*T^33 + 39/343*T^32 - 1186/2401*T^31 + 1688/2401*T^30 - 
        1611/2401*T^29 + 4/7*T^28 - 1611/2401*T^27 + 1688/2401*T^26 - 1186/2401*T^25
        + 39/343*T^24 - 5/343*T^23 + 3/2401*T^22 + 859/2401*T^21 - 310/343*T^20 + 
        3124/2401*T^19 - 2958/2401*T^18 + 429/343*T^17 - 2985/2401*T^16 + 
        1852/2401*T^15 + 456/2401*T^14 - 1864/2401*T^13 + 414/343*T^12 - 
        654/343*T^11 + 6700/2401*T^10 - 8336/2401*T^9 + 9056/2401*T^8 - 
        10499/2401*T^7 + 12130/2401*T^6 - 12200/2401*T^5 + 1535/343*T^4 - 
        1394/343*T^3 + 178/49*T^2 - 18/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + 6*X*Y^11 + 5*X*Y^10 + 3*X*Y^8 + 5*X*Y^7 +
        4*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 4*X*Y + 4*X + 2*Y^30 + 
        4*Y^29 + 3*Y^27 + 5*Y^26 + 3*Y^25 + Y^24 + 2*Y^23 + 5*Y^22 + 4*Y^21 + 3*Y^19
        + 2*Y^17 + 5*Y^16 + 6*Y^14 + 5*Y^13 + 3*Y^12 + 3*Y^11 + 2*Y^9 + Y^8 + 2*Y^7 
        + 5*Y^6 + 3*Y^5 + 5*Y^4 + 6*Y^3 + Y^2 + 3*Y + 4,
    T^56 + 1/7*T^55 - 22/49*T^54 + 150/343*T^53 + 258/2401*T^52 - 538/2401*T^51 - 
        1200/2401*T^50 - 208/2401*T^49 + 1201/2401*T^48 - 970/2401*T^47 - 
        208/2401*T^46 - 50/2401*T^45 + 298/2401*T^44 - 1217/2401*T^43 - 
        1083/2401*T^42 + 293/2401*T^41 - 1403/2401*T^40 - 837/2401*T^39 - 
        433/2401*T^38 + 272/2401*T^37 + 222/2401*T^36 - 774/2401*T^35 + 
        1327/2401*T^34 + 320/2401*T^33 + 1292/2401*T^32 - 288/2401*T^31 + 
        556/2401*T^30 + 1240/2401*T^29 - 1403/2401*T^28 + 1240/2401*T^27 + 
        556/2401*T^26 - 288/2401*T^25 + 1292/2401*T^24 + 320/2401*T^23 + 
        1327/2401*T^22 - 774/2401*T^21 + 222/2401*T^20 + 272/2401*T^19 - 
        433/2401*T^18 - 837/2401*T^17 - 1403/2401*T^16 + 293/2401*T^15 - 
        1083/2401*T^14 - 1217/2401*T^13 + 298/2401*T^12 - 50/2401*T^11 - 
        208/2401*T^10 - 970/2401*T^9 + 1201/2401*T^8 - 208/2401*T^7 - 1200/2401*T^6 
        - 538/2401*T^5 + 258/2401*T^4 + 150/343*T^3 - 22/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^13 + 6*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + X*Y^9 + 4*X*Y^8 + 
        3*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + X*Y^2 + 4*X*Y + 6*X + Y^30
        + 4*Y^29 + 3*Y^28 + Y^27 + Y^26 + Y^23 + 5*Y^22 + Y^21 + 2*Y^20 + 2*Y^19 + 
        Y^18 + Y^17 + 6*Y^16 + 2*Y^14 + 5*Y^13 + 6*Y^12 + Y^11 + 2*Y^10 + 5*Y^9 + 
        2*Y^8 + 6*Y^7 + 4*Y^6 + 6*Y^5 + 2*Y^4 + 2*Y^3 + Y^2 + 5*Y + 5,
    -T^56 - 2/7*T^55 + 68/49*T^54 + 110/343*T^53 - 1961/2401*T^52 + 1919/2401*T^51 +
        1153/2401*T^50 - 662/343*T^49 + 705/2401*T^48 + 3162/2401*T^47 - 
        2346/2401*T^46 + 10/343*T^45 + 2361/2401*T^44 - 3289/2401*T^43 - 
        445/2401*T^42 + 4554/2401*T^41 - 327/343*T^40 - 11/2401*T^39 + 
        3719/2401*T^38 - 4813/2401*T^37 - 3243/2401*T^36 + 5484/2401*T^35 - 
        1202/2401*T^34 - 2897/2401*T^33 + 6387/2401*T^32 - 142/343*T^31 - 
        5027/2401*T^30 + 3783/2401*T^29 - 3783/2401*T^27 + 5027/2401*T^26 + 
        142/343*T^25 - 6387/2401*T^24 + 2897/2401*T^23 + 1202/2401*T^22 - 
        5484/2401*T^21 + 3243/2401*T^20 + 4813/2401*T^19 - 3719/2401*T^18 + 
        11/2401*T^17 + 327/343*T^16 - 4554/2401*T^15 + 445/2401*T^14 + 
        3289/2401*T^13 - 2361/2401*T^12 - 10/343*T^11 + 2346/2401*T^10 - 
        3162/2401*T^9 - 705/2401*T^8 + 662/343*T^7 - 1153/2401*T^6 - 1919/2401*T^5 +
        1961/2401*T^4 - 110/343*T^3 - 68/49*T^2 + 2/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 6*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 2*X*Y^8 + 
        4*X*Y^7 + 4*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + X*Y + 3*X + 
        4*Y^30 + 4*Y^29 + Y^28 + 5*Y^27 + 5*Y^26 + 6*Y^25 + 5*Y^24 + Y^22 + 6*Y^21 +
        Y^20 + 2*Y^19 + 3*Y^17 + 5*Y^16 + 5*Y^13 + Y^12 + Y^11 + 2*Y^9 + Y^8 + 2*Y^7
        + Y^6 + Y^5 + 5*Y^4 + 5*Y^3 + 5,
    -T^56 - T^55 + 4/49*T^54 + 282/343*T^53 + 2062/2401*T^52 + 1866/2401*T^51 + 
        246/2401*T^50 - 1549/2401*T^49 - 829/2401*T^48 + 1524/2401*T^47 + 
        3953/2401*T^46 + 1692/2401*T^45 - 2187/2401*T^44 - 3308/2401*T^43 - 
        349/343*T^42 - 1790/2401*T^41 + 1135/2401*T^40 + 3518/2401*T^39 + 
        1583/2401*T^38 - 1639/2401*T^37 - 2141/2401*T^36 - 1279/2401*T^35 + 
        496/2401*T^34 + 2068/2401*T^33 + 926/2401*T^32 - 429/2401*T^31 - 
        2470/2401*T^30 - 3438/2401*T^29 + 3438/2401*T^27 + 2470/2401*T^26 + 
        429/2401*T^25 - 926/2401*T^24 - 2068/2401*T^23 - 496/2401*T^22 + 
        1279/2401*T^21 + 2141/2401*T^20 + 1639/2401*T^19 - 1583/2401*T^18 - 
        3518/2401*T^17 - 1135/2401*T^16 + 1790/2401*T^15 + 349/343*T^14 + 
        3308/2401*T^13 + 2187/2401*T^12 - 1692/2401*T^11 - 3953/2401*T^10 - 
        1524/2401*T^9 + 829/2401*T^8 + 1549/2401*T^7 - 246/2401*T^6 - 1866/2401*T^5 
        - 2062/2401*T^4 - 282/343*T^3 - 4/49*T^2 + T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^13 + 3*X*Y^12 + 2*X*Y^11 + 6*X*Y^9 + 6*X*Y^8 + 4*X*Y^7 + 
        2*X*Y^6 + 2*X*Y^5 + X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 6*X*Y + 2*X + 4*Y^30 + 
        6*Y^29 + 3*Y^27 + 2*Y^26 + 5*Y^25 + 6*Y^24 + 3*Y^23 + 6*Y^22 + 6*Y^21 + 
        2*Y^20 + 2*Y^19 + 5*Y^18 + 3*Y^17 + 6*Y^16 + 4*Y^15 + 6*Y^14 + Y^12 + 3*Y^10
        + 5*Y^9 + 2*Y^8 + Y^7 + 4*Y^6 + 5*Y^5 + 2*Y^4 + 5*Y^3 + 6*Y^2 + 5*Y + 1,
    T^56 + 8/7*T^55 - 9/7*T^54 - 624/343*T^53 - 339/2401*T^52 + 57/343*T^51 + 
        2190/2401*T^50 + 3999/2401*T^49 - 963/2401*T^48 - 4929/2401*T^47 - 
        1511/2401*T^46 + 1936/2401*T^45 + 787/2401*T^44 + 828/2401*T^43 + 
        2956/2401*T^42 - 383/2401*T^41 - 3525/2401*T^40 + 499/2401*T^39 + 
        1247/2401*T^38 - 2288/2401*T^37 - 76/343*T^36 + 3036/2401*T^35 + 
        1345/2401*T^34 - 1954/2401*T^33 - 158/2401*T^32 + 824/2401*T^31 - 
        2832/2401*T^30 - 291/2401*T^29 + 4227/2401*T^28 - 291/2401*T^27 - 
        2832/2401*T^26 + 824/2401*T^25 - 158/2401*T^24 - 1954/2401*T^23 + 
        1345/2401*T^22 + 3036/2401*T^21 - 76/343*T^20 - 2288/2401*T^19 + 
        1247/2401*T^18 + 499/2401*T^17 - 3525/2401*T^16 - 383/2401*T^15 + 
        2956/2401*T^14 + 828/2401*T^13 + 787/2401*T^12 + 1936/2401*T^11 - 
        1511/2401*T^10 - 4929/2401*T^9 - 963/2401*T^8 + 3999/2401*T^7 + 
        2190/2401*T^6 + 57/343*T^5 - 339/2401*T^4 - 624/343*T^3 - 9/7*T^2 + 8/7*T + 
        1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 6*X*Y^11 + X*Y^9 + X*Y^8 + 4*X*Y^7 + 
        X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 3*X*Y^2 + 4*X*Y + 3*X + 4*Y^30 + Y^28 
        + 5*Y^27 + 4*Y^26 + 2*Y^25 + 6*Y^24 + 2*Y^22 + 4*Y^20 + 5*Y^19 + 6*Y^18 + 
        4*Y^17 + 6*Y^15 + Y^14 + 5*Y^13 + 2*Y^12 + 2*Y^11 + 5*Y^10 + 5*Y^9 + 2*Y^8 +
        6*Y^7 + 6*Y^6 + 5*Y^5 + 2*Y^4 + 2*Y^3 + 4*Y^2 + 4*Y + 6,
    T^56 + 10/7*T^55 + 10/7*T^54 + 202/343*T^53 - 400/2401*T^52 - 1292/2401*T^51 - 
        274/2401*T^50 + 61/2401*T^49 + 164/2401*T^48 - 44/2401*T^47 - 237/2401*T^46 
        - 516/2401*T^45 - 1574/2401*T^44 - 2556/2401*T^43 - 2335/2401*T^42 - 
        487/2401*T^41 + 774/2401*T^40 + 1215/2401*T^39 + 640/2401*T^38 + 
        1011/2401*T^37 + 1698/2401*T^36 + 1787/2401*T^35 + 16/2401*T^34 - 
        1346/2401*T^33 - 1409/2401*T^32 + 1/49*T^31 + 652/2401*T^30 + 753/2401*T^29 
        + 50/343*T^28 + 753/2401*T^27 + 652/2401*T^26 + 1/49*T^25 - 1409/2401*T^24 -
        1346/2401*T^23 + 16/2401*T^22 + 1787/2401*T^21 + 1698/2401*T^20 + 
        1011/2401*T^19 + 640/2401*T^18 + 1215/2401*T^17 + 774/2401*T^16 - 
        487/2401*T^15 - 2335/2401*T^14 - 2556/2401*T^13 - 1574/2401*T^12 - 
        516/2401*T^11 - 237/2401*T^10 - 44/2401*T^9 + 164/2401*T^8 + 61/2401*T^7 - 
        274/2401*T^6 - 1292/2401*T^5 - 400/2401*T^4 + 202/343*T^3 + 10/7*T^2 + 
        10/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + X*Y^10 + 4*X*Y^9 + 
        5*X*Y^8 + 2*X*Y^7 + 2*X*Y^6 + 4*X*Y^3 + 6*X*Y^2 + 2*X*Y + 5*X + 4*Y^30 + 
        2*Y^29 + 6*Y^27 + 5*Y^26 + Y^25 + Y^24 + 5*Y^22 + 3*Y^20 + 3*Y^19 + 6*Y^18 +
        4*Y^16 + 6*Y^14 + 2*Y^13 + 6*Y^11 + 4*Y^10 + 5*Y^9 + 3*Y^7 + 5*Y^6 + 2*Y^5 +
        3*Y^4 + 4*Y^3 + 5*Y^2 + 5*Y,
    -T^56 - 6/7*T^55 - 2/49*T^54 - 58/343*T^53 - 69/343*T^52 - 75/343*T^51 - 
        486/2401*T^50 + 800/2401*T^49 + 1369/2401*T^48 - 57/343*T^47 - 942/2401*T^46
        - 1089/2401*T^45 - 1217/2401*T^44 + 341/2401*T^43 + 1304/2401*T^42 + 
        829/2401*T^41 - 292/2401*T^40 + 47/343*T^39 + 1438/2401*T^38 + 514/2401*T^37
        + 199/2401*T^36 - 654/2401*T^35 - 1055/2401*T^34 + 117/2401*T^33 + 
        312/2401*T^32 - 215/2401*T^31 - 258/2401*T^30 - 148/2401*T^29 + 
        148/2401*T^27 + 258/2401*T^26 + 215/2401*T^25 - 312/2401*T^24 - 
        117/2401*T^23 + 1055/2401*T^22 + 654/2401*T^21 - 199/2401*T^20 - 
        514/2401*T^19 - 1438/2401*T^18 - 47/343*T^17 + 292/2401*T^16 - 829/2401*T^15
        - 1304/2401*T^14 - 341/2401*T^13 + 1217/2401*T^12 + 1089/2401*T^11 + 
        942/2401*T^10 + 57/343*T^9 - 1369/2401*T^8 - 800/2401*T^7 + 486/2401*T^6 + 
        75/343*T^5 + 69/343*T^4 + 58/343*T^3 + 2/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^12 + X*Y^11 + 2*X*Y^10 + 2*X*Y^8 + 4*X*Y^7 + X*Y^6 + 
        5*X*Y^5 + 4*X*Y^4 + 4*X*Y^2 + 2*X*Y + 5*X + 2*Y^30 + 3*Y^29 + 2*Y^28 + Y^27 
        + 3*Y^26 + 4*Y^25 + 2*Y^24 + 5*Y^22 + Y^21 + 6*Y^20 + 2*Y^18 + 6*Y^16 + Y^14
        + 6*Y^13 + 3*Y^12 + 6*Y^11 + 6*Y^10 + 4*Y^9 + 4*Y^8 + 3*Y^7 + 6*Y^6 + 6*Y^5 
        + 3*Y^4 + Y^3 + 5*Y^2 + 3*Y + 2,
    -T^56 - 3/7*T^55 + 58/49*T^54 + 212/343*T^53 - 1657/2401*T^52 - 85/2401*T^51 + 
        1779/2401*T^50 + 96/2401*T^49 - 1084/2401*T^48 - 271/2401*T^47 - 61/343*T^46
        - 163/343*T^45 + 1705/2401*T^44 + 1700/2401*T^43 - 1255/2401*T^42 + 
        597/2401*T^41 + 1501/2401*T^40 - 1709/2401*T^39 - 1598/2401*T^38 + 
        1020/2401*T^37 - 396/2401*T^36 - 995/2401*T^35 + 1702/2401*T^34 + 
        873/2401*T^33 - 1672/2401*T^32 - 829/2401*T^31 + 827/2401*T^30 + 44/343*T^29
        - 44/343*T^27 - 827/2401*T^26 + 829/2401*T^25 + 1672/2401*T^24 - 
        873/2401*T^23 - 1702/2401*T^22 + 995/2401*T^21 + 396/2401*T^20 - 
        1020/2401*T^19 + 1598/2401*T^18 + 1709/2401*T^17 - 1501/2401*T^16 - 
        597/2401*T^15 + 1255/2401*T^14 - 1700/2401*T^13 - 1705/2401*T^12 + 
        163/343*T^11 + 61/343*T^10 + 271/2401*T^9 + 1084/2401*T^8 - 96/2401*T^7 - 
        1779/2401*T^6 + 85/2401*T^5 + 1657/2401*T^4 - 212/343*T^3 - 58/49*T^2 + 
        3/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 6*X*Y^14 + 6*X*Y^13 + 5*X*Y^11 + 6*X*Y^10 + X*Y^9 + 5*X*Y^8 + 
        4*X*Y^7 + X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 2*X*Y + 5*X + 
        6*Y^30 + 3*Y^29 + 3*Y^28 + 4*Y^27 + Y^26 + Y^25 + 4*Y^24 + 3*Y^23 + Y^22 + 
        3*Y^20 + 4*Y^19 + Y^18 + 6*Y^17 + 4*Y^15 + Y^14 + 6*Y^13 + 3*Y^11 + 3*Y^9 + 
        3*Y^8 + 6*Y^7 + 4*Y^5 + Y^4 + 4*Y^3 + 2*Y^2 + 2*Y + 5,
    T^56 - 1/7*T^55 + 26/49*T^54 + 47/343*T^53 + 2768/2401*T^52 - 453/2401*T^51 + 
        895/2401*T^50 - 1047/2401*T^49 + 3084/2401*T^48 - 593/2401*T^47 + 
        41/2401*T^46 - 1271/2401*T^45 + 2553/2401*T^44 - 542/2401*T^43 + 
        268/2401*T^42 - 2019/2401*T^41 + 2134/2401*T^40 - 30/343*T^39 + 
        131/2401*T^38 - 1654/2401*T^37 + 737/2401*T^36 - 912/2401*T^35 + 
        423/2401*T^34 - 2077/2401*T^33 - 253/2401*T^32 - 580/2401*T^31 + 50/343*T^30
        - 1487/2401*T^29 + 206/2401*T^28 - 1487/2401*T^27 + 50/343*T^26 - 
        580/2401*T^25 - 253/2401*T^24 - 2077/2401*T^23 + 423/2401*T^22 - 
        912/2401*T^21 + 737/2401*T^20 - 1654/2401*T^19 + 131/2401*T^18 - 30/343*T^17
        + 2134/2401*T^16 - 2019/2401*T^15 + 268/2401*T^14 - 542/2401*T^13 + 
        2553/2401*T^12 - 1271/2401*T^11 + 41/2401*T^10 - 593/2401*T^9 + 
        3084/2401*T^8 - 1047/2401*T^7 + 895/2401*T^6 - 453/2401*T^5 + 2768/2401*T^4 
        + 47/343*T^3 + 26/49*T^2 - 1/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 5*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 5*X*Y^9 + 6*X*Y^8 +
        5*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 5*X*Y^2 + 5*X*Y + 3*X + 
        5*Y^30 + 6*Y^29 + 4*Y^28 + 2*Y^27 + 5*Y^26 + 3*Y^25 + 2*Y^24 + 3*Y^23 + 
        6*Y^22 + 3*Y^21 + 6*Y^20 + 2*Y^19 + 4*Y^18 + 6*Y^17 + 3*Y^16 + Y^15 + 3*Y^14
        + 5*Y^13 + 3*Y^12 + 3*Y^11 + 2*Y^10 + 5*Y^9 + 5*Y^8 + 3*Y^7 + 3*Y^4 + Y^2 + 
        2*Y + 6,
    T^56 + 1/7*T^55 - 80/49*T^54 - 95/343*T^53 + 2417/2401*T^52 + 121/343*T^51 - 
        178/2401*T^50 - 1269/2401*T^49 - 2120/2401*T^48 + 216/2401*T^47 + 
        3099/2401*T^46 + 452/2401*T^45 - 2092/2401*T^44 - 2115/2401*T^43 + 
        32/2401*T^42 + 3148/2401*T^41 + 1522/2401*T^40 - 1566/2401*T^39 - 
        1999/2401*T^38 + 9/343*T^37 + 1194/2401*T^36 + 600/2401*T^35 + 64/2401*T^34 
        - 1299/2401*T^33 - 556/2401*T^32 + 122/343*T^31 + 1138/2401*T^30 + 
        25/343*T^29 - 1536/2401*T^28 + 25/343*T^27 + 1138/2401*T^26 + 122/343*T^25 -
        556/2401*T^24 - 1299/2401*T^23 + 64/2401*T^22 + 600/2401*T^21 + 
        1194/2401*T^20 + 9/343*T^19 - 1999/2401*T^18 - 1566/2401*T^17 + 
        1522/2401*T^16 + 3148/2401*T^15 + 32/2401*T^14 - 2115/2401*T^13 - 
        2092/2401*T^12 + 452/2401*T^11 + 3099/2401*T^10 + 216/2401*T^9 - 
        2120/2401*T^8 - 1269/2401*T^7 - 178/2401*T^6 + 121/343*T^5 + 2417/2401*T^4 -
        95/343*T^3 - 80/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 4*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 
        + 4*X*Y^8 + 2*X*Y^7 + 6*X*Y^5 + 4*X*Y^4 + 3*X*Y^3 + 3*X*Y^2 + 4*X*Y + X + 
        3*Y^30 + 6*Y^29 + 5*Y^28 + 4*Y^27 + 3*Y^26 + 2*Y^25 + Y^24 + 5*Y^23 + Y^22 +
        2*Y^21 + 3*Y^19 + 6*Y^18 + 6*Y^17 + 4*Y^16 + 4*Y^15 + 6*Y^14 + 4*Y^11 + 
        3*Y^10 + 6*Y^9 + 4*Y^8 + 6*Y^7 + Y^6 + 5*Y^5 + 4*Y^4 + 4*Y^3 + 6*Y^2 + 2*Y +
        1,
    T^56 - 10/7*T^55 - 23/49*T^54 + 470/343*T^53 - 1207/2401*T^52 + 461/2401*T^51 - 
        1667/2401*T^50 + 5/7*T^49 + 647/2401*T^48 - 1975/2401*T^47 + 838/2401*T^46 -
        788/2401*T^45 + 1902/2401*T^44 + 306/2401*T^43 - 2649/2401*T^42 + 
        396/2401*T^41 + 1217/2401*T^40 + 696/2401*T^39 - 1070/2401*T^38 - 
        393/2401*T^37 - 96/343*T^36 + 892/2401*T^35 + 1535/2401*T^34 - 
        1230/2401*T^33 - 130/343*T^32 + 773/2401*T^31 + 78/343*T^30 - 713/2401*T^29 
        + 433/2401*T^28 - 713/2401*T^27 + 78/343*T^26 + 773/2401*T^25 - 130/343*T^24
        - 1230/2401*T^23 + 1535/2401*T^22 + 892/2401*T^21 - 96/343*T^20 - 
        393/2401*T^19 - 1070/2401*T^18 + 696/2401*T^17 + 1217/2401*T^16 + 
        396/2401*T^15 - 2649/2401*T^14 + 306/2401*T^13 + 1902/2401*T^12 - 
        788/2401*T^11 + 838/2401*T^10 - 1975/2401*T^9 + 647/2401*T^8 + 5/7*T^7 - 
        1667/2401*T^6 + 461/2401*T^5 - 1207/2401*T^4 + 470/343*T^3 - 23/49*T^2 - 
        10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 2*X*Y^12 + 4*X*Y^10 + 4*X*Y^8 + 4*X*Y^7 +
        4*X*Y^5 + X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 4*X*Y + 4*X + 2*Y^30 + 6*Y^29 + Y^28 +
        3*Y^27 + 5*Y^26 + Y^25 + 2*Y^24 + 2*Y^23 + 4*Y^22 + 2*Y^21 + 6*Y^20 + 6*Y^18
        + 6*Y^16 + 2*Y^15 + 3*Y^14 + 6*Y^13 + 2*Y^12 + 2*Y^10 + 4*Y^9 + 4*Y^8 + 
        5*Y^5 + 6*Y^4 + 5*Y^3 + 3*Y^2 + 3,
    -T^56 + 2/7*T^55 + 13/7*T^54 - 69/343*T^53 - 524/343*T^52 + 547/2401*T^51 + 
        2542/2401*T^50 - 2729/2401*T^49 - 2836/2401*T^48 + 4196/2401*T^47 + 
        585/343*T^46 - 3613/2401*T^45 - 4195/2401*T^44 + 3439/2401*T^43 + 
        2923/2401*T^42 - 4724/2401*T^41 - 1907/2401*T^40 + 6057/2401*T^39 + 
        571/2401*T^38 - 5514/2401*T^37 - 65/343*T^36 + 4339/2401*T^35 + 
        1254/2401*T^34 - 3737/2401*T^33 - 89/343*T^32 + 3501/2401*T^31 + 
        535/2401*T^30 - 13/7*T^29 + 13/7*T^27 - 535/2401*T^26 - 3501/2401*T^25 + 
        89/343*T^24 + 3737/2401*T^23 - 1254/2401*T^22 - 4339/2401*T^21 + 65/343*T^20
        + 5514/2401*T^19 - 571/2401*T^18 - 6057/2401*T^17 + 1907/2401*T^16 + 
        4724/2401*T^15 - 2923/2401*T^14 - 3439/2401*T^13 + 4195/2401*T^12 + 
        3613/2401*T^11 - 585/343*T^10 - 4196/2401*T^9 + 2836/2401*T^8 + 
        2729/2401*T^7 - 2542/2401*T^6 - 547/2401*T^5 + 524/343*T^4 + 69/343*T^3 - 
        13/7*T^2 - 2/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 
        + 6*X*Y^8 + 5*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + X*Y^2 + 5*X*Y 
        + 4*X + 2*Y^30 + 5*Y^29 + Y^28 + 6*Y^26 + 4*Y^25 + 3*Y^24 + 3*Y^23 + 2*Y^22 
        + 6*Y^21 + 6*Y^20 + 3*Y^19 + 3*Y^18 + 3*Y^17 + 5*Y^16 + 3*Y^14 + 5*Y^13 + 
        6*Y^12 + 6*Y^9 + 5*Y^8 + 5*Y^7 + 2*Y^6 + Y^5 + 4*Y^4 + 4*Y^3 + 4*Y,
    -T^56 + T^55 + 5/7*T^54 - 575/343*T^53 + 328/343*T^52 + 404/2401*T^51 - 
        2225/2401*T^50 + 2313/2401*T^49 - 1695/2401*T^48 + 906/2401*T^47 + 
        676/2401*T^46 - 2549/2401*T^45 + 2391/2401*T^44 - 439/2401*T^43 - 
        1049/2401*T^42 + 920/2401*T^41 - 1277/2401*T^40 + 2641/2401*T^39 - 
        31/49*T^38 - 2294/2401*T^37 + 3798/2401*T^36 - 2160/2401*T^35 - 
        433/2401*T^34 + 2145/2401*T^33 - 1634/2401*T^32 + 117/343*T^31 - 
        94/2401*T^30 - 363/2401*T^29 + 363/2401*T^27 + 94/2401*T^26 - 117/343*T^25 +
        1634/2401*T^24 - 2145/2401*T^23 + 433/2401*T^22 + 2160/2401*T^21 - 
        3798/2401*T^20 + 2294/2401*T^19 + 31/49*T^18 - 2641/2401*T^17 + 
        1277/2401*T^16 - 920/2401*T^15 + 1049/2401*T^14 + 439/2401*T^13 - 
        2391/2401*T^12 + 2549/2401*T^11 - 676/2401*T^10 - 906/2401*T^9 + 
        1695/2401*T^8 - 2313/2401*T^7 + 2225/2401*T^6 - 404/2401*T^5 - 328/343*T^4 +
        575/343*T^3 - 5/7*T^2 - T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 
        2*X*Y^8 + 5*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 5*X*Y^4 + 6*X*Y^3 + 2*X*Y^2 + 2*X*Y 
        + 5*Y^30 + 6*Y^29 + 2*Y^28 + 4*Y^26 + 2*Y^25 + 3*Y^24 + Y^23 + 4*Y^21 + 
        5*Y^20 + 2*Y^19 + 6*Y^18 + 6*Y^17 + 3*Y^15 + 3*Y^14 + 6*Y^13 + 2*Y^12 + Y^11
        + 5*Y^10 + Y^9 + 4*Y^8 + 5*Y^7 + 5*Y^6 + 6*Y^5 + 5*Y^3 + 6*Y^2 + 2*Y + 4,
    T^56 - 6/7*T^55 + 264/343*T^53 - 550/2401*T^52 - 332/2401*T^51 + 1892/2401*T^50 
        - 2314/2401*T^49 + 1335/2401*T^48 + 1324/2401*T^47 - 733/2401*T^46 - 
        629/2401*T^45 + 369/2401*T^44 + 264/2401*T^43 + 205/2401*T^42 - 
        400/2401*T^41 - 6/2401*T^40 + 475/2401*T^39 - 275/2401*T^38 + 116/2401*T^37 
        - 1049/2401*T^36 + 211/2401*T^35 - 46/343*T^34 + 542/2401*T^33 - 
        1401/2401*T^32 + 687/2401*T^31 - 804/2401*T^30 + 66/343*T^29 - 
        1291/2401*T^28 + 66/343*T^27 - 804/2401*T^26 + 687/2401*T^25 - 
        1401/2401*T^24 + 542/2401*T^23 - 46/343*T^22 + 211/2401*T^21 - 
        1049/2401*T^20 + 116/2401*T^19 - 275/2401*T^18 + 475/2401*T^17 - 6/2401*T^16
        - 400/2401*T^15 + 205/2401*T^14 + 264/2401*T^13 + 369/2401*T^12 - 
        629/2401*T^11 - 733/2401*T^10 + 1324/2401*T^9 + 1335/2401*T^8 - 
        2314/2401*T^7 + 1892/2401*T^6 - 332/2401*T^5 - 550/2401*T^4 + 264/343*T^3 - 
        6/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + X*Y^9 + 4*X*Y^8 + 
        2*X*Y^6 + 2*X*Y^5 + 2*X*Y^4 + 6*X*Y^3 + X*Y^2 + 4*X*Y + 6*X + 2*Y^30 + 
        4*Y^26 + 3*Y^25 + 3*Y^24 + 3*Y^23 + 2*Y^20 + 2*Y^19 + Y^18 + 5*Y^15 + 3*Y^14
        + 6*Y^13 + Y^12 + 2*Y^11 + Y^10 + Y^8 + 2*Y^6 + 2*Y^5 + 5*Y^4 + 3*Y^3 + 
        3*Y^2 + 5,
    -T^56 - 23/49*T^54 - 96/343*T^53 - 92/2401*T^52 - 446/2401*T^51 + 1623/2401*T^50
        - 3126/2401*T^49 + 1378/2401*T^48 - 306/2401*T^47 - 62/343*T^46 + 
        209/2401*T^45 - 2143/2401*T^44 + 3070/2401*T^43 - 3875/2401*T^42 + 
        167/2401*T^41 + 386/2401*T^40 - 1812/2401*T^39 + 774/2401*T^38 - 
        3793/2401*T^37 + 3589/2401*T^36 - 2839/2401*T^35 - 1311/2401*T^34 + 
        2336/2401*T^33 - 2019/2401*T^32 + 2347/2401*T^31 - 474/343*T^30 + 
        2987/2401*T^29 - 2987/2401*T^27 + 474/343*T^26 - 2347/2401*T^25 + 
        2019/2401*T^24 - 2336/2401*T^23 + 1311/2401*T^22 + 2839/2401*T^21 - 
        3589/2401*T^20 + 3793/2401*T^19 - 774/2401*T^18 + 1812/2401*T^17 - 
        386/2401*T^16 - 167/2401*T^15 + 3875/2401*T^14 - 3070/2401*T^13 + 
        2143/2401*T^12 - 209/2401*T^11 + 62/343*T^10 + 306/2401*T^9 - 1378/2401*T^8 
        + 3126/2401*T^7 - 1623/2401*T^6 + 446/2401*T^5 + 92/2401*T^4 + 96/343*T^3 + 
        23/49*T^2 + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + X*Y^13 + 4*X*Y^12 + 4*X*Y^11 + 4*X*Y^9 + 4*X*Y^8 + 
        X*Y^7 + 4*X*Y^6 + 3*X*Y^4 + 6*X*Y^2 + 4*X*Y + 5*X + 6*Y^30 + 4*Y^29 + Y^28 +
        3*Y^27 + 3*Y^26 + 5*Y^25 + 3*Y^24 + 4*Y^23 + 5*Y^22 + 3*Y^21 + 4*Y^18 + Y^17
        + 2*Y^15 + 5*Y^14 + 6*Y^13 + 6*Y^12 + 4*Y^11 + 4*Y^10 + 6*Y^9 + Y^8 + 4*Y^7 
        + 2*Y^6 + 6*Y^5 + 2*Y^4 + 3*Y^3 + 2*Y + 6,
    T^56 - 3/7*T^55 - 13/49*T^54 + 395/343*T^53 - 3505/2401*T^52 - 478/2401*T^51 + 
        3217/2401*T^50 - 2573/2401*T^49 + 1332/2401*T^48 + 129/343*T^47 - 
        80/343*T^46 + 1108/2401*T^45 - 2222/2401*T^44 + 1132/2401*T^43 - 
        724/2401*T^42 - 468/343*T^41 + 2196/2401*T^40 - 15/49*T^39 + 321/2401*T^38 +
        360/343*T^37 - 646/2401*T^36 + 677/2401*T^35 - 1429/2401*T^34 - 
        1914/2401*T^33 + 870/2401*T^32 - 1658/2401*T^31 + 827/2401*T^30 + 
        1798/2401*T^29 - 1038/2401*T^28 + 1798/2401*T^27 + 827/2401*T^26 - 
        1658/2401*T^25 + 870/2401*T^24 - 1914/2401*T^23 - 1429/2401*T^22 + 
        677/2401*T^21 - 646/2401*T^20 + 360/343*T^19 + 321/2401*T^18 - 15/49*T^17 + 
        2196/2401*T^16 - 468/343*T^15 - 724/2401*T^14 + 1132/2401*T^13 - 
        2222/2401*T^12 + 1108/2401*T^11 - 80/343*T^10 + 129/343*T^9 + 1332/2401*T^8 
        - 2573/2401*T^7 + 3217/2401*T^6 - 478/2401*T^5 - 3505/2401*T^4 + 395/343*T^3
        - 13/49*T^2 - 3/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + X*Y^11 + X*Y^10 + 3*X*Y^9 + 
        3*X*Y^7 + 5*X*Y^6 + 6*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 4*X*Y^2 + 5*X + 6*Y^30 + 
        Y^29 + Y^28 + 4*Y^27 + 6*Y^26 + 6*Y^25 + 2*Y^24 + 4*Y^23 + 2*Y^22 + 6*Y^21 +
        4*Y^20 + Y^19 + 6*Y^18 + 4*Y^17 + 5*Y^16 + 6*Y^15 + 2*Y^14 + 3*Y^13 + Y^12 +
        3*Y^11 + 2*Y^9 + 3*Y^8 + 5*Y^7 + 2*Y^6 + 3*Y^5 + 6*Y^4 + 2*Y^2 + 4*Y + 2,
    T^56 - 5/7*T^55 - 30/49*T^54 + 235/343*T^53 - 837/2401*T^52 + 440/2401*T^51 - 
        45/2401*T^50 + 401/2401*T^49 + 327/343*T^48 - 2134/2401*T^47 - 790/2401*T^46
        + 473/2401*T^45 - 513/2401*T^44 + 1550/2401*T^43 - 1520/2401*T^42 + 
        905/2401*T^41 + 2025/2401*T^40 - 2846/2401*T^39 - 808/2401*T^38 - 
        9/2401*T^37 + 960/2401*T^36 + 1656/2401*T^35 - 1770/2401*T^34 - 15/2401*T^33
        + 710/2401*T^32 - 782/2401*T^31 - 1349/2401*T^30 + 32/2401*T^29 + 
        2236/2401*T^28 + 32/2401*T^27 - 1349/2401*T^26 - 782/2401*T^25 + 
        710/2401*T^24 - 15/2401*T^23 - 1770/2401*T^22 + 1656/2401*T^21 + 
        960/2401*T^20 - 9/2401*T^19 - 808/2401*T^18 - 2846/2401*T^17 + 
        2025/2401*T^16 + 905/2401*T^15 - 1520/2401*T^14 + 1550/2401*T^13 - 
        513/2401*T^12 + 473/2401*T^11 - 790/2401*T^10 - 2134/2401*T^9 + 327/343*T^8 
        + 401/2401*T^7 - 45/2401*T^6 + 440/2401*T^5 - 837/2401*T^4 + 235/343*T^3 - 
        30/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 3*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 5*X*Y^8 +
        5*X*Y^7 + 4*X*Y^6 + X*Y^5 + X*Y^3 + 4*X*Y^2 + 5*X*Y + 6*X + Y^30 + 6*Y^29 + 
        2*Y^28 + 2*Y^27 + 5*Y^26 + 5*Y^25 + 6*Y^23 + 6*Y^22 + Y^21 + 2*Y^20 + 5*Y^19
        + 4*Y^17 + 5*Y^16 + 3*Y^15 + 6*Y^14 + 6*Y^13 + 3*Y^12 + 2*Y^11 + 4*Y^10 + 
        6*Y^9 + 6*Y^8 + 2*Y^7 + Y^5 + Y^4 + Y^3 + 5*Y + 5,
    T^56 + 5/7*T^55 - 50/49*T^54 - 395/343*T^53 + 1975/2401*T^52 + 2944/2401*T^51 - 
        3469/2401*T^50 - 5175/2401*T^49 + 1954/2401*T^48 + 523/343*T^47 - 
        265/343*T^46 - 358/343*T^45 + 1963/2401*T^44 + 325/343*T^43 - 1459/2401*T^42
        - 793/2401*T^41 + 257/343*T^40 + 739/2401*T^39 - 2/2401*T^38 + 
        1139/2401*T^37 - 8/343*T^36 - 1986/2401*T^35 - 652/2401*T^34 + 
        1845/2401*T^33 - 54/2401*T^32 - 2398/2401*T^31 - 1338/2401*T^30 + 
        1217/2401*T^29 + 2671/2401*T^28 + 1217/2401*T^27 - 1338/2401*T^26 - 
        2398/2401*T^25 - 54/2401*T^24 + 1845/2401*T^23 - 652/2401*T^22 - 
        1986/2401*T^21 - 8/343*T^20 + 1139/2401*T^19 - 2/2401*T^18 + 739/2401*T^17 +
        257/343*T^16 - 793/2401*T^15 - 1459/2401*T^14 + 325/343*T^13 + 
        1963/2401*T^12 - 358/343*T^11 - 265/343*T^10 + 523/343*T^9 + 1954/2401*T^8 -
        5175/2401*T^7 - 3469/2401*T^6 + 2944/2401*T^5 + 1975/2401*T^4 - 395/343*T^3 
        - 50/49*T^2 + 5/7*T + 1
*], [*
    X^3 + 2*X*Y^14 + 3*X*Y^12 + 3*X*Y^11 + 2*X*Y^10 + 2*X*Y^8 + 4*X*Y^7 + 3*X*Y^6 + 
        4*X*Y^4 + X*Y^2 + 2*X*Y + 5*X + 3*Y^30 + 6*Y^29 + 6*Y^28 + 6*Y^27 + 4*Y^25 +
        6*Y^24 + 3*Y^23 + Y^22 + 5*Y^21 + Y^20 + 3*Y^18 + Y^17 + 6*Y^16 + 3*Y^15 + 
        5*Y^14 + 5*Y^13 + 6*Y^12 + 4*Y^11 + 4*Y^10 + 2*Y^9 + 4*Y^8 + Y^7 + 3*Y^6 + 
        Y^4 + 5*Y^3 + 2*Y^2 + 6*Y,
    T^56 - 5/7*T^55 - 39/49*T^54 + 424/343*T^53 - 205/343*T^52 - 1250/2401*T^51 + 
        2036/2401*T^50 - 1325/2401*T^49 - 1578/2401*T^48 + 409/343*T^47 + 2/343*T^46
        - 1949/2401*T^45 + 537/2401*T^44 + 179/2401*T^43 + 131/2401*T^42 + 
        131/343*T^41 - 1598/2401*T^40 + 345/2401*T^39 + 1102/2401*T^38 - 5/2401*T^37
        - 107/2401*T^36 - 527/2401*T^35 + 24/343*T^34 - 108/343*T^33 + 221/343*T^32 
        - 418/2401*T^31 - 1892/2401*T^30 + 790/2401*T^29 + 1420/2401*T^28 + 
        790/2401*T^27 - 1892/2401*T^26 - 418/2401*T^25 + 221/343*T^24 - 108/343*T^23
        + 24/343*T^22 - 527/2401*T^21 - 107/2401*T^20 - 5/2401*T^19 + 1102/2401*T^18
        + 345/2401*T^17 - 1598/2401*T^16 + 131/343*T^15 + 131/2401*T^14 + 
        179/2401*T^13 + 537/2401*T^12 - 1949/2401*T^11 + 2/343*T^10 + 409/343*T^9 - 
        1578/2401*T^8 - 1325/2401*T^7 + 2036/2401*T^6 - 1250/2401*T^5 - 205/343*T^4 
        + 424/343*T^3 - 39/49*T^2 - 5/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^13 + 3*X*Y^12 + 4*X*Y^9 + 4*X*Y^8 + 2*X*Y^7 + X*Y^6 + 
        6*X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 5*X*Y + 6*X + 5*Y^30 + 4*Y^29 + 
        2*Y^27 + 2*Y^26 + 5*Y^24 + 3*Y^23 + Y^22 + Y^21 + 4*Y^20 + 4*Y^19 + Y^18 + 
        5*Y^15 + 3*Y^14 + 4*Y^13 + 4*Y^12 + 4*Y^10 + 5*Y^9 + Y^8 + 5*Y^7 + 3*Y^6 + 
        Y^5 + 5*Y^4 + 6*Y^3 + 2*Y^2 + 4*Y,
    T^56 + 3/7*T^55 - 54/49*T^54 - 235/343*T^53 + 1041/2401*T^52 + 852/2401*T^51 - 
        227/343*T^50 - 680/2401*T^49 + 313/343*T^48 + 55/2401*T^47 - 1653/2401*T^46 
        + 776/2401*T^45 + 249/2401*T^44 - 295/2401*T^43 - 373/2401*T^42 - 
        366/2401*T^41 + 24/49*T^40 + 53/343*T^39 - 90/2401*T^38 - 246/2401*T^37 - 
        1138/2401*T^36 + 1135/2401*T^35 + 338/2401*T^34 - 1264/2401*T^33 + 
        568/2401*T^32 - 8/49*T^31 - 144/2401*T^30 + 870/2401*T^29 + 27/2401*T^28 + 
        870/2401*T^27 - 144/2401*T^26 - 8/49*T^25 + 568/2401*T^24 - 1264/2401*T^23 +
        338/2401*T^22 + 1135/2401*T^21 - 1138/2401*T^20 - 246/2401*T^19 - 
        90/2401*T^18 + 53/343*T^17 + 24/49*T^16 - 366/2401*T^15 - 373/2401*T^14 - 
        295/2401*T^13 + 249/2401*T^12 + 776/2401*T^11 - 1653/2401*T^10 + 55/2401*T^9
        + 313/343*T^8 - 680/2401*T^7 - 227/343*T^6 + 852/2401*T^5 + 1041/2401*T^4 - 
        235/343*T^3 - 54/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + 5*X*Y^13 + X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 
        X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + 4*X*Y^3 + X*Y^2 + 3*X + 3*Y^30 + 2*Y^29 + 5*Y^28
        + 3*Y^27 + 3*Y^26 + 2*Y^25 + 3*Y^24 + 5*Y^23 + 3*Y^22 + Y^21 + 4*Y^20 + 
        6*Y^19 + Y^18 + 5*Y^16 + 3*Y^15 + 3*Y^14 + 2*Y^13 + 6*Y^12 + Y^11 + Y^10 + 
        Y^9 + Y^8 + 6*Y^7 + 3*Y^6 + Y^5 + Y^4 + 5*Y^2 + 4,
    -T^56 + 4/7*T^55 - 3/7*T^54 + 319/343*T^53 - 18/49*T^52 - 2269/2401*T^51 + 
        1507/2401*T^50 - 155/2401*T^49 - 131/2401*T^48 + 663/2401*T^47 - 
        3075/2401*T^46 + 2715/2401*T^45 - 1642/2401*T^44 - 545/2401*T^43 + 
        254/2401*T^42 + 86/343*T^41 - 81/2401*T^40 + 1548/2401*T^39 - 3163/2401*T^38
        + 1457/2401*T^37 - 601/2401*T^36 - 830/2401*T^35 + 1040/2401*T^34 - 
        1230/2401*T^33 - 19/2401*T^32 + 1668/2401*T^31 - 1852/2401*T^30 + 
        1138/2401*T^29 - 1138/2401*T^27 + 1852/2401*T^26 - 1668/2401*T^25 + 
        19/2401*T^24 + 1230/2401*T^23 - 1040/2401*T^22 + 830/2401*T^21 + 
        601/2401*T^20 - 1457/2401*T^19 + 3163/2401*T^18 - 1548/2401*T^17 + 
        81/2401*T^16 - 86/343*T^15 - 254/2401*T^14 + 545/2401*T^13 + 1642/2401*T^12 
        - 2715/2401*T^11 + 3075/2401*T^10 - 663/2401*T^9 + 131/2401*T^8 + 
        155/2401*T^7 - 1507/2401*T^6 + 2269/2401*T^5 + 18/49*T^4 - 319/343*T^3 + 
        3/7*T^2 - 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 
        3*X*Y^8 + X*Y^7 + X*Y^6 + 5*X*Y^4 + 2*X*Y^2 + X*Y + 3*X + 2*Y^30 + Y^29 + 
        5*Y^28 + 3*Y^27 + 4*Y^26 + 4*Y^25 + 4*Y^24 + 6*Y^23 + 6*Y^21 + 2*Y^19 + 
        4*Y^18 + 6*Y^17 + 6*Y^16 + 2*Y^15 + 3*Y^14 + 2*Y^13 + 2*Y^12 + 5*Y^11 + 
        5*Y^10 + 3*Y^9 + 3*Y^8 + 2*Y^7 + Y^6 + 4*Y^5 + Y^4 + Y^3 + 4*Y + 4,
    -T^56 + 12/7*T^55 - 52/49*T^54 + 284/343*T^53 - 2285/2401*T^52 + 1707/2401*T^51 
        - 1271/2401*T^50 + 178/343*T^49 - 529/2401*T^48 - 1354/2401*T^47 + 
        3146/2401*T^46 - 3330/2401*T^45 + 246/343*T^44 - 1378/2401*T^43 + 
        389/343*T^42 - 3694/2401*T^41 + 2769/2401*T^40 - 159/2401*T^39 - 
        521/2401*T^38 - 321/2401*T^37 + 520/2401*T^36 - 111/343*T^35 + 
        1179/2401*T^34 - 579/2401*T^33 - 919/2401*T^32 + 975/2401*T^31 + 
        939/2401*T^30 - 1655/2401*T^29 + 1655/2401*T^27 - 939/2401*T^26 - 
        975/2401*T^25 + 919/2401*T^24 + 579/2401*T^23 - 1179/2401*T^22 + 
        111/343*T^21 - 520/2401*T^20 + 321/2401*T^19 + 521/2401*T^18 + 159/2401*T^17
        - 2769/2401*T^16 + 3694/2401*T^15 - 389/343*T^14 + 1378/2401*T^13 - 
        246/343*T^12 + 3330/2401*T^11 - 3146/2401*T^10 + 1354/2401*T^9 + 
        529/2401*T^8 - 178/343*T^7 + 1271/2401*T^6 - 1707/2401*T^5 + 2285/2401*T^4 -
        284/343*T^3 + 52/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 3*X*Y^14 + 3*X*Y^13 + 6*X*Y^11 + 4*X*Y^10 + 3*X*Y^9 + 4*X*Y^8 +
        X*Y^7 + X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + X*Y^3 + 6*X*Y^2 + 6*X*Y + 3*Y^30 + 
        5*Y^29 + 6*Y^27 + 5*Y^26 + Y^24 + 5*Y^22 + 2*Y^21 + 4*Y^20 + 2*Y^19 + 6*Y^18
        + 5*Y^17 + 4*Y^15 + 2*Y^13 + 3*Y^12 + 4*Y^11 + 5*Y^10 + 4*Y^9 + 6*Y^8 + Y^7 
        + 3*Y^6 + 3*Y^5 + 3*Y^4 + 5*Y^2 + 4*Y + 4,
    T^56 - 4/7*T^55 - 65/49*T^54 + 281/343*T^53 + 648/2401*T^52 + 88/2401*T^51 - 
        1373/2401*T^50 - 187/2401*T^49 + 1369/2401*T^48 - 9/49*T^47 + 1219/2401*T^46
        - 253/2401*T^45 - 107/343*T^44 - 2/7*T^43 - 103/2401*T^42 + 666/2401*T^41 + 
        724/2401*T^40 - 932/2401*T^39 - 419/2401*T^38 + 213/343*T^37 - 55/343*T^36 +
        234/2401*T^35 - 1273/2401*T^34 + 423/2401*T^33 + 334/2401*T^32 - 
        970/2401*T^31 - 249/2401*T^30 - 78/2401*T^29 + 2207/2401*T^28 - 78/2401*T^27
        - 249/2401*T^26 - 970/2401*T^25 + 334/2401*T^24 + 423/2401*T^23 - 
        1273/2401*T^22 + 234/2401*T^21 - 55/343*T^20 + 213/343*T^19 - 419/2401*T^18 
        - 932/2401*T^17 + 724/2401*T^16 + 666/2401*T^15 - 103/2401*T^14 - 2/7*T^13 -
        107/343*T^12 - 253/2401*T^11 + 1219/2401*T^10 - 9/49*T^9 + 1369/2401*T^8 - 
        187/2401*T^7 - 1373/2401*T^6 + 88/2401*T^5 + 648/2401*T^4 + 281/343*T^3 - 
        65/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^13 + 2*X*Y^11 + 2*X*Y^10 + X*Y^9 + 3*X*Y^8 + 5*X*Y^7 + 
        6*X*Y^6 + 2*X*Y^5 + 4*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + 4*X*Y + 2*X + 4*Y^30 + 
        Y^29 + Y^28 + 5*Y^27 + Y^25 + 5*Y^24 + Y^23 + 6*Y^22 + Y^21 + 5*Y^20 + 
        3*Y^19 + Y^18 + 4*Y^17 + 3*Y^16 + Y^14 + 6*Y^13 + 2*Y^12 + 6*Y^11 + Y^10 + 
        2*Y^9 + 5*Y^8 + 4*Y^5 + 2*Y^4 + Y^3 + 5*Y^2 + 3*Y + 3,
    T^56 + 11/7*T^55 + 101/49*T^54 + 425/343*T^53 - 61/2401*T^52 - 52/49*T^51 - 
        480/343*T^50 - 2663/2401*T^49 - 53/343*T^48 + 628/2401*T^47 + 583/2401*T^46 
        - 205/343*T^45 - 3635/2401*T^44 - 5596/2401*T^43 - 3814/2401*T^42 - 
        599/2401*T^41 + 2689/2401*T^40 + 4257/2401*T^39 + 291/343*T^38 - 
        241/2401*T^37 - 2925/2401*T^36 - 450/343*T^35 - 173/343*T^34 + 
        2096/2401*T^33 + 3842/2401*T^32 + 4304/2401*T^31 + 1116/2401*T^30 - 
        1639/2401*T^29 - 3715/2401*T^28 - 1639/2401*T^27 + 1116/2401*T^26 + 
        4304/2401*T^25 + 3842/2401*T^24 + 2096/2401*T^23 - 173/343*T^22 - 
        450/343*T^21 - 2925/2401*T^20 - 241/2401*T^19 + 291/343*T^18 + 
        4257/2401*T^17 + 2689/2401*T^16 - 599/2401*T^15 - 3814/2401*T^14 - 
        5596/2401*T^13 - 3635/2401*T^12 - 205/343*T^11 + 583/2401*T^10 + 
        628/2401*T^9 - 53/343*T^8 - 2663/2401*T^7 - 480/343*T^6 - 52/49*T^5 - 
        61/2401*T^4 + 425/343*T^3 + 101/49*T^2 + 11/7*T + 1
*], [*
    X^3 + X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + X*Y^11 + 3*X*Y^10 + X*Y^9 + 
        X*Y^8 + 5*X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + X + 2*Y^30
        + 2*Y^29 + 5*Y^28 + 5*Y^26 + 5*Y^25 + 2*Y^24 + 3*Y^23 + 2*Y^22 + 5*Y^21 + 
        2*Y^19 + Y^18 + 6*Y^17 + 2*Y^16 + 3*Y^14 + Y^12 + 4*Y^11 + 3*Y^9 + 6*Y^8 + 
        Y^7 + Y^5 + 4*Y^4 + 4*Y^3 + Y^2 + 4*Y,
    T^56 + 2/7*T^55 + 11/49*T^54 - 36/343*T^53 - 50/343*T^52 + 1541/2401*T^51 - 
        970/2401*T^50 + 913/2401*T^49 - 61/343*T^48 - 1625/2401*T^47 + 309/2401*T^46
        + 349/2401*T^45 + 2385/2401*T^44 - 904/2401*T^43 - 1719/2401*T^42 - 
        618/2401*T^41 + 211/2401*T^40 + 820/2401*T^39 - 320/2401*T^38 - 
        237/2401*T^37 - 1661/2401*T^36 - 578/2401*T^35 + 911/2401*T^34 + 
        1180/2401*T^33 + 118/2401*T^32 - 1746/2401*T^31 - 606/2401*T^30 + 
        975/2401*T^29 + 225/343*T^28 + 975/2401*T^27 - 606/2401*T^26 - 
        1746/2401*T^25 + 118/2401*T^24 + 1180/2401*T^23 + 911/2401*T^22 - 
        578/2401*T^21 - 1661/2401*T^20 - 237/2401*T^19 - 320/2401*T^18 + 
        820/2401*T^17 + 211/2401*T^16 - 618/2401*T^15 - 1719/2401*T^14 - 
        904/2401*T^13 + 2385/2401*T^12 + 349/2401*T^11 + 309/2401*T^10 - 
        1625/2401*T^9 - 61/343*T^8 + 913/2401*T^7 - 970/2401*T^6 + 1541/2401*T^5 - 
        50/343*T^4 - 36/343*T^3 + 11/49*T^2 + 2/7*T + 1
*], [*
    X^3 + X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + 6*X*Y^10 + 5*X*Y^8 + 3*X*Y^6 + 6*X*Y^5 + 
        6*X*Y^4 + 4*X*Y^3 + 4*X*Y^2 + 6*X + 2*Y^30 + 4*Y^29 + 4*Y^28 + 2*Y^27 + 
        2*Y^26 + 5*Y^25 + 3*Y^24 + Y^23 + 4*Y^22 + 3*Y^21 + 2*Y^20 + 5*Y^19 + 4*Y^17
        + Y^16 + 3*Y^14 + Y^13 + 6*Y^12 + 5*Y^10 + 2*Y^9 + 6*Y^8 + 5*Y^6 + 4*Y^5 + 
        5*Y + 1,
    -T^56 + 19/49*T^54 + 223/343*T^53 - 1342/2401*T^52 - 605/2401*T^51 + 
        386/2401*T^50 - 26/2401*T^49 + 50/343*T^48 + 79/343*T^47 + 1786/2401*T^46 - 
        101/343*T^45 - 396/2401*T^44 - 19/343*T^43 + 1105/2401*T^42 - 799/2401*T^41 
        - 647/2401*T^40 + 843/2401*T^39 + 309/2401*T^38 - 48/343*T^37 - 206/343*T^36
        + 1382/2401*T^35 - 554/2401*T^34 - 9/49*T^33 - 164/2401*T^32 + 
        2146/2401*T^31 - 464/2401*T^30 - 2066/2401*T^29 + 2066/2401*T^27 + 
        464/2401*T^26 - 2146/2401*T^25 + 164/2401*T^24 + 9/49*T^23 + 554/2401*T^22 -
        1382/2401*T^21 + 206/343*T^20 + 48/343*T^19 - 309/2401*T^18 - 843/2401*T^17 
        + 647/2401*T^16 + 799/2401*T^15 - 1105/2401*T^14 + 19/343*T^13 + 
        396/2401*T^12 + 101/343*T^11 - 1786/2401*T^10 - 79/343*T^9 - 50/343*T^8 + 
        26/2401*T^7 - 386/2401*T^6 + 605/2401*T^5 + 1342/2401*T^4 - 223/343*T^3 - 
        19/49*T^2 + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + 5*X*Y^13 + 6*X*Y^11 + 2*X*Y^10 + 2*X*Y^8 + 2*X*Y^7 + 
        6*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + X*Y^3 + X*Y^2 + 3*X*Y + 2*X + 3*Y^30 + 2*Y^29 
        + 4*Y^28 + 4*Y^26 + 3*Y^25 + 6*Y^22 + 5*Y^21 + 5*Y^20 + Y^19 + 4*Y^18 + Y^17
        + Y^16 + Y^15 + 3*Y^14 + 2*Y^13 + 4*Y^12 + 5*Y^11 + 5*Y^10 + 2*Y^9 + 3*Y^8 +
        3*Y^7 + Y^5 + Y^4 + 2*Y^3 + 4*Y + 4,
    T^56 - 10/7*T^55 + 53/49*T^54 - 341/343*T^53 + 1359/2401*T^52 - 1515/2401*T^51 +
        618/2401*T^50 + 1138/2401*T^49 - 750/2401*T^48 - 480/2401*T^47 + 
        1115/2401*T^46 + 104/343*T^45 - 1606/2401*T^44 + 1175/2401*T^43 - 
        158/2401*T^42 - 1151/2401*T^41 - 662/2401*T^40 + 922/2401*T^39 - 48/343*T^38
        + 1619/2401*T^37 - 2844/2401*T^36 + 3652/2401*T^35 - 2005/2401*T^34 - 
        438/2401*T^33 + 1089/2401*T^32 - 131/2401*T^31 - 579/2401*T^30 + 
        250/2401*T^29 - 318/2401*T^28 + 250/2401*T^27 - 579/2401*T^26 - 
        131/2401*T^25 + 1089/2401*T^24 - 438/2401*T^23 - 2005/2401*T^22 + 
        3652/2401*T^21 - 2844/2401*T^20 + 1619/2401*T^19 - 48/343*T^18 + 
        922/2401*T^17 - 662/2401*T^16 - 1151/2401*T^15 - 158/2401*T^14 + 
        1175/2401*T^13 - 1606/2401*T^12 + 104/343*T^11 + 1115/2401*T^10 - 
        480/2401*T^9 - 750/2401*T^8 + 1138/2401*T^7 + 618/2401*T^6 - 1515/2401*T^5 +
        1359/2401*T^4 - 341/343*T^3 + 53/49*T^2 - 10/7*T + 1
*], [*
    X^3 + X*Y^15 + 5*X*Y^14 + 6*X*Y^12 + 4*X*Y^11 + 2*X*Y^10 + 3*X*Y^8 + 4*X*Y^6 + 
        3*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + X*Y^2 + 3*X + Y^30 + 4*Y^29 + Y^28 + 5*Y^27 + 
        4*Y^26 + 6*Y^25 + 4*Y^24 + Y^23 + 3*Y^22 + 5*Y^20 + 2*Y^19 + 2*Y^17 + 4*Y^16
        + 5*Y^15 + Y^14 + 4*Y^12 + 4*Y^11 + 3*Y^10 + 4*Y^9 + 5*Y^7 + Y^6 + 6*Y^4 + 
        Y^3 + 5*Y^2 + 6,
    T^56 - 6/7*T^55 + 40/49*T^54 - 121/343*T^53 + 914/2401*T^52 - 2229/2401*T^51 + 
        1098/2401*T^50 - 993/2401*T^49 - 695/2401*T^48 + 1033/2401*T^47 - 
        143/343*T^46 + 279/2401*T^45 - 982/2401*T^44 + 1275/2401*T^43 - 
        787/2401*T^42 + 205/343*T^41 + 557/2401*T^40 + 125/2401*T^39 + 585/2401*T^38
        - 183/2401*T^37 - 740/2401*T^36 - 1046/2401*T^35 - 397/2401*T^34 + 
        549/2401*T^33 - 573/2401*T^32 + 846/2401*T^31 - 872/2401*T^30 + 
        1321/2401*T^29 - 258/343*T^28 + 1321/2401*T^27 - 872/2401*T^26 + 
        846/2401*T^25 - 573/2401*T^24 + 549/2401*T^23 - 397/2401*T^22 - 
        1046/2401*T^21 - 740/2401*T^20 - 183/2401*T^19 + 585/2401*T^18 + 
        125/2401*T^17 + 557/2401*T^16 + 205/343*T^15 - 787/2401*T^14 + 
        1275/2401*T^13 - 982/2401*T^12 + 279/2401*T^11 - 143/343*T^10 + 
        1033/2401*T^9 - 695/2401*T^8 - 993/2401*T^7 + 1098/2401*T^6 - 2229/2401*T^5 
        + 914/2401*T^4 - 121/343*T^3 + 40/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + 3*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + 5*X*Y^8 + 5*X*Y^7 + 
        5*X*Y^6 + 3*X*Y^5 + X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 2*X*Y + 6*X + 4*Y^30 + 
        5*Y^29 + Y^28 + Y^27 + 6*Y^26 + 2*Y^25 + 3*Y^23 + 3*Y^21 + 2*Y^20 + 2*Y^19 +
        5*Y^18 + Y^17 + 3*Y^16 + 2*Y^15 + 2*Y^14 + 5*Y^13 + 4*Y^11 + 6*Y^10 + 3*Y^9 
        + Y^8 + Y^7 + 3*Y^6 + 4*Y^5 + 4*Y^4 + 2*Y^2 + 6*Y,
    T^56 + 11/7*T^55 + 36/49*T^54 + 290/343*T^53 + 1902/2401*T^52 - 143/2401*T^51 - 
        1228/2401*T^50 - 461/343*T^49 - 3925/2401*T^48 - 1763/2401*T^47 - 
        3200/2401*T^46 - 4234/2401*T^45 - 76/343*T^44 + 744/2401*T^43 + 
        949/2401*T^42 + 1698/2401*T^41 + 1650/2401*T^40 + 3032/2401*T^39 + 
        3529/2401*T^38 + 613/2401*T^37 + 465/2401*T^36 + 2516/2401*T^35 + 
        578/2401*T^34 - 614/2401*T^33 - 157/343*T^32 - 1769/2401*T^31 + 
        395/2401*T^30 - 544/2401*T^29 - 3058/2401*T^28 - 544/2401*T^27 + 
        395/2401*T^26 - 1769/2401*T^25 - 157/343*T^24 - 614/2401*T^23 + 
        578/2401*T^22 + 2516/2401*T^21 + 465/2401*T^20 + 613/2401*T^19 + 
        3529/2401*T^18 + 3032/2401*T^17 + 1650/2401*T^16 + 1698/2401*T^15 + 
        949/2401*T^14 + 744/2401*T^13 - 76/343*T^12 - 4234/2401*T^11 - 
        3200/2401*T^10 - 1763/2401*T^9 - 3925/2401*T^8 - 461/343*T^7 - 1228/2401*T^6
        - 143/2401*T^5 + 1902/2401*T^4 + 290/343*T^3 + 36/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + X*Y^13 + 6*X*Y^12 + 2*X*Y^11 + 2*X*Y^9 + 3*X*Y^7 + 
        6*X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + X*Y^2 + 2*X*Y + 5*X + 5*Y^30 + 6*Y^29 + Y^28 +
        Y^27 + Y^26 + 2*Y^24 + 6*Y^22 + 4*Y^21 + 4*Y^20 + 6*Y^19 + 4*Y^18 + Y^17 + 
        2*Y^16 + 6*Y^15 + 6*Y^14 + 4*Y^11 + 5*Y^10 + 2*Y^9 + 4*Y^8 + 5*Y^7 + 6*Y^6 +
        5*Y^5 + 2*Y^4 + 6*Y^3 + 4*Y,
    T^56 + 6/7*T^55 - 26/49*T^54 - 249/343*T^53 + 1860/2401*T^52 + 1802/2401*T^51 - 
        2529/2401*T^50 - 2570/2401*T^49 + 3/7*T^48 + 113/2401*T^47 - 3277/2401*T^46 
        - 1493/2401*T^45 + 526/343*T^44 + 3362/2401*T^43 - 2399/2401*T^42 - 
        1859/2401*T^41 + 3879/2401*T^40 + 2802/2401*T^39 - 3327/2401*T^38 - 
        2084/2401*T^37 + 2538/2401*T^36 - 583/2401*T^35 - 5170/2401*T^34 - 
        1728/2401*T^33 + 3394/2401*T^32 + 192/343*T^31 - 1641/2401*T^30 + 
        883/2401*T^29 + 3176/2401*T^28 + 883/2401*T^27 - 1641/2401*T^26 + 
        192/343*T^25 + 3394/2401*T^24 - 1728/2401*T^23 - 5170/2401*T^22 - 
        583/2401*T^21 + 2538/2401*T^20 - 2084/2401*T^19 - 3327/2401*T^18 + 
        2802/2401*T^17 + 3879/2401*T^16 - 1859/2401*T^15 - 2399/2401*T^14 + 
        3362/2401*T^13 + 526/343*T^12 - 1493/2401*T^11 - 3277/2401*T^10 + 
        113/2401*T^9 + 3/7*T^8 - 2570/2401*T^7 - 2529/2401*T^6 + 1802/2401*T^5 + 
        1860/2401*T^4 - 249/343*T^3 - 26/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 2*X*Y^14 + X*Y^12 + X*Y^11 + 6*X*Y^9 + X*Y^8 + 4*X*Y^7 + 
        3*X*Y^6 + 2*X*Y^5 + 2*X*Y^3 + 6*X*Y^2 + 2*X*Y + 6*X + Y^30 + 3*Y^29 + 6*Y^28
        + 3*Y^27 + 2*Y^26 + 4*Y^25 + 2*Y^22 + 4*Y^20 + Y^19 + 4*Y^18 + 3*Y^16 + 
        4*Y^14 + Y^13 + 5*Y^12 + 5*Y^11 + 6*Y^10 + 6*Y^9 + 3*Y^8 + Y^7 + 2*Y^5 + 
        2*Y^4 + 6*Y^3 + 5*Y^2 + 5*Y + 6,
    T^56 - 6/7*T^55 + 20/49*T^54 - 265/343*T^53 + 1732/2401*T^52 - 757/2401*T^51 + 
        960/2401*T^50 - 1976/2401*T^49 + 207/343*T^48 - 898/2401*T^47 - 6/343*T^46 -
        428/2401*T^45 + 736/2401*T^44 + 187/2401*T^43 + 653/2401*T^42 - 
        1693/2401*T^41 + 500/2401*T^40 + 440/2401*T^39 - 23/343*T^38 + 16/49*T^37 - 
        379/2401*T^36 + 185/2401*T^35 - 697/2401*T^34 + 73/343*T^33 - 282/2401*T^32 
        + 901/2401*T^31 - 317/2401*T^30 - 61/343*T^29 - 673/2401*T^28 - 61/343*T^27 
        - 317/2401*T^26 + 901/2401*T^25 - 282/2401*T^24 + 73/343*T^23 - 
        697/2401*T^22 + 185/2401*T^21 - 379/2401*T^20 + 16/49*T^19 - 23/343*T^18 + 
        440/2401*T^17 + 500/2401*T^16 - 1693/2401*T^15 + 653/2401*T^14 + 
        187/2401*T^13 + 736/2401*T^12 - 428/2401*T^11 - 6/343*T^10 - 898/2401*T^9 + 
        207/343*T^8 - 1976/2401*T^7 + 960/2401*T^6 - 757/2401*T^5 + 1732/2401*T^4 - 
        265/343*T^3 + 20/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 3*X*Y^9 + 6*X*Y^8 + 2*X*Y^7 + 
        X*Y^6 + X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 6*X*Y + 2*Y^30 + 5*Y^29 + 
        3*Y^28 + 6*Y^27 + Y^25 + 3*Y^24 + 3*Y^23 + Y^22 + 4*Y^21 + 4*Y^20 + 2*Y^19 +
        6*Y^18 + 2*Y^15 + 2*Y^14 + 6*Y^13 + 6*Y^12 + 3*Y^11 + 4*Y^10 + Y^9 + 2*Y^8 +
        Y^7 + 5*Y^6 + 3*Y^5 + 2*Y^3 + Y^2 + Y + 4,
    -T^56 - 3/7*T^55 + 30/49*T^54 + 50/49*T^53 + 67/49*T^52 + 536/2401*T^51 - 
        2185/2401*T^50 - 4026/2401*T^49 - 285/343*T^48 + 794/2401*T^47 + 
        276/343*T^46 + 2117/2401*T^45 + 1298/2401*T^44 - 2096/2401*T^43 - 
        2761/2401*T^42 - 660/2401*T^41 + 1895/2401*T^40 + 2602/2401*T^39 + 
        1804/2401*T^38 - 587/2401*T^37 - 3817/2401*T^36 - 1681/2401*T^35 + 
        629/2401*T^34 + 2985/2401*T^33 + 1079/2401*T^32 - 489/2401*T^31 - 
        1825/2401*T^30 - 2848/2401*T^29 + 2848/2401*T^27 + 1825/2401*T^26 + 
        489/2401*T^25 - 1079/2401*T^24 - 2985/2401*T^23 - 629/2401*T^22 + 
        1681/2401*T^21 + 3817/2401*T^20 + 587/2401*T^19 - 1804/2401*T^18 - 
        2602/2401*T^17 - 1895/2401*T^16 + 660/2401*T^15 + 2761/2401*T^14 + 
        2096/2401*T^13 - 1298/2401*T^12 - 2117/2401*T^11 - 276/343*T^10 - 
        794/2401*T^9 + 285/343*T^8 + 4026/2401*T^7 + 2185/2401*T^6 - 536/2401*T^5 - 
        67/49*T^4 - 50/49*T^3 - 30/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^13 + X*Y^12 + 5*X*Y^11 + 3*X*Y^9 + X*Y^7 + 6*X*Y^6 + 
        6*X*Y^5 + X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 5*X*Y + 2*X + Y^30 + 3*Y^29 + 4*Y^28 +
        6*Y^26 + 4*Y^25 + 2*Y^24 + 6*Y^23 + 2*Y^21 + 5*Y^20 + 2*Y^19 + Y^17 + 5*Y^16
        + 6*Y^15 + 5*Y^14 + 4*Y^13 + 6*Y^12 + 3*Y^11 + 2*Y^10 + 3*Y^9 + 6*Y^8 + 
        6*Y^7 + Y^6 + 6*Y^5 + 3*Y^4 + 6*Y^3 + 3*Y,
    T^56 + 1/7*T^55 - 61/49*T^54 - 397/343*T^53 + 573/2401*T^52 + 2208/2401*T^51 + 
        2055/2401*T^50 + 114/343*T^49 - 622/2401*T^48 - 1423/2401*T^47 - 
        1366/2401*T^46 - 142/343*T^45 + 726/2401*T^44 + 1168/2401*T^43 + 
        785/2401*T^42 - 83/2401*T^41 - 503/2401*T^40 - 200/2401*T^39 + 
        1090/2401*T^38 + 1150/2401*T^37 - 1139/2401*T^36 - 3057/2401*T^35 - 
        390/2401*T^34 + 796/2401*T^33 + 1507/2401*T^32 + 2603/2401*T^31 + 
        1258/2401*T^30 - 1682/2401*T^29 - 556/343*T^28 - 1682/2401*T^27 + 
        1258/2401*T^26 + 2603/2401*T^25 + 1507/2401*T^24 + 796/2401*T^23 - 
        390/2401*T^22 - 3057/2401*T^21 - 1139/2401*T^20 + 1150/2401*T^19 + 
        1090/2401*T^18 - 200/2401*T^17 - 503/2401*T^16 - 83/2401*T^15 + 
        785/2401*T^14 + 1168/2401*T^13 + 726/2401*T^12 - 142/343*T^11 - 
        1366/2401*T^10 - 1423/2401*T^9 - 622/2401*T^8 + 114/343*T^7 + 2055/2401*T^6 
        + 2208/2401*T^5 + 573/2401*T^4 - 397/343*T^3 - 61/49*T^2 + 1/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^14 + 4*X*Y^13 + 6*X*Y^11 + 2*X*Y^10 + X*Y^9 + 4*X*Y^8 + 
        3*X*Y^7 + 5*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 4*X*Y + 3*X + 
        5*Y^30 + Y^29 + Y^28 + 2*Y^27 + 3*Y^26 + 2*Y^24 + 5*Y^23 + Y^22 + 3*Y^21 + 
        3*Y^19 + 6*Y^18 + 3*Y^17 + 4*Y^16 + 5*Y^15 + 6*Y^14 + 5*Y^13 + 2*Y^12 + Y^11
        + 4*Y^10 + Y^9 + 4*Y^8 + Y^7 + 3*Y^6 + 6*Y^4 + 5*Y^2 + 3*Y + 5,
    T^56 + 3/7*T^55 - 19/49*T^54 + 71/343*T^53 - 719/2401*T^52 + 30/2401*T^51 + 
        1146/2401*T^50 - 22/343*T^49 + 1004/2401*T^48 + 482/2401*T^47 + 
        365/2401*T^46 + 318/2401*T^45 - 1270/2401*T^44 + 177/343*T^43 + 125/343*T^42
        + 418/2401*T^41 + 1031/2401*T^40 - 428/2401*T^39 + 1026/2401*T^38 + 
        1338/2401*T^37 - 1080/2401*T^36 - 573/2401*T^35 + 97/2401*T^34 + 
        1321/2401*T^33 + 2344/2401*T^32 + 557/2401*T^31 + 488/2401*T^30 + 
        376/2401*T^29 - 533/2401*T^28 + 376/2401*T^27 + 488/2401*T^26 + 
        557/2401*T^25 + 2344/2401*T^24 + 1321/2401*T^23 + 97/2401*T^22 - 
        573/2401*T^21 - 1080/2401*T^20 + 1338/2401*T^19 + 1026/2401*T^18 - 
        428/2401*T^17 + 1031/2401*T^16 + 418/2401*T^15 + 125/343*T^14 + 177/343*T^13
        - 1270/2401*T^12 + 318/2401*T^11 + 365/2401*T^10 + 482/2401*T^9 + 
        1004/2401*T^8 - 22/343*T^7 + 1146/2401*T^6 + 30/2401*T^5 - 719/2401*T^4 + 
        71/343*T^3 - 19/49*T^2 + 3/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 3*X*Y^11 + X*Y^10 + 2*X*Y^9 + 
        2*X*Y^8 + X*Y^7 + 5*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + X*Y^2 + 6*X*Y + 
        5*X + Y^30 + 3*Y^28 + 4*Y^27 + 3*Y^26 + 5*Y^25 + 2*Y^24 + 2*Y^23 + 4*Y^22 + 
        5*Y^21 + 4*Y^19 + Y^18 + 4*Y^17 + 3*Y^15 + 3*Y^14 + Y^13 + Y^12 + 4*Y^11 + 
        Y^10 + 2*Y^9 + 3*Y^8 + 5*Y^7 + 5*Y^6 + 3*Y^5 + 4*Y^4 + 3*Y^3 + 4*Y^2 + 2,
    -T^56 + 6/7*T^55 + 23/49*T^54 - 179/343*T^53 - 654/2401*T^52 + 883/2401*T^51 + 
        772/2401*T^50 - 1524/2401*T^49 + 446/2401*T^48 + 683/2401*T^47 + 
        424/2401*T^46 - 2306/2401*T^45 + 1647/2401*T^44 + 636/2401*T^43 - 
        1625/2401*T^42 - 31/2401*T^41 + 673/2401*T^40 - 164/2401*T^39 - 
        386/2401*T^38 + 842/2401*T^37 - 446/2401*T^36 - 206/2401*T^35 - 
        226/2401*T^34 + 734/2401*T^33 + 137/2401*T^32 - 736/2401*T^31 + 
        351/2401*T^30 + 670/2401*T^29 - 670/2401*T^27 - 351/2401*T^26 + 
        736/2401*T^25 - 137/2401*T^24 - 734/2401*T^23 + 226/2401*T^22 + 
        206/2401*T^21 + 446/2401*T^20 - 842/2401*T^19 + 386/2401*T^18 + 
        164/2401*T^17 - 673/2401*T^16 + 31/2401*T^15 + 1625/2401*T^14 - 
        636/2401*T^13 - 1647/2401*T^12 + 2306/2401*T^11 - 424/2401*T^10 - 
        683/2401*T^9 - 446/2401*T^8 + 1524/2401*T^7 - 772/2401*T^6 - 883/2401*T^5 + 
        654/2401*T^4 + 179/343*T^3 - 23/49*T^2 - 6/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 5*X*Y^6 +
        3*X*Y^5 + 5*X*Y^3 + 2*X*Y + 3*Y^30 + 5*Y^29 + 6*Y^26 + 2*Y^25 + 6*Y^24 + 
        4*Y^23 + 4*Y^22 + 6*Y^21 + Y^20 + 3*Y^19 + 5*Y^17 + 2*Y^16 + 3*Y^15 + 3*Y^14
        + 4*Y^13 + 3*Y^12 + 3*Y^11 + 3*Y^10 + 6*Y^9 + 6*Y^8 + 4*Y^7 + 5*Y^6 + 2*Y^4 
        + 3*Y^3 + 5*Y^2 + 6*Y + 6,
    -T^56 + T^55 - 34/49*T^54 - 48/343*T^53 + 152/343*T^52 - 1741/2401*T^51 + 
        366/2401*T^50 + 1495/2401*T^49 - 533/343*T^48 + 3839/2401*T^47 - 
        2843/2401*T^46 - 60/343*T^45 + 370/343*T^44 - 501/343*T^43 + 1623/2401*T^42 
        + 589/2401*T^41 - 2658/2401*T^40 + 3662/2401*T^39 - 2120/2401*T^38 - 
        676/2401*T^37 + 2507/2401*T^36 - 443/343*T^35 + 2533/2401*T^34 - 
        578/2401*T^33 - 816/2401*T^32 + 1794/2401*T^31 - 1530/2401*T^30 + 
        1094/2401*T^29 - 1094/2401*T^27 + 1530/2401*T^26 - 1794/2401*T^25 + 
        816/2401*T^24 + 578/2401*T^23 - 2533/2401*T^22 + 443/343*T^21 - 
        2507/2401*T^20 + 676/2401*T^19 + 2120/2401*T^18 - 3662/2401*T^17 + 
        2658/2401*T^16 - 589/2401*T^15 - 1623/2401*T^14 + 501/343*T^13 - 
        370/343*T^12 + 60/343*T^11 + 2843/2401*T^10 - 3839/2401*T^9 + 533/343*T^8 - 
        1495/2401*T^7 - 366/2401*T^6 + 1741/2401*T^5 - 152/343*T^4 + 48/343*T^3 + 
        34/49*T^2 - T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^14 + 6*X*Y^12 + 2*X*Y^11 + 6*X*Y^9 + 3*X*Y^6 + 4*X*Y^5 + 
        6*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 6*X*Y + 2*X + 2*Y^30 + 6*Y^29 + 6*Y^28 + 
        5*Y^27 + 4*Y^26 + 3*Y^25 + 3*Y^23 + 6*Y^22 + 5*Y^21 + 4*Y^20 + 2*Y^19 + 
        2*Y^18 + 4*Y^16 + 3*Y^15 + 5*Y^14 + 4*Y^13 + Y^12 + 3*Y^11 + 3*Y^10 + 6*Y^9 
        + 3*Y^8 + 6*Y^7 + 5*Y^6 + Y^5 + 5*Y^3 + 2*Y^2 + 2*Y + 1,
    -T^56 - 4/7*T^55 - 3/49*T^54 - 68/343*T^53 + 731/2401*T^52 + 166/2401*T^51 + 
        1226/2401*T^50 + 1342/2401*T^49 + 17/2401*T^48 - 526/2401*T^47 - 
        1196/2401*T^46 + 571/2401*T^45 - 36/2401*T^44 - 1238/2401*T^43 + 32/343*T^42
        - 681/2401*T^41 + 4/49*T^40 - 1074/2401*T^39 - 1346/2401*T^38 + 1/49*T^37 - 
        425/2401*T^36 + 591/2401*T^35 - 73/2401*T^34 - 16/343*T^33 + 190/343*T^32 + 
        705/2401*T^31 + 128/343*T^30 - 5/2401*T^29 + 5/2401*T^27 - 128/343*T^26 - 
        705/2401*T^25 - 190/343*T^24 + 16/343*T^23 + 73/2401*T^22 - 591/2401*T^21 + 
        425/2401*T^20 - 1/49*T^19 + 1346/2401*T^18 + 1074/2401*T^17 - 4/49*T^16 + 
        681/2401*T^15 - 32/343*T^14 + 1238/2401*T^13 + 36/2401*T^12 - 571/2401*T^11 
        + 1196/2401*T^10 + 526/2401*T^9 - 17/2401*T^8 - 1342/2401*T^7 - 
        1226/2401*T^6 - 166/2401*T^5 - 731/2401*T^4 + 68/343*T^3 + 3/49*T^2 + 4/7*T 
        + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 5*X*Y^13 + X*Y^12 + 2*X*Y^11 + X*Y^10 + 5*X*Y^9 + 
        2*X*Y^7 + X*Y^6 + 4*X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + X*Y^2 + 4*X*Y + 5*X + 3*Y^30
        + 6*Y^29 + 2*Y^28 + 2*Y^26 + 4*Y^25 + 5*Y^24 + 2*Y^23 + 2*Y^22 + 2*Y^21 + 
        6*Y^19 + 5*Y^18 + 5*Y^17 + 4*Y^16 + 5*Y^15 + 3*Y^14 + 2*Y^13 + 4*Y^12 + 
        4*Y^11 + Y^10 + 3*Y^9 + Y^8 + 4*Y^7 + 5*Y^6 + 6*Y^5 + 5*Y^4 + Y^3 + 3*Y^2 + 
        Y + 4,
    T^56 - 8/7*T^55 + 1/7*T^54 + 55/49*T^53 - 675/2401*T^52 - 246/343*T^51 + 
        1583/2401*T^50 + 513/2401*T^49 - 1040/2401*T^48 - 622/2401*T^47 + 
        1177/2401*T^46 - 766/2401*T^45 + 1643/2401*T^44 - 2453/2401*T^43 + 
        696/2401*T^42 + 2371/2401*T^41 - 376/343*T^40 - 288/2401*T^39 + 
        1871/2401*T^38 - 394/2401*T^37 - 1256/2401*T^36 - 3/7*T^35 + 1709/2401*T^34 
        + 456/2401*T^33 - 167/343*T^32 - 1983/2401*T^31 + 2993/2401*T^30 + 
        1642/2401*T^29 - 4615/2401*T^28 + 1642/2401*T^27 + 2993/2401*T^26 - 
        1983/2401*T^25 - 167/343*T^24 + 456/2401*T^23 + 1709/2401*T^22 - 3/7*T^21 - 
        1256/2401*T^20 - 394/2401*T^19 + 1871/2401*T^18 - 288/2401*T^17 - 
        376/343*T^16 + 2371/2401*T^15 + 696/2401*T^14 - 2453/2401*T^13 + 
        1643/2401*T^12 - 766/2401*T^11 + 1177/2401*T^10 - 622/2401*T^9 - 
        1040/2401*T^8 + 513/2401*T^7 + 1583/2401*T^6 - 246/343*T^5 - 675/2401*T^4 + 
        55/49*T^3 + 1/7*T^2 - 8/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + X*Y^14 + X*Y^13 + 4*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 
        5*X*Y^8 + 4*X*Y^7 + 5*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 5*X*Y 
        + 6*X + 2*Y^30 + 3*Y^29 + 2*Y^28 + 3*Y^27 + 2*Y^26 + 4*Y^25 + 6*Y^24 + 
        5*Y^23 + 4*Y^22 + Y^21 + 3*Y^20 + 5*Y^19 + 6*Y^18 + 5*Y^16 + 6*Y^15 + 2*Y^14
        + 5*Y^13 + Y^12 + Y^11 + 3*Y^10 + 5*Y^8 + 6*Y^7 + 4*Y^5 + Y^4 + 6*Y^3 + 
        2*Y^2 + Y + 2,
    T^56 + 3/7*T^55 - 113/49*T^54 - 229/343*T^53 + 1158/343*T^52 - 97/2401*T^51 - 
        9281/2401*T^50 + 2717/2401*T^49 + 8486/2401*T^48 - 4190/2401*T^47 - 
        5694/2401*T^46 + 4560/2401*T^45 + 2063/2401*T^44 - 2962/2401*T^43 + 
        2116/2401*T^42 + 1552/2401*T^41 - 5746/2401*T^40 - 1135/2401*T^39 + 
        6627/2401*T^38 - 129/2401*T^37 - 6675/2401*T^36 + 1382/2401*T^35 + 
        6136/2401*T^34 - 1712/2401*T^33 - 4078/2401*T^32 + 1753/2401*T^31 + 
        2477/2401*T^30 - 1065/2401*T^29 - 2377/2401*T^28 - 1065/2401*T^27 + 
        2477/2401*T^26 + 1753/2401*T^25 - 4078/2401*T^24 - 1712/2401*T^23 + 
        6136/2401*T^22 + 1382/2401*T^21 - 6675/2401*T^20 - 129/2401*T^19 + 
        6627/2401*T^18 - 1135/2401*T^17 - 5746/2401*T^16 + 1552/2401*T^15 + 
        2116/2401*T^14 - 2962/2401*T^13 + 2063/2401*T^12 + 4560/2401*T^11 - 
        5694/2401*T^10 - 4190/2401*T^9 + 8486/2401*T^8 + 2717/2401*T^7 - 
        9281/2401*T^6 - 97/2401*T^5 + 1158/343*T^4 - 229/343*T^3 - 113/49*T^2 + 
        3/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 6*X*Y^14 + X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + X*Y^9 + 3*X*Y^8 + 
        2*X*Y^7 + X*Y^6 + 6*X*Y^5 + 2*X*Y^4 + 3*X*Y^2 + 4*X + 2*Y^30 + Y^29 + 3*Y^28
        + 6*Y^27 + 6*Y^26 + 3*Y^24 + 2*Y^23 + 5*Y^22 + Y^21 + 3*Y^20 + 6*Y^19 + 
        4*Y^18 + 2*Y^17 + 3*Y^16 + 6*Y^15 + 3*Y^14 + 5*Y^13 + 6*Y^12 + 2*Y^11 + Y^10
        + Y^9 + 2*Y^8 + Y^7 + 5*Y^6 + 3*Y^5 + Y^4 + 6*Y^3 + Y^2 + Y + 1,
    -T^56 + 5/7*T^55 + 46/49*T^54 + 109/343*T^53 - 1716/2401*T^52 - 1632/2401*T^51 -
        46/2401*T^50 - 1375/2401*T^49 + 2395/2401*T^48 + 1721/2401*T^47 + 
        407/2401*T^46 - 1027/2401*T^45 - 2550/2401*T^44 + 599/2401*T^43 + 
        454/2401*T^42 - 59/2401*T^41 + 668/2401*T^40 + 1049/2401*T^39 + 
        1143/2401*T^38 - 3749/2401*T^37 - 22/343*T^36 + 1102/2401*T^35 + 
        1277/2401*T^34 + 41/2401*T^33 - 1052/2401*T^32 + 864/2401*T^31 - 
        948/2401*T^30 - 120/343*T^29 + 120/343*T^27 + 948/2401*T^26 - 864/2401*T^25 
        + 1052/2401*T^24 - 41/2401*T^23 - 1277/2401*T^22 - 1102/2401*T^21 + 
        22/343*T^20 + 3749/2401*T^19 - 1143/2401*T^18 - 1049/2401*T^17 - 
        668/2401*T^16 + 59/2401*T^15 - 454/2401*T^14 - 599/2401*T^13 + 
        2550/2401*T^12 + 1027/2401*T^11 - 407/2401*T^10 - 1721/2401*T^9 - 
        2395/2401*T^8 + 1375/2401*T^7 + 46/2401*T^6 + 1632/2401*T^5 + 1716/2401*T^4 
        - 109/343*T^3 - 46/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 5*X*Y^14 + X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + X*Y^8 + 4*X*Y^6 + 2*X*Y^5 + 
        2*X*Y^4 + 6*X*Y^3 + 4*X*Y^2 + 5*X*Y + 5*X + 5*Y^30 + 5*Y^29 + 4*Y^28 + 
        4*Y^27 + 5*Y^25 + 5*Y^24 + 2*Y^23 + Y^21 + 5*Y^20 + 6*Y^19 + 3*Y^17 + Y^16 +
        2*Y^15 + 4*Y^14 + 6*Y^12 + 5*Y^11 + 3*Y^10 + Y^9 + 2*Y^8 + Y^7 + 2*Y^6 + 
        5*Y^5 + 4*Y^4 + 4*Y^3 + 4*Y^2 + 3*Y + 4,
    T^56 - 4/7*T^55 - 37/49*T^54 + 96/343*T^53 + 758/2401*T^52 + 564/2401*T^51 - 
        964/2401*T^50 - 150/343*T^49 + 858/2401*T^48 + 1114/2401*T^47 - 268/343*T^46
        + 102/2401*T^45 + 174/343*T^44 - 552/2401*T^43 - 1138/2401*T^42 - 
        46/2401*T^41 + 765/2401*T^40 + 278/343*T^39 - 775/2401*T^38 - 620/2401*T^37 
        + 496/2401*T^36 + 43/2401*T^35 + 515/2401*T^34 + 87/2401*T^33 - 
        479/2401*T^32 - 435/2401*T^31 - 6/49*T^30 - 453/2401*T^29 + 1440/2401*T^28 -
        453/2401*T^27 - 6/49*T^26 - 435/2401*T^25 - 479/2401*T^24 + 87/2401*T^23 + 
        515/2401*T^22 + 43/2401*T^21 + 496/2401*T^20 - 620/2401*T^19 - 775/2401*T^18
        + 278/343*T^17 + 765/2401*T^16 - 46/2401*T^15 - 1138/2401*T^14 - 
        552/2401*T^13 + 174/343*T^12 + 102/2401*T^11 - 268/343*T^10 + 1114/2401*T^9 
        + 858/2401*T^8 - 150/343*T^7 - 964/2401*T^6 + 564/2401*T^5 + 758/2401*T^4 + 
        96/343*T^3 - 37/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 3*X*Y^11 + 2*X*Y^10 + 5*X*Y^9 + X*Y^8 + 
        4*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 3*X*Y^2 + 5*X*Y + X + 
        3*Y^30 + 6*Y^29 + 3*Y^28 + Y^27 + 6*Y^25 + 5*Y^24 + 2*Y^23 + 2*Y^22 + 6*Y^21
        + 2*Y^20 + 3*Y^18 + 3*Y^17 + 5*Y^16 + 4*Y^15 + Y^14 + 3*Y^13 + 3*Y^12 + 
        5*Y^11 + Y^10 + 3*Y^9 + 5*Y^8 + Y^6 + 5*Y^5 + 3*Y^4 + 5*Y^2 + 1,
    T^56 - 1/7*T^55 + 15/49*T^54 - 309/343*T^53 - 344/2401*T^52 - 186/2401*T^51 + 
        1391/2401*T^50 - 940/2401*T^49 - 1961/2401*T^48 - 845/2401*T^47 - 
        1061/2401*T^46 + 2818/2401*T^45 + 160/343*T^44 - 80/2401*T^43 - 
        1773/2401*T^42 + 69/2401*T^41 + 885/2401*T^40 + 2207/2401*T^39 + 
        346/2401*T^38 - 2281/2401*T^37 - 2082/2401*T^36 - 43/2401*T^35 + 
        732/2401*T^34 + 1530/2401*T^33 + 92/2401*T^32 - 2287/2401*T^31 + 
        17/2401*T^30 + 872/2401*T^29 + 2384/2401*T^28 + 872/2401*T^27 + 17/2401*T^26
        - 2287/2401*T^25 + 92/2401*T^24 + 1530/2401*T^23 + 732/2401*T^22 - 
        43/2401*T^21 - 2082/2401*T^20 - 2281/2401*T^19 + 346/2401*T^18 + 
        2207/2401*T^17 + 885/2401*T^16 + 69/2401*T^15 - 1773/2401*T^14 - 
        80/2401*T^13 + 160/343*T^12 + 2818/2401*T^11 - 1061/2401*T^10 - 845/2401*T^9
        - 1961/2401*T^8 - 940/2401*T^7 + 1391/2401*T^6 - 186/2401*T^5 - 344/2401*T^4
        - 309/343*T^3 + 15/49*T^2 - 1/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 2*X*Y^9 + 
        X*Y^8 + 5*X*Y^7 + 5*X*Y^5 + 2*X*Y^4 + 2*X*Y^3 + 6*X*Y^2 + 2*X*Y + 2*X + 
        2*Y^30 + 5*Y^29 + 2*Y^28 + 3*Y^27 + 6*Y^26 + 3*Y^25 + 6*Y^24 + 2*Y^23 + 
        2*Y^22 + 3*Y^21 + 6*Y^20 + 4*Y^19 + 6*Y^17 + 4*Y^16 + 2*Y^15 + 4*Y^13 + 
        3*Y^12 + Y^11 + 5*Y^10 + Y^8 + 3*Y^7 + 4*Y^6 + 3*Y^5 + 3*Y^4 + 2*Y^3 + 
        6*Y^2,
    T^56 + 3/7*T^55 - 47/49*T^54 - 212/343*T^53 - 1222/2401*T^52 + 60/343*T^51 + 
        2559/2401*T^50 + 1943/2401*T^49 - 361/2401*T^48 - 1598/2401*T^47 - 
        453/2401*T^46 - 755/2401*T^45 + 202/2401*T^44 + 108/343*T^43 + 282/2401*T^42
        + 1258/2401*T^41 + 419/2401*T^40 - 141/2401*T^39 - 345/2401*T^38 - 
        950/2401*T^37 - 36/343*T^36 + 780/2401*T^35 + 508/2401*T^34 - 396/2401*T^33 
        + 607/2401*T^32 + 562/2401*T^31 + 218/2401*T^30 - 46/2401*T^29 - 
        1035/2401*T^28 - 46/2401*T^27 + 218/2401*T^26 + 562/2401*T^25 + 
        607/2401*T^24 - 396/2401*T^23 + 508/2401*T^22 + 780/2401*T^21 - 36/343*T^20 
        - 950/2401*T^19 - 345/2401*T^18 - 141/2401*T^17 + 419/2401*T^16 + 
        1258/2401*T^15 + 282/2401*T^14 + 108/343*T^13 + 202/2401*T^12 - 
        755/2401*T^11 - 453/2401*T^10 - 1598/2401*T^9 - 361/2401*T^8 + 1943/2401*T^7
        + 2559/2401*T^6 + 60/343*T^5 - 1222/2401*T^4 - 212/343*T^3 - 47/49*T^2 + 
        3/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 3*X*Y^11 + 3*X*Y^10 + 5*X*Y^9 
        + 2*X*Y^8 + 5*X*Y^7 + X*Y^6 + 4*X*Y^5 + 3*X*Y^3 + X*Y^2 + 2*Y^30 + 4*Y^29 + 
        4*Y^28 + 3*Y^27 + 3*Y^26 + 4*Y^25 + Y^24 + Y^23 + 6*Y^22 + 6*Y^21 + 2*Y^20 +
        5*Y^19 + 2*Y^18 + Y^17 + 6*Y^16 + 5*Y^15 + 4*Y^14 + 2*Y^13 + 5*Y^12 + 5*Y^10
        + 5*Y^9 + Y^8 + 2*Y^6 + 5*Y^5 + Y^3 + 2*Y^2 + 2*Y + 1,
    -T^56 + 16/7*T^55 - 135/49*T^54 + 466/343*T^53 + 2596/2401*T^52 - 7628/2401*T^51
        + 9705/2401*T^50 - 1231/343*T^49 + 4605/2401*T^48 + 295/2401*T^47 - 
        3540/2401*T^46 + 4400/2401*T^45 - 3877/2401*T^44 + 3105/2401*T^43 - 
        2853/2401*T^42 + 3396/2401*T^41 - 535/343*T^40 + 3657/2401*T^39 - 
        2059/2401*T^38 + 233/2401*T^37 + 1800/2401*T^36 - 3435/2401*T^35 + 
        4740/2401*T^34 - 4938/2401*T^33 + 3952/2401*T^32 - 2864/2401*T^31 + 
        2521/2401*T^30 - 1768/2401*T^29 + 1768/2401*T^27 - 2521/2401*T^26 + 
        2864/2401*T^25 - 3952/2401*T^24 + 4938/2401*T^23 - 4740/2401*T^22 + 
        3435/2401*T^21 - 1800/2401*T^20 - 233/2401*T^19 + 2059/2401*T^18 - 
        3657/2401*T^17 + 535/343*T^16 - 3396/2401*T^15 + 2853/2401*T^14 - 
        3105/2401*T^13 + 3877/2401*T^12 - 4400/2401*T^11 + 3540/2401*T^10 - 
        295/2401*T^9 - 4605/2401*T^8 + 1231/343*T^7 - 9705/2401*T^6 + 7628/2401*T^5 
        - 2596/2401*T^4 - 466/343*T^3 + 135/49*T^2 - 16/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 6*X*Y^12 + 6*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 2*X*Y^8 + 
        4*X*Y^6 + X*Y^5 + 3*X*Y^4 + 4*X*Y^2 + 2*X + 3*Y^30 + 4*Y^29 + 2*Y^28 + 
        3*Y^25 + 5*Y^24 + Y^23 + Y^22 + Y^20 + 6*Y^19 + 2*Y^18 + 2*Y^17 + 6*Y^15 + 
        5*Y^14 + Y^13 + Y^11 + 5*Y^10 + 2*Y^9 + Y^7 + Y^6 + 6*Y^2 + Y,
    T^56 - 10/7*T^55 + 17/49*T^54 + 492/343*T^53 - 3281/2401*T^52 - 152/343*T^51 + 
        2224/2401*T^50 + 96/2401*T^49 - 3200/2401*T^48 + 1007/2401*T^47 + 
        1772/2401*T^46 - 1929/2401*T^45 - 634/2401*T^44 + 2203/2401*T^43 - 
        1051/2401*T^42 + 1222/2401*T^41 - 743/2401*T^40 + 155/2401*T^39 + 
        1891/2401*T^38 - 41/49*T^37 - 58/343*T^36 + 1149/2401*T^35 - 18/2401*T^34 - 
        2491/2401*T^33 + 976/2401*T^32 + 54/49*T^31 - 2873/2401*T^30 - 
        1341/2401*T^29 + 4903/2401*T^28 - 1341/2401*T^27 - 2873/2401*T^26 + 
        54/49*T^25 + 976/2401*T^24 - 2491/2401*T^23 - 18/2401*T^22 + 1149/2401*T^21 
        - 58/343*T^20 - 41/49*T^19 + 1891/2401*T^18 + 155/2401*T^17 - 743/2401*T^16 
        + 1222/2401*T^15 - 1051/2401*T^14 + 2203/2401*T^13 - 634/2401*T^12 - 
        1929/2401*T^11 + 1772/2401*T^10 + 1007/2401*T^9 - 3200/2401*T^8 + 
        96/2401*T^7 + 2224/2401*T^6 - 152/343*T^5 - 3281/2401*T^4 + 492/343*T^3 + 
        17/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^13 + 4*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 +
        3*X*Y^7 + X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 2*X*Y^2 + X*Y + 4*X + 3*Y^30
        + 6*Y^29 + 4*Y^28 + 4*Y^27 + 2*Y^26 + 3*Y^25 + 4*Y^24 + 3*Y^23 + 4*Y^22 + 
        2*Y^18 + 6*Y^17 + 2*Y^16 + 5*Y^15 + 6*Y^14 + 2*Y^13 + 6*Y^12 + 3*Y^9 + Y^8 +
        5*Y^7 + Y^6 + 4*Y^5 + 2*Y^3 + 2*Y,
    -T^56 + 4/7*T^55 + 19/49*T^54 + 544/343*T^53 - 2245/2401*T^52 - 558/343*T^51 - 
        611/2401*T^50 + 1686/2401*T^49 + 3975/2401*T^48 - 648/2401*T^47 - 
        1348/2401*T^46 - 1551/2401*T^45 - 1325/2401*T^44 + 647/2401*T^43 + 
        2958/2401*T^42 + 1276/2401*T^41 - 821/2401*T^40 - 3433/2401*T^39 - 
        1618/2401*T^38 + 2386/2401*T^37 + 771/2401*T^36 + 361/343*T^35 - 34/343*T^34
        - 1880/2401*T^33 - 2452/2401*T^32 - 2647/2401*T^31 + 4874/2401*T^30 + 
        3827/2401*T^29 - 3827/2401*T^27 - 4874/2401*T^26 + 2647/2401*T^25 + 
        2452/2401*T^24 + 1880/2401*T^23 + 34/343*T^22 - 361/343*T^21 - 771/2401*T^20
        - 2386/2401*T^19 + 1618/2401*T^18 + 3433/2401*T^17 + 821/2401*T^16 - 
        1276/2401*T^15 - 2958/2401*T^14 - 647/2401*T^13 + 1325/2401*T^12 + 
        1551/2401*T^11 + 1348/2401*T^10 + 648/2401*T^9 - 3975/2401*T^8 - 
        1686/2401*T^7 + 611/2401*T^6 + 558/343*T^5 + 2245/2401*T^4 - 544/343*T^3 - 
        19/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + X*Y^10 + 4*X*Y^9 + 
        4*X*Y^8 + 2*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 3*X*Y 
        + 3*Y^30 + 3*Y^29 + 4*Y^28 + Y^27 + 2*Y^26 + 4*Y^25 + Y^24 + 3*Y^23 + 2*Y^22
        + 5*Y^20 + 2*Y^19 + 5*Y^18 + 4*Y^17 + 6*Y^16 + 2*Y^13 + 6*Y^11 + 5*Y^9 + 
        3*Y^8 + 3*Y^7 + 5*Y^6 + 3*Y^5 + 6*Y^4 + Y^3 + Y^2 + 6*Y + 1,
    T^56 - 12/7*T^55 + 59/49*T^54 - 268/343*T^53 + 2125/2401*T^52 - 351/343*T^51 + 
        1347/2401*T^50 - 48/343*T^49 - 30/343*T^48 + 235/2401*T^47 + 2039/2401*T^46 
        - 3187/2401*T^45 + 34/49*T^44 + 242/2401*T^43 + 254/2401*T^42 - 
        2034/2401*T^41 + 961/2401*T^40 + 1853/2401*T^39 - 2921/2401*T^38 + 
        221/343*T^37 + 46/2401*T^36 + 417/2401*T^35 - 2718/2401*T^34 + 
        3970/2401*T^33 - 3405/2401*T^32 + 1360/2401*T^31 - 762/2401*T^30 + 
        2920/2401*T^29 - 4423/2401*T^28 + 2920/2401*T^27 - 762/2401*T^26 + 
        1360/2401*T^25 - 3405/2401*T^24 + 3970/2401*T^23 - 2718/2401*T^22 + 
        417/2401*T^21 + 46/2401*T^20 + 221/343*T^19 - 2921/2401*T^18 + 
        1853/2401*T^17 + 961/2401*T^16 - 2034/2401*T^15 + 254/2401*T^14 + 
        242/2401*T^13 + 34/49*T^12 - 3187/2401*T^11 + 2039/2401*T^10 + 235/2401*T^9 
        - 30/343*T^8 - 48/343*T^7 + 1347/2401*T^6 - 351/343*T^5 + 2125/2401*T^4 - 
        268/343*T^3 + 59/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + X*Y^10 + 5*X*Y^9 + X*Y^8 + 
        3*X*Y^7 + 2*X*Y^6 + X*Y^5 + 5*X*Y^4 + 2*X*Y^3 + 2*X*Y + 2*X + 6*Y^30 + 
        2*Y^29 + 3*Y^27 + 3*Y^26 + Y^25 + 5*Y^24 + 5*Y^23 + Y^22 + 5*Y^21 + 2*Y^20 +
        6*Y^18 + Y^17 + 4*Y^16 + 4*Y^15 + 5*Y^14 + 5*Y^13 + 6*Y^11 + Y^9 + 3*Y^8 + 
        5*Y^7 + 6*Y^6 + 4*Y^5 + 6*Y^4 + Y^3 + 3*Y^2 + Y + 6,
    T^56 - 2/7*T^55 - 62/49*T^54 - 345/343*T^53 + 2287/2401*T^52 + 2481/2401*T^51 + 
        258/343*T^50 - 2690/2401*T^49 - 3457/2401*T^48 + 1462/2401*T^47 + 
        3970/2401*T^46 + 660/2401*T^45 - 2087/2401*T^44 - 227/343*T^43 - 
        446/2401*T^42 + 2202/2401*T^41 + 984/2401*T^40 - 3058/2401*T^39 - 
        1647/2401*T^38 + 1975/2401*T^37 + 1611/2401*T^36 + 542/2401*T^35 - 
        526/2401*T^34 - 692/2401*T^33 - 2/2401*T^32 + 1726/2401*T^31 - 
        2035/2401*T^30 + 46/2401*T^29 + 65/343*T^28 + 46/2401*T^27 - 2035/2401*T^26 
        + 1726/2401*T^25 - 2/2401*T^24 - 692/2401*T^23 - 526/2401*T^22 + 
        542/2401*T^21 + 1611/2401*T^20 + 1975/2401*T^19 - 1647/2401*T^18 - 
        3058/2401*T^17 + 984/2401*T^16 + 2202/2401*T^15 - 446/2401*T^14 - 
        227/343*T^13 - 2087/2401*T^12 + 660/2401*T^11 + 3970/2401*T^10 + 
        1462/2401*T^9 - 3457/2401*T^8 - 2690/2401*T^7 + 258/343*T^6 + 2481/2401*T^5 
        + 2287/2401*T^4 - 345/343*T^3 - 62/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + 4*X*Y^13 + X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 3*X*Y^9 + 2*X*Y^8 + 
        4*X*Y^7 + 5*X*Y^6 + 4*X*Y^4 + 6*X*Y^2 + 4*X*Y + 2*X + 5*Y^30 + 6*Y^29 + 
        3*Y^28 + 4*Y^27 + 4*Y^26 + 4*Y^25 + 4*Y^23 + 3*Y^22 + 5*Y^20 + 6*Y^19 + 
        3*Y^18 + 3*Y^16 + Y^15 + 5*Y^14 + 2*Y^12 + 5*Y^11 + 5*Y^10 + 5*Y^9 + 3*Y^7 +
        5*Y^6 + 5*Y^5 + Y^4 + 5*Y^3 + 3*Y^2 + 6,
    T^56 - 2/7*T^55 - 39/49*T^54 + 34/343*T^53 - 178/2401*T^52 + 857/2401*T^51 - 
        1632/2401*T^50 + 1324/2401*T^49 + 636/2401*T^48 - 1789/2401*T^47 + 
        24/2401*T^46 - 296/2401*T^45 + 183/343*T^44 - 67/343*T^43 - 437/2401*T^42 + 
        109/343*T^41 - 139/2401*T^40 + 535/2401*T^39 - 1038/2401*T^38 - 
        262/2401*T^37 + 326/343*T^36 - 106/2401*T^35 - 1224/2401*T^34 - 
        1268/2401*T^33 + 1688/2401*T^32 + 963/2401*T^31 - 1940/2401*T^30 + 4/49*T^29
        + 495/2401*T^28 + 4/49*T^27 - 1940/2401*T^26 + 963/2401*T^25 + 
        1688/2401*T^24 - 1268/2401*T^23 - 1224/2401*T^22 - 106/2401*T^21 + 
        326/343*T^20 - 262/2401*T^19 - 1038/2401*T^18 + 535/2401*T^17 - 
        139/2401*T^16 + 109/343*T^15 - 437/2401*T^14 - 67/343*T^13 + 183/343*T^12 - 
        296/2401*T^11 + 24/2401*T^10 - 1789/2401*T^9 + 636/2401*T^8 + 1324/2401*T^7 
        - 1632/2401*T^6 + 857/2401*T^5 - 178/2401*T^4 + 34/343*T^3 - 39/49*T^2 - 
        2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 5*X*Y^14 + X*Y^12 + 4*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 3*X*Y^8 + 
        5*X*Y^7 + 4*X*Y^5 + 5*X*Y^3 + 4*X*Y^2 + 6*X*Y + 3*X + 5*Y^30 + 5*Y^29 + 
        6*Y^28 + 4*Y^25 + 4*Y^24 + 6*Y^23 + 2*Y^22 + 5*Y^21 + 3*Y^20 + Y^19 + Y^16 +
        Y^15 + Y^14 + 2*Y^13 + 3*Y^12 + 2*Y^11 + 5*Y^10 + Y^9 + Y^8 + 6*Y^7 + 4*Y^6 
        + 3*Y^5 + 2*Y^4 + 5*Y^3 + 2*Y + 3,
    -T^56 - 9/7*T^55 - 38/49*T^54 + 72/343*T^53 + 2193/2401*T^52 + 2110/2401*T^51 + 
        1423/2401*T^50 + 93/2401*T^49 - 592/2401*T^48 - 24/2401*T^47 - 251/2401*T^46
        + 393/2401*T^45 + 653/2401*T^44 + 118/343*T^43 - 93/2401*T^42 - 39/343*T^41 
        + 484/2401*T^40 + 1571/2401*T^39 + 503/2401*T^38 - 1537/2401*T^37 - 
        2346/2401*T^36 - 1196/2401*T^35 + 8/49*T^34 + 635/2401*T^33 - 699/2401*T^32 
        - 1796/2401*T^31 - 2041/2401*T^30 - 818/2401*T^29 + 818/2401*T^27 + 
        2041/2401*T^26 + 1796/2401*T^25 + 699/2401*T^24 - 635/2401*T^23 - 8/49*T^22 
        + 1196/2401*T^21 + 2346/2401*T^20 + 1537/2401*T^19 - 503/2401*T^18 - 
        1571/2401*T^17 - 484/2401*T^16 + 39/343*T^15 + 93/2401*T^14 - 118/343*T^13 -
        653/2401*T^12 - 393/2401*T^11 + 251/2401*T^10 + 24/2401*T^9 + 592/2401*T^8 -
        93/2401*T^7 - 1423/2401*T^6 - 2110/2401*T^5 - 2193/2401*T^4 - 72/343*T^3 + 
        38/49*T^2 + 9/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 4*X*Y^13 + 6*X*Y^12 + X*Y^11 + 6*X*Y^9 + 6*X*Y^8 + 
        X*Y^7 + 3*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + X*Y^2 + 6*X*Y + 2*X + 3*Y^30 + 2*Y^29 
        + 5*Y^28 + 4*Y^27 + 4*Y^26 + 3*Y^24 + 5*Y^23 + 4*Y^22 + 4*Y^21 + 3*Y^19 + 
        5*Y^18 + Y^17 + 3*Y^15 + 4*Y^14 + 4*Y^13 + 3*Y^12 + 6*Y^11 + 5*Y^10 + 3*Y^9 
        + 3*Y^8 + 3*Y^6 + 6*Y^5 + 5*Y^4 + Y^3 + 5*Y^2 + 4*Y + 6,
    -T^56 - 47/49*T^54 - 246/343*T^53 - 467/2401*T^52 - 2441/2401*T^51 - 
        2601/2401*T^50 + 759/2401*T^49 - 2879/2401*T^48 - 390/2401*T^47 + 
        201/2401*T^46 - 152/343*T^45 - 58/2401*T^44 + 1720/2401*T^43 - 135/343*T^42 
        + 2269/2401*T^41 + 2396/2401*T^40 + 2216/2401*T^39 + 3090/2401*T^38 + 
        2903/2401*T^37 + 2274/2401*T^36 + 3207/2401*T^35 + 2179/2401*T^34 + 
        2623/2401*T^33 + 1958/2401*T^32 + 1298/2401*T^31 + 891/2401*T^30 - 
        80/2401*T^29 + 80/2401*T^27 - 891/2401*T^26 - 1298/2401*T^25 - 
        1958/2401*T^24 - 2623/2401*T^23 - 2179/2401*T^22 - 3207/2401*T^21 - 
        2274/2401*T^20 - 2903/2401*T^19 - 3090/2401*T^18 - 2216/2401*T^17 - 
        2396/2401*T^16 - 2269/2401*T^15 + 135/343*T^14 - 1720/2401*T^13 + 
        58/2401*T^12 + 152/343*T^11 - 201/2401*T^10 + 390/2401*T^9 + 2879/2401*T^8 -
        759/2401*T^7 + 2601/2401*T^6 + 2441/2401*T^5 + 467/2401*T^4 + 246/343*T^3 + 
        47/49*T^2 + 1
*], [*
    X^3 + 2*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 2*X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        3*X*Y^8 + 5*X*Y^7 + X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 2*X + 3*Y^30 + 6*Y^29 + 
        5*Y^28 + 4*Y^27 + Y^25 + 5*Y^24 + 4*Y^23 + 4*Y^22 + Y^21 + 4*Y^20 + Y^19 + 
        6*Y^18 + 5*Y^17 + 4*Y^15 + 2*Y^14 + Y^13 + 6*Y^12 + 2*Y^11 + 3*Y^10 + 5*Y^9 
        + 5*Y^7 + Y^6 + 3*Y^5 + 3*Y^4 + 2*Y^3 + 5*Y^2 + 5*Y + 6,
    -T^56 + 12/7*T^55 - 131/49*T^54 + 1074/343*T^53 - 8579/2401*T^52 + 
        7242/2401*T^51 - 4755/2401*T^50 + 2738/2401*T^49 - 907/2401*T^48 - 
        55/2401*T^47 + 1339/2401*T^46 + 71/343*T^45 - 822/2401*T^44 + 1345/2401*T^43
        + 1195/2401*T^42 - 337/343*T^41 + 4922/2401*T^40 - 6287/2401*T^39 + 
        6617/2401*T^38 - 7097/2401*T^37 + 801/343*T^36 - 6169/2401*T^35 + 
        4496/2401*T^34 - 5920/2401*T^33 + 4442/2401*T^32 - 748/343*T^31 + 
        3972/2401*T^30 - 3075/2401*T^29 + 3075/2401*T^27 - 3972/2401*T^26 + 
        748/343*T^25 - 4442/2401*T^24 + 5920/2401*T^23 - 4496/2401*T^22 + 
        6169/2401*T^21 - 801/343*T^20 + 7097/2401*T^19 - 6617/2401*T^18 + 
        6287/2401*T^17 - 4922/2401*T^16 + 337/343*T^15 - 1195/2401*T^14 - 
        1345/2401*T^13 + 822/2401*T^12 - 71/343*T^11 - 1339/2401*T^10 + 55/2401*T^9 
        + 907/2401*T^8 - 2738/2401*T^7 + 4755/2401*T^6 - 7242/2401*T^5 + 
        8579/2401*T^4 - 1074/343*T^3 + 131/49*T^2 - 12/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 5*X*Y^11 + 5*X*Y^10 + 6*X*Y^9 
        + 2*X*Y^8 + 2*X*Y^7 + 2*X*Y^6 + 2*X*Y^5 + 5*X*Y^4 + 5*X*Y^3 + 6*X*Y^2 + 
        6*X*Y + 3*Y^30 + Y^29 + 4*Y^27 + 2*Y^26 + Y^25 + 3*Y^24 + 5*Y^23 + 3*Y^22 + 
        3*Y^21 + 6*Y^20 + 5*Y^19 + 3*Y^18 + 6*Y^17 + 5*Y^16 + 2*Y^15 + 5*Y^13 + 
        4*Y^12 + 2*Y^11 + 6*Y^9 + 2*Y^8 + 6*Y^7 + 5*Y^6 + Y^5 + 3*Y^4 + 5*Y^3 + 
        5*Y^2 + 4*Y + 6,
    -T^56 + 10/7*T^55 - 20/49*T^54 + 78/343*T^53 - 151/343*T^52 + 2395/2401*T^51 - 
        3284/2401*T^50 + 2364/2401*T^49 - 1404/2401*T^48 - 25/343*T^47 - 
        956/2401*T^46 + 2605/2401*T^45 - 258/343*T^44 + 200/343*T^43 - 991/2401*T^42
        - 92/2401*T^41 - 426/2401*T^40 + 2012/2401*T^39 - 1280/2401*T^38 + 
        172/2401*T^37 + 12/343*T^36 - 549/2401*T^35 + 942/2401*T^34 + 129/2401*T^33 
        - 1317/2401*T^32 - 243/2401*T^31 + 1434/2401*T^30 - 764/2401*T^29 + 
        764/2401*T^27 - 1434/2401*T^26 + 243/2401*T^25 + 1317/2401*T^24 - 
        129/2401*T^23 - 942/2401*T^22 + 549/2401*T^21 - 12/343*T^20 - 172/2401*T^19 
        + 1280/2401*T^18 - 2012/2401*T^17 + 426/2401*T^16 + 92/2401*T^15 + 
        991/2401*T^14 - 200/343*T^13 + 258/343*T^12 - 2605/2401*T^11 + 956/2401*T^10
        + 25/343*T^9 + 1404/2401*T^8 - 2364/2401*T^7 + 3284/2401*T^6 - 2395/2401*T^5
        + 151/343*T^4 - 78/343*T^3 + 20/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + X*Y^11 + 4*X*Y^10 + 2*X*Y^9 + 
        3*X*Y^8 + 4*X*Y^7 + 6*X*Y^6 + 3*X*Y^5 + X*Y^4 + 6*X*Y^2 + 6*X*Y + 6*Y^30 + 
        2*Y^29 + 5*Y^28 + 2*Y^27 + Y^26 + 4*Y^25 + 6*Y^24 + 6*Y^22 + 5*Y^21 + 6*Y^20
        + 3*Y^19 + 4*Y^18 + 5*Y^17 + 6*Y^16 + 3*Y^15 + 6*Y^14 + 2*Y^13 + 3*Y^12 + 
        Y^11 + 6*Y^9 + Y^8 + 6*Y^6 + 4*Y^5 + 4*Y^4 + 6*Y^3 + 2*Y^2 + 2*Y + 3,
    T^56 + 6/7*T^55 - 3/49*T^54 - 61/49*T^53 - 2047/2401*T^52 - 76/2401*T^51 + 
        925/2401*T^50 + 282/2401*T^49 + 703/2401*T^48 + 663/2401*T^47 - 
        894/2401*T^46 - 501/2401*T^45 + 1026/2401*T^44 + 1828/2401*T^43 + 
        85/2401*T^42 - 751/2401*T^41 - 1550/2401*T^40 - 692/2401*T^39 - 
        635/2401*T^38 - 330/2401*T^37 + 346/2401*T^36 + 1465/2401*T^35 + 
        1410/2401*T^34 - 26/2401*T^33 - 806/2401*T^32 - 768/2401*T^31 + 
        729/2401*T^30 - 19/49*T^29 - 1492/2401*T^28 - 19/49*T^27 + 729/2401*T^26 - 
        768/2401*T^25 - 806/2401*T^24 - 26/2401*T^23 + 1410/2401*T^22 + 
        1465/2401*T^21 + 346/2401*T^20 - 330/2401*T^19 - 635/2401*T^18 - 
        692/2401*T^17 - 1550/2401*T^16 - 751/2401*T^15 + 85/2401*T^14 + 
        1828/2401*T^13 + 1026/2401*T^12 - 501/2401*T^11 - 894/2401*T^10 + 
        663/2401*T^9 + 703/2401*T^8 + 282/2401*T^7 + 925/2401*T^6 - 76/2401*T^5 - 
        2047/2401*T^4 - 61/49*T^3 - 3/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + 4*X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 2*X*Y^9 + 4*X*Y^8 + 
        3*X*Y^7 + 3*X*Y^5 + 3*X*Y^4 + 2*X*Y^3 + 3*X*Y^2 + 5*X*Y + X + Y^30 + 2*Y^29 
        + 3*Y^28 + 4*Y^27 + 4*Y^26 + 3*Y^25 + 2*Y^24 + 5*Y^23 + Y^22 + 6*Y^21 + 
        2*Y^20 + 2*Y^19 + 3*Y^18 + 4*Y^17 + Y^16 + 5*Y^15 + 2*Y^14 + 2*Y^13 + 2*Y^12
        + Y^11 + 2*Y^10 + 3*Y^9 + 4*Y^8 + 3*Y^7 + 6*Y^6 + 6*Y^5 + 5*Y^4 + 4*Y^3 + 
        4*Y^2 + 2*Y + 3,
    T^56 - 4/7*T^55 + 10/49*T^54 - 96/343*T^53 + 53/343*T^52 + 141/2401*T^51 - 
        16/343*T^50 - 530/2401*T^49 - 370/2401*T^48 + 176/2401*T^47 - 61/2401*T^46 +
        1250/2401*T^45 - 1032/2401*T^44 + 150/2401*T^43 - 1346/2401*T^42 + 
        561/2401*T^41 + 237/2401*T^40 - 82/2401*T^39 + 907/2401*T^38 - 654/2401*T^37
        - 275/2401*T^36 - 27/343*T^35 + 59/343*T^34 + 422/2401*T^33 - 750/2401*T^32 
        - 409/2401*T^31 - 984/2401*T^30 + 1180/2401*T^29 + 41/343*T^28 + 
        1180/2401*T^27 - 984/2401*T^26 - 409/2401*T^25 - 750/2401*T^24 + 
        422/2401*T^23 + 59/343*T^22 - 27/343*T^21 - 275/2401*T^20 - 654/2401*T^19 + 
        907/2401*T^18 - 82/2401*T^17 + 237/2401*T^16 + 561/2401*T^15 - 
        1346/2401*T^14 + 150/2401*T^13 - 1032/2401*T^12 + 1250/2401*T^11 - 
        61/2401*T^10 + 176/2401*T^9 - 370/2401*T^8 - 530/2401*T^7 - 16/343*T^6 + 
        141/2401*T^5 + 53/343*T^4 - 96/343*T^3 + 10/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 4*X*Y^14 + 6*X*Y^13 + 3*X*Y^12 + 6*X*Y^11 + 2*X*Y^10 + 6*X*Y^9 
        + 3*X*Y^8 + 3*X*Y^6 + 5*X*Y^5 + 3*X*Y^4 + 2*X*Y^2 + 3*X*Y + 2*X + Y^30 + 
        4*Y^28 + 6*Y^27 + 6*Y^26 + 5*Y^24 + Y^23 + 3*Y^22 + Y^21 + 2*Y^20 + Y^19 + 
        4*Y^17 + Y^16 + 6*Y^15 + 4*Y^14 + 3*Y^13 + 4*Y^12 + 6*Y^11 + Y^10 + 2*Y^9 + 
        6*Y^8 + 5*Y^7 + 3*Y^6 + 4*Y^5 + 3*Y^4 + 2*Y^3 + 4*Y + 3,
    T^56 - 8/7*T^55 + 31/49*T^54 + 4/343*T^53 - 2010/2401*T^52 + 2645/2401*T^51 - 
        446/343*T^50 + 1590/2401*T^49 - 201/2401*T^48 - 186/343*T^47 + 831/2401*T^46
        - 52/343*T^45 + 684/2401*T^44 - 893/2401*T^43 + 192/343*T^42 - 815/2401*T^41
        + 668/2401*T^40 + 82/343*T^39 - 1248/2401*T^38 + 2155/2401*T^37 - 
        1940/2401*T^36 - 58/2401*T^35 + 1125/2401*T^34 - 680/2401*T^33 - 
        99/2401*T^32 + 36/2401*T^31 + 368/2401*T^30 - 514/2401*T^29 + 45/2401*T^28 -
        514/2401*T^27 + 368/2401*T^26 + 36/2401*T^25 - 99/2401*T^24 - 680/2401*T^23 
        + 1125/2401*T^22 - 58/2401*T^21 - 1940/2401*T^20 + 2155/2401*T^19 - 
        1248/2401*T^18 + 82/343*T^17 + 668/2401*T^16 - 815/2401*T^15 + 192/343*T^14 
        - 893/2401*T^13 + 684/2401*T^12 - 52/343*T^11 + 831/2401*T^10 - 186/343*T^9 
        - 201/2401*T^8 + 1590/2401*T^7 - 446/343*T^6 + 2645/2401*T^5 - 2010/2401*T^4
        + 4/343*T^3 + 31/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 3*X*Y^13 + 2*X*Y^12 + 6*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 
        + 4*X*Y^8 + 6*X*Y^7 + 2*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 
        2*Y^30 + 6*Y^29 + 5*Y^28 + 5*Y^26 + 2*Y^24 + 5*Y^23 + 3*Y^22 + 6*Y^21 + 
        2*Y^20 + Y^19 + 5*Y^18 + 4*Y^17 + 6*Y^16 + 4*Y^15 + Y^14 + 3*Y^13 + 4*Y^12 +
        2*Y^11 + 2*Y^10 + 4*Y^9 + Y^8 + 5*Y^7 + 3*Y^6 + Y^5 + 5*Y^4 + 5*Y^3 + 3*Y^2 
        + 4*Y + 3,
    -T^56 + T^55 - 29/49*T^54 + 16/343*T^53 + 2490/2401*T^52 - 3168/2401*T^51 + 
        3446/2401*T^50 - 2111/2401*T^49 + 190/2401*T^48 + 1649/2401*T^47 - 
        2372/2401*T^46 + 2035/2401*T^45 - 1796/2401*T^44 + 166/2401*T^43 + 
        1350/2401*T^42 - 123/343*T^41 + 1168/2401*T^40 - 436/2401*T^39 + 
        283/2401*T^38 - 921/2401*T^37 + 969/2401*T^36 - 1241/2401*T^35 + 
        187/2401*T^34 + 132/343*T^33 - 2512/2401*T^32 + 3863/2401*T^31 - 
        2517/2401*T^30 + 2048/2401*T^29 - 2048/2401*T^27 + 2517/2401*T^26 - 
        3863/2401*T^25 + 2512/2401*T^24 - 132/343*T^23 - 187/2401*T^22 + 
        1241/2401*T^21 - 969/2401*T^20 + 921/2401*T^19 - 283/2401*T^18 + 
        436/2401*T^17 - 1168/2401*T^16 + 123/343*T^15 - 1350/2401*T^14 - 
        166/2401*T^13 + 1796/2401*T^12 - 2035/2401*T^11 + 2372/2401*T^10 - 
        1649/2401*T^9 - 190/2401*T^8 + 2111/2401*T^7 - 3446/2401*T^6 + 3168/2401*T^5
        - 2490/2401*T^4 - 16/343*T^3 + 29/49*T^2 - T + 1
*], [*
    X^3 + 2*X*Y^15 + 4*X*Y^14 + 5*X*Y^13 + 6*X*Y^11 + X*Y^10 + 2*X*Y^9 + 4*X*Y^8 + 
        X*Y^7 + 5*X*Y^6 + 3*X*Y^5 + 5*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + 5*X*Y + 3*X + 
        2*Y^30 + 2*Y^29 + 6*Y^28 + 2*Y^27 + 5*Y^26 + 6*Y^25 + 3*Y^24 + 6*Y^23 + 
        3*Y^20 + Y^18 + 3*Y^17 + 3*Y^16 + 2*Y^15 + 3*Y^13 + Y^12 + 4*Y^11 + 6*Y^10 +
        Y^9 + 5*Y^8 + 2*Y^7 + 3*Y^6 + 4*Y^5 + Y^4 + 4*Y^2 + 2,
    -T^56 + 3/7*T^55 + 68/49*T^54 - 270/343*T^53 - 676/2401*T^52 + 1069/2401*T^51 - 
        611/2401*T^50 + 208/2401*T^49 + 50/343*T^48 - 1340/2401*T^47 - 
        1555/2401*T^46 + 1326/2401*T^45 + 1958/2401*T^44 - 620/2401*T^43 - 
        1035/2401*T^42 + 148/343*T^41 + 289/2401*T^40 - 834/2401*T^39 + 
        309/2401*T^38 - 85/343*T^37 + 145/2401*T^36 + 369/2401*T^35 - 298/2401*T^34 
        + 85/343*T^33 - 624/2401*T^32 + 806/2401*T^31 + 887/2401*T^30 - 
        2799/2401*T^29 + 2799/2401*T^27 - 887/2401*T^26 - 806/2401*T^25 + 
        624/2401*T^24 - 85/343*T^23 + 298/2401*T^22 - 369/2401*T^21 - 145/2401*T^20 
        + 85/343*T^19 - 309/2401*T^18 + 834/2401*T^17 - 289/2401*T^16 - 148/343*T^15
        + 1035/2401*T^14 + 620/2401*T^13 - 1958/2401*T^12 - 1326/2401*T^11 + 
        1555/2401*T^10 + 1340/2401*T^9 - 50/343*T^8 - 208/2401*T^7 + 611/2401*T^6 - 
        1069/2401*T^5 + 676/2401*T^4 + 270/343*T^3 - 68/49*T^2 - 3/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 4*X*Y^13 + 4*X*Y^12 + 6*X*Y^10 + 3*X*Y^9 + 4*X*Y^8 + 
        5*X*Y^6 + 6*X*Y^5 + X*Y^4 + X*Y^3 + 5*X*Y + 3*X + 2*Y^30 + 2*Y^29 + 4*Y^28 +
        3*Y^27 + 5*Y^26 + 6*Y^25 + 2*Y^24 + 3*Y^22 + 5*Y^21 + 2*Y^20 + 2*Y^19 + Y^18
        + 6*Y^17 + 3*Y^15 + 5*Y^14 + Y^13 + 3*Y^12 + 3*Y^11 + 2*Y^10 + 3*Y^9 + 6*Y^8
        + 4*Y^7 + Y^6 + Y^5 + 4*Y^2 + 2,
    T^56 - 23/49*T^54 + 9/49*T^53 + 388/2401*T^52 - 1101/2401*T^51 + 521/2401*T^50 +
        1009/2401*T^49 - 1208/2401*T^48 - 923/2401*T^47 - 402/2401*T^46 - 
        418/2401*T^45 - 732/2401*T^44 - 5/2401*T^43 + 157/343*T^42 - 250/2401*T^41 +
        933/2401*T^40 + 860/2401*T^39 - 1473/2401*T^38 + 32/343*T^37 + 
        2537/2401*T^36 - 3/7*T^35 + 8/343*T^34 + 1584/2401*T^33 - 223/343*T^32 - 
        1224/2401*T^31 + 951/2401*T^30 + 432/2401*T^29 - 2202/2401*T^28 + 
        432/2401*T^27 + 951/2401*T^26 - 1224/2401*T^25 - 223/343*T^24 + 
        1584/2401*T^23 + 8/343*T^22 - 3/7*T^21 + 2537/2401*T^20 + 32/343*T^19 - 
        1473/2401*T^18 + 860/2401*T^17 + 933/2401*T^16 - 250/2401*T^15 + 
        157/343*T^14 - 5/2401*T^13 - 732/2401*T^12 - 418/2401*T^11 - 402/2401*T^10 -
        923/2401*T^9 - 1208/2401*T^8 + 1009/2401*T^7 + 521/2401*T^6 - 1101/2401*T^5 
        + 388/2401*T^4 + 9/49*T^3 - 23/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^14 + 2*X*Y^13 + 5*X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 6*X*Y^8 +
        6*X*Y^7 + 6*X*Y^6 + 6*X*Y^4 + X*Y^3 + 2*X*Y^2 + 5*X*Y + X + 5*Y^30 + 6*Y^29 
        + 4*Y^28 + 4*Y^27 + 4*Y^26 + 4*Y^25 + 4*Y^24 + 6*Y^22 + 3*Y^21 + 3*Y^20 + 
        3*Y^19 + 2*Y^18 + 6*Y^17 + 2*Y^15 + Y^14 + 6*Y^13 + 3*Y^12 + 4*Y^11 + 3*Y^9 
        + 2*Y^7 + 4*Y^6 + 4*Y^5 + Y^3 + Y^2 + 1,
    -T^56 + 4/7*T^55 - 10/49*T^54 - 279/343*T^53 + 834/2401*T^52 + 101/2401*T^51 - 
        262/2401*T^50 - 641/2401*T^49 + 1331/2401*T^48 - 282/2401*T^47 - 
        541/2401*T^46 + 1285/2401*T^45 + 332/2401*T^44 + 18/343*T^43 + 30/343*T^42 +
        1192/2401*T^41 - 47/343*T^40 + 450/2401*T^39 + 1528/2401*T^38 - 
        1653/2401*T^37 + 1150/2401*T^36 + 681/2401*T^35 - 1215/2401*T^34 - 
        102/2401*T^33 + 1072/2401*T^32 - 295/2401*T^31 - 1087/2401*T^30 + 
        1703/2401*T^29 - 1703/2401*T^27 + 1087/2401*T^26 + 295/2401*T^25 - 
        1072/2401*T^24 + 102/2401*T^23 + 1215/2401*T^22 - 681/2401*T^21 - 
        1150/2401*T^20 + 1653/2401*T^19 - 1528/2401*T^18 - 450/2401*T^17 + 
        47/343*T^16 - 1192/2401*T^15 - 30/343*T^14 - 18/343*T^13 - 332/2401*T^12 - 
        1285/2401*T^11 + 541/2401*T^10 + 282/2401*T^9 - 1331/2401*T^8 + 641/2401*T^7
        + 262/2401*T^6 - 101/2401*T^5 - 834/2401*T^4 + 279/343*T^3 + 10/49*T^2 - 
        4/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 6*X*Y^14 + 3*X*Y^13 + X*Y^12 + 4*X*Y^9 + 3*X*Y^7 + 5*X*Y^6 + 
        3*X*Y^4 + 6*X*Y^3 + X*Y^2 + 5*X*Y + 5*Y^30 + Y^29 + 2*Y^28 + 3*Y^27 + 6*Y^26
        + Y^25 + 5*Y^24 + Y^23 + 2*Y^22 + 6*Y^21 + 5*Y^20 + 3*Y^18 + 2*Y^17 + 4*Y^16
        + 5*Y^15 + 3*Y^14 + 4*Y^13 + 4*Y^12 + 3*Y^11 + 2*Y^10 + Y^7 + 5*Y^6 + 3*Y^5 
        + 6*Y^4 + 6*Y^2 + 6*Y + 2,
    T^56 - 2/7*T^55 - 59/49*T^54 + 503/343*T^53 + 2663/2401*T^52 - 734/343*T^51 - 
        254/2401*T^50 + 5707/2401*T^49 - 1122/2401*T^48 - 5749/2401*T^47 + 
        3113/2401*T^46 + 629/343*T^45 - 3972/2401*T^44 - 2580/2401*T^43 + 
        3918/2401*T^42 + 1305/2401*T^41 - 2881/2401*T^40 - 85/2401*T^39 + 
        1741/2401*T^38 - 626/2401*T^37 - 1678/2401*T^36 + 668/2401*T^35 + 
        45/2401*T^34 - 1693/2401*T^33 + 675/2401*T^32 + 1131/2401*T^31 - 
        1774/2401*T^30 - 283/2401*T^29 + 1266/2401*T^28 - 283/2401*T^27 - 
        1774/2401*T^26 + 1131/2401*T^25 + 675/2401*T^24 - 1693/2401*T^23 + 
        45/2401*T^22 + 668/2401*T^21 - 1678/2401*T^20 - 626/2401*T^19 + 
        1741/2401*T^18 - 85/2401*T^17 - 2881/2401*T^16 + 1305/2401*T^15 + 
        3918/2401*T^14 - 2580/2401*T^13 - 3972/2401*T^12 + 629/343*T^11 + 
        3113/2401*T^10 - 5749/2401*T^9 - 1122/2401*T^8 + 5707/2401*T^7 - 
        254/2401*T^6 - 734/343*T^5 + 2663/2401*T^4 + 503/343*T^3 - 59/49*T^2 - 2/7*T
        + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + 6*X*Y^13 + 4*X*Y^11 + 4*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 + 
        6*X*Y^5 + 2*X*Y^3 + 4*X*Y^2 + 6*X*Y + 6*X + Y^30 + 5*Y^29 + 2*Y^28 + 6*Y^27 
        + 6*Y^26 + Y^25 + 5*Y^24 + 6*Y^23 + 2*Y^22 + 5*Y^20 + 4*Y^19 + 6*Y^18 + Y^17
        + 3*Y^15 + 4*Y^12 + 5*Y^11 + 2*Y^10 + Y^8 + 5*Y^6 + 6*Y^5 + 6*Y^4 + Y^2 + Y 
        + 4,
    T^56 - 11/7*T^55 + 11/49*T^54 + 40/49*T^53 - 4309/2401*T^52 + 5545/2401*T^51 - 
        1747/2401*T^50 - 2473/2401*T^49 + 2808/2401*T^48 - 365/2401*T^47 - 
        886/2401*T^46 + 1/7*T^45 + 421/2401*T^44 - 2726/2401*T^43 + 561/343*T^42 - 
        1255/2401*T^41 - 1353/2401*T^40 + 1195/2401*T^39 - 1186/2401*T^38 + 
        1923/2401*T^37 - 55/343*T^36 - 471/2401*T^35 - 1118/2401*T^34 + 
        1178/2401*T^33 - 725/2401*T^32 + 757/2401*T^31 + 202/2401*T^30 - 
        274/343*T^29 + 2986/2401*T^28 - 274/343*T^27 + 202/2401*T^26 + 757/2401*T^25
        - 725/2401*T^24 + 1178/2401*T^23 - 1118/2401*T^22 - 471/2401*T^21 - 
        55/343*T^20 + 1923/2401*T^19 - 1186/2401*T^18 + 1195/2401*T^17 - 
        1353/2401*T^16 - 1255/2401*T^15 + 561/343*T^14 - 2726/2401*T^13 + 
        421/2401*T^12 + 1/7*T^11 - 886/2401*T^10 - 365/2401*T^9 + 2808/2401*T^8 - 
        2473/2401*T^7 - 1747/2401*T^6 + 5545/2401*T^5 - 4309/2401*T^4 + 40/49*T^3 + 
        11/49*T^2 - 11/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^12 + 5*X*Y^11 + 6*X*Y^10 + X*Y^9 + 4*X*Y^8 + 4*X*Y^7 + 
        3*X*Y^5 + 2*X*Y^4 + X*Y^3 + 4*X*Y^2 + 3*X + Y^30 + 3*Y^29 + Y^28 + 4*Y^27 + 
        Y^26 + 5*Y^24 + Y^23 + Y^22 + 2*Y^18 + 2*Y^17 + 6*Y^16 + 5*Y^15 + 5*Y^14 + 
        5*Y^13 + 2*Y^12 + 2*Y^11 + 3*Y^10 + 5*Y^9 + 4*Y^8 + 3*Y^6 + 4*Y^5 + 2*Y^4 + 
        2*Y^3 + 2*Y^2 + 2*Y + 3,
    T^56 + 6/7*T^55 + 5/49*T^54 + 193/343*T^53 - 435/2401*T^52 - 2294/2401*T^51 - 
        1937/2401*T^50 - 1047/2401*T^49 - 813/2401*T^48 - 978/2401*T^47 + 
        1272/2401*T^46 + 1942/2401*T^45 + 1895/2401*T^44 + 626/2401*T^43 - 
        883/2401*T^42 - 816/2401*T^41 - 3028/2401*T^40 - 3043/2401*T^39 - 
        1943/2401*T^38 - 1726/2401*T^37 - 307/2401*T^36 + 1690/2401*T^35 + 
        3389/2401*T^34 + 2823/2401*T^33 + 2169/2401*T^32 + 911/2401*T^31 - 
        1195/2401*T^30 - 1488/2401*T^29 - 1578/2401*T^28 - 1488/2401*T^27 - 
        1195/2401*T^26 + 911/2401*T^25 + 2169/2401*T^24 + 2823/2401*T^23 + 
        3389/2401*T^22 + 1690/2401*T^21 - 307/2401*T^20 - 1726/2401*T^19 - 
        1943/2401*T^18 - 3043/2401*T^17 - 3028/2401*T^16 - 816/2401*T^15 - 
        883/2401*T^14 + 626/2401*T^13 + 1895/2401*T^12 + 1942/2401*T^11 + 
        1272/2401*T^10 - 978/2401*T^9 - 813/2401*T^8 - 1047/2401*T^7 - 1937/2401*T^6
        - 2294/2401*T^5 - 435/2401*T^4 + 193/343*T^3 + 5/49*T^2 + 6/7*T + 1
*], [*
    X^3 + 3*X*Y^14 + X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 2*X*Y^9 + 5*X*Y^8 + X*Y^7 + 
        2*X*Y^5 + 3*X*Y^4 + 3*X*Y^3 + X*Y + 2*X + 5*Y^30 + 6*Y^29 + 3*Y^28 + 3*Y^27 
        + 5*Y^26 + 4*Y^25 + Y^24 + 5*Y^23 + 3*Y^22 + 2*Y^21 + 2*Y^20 + Y^19 + 6*Y^18
        + 5*Y^17 + 4*Y^16 + 3*Y^15 + 3*Y^14 + 4*Y^13 + 4*Y^12 + 2*Y^11 + 6*Y^10 + 
        4*Y^8 + 4*Y^6 + 2*Y^5 + Y^4 + 6*Y^3 + 2*Y^2 + 2*Y + 6,
    T^56 - 10/7*T^55 + 52/49*T^54 - 258/343*T^53 + 1227/2401*T^52 + 362/2401*T^51 - 
        1184/2401*T^50 + 1097/2401*T^49 - 117/2401*T^48 - 240/2401*T^47 + 
        475/2401*T^46 + 591/2401*T^45 - 1492/2401*T^44 + 1117/2401*T^43 - 
        95/343*T^42 + 277/2401*T^41 + 1220/2401*T^40 - 1704/2401*T^39 + 
        920/2401*T^38 - 121/343*T^37 + 109/2401*T^36 + 583/2401*T^35 - 
        1286/2401*T^34 + 1122/2401*T^33 - 1291/2401*T^32 + 1838/2401*T^31 - 
        1825/2401*T^30 + 1180/2401*T^29 - 1784/2401*T^28 + 1180/2401*T^27 - 
        1825/2401*T^26 + 1838/2401*T^25 - 1291/2401*T^24 + 1122/2401*T^23 - 
        1286/2401*T^22 + 583/2401*T^21 + 109/2401*T^20 - 121/343*T^19 + 
        920/2401*T^18 - 1704/2401*T^17 + 1220/2401*T^16 + 277/2401*T^15 - 
        95/343*T^14 + 1117/2401*T^13 - 1492/2401*T^12 + 591/2401*T^11 + 
        475/2401*T^10 - 240/2401*T^9 - 117/2401*T^8 + 1097/2401*T^7 - 1184/2401*T^6 
        + 362/2401*T^5 + 1227/2401*T^4 - 258/343*T^3 + 52/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + 5*X*Y^11 + 6*X*Y^10 + 4*X*Y^9 + 6*X*Y^8 + X*Y^7 + 
        4*X*Y^6 + 5*X*Y^5 + 6*X*Y^4 + 5*X*Y^3 + 5*X*Y^2 + 4*X + 6*Y^30 + 3*Y^28 + 
        6*Y^27 + 3*Y^26 + 4*Y^25 + Y^24 + 2*Y^22 + 2*Y^21 + 5*Y^20 + 4*Y^19 + 2*Y^17
        + 3*Y^16 + Y^14 + 6*Y^12 + 5*Y^11 + 2*Y^10 + 5*Y^8 + 4*Y^6 + 3*Y^5 + 4*Y^4 +
        2*Y^3 + 3*Y^2 + 6*Y + 6,
    T^56 + 2/7*T^55 + 41/49*T^54 + 163/343*T^53 + 1604/2401*T^52 + 760/2401*T^51 + 
        164/343*T^50 + 150/2401*T^49 + 1515/2401*T^48 + 1588/2401*T^47 + 
        1471/2401*T^46 + 690/2401*T^45 - 2/343*T^44 + 410/2401*T^43 - 440/2401*T^42 
        - 107/343*T^41 - 730/2401*T^40 - 799/2401*T^39 - 361/2401*T^38 - 
        173/343*T^37 - 961/2401*T^36 - 131/343*T^35 - 575/2401*T^34 + 13/49*T^33 - 
        41/2401*T^32 + 334/2401*T^31 - 374/2401*T^30 + 248/2401*T^29 - 
        1284/2401*T^28 + 248/2401*T^27 - 374/2401*T^26 + 334/2401*T^25 - 
        41/2401*T^24 + 13/49*T^23 - 575/2401*T^22 - 131/343*T^21 - 961/2401*T^20 - 
        173/343*T^19 - 361/2401*T^18 - 799/2401*T^17 - 730/2401*T^16 - 107/343*T^15 
        - 440/2401*T^14 + 410/2401*T^13 - 2/343*T^12 + 690/2401*T^11 + 
        1471/2401*T^10 + 1588/2401*T^9 + 1515/2401*T^8 + 150/2401*T^7 + 164/343*T^6 
        + 760/2401*T^5 + 1604/2401*T^4 + 163/343*T^3 + 41/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 4*X*Y^14 + 2*X*Y^13 + X*Y^12 + 2*X*Y^11 + 6*X*Y^10 + 3*X*Y^9 + 
        X*Y^8 + 6*X*Y^7 + X*Y^6 + 4*X*Y^5 + X*Y^4 + X*Y^3 + X*Y^2 + 3*X + 3*Y^30 + 
        5*Y^29 + Y^28 + Y^27 + 2*Y^26 + 5*Y^25 + 3*Y^24 + 4*Y^23 + 6*Y^22 + 4*Y^21 +
        6*Y^20 + 5*Y^19 + 5*Y^17 + 6*Y^16 + Y^13 + 5*Y^12 + 5*Y^11 + 3*Y^9 + Y^8 + 
        5*Y^7 + 4*Y^6 + 4*Y^5 + Y^3 + 3*Y^2 + 6*Y + 3,
    -T^56 - 6/7*T^55 + 44/49*T^54 + 428/343*T^53 + 2266/2401*T^52 - 16/49*T^51 - 
        2733/2401*T^50 - 779/2401*T^49 - 151/2401*T^48 - 83/2401*T^47 + 90/343*T^46 
        + 633/2401*T^45 + 313/2401*T^44 + 533/2401*T^43 - 1032/2401*T^42 - 
        740/2401*T^41 + 479/2401*T^40 - 1881/2401*T^39 - 528/2401*T^38 + 
        1795/2401*T^37 + 1990/2401*T^36 + 281/343*T^35 - 188/343*T^34 - 
        3317/2401*T^33 - 260/2401*T^32 + 1926/2401*T^31 + 4/343*T^30 - 424/2401*T^29
        + 424/2401*T^27 - 4/343*T^26 - 1926/2401*T^25 + 260/2401*T^24 + 
        3317/2401*T^23 + 188/343*T^22 - 281/343*T^21 - 1990/2401*T^20 - 
        1795/2401*T^19 + 528/2401*T^18 + 1881/2401*T^17 - 479/2401*T^16 + 
        740/2401*T^15 + 1032/2401*T^14 - 533/2401*T^13 - 313/2401*T^12 - 
        633/2401*T^11 - 90/343*T^10 + 83/2401*T^9 + 151/2401*T^8 + 779/2401*T^7 + 
        2733/2401*T^6 + 16/49*T^5 - 2266/2401*T^4 - 428/343*T^3 - 44/49*T^2 + 6/7*T 
        + 1
*], [*
    X^3 + 4*X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 4*X*Y^9 + 6*X*Y^8 + 4*X*Y^7 + 
        2*X*Y^6 + X*Y^5 + 6*X*Y^4 + 3*X*Y^3 + 5*X*Y^2 + X*Y + 2*Y^30 + Y^29 + 6*Y^28
        + 3*Y^27 + 6*Y^26 + 3*Y^25 + 3*Y^24 + 2*Y^23 + 2*Y^22 + 5*Y^21 + 3*Y^20 + 
        3*Y^19 + 5*Y^18 + 4*Y^17 + 5*Y^16 + 3*Y^15 + Y^14 + 3*Y^13 + 6*Y^12 + Y^11 +
        3*Y^10 + Y^9 + Y^8 + 2*Y^7 + 2*Y^6 + 2*Y^4 + 5*Y^3 + Y^2 + 6*Y + 3,
    -T^56 + 13/7*T^55 - 109/49*T^54 + 1300/343*T^53 - 11726/2401*T^52 + 
        2043/343*T^51 - 15678/2401*T^50 + 13838/2401*T^49 - 14219/2401*T^48 + 
        10258/2401*T^47 - 3807/2401*T^46 - 948/2401*T^45 + 9756/2401*T^44 - 
        2183/343*T^43 + 20512/2401*T^42 - 26660/2401*T^41 + 25672/2401*T^40 - 
        24660/2401*T^39 + 20931/2401*T^38 - 14026/2401*T^37 + 1139/343*T^36 + 
        1028/2401*T^35 - 1053/343*T^34 + 1679/343*T^33 - 15140/2401*T^32 + 
        13964/2401*T^31 - 11393/2401*T^30 + 6583/2401*T^29 - 6583/2401*T^27 + 
        11393/2401*T^26 - 13964/2401*T^25 + 15140/2401*T^24 - 1679/343*T^23 + 
        1053/343*T^22 - 1028/2401*T^21 - 1139/343*T^20 + 14026/2401*T^19 - 
        20931/2401*T^18 + 24660/2401*T^17 - 25672/2401*T^16 + 26660/2401*T^15 - 
        20512/2401*T^14 + 2183/343*T^13 - 9756/2401*T^12 + 948/2401*T^11 + 
        3807/2401*T^10 - 10258/2401*T^9 + 14219/2401*T^8 - 13838/2401*T^7 + 
        15678/2401*T^6 - 2043/343*T^5 + 11726/2401*T^4 - 1300/343*T^3 + 109/49*T^2 -
        13/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 6*X*Y^13 + 4*X*Y^12 + X*Y^10 + 3*X*Y^9 + X*Y^8 + X*Y^7 +
        5*X*Y^6 + 3*X*Y^5 + 3*X*Y^4 + 5*X*Y^3 + 3*X*Y + 5*X + 3*Y^30 + 5*Y^28 + 
        3*Y^27 + 2*Y^26 + 4*Y^24 + 2*Y^23 + 6*Y^21 + 4*Y^18 + 4*Y^16 + Y^15 + 6*Y^13
        + 3*Y^12 + 5*Y^11 + 2*Y^10 + 3*Y^9 + 4*Y^8 + 5*Y^7 + Y^6 + 4*Y^5 + Y^3 + 
        4*Y^2 + Y,
    T^56 - 8/7*T^55 - 16/49*T^54 + 367/343*T^53 - 3132/2401*T^52 + 820/2401*T^51 + 
        4164/2401*T^50 - 4313/2401*T^49 + 1816/2401*T^48 + 1359/2401*T^47 - 
        5059/2401*T^46 + 348/343*T^45 + 45/49*T^44 - 3060/2401*T^43 + 2318/2401*T^42
        + 444/2401*T^41 - 558/343*T^40 + 2789/2401*T^39 + 988/2401*T^38 - 
        2840/2401*T^37 + 326/343*T^36 - 141/2401*T^35 - 2195/2401*T^34 + 38/49*T^33 
        - 181/343*T^32 + 4/7*T^31 + 561/2401*T^30 - 1053/2401*T^29 + 241/2401*T^28 -
        1053/2401*T^27 + 561/2401*T^26 + 4/7*T^25 - 181/343*T^24 + 38/49*T^23 - 
        2195/2401*T^22 - 141/2401*T^21 + 326/343*T^20 - 2840/2401*T^19 + 
        988/2401*T^18 + 2789/2401*T^17 - 558/343*T^16 + 444/2401*T^15 + 
        2318/2401*T^14 - 3060/2401*T^13 + 45/49*T^12 + 348/343*T^11 - 5059/2401*T^10
        + 1359/2401*T^9 + 1816/2401*T^8 - 4313/2401*T^7 + 4164/2401*T^6 + 
        820/2401*T^5 - 3132/2401*T^4 + 367/343*T^3 - 16/49*T^2 - 8/7*T + 1
*], [*
    X^3 + 4*X*Y^14 + 6*X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 3*X*Y^10 + 6*X*Y^9 + 4*X*Y^8 +
        5*X*Y^7 + 3*X*Y^6 + 6*X*Y^5 + 6*X*Y^4 + 2*X*Y^3 + 5*X*Y^2 + 2*X*Y + X + 
        5*Y^30 + 5*Y^29 + Y^28 + 5*Y^27 + 2*Y^26 + Y^25 + 2*Y^24 + 2*Y^23 + 3*Y^22 +
        4*Y^21 + 5*Y^20 + 5*Y^18 + 4*Y^17 + Y^16 + 3*Y^15 + 3*Y^14 + 5*Y^13 + 2*Y^12
        + 3*Y^10 + 3*Y^9 + Y^8 + 4*Y^6 + 2*Y^5 + 2*Y^3 + Y^2 + 3*Y,
    T^56 - 4/7*T^55 - 38/49*T^54 - 27/49*T^53 + 3343/2401*T^52 + 657/2401*T^51 - 
        1615/2401*T^50 - 1121/2401*T^49 + 2115/2401*T^48 + 939/2401*T^47 - 
        45/2401*T^46 - 696/2401*T^45 - 1405/2401*T^44 - 587/2401*T^43 + 
        1622/2401*T^42 + 834/2401*T^41 - 739/2401*T^40 - 2458/2401*T^39 + 
        440/343*T^38 + 1975/2401*T^37 - 487/2401*T^36 - 3021/2401*T^35 + 
        935/2401*T^34 + 1193/2401*T^33 - 824/2401*T^32 - 1619/2401*T^31 + 
        146/2401*T^30 + 1511/2401*T^29 + 30/343*T^28 + 1511/2401*T^27 + 
        146/2401*T^26 - 1619/2401*T^25 - 824/2401*T^24 + 1193/2401*T^23 + 
        935/2401*T^22 - 3021/2401*T^21 - 487/2401*T^20 + 1975/2401*T^19 + 
        440/343*T^18 - 2458/2401*T^17 - 739/2401*T^16 + 834/2401*T^15 + 
        1622/2401*T^14 - 587/2401*T^13 - 1405/2401*T^12 - 696/2401*T^11 - 
        45/2401*T^10 + 939/2401*T^9 + 2115/2401*T^8 - 1121/2401*T^7 - 1615/2401*T^6 
        + 657/2401*T^5 + 3343/2401*T^4 - 27/49*T^3 - 38/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 5*X*Y^14 + 4*X*Y^12 + 3*X*Y^11 + 5*X*Y^8 + 3*X*Y^6 + 6*X*Y^5 + 
        4*X*Y^4 + 2*X*Y^2 + X + 5*Y^30 + 5*Y^29 + 2*Y^28 + 4*Y^27 + 6*Y^26 + 6*Y^25 
        + 3*Y^24 + 6*Y^23 + Y^22 + 5*Y^21 + 2*Y^20 + Y^18 + 4*Y^17 + 6*Y^16 + 6*Y^15
        + 6*Y^14 + 5*Y^13 + 4*Y^11 + 6*Y^10 + 4*Y^9 + 5*Y^8 + Y^7 + 3*Y^6 + 6*Y^5 + 
        4*Y^3 + Y^2 + 4*Y,
    T^56 - T^55 + 2/7*T^54 + 113/343*T^53 - 222/343*T^52 - 713/2401*T^51 + 
        2252/2401*T^50 + 200/2401*T^49 - 377/2401*T^48 + 886/2401*T^47 - 
        1220/2401*T^46 + 1087/2401*T^45 - 1343/2401*T^44 + 135/2401*T^43 + 
        983/2401*T^42 - 1457/2401*T^41 + 576/2401*T^40 + 900/2401*T^39 - 
        1325/2401*T^38 + 1042/2401*T^37 + 1728/2401*T^36 - 4233/2401*T^35 + 3/7*T^34
        + 37/49*T^33 - 408/343*T^32 + 2122/2401*T^31 + 130/2401*T^30 - 18/2401*T^29 
        - 241/343*T^28 - 18/2401*T^27 + 130/2401*T^26 + 2122/2401*T^25 - 
        408/343*T^24 + 37/49*T^23 + 3/7*T^22 - 4233/2401*T^21 + 1728/2401*T^20 + 
        1042/2401*T^19 - 1325/2401*T^18 + 900/2401*T^17 + 576/2401*T^16 - 
        1457/2401*T^15 + 983/2401*T^14 + 135/2401*T^13 - 1343/2401*T^12 + 
        1087/2401*T^11 - 1220/2401*T^10 + 886/2401*T^9 - 377/2401*T^8 + 200/2401*T^7
        + 2252/2401*T^6 - 713/2401*T^5 - 222/343*T^4 + 113/343*T^3 + 2/7*T^2 - T + 1
*], [*
    X^3 + 2*X*Y^15 + X*Y^14 + X*Y^13 + 5*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 4*X*Y^8 + 
        X*Y^6 + 3*X*Y^5 + 4*X*Y^2 + X*Y + 2*X + 2*Y^30 + Y^28 + Y^27 + Y^26 + 5*Y^25
        + 3*Y^24 + 2*Y^23 + 2*Y^22 + 5*Y^21 + 5*Y^20 + 2*Y^18 + 4*Y^17 + 2*Y^16 + 
        4*Y^15 + 6*Y^14 + 6*Y^13 + 5*Y^12 + 4*Y^11 + 6*Y^10 + 5*Y^9 + 4*Y^8 + 5*Y^7 
        + Y^6 + 3*Y^5 + 2*Y^4 + 6*Y^3 + 6*Y^2 + 6*Y,
    -T^56 - 2/7*T^55 + 10/49*T^54 + 288/343*T^53 - 36/343*T^52 - 3152/2401*T^51 - 
        204/2401*T^50 + 2245/2401*T^49 + 3665/2401*T^48 - 821/2401*T^47 - 
        3964/2401*T^46 - 334/2401*T^45 + 3001/2401*T^44 + 2319/2401*T^43 - 
        2563/2401*T^42 - 4300/2401*T^41 - 471/2401*T^40 + 3630/2401*T^39 + 
        1452/2401*T^38 - 3317/2401*T^37 - 3653/2401*T^36 + 1593/2401*T^35 + 
        4755/2401*T^34 + 953/2401*T^33 - 3589/2401*T^32 - 2414/2401*T^31 + 
        2417/2401*T^30 + 4744/2401*T^29 - 4744/2401*T^27 - 2417/2401*T^26 + 
        2414/2401*T^25 + 3589/2401*T^24 - 953/2401*T^23 - 4755/2401*T^22 - 
        1593/2401*T^21 + 3653/2401*T^20 + 3317/2401*T^19 - 1452/2401*T^18 - 
        3630/2401*T^17 + 471/2401*T^16 + 4300/2401*T^15 + 2563/2401*T^14 - 
        2319/2401*T^13 - 3001/2401*T^12 + 334/2401*T^11 + 3964/2401*T^10 + 
        821/2401*T^9 - 3665/2401*T^8 - 2245/2401*T^7 + 204/2401*T^6 + 3152/2401*T^5 
        + 36/343*T^4 - 288/343*T^3 - 10/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + X*Y^14 + X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 + 
        X*Y^8 + X*Y^7 + 2*X*Y^6 + X*Y^5 + X*Y^4 + 5*X*Y^2 + 3*X + Y^30 + 6*Y^28 + 
        3*Y^27 + 4*Y^26 + 5*Y^25 + 4*Y^24 + 4*Y^23 + 6*Y^22 + 2*Y^21 + 2*Y^20 + 
        5*Y^19 + Y^18 + Y^17 + 6*Y^16 + 2*Y^15 + 5*Y^13 + 5*Y^12 + 2*Y^11 + 2*Y^10 +
        2*Y^9 + 6*Y^8 + 2*Y^7 + Y^6 + 6*Y^5 + 6*Y^4 + 6*Y^3 + 6*Y^2 + 4*Y + 4,
    T^56 - 5/7*T^55 - 4/49*T^54 - 262/343*T^53 + 1252/2401*T^52 - 695/2401*T^51 - 
        151/2401*T^50 + 110/2401*T^49 + 213/2401*T^48 + 1793/2401*T^47 - 
        200/343*T^46 + 1017/2401*T^45 - 624/2401*T^44 + 1411/2401*T^43 - 
        1875/2401*T^42 + 289/2401*T^41 - 1123/2401*T^40 + 44/343*T^39 + 
        534/2401*T^38 + 101/2401*T^37 + 928/2401*T^36 - 124/2401*T^35 + 30/343*T^34 
        - 143/343*T^33 + 16/343*T^32 + 148/2401*T^31 + 107/2401*T^30 - 32/2401*T^29 
        - 324/2401*T^28 - 32/2401*T^27 + 107/2401*T^26 + 148/2401*T^25 + 16/343*T^24
        - 143/343*T^23 + 30/343*T^22 - 124/2401*T^21 + 928/2401*T^20 + 101/2401*T^19
        + 534/2401*T^18 + 44/343*T^17 - 1123/2401*T^16 + 289/2401*T^15 - 
        1875/2401*T^14 + 1411/2401*T^13 - 624/2401*T^12 + 1017/2401*T^11 - 
        200/343*T^10 + 1793/2401*T^9 + 213/2401*T^8 + 110/2401*T^7 - 151/2401*T^6 - 
        695/2401*T^5 + 1252/2401*T^4 - 262/343*T^3 - 4/49*T^2 - 5/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 2*X*Y^14 + 4*X*Y^13 + 2*X*Y^12 + 5*X*Y^9 + 3*X*Y^7 + X*Y^6 + 
        5*X*Y^4 + 4*X*Y^3 + 2*X*Y + 5*X + 4*Y^30 + 5*Y^29 + 5*Y^28 + 6*Y^27 + 5*Y^26
        + 4*Y^25 + 5*Y^24 + 6*Y^23 + 3*Y^22 + 4*Y^21 + 6*Y^19 + 5*Y^18 + Y^17 + 
        5*Y^16 + 6*Y^15 + 5*Y^14 + 3*Y^12 + 3*Y^10 + 4*Y^8 + Y^7 + Y^6 + 5*Y^5 + 
        2*Y^4 + 6*Y^3 + 4*Y^2 + 4,
    T^56 + 19/49*T^54 + 64/343*T^53 - 239/343*T^52 - 121/2401*T^51 - 359/2401*T^50 +
        712/2401*T^49 + 1011/2401*T^48 + 857/2401*T^47 + 701/2401*T^46 + 
        15/2401*T^45 - 1205/2401*T^44 - 53/2401*T^43 - 1796/2401*T^42 - 9/343*T^41 -
        202/2401*T^40 - 163/2401*T^39 - 401/2401*T^38 + 706/2401*T^37 - 
        548/2401*T^36 + 303/2401*T^35 + 753/2401*T^34 - 176/343*T^33 + 27/343*T^32 -
        149/343*T^31 + 604/2401*T^30 + 622/2401*T^29 + 1308/2401*T^28 + 
        622/2401*T^27 + 604/2401*T^26 - 149/343*T^25 + 27/343*T^24 - 176/343*T^23 + 
        753/2401*T^22 + 303/2401*T^21 - 548/2401*T^20 + 706/2401*T^19 - 
        401/2401*T^18 - 163/2401*T^17 - 202/2401*T^16 - 9/343*T^15 - 1796/2401*T^14 
        - 53/2401*T^13 - 1205/2401*T^12 + 15/2401*T^11 + 701/2401*T^10 + 
        857/2401*T^9 + 1011/2401*T^8 + 712/2401*T^7 - 359/2401*T^6 - 121/2401*T^5 - 
        239/343*T^4 + 64/343*T^3 + 19/49*T^2 + 1
*], [*
    X^3 + 6*X*Y^15 + 4*X*Y^13 + 5*X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 5*X*Y^9 + 2*X*Y^8 +
        3*X*Y^7 + 6*X*Y^5 + X*Y^4 + 2*X*Y^3 + X*Y^2 + 6*X + 3*Y^30 + 4*Y^29 + Y^28 +
        6*Y^27 + 3*Y^26 + 4*Y^25 + 3*Y^24 + 6*Y^23 + 6*Y^22 + 4*Y^21 + 2*Y^20 + 
        6*Y^19 + 4*Y^17 + 2*Y^16 + 5*Y^15 + 5*Y^14 + 4*Y^13 + Y^12 + 5*Y^11 + 4*Y^8 
        + 4*Y^7 + 4*Y^6 + 5*Y^5 + 3*Y^4 + 5*Y^2 + 3*Y + 6,
    T^56 + 4/7*T^55 - 1/49*T^54 + 25/343*T^53 - 1732/2401*T^52 - 1930/2401*T^51 + 
        1711/2401*T^50 + 892/2401*T^49 + 600/2401*T^48 + 1944/2401*T^47 - 
        1563/2401*T^46 - 66/49*T^45 - 135/2401*T^44 - 402/2401*T^43 + 825/2401*T^42 
        + 393/343*T^41 - 11/2401*T^40 - 549/2401*T^39 + 830/2401*T^38 - 
        933/2401*T^37 + 260/2401*T^36 + 2403/2401*T^35 - 446/2401*T^34 + 
        505/2401*T^33 + 102/343*T^32 - 1966/2401*T^31 + 410/2401*T^30 + 
        960/2401*T^29 - 1805/2401*T^28 + 960/2401*T^27 + 410/2401*T^26 - 
        1966/2401*T^25 + 102/343*T^24 + 505/2401*T^23 - 446/2401*T^22 + 
        2403/2401*T^21 + 260/2401*T^20 - 933/2401*T^19 + 830/2401*T^18 - 
        549/2401*T^17 - 11/2401*T^16 + 393/343*T^15 + 825/2401*T^14 - 402/2401*T^13 
        - 135/2401*T^12 - 66/49*T^11 - 1563/2401*T^10 + 1944/2401*T^9 + 600/2401*T^8
        + 892/2401*T^7 + 1711/2401*T^6 - 1930/2401*T^5 - 1732/2401*T^4 + 25/343*T^3 
        - 1/49*T^2 + 4/7*T + 1
*], [*
    X^3 + 6*X*Y^15 + 3*X*Y^14 + X*Y^13 + 5*X*Y^12 + 2*X*Y^11 + 4*X*Y^10 + 4*X*Y^9 + 
        3*X*Y^8 + 5*X*Y^7 + X*Y^6 + 5*X*Y^4 + 3*X*Y^3 + 4*X*Y^2 + 5*X*Y + 3*X + 
        3*Y^30 + 3*Y^27 + 6*Y^26 + Y^25 + 5*Y^23 + 6*Y^22 + 6*Y^21 + 4*Y^20 + 4*Y^19
        + 6*Y^18 + Y^17 + 3*Y^16 + Y^15 + 6*Y^14 + 4*Y^13 + 6*Y^12 + 5*Y^10 + 4*Y^9 
        + 2*Y^7 + 3*Y^6 + 2*Y^5 + Y^4 + 4*Y^3 + 5*Y + 4,
    T^56 - 10/7*T^55 + 34/49*T^54 + 242/343*T^53 - 5345/2401*T^52 + 6801/2401*T^51 -
        4097/2401*T^50 - 396/2401*T^49 + 4157/2401*T^48 - 5228/2401*T^47 + 
        4026/2401*T^46 - 1829/2401*T^45 + 741/2401*T^44 - 228/2401*T^43 - 
        18/343*T^42 + 871/2401*T^41 - 43/49*T^40 + 3922/2401*T^39 - 3912/2401*T^38 +
        285/343*T^37 + 234/2401*T^36 - 2782/2401*T^35 + 431/343*T^34 - 
        3065/2401*T^33 + 2749/2401*T^32 - 1434/2401*T^31 - 1080/2401*T^30 + 
        3109/2401*T^29 - 4023/2401*T^28 + 3109/2401*T^27 - 1080/2401*T^26 - 
        1434/2401*T^25 + 2749/2401*T^24 - 3065/2401*T^23 + 431/343*T^22 - 
        2782/2401*T^21 + 234/2401*T^20 + 285/343*T^19 - 3912/2401*T^18 + 
        3922/2401*T^17 - 43/49*T^16 + 871/2401*T^15 - 18/343*T^14 - 228/2401*T^13 + 
        741/2401*T^12 - 1829/2401*T^11 + 4026/2401*T^10 - 5228/2401*T^9 + 
        4157/2401*T^8 - 396/2401*T^7 - 4097/2401*T^6 + 6801/2401*T^5 - 5345/2401*T^4
        + 242/343*T^3 + 34/49*T^2 - 10/7*T + 1
*], [*
    X^3 + 2*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 4*X*Y^12 + 2*X*Y^11 + 5*X*Y^10 + 3*X*Y^9 
        + 2*X*Y^8 + 3*X*Y^7 + 4*X*Y^6 + 5*X*Y^5 + 2*X*Y^3 + 5*X*Y^2 + 3*X + Y^30 + 
        3*Y^28 + 6*Y^27 + Y^25 + Y^24 + 5*Y^23 + 3*Y^22 + 2*Y^21 + 4*Y^20 + 5*Y^19 +
        Y^17 + 2*Y^16 + 5*Y^15 + 5*Y^14 + Y^13 + 5*Y^12 + 6*Y^11 + 5*Y^10 + Y^9 + 
        3*Y^8 + 4*Y^5 + Y^4 + 5*Y^3 + 5*Y^2 + 5*Y + 3,
    T^56 - 4/7*T^55 + 5/49*T^54 + 262/343*T^53 - 622/2401*T^52 + 1821/2401*T^51 - 
        302/2401*T^50 + 904/2401*T^49 + 22/343*T^48 + 474/2401*T^47 + 1418/2401*T^46
        - 1103/2401*T^45 + 170/2401*T^44 + 1578/2401*T^43 - 477/2401*T^42 - 
        733/2401*T^41 + 858/2401*T^40 + 411/2401*T^39 - 1014/2401*T^38 + 
        291/2401*T^37 + 776/2401*T^36 - 424/2401*T^35 - 940/2401*T^34 + 
        2670/2401*T^33 - 853/2401*T^32 - 1216/2401*T^31 + 1879/2401*T^30 - 
        130/343*T^29 + 152/343*T^28 - 130/343*T^27 + 1879/2401*T^26 - 1216/2401*T^25
        - 853/2401*T^24 + 2670/2401*T^23 - 940/2401*T^22 - 424/2401*T^21 + 
        776/2401*T^20 + 291/2401*T^19 - 1014/2401*T^18 + 411/2401*T^17 + 
        858/2401*T^16 - 733/2401*T^15 - 477/2401*T^14 + 1578/2401*T^13 + 
        170/2401*T^12 - 1103/2401*T^11 + 1418/2401*T^10 + 474/2401*T^9 + 22/343*T^8 
        + 904/2401*T^7 - 302/2401*T^6 + 1821/2401*T^5 - 622/2401*T^4 + 262/343*T^3 +
        5/49*T^2 - 4/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + 5*X*Y^13 + 5*X*Y^12 + 6*X*Y^11 + 2*X*Y^9 + 3*X*Y^8 +
        2*X*Y^5 + 4*X*Y^4 + 2*X*Y^3 + 4*X*Y^2 + 2*X*Y + 3*X + Y^30 + 2*Y^29 + 3*Y^27
        + 5*Y^22 + 4*Y^21 + 3*Y^20 + 4*Y^18 + 5*Y^17 + 3*Y^15 + 2*Y^14 + Y^13 + 
        6*Y^11 + 3*Y^9 + 3*Y^8 + 2*Y^7 + 4*Y^6 + 3*Y^5 + Y^4 + 3*Y^3 + Y^2 + Y + 1,
    T^56 - 3/7*T^55 - 19/49*T^54 - 639/2401*T^52 + 1445/2401*T^51 - 1153/2401*T^50 +
        1807/2401*T^49 - 685/2401*T^48 - 1328/2401*T^47 + 211/343*T^46 - 
        619/2401*T^45 + 1830/2401*T^44 - 293/343*T^43 + 10/2401*T^42 + 
        1343/2401*T^41 - 184/343*T^40 + 2416/2401*T^39 - 1019/2401*T^38 - 
        269/2401*T^37 - 1249/2401*T^36 - 1109/2401*T^35 + 3037/2401*T^34 - 
        113/343*T^33 + 20/49*T^32 - 1114/2401*T^31 - 624/2401*T^30 + 1875/2401*T^29 
        - 1846/2401*T^28 + 1875/2401*T^27 - 624/2401*T^26 - 1114/2401*T^25 + 
        20/49*T^24 - 113/343*T^23 + 3037/2401*T^22 - 1109/2401*T^21 - 1249/2401*T^20
        - 269/2401*T^19 - 1019/2401*T^18 + 2416/2401*T^17 - 184/343*T^16 + 
        1343/2401*T^15 + 10/2401*T^14 - 293/343*T^13 + 1830/2401*T^12 - 
        619/2401*T^11 + 211/343*T^10 - 1328/2401*T^9 - 685/2401*T^8 + 1807/2401*T^7 
        - 1153/2401*T^6 + 1445/2401*T^5 - 639/2401*T^4 - 19/49*T^2 - 3/7*T + 1
*], [*
    X^3 + X*Y^15 + X*Y^14 + 6*X*Y^13 + 6*X*Y^12 + X*Y^11 + 3*X*Y^9 + 4*X*Y^8 + 
        3*X*Y^7 + 6*X*Y^6 + 4*X*Y^5 + 6*X*Y^4 + 2*X*Y + 3*X + 2*Y^30 + 4*Y^29 + Y^27
        + 4*Y^26 + Y^25 + Y^24 + Y^23 + 4*Y^22 + 3*Y^20 + 2*Y^19 + 5*Y^18 + Y^17 + 
        Y^16 + Y^15 + 3*Y^14 + 6*Y^13 + 4*Y^12 + 2*Y^11 + 4*Y^10 + 2*Y^9 + 4*Y^8 + 
        3*Y^7 + 6*Y^5 + 2*Y^4 + 5*Y^3 + 4*Y^2 + 5*Y + 4,
    T^56 - 2/7*T^55 + 20/49*T^54 + 193/343*T^53 + 625/2401*T^52 + 1601/2401*T^51 + 
        426/2401*T^50 + 871/2401*T^49 - 502/2401*T^48 + 407/343*T^47 - 783/2401*T^46
        - 828/2401*T^45 + 1328/2401*T^44 - 1423/2401*T^43 + 633/2401*T^42 - 
        542/2401*T^41 - 1706/2401*T^40 - 334/2401*T^39 + 664/2401*T^38 - 
        949/2401*T^37 - 1172/2401*T^36 + 1733/2401*T^35 - 1299/2401*T^34 + 
        817/2401*T^33 + 1125/2401*T^32 - 596/2401*T^31 + 1773/2401*T^30 + 
        828/2401*T^29 + 57/343*T^28 + 828/2401*T^27 + 1773/2401*T^26 - 596/2401*T^25
        + 1125/2401*T^24 + 817/2401*T^23 - 1299/2401*T^22 + 1733/2401*T^21 - 
        1172/2401*T^20 - 949/2401*T^19 + 664/2401*T^18 - 334/2401*T^17 - 
        1706/2401*T^16 - 542/2401*T^15 + 633/2401*T^14 - 1423/2401*T^13 + 
        1328/2401*T^12 - 828/2401*T^11 - 783/2401*T^10 + 407/343*T^9 - 502/2401*T^8 
        + 871/2401*T^7 + 426/2401*T^6 + 1601/2401*T^5 + 625/2401*T^4 + 193/343*T^3 +
        20/49*T^2 - 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 2*X*Y^13 + 2*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + 6*X*Y^9 
        + 4*X*Y^8 + 6*X*Y^7 + 3*X*Y^6 + 5*X*Y^5 + 4*X*Y^4 + 6*X*Y^3 + 5*X*Y^2 + 
        2*X*Y + X + 3*Y^30 + 3*Y^28 + 6*Y^27 + Y^24 + 4*Y^22 + 5*Y^21 + Y^20 + 
        4*Y^19 + 2*Y^18 + 4*Y^17 + 2*Y^16 + Y^15 + 6*Y^14 + 4*Y^13 + 3*Y^12 + 5*Y^11
        + 4*Y^9 + 5*Y^8 + 6*Y^7 + 5*Y^6 + 5*Y^5 + 6*Y^4 + 3*Y^3 + Y^2 + 6*Y + 3,
    -T^56 - 2/7*T^55 + 39/49*T^54 + 157/343*T^53 - 162/343*T^52 - 192/2401*T^51 + 
        568/2401*T^50 + 482/2401*T^49 + 594/2401*T^48 - 456/2401*T^47 + 135/343*T^46
        + 986/2401*T^45 - 37/2401*T^44 - 171/2401*T^43 - 37/343*T^42 - 164/2401*T^41
        + 982/2401*T^40 - 101/2401*T^39 - 1850/2401*T^38 + 27/343*T^37 + 
        136/343*T^36 + 37/2401*T^35 - 1028/2401*T^34 - 1556/2401*T^33 - 
        572/2401*T^32 + 1173/2401*T^31 + 419/2401*T^30 - 110/343*T^29 + 110/343*T^27
        - 419/2401*T^26 - 1173/2401*T^25 + 572/2401*T^24 + 1556/2401*T^23 + 
        1028/2401*T^22 - 37/2401*T^21 - 136/343*T^20 - 27/343*T^19 + 1850/2401*T^18 
        + 101/2401*T^17 - 982/2401*T^16 + 164/2401*T^15 + 37/343*T^14 + 
        171/2401*T^13 + 37/2401*T^12 - 986/2401*T^11 - 135/343*T^10 + 456/2401*T^9 -
        594/2401*T^8 - 482/2401*T^7 - 568/2401*T^6 + 192/2401*T^5 + 162/343*T^4 - 
        157/343*T^3 - 39/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 2*X*Y^14 + 3*X*Y^13 + 5*X*Y^12 + X*Y^11 + 6*X*Y^10 + X*Y^9 + 
        2*X*Y^8 + 2*X*Y^6 + 5*X*Y^5 + 2*X*Y^4 + 4*X*Y^3 + 3*X*Y^2 + 4*X*Y + X + 
        5*Y^30 + 3*Y^29 + Y^27 + 5*Y^26 + 4*Y^25 + 5*Y^23 + 6*Y^22 + 6*Y^20 + 4*Y^18
        + Y^17 + 6*Y^15 + 4*Y^13 + 3*Y^12 + 5*Y^11 + 6*Y^10 + 5*Y^9 + 3*Y^6 + 2*Y^5 
        + 3*Y^3 + 3*Y^2 + 5*Y + 1,
    -T^56 - 5/7*T^55 + 17/49*T^54 + 127/343*T^53 - 1805/2401*T^52 - 2645/2401*T^51 +
        171/2401*T^50 + 1773/2401*T^49 - 323/2401*T^48 - 1368/2401*T^47 - 
        20/2401*T^46 + 353/2401*T^45 + 689/2401*T^44 + 15/2401*T^43 - 772/2401*T^42 
        - 1083/2401*T^41 - 16/343*T^40 + 1158/2401*T^39 + 1613/2401*T^38 - 
        921/2401*T^37 - 120/343*T^36 + 186/2401*T^35 + 1940/2401*T^34 + 
        1265/2401*T^33 - 1826/2401*T^32 - 1971/2401*T^31 + 1338/2401*T^30 + 
        2353/2401*T^29 - 2353/2401*T^27 - 1338/2401*T^26 + 1971/2401*T^25 + 
        1826/2401*T^24 - 1265/2401*T^23 - 1940/2401*T^22 - 186/2401*T^21 + 
        120/343*T^20 + 921/2401*T^19 - 1613/2401*T^18 - 1158/2401*T^17 + 16/343*T^16
        + 1083/2401*T^15 + 772/2401*T^14 - 15/2401*T^13 - 689/2401*T^12 - 
        353/2401*T^11 + 20/2401*T^10 + 1368/2401*T^9 + 323/2401*T^8 - 1773/2401*T^7 
        - 171/2401*T^6 + 2645/2401*T^5 + 1805/2401*T^4 - 127/343*T^3 - 17/49*T^2 + 
        5/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + 5*X*Y^12 + 6*X*Y^11 + X*Y^10 + 6*X*Y^9 + 6*X*Y^8 + 6*X*Y^7 + 
        X*Y^5 + 3*X*Y^4 + 6*X*Y^3 + X*Y^2 + 4*X + 5*Y^30 + 3*Y^29 + Y^28 + 6*Y^27 + 
        6*Y^25 + 2*Y^24 + 3*Y^23 + 6*Y^22 + Y^21 + 5*Y^20 + 3*Y^19 + 4*Y^18 + 4*Y^17
        + 4*Y^16 + 5*Y^15 + 5*Y^14 + 3*Y^13 + 6*Y^12 + 2*Y^11 + 6*Y^9 + 2*Y^8 + 
        4*Y^7 + 6*Y^6 + 2*Y^5 + 4*Y^4 + 2*Y^3 + 5*Y^2 + 2*Y + 1,
    T^56 + 2/7*T^55 + 12/49*T^54 - 198/343*T^53 + 310/2401*T^52 - 38/2401*T^51 + 
        39/2401*T^50 + 233/2401*T^49 - 1457/2401*T^48 - 1514/2401*T^47 - 
        1901/2401*T^46 + 1250/2401*T^45 + 223/2401*T^44 + 235/2401*T^43 - 
        1373/2401*T^42 + 1139/2401*T^41 - 27/343*T^40 + 347/2401*T^39 + 65/343*T^38 
        + 1180/2401*T^37 + 101/343*T^36 - 776/2401*T^35 + 622/2401*T^34 - 
        626/2401*T^33 + 172/2401*T^32 + 45/2401*T^31 + 996/2401*T^30 - 940/2401*T^29
        - 296/343*T^28 - 940/2401*T^27 + 996/2401*T^26 + 45/2401*T^25 + 
        172/2401*T^24 - 626/2401*T^23 + 622/2401*T^22 - 776/2401*T^21 + 101/343*T^20
        + 1180/2401*T^19 + 65/343*T^18 + 347/2401*T^17 - 27/343*T^16 + 
        1139/2401*T^15 - 1373/2401*T^14 + 235/2401*T^13 + 223/2401*T^12 + 
        1250/2401*T^11 - 1901/2401*T^10 - 1514/2401*T^9 - 1457/2401*T^8 + 
        233/2401*T^7 + 39/2401*T^6 - 38/2401*T^5 + 310/2401*T^4 - 198/343*T^3 + 
        12/49*T^2 + 2/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 3*X*Y^14 + X*Y^13 + 6*X*Y^12 + 5*X*Y^11 + 4*X*Y^10 + X*Y^9 + 
        4*X*Y^8 + 5*X*Y^7 + 5*X*Y^6 + 4*X*Y^5 + 2*X*Y^4 + X*Y^3 + 5*X*Y^2 + 5*X*Y + 
        6*X + 6*Y^30 + Y^29 + 2*Y^28 + 5*Y^26 + 5*Y^24 + Y^23 + 6*Y^22 + 4*Y^21 + 
        6*Y^20 + 2*Y^19 + 5*Y^18 + 3*Y^17 + 6*Y^16 + 2*Y^14 + 4*Y^13 + 4*Y^12 + 
        2*Y^11 + Y^10 + 3*Y^9 + 6*Y^8 + 3*Y^7 + 5*Y^6 + 4*Y^5 + 3*Y^4 + 3*Y^3 + 
        5*Y^2 + 3*Y,
    -T^56 + 1/7*T^55 + 82/49*T^54 - 34/49*T^53 - 2726/2401*T^52 + 2516/2401*T^51 + 
        761/2401*T^50 - 1237/2401*T^49 + 888/2401*T^48 - 218/2401*T^47 - 90/343*T^46
        + 1343/2401*T^45 - 1146/2401*T^44 - 572/2401*T^43 + 1625/2401*T^42 - 
        293/2401*T^41 + 128/2401*T^40 - 375/2401*T^39 - 977/2401*T^38 + 
        1058/2401*T^37 + 344/2401*T^36 - 1696/2401*T^35 - 325/2401*T^34 + 
        941/2401*T^33 + 39/343*T^32 + 554/2401*T^31 + 213/2401*T^30 - 785/2401*T^29 
        + 785/2401*T^27 - 213/2401*T^26 - 554/2401*T^25 - 39/343*T^24 - 
        941/2401*T^23 + 325/2401*T^22 + 1696/2401*T^21 - 344/2401*T^20 - 
        1058/2401*T^19 + 977/2401*T^18 + 375/2401*T^17 - 128/2401*T^16 + 
        293/2401*T^15 - 1625/2401*T^14 + 572/2401*T^13 + 1146/2401*T^12 - 
        1343/2401*T^11 + 90/343*T^10 + 218/2401*T^9 - 888/2401*T^8 + 1237/2401*T^7 -
        761/2401*T^6 - 2516/2401*T^5 + 2726/2401*T^4 + 34/49*T^3 - 82/49*T^2 - 1/7*T
        + 1
*], [*
    X^3 + 6*X*Y^15 + 6*X*Y^14 + 2*X*Y^13 + 6*X*Y^12 + X*Y^11 + 6*X*Y^10 + 5*X*Y^9 + 
        X*Y^7 + 3*X*Y^6 + 2*X*Y^5 + 6*X*Y^4 + 4*X*Y^3 + 2*X*Y^2 + 6*X*Y + 4*X + 
        2*Y^30 + 5*Y^29 + 6*Y^28 + 6*Y^27 + 3*Y^26 + 3*Y^25 + 3*Y^24 + 3*Y^23 + Y^21
        + 6*Y^20 + 4*Y^19 + 2*Y^18 + Y^17 + 4*Y^16 + Y^15 + 3*Y^14 + 5*Y^13 + 5*Y^12
        + Y^11 + 4*Y^10 + 4*Y^9 + 2*Y^8 + 5*Y^7 + 2*Y^6 + 2*Y^5 + Y^4 + 4*Y^3 + 6*Y 
        + 1,
    T^56 + 6/7*T^55 - 44/49*T^54 - 127/343*T^53 + 1084/2401*T^52 + 642/2401*T^51 - 
        450/2401*T^50 - 611/2401*T^49 - 66/2401*T^48 - 1166/2401*T^47 - 53/2401*T^46
        + 100/343*T^45 + 344/2401*T^44 - 319/2401*T^43 + 892/2401*T^42 + 
        1493/2401*T^41 - 767/2401*T^40 + 75/343*T^39 + 598/2401*T^38 - 751/2401*T^37
        + 963/2401*T^36 + 2075/2401*T^35 - 423/2401*T^34 - 232/343*T^33 + 
        1045/2401*T^32 + 603/2401*T^31 - 1334/2401*T^30 - 33/2401*T^29 + 
        1254/2401*T^28 - 33/2401*T^27 - 1334/2401*T^26 + 603/2401*T^25 + 
        1045/2401*T^24 - 232/343*T^23 - 423/2401*T^22 + 2075/2401*T^21 + 
        963/2401*T^20 - 751/2401*T^19 + 598/2401*T^18 + 75/343*T^17 - 767/2401*T^16 
        + 1493/2401*T^15 + 892/2401*T^14 - 319/2401*T^13 + 344/2401*T^12 + 
        100/343*T^11 - 53/2401*T^10 - 1166/2401*T^9 - 66/2401*T^8 - 611/2401*T^7 - 
        450/2401*T^6 + 642/2401*T^5 + 1084/2401*T^4 - 127/343*T^3 - 44/49*T^2 + 
        6/7*T + 1
*], [*
    X^3 + 5*X*Y^15 + 6*X*Y^13 + X*Y^12 + 4*X*Y^11 + 5*X*Y^10 + 5*X*Y^8 + 5*X*Y^6 + 
        X*Y^5 + 5*X*Y^4 + 6*X*Y^2 + Y^30 + Y^28 + 2*Y^26 + 3*Y^25 + 3*Y^24 + 5*Y^23 
        + 6*Y^22 + 5*Y^21 + 4*Y^20 + 6*Y^19 + 6*Y^18 + Y^17 + 2*Y^16 + 3*Y^15 + 
        6*Y^14 + 4*Y^13 + 4*Y^12 + 2*Y^11 + 4*Y^10 + Y^9 + Y^8 + 3*Y^7 + 6*Y^6 + 
        6*Y^5 + 6*Y^4 + 4*Y^3 + 5*Y^2 + 6*Y + 5,
    T^56 - 8/7*T^55 + 10/49*T^54 - 15/49*T^53 + 1821/2401*T^52 - 1129/2401*T^51 - 
        660/2401*T^50 + 1366/2401*T^49 - 1261/2401*T^48 + 498/2401*T^47 - 
        1380/2401*T^46 + 2080/2401*T^45 - 289/343*T^44 + 2271/2401*T^43 - 
        3036/2401*T^42 + 2628/2401*T^41 - 1597/2401*T^40 + 1985/2401*T^39 - 
        1709/2401*T^38 + 657/2401*T^37 + 1135/2401*T^36 - 32/2401*T^35 - 
        797/2401*T^34 - 1608/2401*T^33 + 2619/2401*T^32 - 1772/2401*T^31 + 
        2236/2401*T^30 - 3573/2401*T^29 + 3747/2401*T^28 - 3573/2401*T^27 + 
        2236/2401*T^26 - 1772/2401*T^25 + 2619/2401*T^24 - 1608/2401*T^23 - 
        797/2401*T^22 - 32/2401*T^21 + 1135/2401*T^20 + 657/2401*T^19 - 
        1709/2401*T^18 + 1985/2401*T^17 - 1597/2401*T^16 + 2628/2401*T^15 - 
        3036/2401*T^14 + 2271/2401*T^13 - 289/343*T^12 + 2080/2401*T^11 - 
        1380/2401*T^10 + 498/2401*T^9 - 1261/2401*T^8 + 1366/2401*T^7 - 660/2401*T^6
        - 1129/2401*T^5 + 1821/2401*T^4 - 15/49*T^3 + 10/49*T^2 - 8/7*T + 1
*], [*
    X^3 + X*Y^15 + 4*X*Y^14 + 3*X*Y^13 + X*Y^12 + 5*X*Y^10 + 2*X*Y^9 + X*Y^8 + X*Y^7
        + 3*X*Y^6 + 4*X*Y^4 + X*Y^3 + 2*X*Y + 5*Y^30 + 2*Y^28 + 5*Y^27 + Y^26 + 
        5*Y^25 + 4*Y^24 + 4*Y^23 + Y^21 + 2*Y^20 + 2*Y^19 + 4*Y^18 + 6*Y^17 + 3*Y^15
        + 2*Y^14 + 3*Y^13 + 4*Y^12 + 3*Y^11 + 2*Y^9 + Y^8 + Y^6 + 3*Y^5 + 5*Y^4 + 
        5*Y^3 + 6*Y^2 + 3*Y + 6,
    T^56 + 10/7*T^55 + 72/49*T^54 + 505/343*T^53 + 3191/2401*T^52 + 1574/2401*T^51 +
        47/2401*T^50 - 617/2401*T^49 - 985/2401*T^48 - 2154/2401*T^47 - 334/343*T^46
        - 2371/2401*T^45 - 1171/2401*T^44 - 267/2401*T^43 + 1173/2401*T^42 + 
        1956/2401*T^41 + 2375/2401*T^40 + 1696/2401*T^39 - 97/2401*T^38 - 
        233/343*T^37 - 2199/2401*T^36 - 2984/2401*T^35 - 3532/2401*T^34 - 
        2650/2401*T^33 - 1524/2401*T^32 - 692/2401*T^31 - 26/343*T^30 + 
        905/2401*T^29 + 1567/2401*T^28 + 905/2401*T^27 - 26/343*T^26 - 692/2401*T^25
        - 1524/2401*T^24 - 2650/2401*T^23 - 3532/2401*T^22 - 2984/2401*T^21 - 
        2199/2401*T^20 - 233/343*T^19 - 97/2401*T^18 + 1696/2401*T^17 + 
        2375/2401*T^16 + 1956/2401*T^15 + 1173/2401*T^14 - 267/2401*T^13 - 
        1171/2401*T^12 - 2371/2401*T^11 - 334/343*T^10 - 2154/2401*T^9 - 
        985/2401*T^8 - 617/2401*T^7 + 47/2401*T^6 + 1574/2401*T^5 + 3191/2401*T^4 + 
        505/343*T^3 + 72/49*T^2 + 10/7*T + 1
*], [*
    X^3 + 3*X*Y^15 + 5*X*Y^14 + 5*X*Y^13 + 3*X*Y^12 + 6*X*Y^10 + 2*X*Y^9 + 2*X*Y^6 +
        4*X*Y^5 + X*Y^3 + 4*X*Y^2 + 5*X*Y + 6*X + 6*Y^30 + Y^29 + 2*Y^28 + 4*Y^27 + 
        4*Y^26 + 6*Y^25 + 6*Y^24 + 3*Y^23 + 2*Y^22 + 5*Y^21 + 3*Y^20 + 2*Y^19 + Y^18
        + 4*Y^17 + 3*Y^16 + 2*Y^15 + 3*Y^14 + 5*Y^13 + 2*Y^12 + 3*Y^11 + 2*Y^10 + 
        4*Y^8 + 2*Y^7 + 6*Y^6 + 6*Y^5 + 2*Y^4 + 2*Y^3 + 4*Y^2 + 6*Y + 6,
    -T^56 - 11/7*T^55 - 33/49*T^54 + 68/49*T^53 + 719/343*T^52 + 510/2401*T^51 - 
        2496/2401*T^50 - 3167/2401*T^49 - 1731/2401*T^48 - 88/343*T^47 + 
        1455/2401*T^46 + 577/343*T^45 + 2195/2401*T^44 + 430/2401*T^43 - 
        941/2401*T^42 - 1647/2401*T^41 - 1845/2401*T^40 - 79/2401*T^39 + 
        3616/2401*T^38 + 2563/2401*T^37 - 164/2401*T^36 - 1420/2401*T^35 - 
        674/2401*T^34 - 89/2401*T^33 - 361/2401*T^32 + 591/2401*T^31 + 83/2401*T^30 
        - 296/2401*T^29 + 296/2401*T^27 - 83/2401*T^26 - 591/2401*T^25 + 
        361/2401*T^24 + 89/2401*T^23 + 674/2401*T^22 + 1420/2401*T^21 + 
        164/2401*T^20 - 2563/2401*T^19 - 3616/2401*T^18 + 79/2401*T^17 + 
        1845/2401*T^16 + 1647/2401*T^15 + 941/2401*T^14 - 430/2401*T^13 - 
        2195/2401*T^12 - 577/343*T^11 - 1455/2401*T^10 + 88/343*T^9 + 1731/2401*T^8 
        + 3167/2401*T^7 + 2496/2401*T^6 - 510/2401*T^5 - 719/343*T^4 - 68/49*T^3 + 
        33/49*T^2 + 11/7*T + 1
*], [*
    X^3 + 4*X*Y^15 + X*Y^14 + X*Y^12 + 3*X*Y^11 + 4*X*Y^10 + X*Y^9 + X*Y^8 + 5*X*Y^7
        + 5*X*Y^6 + 3*X*Y^5 + 2*X*Y^4 + X*Y^3 + 6*X*Y^2 + 5*X*Y + 3*X + 6*Y^30 + 
        6*Y^29 + 6*Y^28 + Y^27 + 5*Y^26 + Y^25 + Y^24 + 4*Y^23 + 6*Y^22 + Y^21 + 
        5*Y^20 + 2*Y^19 + 4*Y^18 + 2*Y^17 + 2*Y^16 + 6*Y^15 + 5*Y^14 + Y^13 + Y^12 +
        4*Y^11 + 4*Y^10 + 6*Y^9 + Y^7 + 5*Y^5 + 4*Y^4 + 6*Y^3 + 4*Y^2 + 5*Y,
    T^56 - 4/7*T^55 + 36/49*T^54 - 41/49*T^53 + 228/343*T^52 - 830/2401*T^51 - 
        639/2401*T^50 + 1565/2401*T^49 - 2250/2401*T^48 + 2113/2401*T^47 - 
        314/343*T^46 + 1208/2401*T^45 - 100/2401*T^44 - 748/2401*T^43 + 
        894/2401*T^42 - 2008/2401*T^41 + 2017/2401*T^40 - 261/2401*T^39 - 
        94/2401*T^38 + 170/343*T^37 - 1474/2401*T^36 + 2330/2401*T^35 - 
        1795/2401*T^34 + 1473/2401*T^33 - 649/2401*T^32 - 712/2401*T^31 + 
        613/2401*T^30 - 2015/2401*T^29 + 1276/2401*T^28 - 2015/2401*T^27 + 
        613/2401*T^26 - 712/2401*T^25 - 649/2401*T^24 + 1473/2401*T^23 - 
        1795/2401*T^22 + 2330/2401*T^21 - 1474/2401*T^20 + 170/343*T^19 - 
        94/2401*T^18 - 261/2401*T^17 + 2017/2401*T^16 - 2008/2401*T^15 + 
        894/2401*T^14 - 748/2401*T^13 - 100/2401*T^12 + 1208/2401*T^11 - 
        314/343*T^10 + 2113/2401*T^9 - 2250/2401*T^8 + 1565/2401*T^7 - 639/2401*T^6 
        - 830/2401*T^5 + 228/343*T^4 - 41/49*T^3 + 36/49*T^2 - 4/7*T + 1
*], [*
    X^3 + X*Y^15 + 3*X*Y^14 + X*Y^13 + 3*X*Y^12 + 4*X*Y^11 + 6*X*Y^10 + 6*X*Y^9 + 
        3*X*Y^8 + 3*X*Y^7 + 3*X*Y^6 + X*Y^5 + 6*X*Y^4 + 2*X*Y^2 + X*Y + 6*X + 3*Y^30
        + Y^29 + 2*Y^28 + 3*Y^25 + 3*Y^24 + 2*Y^23 + 4*Y^22 + 6*Y^21 + 4*Y^20 + 
        4*Y^19 + 6*Y^18 + 3*Y^17 + 2*Y^15 + 4*Y^11 + 5*Y^10 + 2*Y^9 + Y^8 + 6*Y^7 + 
        5*Y^6 + 6*Y^4 + 2*Y^3 + 6*Y + 3,
    T^56 - 5/7*T^54 + 27/343*T^53 - 341/2401*T^52 + 307/2401*T^51 - 78/343*T^50 - 
        507/2401*T^49 + 485/2401*T^48 + 788/2401*T^47 - 153/2401*T^46 - 137/343*T^45
        - 216/2401*T^44 - 377/2401*T^43 + 33/343*T^42 + 347/2401*T^41 - 145/343*T^40
        - 26/2401*T^39 + 1409/2401*T^38 - 1098/2401*T^37 - 555/2401*T^36 + 
        517/2401*T^35 - 783/2401*T^34 + 625/2401*T^33 + 769/2401*T^32 - 68/2401*T^31
        + 685/2401*T^30 + 249/2401*T^29 - 1142/2401*T^28 + 249/2401*T^27 + 
        685/2401*T^26 - 68/2401*T^25 + 769/2401*T^24 + 625/2401*T^23 - 783/2401*T^22
        + 517/2401*T^21 - 555/2401*T^20 - 1098/2401*T^19 + 1409/2401*T^18 - 
        26/2401*T^17 - 145/343*T^16 + 347/2401*T^15 + 33/343*T^14 - 377/2401*T^13 - 
        216/2401*T^12 - 137/343*T^11 - 153/2401*T^10 + 788/2401*T^9 + 485/2401*T^8 -
        507/2401*T^7 - 78/343*T^6 + 307/2401*T^5 - 341/2401*T^4 + 27/343*T^3 - 
        5/7*T^2 + 1
*] ];
