Qx<x>:=PolynomialRing(Rationals());
basis_list:=[**];
G:=FullDirichletGroup(
401
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
400
);
qprec:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
401
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
80
);
qprec:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
401
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
25*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
402
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
402
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
402
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
402
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
402
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a^6*q^3 + a^2*q^4 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 - a^2 + a - 
        1)*q^7 - a*q^9 + a^8*q^12 + (-a^9 - a^7)*q^13 + a^4*q^16 + (-a^5 + 
        a^4)*q^19 + (-a^9 - a^5)*q^21 + a^8*q^25 - a^7*q^27 + (-a^5 - a)*q^28 + 
        (a^9 - a^8 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^31 - a^3*q^36 + (a^8
        - a^3)*q^37 + (a^4 + a^2)*q^39 + (a^6 - a)*q^43 + (a^9 - a^8 + a^7 - a^6
        + a^5 - a^4 + a^3 - a^2 + a - 1)*q^48 + (-a^9 + a^6 + a^2)*q^49 + (-a^9 
        + 1)*q^52 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a)*q^57 + 
        (a^2 - a)*q^61 + (a^4 + 1)*q^63 + a^6*q^64 + a^8*q^67 + (-a^3 + 1)*q^73 
        - a^3*q^75 + (-a^7 + a^6)*q^76 + (-a^5 + 1)*q^79 + a^2*q^81 + (-a^7 + 
        1)*q^84 + (a^9 + a^7 + a^5 - a^4 + a^3 - a^2 - 1)*q^91 + (-a^5 + 
        a^2)*q^93 + (a^6 - a^5)*q^97 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 
        - a^2 + a - 1)*q^100 + (a^4 + a^2)*q^103 - a^9*q^108 + (a^4 - a)*q^109 +
        (-a^9 - a^3)*q^111 + (-a^7 - a^3)*q^112 + (a^9 + a^7 - a^6 + a^5 - a^4 +
        a^3 - a^2 + a - 1)*q^117 + a^8*q^121 + (-a^9 - a)*q^124 + (-a^9 + 
        a^4)*q^127 + (-a^7 - a)*q^129 + O(q^130),
    q^2 + a^6*q^6 + a^2*q^8 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 - a^2 + a - 
        1)*q^14 - a*q^18 + a^8*q^24 + (-a^9 - a^7)*q^26 + a^4*q^32 + (-a^5 + 
        a^4)*q^38 + (-a^9 - a^5)*q^42 + a^8*q^50 - a^7*q^54 + (-a^5 - a)*q^56 + 
        (a^9 - a^8 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^62 - a^3*q^72 + (a^8
        - a^3)*q^74 + (a^4 + a^2)*q^78 + (a^6 - a)*q^86 + (a^9 - a^8 + a^7 - a^6
        + a^5 - a^4 + a^3 - a^2 + a - 1)*q^96 + (-a^9 + a^6 + a^2)*q^98 + (-a^9 
        + 1)*q^104 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a)*q^114 +
        (a^2 - a)*q^122 + (a^4 + 1)*q^126 + a^6*q^128 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
402
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
402
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 22*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^6 + (a - 1)*q^7 - q^9 - a*q^13 + a*q^16 + a*q^19 - q^22 + q^24 + 
        q^25 + (-a + 1)*q^31 + (a - 1)*q^33 + (-a + 1)*q^34 - a*q^37 + q^42 + (a
        - 1)*q^46 - a*q^51 + a*q^54 - q^58 - a*q^61 + (-a + 1)*q^63 - q^64 - 
        q^67 + a*q^69 + a*q^73 + (a - 1)*q^78 + (a - 1)*q^79 + q^81 + q^82 + (a 
        - 1)*q^87 + (-a + 1)*q^88 + q^91 - q^94 - a*q^97 + (-a + 1)*q^103 - 
        q^112 + (-a + 1)*q^114 + a*q^117 + (-a + 1)*q^123 + (-a + 1)*q^127 + 
        O(q^130),
    q^2 - a*q^12 + (a - 1)*q^14 - q^18 - a*q^26 + a*q^32 + a*q^38 - q^44 + q^48 
        + q^50 + (-a + 1)*q^62 + (a - 1)*q^66 + (-a + 1)*q^68 - a*q^74 + q^84 + 
        (a - 1)*q^92 - a*q^102 + a*q^108 - q^116 - a*q^122 + (-a + 1)*q^126 - 
        q^128 + O(q^130),
    q^3 - q^8 + (-a + 1)*q^11 + (a - 1)*q^12 + a*q^17 + (a - 1)*q^21 - a*q^23 - 
        q^27 + (-a + 1)*q^29 + (-a + 1)*q^32 - a*q^39 + (a - 1)*q^41 + a*q^44 + 
        (-a + 1)*q^47 + (-a + 1)*q^56 + a*q^57 - q^68 + (a - 1)*q^71 + q^72 + 
        q^75 + a*q^77 + a*q^83 - a*q^84 - 2*q^89 + q^92 + (-a + 1)*q^93 + (a - 
        1)*q^99 + (a - 1)*q^101 + a*q^104 + (-a + 1)*q^108 - a*q^111 + (-a + 
        1)*q^113 + a*q^116 - q^119 + O(q^130),
    q^4 + (-a + 1)*q^6 + (a - 1)*q^16 - a*q^22 + (a - 1)*q^28 + q^34 - q^36 + 
        a*q^42 - q^46 - a*q^52 + (a - 1)*q^54 - a*q^58 + a*q^76 - q^78 + a*q^82 
        - a*q^94 + q^96 + q^100 - a*q^112 + q^114 + (-a + 1)*q^124 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
402
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
33*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 - q^5 - q^7 + q^8 + q^9 + q^10 + q^14 - q^16 - q^18 - q^19 + q^31 + 
        q^35 + q^38 - q^40 - q^41 - q^45 + 2*q^47 - q^56 - q^59 - q^62 - q^63 + 
        q^64 + 2*q^67 - q^70 - q^71 + O(q^72),
    q^13 - q^26 - q^65 + O(q^72)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + (-a + 1)*q^7 - q^8 - q^14 + a*q^16 + (-a + 1)*q^19 - q^25 + (a -
        1)*q^33 - q^38 + a*q^39 + a*q^41 + a*q^50 + q^51 + (a - 1)*q^56 + (-a + 
        1)*q^59 + q^64 + q^66 + a*q^67 + (a - 1)*q^69 + (a - 1)*q^71 + O(q^72),
    q^3 - a*q^6 - q^11 + (a - 1)*q^13 + a*q^17 + (-a + 1)*q^21 + a*q^22 - q^23 -
        q^24 + q^26 + (a - 1)*q^27 + q^29 + (-a + 1)*q^31 + (-a + 1)*q^34 - q^37
        - q^42 - a*q^43 + a*q^46 + a*q^48 + (-2*a + 2)*q^53 + q^54 + (-a + 
        1)*q^57 - a*q^58 + a*q^61 - q^62 + O(q^72)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
403
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
404
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
404
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
100
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
404
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
50
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
404
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
50
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + a^2*q^4 + (-a^17 + a^6)*q^5 - a^3*q^8 - a^13*q^9 + (a^18 - 
        a^7)*q^10 + (a^17 - a^12 + a^10 + a^7 - a^2)*q^13 + a^4*q^16 + (-a^10 + 
        a^5 - 1)*q^17 + a^14*q^18 + (-a^19 + a^8)*q^20 + (-a^18 + a^13 + a^12 - 
        a^9 - a^8 + a^3)*q^25 + (-a^18 + a^13 - a^11 - a^8 + a^3)*q^26 + (-a^16 
        - a^6 + a)*q^29 - a^5*q^32 + (a^11 - a^6 + a)*q^34 - a^15*q^36 + (a^8 + 
        a^4)*q^37 + (a^15 - a^10 - a^9 + a^5 - 1)*q^40 + (a^19 + a^16 - a^14 + 
        a^9 - a^4)*q^41 + (-a^19 - a^5)*q^45 + a^18*q^49 + (a^19 - a^14 - a^13 +
        a^10 + a^9 - a^4)*q^50 + (a^19 - a^14 + a^12 + a^9 - a^4)*q^52 + (a^14 -
        a^7)*q^53 + (a^17 + a^7 - a^2)*q^58 + (a^19 - a^14 + a^9 - a^5 - 
        a^4)*q^61 + a^6*q^64 + (a^16 + a^14 - a^3 + a^2)*q^65 + (-a^12 + a^7 - 
        a^2)*q^68 + a^16*q^72 + (-a^19 - a^3)*q^73 + (-a^9 - a^5)*q^74 + (-a^16 
        + a^11 + a^10 - a^6 + a)*q^80 - a*q^81 + (-a^17 + 1)*q^82 + (-a^16 + 
        a^12 + a^11 - a^7 - a^6)*q^85 + (-a^9 + a^8)*q^89 + (a^15 - a^10 + a^6 +
        a^5 - 1)*q^90 + (a^18 - a^11)*q^97 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
404
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
404
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
404
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + a^2*q^4 + (a^2 - a)*q^5 - a^3*q^8 - a^3*q^9 + (-a^3 + a^2)*q^10 
        + (a^2 + 1)*q^13 + (a^3 - a^2 + a - 1)*q^16 + 2*q^17 + (a^3 - a^2 + a - 
        1)*q^18 + (-a^2 + a - 1)*q^20 + (a - 1)*q^25 + (-a^3 - a)*q^26 - 
        2*a*q^29 + q^32 - 2*a*q^34 + q^36 + (-a^2 + a - 1)*q^37 + (a^3 - a^2 + 
        a)*q^40 + (a^3 - a^2 - 1)*q^41 + (a^3 - a^2 + a)*q^45 - a^3*q^49 + (-a^2
        + a)*q^50 + (a^3 + a - 1)*q^52 + (a^3 + a - 1)*q^53 + 2*a^2*q^58 + (a^3 
        - a^2 + a)*q^61 - a*q^64 - q^65 + 2*a^2*q^68 - a*q^72 + (-a^2 + a - 
        1)*q^73 + (a^3 - a^2 + a)*q^74 + (-a + 1)*q^80 - a*q^81 + (a^2 + 1)*q^82
        + (2*a^2 - 2*a)*q^85 + (-a^2 + a - 1)*q^89 + (-a + 1)*q^90 + (-a^3 - 
        a)*q^97 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
404
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
25*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a - 1)*q^3 + q^5 + (a + 1)*q^7 + a*q^9 + (-a - 1)*q^11 - a*q^13 + (-a 
        - 1)*q^15 + a*q^17 + q^19 - 2*a*q^21 - a*q^23 - q^31 + 2*a*q^33 + (a + 
        1)*q^35 + (a - 1)*q^39 + 2*a*q^43 + a*q^45 + a*q^47 + a*q^49 + (-a + 
        1)*q^51 + (a - 1)*q^53 + (-a - 1)*q^55 + (-a - 1)*q^57 + (-a - 1)*q^59 +
        (a - 1)*q^63 - a*q^65 + (a + 1)*q^67 + (a - 1)*q^69 + q^71 - 2*a*q^77 + 
        q^79 + q^81 + a*q^85 + (-a - 1)*q^89 + (-a + 1)*q^91 + (a + 1)*q^93 + 
        q^95 - 2*q^97 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
404
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 50*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^13 - q^14 + q^16 + q^25 - q^30 - q^33 - q^45 + q^49 - q^52 - 
        q^56 + q^64 - q^65 - q^70 - q^77 - q^85 + O(q^98),
    q^2 + q^8 - q^10 - q^11 - q^15 + q^18 - q^27 + q^32 - q^39 - q^40 - q^42 - 
        q^44 + q^50 + 2*q^51 + 2*q^55 - q^60 + q^63 - q^66 + q^72 + 2*q^75 - 
        q^83 - q^90 + q^91 + O(q^98),
    q^3 - q^10 - q^11 + q^12 - q^15 + q^34 + q^35 - q^40 - q^44 + q^48 + q^50 + 
        q^55 - q^60 - q^63 - q^66 + q^67 + q^74 + q^75 - q^83 - q^91 + O(q^98),
    q^5 - q^9 - q^13 - q^14 + q^20 + q^21 + q^22 - q^36 + q^49 - q^52 + q^54 - 
        q^56 - q^65 - q^70 - q^77 + q^78 + q^80 + q^84 + q^88 + q^97 + O(q^98),
    q^6 - q^9 - q^13 - q^14 + q^17 + q^21 + q^24 + q^25 - q^30 - q^33 - q^36 + 
        q^37 - q^52 + q^54 - q^56 + q^68 + q^78 - q^81 + q^84 - q^85 + q^96 + 
        O(q^98),
    q^7 - q^10 - q^11 + q^18 + q^26 - q^27 + q^28 + q^35 - q^39 - q^40 - q^42 - 
        q^44 + q^51 + q^59 + q^72 + q^75 - q^83 - q^91 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
108
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
18*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^10 + (-a + 1)*q^16 - q^19 + (a - 1)*q^25 + a*q^31 + (a - 1)*q^34 - 
        a*q^40 + q^46 - a*q^49 + (-a + 1)*q^61 + q^64 + (-a + 1)*q^79 + a*q^85 +
        O(q^86),
    q^2 + (-a + 1)*q^5 + a*q^8 - a*q^17 + (a - 1)*q^23 - q^38 - 2*q^47 + (a - 
        1)*q^50 - a*q^53 + a*q^62 - a*q^80 + q^83 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
405
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^10 - q^16 - q^19 + q^25 - q^31 + q^34 + q^40 + q^46 + q^49 - q^61 + 
        q^64 - q^79 - q^85 + O(q^86),
    q^2 - q^5 - q^8 + q^17 + q^23 - q^38 - 2*q^47 + q^50 + q^53 - q^62 + q^80 + 
        q^83 + O(q^86),
    q^3 - q^30 - q^48 - q^57 + q^75 + O(q^86),
    q^6 - q^15 - q^24 + q^51 + q^69 + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
84
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + (-a^5 + a^4 - a^3 + a^2 - a + 1)*q^7 + (a^5 - 2*a^4 + a^3 - a^2 
        + a - 1)*q^8 + a^5*q^9 + (a^4 - 1)*q^11 + (a^4 - a^2 + 1)*q^16 + (-a^4 -
        a^2)*q^23 - a*q^25 - q^28 + a*q^29 + (-a^5 + a^3 + a^2 - 1)*q^32 + (-a^5
        + a^4 - a^3 + a^2 - a + 1)*q^36 + (a^2 + a)*q^37 + (-a^5 + a)*q^44 - 
        a^5*q^49 + (a^5 - a^4 + a^3 + a - 1)*q^53 + (a^5 - a^3)*q^56 + a^4*q^63 
        + (2*a^5 - a^4 - a^2 + 2*a)*q^64 + (-a^5 - a^3 + a^2 - a + 1)*q^67 + 
        (-a^4 + a^3 - a^2 + a - 1)*q^71 + (-a^4 + a^2)*q^72 + (a^5 - a^4 + 2*a^3
        - a^2 + a - 1)*q^77 + (-a^3 - 1)*q^79 - a^3*q^81 + (-a^5 + 2*a^4 - 2*a^3
        + a^2 + 1)*q^88 + (a^5 + a^3)*q^92 + (-a^5 - a^2)*q^99 + a^2*q^100 + 
        (a^2 - a)*q^107 + (a^3 - a^2)*q^109 + (-a^5 + a^4 + a^2 - 2*a + 1)*q^112
        + (a^5 + 1)*q^113 + O(q^114),
    q^2 + (-a^5 + a^3)*q^4 + (a^5 - a^4 - a^2 + 2*a - 1)*q^8 + (-a^5 + a^4 - a^3
        + a^2 - a + 1)*q^14 + (-a^5 + 2*a^4 - a^3 - 2*a + 1)*q^16 + a^5*q^18 + 
        (a^4 - 1)*q^22 + (-a^4 + a^2)*q^28 + (-2*a^4 + a^3 + a - 2)*q^32 + (a^3 
        - a)*q^36 + (a^5 - a^3 + a^2 - 1)*q^44 + (-a^4 - a^2)*q^46 - a*q^50 + 
        (a^5 - a^2 + 1)*q^56 + a*q^58 + (a^5 + a^4 - a^3 - a^2 + a + 1)*q^64 + 
        (a^5 - 2*a^4 + a^3 - a^2 + 2*a - 1)*q^72 + (a^2 + a)*q^74 + (a^4 - a^3 +
        a^2 - 2*a + 2)*q^88 + (-a^5 - a^2)*q^92 - a^5*q^98 + (a^5 - 2*a^4 + a^3 
        - a^2 + a - 1)*q^100 + (a^5 - a^4 + a^3 + a - 1)*q^106 + (-a^5 + a^3 - a
        - 1)*q^112 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a^2*q^4 - a^5*q^7 + (a^5 + a)*q^8 - a^3*q^9 + (-a + 1)*q^11 + (-a^4 + a 
        - 1)*q^16 + (a^4 - a)*q^23 + a^2*q^25 - q^28 + a^2*q^29 + (-a^5 + a^2 - 
        a)*q^32 + a^5*q^36 + (a^4 + a^2)*q^37 + (2*a^5 - 2*a^4 + 2*a^3 - 2*a^2 +
        2*a - 2)*q^43 + (a^3 - a^2)*q^44 - a^3*q^49 + (-a^5 + a^4)*q^53 + (-a^5 
        + a^4 + a^2 - a + 1)*q^56 - a*q^63 + (a^4 - a)*q^64 + (-a^5 - a)*q^67 + 
        (-a^5 - a^3)*q^71 + (-a^4 + a)*q^72 + (-a^4 + a^3 - a^2 + a - 1)*q^77 + 
        (a^5 - a^4 + a^3 - a^2 + a)*q^79 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^81 
        + (a^4 - a^3 + 1)*q^88 + (-a^5 + a^4 + a^2 - a + 1)*q^92 + (a^4 - 
        a^3)*q^99 - a^4*q^100 + (a^4 + a^2)*q^107 + (a^5 + a^3 - a^2 + a - 
        1)*q^109 + (a^4 - a^3 - a + 1)*q^112 + (-a^3 + 1)*q^113 + O(q^114),
    q^2 + (a^5 - a^4 - a^2 + a - 1)*q^4 + (-a^4 + a^3 + a - 1)*q^8 - a^5*q^14 + 
        (-a^5 + a^4 + a^2 - a)*q^16 - a^3*q^18 + (-a + 1)*q^22 + (a^4 - a)*q^28 
        + (-a^5 + a^4 - a^3 - a + 1)*q^32 + (a^5 - a^4 + a^3 + a - 1)*q^36 + 
        (a^5 - a^2 + a)*q^44 + (a^4 - a)*q^46 + a^2*q^50 + (a^4 - a^3 + 1)*q^56 
        + a^2*q^58 + a^5*q^64 + (-a^5 + a^2 - a)*q^72 + (a^4 + a^2)*q^74 + 
        (2*a^5 - 2*a^4 + 2*a^3 - 2*a^2 + 2*a - 2)*q^86 + (a^5 - 2*a^4 + a^3 - 
        a^2 + 2*a - 1)*q^88 + (a^4 - a^3 + 2)*q^92 - a^3*q^98 + (-a^5 - a)*q^100
        + (-a^5 + a^4)*q^106 + (a^5 - a^4 + a)*q^112 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
406
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^7 - q^9 + q^16 - 2*q^23 + q^25 - q^28 - q^29 - q^36 + q^49 + 
        2*q^53 + q^63 + q^64 - 2*q^67 + 2*q^71 + q^81 - 2*q^92 + q^100 + 2*q^107
        - 2*q^109 - q^112 + O(q^114),
    q^2 + q^8 - q^14 - q^18 + q^32 - 2*q^46 + q^50 - q^56 - q^58 - q^72 + q^98 +
        2*q^106 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
180
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^3 - a^2 + 1)*q^3 + a*q^4 + (-a^4 - a)*q^5 + (a^5 + a^4 - a^3 - 
        a^2)*q^9 + (a^3 - 1)*q^11 + (-a^4 - a^3 + a)*q^12 + (a^4 + 2*a^3 - 2*a -
        1)*q^15 + a^2*q^16 + (-a^5 - a^2)*q^20 + (-a^5 - a^4 + a^2 + a)*q^23 + 
        2*a^5*q^25 + (a^5 - a^3 + a)*q^27 + (-a^5 + a^3 + a^2)*q^33 + (a^5 - a^4
        - 1)*q^36 - a^5*q^37 + (a^4 - a)*q^44 + (-2*a^5 + 2*a^4 + a^3 + a^2 - a 
        + 1)*q^45 + (a^4 + a^2)*q^47 + (-a^5 - a^4 + a^2)*q^48 - a^5*q^49 + (a^4
        - a^3 - a + 1)*q^53 + (-a^4 + 2*a)*q^55 + (a^4 - 1)*q^59 + (a^5 + 2*a^4 
        - 2*a^2 - a)*q^60 + a^3*q^64 + (a^5 + a^3 - a^2 - 1)*q^67 + (-a^5 - a^4 
        - a - 1)*q^69 + (a^5 + a^3)*q^71 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^4 - a^3)*q^3 + a^2*q^4 + a^5*q^5 + (a^5 - a^4 + a^3 - a^2 + a - 
        1)*q^9 - a^3*q^11 + (-a^5 + a^3 - 1)*q^12 + (-a^5 + a^2 - 1)*q^15 + 
        a^4*q^16 + (a^4 - a)*q^20 + (-a^5 - a^4 + a)*q^23 + (-a^3 + a^2 - a + 
        1)*q^27 + 2*q^31 + (-a^4 + a^3 + a - 1)*q^33 + (a^5 - a^2 - a + 1)*q^36 
        - a*q^37 - a^5*q^44 + (-a^4 + a^3 - a^2)*q^45 + (a^5 + a^4 - a^2)*q^47 +
        (a^5 - a^4 - a^2 + a)*q^48 - a*q^49 + (-a^5 - a^3)*q^53 + (-a^5 + 
        a^2)*q^55 + (a^5 - a^2 + 1)*q^59 + (-a^2 + a)*q^60 + (a^3 - 1)*q^64 + 
        (-a^4 - a^3 + a)*q^67 + (a^5 - a + 1)*q^69 + (a^3 - a - 1)*q^71 + 
        O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + a*q^4 + q^11 + (-a + 1)*q^12 + (a - 1)*q^16 + (-2*a + 1)*q^23 + 
        (a - 1)*q^25 - q^27 - a*q^33 + (a - 1)*q^37 + a*q^44 - q^47 + q^48 + (a 
        - 1)*q^49 + (a - 1)*q^53 + (-a - 1)*q^59 - q^64 + a*q^67 + (a - 2)*q^69 
        - a*q^71 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^3 + (a - 1)*q^4 + (2*a - 2)*q^5 + q^11 + a*q^12 + 2*a*q^15 - 
        a*q^16 - 2*a*q^20 - q^23 - 3*a*q^25 + q^27 + 2*q^31 + (-a + 1)*q^33 - 
        a*q^37 + (a - 1)*q^44 - q^47 - q^48 - a*q^49 + a*q^53 + (2*a - 2)*q^55 +
        a*q^59 - 2*q^60 + q^64 + (-a + 1)*q^67 + (a - 1)*q^69 + (-a + 1)*q^71 + 
        O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
407
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^11 + q^12 - q^16 + q^25 - 2*q^26 - q^27 - q^33 + 2*q^34 - 2*q^36 + 
        q^37 - q^38 + q^44 - q^47 + q^49 - q^53 - q^58 - q^64 - q^67 - q^71 + 
        O(q^74),
    q^2 - q^13 - q^24 - q^39 + q^50 + q^57 + q^61 + O(q^74),
    q^3 - q^11 - q^12 + q^27 - q^34 + q^36 - q^37 + q^38 + q^58 + q^64 + 
        O(q^74),
    q^4 - q^11 - 2*q^12 + q^16 + q^26 + q^27 + q^33 - 2*q^34 + 2*q^36 - q^37 - 
        q^44 - q^48 + q^53 + q^64 + q^71 + O(q^74),
    q^6 - q^8 - q^13 + q^19 + q^29 - q^39 - q^51 + q^57 - q^66 + q^68 - q^72 + 
        O(q^74),
    q^9 - q^11 - q^12 + q^16 + q^26 - 2*q^34 + q^36 - q^37 + q^38 - q^44 + q^47 
        - q^48 + q^58 + q^64 + q^67 + O(q^74),
    q^17 - q^18 - q^19 + q^22 + q^24 - q^29 - q^32 + q^39 + q^43 - q^52 - q^57 +
        q^68 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + 1/2*(-a^7 + a^2)*q^3 + a^6*q^4 + 1/2*(-a^5 + a^2)*q^6 + 1/2*(-a^6 + 
        a^4)*q^9 + 1/2*(a^5 - 1)*q^12 - a^4*q^16 + 1/2*(-a^7 + a)*q^18 + (a^5 - 
        a)*q^19 + (a^7 - a^6)*q^22 + 1/2*(a^3 - 1)*q^24 - a^5*q^25 + 1/2*(a^6 - 
        a^5)*q^27 + 1/2*(-a^6 + a^5 + a^3 - a^2)*q^33 - a^2*q^34 + 1/2*(a^4 - 
        a^2)*q^36 + (-a^2 - 1)*q^43 + 1/2*(-a^6 - a^3)*q^48 - a^3*q^49 + 
        1/2*(a^6 + a)*q^51 + 1/2*(a + 1)*q^54 + 1/2*(a^7 + a^4 - a^3 - 1)*q^57 +
        a^2*q^64 + 1/2*(a^6 - a^5 - a + 1)*q^66 + (a^7 + a)*q^67 + 1/2*(a^7 + 
        a^5)*q^72 + (a^3 + a^2)*q^73 + 1/2*(-a^7 - a^4)*q^75 + (-a^7 - a^3)*q^76
        + 1/2*(-a^4 - 1)*q^81 + (a^5 + a^4)*q^82 + (-a^5 + a^4)*q^88 + 1/2*(-a^6
        - a)*q^96 + (-a^4 + a)*q^97 + 1/2*(a^7 + a^2 - a + 1)*q^99 + a^3*q^100 +
        1/2*(-a^4 - a)*q^102 + 1/2*(-a^4 + a^3)*q^108 + 1/2*(a^7 + a^6 - a^3 + 
        a^2)*q^114 + (-a^7 - a)*q^118 + (-a^7 + a^6 - 1)*q^121 + 1/2*(-a^4 - a^3
        + a + 1)*q^123 + 1/2*(a^7 - a^4 - a^2 - a)*q^129 + O(q^130),
    q^2 + 1/2*(a^7 - a^4)*q^3 + 1/2*(-a^7 + a^2)*q^6 + a^6*q^8 + 1/2*(-a^3 - 
        a)*q^9 + (a - 1)*q^11 + 1/2*(-a^5 + a^2)*q^12 + a^4*q^17 + 1/2*(-a^6 + 
        a^4)*q^18 + 1/2*(a^5 - 1)*q^24 + 1/2*(-a^3 - a^2)*q^27 - a^4*q^32 + 
        1/2*(a^7 + a^3 - a^2 + 1)*q^33 + 1/2*(-a^7 + a)*q^36 + (a^5 - a)*q^38 + 
        (-a^7 - a^6)*q^41 + (a^7 - a^6)*q^44 + 1/2*(a^3 - 1)*q^48 - a^5*q^50 + 
        1/2*(a^6 + a^3)*q^51 + 1/2*(a^6 - a^5)*q^54 + 1/2*(a^5 - a^4 + a + 
        1)*q^57 + (a^3 - a)*q^59 + 1/2*(-a^6 + a^5 + a^3 - a^2)*q^66 - a^2*q^68 
        + 1/2*(a^4 - a^2)*q^72 + 1/2*(a^4 - a)*q^75 + 1/2*(-a^5 - a)*q^81 + 
        (-a^5 - a^3)*q^83 + (-a^2 - 1)*q^86 + (-a^4 + a^2)*q^89 + 1/2*(-a^6 - 
        a^3)*q^96 - a^3*q^98 + 1/2*(-a^7 + a^6 + a^5 - a^4)*q^99 + 1/2*(a^6 + 
        a)*q^102 + (a^5 + a^2)*q^107 + 1/2*(a + 1)*q^108 + (a^6 + a^3)*q^113 + 
        1/2*(a^7 + a^4 - a^3 - 1)*q^114 + 1/2*(-a^6 - a^5 + a + 1)*q^123 + 
        a^2*q^128 + 1/2*(-a^7 + a^6 + a^4 + a)*q^129 + O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a^3*q^2 - a^2*q^4 + a*q^8 - a*q^9 + (a^3 - 1)*q^11 - q^16 - a^3*q^17 + 
        q^18 + (-a^3 - a^2)*q^22 - a*q^25 + (-a^3 - 1)*q^27 - a^3*q^32 + 
        a^2*q^34 + a^3*q^36 + (a^2 + a)*q^41 + (a^2 + 1)*q^43 + (a^2 + a)*q^44 +
        a^3*q^49 + q^50 + (-a^3 + a^2)*q^54 + (-a^2 - 1)*q^59 + a^2*q^64 + (-a^3
        + a)*q^67 - a*q^68 - a^2*q^72 + (a^3 + a^2)*q^73 + (a^3 - a^2 + a)*q^81 
        + (-a - 1)*q^82 + (-a^2 + 1)*q^83 + (a^3 - a)*q^86 + (-a - 1)*q^88 + 
        (-a^3 - a)*q^89 + (a - 1)*q^97 - a^2*q^98 + (a + 1)*q^99 + a^3*q^100 + 
        (-a + 1)*q^107 + (a^2 - a)*q^108 + (-a^2 + a)*q^113 + (-a^3 + a)*q^118 +
        (-a^3 - a^2 + 1)*q^121 - a*q^128 + O(q^130),
    q^3 + a^3*q^6 + (-a^3 + a^2)*q^9 - a^2*q^12 + (a^2 - a)*q^18 + a*q^24 + 
        (-a^2 + a - 1)*q^27 + (a^3 - 1)*q^33 + (-a + 1)*q^36 - q^48 - a^3*q^51 +
        (-a^3 + a - 1)*q^54 + (-a^3 - a^2)*q^66 + (a^3 + 1)*q^72 - a*q^75 + (a^3
        - a^2 - a + 1)*q^81 - a^3*q^96 + (a^3 - a)*q^99 + a^2*q^102 + (-a^3 + 
        a^2 - 1)*q^108 + (a^2 + a)*q^123 + (a^2 + 1)*q^129 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a - 1)*q^5 + a*q^9 - q^17 + a*q^25 + (a + 1)*q^29 + (-a - 1)*q^37 + 
        (-a + 1)*q^41 + (-a + 1)*q^45 - a*q^49 + (a - 1)*q^61 + (a + 1)*q^73 - 
        q^81 + (a + 1)*q^85 + (-a - 1)*q^97 + (a - 1)*q^109 + (a - 1)*q^113 - 
        a*q^121 + O(q^130),
    q^2 + a*q^4 - q^8 + (-a - 1)*q^10 - a*q^16 + a*q^18 + (-a + 1)*q^20 + q^32 -
        q^34 - q^36 + (a + 1)*q^40 + a*q^50 + (a + 1)*q^58 + a*q^64 - a*q^68 - 
        a*q^72 + (-a - 1)*q^74 + (a - 1)*q^80 + (-a + 1)*q^82 + (-a + 1)*q^90 - 
        a*q^98 - q^100 + (a - 1)*q^116 + (a - 1)*q^122 - q^128 + O(q^130),
    q^3 + (-a - 1)*q^15 + a*q^27 - q^51 + a*q^75 + (a + 1)*q^87 + (-a - 1)*q^111
        + (-a + 1)*q^123 + O(q^130),
    q^6 + a*q^12 - q^24 + (-a - 1)*q^30 - a*q^48 + a*q^54 + (-a + 1)*q^60 + q^96
        - q^102 - q^108 + (a + 1)*q^120 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 - q^4 + a*q^8 - a*q^9 + (-a + 1)*q^11 + q^16 - a*q^17 - q^18 + 
        2*a*q^19 + (-a - 1)*q^22 + a*q^25 + (a - 1)*q^27 - a*q^32 - q^34 + 
        a*q^36 + 2*q^38 + (a - 1)*q^41 + (a - 1)*q^44 - a*q^49 + q^50 + (a + 
        1)*q^54 - q^64 + a*q^68 + q^72 + (-a - 1)*q^73 - 2*a*q^76 + q^81 + (a + 
        1)*q^82 + (a + 1)*q^88 + (a + 1)*q^97 - q^98 + (-a - 1)*q^99 - a*q^100 +
        (a + 1)*q^107 + (-a + 1)*q^108 + (a - 1)*q^113 - a*q^121 + a*q^128 + 
        O(q^130),
    q^3 - a*q^6 + (-a - 1)*q^9 - q^12 + (a - 1)*q^18 + a*q^24 + a*q^27 + (-a + 
        1)*q^33 + (a + 1)*q^36 + q^48 - a*q^51 + q^54 + 2*a*q^57 + (-a - 1)*q^66
        + (-a + 1)*q^72 + a*q^75 - a*q^96 - 2*q^99 - q^102 - a*q^108 + 2*q^114 +
        (a - 1)*q^123 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^7 - a*q^9 - q^13 - a*q^15 + a*q^19 + q^33 + (a + 1)*q^37 - 
        a*q^43 - a*q^49 - q^51 + q^55 + (a - 1)*q^61 + (a + 1)*q^63 - q^69 + (-a
        + 1)*q^79 - q^81 - q^85 + (-a + 1)*q^91 - q^103 + (a + 1)*q^105 - q^115 
        + a*q^117 + q^123 - a*q^127 + O(q^130),
    q^3 + q^5 + a*q^11 - a*q^17 + (a - 1)*q^21 - a*q^23 - a*q^27 + (a - 1)*q^35 
        - q^39 + a*q^41 - a*q^45 + a*q^57 + (-a - 1)*q^59 - q^65 + (-a - 1)*q^77
        + (-a + 1)*q^89 + a*q^95 + q^99 + q^107 + (a + 1)*q^111 + a*q^113 + (a +
        1)*q^119 + a*q^125 - a*q^129 + O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 - 2*q^13 + q^17 + q^25 - q^49 + 2*q^53 + q^81 - 2*q^89 - 2*q^101 + 
        2*q^117 - q^121 + O(q^130),
    q^2 - q^4 + q^8 - q^16 - q^18 - 2*q^26 + q^32 + q^34 + q^36 + q^50 + 2*q^52 
        - q^64 - q^68 - q^72 - q^98 - q^100 - 2*q^104 + 2*q^106 + q^128 + 
        O(q^130),
    q^3 - q^27 - 2*q^39 + q^51 + q^75 + O(q^130),
    q^6 - q^12 + q^24 - q^48 - q^54 - 2*q^78 + q^96 + q^102 + q^108 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 8*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 + q^4 - q^8 + q^9 + q^16 - q^17 - q^18 - 2*q^19 - q^25 - q^32 + q^34
        + q^36 + 2*q^38 + 2*q^43 - q^49 + q^50 + 2*q^59 + q^64 - 2*q^67 - q^68 -
        q^72 - 2*q^76 + q^81 + 2*q^83 - 2*q^86 - 2*q^89 + q^98 - q^100 - 2*q^118
        + q^121 - q^128 + O(q^130),
    q^3 - q^6 + q^12 - q^24 + q^27 + q^48 - q^51 - q^54 - 2*q^57 - q^75 - q^96 +
        q^102 + q^108 + 2*q^114 + 2*q^129 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 8*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^13 - q^15 - q^19 - q^33 - q^43 + q^49 + q^51 + q^55 + 2*q^67 - 
        q^69 + q^81 - q^85 + 2*q^87 - q^103 + q^115 - q^117 - q^123 - q^127 + 
        O(q^130),
    q^2 + q^18 - q^26 - q^30 - q^38 - q^66 - q^86 + q^98 + q^102 + q^110 + 
        O(q^130),
    q^3 - q^5 - q^11 + q^17 - q^23 + q^27 + 2*q^29 - q^39 - q^41 - q^45 - q^57 +
        q^65 + 2*q^71 + q^95 - q^99 - q^107 - q^113 + q^125 - q^129 + O(q^130),
    q^6 - q^10 - q^22 + q^34 - q^46 + q^54 + 2*q^58 - q^78 - q^82 - q^90 - q^114
        + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
408
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 8*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
409
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
408
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
409
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
136
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
409
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
409
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
51*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
410
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
411
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
411
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
136
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
411
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
68
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
411
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
411
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
411
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
411
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 34*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
411
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 68*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^7 + q^9 - q^15 + q^16 - q^19 - q^28 + q^36 - q^37 - q^60 - q^61 
        - q^63 + q^64 - q^69 - q^73 - q^76 + q^81 - q^87 + O(q^90),
    q^3 - q^5 + q^12 - q^20 - q^21 - q^23 + q^27 - q^29 + q^35 + 2*q^41 - q^45 -
        q^47 + q^48 + 2*q^53 - q^57 + 2*q^71 - q^80 - q^83 - q^84 - q^89 + 
        O(q^90)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
412
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
412
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
102
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
412
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
102
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
412
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
412
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
412
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
412
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 34*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
412
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
51*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^13 - q^19 - q^23 + q^25 - q^41 - q^79 + q^81 - q^91 + O(q^100),
    q^2 + q^18 - q^26 - q^28 - q^32 - q^38 - q^46 + q^50 + q^52 + q^64 - q^68 + 
        q^76 - q^82 + q^92 + O(q^100),
    q^4 - q^28 - q^32 + q^36 - q^56 - q^68 + O(q^100),
    q^7 - q^13 + q^17 - q^19 - q^23 + q^29 - q^41 - q^49 + q^59 + q^61 + q^63 - 
        q^79 + q^83 + q^97 + O(q^100),
    q^8 - q^16 - q^28 + q^52 - q^68 + q^72 + q^76 + q^92 + O(q^100),
    q^14 + q^16 - q^26 - q^32 + q^34 - q^38 - q^46 - q^56 + q^58 - q^82 - q^98 +
        O(q^100)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
413
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
413
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
413
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
413
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
174
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
413
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
174
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
413
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
413
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
29*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + q^4 - q^5 - q^12 + q^15 + q^16 + 2*q^17 - q^19 - q^20 + q^27 - 
        q^29 - q^41 - q^48 - q^49 - 2*q^51 - q^53 + q^57 + q^59 + q^60 + q^64 + 
        2*q^68 + 2*q^71 - q^76 + O(q^78),
    q^7 - q^21 + q^28 - q^35 - q^49 + O(q^78)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
413
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 29*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (a - 1)*q^9 - q^15 + (a - 1)*q^16 + a*q^17 - a*q^21 - a*q^25 + 
        2*q^27 - a*q^35 + q^36 + a*q^45 - q^57 - a*q^59 + a*q^60 + (a - 1)*q^63 
        + q^64 + (-a + 1)*q^68 - q^71 + (-a + 1)*q^75 + O(q^78),
    q^3 + 1/3*(a - 2)*q^7 - a*q^9 - a*q^12 + (-a + 1)*q^15 + a*q^19 + 1/3*(-a + 
        2)*q^21 + (a - 1)*q^27 + 1/3*(a + 1)*q^28 + 1/3*(2*a - 1)*q^35 + (a - 
        1)*q^36 + (-a + 1)*q^41 - q^45 + (a - 1)*q^48 + 1/3*(2*a - 1)*q^49 + 
        a*q^51 - q^53 - q^60 - a*q^63 + (-a + 1)*q^76 + O(q^78),
    q^5 + 1/3*(-a + 2)*q^7 + a*q^15 - q^19 - a*q^20 + 1/3*(a + 1)*q^21 + (a - 
        1)*q^25 + 1/3*(-a - 1)*q^28 - a*q^29 + 1/3*(a - 2)*q^35 + a*q^41 + 
        1/3*(a - 2)*q^49 + (-a + 1)*q^53 - a*q^57 + (-a + 1)*q^60 - q^75 + 
        a*q^76 + O(q^78)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
414
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
414
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
414
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
414
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
414
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
414
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
414
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^13 - q^16 + q^25 - q^31 - q^46 + q^49 + q^58 + q^64 - q^73 + q^82 + 
        q^94 - 2*q^118 + q^121 - q^127 + O(q^130),
    q^2 - q^26 - q^32 + q^50 - q^62 - q^92 + q^98 + q^116 + q^128 + O(q^130),
    q^3 - q^12 + q^24 - q^27 - q^39 + q^69 + q^75 + q^81 - q^87 - q^93 - q^96 + 
        q^108 - q^123 + O(q^130),
    q^4 - q^16 - q^46 - q^52 + q^58 + q^82 + q^94 + q^100 - 2*q^118 - q^124 + 
        O(q^130),
    q^6 - q^12 + q^48 - q^54 - q^78 - q^96 + q^108 + O(q^130),
    q^8 + q^23 - q^29 - q^32 - q^41 - q^47 + 2*q^59 - q^71 - q^92 + 2*q^101 - 
        q^104 + q^116 + O(q^130),
    q^9 - q^27 - q^36 + q^72 + q^108 - q^117 + O(q^130),
    q^18 - q^36 - q^54 + q^108 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
414
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^9 + q^12 + q^13 - q^16 + (a - 1)*q^18 + (a - 1)*q^23 + (-a + 
        1)*q^24 - a*q^25 + q^26 - a*q^27 - a*q^29 + (a - 1)*q^31 - q^32 + a*q^36
        - q^39 - a*q^41 + q^47 + (-a + 1)*q^48 + (a - 1)*q^49 - a*q^58 + (-a + 
        1)*q^59 + (a - 1)*q^62 - q^64 + q^71 + q^73 - a*q^78 - a*q^82 + (-a + 
        1)*q^87 - q^93 + q^94 + a*q^101 + a*q^104 + (a - 2)*q^116 + q^117 + (a -
        1)*q^121 + 2*q^123 + (a + 1)*q^124 + (a - 1)*q^127 + q^128 + O(q^130),
    q^2 + q^9 - a*q^12 - a*q^13 + (a - 1)*q^16 + (a - 1)*q^29 + q^31 + (a - 
        1)*q^39 + (a - 1)*q^41 + (a - 1)*q^46 - a*q^47 - a*q^50 + q^52 - a*q^54 
        - a*q^71 + (a - 1)*q^72 - a*q^73 + (a - 1)*q^78 + (a - 1)*q^87 + q^93 + 
        q^96 + (a - 1)*q^98 + q^104 + q^116 + (-a + 1)*q^118 - a*q^123 - a*q^124
        + q^127 - a*q^128 + O(q^130),
    q^3 + a*q^9 + (-a + 1)*q^12 + (a - 2)*q^16 - a*q^24 + (a - 2)*q^29 + (a + 
        1)*q^31 + q^36 - q^39 + (-a - 1)*q^41 + (-a + 2)*q^47 + (a - 1)*q^69 + 
        (-2*a + 1)*q^71 - q^72 + (-2*a + 1)*q^73 - a*q^75 - a*q^81 - q^87 + 
        a*q^93 + a*q^96 + (a + 1)*q^104 + (2*a - 1)*q^116 + (a - 1)*q^117 + (-a 
        + 1)*q^123 + (-a + 2)*q^124 + (2*a - 1)*q^127 + (-a + 2)*q^128 + 
        O(q^130),
    q^4 + q^9 - a*q^12 - a*q^13 + (2*a - 1)*q^16 + q^18 + (-a - 1)*q^24 - a*q^26
        + (a - 1)*q^29 + q^31 + (a - 1)*q^32 + (-a + 1)*q^36 + (a - 1)*q^39 + (a
        - 1)*q^41 - a*q^47 + (a - 1)*q^58 + q^62 - a*q^71 + (a - 1)*q^72 - 
        a*q^73 + (a - 1)*q^78 + (a - 1)*q^82 + (a - 1)*q^87 + (a - 1)*q^92 + 
        q^93 - a*q^94 + q^96 - a*q^100 + (-a + 3)*q^104 - a*q^108 + (a + 
        1)*q^116 - a*q^123 + (-2*a + 1)*q^124 + q^127 + (-2*a + 1)*q^128 + 
        O(q^130),
    q^6 + (2*a - 1)*q^9 + (-a + 1)*q^12 + (-a + 2)*q^13 + (a - 2)*q^16 + a*q^18 
        + (-2*a + 1)*q^24 + (-a - 1)*q^29 + (2*a - 1)*q^31 + (a - 2)*q^32 + q^36
        + (-a - 1)*q^39 + (-a - 1)*q^41 + (-a + 2)*q^47 - a*q^48 + (a - 2)*q^58 
        + (a + 1)*q^62 + (-a + 2)*q^71 + (-a + 2)*q^73 - q^78 + (-a - 1)*q^82 + 
        (-a - 1)*q^87 + (2*a - 1)*q^93 + (-a + 2)*q^94 + a*q^96 + (a + 1)*q^104 
        + (2*a - 1)*q^116 + (-a + 2)*q^123 + (-a + 2)*q^124 + (2*a - 1)*q^127 + 
        (-a + 2)*q^128 + O(q^130),
    q^8 + a*q^9 + (-a + 1)*q^13 + (a - 1)*q^16 - a*q^24 - q^29 + a*q^31 + (a - 
        1)*q^32 + q^36 - q^39 - q^41 + (-a + 1)*q^47 - a*q^48 - a*q^52 - q^64 + 
        (-a + 1)*q^71 + (-a + 1)*q^73 - q^87 + a*q^93 + q^96 + q^104 + (a - 
        1)*q^116 + (-a + 1)*q^123 + q^124 + a*q^127 + (-a + 1)*q^128 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
415
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
415
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
82
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
415
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
82
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
415
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
164
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
415
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
41*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + q^4 - q^7 - q^11 - q^12 + q^16 - q^17 + q^21 + 2*q^23 + q^25 + 
        q^27 - q^28 - q^29 - q^31 + q^33 - q^37 + 2*q^41 - q^44 - q^48 + q^51 - 
        q^59 - q^61 + q^64 - q^68 - 2*q^69 - q^75 + q^77 - q^81 + O(q^82),
    q^5 - q^15 + q^20 - q^35 - q^55 - q^60 + q^80 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
415
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 41*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^26 - q^29 - q^31 - q^40 - q^44 + q^49 - q^59 - q^65 + 
        q^81 + O(q^82),
    q^2 - q^13 + q^18 - q^20 - q^22 - q^43 - q^47 + q^50 + q^53 + q^55 + q^67 + 
        q^73 + O(q^82),
    q^4 - q^10 - q^11 + q^29 + q^31 + q^36 - q^41 - q^44 + q^59 - q^61 - q^64 + 
        q^65 + O(q^82),
    q^5 - q^8 - q^13 + q^22 + q^32 - q^43 + q^45 - q^47 + q^52 - q^58 - q^62 - 
        q^72 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^2 + a)*q^5 + (-a^2 + 1)*q^9 + (a^3 - a)*q^13 + a*q^17 + (-a^3 + 
        2*a^2 - 1)*q^25 + (-a^3 - a)*q^29 + (a^3 + a^2 - 1)*q^37 + (-a - 1)*q^41
        + (-a^3 + a - 1)*q^45 + (a^3 - a)*q^49 + q^53 + (a^2 - 1)*q^61 + (a - 
        1)*q^65 + (-a^2 - a)*q^73 - a^2*q^81 + (-a^3 + a^2)*q^85 + (a^3 + a^2 - 
        a)*q^89 + (a^2 + a - 1)*q^97 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (2*a - 1)*q^5 - a*q^9 + (-a + 1)*q^13 - a*q^17 - 2*q^25 + (a - 1)*q^29 +
        (-a - 1)*q^37 + (a + 1)*q^41 + (-a + 2)*q^45 + (-a + 1)*q^49 - q^53 + 
        a*q^61 + (a + 1)*q^65 + (2*a - 1)*q^73 + (a - 1)*q^81 + (-a + 2)*q^85 + 
        O(q^98),
    q^2 + (2*a - 1)*q^10 - a*q^18 + (-a + 1)*q^26 - a*q^34 - 2*q^50 + (a - 
        1)*q^58 + (-a - 1)*q^74 + (a + 1)*q^82 + (-a + 2)*q^90 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a + 1)*q^5 - q^9 + a*q^13 - 2*a*q^17 + a*q^25 + (-a + 1)*q^37 + (-a - 
        1)*q^41 + (-a - 1)*q^45 + a*q^49 - 2*q^53 - 2*q^61 + (a - 1)*q^65 + (-a 
        + 1)*q^73 + q^81 + (-2*a + 2)*q^85 + (a - 1)*q^89 + (a + 1)*q^97 + 
        O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^13 + (a - 1)*q^17 - q^21 - q^25 + a*q^29 + (-a + 1)*q^33 - a*q^37 - 
        a*q^41 - q^57 + (-a + 1)*q^61 + (a - 1)*q^69 - q^77 + a*q^81 + a*q^89 + 
        (-a + 1)*q^97 + O(q^98),
    q^3 - a*q^7 + q^11 - a*q^19 - q^23 + (a - 1)*q^27 + q^39 + a*q^43 + (2*a - 
        2)*q^47 + (a - 1)*q^51 - a*q^59 - q^67 + a*q^71 - q^75 + (-2*a + 2)*q^79
        + a*q^87 - a*q^91 + O(q^98)
]
;
Bo:=
[
    q - q^5 + (a - 1)*q^9 - a*q^13 + (-a + 1)*q^17 + a*q^29 + a*q^37 + a*q^41 + 
        (-a + 1)*q^45 - a*q^49 - q^53 + (-a + 1)*q^61 + a*q^65 - q^73 - a*q^81 +
        (a - 1)*q^85 - 2*a*q^89 + (2*a - 2)*q^97 + O(q^98),
    q^2 - q^10 + (a - 1)*q^18 - a*q^26 + (-a + 1)*q^34 + a*q^58 + a*q^74 + 
        a*q^82 + (-a + 1)*q^90 + O(q^98),
    q^4 - q^20 + (a - 1)*q^36 - a*q^52 + (-a + 1)*q^68 + O(q^98),
    q^8 - a*q^16 + (a - 1)*q^32 - q^40 + q^64 + (a - 1)*q^72 + a*q^80 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^13 - 2*q^17 + q^25 - 2*q^29 - q^49 + 2*q^53 + 2*q^61 + q^81 + 
        O(q^98),
    q^2 + q^18 - q^26 - 2*q^34 + q^50 - 2*q^58 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
416
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^3 - q^17 - q^27 - q^35 + q^43 - q^51 - q^65 - q^81 + q^91 + O(q^98),
    q^5 - q^7 - q^13 + q^15 - q^21 + 2*q^31 + q^37 - q^39 - q^47 - q^71 - q^85 +
        2*q^93 + O(q^98)
]
;
Bo:=
[
    q - q^3 - q^17 + q^27 + q^35 - q^43 + q^51 - q^65 - q^81 - q^91 + O(q^98),
    q^2 - q^6 - q^34 + q^54 + q^70 - q^86 + O(q^98),
    q^4 - q^12 + q^16 - q^40 - q^48 - q^56 + q^64 - q^68 + O(q^98),
    q^5 + q^7 - q^13 - q^15 - q^21 - 2*q^31 + q^37 + q^39 + q^47 + q^71 - q^85 +
        2*q^93 + O(q^98),
    q^8 - q^20 - q^24 - q^28 + q^32 + q^52 + q^60 - q^80 + q^84 - q^96 + 
        O(q^98),
    q^10 + q^14 - q^26 - q^30 - q^42 - 2*q^62 + q^74 + q^78 + q^94 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
417
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
417
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
138
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
417
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
138
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
417
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
417
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^18*q^3 + a^2*q^4 + (-a^17 + a^14)*q^7 - a^13*q^9 + a^20*q^12 + (a^10 -
        a^3)*q^13 + a^4*q^16 + (a^6 - a)*q^19 + (a^12 - a^9)*q^21 - a^11*q^25 + 
        a^8*q^27 + (-a^19 + a^16)*q^28 + (-a^20 + a^19 - a^18 + a^17 - a^16 + 
        a^15 - a^14 + a^13 - a^12 + a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - 
        a^4 + a^3 - a^2 + a - 1)*q^31 - a^15*q^36 + (-a^15 - a^7)*q^37 + (-a^21 
        - a^5)*q^39 + (a^16 - a^7)*q^43 + (a^21 - a^20 + a^19 - a^18 + a^17 - 
        a^16 + a^15 - a^14 + a^13 - a^12 + a^11 - a^10 + a^9 - a^8 + a^7 - a^6 +
        a^5 - a^4 + a^3 - a^2 + a - 1)*q^48 + (-a^11 + a^8 - a^5)*q^49 + (a^12 -
        a^5)*q^52 + (-a^19 - a)*q^57 + (-a^19 - a^9)*q^61 + (-a^7 + a^4)*q^63 + 
        a^6*q^64 + (a^21 - a^20 + a^19 - a^18 + a^17 - a^16 + a^15 - a^14 + a^13
        - a^12 + a^11 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 
        1)*q^67 + (a^20 - a^9)*q^73 + a^6*q^75 + (a^8 - a^3)*q^76 + (-a^15 - 
        a^13)*q^79 - a^3*q^81 + (a^14 - a^11)*q^84 + O(q^91)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
417
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
417
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 46*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
417
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
69*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^5 - q^7 + q^9 - q^11 - q^13 + q^16 - q^20 - q^28 - q^29 - q^31 +
        q^35 + q^36 + 2*q^37 + 2*q^41 - q^44 - q^45 + 2*q^47 - q^52 + q^55 - 
        q^63 + q^64 + q^65 - q^67 - q^71 + q^77 - q^79 - q^80 + q^81 - q^83 - 
        q^89 + O(q^91),
    q^3 + q^12 - q^15 - q^21 + q^27 - q^33 - q^39 + q^48 - q^60 - q^84 - q^87 + 
        O(q^91)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 - a*q^5 + (a - 1)*q^15 + a*q^16 + a*q^22 + (a - 1)*q^23 + q^26 - 
        q^27 + (a - 1)*q^34 - a*q^38 + (a - 1)*q^47 + (-a + 1)*q^48 + q^49 + (-a
        + 1)*q^53 - q^58 - a*q^59 - q^64 + (-a + 1)*q^66 + (-a + 1)*q^67 + q^69 
        + a*q^71 - a*q^78 + (-a + 1)*q^80 + a*q^81 + (-a + 1)*q^82 + (a - 
        1)*q^86 - q^88 + (-a + 1)*q^89 + a*q^97 + q^102 + (a - 1)*q^104 + (-a + 
        1)*q^110 + O(q^114),
    q^2 - a*q^6 - a*q^10 + (a - 1)*q^30 + a*q^32 + a*q^44 + (a - 1)*q^46 + q^52 
        - q^54 + (a - 1)*q^68 - a*q^76 + (a - 1)*q^94 + (-a + 1)*q^96 + q^98 + 
        (-a + 1)*q^106 + O(q^114),
    q^4 - a*q^12 + (a - 1)*q^16 - a*q^20 + (a - 1)*q^22 + a*q^26 - q^34 + (-a + 
        1)*q^38 + q^48 - a*q^58 + (a - 1)*q^60 + q^66 + (-a + 1)*q^78 + q^80 + 
        q^82 - q^86 + (a - 1)*q^92 + a*q^102 - q^108 + q^110 + O(q^114),
    q^8 + q^11 + (-a + 1)*q^13 + a*q^17 - q^19 - a*q^24 + (a - 1)*q^29 + (a - 
        1)*q^32 - a*q^33 - q^39 - a*q^40 - a*q^41 + a*q^43 + (a - 1)*q^44 + (-a 
        + 1)*q^51 + a*q^52 - a*q^55 + a*q^57 + (a - 1)*q^61 - q^65 - q^68 + 
        a*q^73 + (-a + 1)*q^76 + a*q^79 + (-a + 1)*q^85 + q^87 + a*q^95 + q^96 +
        (-a + 1)*q^101 - 2*q^107 - a*q^109 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
418
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a^2*q^4 + (a^2 - a)*q^5 + (a^3 - a^2 + a)*q^7 - a*q^9 - a^3*q^11 + (a^3 
        - a^2 + a - 1)*q^16 + (-a^3 + 1)*q^17 - a^3*q^19 + (-a^2 + a - 1)*q^20 +
        (a^3 - a^2 - 1)*q^23 + (a - 1)*q^25 + (a^2 - a)*q^28 + (a^2 - 2*a + 
        1)*q^35 - a^3*q^36 + (a^3 - a^2 - 1)*q^43 + q^44 + (-a^3 + a^2)*q^45 + 
        (a^3 + a - 1)*q^47 + (-a^2 + a)*q^49 + (a^3 - a^2 + a)*q^55 + (-a^3 + 
        1)*q^61 + (-a + 1)*q^63 - a*q^64 + (a^2 + 1)*q^68 + 2*a^2*q^73 + q^76 + 
        (-a^3 + a^2)*q^77 + (-a + 1)*q^80 + a^2*q^81 + (a^2 - a)*q^83 + a^3*q^85
        + (-a^3 - a)*q^92 + (a^3 - a^2 + a)*q^95 + (a^3 - a^2 + a - 1)*q^99 + 
        (a^3 - a^2)*q^100 + (-a^2 + a - 1)*q^101 + (-a^2 + a - 1)*q^112 + 
        O(q^114),
    q^2 + a^2*q^8 + (a^2 - a)*q^10 + (a^3 - a^2 + a)*q^14 - a*q^18 - a^3*q^22 + 
        (a^3 - a^2 + a - 1)*q^32 + (-a^3 + 1)*q^34 - a^3*q^38 + (-a^2 + a - 
        1)*q^40 + (a^3 - a^2 - 1)*q^46 + (a - 1)*q^50 + (a^2 - a)*q^56 + (a^2 - 
        2*a + 1)*q^70 - a^3*q^72 + (a^3 - a^2 - 1)*q^86 + q^88 + (-a^3 + 
        a^2)*q^90 + (a^3 + a - 1)*q^94 + (-a^2 + a)*q^98 + (a^3 - a^2 + a)*q^110
        + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
419
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
418
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
419
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
38
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
419
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
19*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
419
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
209*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^13 - q^15 + q^16 + q^25 - q^29 - q^35 - q^47 + q^49 - q^52 - 
        q^60 - q^63 + q^64 + O(q^70),
    q^3 - q^9 + q^12 - q^13 - q^15 + q^27 - q^29 - q^36 + q^37 + q^39 + q^45 - 
        q^47 + q^48 + q^49 - q^52 + q^59 - q^60 - q^63 + q^65 + O(q^70),
    q^5 - q^9 - q^13 - q^15 + q^20 + q^21 + q^25 + q^27 - q^29 - q^35 - q^36 + 
        q^39 + q^43 + q^45 - q^47 - q^52 - q^60 + q^69 + O(q^70),
    q^7 - q^9 - q^13 + q^21 + q^23 + q^28 - q^29 - q^35 - q^36 + q^41 + q^45 - 
        q^47 - q^52 + q^65 + q^69 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^4 + 1/2*(2*a - 1)*q^6 - 1/2*a*q^9 - a*q^16 - 1/2*a*q^21 + 
        1/2*(a + 1)*q^24 + (a - 1)*q^25 + 1/2*a*q^30 - 1/2*q^36 + 1/2*(-a - 
        1)*q^45 + (a - 1)*q^46 + a*q^49 + (a - 2)*q^61 - q^64 + 1/2*(-2*a + 
        1)*q^69 - a*q^70 + 1/2*(-a + 1)*q^81 - 1/2*q^84 + 1/2*(-a + 2)*q^96 + 
        a*q^100 + 1/2*(a + 1)*q^105 + (-a + 1)*q^109 + 1/2*q^120 + a*q^121 + 
        1/2*(-a + 2)*q^126 + 1/2*(a + 1)*q^129 + 1/2*(a - 1)*q^144 + (-a + 
        2)*q^145 + 1/2*(-a - 1)*q^150 + (-a + 2)*q^166 - q^169 + O(q^170),
    q^2 + (a - 2)*q^7 + (-a + 1)*q^8 + (-a + 2)*q^10 + (2*a - 2)*q^15 + a*q^18 -
        q^23 + (-a - 1)*q^27 + (2*a - 1)*q^28 - a*q^32 + (-a + 1)*q^35 + (-2*a +
        1)*q^40 - 2*a*q^42 + (-3*a + 3)*q^43 + (a - 1)*q^50 - 3*q^58 + 2*a*q^60 
        + (a + 1)*q^63 + 3*a*q^67 + q^72 + (2*a - 1)*q^82 + (a + 1)*q^83 + (-2*a
        + 4)*q^87 + (-a - 1)*q^90 + (a - 1)*q^92 + a*q^98 + (-2*a + 1)*q^103 + 
        q^107 + (a - 2)*q^108 + (a + 1)*q^112 + (a - 2)*q^115 + (a - 2)*q^122 - 
        2*a*q^123 - q^128 + q^135 - a*q^140 + (-a - 1)*q^160 + (-2*a + 2)*q^162 
        + (-a - 1)*q^167 - 2*q^168 + O(q^170),
    q^3 - 2*q^7 + 2*q^10 + (-a + 1)*q^12 + (a - 2)*q^15 + (2*a - 1)*q^18 - 
        2*a*q^27 + (2*a - 2)*q^28 + (-2*a + 2)*q^40 + (-2*a + 1)*q^42 + (-2*a + 
        4)*q^43 - a*q^48 + (-2*a - 2)*q^58 + (2*a - 1)*q^60 + a*q^63 + (4*a - 
        2)*q^67 + (a + 1)*q^72 + (a - 1)*q^75 + (2*a - 2)*q^82 + 3*q^87 - a*q^90
        + (-2*a + 2)*q^103 - 2*q^108 + 2*a*q^112 - 2*q^115 + (-2*a + 1)*q^123 + 
        (a - 1)*q^138 + a*q^147 - 2*a*q^160 + (-a + 2)*q^162 + (-a - 1)*q^168 + 
        O(q^170),
    q^5 + 1/2*(-a + 1)*q^6 + 1/2*(2*a - 1)*q^9 + (a - 1)*q^14 + (-a + 1)*q^20 + 
        1/2*(-2*a + 1)*q^21 - 1/2*a*q^24 + (-a - 1)*q^29 + 1/2*(2*a - 1)*q^30 + 
        1/2*(a + 1)*q^36 + (a - 1)*q^41 - 1/2*a*q^45 - q^54 + a*q^56 + 1/2*(a - 
        1)*q^69 - a*q^80 + 1/2*(-a + 2)*q^81 + 1/2*(-a - 1)*q^84 + (-2*a + 
        1)*q^86 + q^89 - 1/2*q^96 + a*q^101 - 1/2*a*q^105 + (a - 2)*q^116 + 
        1/2*(a + 1)*q^120 + (a - 1)*q^125 + 1/2*q^126 + 3/2*a*q^129 + (a + 
        1)*q^134 + 1/2*(-a + 2)*q^144 + (-2*a + 1)*q^149 + 1/2*a*q^150 + (-a + 
        1)*q^161 + a*q^164 + O(q^170)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 + (a - 1)*q^7 + (a - 1)*q^9 - q^13 + (-a + 1)*q^19 + q^21 - a*q^25
        + q^27 + a*q^31 + (-a + 1)*q^37 + a*q^39 - q^43 - a*q^49 - q^57 + (2*a -
        2)*q^61 - a*q^63 + a*q^67 + a*q^73 + (a - 1)*q^75 + (-a + 1)*q^79 - 
        a*q^81 + (-a + 1)*q^91 + (-a + 1)*q^93 + 2*q^97 + (-a + 1)*q^103 + 
        a*q^109 - q^111 + (-a + 1)*q^117 + (a - 1)*q^121 - q^127 + a*q^129 + 
        a*q^133 - q^139 + (a - 1)*q^147 - 2*a*q^151 - 2*a*q^157 + (2*a - 
        2)*q^163 + O(q^170),
    q^5 - a*q^15 + (a - 1)*q^35 + (a - 1)*q^45 - q^65 + (-a + 1)*q^95 + q^105 - 
        a*q^125 + q^135 + a*q^155 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + (a - 1)*q^5 + (-a + 1)*q^9 + q^14 + (a - 1)*q^16 + q^20 - a*q^25
        - q^29 - q^36 - q^41 + a*q^45 + a*q^46 + (a - 1)*q^49 + (a - 1)*q^54 - 
        a*q^56 + (-a + 1)*q^61 + q^64 + (a - 1)*q^70 - a*q^80 + (-a + 1)*q^86 + 
        (-a + 1)*q^89 - 2*a*q^94 + (a - 1)*q^100 + a*q^101 + a*q^109 + a*q^116 +
        (a - 1)*q^121 + q^125 + (-a + 1)*q^126 - q^134 + a*q^144 + (-a + 
        1)*q^145 + (-a + 1)*q^149 - q^161 + a*q^164 + (-a + 1)*q^166 + q^169 + 
        O(q^170),
    q^2 + (a - 1)*q^7 - a*q^8 + (a - 1)*q^10 + (-a + 1)*q^18 - q^23 - a*q^27 + 
        q^28 + (a - 1)*q^32 - a*q^35 + q^40 + a*q^43 + 2*q^47 - a*q^50 - q^58 + 
        a*q^63 + (-a + 1)*q^67 - q^72 - q^82 + a*q^83 + a*q^90 + a*q^92 + (a - 
        1)*q^98 - q^103 - q^107 + (a - 1)*q^108 - a*q^112 + (-a + 1)*q^115 + (-a
        + 1)*q^122 - 2*a*q^127 + q^128 + q^135 + (a - 1)*q^140 - a*q^160 + 
        2*q^163 + a*q^167 + O(q^170),
    q^3 - a*q^12 + (a - 1)*q^15 - q^18 + q^42 + (a - 1)*q^48 + q^60 + (-a + 
        1)*q^63 + a*q^72 - a*q^75 - q^87 + (-a + 1)*q^90 - q^123 + a*q^138 + (a 
        - 1)*q^147 + (a - 1)*q^162 - a*q^168 + O(q^170),
    q^6 + (-a + 1)*q^9 + (a - 1)*q^21 - a*q^24 + (a - 1)*q^30 - q^36 + a*q^45 - 
        q^69 - a*q^81 + q^84 + (a - 1)*q^96 - a*q^105 + q^120 + (-a + 1)*q^126 +
        a*q^129 + 2*q^141 + a*q^144 - a*q^150 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^11 - q^15 - q^21 + q^25 - q^29 + q^35 + q^39 + q^49 + q^51 - q^65 + 
        2*q^71 - q^79 - q^81 - q^85 - q^91 - q^109 - q^119 + q^135 + q^141 + 
        2*q^149 - q^151 + q^165 + O(q^170),
    q^3 - q^33 - q^45 - q^63 + q^75 - q^87 + q^105 + q^117 + q^147 + q^153 + 
        O(q^170),
    q^5 + q^7 - q^13 - q^17 + q^27 - q^45 - q^47 - q^55 - q^63 + 2*q^73 - q^77 +
        2*q^83 - q^97 - q^103 + q^117 + q^125 + q^143 - q^145 + q^153 + 2*q^157 
        - q^167 + O(q^170),
    q^9 - q^15 - q^21 + q^39 + q^51 - q^81 - q^99 + q^141 + q^165 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
420
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 - q^9 + q^16 - q^21 + q^25 + q^30 + q^36 - 2*q^46 - q^49 - q^64 + 
        q^70 + q^81 + q^84 - q^100 + 2*q^109 - q^120 - q^121 - q^144 - q^169 + 
        O(q^170),
    q^2 - q^8 - q^15 - q^18 + 2*q^23 + q^32 - q^35 - q^42 + q^50 + q^60 + q^72 -
        2*q^92 - q^98 - 2*q^107 + 2*q^123 - q^128 + q^135 + q^140 + q^162 + 
        q^168 + O(q^170),
    q^3 + q^7 - q^10 - q^12 - q^27 - q^28 + q^40 + q^48 - q^63 + q^75 + 2*q^82 +
        q^90 - 2*q^103 + q^108 + q^112 - 2*q^115 - 2*q^138 - q^147 - q^160 + 
        O(q^170),
    q^5 + q^6 + q^14 - q^20 - q^24 - 2*q^41 - q^45 - q^54 - q^56 + 2*q^69 + q^80
        - 2*q^89 + q^96 + 2*q^101 - q^105 + q^125 - q^126 + q^150 + 2*q^161 + 
        2*q^164 + O(q^170)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
421
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
420
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
421
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
140
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
421
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
84
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
421
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
421
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
421
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
421
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
35*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
421
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
105*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
422
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
210
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
422
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
422
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
422
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
422
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
422
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
422
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
35*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
422
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
105*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^5 + q^9 - q^11 - q^13 + q^16 - q^19 - q^20 + q^36 - q^37 - q^43 
        - q^44 - q^45 - q^47 + q^49 - q^52 + 2*q^53 + q^55 + 2*q^59 + q^64 + 
        q^65 - q^71 + 2*q^73 - q^76 - q^79 - q^80 + q^81 + 2*q^83 + q^95 - q^99 
        - q^101 - q^103 + O(q^104),
    q^2 + q^8 - q^10 + q^18 - q^22 - q^26 + q^32 - q^38 - q^40 + q^72 - q^74 - 
        q^86 - q^88 - q^90 - q^94 + q^98 + O(q^104)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
423
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
423
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
423
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
423
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
138
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
423
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
138
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
423
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
423
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^8 - q^14 + q^17 + q^25 - q^28 - q^32 - q^34 - q^37 - q^47 - q^68 + 
        q^71 + q^74 - q^79 - 2*q^83 + O(q^90),
    q^2 + q^4 - q^7 - q^14 - q^17 - q^28 + q^37 + q^49 + q^50 + q^53 - q^56 + 
        q^59 - q^61 - q^64 - q^71 + q^79 + q^89 + O(q^90)
]
;
Bo:=
[
    q - q^8 + q^14 - q^17 + q^25 - q^28 + q^32 - q^34 - q^37 + q^47 + q^68 - 
        q^71 - q^74 - q^79 + 2*q^83 + O(q^90),
    q^2 - q^4 + q^7 - q^14 - q^17 + q^28 - q^37 - q^49 + q^50 + q^53 - q^56 + 
        q^59 + q^61 + q^64 - q^71 - q^79 + q^89 + O(q^90),
    q^3 - q^24 - q^27 + q^42 - q^51 + q^75 + q^81 - q^84 + O(q^90),
    q^6 - q^12 + q^21 - q^42 - q^51 - q^54 + q^81 + q^84 + O(q^90),
    q^9 - q^27 - q^54 - q^72 + q^81 + O(q^90),
    q^18 - q^27 - q^36 + q^63 + q^81 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
423
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 23*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 2)*q^7 - q^8 - q^9 - a*q^14 + (-a + 1)*q^17 + (a - 2)*q^21 - 
        a*q^25 + q^27 + (-a + 1)*q^28 + (a - 1)*q^32 - q^34 + a*q^37 + (a + 
        1)*q^42 - a*q^47 + (2*a - 1)*q^49 + (2*a - 1)*q^51 + (2*a - 1)*q^53 - 
        a*q^54 + (a - 2)*q^56 + (a + 1)*q^59 + (a - 2)*q^61 + (-a + 2)*q^63 - 
        a*q^68 + a*q^71 + q^72 + (-a + 1)*q^74 - q^79 - q^81 + a*q^83 + (2*a - 
        1)*q^84 + (-2*a + 1)*q^89 + O(q^90),
    q^2 - a*q^7 + (a - 1)*q^8 + (a - 1)*q^9 - a*q^12 + q^16 + (a - 1)*q^24 + (-a
        + 1)*q^28 - a*q^32 + (a - 1)*q^34 - a*q^36 + q^42 + q^48 - a*q^50 + q^51
        + q^53 + (a - 1)*q^56 + q^59 + (a - 1)*q^61 + (2*a - 2)*q^64 + (a - 
        1)*q^68 - a*q^74 + q^84 - a*q^89 + O(q^90),
    q^3 + (-a + 2)*q^7 - q^9 + (-a - 1)*q^14 + (-2*a + 1)*q^17 + a*q^18 + (a - 
        2)*q^21 - q^24 + q^27 + (-2*a + 1)*q^28 + (a - 1)*q^36 + (2*a - 1)*q^37 
        + q^42 + (a + 1)*q^49 + a*q^51 + (2*a - 1)*q^53 - a*q^54 + (a - 2)*q^56 
        + (a + 1)*q^59 + (a - 2)*q^61 + (-a + 1)*q^63 + (2*a - 1)*q^71 + q^72 - 
        a*q^75 + (a - 2)*q^79 - q^81 + a*q^84 + (-2*a + 1)*q^89 + O(q^90),
    q^4 + (a + 1)*q^7 - a*q^8 - a*q^9 + q^12 - a*q^14 + (a - 1)*q^16 + q^17 + (a
        - 1)*q^18 + (-a - 1)*q^21 - a*q^24 + a*q^27 + q^28 + q^32 - a*q^34 + (a 
        - 1)*q^37 + (a - 1)*q^42 + (a - 1)*q^48 + (a - 1)*q^49 + (a - 1)*q^51 + 
        (a - 2)*q^53 - 2*a*q^56 + (2*a - 1)*q^59 + (-a - 1)*q^61 + q^63 - a*q^64
        - a*q^68 + (a - 1)*q^71 + q^74 - a*q^79 - a*q^81 + (a - 1)*q^84 + (-a + 
        2)*q^89 + O(q^90),
    q^6 + (2*a - 1)*q^7 + (-a + 1)*q^9 + a*q^12 - a*q^21 + (a - 1)*q^27 + (-2*a 
        + 1)*q^34 - q^42 - q^51 + (-a - 1)*q^53 + (-2*a + 1)*q^56 + (a - 2)*q^59
        + (-2*a + 1)*q^61 + (-a + 2)*q^68 + (a - 1)*q^72 + (2*a - 1)*q^74 - 
        a*q^84 + (a + 1)*q^89 + O(q^90)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a^10 + a^6)*q^5 + a^8*q^9 + (-a^5 + a^4)*q^13 + (-a^11 - a^9)*q^17 + 
        (a^11 - a^10 + a^9 - a^8 - a^6 + a^5 - a^4 - a^2 + a - 1)*q^25 + (a^11 -
        a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 + a - 1)*q^29 + (-a^7 - 
        a)*q^37 + (-a^9 - a^3)*q^41 + (-a^5 - a)*q^45 + a^2*q^49 + a^4*q^53 + 
        (-a^11 + a^8)*q^61 + (-a^11 + a^10 + a^2 - a)*q^65 + (a^6 - a)*q^73 - 
        a^3*q^81 + (a^8 + a^6 + a^4 + a^2)*q^85 + (-a^7 + 1)*q^89 + (-a^3 + 
        1)*q^97 + (-a^9 - a^7)*q^101 + O(q^102),
    q^2 - a*q^4 + a^2*q^8 + (a^10 + a^6)*q^10 - a^3*q^16 + a^8*q^18 + (-a^11 - 
        a^7)*q^20 + (-a^5 + a^4)*q^26 + a^4*q^32 + (-a^11 - a^9)*q^34 - a^9*q^36
        + (a^11 - a^10 + a^9 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^40 +
        (a^11 - a^10 + a^9 - a^8 - a^6 + a^5 - a^4 - a^2 + a - 1)*q^50 + (a^6 - 
        a^5)*q^52 + (a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 + a -
        1)*q^58 - a^5*q^64 + (a^11 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - 
        a^2 + a - 1)*q^68 + a^10*q^72 + (-a^7 - a)*q^74 + (-a^9 + 1)*q^80 + 
        (-a^9 - a^3)*q^82 + (-a^5 - a)*q^90 + a^2*q^98 + (a^8 + a^4 + 1)*q^100 +
        O(q^102)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 13*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 26*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^13 - q^17 + q^25 - q^29 - q^37 + q^49 + q^53 + q^57 + q^69 - q^81 + 
        2*q^89 - 2*q^93 - q^97 + O(q^102),
    q^2 + q^8 - q^12 - q^26 + q^32 - q^34 - q^48 + q^50 - q^58 - q^74 - q^76 - 
        q^92 + q^98 + O(q^102),
    q^3 + q^19 + q^23 - q^27 - 2*q^31 - q^39 - q^51 - 2*q^67 + q^71 + q^75 + 
        q^79 + q^83 - q^87 + O(q^102),
    q^4 - q^6 + q^16 - q^24 - q^38 - q^46 - q^52 + q^54 + 2*q^62 + q^64 - q^68 +
        q^78 - q^96 + q^100 + O(q^102)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
424
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 26*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 + q^9 - q^10 - q^11 + q^16 - q^17 + q^36 - q^40 - q^43 - q^44 - q^46
        + q^49 - q^59 - q^62 + q^64 - q^68 + q^81 - q^89 - q^90 - q^97 - q^99 + 
        O(q^102),
    q^2 - q^5 + q^8 + q^18 - q^20 - q^22 - q^23 - q^31 + q^32 - q^34 - q^45 + 
        q^53 + q^55 + 2*q^61 + 2*q^71 + q^72 - q^79 - q^80 + q^85 - q^86 - q^88 
        - q^92 + q^98 - q^101 + O(q^102)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
80
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
80
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
425
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
426
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
426
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
426
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
426
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
426
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
426
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
426
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
426
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
35*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^16 + q^24 - q^29 - q^36 + q^38 - q^45 + q^49 - q^50 + q^54 - q^57 - 
        q^58 + q^71 - q^72 + q^74 + q^75 + q^87 - q^89 - q^95 - q^103 + 2*q^107 
        + q^108 - q^109 - q^111 + q^121 + q^128 + O(q^138),
    q^2 - q^16 + q^19 - q^20 - q^24 - q^25 + q^27 - q^29 - q^30 + q^37 + q^40 + 
        q^48 + q^54 - q^58 + q^60 + q^76 - q^81 + q^83 - q^89 - q^90 + q^98 + 
        q^101 - q^103 - q^108 - q^109 + q^125 - q^135 + O(q^138),
    q^3 - q^30 - q^36 - q^45 + q^54 - q^57 + q^60 + q^75 - q^111 + q^114 - q^135
        + O(q^138),
    q^4 - q^32 - q^36 + q^38 - q^40 - q^50 + q^54 - q^58 + q^74 + q^80 + q^108 -
        q^116 + O(q^138),
    q^5 - q^16 - q^20 - q^25 + q^27 - q^29 + q^32 + q^40 + q^43 - q^45 + q^73 + 
        q^79 - q^89 - q^95 + q^100 - q^103 - q^108 - q^109 + q^116 + q^125 + 
        q^131 - q^135 + O(q^138),
    q^6 - q^30 - q^36 + q^54 - q^72 - q^90 + q^108 + q^120 + O(q^138),
    q^8 - q^19 + q^25 - q^27 + q^29 - q^37 - q^64 - q^72 + q^76 - q^80 + q^81 - 
        q^83 + q^89 - q^100 - q^101 + q^103 + q^108 + q^109 - q^116 - q^125 + 
        q^135 + O(q^138),
    q^9 + q^24 - q^27 - q^36 - q^45 - q^57 - q^72 + q^75 + q^81 + q^87 + q^108 -
        q^111 + O(q^138),
    q^10 - q^16 + q^19 - q^20 - q^25 + q^27 - q^29 + q^37 - q^50 + q^54 - q^58 +
        q^64 + q^80 - q^81 + q^83 + q^86 - q^89 - q^90 + q^100 + q^101 - q^103 -
        q^108 - q^109 + q^116 + q^125 - q^135 + O(q^138),
    q^12 - q^24 - q^30 - q^36 + q^48 + q^54 + q^60 - q^96 + q^114 - q^120 + 
        O(q^138),
    q^15 + q^24 - q^27 - q^48 - q^57 - q^60 - q^72 + q^81 + q^96 + q^108 - q^111
        + q^120 + q^129 + O(q^138),
    q^18 - q^24 - q^30 + q^48 + q^60 - q^90 - q^108 + O(q^138)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 30*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
427
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 30*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
428
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
428
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
106
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
428
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
106
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
428
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
53*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^11 + q^13 - q^19 - q^23 + q^25 - q^27 - q^29 - q^47 + q^49 - q^53 - 
        q^57 - q^61 - q^69 + q^79 + q^81 - q^83 + q^89 - q^99 + O(q^104),
    q^3 - q^11 - q^13 + q^27 - q^33 + q^37 - q^39 + q^41 + q^57 + q^69 + q^75 - 
        q^79 - q^81 - q^87 - q^89 - q^99 + q^101 + O(q^104),
    q^9 - q^11 - q^13 + q^19 + q^23 - q^33 - q^39 + q^53 + q^61 - q^79 - q^89 + 
        O(q^104)
]
;
Bo:=
[
    q - q^3 - q^11 - q^13 - q^19 - q^23 + q^25 + q^27 + 2*q^29 + q^33 - q^37 + 
        q^39 - q^41 + 2*q^47 + q^49 - q^53 + q^57 - q^61 + q^69 - q^75 - q^79 - 
        q^81 + 2*q^83 - 2*q^87 - q^89 - q^101 + O(q^104),
    q^2 - q^6 + q^8 - q^22 - q^24 - q^26 + q^32 - q^38 - q^46 + q^50 + q^54 + 
        2*q^58 + q^66 - q^74 + q^78 - q^82 - q^88 + 2*q^94 - q^96 + q^98 + 
        O(q^104),
    q^4 - q^12 + q^16 - q^44 - q^48 - q^52 + q^64 - q^76 - q^92 + q^100 + 
        O(q^104)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 - q^4 + q^9 + q^12 - q^13 + q^16 - q^25 - q^27 - q^36 + q^39 + 
        2*q^43 - q^48 + q^49 + q^52 - 2*q^61 - q^64 + q^75 - 2*q^79 + q^81 + 
        q^100 + 2*q^103 + O(q^106),
    q^11 - q^33 - q^44 + q^99 + O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 - a*q^9 + (a^3 - a^2 - 1)*q^10 + (-a^3 + a^2)*q^12 + (-a^2 + 
        a)*q^16 + (a^3 - a^2 + a - 1)*q^22 - a^3*q^25 + (-a + 1)*q^30 - a^3*q^36
        + (a^3 - a^2 + a - 1)*q^39 + (-a^3 + 2*a^2 - a)*q^40 + (-a^3 + a^2)*q^43
        + (a^3 - a^2 + a)*q^48 + (a^3 - a^2 + a - 1)*q^49 + (-a + 1)*q^52 - 
        a*q^55 + (a^2 - a + 1)*q^64 + (a^3 - a^2 + a - 1)*q^66 + (a^2 + 1)*q^75 
        + a^2*q^81 + (-a^3 + 1)*q^82 + (-a + 1)*q^88 + (a^2 + 1)*q^90 + (a^2 - 
        a)*q^94 + (a^3 - a^2 + a)*q^103 + O(q^106),
    q^2 + (-a^3 - a + 1)*q^6 + a^2*q^8 + 1/5*(2*a^3 + a^2 + a - 3)*q^11 + a*q^15
        - a*q^18 + (a^3 - a^2)*q^20 + (-a^3 + a^2)*q^24 + (-a^2 - 1)*q^26 + 
        (-a^2 + a)*q^32 + 1/5*(-2*a^3 + 4*a^2 - a + 3)*q^33 + (-a^3 - a)*q^41 + 
        1/5*(3*a^3 - 6*a^2 + 4*a - 7)*q^44 + (a^3 + a)*q^47 + (a^3 + a - 1)*q^50
        + (a^3 - 1)*q^54 - a*q^59 + a^3*q^60 + (-a^3 + a^2 - a + 1)*q^65 + (a^3 
        + a - 1)*q^71 - a^3*q^72 + (a^3 - a^2 + a - 1)*q^78 + (-a^3 + a^2 - 
        a)*q^80 + a^3*q^83 + (-a^3 + a^2)*q^86 + (-a^3 + 1)*q^89 - a^2*q^96 + 
        (a^3 - a^2 + a - 1)*q^98 + 1/5*(-3*a^3 + a^2 + a + 2)*q^99 + (-a + 
        1)*q^104 + O(q^106),
    q^3 + (a^2 - a)*q^4 + (a^3 - a^2 + a)*q^10 + a^2*q^12 - a^3*q^13 + (-a^2 + a
        - 1)*q^16 - a^3*q^22 + (a^3 - a^2 - 1)*q^25 - a*q^27 + (a^3 - a^2 - 
        1)*q^30 + (-a^3 + a^2)*q^36 + (-a^3 + a^2 - a + 1)*q^40 + (-a^2 + 
        a)*q^48 + q^52 + a^2*q^55 + (a^2 + 1)*q^61 + a^3*q^64 + (a^3 - a^2 + a -
        1)*q^66 - a^3*q^75 + (a^3 + a - 1)*q^79 + (a^2 + 1)*q^82 + (-a + 1)*q^88
        + (-a + 1)*q^90 - 2*a*q^94 - a^2*q^100 + O(q^106),
    q^5 + (-a^3 + a^2 + 1)*q^6 + (a^3 - a^2 + a - 1)*q^8 + 1/5*(-2*a^3 - a^2 - a
        - 2)*q^11 + (a^3 + a - 1)*q^15 + (-a^3 - a + 1)*q^26 + 1/5*(2*a^3 + a^2 
        + a + 2)*q^33 + (-a^3 + a^2 - a + 1)*q^41 + 1/5*(-3*a^3 + a^2 - 4*a + 
        2)*q^44 - a*q^45 + (a^3 - 1)*q^47 + (a^3 - a^2 - 2)*q^50 + (-a^2 - 
        1)*q^54 - q^60 + (a^2 + 1)*q^65 - q^71 + q^72 + (-a^3 + 1)*q^80 + (a^3 -
        a^2 - 1)*q^83 + a*q^89 + (-a^3 + a^2 - a + 1)*q^96 + 1/5*(3*a^3 - a^2 + 
        4*a - 2)*q^99 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
429
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^12 - q^14 - q^23 + q^25 - q^27 + q^36 + q^38 + q^49 + q^56 + q^66 - 
        q^69 - q^77 + q^78 - q^82 - q^88 - q^91 + q^92 - q^103 - q^104 + 
        O(q^106),
    q^2 + q^8 - q^11 - q^13 + q^19 - q^21 - q^24 - q^28 - q^32 + q^33 + q^39 - 
        q^44 + q^46 + q^50 - q^52 + q^54 - q^63 - q^72 + q^73 + 2*q^76 + q^84 + 
        q^96 - q^98 + q^99 + O(q^106),
    q^3 - q^36 - q^42 - q^69 + q^75 - q^81 + O(q^106),
    q^4 - q^22 + q^23 - q^26 + q^27 - q^36 + q^38 - q^49 - q^53 - q^56 - q^64 + 
        q^77 - q^81 + q^91 + q^100 + q^103 + O(q^106),
    q^6 - 2*q^21 - q^24 + q^33 + q^39 + q^57 - q^63 - q^72 + q^84 + q^96 + q^99 
        + O(q^106),
    q^7 + q^8 - q^11 - q^13 - q^28 - q^32 + q^41 + q^46 + q^54 - q^63 - q^72 + 
        q^76 + q^83 - q^98 + q^99 + O(q^106),
    q^9 - q^12 - q^27 + q^36 + q^66 - q^69 + q^78 + O(q^106),
    q^18 - q^21 - q^24 + q^33 + q^39 - q^54 - q^63 + q^84 + q^96 + O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
84
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
430
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^14 - q^16 + q^25 - q^31 - q^35 + q^49 + q^54 + q^56 + q^74 - q^90 + 
        q^96 - q^99 - q^101 - q^109 + q^110 - q^111 + q^121 + O(q^126),
    q^2 + q^20 + q^22 - 2*q^28 - q^30 - q^32 + q^50 - q^62 - q^70 - q^72 - q^82 
        + q^88 + 2*q^98 + q^108 + q^112 - q^118 + O(q^126),
    q^3 + q^20 + q^22 - q^28 - q^30 - q^33 - q^37 - q^55 - q^63 - q^72 + q^73 + 
        q^75 + q^77 - q^82 + q^88 + q^98 - q^118 + O(q^126),
    q^4 - q^14 - q^24 + q^54 + q^74 - q^90 + q^100 + q^110 - q^124 + O(q^126),
    q^5 + q^12 + q^22 - q^27 - q^28 - q^30 - q^33 - q^37 + q^43 + q^45 - q^48 - 
        q^55 + q^63 - q^82 - q^93 + q^98 - q^105 + q^108 + q^112 - q^118 + 
        2*q^123 + q^125 + O(q^126),
    q^6 - q^14 - q^16 + q^40 + q^44 + q^54 - q^60 - q^66 - q^90 + q^96 + 
        O(q^126),
    q^7 + q^12 + q^20 + q^22 - q^27 - 2*q^28 - q^30 - q^32 - q^37 + q^45 - q^55 
        - q^72 + q^77 + q^80 - q^82 + 2*q^88 - q^93 + q^98 - q^105 + q^108 + 
        q^113 - q^118 - q^120 + q^123 + O(q^126),
    q^8 - q^12 - q^20 - q^22 + q^28 + q^30 + q^32 - q^48 + q^72 - q^80 + q^82 - 
        2*q^88 - q^98 + q^118 + q^120 + O(q^126),
    q^9 - q^15 + q^16 - q^21 - q^24 + q^31 + q^35 - q^36 - q^41 - q^59 + q^60 + 
        q^81 + q^84 + q^101 + q^109 + q^111 - q^121 - q^124 + O(q^126),
    q^10 - q^14 - q^16 + q^24 - q^36 + q^40 + 2*q^44 - q^56 - q^60 - q^64 - q^66
        + q^84 + q^86 + q^96 - q^124 + O(q^126),
    q^11 - q^15 + q^16 - q^24 - q^40 - q^41 - q^44 + q^49 + q^56 - q^59 + q^60 +
        q^64 + q^79 + q^81 - q^96 + q^111 - q^121 + O(q^126),
    q^18 - q^20 - q^22 + q^28 + q^32 - q^42 - q^48 + q^62 + q^70 - q^88 - q^98 +
        q^120 + O(q^126)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
431
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
430
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
431
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
86
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
431
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
43*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
431
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
215*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^10 + q^15 - q^20 - q^22 + q^25 - q^27 + q^29 - q^30 - q^32 - q^36 + 
        q^38 + q^40 - q^41 + q^44 - q^45 - q^46 + q^49 - q^50 - q^55 - q^59 + 
        O(q^72),
    q^2 - q^15 - q^16 + q^19 + q^20 - q^23 - q^25 - q^40 - q^44 + q^50 + q^53 + 
        q^55 + q^57 + q^58 - q^61 - q^66 + O(q^72),
    q^3 - q^10 - q^15 + q^27 - q^29 + q^36 - q^44 + q^46 + q^50 + O(q^72),
    q^4 - q^10 - q^12 - q^15 + q^16 + q^27 - q^29 + q^30 + q^32 + q^36 - q^38 - 
        q^40 + q^41 - q^44 + q^45 - q^48 + q^64 + O(q^72),
    q^5 - q^10 - q^12 - q^15 + q^20 + q^22 + q^24 - q^29 + q^30 + q^36 - q^38 - 
        q^40 - q^44 + q^45 + q^58 - q^60 - q^66 + O(q^72),
    q^6 - q^10 - q^12 - q^15 + q^19 + q^20 + q^24 - q^29 + q^30 + q^33 - q^38 - 
        q^40 - q^44 - q^48 + q^53 + q^54 + q^58 - q^60 - q^66 + O(q^72),
    q^8 - q^10 - q^12 + q^16 - q^29 + q^30 + q^32 + q^33 - q^38 - q^40 - q^44 - 
        q^48 + q^54 + q^61 + q^64 + O(q^72),
    q^9 - q^10 - q^15 + q^20 + q^22 - q^29 + q^36 - q^38 - q^40 - q^44 + q^46 + 
        q^50 + q^55 + q^59 - q^60 - q^66 + O(q^72),
    q^11 - q^12 - q^15 + q^19 + q^20 - q^23 + q^24 - q^25 - q^29 + q^30 + q^33 -
        q^38 - q^40 - q^44 + q^45 + q^53 + q^57 + q^58 - q^66 - q^69 + O(q^72),
    q^18 - q^19 - q^20 + q^23 + q^25 - q^30 - q^33 + q^40 + q^44 - q^53 - q^58 +
        q^69 + O(q^72)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^13 - q^25 - q^37 - 2*q^49 - q^61 + q^73 + q^97 - 2*q^109 + O(q^110),
    q^7 - q^19 - q^67 - q^79 + q^91 + q^103 + O(q^110)
]
;
Bo:=
[
    q - 2*q^13 - q^25 + 2*q^37 + q^49 + 2*q^61 - 2*q^73 - 2*q^97 - 2*q^109 + 
        O(q^110),
    q^3 - 2*q^39 - q^75 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a^4*q^3 + (a^5 - a^2)*q^9 + (a^3 + a^2 - 1)*q^11 + (-a^5 - a^4 + a)*q^17
        + (a^5 - a^4 - a^2 + a)*q^19 - a*q^25 - a^3*q^27 + (a^3 - a - 1)*q^33 + 
        (a^4 - a^3)*q^41 + (-a^5 - a^3)*q^43 - a^5*q^49 + (a^2 + 1)*q^51 + (-a^3
        + a^2)*q^57 + (-a + 1)*q^59 + (a^3 - a - 1)*q^67 + (a^4 + a^2)*q^73 - 
        a^5*q^75 + (-a^4 + a)*q^81 + a*q^83 + a^3*q^89 + (a^3 + a^2 - 1)*q^97 + 
        (-a^5 - a)*q^99 + (a^5 - a^2 - a)*q^107 + O(q^110),
    q^2 - a*q^4 + a^4*q^6 + a^2*q^8 - a^5*q^12 - a^3*q^16 + (a^5 - a^2)*q^18 + 
        (a^3 + a^2 - 1)*q^22 + (a^3 - 1)*q^24 + a^4*q^32 + (-a^5 - a^4 + a)*q^34
        + q^36 + (a^5 - a^4 - a^2 + a)*q^38 + (-a^4 - a^3 + a)*q^44 + (-a^4 + 
        a)*q^48 - a*q^50 - a^3*q^54 - a^5*q^64 + (a^3 - a - 1)*q^66 + (a^5 + a^3
        - a^2 - 1)*q^68 - a*q^72 + (a^5 - a^2 + 1)*q^76 + (a^4 - a^3)*q^82 + 
        (-a^5 - a^3)*q^86 + (a^5 + a^4 - a^2)*q^88 + (a^5 - a^2)*q^96 - a^5*q^98
        + a^2*q^100 + (a^2 + 1)*q^102 + a^4*q^108 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^19 - a*q^25 + a*q^43 + (a - 1)*q^49 + (-a + 1)*q^67 - q^73 + a*q^97 + 
        O(q^110),
    q^2 + (a - 1)*q^8 - a*q^32 - q^38 + (-a + 1)*q^44 - a*q^50 + a*q^68 + a*q^86
        + (a - 1)*q^98 + O(q^110),
    q^3 - a*q^9 + (a - 1)*q^27 + a*q^33 - q^51 - q^57 - a*q^75 + q^81 + (-a + 
        1)*q^99 + O(q^110),
    q^4 + (a - 1)*q^16 - q^22 + (-a + 1)*q^34 - a*q^64 - q^76 + a*q^82 + (-a + 
        1)*q^88 - a*q^100 + O(q^110),
    q^6 - a*q^12 - a*q^18 + (a - 1)*q^24 + (a - 1)*q^36 + q^48 + (a - 1)*q^54 + 
        a*q^66 + q^72 - a*q^96 - q^102 + q^108 + O(q^110),
    q^11 + (a - 1)*q^17 - a*q^41 - a*q^59 - 2*q^83 + (-2*a + 2)*q^89 + (a - 
        1)*q^107 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^7 - q^13 + q^19 + q^25 - 2*q^31 - q^37 - 2*q^43 - q^61 + q^67 - q^73 +
        q^79 - q^91 - q^97 + q^103 + 2*q^109 + O(q^110)
]
;
Bo:=
[
    q - q^7 - q^13 - q^19 + q^25 + 2*q^31 - q^37 + 2*q^43 - q^61 - q^67 - q^73 -
        q^79 + q^91 - q^97 - q^103 + 2*q^109 + O(q^110),
    q^2 - q^14 - q^26 - q^38 + q^50 + 2*q^62 - q^74 + 2*q^86 + O(q^110),
    q^4 - q^28 - q^52 - q^76 + q^100 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + a*q^7 - a*q^10 + (a - 1)*q^13 - q^16 + a*q^22 + q^28 + q^31 + 
        (-a - 1)*q^34 - q^40 + (-a - 1)*q^43 + (a + 1)*q^52 + a*q^55 + a*q^64 + 
        (-a + 1)*q^67 + q^70 - a*q^73 + (-a - 1)*q^85 + q^88 + (-a - 1)*q^91 + 
        (a + 1)*q^94 + q^97 + a*q^106 + O(q^110),
    q^2 + q^5 - a*q^8 - q^11 + a*q^14 + (-a + 1)*q^17 - a*q^20 + (a - 1)*q^26 - 
        q^32 + a*q^35 + a*q^44 + (a - 1)*q^47 - q^53 + q^56 + q^62 + (a - 
        1)*q^65 + (-a - 1)*q^68 + (-a - 1)*q^71 - a*q^77 - q^80 - a*q^83 + (-a -
        1)*q^86 + (a + 1)*q^89 + q^101 + (a + 1)*q^104 + q^107 + O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
432
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 - q^31 + q^55 - q^73 + 2*q^79 - q^97 + 2*q^103 + O(q^110),
    q^2 + q^8 - q^14 - q^20 + q^32 - q^44 - q^56 - q^62 - q^80 + O(q^110),
    q^4 - q^10 + q^16 - q^22 - q^28 - q^40 + 2*q^58 + q^64 + q^70 - q^88 - q^106
        + O(q^110),
    q^5 + q^11 - 2*q^29 - q^35 + q^53 - 2*q^59 - q^77 + q^83 + q^101 + q^107 + 
        O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
433
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
432
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
433
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
144
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
433
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
433
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^4 - q^5 + q^8 + q^9 - q^19 + q^20 + q^31 - q^32 - q^36 - q^40 - q^41 -
        q^45 + 2*q^47 - q^49 - q^59 + q^64 + 2*q^67 - q^71 + q^72 + q^76 + q^81 
        + q^95 - q^97 - q^101 - q^103 - q^107 - q^109 - q^113 + q^121 + 
        O(q^122),
    q^2 - q^4 - q^10 + q^16 + q^18 + q^20 - q^32 - q^36 - q^38 + q^62 + q^76 - 
        q^80 - q^82 - q^90 + 2*q^94 - q^98 - q^118 + O(q^122),
    q^7 - q^28 - q^35 - q^49 + q^56 + q^63 + O(q^122),
    q^14 - q^28 - q^70 - q^98 + q^112 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
434
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^9 + 1/3*(-a - 1)*q^14 + q^20 - a*q^25 + 1/3*(-2*a + 1)*q^28 - 
        a*q^31 + (a - 1)*q^35 + a*q^38 + (-a + 1)*q^47 - q^50 - q^64 + a*q^67 + 
        1/3*(a + 1)*q^70 - q^76 + a*q^80 - a*q^81 + (a - 1)*q^82 + a*q^95 + 
        1/3*(-2*a + 1)*q^98 + (-a + 1)*q^100 + 1/3*(-a + 2)*q^112 + q^118 + (a -
        1)*q^121 + O(q^122),
    q^2 + (-a + 1)*q^10 + 1/3*(-a - 1)*q^14 - q^16 + (a - 1)*q^18 + a*q^20 + 
        1/3*(-2*a + 1)*q^28 + (a - 1)*q^32 + (a - 1)*q^38 + 2*q^40 - 2*a*q^50 - 
        a*q^56 - a*q^62 + 1/3*(4*a - 5)*q^70 + a*q^90 + (-a + 1)*q^94 + 1/3*(a +
        1)*q^98 + 1/3*(2*a - 1)*q^112 + O(q^122),
    q^4 + 1/3*(-a + 2)*q^14 - a*q^16 + (a - 1)*q^20 + 1/3*(a + 1)*q^28 - q^32 + 
        (a - 1)*q^36 - q^38 + a*q^40 + (-a + 1)*q^50 - a*q^56 + 1/3*(a - 2)*q^70
        + (-a + 1)*q^76 + q^80 - a*q^82 + 1/3*(a + 1)*q^98 + 1/3*(-a - 1)*q^112 
        + (a - 1)*q^118 + O(q^122),
    q^5 - a*q^10 + 1/3*(a - 2)*q^14 - q^16 - a*q^19 + a*q^20 + q^25 + 1/3*(-a + 
        2)*q^28 + a*q^32 - a*q^35 + a*q^38 + (-a + 1)*q^40 + q^41 + (a - 1)*q^45
        + (a - 1)*q^49 - q^50 - q^56 - a*q^59 + 1/3*(2*a - 1)*q^70 + (a - 
        1)*q^71 - a*q^76 + q^90 + (a - 1)*q^95 + (a - 1)*q^97 + 1/3*(-a + 
        2)*q^98 + q^100 + q^101 + (a - 1)*q^103 - a*q^107 + (a - 1)*q^109 + 
        1/3*(a + 1)*q^112 - a*q^113 + O(q^122),
    q^7 + (a - 2)*q^10 + a*q^14 + (-a - 1)*q^19 + (-a + 2)*q^25 + (-a + 2)*q^32 
        - q^35 + (-a + 2)*q^38 + (-a - 1)*q^40 + (-2*a + 1)*q^41 + a*q^49 + (2*a
        - 1)*q^50 + (a - 1)*q^56 + (a - 2)*q^59 + (a - 1)*q^63 + q^70 + (2*a - 
        1)*q^71 + (-2*a + 1)*q^90 + (2*a - 1)*q^97 - a*q^98 + (-a + 2)*q^101 + 
        (a + 1)*q^103 + (-a - 1)*q^107 + (-a + 1)*q^112 + O(q^122),
    q^8 - a*q^10 + 1/3*(a - 2)*q^14 + 1/3*(-a + 2)*q^28 + a*q^38 - q^50 - q^64 +
        1/3*(2*a - 1)*q^70 + (a - 1)*q^72 - q^76 + a*q^80 + q^90 + 1/3*(-a + 
        2)*q^98 + (-a + 1)*q^100 + 1/3*(-2*a + 1)*q^112 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^4 - a*q^5 + a*q^9 + (-a - 1)*q^11 - q^16 + (-a - 1)*q^19 + q^20 - 
        q^25 + a*q^29 + (a + 1)*q^31 - q^36 + (-a + 1)*q^41 + (-a + 1)*q^44 + 
        q^45 + q^49 + (a - 1)*q^55 + (a + 1)*q^61 - a*q^64 + 2*a*q^71 + (-a + 
        1)*q^76 + (-a - 1)*q^79 + a*q^80 - q^81 + (-a - 1)*q^89 + (a - 1)*q^95 +
        (-a + 1)*q^99 - a*q^100 + (-a - 1)*q^101 + O(q^114),
    q^3 + a*q^12 - a*q^15 + a*q^27 + (-a - 1)*q^33 - q^48 + (-a - 1)*q^57 + q^60
        - q^75 + a*q^87 + (a + 1)*q^93 - q^108 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^6 - q^7 + q^9 - q^13 - q^16 + q^22 + q^24 + q^25 - q^33 + q^34 + q^42 
        - q^51 - q^54 - q^58 - q^63 + q^64 - q^67 + q^78 + q^81 - 2*q^82 + q^87 
        - q^88 + q^91 + q^94 + 2*q^103 - q^109 + q^112 + O(q^114),
    q^2 - q^3 - q^8 + q^11 - q^14 + q^17 + q^18 + q^21 - q^26 - q^27 - q^29 + 
        q^39 - 2*q^41 + q^47 + q^48 + q^50 + q^56 - q^66 - q^72 - q^75 - q^77 + 
        q^89 + q^99 + q^101 - q^102 + q^104 + q^113 + O(q^114),
    q^5 - q^30 - q^35 + q^45 - q^65 - q^80 + q^110 + O(q^114),
    q^10 - q^15 - q^40 + q^55 - q^70 + q^85 + q^90 + q^105 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^4 + a*q^5 + (-a - 1)*q^7 - a*q^9 + (-a + 1)*q^13 - q^16 - q^20 + (a 
        - 1)*q^23 - q^25 + (-a + 1)*q^28 + a*q^29 + (-a + 1)*q^35 + q^36 + q^45 
        + a*q^49 + (a + 1)*q^52 + (a - 1)*q^53 - 2*a*q^59 + (a - 1)*q^63 - 
        a*q^64 + (a + 1)*q^65 + (a + 1)*q^67 - a*q^80 - q^81 + (-a + 1)*q^83 - 
        2*q^91 + (-a - 1)*q^92 - a*q^100 + (a - 1)*q^103 + (a + 1)*q^107 + (a + 
        1)*q^112 + O(q^114),
    q^3 + a*q^12 + a*q^15 + (-a - 1)*q^21 - a*q^27 + (-a + 1)*q^39 - q^48 - q^60
        + (a - 1)*q^69 - q^75 + (-a + 1)*q^84 + a*q^87 + (-a + 1)*q^105 + q^108 
        + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
435
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 + q^6 - q^16 - q^25 + q^30 - 2*q^34 - q^45 + q^49 + q^51 + q^54 + 
        q^64 - q^81 + 2*q^94 - q^96 + q^100 + 2*q^109 - q^111 + O(q^114),
    q^2 + q^10 - q^15 + q^17 + q^18 - q^27 - q^32 - q^37 - q^43 - q^47 - q^50 - 
        q^58 + q^60 - q^68 + q^73 + q^85 + q^87 - q^90 + q^97 + q^98 + q^108 - 
        q^113 + O(q^114),
    q^3 + 2*q^10 - q^12 - q^15 + 2*q^18 - q^27 - 2*q^37 - 2*q^43 - q^48 - 2*q^58
        + q^60 + 2*q^73 - q^75 + 2*q^85 + q^87 + 2*q^97 - 2*q^102 + q^108 + 
        O(q^114),
    q^5 - q^6 + q^9 - q^20 - q^29 + q^30 - q^36 - q^51 + q^54 - 2*q^59 + 2*q^71 
        + 2*q^74 - q^80 + 2*q^86 + q^96 - q^111 + O(q^114)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
108
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^3*q^2 + a^6*q^4 + (a^16 - a)*q^5 - a^9*q^8 + (-a^14 + a^5)*q^9 + 
        (-a^10 + a^4 + a)*q^10 + (a^9 + a^8 - 1)*q^13 + a^12*q^16 + (a^14 + 
        a^10)*q^17 + (a^17 - a^8)*q^18 + (a^13 - a^7 - a^4)*q^20 + (-a^17 - a^5 
        + a^2)*q^25 + (-a^12 - a^11 + a^3)*q^26 + (-a^12 + a^11 + a^3 - 
        a^2)*q^29 - a^15*q^32 + (-a^17 - a^13)*q^34 + a^2*q^36 + (-a^15 + a^13 -
        a^4)*q^37 + (-a^16 + a^10 + a^7)*q^40 + (-a^16 - a^11 + a^7)*q^41 + 
        (a^15 + a^12 - a^6)*q^45 + (a^17 - a^8)*q^49 + (a^11 + a^8 - a^5 - 
        a^2)*q^50 + (a^15 + a^14 - a^6)*q^52 + (-a^13 + a^4)*q^53 + (a^15 - a^14
        - a^6 + a^5)*q^58 + (-a^13 - a^7)*q^61 + (a^9 - 1)*q^64 + (a^15 - a^10 -
        a^9 - a^7 - a^6 + a)*q^65 + (a^16 + a^11 - a^2)*q^68 - a^5*q^72 + (-a^16
        + a^7 + a^6)*q^73 + (-a^16 + a^9 + a^7 - 1)*q^74 + (-a^13 - a)*q^80 + 
        (-a^10 + a)*q^81 + (a^14 - a)*q^82 + (a^17 - a^15 - a^11 - a^8 - 
        a^3)*q^85 + (a^11 - a^9 - a^2)*q^89 + (-a^15 + 1)*q^90 + (-a^5 - 
        a^3)*q^97 + a^2*q^98 + (-a^14 - a^11 + a^8 + a^5)*q^100 + (a^12 + 
        a^6)*q^101 + (-a^17 + 1)*q^104 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^3*q^2 + (a^3 - 1)*q^4 - a^4*q^5 + q^8 - a^5*q^9 + (a^4 - a)*q^10 + 
        (a^5 - a^2 + 1)*q^13 - a^3*q^16 + (-a^5 - a)*q^17 + (a^5 - a^2)*q^18 + 
        a*q^20 + (-a^3 + a^2)*q^26 + (-a^3 + a^2)*q^29 + (a^3 - 1)*q^32 + (a^5 +
        a^4 - a^2)*q^34 + a^2*q^36 + (a^4 + a^3 - 1)*q^37 - a^4*q^40 + (-a^4 + 
        a^2 + a)*q^41 - q^45 + (a^5 - a^2)*q^49 + (-a^5 + a^3 - 1)*q^52 + 
        2*a^4*q^53 + (-a^5 + a^3 - 1)*q^58 + a*q^61 + q^64 + (-a^4 + a^3)*q^65 +
        (-a^4 + a^2 + a)*q^68 - a^5*q^72 + (-a^4 + a^3 + a - 1)*q^73 + (-a^4 + a
        + 1)*q^74 + (a^4 - a)*q^80 - a*q^81 + (-a^5 - a)*q^82 + (a^5 - 1)*q^85 +
        (a^2 + 1)*q^89 + a^3*q^90 + (-a^5 - a^3)*q^97 + a^2*q^98 - q^101 + (a^5 
        - a^2 + 1)*q^104 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 36*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^2 + q^4 - 2*a*q^5 + q^8 + (a - 1)*q^9 - 2*a*q^10 + a*q^13 + q^16 - 
        q^17 + (a - 1)*q^18 - 2*a*q^20 + (3*a - 3)*q^25 + a*q^26 + a*q^29 + q^32
        - q^34 + (a - 1)*q^36 + (-a + 1)*q^37 - 2*a*q^40 - q^41 + 2*q^45 + (a - 
        1)*q^49 + (3*a - 3)*q^50 + a*q^52 - 2*a*q^53 + a*q^58 - 2*a*q^61 + q^64 
        + (-2*a + 2)*q^65 - q^68 + (a - 1)*q^72 + (-a + 1)*q^73 + (-a + 1)*q^74 
        - 2*a*q^80 - a*q^81 - q^82 + 2*a*q^85 + a*q^89 + 2*q^90 + a*q^97 + (a - 
        1)*q^98 + (3*a - 3)*q^100 + 2*q^101 + a*q^104 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
436
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 54*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^5 + q^9 + q^16 - q^20 - q^22 - q^29 + q^36 - q^38 - q^45 - q^46 
        + q^49 - q^61 + q^64 - q^73 - q^80 + q^81 - q^88 - q^89 - q^94 - q^97 + 
        O(q^106),
    q^2 + q^8 - q^10 - q^11 + q^18 - q^19 - q^23 + q^32 - q^40 - q^44 - q^47 + 
        q^55 - q^58 + 2*q^59 + 2*q^67 + q^72 - q^76 + 2*q^79 - q^90 - q^92 + 
        q^95 + q^98 - q^99 - q^103 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
198
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
198
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^4*q^4 + (-a^7 + a^6)*q^5 + (-a^9 - a^7)*q^7 + (a^9 - a^8 + a^7 - a^6 +
        a^5 - a^4 + a^3 - a^2 + a - 1)*q^9 + (a^6 - a)*q^11 + a^8*q^16 + (-a^9 -
        a^5)*q^17 + a^4*q^19 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + 
        a)*q^20 + a^8*q^23 + (-a^3 + a^2 - a)*q^25 + (a^2 + 1)*q^28 + (-a^5 + 
        a^4 - a^3 + a^2)*q^35 - a^3*q^36 + (-a^9 - a)*q^43 + (a^9 - a^8 + a^7 - 
        a^6 - a^4 + a^3 - a^2 + a - 1)*q^44 + (a^6 - a^5)*q^45 + (a^8 - 
        a^3)*q^47 + (-a^7 - a^5 - a^3)*q^49 + (a^8 - a^7 + a^2 - a)*q^55 + (a^9 
        - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 + a - 1)*q^61 + (a^8 + a^6)*q^63 - 
        a*q^64 + (-a^9 + a^2)*q^68 + (-a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 +
        a - 1)*q^73 + a^8*q^76 + (a^9 + a^7 - a^6 + a^5 + a^3 + a - 1)*q^77 + 
        O(q^78)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 - q^3 + q^6 + q^8 - q^13 - q^16 + q^23 - q^24 + q^25 + q^26 + q^27 -
        q^29 - q^31 + q^39 - q^41 - q^46 - q^47 + q^48 + q^49 - q^50 - q^54 + 
        q^58 + 2*q^59 + q^62 + q^64 - q^69 - q^71 - q^73 - q^75 + O(q^78),
    q^19 - q^38 - q^57 + O(q^78)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
437
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
72
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a^3*q^3 - a^2*q^4 + (a^2 - a)*q^7 - q^9 + (a^3 - a)*q^12 + (-a^2 + a + 
        1)*q^13 + (a^2 - 1)*q^16 + a*q^19 + (-a^3 + a^2 + a - 1)*q^21 + a*q^25 +
        a^3*q^27 + (a^3 - a^2 + 1)*q^28 + (a^3 - a - 1)*q^31 + a^2*q^36 + (-a^2 
        - a + 1)*q^39 + (-a^2 - a)*q^43 + a*q^48 + (-a^3 + 2*a^2 - 1)*q^49 + 
        (-a^3 - 1)*q^52 + (-a^2 + 1)*q^57 + (a^2 - 2)*q^61 + (-a^2 + a)*q^63 + 
        q^64 + (a^2 + 1)*q^67 - a^3*q^73 + (-a^2 + 1)*q^75 - a^3*q^76 - a*q^79 +
        q^81 + (-a + 1)*q^84 + (2*a^3 - a^2 - a + 1)*q^91 + (a^3 + a^2)*q^93 + 
        (-2*a^2 + 1)*q^97 - a^3*q^100 + (-a^3 - 1)*q^103 + (-a^3 + a)*q^108 + 
        (a^3 + a)*q^109 + (-a^3 + a - 1)*q^112 + (a^2 - a - 1)*q^117 - a*q^121 +
        (a^2 + a)*q^124 + (a^3 + a^2 - a - 1)*q^129 + (a^3 - a^2)*q^133 + (a^3 +
        a^2 - a - 1)*q^139 + O(q^142),
    q^2 - a^3*q^6 - a^2*q^8 + (a^2 - a)*q^14 - q^18 + (a^3 - a)*q^24 + (-a^2 + a
        + 1)*q^26 + (a^2 - 1)*q^32 + a*q^38 + (-a^3 + a^2 + a - 1)*q^42 + a*q^50
        + a^3*q^54 + (a^3 - a^2 + 1)*q^56 + (a^3 - a - 1)*q^62 + a^2*q^72 + 
        (-a^2 - a + 1)*q^78 + (-a^2 - a)*q^86 + a*q^96 + (-a^3 + 2*a^2 - 1)*q^98
        + (-a^3 - 1)*q^104 + (-a^2 + 1)*q^114 + (a^2 - 2)*q^122 + (-a^2 + 
        a)*q^126 + q^128 + (a^2 + 1)*q^134 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + (a - 1)*q^4 + (2*a - 1)*q^7 + q^9 + (-a + 1)*q^12 - a*q^16 - 
        a*q^19 + (-2*a + 1)*q^21 + a*q^25 - q^27 + (-a - 1)*q^28 + (-a + 2)*q^31
        + (a - 1)*q^36 + (-2*a + 2)*q^37 + (2*a - 1)*q^43 + a*q^48 - 2*q^49 + 
        a*q^57 + (-a + 1)*q^61 + (2*a - 1)*q^63 + q^64 + a*q^67 - q^73 - a*q^75 
        + q^76 - a*q^79 + q^81 + (a + 1)*q^84 + (a - 2)*q^93 - q^97 - q^100 + 
        (-a + 1)*q^108 + (a - 1)*q^109 + (2*a - 2)*q^111 + (-a + 2)*q^112 + 
        a*q^121 + (2*a - 1)*q^124 - 2*a*q^127 + (-2*a + 1)*q^129 + (-a + 
        2)*q^133 + (-2*a + 1)*q^139 + O(q^142),
    q^2 - q^6 + (a - 1)*q^8 + (2*a - 1)*q^14 + q^18 + (-a + 1)*q^24 - a*q^32 - 
        a*q^38 + (-2*a + 1)*q^42 + a*q^50 - q^54 + (-a - 1)*q^56 + (-a + 2)*q^62
        + (a - 1)*q^72 + (-2*a + 2)*q^74 + (2*a - 1)*q^86 + a*q^96 - 2*q^98 + 
        a*q^114 + (-a + 1)*q^122 + (2*a - 1)*q^126 + q^128 + a*q^134 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^3 + q^4 + (-a - 1)*q^7 - q^9 + a*q^12 + (a - 1)*q^13 + q^16 - 
        2*a*q^19 + (-a + 1)*q^21 + a*q^25 - a*q^27 + (-a - 1)*q^28 + (a - 
        1)*q^31 - q^36 + (-a - 1)*q^39 + (-a + 1)*q^43 + a*q^48 + a*q^49 + (a - 
        1)*q^52 + 2*q^57 + (a + 1)*q^63 + q^64 + a*q^73 - q^75 - 2*a*q^76 + 
        2*a*q^79 + q^81 + (-a + 1)*q^84 + 2*q^91 + (-a - 1)*q^93 + a*q^100 + (a 
        - 1)*q^103 - a*q^108 + (-a - 1)*q^112 + (-a + 1)*q^117 - a*q^121 + (a - 
        1)*q^124 + (a + 1)*q^129 + (2*a - 2)*q^133 + (a + 1)*q^139 + O(q^142),
    q^2 + a*q^6 + q^8 + (-a - 1)*q^14 - q^18 + a*q^24 + (a - 1)*q^26 + q^32 - 
        2*a*q^38 + (-a + 1)*q^42 + a*q^50 - a*q^54 + (-a - 1)*q^56 + (a - 
        1)*q^62 - q^72 + (-a - 1)*q^78 + (-a + 1)*q^86 + a*q^96 + a*q^98 + (a - 
        1)*q^104 + 2*q^114 + (a + 1)*q^126 + q^128 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 24*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^8 - q^9 - q^10 - a*q^12 + (-a + 1)*q^13 + (a - 1)*q^14 - a*q^15 + (-a 
        + 1)*q^16 + (-2*a + 2)*q^18 + (a - 1)*q^19 + (-a + 1)*q^20 + q^22 + 
        3*a*q^26 + q^30 + (a - 1)*q^31 + 2*a*q^32 + a*q^33 - a*q^37 - 2*a*q^38 +
        a*q^40 + (a - 1)*q^42 + 2*q^43 + (a - 1)*q^44 - q^46 + (a - 1)*q^48 - 
        q^49 + a*q^50 + (-2*a + 2)*q^54 + (a - 1)*q^55 + q^56 - a*q^58 + a*q^61 
        - 2*a*q^62 - q^64 - q^66 + (-a + 1)*q^67 - a*q^69 - q^72 - q^73 - q^74 +
        3*a*q^78 + (a - 1)*q^79 - q^80 + q^81 - q^82 + (3*a - 3)*q^86 + (-a + 
        1)*q^87 - a*q^88 + q^90 + (-a + 1)*q^92 + q^94 + a*q^96 + (-a + 1)*q^98 
        + (-2*a + 2)*q^104 - a*q^106 + a*q^108 + a*q^109 - a*q^110 - 2*a*q^114 +
        (-a + 1)*q^115 + q^116 + (a - 1)*q^117 + a*q^118 - a*q^123 + (a - 
        1)*q^126 + (a - 1)*q^127 + (-2*a + 2)*q^128 + (a - 1)*q^130 + a*q^135 + 
        q^138 + a*q^141 + O(q^142),
    q^2 + (a - 1)*q^12 - q^18 - q^20 + (-a + 1)*q^26 - a*q^30 + (-a + 1)*q^32 + 
        (a - 1)*q^38 + q^44 + q^48 + (a - 1)*q^62 + a*q^66 - a*q^74 + a*q^80 + 
        2*q^86 - q^92 - q^98 + (-a + 1)*q^108 + (a - 1)*q^110 - a*q^116 + 
        a*q^122 - q^128 + (-a + 1)*q^134 - a*q^138 + O(q^142),
    q^3 - q^7 + 2*q^9 - a*q^12 + (3*a - 3)*q^13 + a*q^15 + (a - 1)*q^16 + (-2*a 
        + 2)*q^19 - q^21 - q^24 + (a - 1)*q^25 + q^27 + a*q^28 + (-2*a + 2)*q^31
        - a*q^33 - 2*a*q^36 - a*q^37 + (2*a - 2)*q^39 - a*q^40 - 3*q^43 + (a - 
        1)*q^48 + q^49 + 3*q^52 + (-a + 1)*q^55 + (-a + 1)*q^57 + (-a + 1)*q^60 
        - q^63 + 2*q^64 + a*q^69 + 2*q^73 + (a - 1)*q^75 - 2*q^76 + (-2*a + 
        2)*q^79 + a*q^84 + (a - 1)*q^87 + a*q^88 + (-2*a + 2)*q^91 + (-a + 
        1)*q^93 + a*q^96 - q^97 + q^100 + 2*q^103 - a*q^108 - 2*a*q^111 + (-a + 
        1)*q^112 + (a - 1)*q^115 + (a - 1)*q^117 + (a - 1)*q^121 + a*q^123 - 
        2*q^124 + (a - 1)*q^127 - q^129 + (a - 1)*q^132 + (a - 1)*q^133 - 
        a*q^135 - q^139 - a*q^141 + O(q^142),
    q^4 + (a - 1)*q^8 + (a - 1)*q^10 - q^12 + a*q^14 - a*q^16 - 2*a*q^18 - 
        a*q^20 + (-a + 1)*q^22 + (a - 1)*q^24 + 3*q^26 + (-a + 1)*q^30 + 2*q^32 
        - q^36 - 2*q^38 + a*q^42 + a*q^44 + (a - 1)*q^46 + a*q^48 + q^50 + (-a +
        1)*q^52 - 2*a*q^54 + (-a + 1)*q^56 - q^58 - a*q^60 - 2*q^62 + (a - 
        1)*q^66 + (a - 1)*q^72 + (a - 1)*q^74 + (a - 1)*q^76 + 3*q^78 + (a - 
        1)*q^80 + (a - 1)*q^82 + 3*a*q^86 + (-a + 1)*q^90 - a*q^92 + (-a + 
        1)*q^94 + 2*q^96 - a*q^98 - 2*a*q^104 - q^106 + q^108 - q^110 - 2*q^114 
        + (-a + 1)*q^116 + q^118 + (a - 1)*q^124 + a*q^126 - 2*a*q^128 + a*q^130
        + a*q^132 + (-a + 1)*q^138 + O(q^142),
    q^5 + (-a + 1)*q^7 + (a - 1)*q^8 + (2*a - 2)*q^9 - q^11 - 3*a*q^13 - q^15 - 
        a*q^16 + 2*a*q^19 - a*q^20 + (-a + 1)*q^21 + q^23 + (-a + 1)*q^24 - 
        a*q^25 + (2*a - 2)*q^27 - q^28 + a*q^29 + 2*a*q^31 + q^32 + q^33 + 
        2*q^36 + q^37 - 3*a*q^39 + q^40 + q^41 + (-3*a + 3)*q^43 + a*q^44 - q^45
        - q^47 - a*q^48 + (a - 1)*q^49 + (3*a - 3)*q^52 + a*q^53 + a*q^55 + 
        2*a*q^57 - a*q^59 + a*q^60 + (-a + 1)*q^63 + (2*a - 2)*q^64 + (-a + 
        1)*q^65 - q^69 - a*q^71 + (-a + 1)*q^72 + (2*a - 2)*q^73 - a*q^75 + 
        (-2*a + 2)*q^76 + 2*a*q^79 - q^84 - a*q^87 - q^88 - a*q^89 + 2*a*q^91 - 
        a*q^92 + 2*a*q^93 + (a - 1)*q^95 - q^96 + (-a + 1)*q^97 + q^99 + (a - 
        1)*q^100 - q^101 + (2*a - 2)*q^103 + a*q^104 - a*q^107 + 2*q^108 + q^111
        + a*q^112 - q^113 - a*q^115 + (-a + 1)*q^116 - a*q^117 + q^120 - a*q^121
        - q^123 + (-2*a + 2)*q^124 + (a - 1)*q^125 - a*q^127 + (-3*a + 3)*q^129 
        + q^131 - a*q^132 - a*q^133 + q^135 + (-a + 1)*q^139 + q^141 + O(q^142),
    q^6 - a*q^8 + (-a + 1)*q^12 - q^14 + 2*q^18 + q^20 - a*q^24 + (3*a - 3)*q^26
        + a*q^30 + (2*a - 2)*q^32 + (-2*a + 2)*q^38 - q^42 - q^44 - q^48 + (a - 
        1)*q^50 + q^54 + a*q^56 + (-2*a + 2)*q^62 - a*q^66 - a*q^72 - a*q^74 + 
        (2*a - 2)*q^78 - a*q^80 - 3*q^86 + q^92 + (a - 1)*q^96 + q^98 + 2*q^104 
        + (a - 1)*q^108 + (-a + 1)*q^110 + (-a + 1)*q^114 + a*q^116 - q^126 + 
        2*q^128 + a*q^138 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
438
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 36*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + q^4 + q^9 - q^12 + q^16 - 2*q^19 - q^25 - q^27 + q^36 - 2*q^37 - 
        q^48 + q^49 + 2*q^57 + 2*q^61 + q^64 + 2*q^67 - q^73 + q^75 - 2*q^76 - 
        2*q^79 + q^81 + 2*q^97 - q^100 - q^108 - 2*q^109 + 2*q^111 - q^121 + 
        2*q^127 + O(q^142),
    q^2 - q^6 + q^8 + q^18 - q^24 + q^32 - 2*q^38 - q^50 - q^54 + q^72 - 2*q^74 
        - q^96 + q^98 + 2*q^114 + 2*q^122 + q^128 + 2*q^134 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
439
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
438
);
qprec:=
73
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
439
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
146
);
qprec:=
73
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
439
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
73*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
73
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
439
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
219*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
73
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^28 - q^29 - q^35 - q^38 + q^49 - q^50 - q^55 + O(q^73),
    q^2 - q^14 + q^18 - q^19 - q^25 - q^40 + q^50 - q^52 + q^55 + q^61 + q^65 + 
        O(q^73),
    q^4 - q^10 - q^13 - q^14 + q^16 + q^28 + q^29 - q^32 + q^36 + q^38 - q^40 - 
        q^44 + q^50 - q^52 + q^55 - q^56 + q^64 - q^71 + O(q^73),
    q^5 - q^10 - q^13 - q^14 + q^20 + q^22 + q^26 + q^28 - q^32 - q^35 + q^45 - 
        q^52 - q^56 + q^64 + q^70 - q^71 + O(q^73),
    q^7 - q^10 - q^13 - q^14 + q^16 + q^20 + q^26 + q^28 - q^32 - q^35 + q^38 - 
        q^40 - q^44 + q^50 - q^52 - q^56 + q^63 + q^64 + q^65 + q^70 - q^71 + 
        O(q^73),
    q^8 - q^10 - q^13 + q^19 + q^25 - q^35 - q^44 + q^58 + q^70 - q^71 + q^72 + 
        O(q^73),
    q^11 - q^13 - q^14 + q^20 + q^22 - q^32 - q^35 + q^49 + q^53 - q^71 + 
        O(q^73)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 + (a^3 + a - 1)*q^3 + a^2*q^4 + (-a^3 + 1)*q^6 - a^3*q^8 + (-a^2 -
        1)*q^9 - a^3*q^11 + (a^3 - a^2 - 1)*q^12 + (a^3 - a^2 + a - 1)*q^16 + 
        (a^2 - a)*q^17 + (a^3 + a)*q^18 + (-a + 1)*q^19 + (a^3 - a^2 + a - 
        1)*q^22 + (a^2 + 1)*q^24 - a^3*q^25 + (-a^3 + a^2 - a + 1)*q^27 + q^32 +
        (a^2 + 1)*q^33 + (-a^3 + a^2)*q^34 + (-a^3 - a + 1)*q^36 + (a^2 - 
        a)*q^38 + (a^3 + a - 1)*q^41 + (a^3 - a^2 - 1)*q^43 + q^44 + (-a^3 - 
        a)*q^48 + (a^3 - a^2 + a - 1)*q^49 + (a^3 - a^2 + a - 1)*q^50 - a^2*q^51
        - q^54 + a*q^57 + (a^3 - a^2 + a)*q^59 - a*q^64 + (-a^3 - a)*q^66 + 
        (-a^3 + a^2)*q^67 + (-a^2 + a - 1)*q^68 + (a^3 - 1)*q^72 + (-a^3 - 
        a)*q^73 + (a^2 + 1)*q^75 + (-a^3 + a^2)*q^76 + (-a^3 + 1)*q^82 + (-a^3 +
        1)*q^83 + (a^2 + 1)*q^86 - a*q^88 + (a^3 - a^2 - 1)*q^89 + (a^3 + a - 
        1)*q^96 + (a^2 + 1)*q^97 + q^98 + (a^3 - 1)*q^99 + q^100 + a^3*q^102 + 
        (a^3 + a - 1)*q^107 + a*q^108 + (-a + 1)*q^113 - a^2*q^114 + (-a + 
        1)*q^118 - a*q^121 + (-a^2 - a - 1)*q^123 + a^2*q^128 + (-2*a^3 - a + 
        1)*q^129 + O(q^130),
    q^5 - a*q^10 + (a^3 + a - 1)*q^15 + a^2*q^20 + (-a^3 + 1)*q^30 - a^3*q^40 + 
        (-a^2 - 1)*q^45 - a^3*q^55 + (a^3 - a^2 - 1)*q^60 + (a^3 - a^2 + a - 
        1)*q^80 + (a^2 - a)*q^85 + (a^3 + a)*q^90 + (-a + 1)*q^95 + (a^3 - a^2 +
        a - 1)*q^110 + (a^2 + 1)*q^120 - a^3*q^125 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 - a*q^9 + q^10 + a^2*q^11 + (-a + 1)*q^14 + (a^3 - a^2 + a - 
        1)*q^16 + (a^3 + a - 1)*q^19 - a^3*q^25 + (-a^3 - a)*q^26 + (-a^2 + a - 
        1)*q^35 - a^3*q^36 + a^2*q^40 + (-a + 1)*q^41 + (a^3 - a^2 + a - 1)*q^44
        + (-a^2 + a - 1)*q^46 + (-a^2 + a)*q^49 + (-a^3 + a^2)*q^56 + (-a^3 - 
        a)*q^59 - a*q^64 + (a^3 - a^2 - 1)*q^65 + (a^3 + a - 1)*q^74 + (a^3 - 
        a^2 - 1)*q^76 + a^2*q^81 + (-a^3 + a^2)*q^89 - a*q^90 + a^3*q^91 + (-a^3
        + 1)*q^94 - a^3*q^99 + q^100 + (-a^3 + 1)*q^104 + (a^3 - a^2 + a)*q^106 
        + a^2*q^110 + (a^2 - a)*q^115 + (a^3 - a^2 + a - 1)*q^121 + (a^2 - 
        a)*q^126 + O(q^130),
    q^2 - a^3*q^5 + (-a^2 + a - 1)*q^7 + a^2*q^8 + (a^3 - a^2 - 1)*q^13 - a*q^18
        + q^20 + a^2*q^22 + (a^2 - a)*q^23 + (-a + 1)*q^28 + (a^3 - a^2 + a - 
        1)*q^32 + (a^2 + 1)*q^37 + (a^3 + a - 1)*q^38 + (a^3 - a^2 + a - 1)*q^45
        + (-a^3 - a)*q^47 - a^3*q^50 + (-a^3 - a)*q^52 + (-a^3 + a^2)*q^53 + 
        q^55 + (a^3 - a^2 + a)*q^63 + (-a^2 + a - 1)*q^70 - a^3*q^72 + (-a + 
        1)*q^77 + a^2*q^80 + (-a + 1)*q^82 + (a^3 - a^2 + a - 1)*q^88 + (-a^2 + 
        a - 1)*q^92 + (a^2 + 1)*q^95 + (-a^2 + a)*q^98 + (a^2 + 1)*q^103 + (-a^3
        + a^2)*q^112 + (a^2 + 1)*q^117 + (-a^3 - a)*q^118 - a*q^125 + (a^3 + a -
        1)*q^127 - a*q^128 + O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + q^11 - q^23 - q^25 + q^27 - q^31 - q^33 - q^37 + 2*q^47 + q^49 + 
        2*q^53 - q^59 - q^67 + q^69 - q^71 + q^75 - q^81 - q^89 + q^93 - q^97 + 
        2*q^103 + q^111 - q^113 + q^121 + q^125 + O(q^130),
    q^2 - q^6 + q^22 - q^46 - q^50 + q^54 - q^62 - q^66 - q^74 + 2*q^94 + q^98 +
        2*q^106 - q^118 + O(q^130),
    q^5 - q^15 - q^25 + q^55 + q^75 - q^115 + O(q^130),
    q^10 - q^30 - q^50 + q^110 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.3 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 - q^11 + q^15 - q^45 - q^49 + 2*q^69 + q^75 + q^81 + q^99 - 2*q^111 
        - q^115 + q^121 - q^125 + O(q^130),
    q^2 - q^18 - q^22 + q^30 - q^90 - q^98 + O(q^130),
    q^3 - q^9 + q^15 - q^23 - q^25 - q^27 + q^31 - q^33 + q^37 + q^45 - q^59 + 
        q^67 + q^69 - q^71 + q^89 + q^93 - q^97 + q^99 - q^111 + q^113 - q^115 +
        O(q^130),
    q^4 - q^16 - q^20 + q^36 - q^44 + q^64 + q^80 + q^100 - 2*q^124 + O(q^130),
    q^5 - 2*q^9 + q^15 - q^25 + 2*q^31 - q^55 - 2*q^59 + 2*q^69 - 2*q^71 + q^75 
        + 2*q^89 + 2*q^99 - 2*q^111 - q^115 + O(q^130),
    q^6 - q^18 + q^30 - q^46 - q^50 - q^54 + q^62 - q^66 + q^74 + q^90 - q^118 +
        O(q^130),
    q^8 - q^32 - q^40 + q^72 - q^88 + q^128 + O(q^130),
    q^10 - 2*q^18 + q^30 - q^50 + 2*q^62 - q^110 - 2*q^118 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
440
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^9 + q^14 - q^16 + q^20 - q^25 - q^26 - q^34 + q^44 + q^49 - q^55 - 
        q^56 + q^70 + 2*q^71 + q^81 + q^86 - q^104 - 2*q^119 - q^121 - q^126 + 
        O(q^130),
    q^2 + q^10 - q^13 - 2*q^17 + q^22 - 2*q^28 - q^30 + q^32 - q^33 + q^35 + 
        q^43 + q^50 - q^52 + q^55 + q^57 - q^62 - q^63 + q^65 + q^72 + q^73 + 
        q^77 - q^83 - q^85 + q^87 - q^90 - q^95 + q^105 - q^107 - 2*q^112 + 
        q^117 - q^120 + 3*q^127 + 2*q^128 + O(q^130),
    q^3 + q^9 + q^11 + q^12 - 3*q^14 - q^15 + 2*q^16 - 2*q^20 - q^22 + 2*q^25 - 
        q^27 - q^31 + q^34 + q^36 + q^37 + q^38 - q^42 - q^44 - q^45 + q^48 - 
        q^49 + q^53 + q^55 - q^56 + q^58 - q^60 + 2*q^64 - q^66 - 2*q^67 + q^70 
        - 3*q^71 + q^75 + q^77 - 2*q^80 - 2*q^81 - q^88 - q^89 - 2*q^91 - q^93 -
        q^99 + 2*q^100 - q^102 + 2*q^104 - q^108 + q^110 + q^111 + q^114 + 
        3*q^119 + 2*q^121 + q^122 - q^124 - 2*q^125 + 2*q^126 + O(q^130),
    q^4 + q^9 - 2*q^14 - q^15 + 2*q^16 - q^20 + 2*q^25 + q^26 - q^31 - q^44 - 
        q^49 + q^55 - q^60 + q^64 - q^66 - q^70 - 3*q^71 - 2*q^81 - q^86 - q^89 
        + q^100 + q^104 + q^110 + q^111 + q^114 + 3*q^119 + 2*q^121 - q^124 + 
        q^126 + O(q^130),
    q^5 + q^9 + q^11 - 3*q^14 - q^15 + 2*q^16 - q^20 + 2*q^25 - q^31 + q^34 + 
        q^36 - q^44 - q^45 - q^49 + q^55 - q^56 - q^60 + 2*q^64 - q^66 - 3*q^71 
        - q^80 - 2*q^81 - q^89 - 2*q^91 - q^99 + 2*q^100 + 2*q^104 + q^110 + 
        q^111 + q^114 + 3*q^119 + 2*q^121 - q^124 - q^125 + 2*q^126 + O(q^130),
    q^6 - q^10 - q^11 + q^19 - q^21 + q^24 + q^29 + q^35 - q^40 - q^44 - q^51 - 
        q^54 + q^61 + q^74 + q^76 - q^84 + q^85 + q^96 - 2*q^101 + q^106 - 
        2*q^109 + q^116 + O(q^130),
    q^7 - q^10 + 2*q^13 + q^17 - q^18 - q^22 + 3*q^28 + q^30 - 2*q^32 + q^33 - 
        2*q^35 + q^40 - 2*q^43 - 2*q^50 - q^55 - q^57 + q^62 - q^68 - q^72 - 
        2*q^73 - 2*q^77 + 2*q^83 + 2*q^85 - q^87 + q^88 + q^90 + q^95 + q^98 - 
        q^105 + 2*q^107 - q^110 + q^112 - 2*q^117 + q^120 - 2*q^127 - 2*q^128 + 
        O(q^130),
    q^8 - 2*q^10 + 3*q^13 + 2*q^17 - q^18 - 2*q^22 + 4*q^28 + q^30 - 2*q^32 + 
        q^33 - 3*q^35 + q^40 - 3*q^43 - 2*q^50 + q^52 - q^55 - q^57 + q^62 + 
        q^63 - q^65 - 2*q^68 - 2*q^72 - q^73 - 3*q^77 + 3*q^83 + 3*q^85 - q^87 +
        q^88 + 2*q^90 + q^95 + q^98 - q^105 + 3*q^107 - q^110 + 2*q^112 - 
        3*q^117 + q^120 - 3*q^127 - 3*q^128 + O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 - q^16 - 2*q^22 + q^25 + 2*q^46 + 2*q^58 + q^64 - 2*q^67 + 2*q^79 + 
        O(q^82),
    q^2 + q^11 - q^23 - q^29 - q^32 - q^44 + q^50 - q^53 + q^71 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^5*q^4 + (-a^5 + a^4 - a^3 + a^2 - a + 1)*q^7 + (a^3 + a^2)*q^13 - 
        a^3*q^16 + (a^5 - a^4 + a^3 - a^2 + 2*a - 1)*q^19 - a*q^25 + a^4*q^28 + 
        (-a^5 - a^2)*q^31 + (-a^4 - 1)*q^37 + (-a^4 - a^2)*q^43 - a^5*q^49 + (-a
        - 1)*q^52 + (a^4 - 1)*q^61 + a*q^64 + (a^4 - a^3)*q^67 + (a^5 - a^4 + 
        2*a^3 - a^2 + a - 1)*q^73 + (a^5 - 2*a^4 + a^3 - a^2 + a - 1)*q^76 + 
        (-a^5 + a^2)*q^79 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a^3*q^4 - a^5*q^7 + (a^5 + a^3 - a^2 + a - 1)*q^13 + (a^5 - a^4 + a^3 - 
        a^2 + a - 1)*q^16 + (-a^5 + a^2)*q^19 + a^2*q^25 - a*q^28 + (a^4 - 
        a^3)*q^31 + (-a + 1)*q^37 + (a^4 - a)*q^43 - a^3*q^49 + (a^2 + 1)*q^52 +
        (-a + 1)*q^61 + a^2*q^64 + (a^5 - a^4 + a^3 - a^2 - 1)*q^67 + (-a^4 + 
        a^3 - a^2 + a - 1)*q^73 + (-a^5 - a)*q^76 + (a^4 - a^3)*q^79 + O(q^82),
    q^3 - a*q^9 - a^3*q^12 - a^5*q^21 + a^2*q^27 + a^4*q^36 + (a^5 + a^3 - a^2 +
        a - 1)*q^39 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^48 + (-a^5 + a^2)*q^57 +
        (a^5 - a^4 + a^3 - a^2 + a - 1)*q^63 + a^2*q^75 - a^3*q^81 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^4 - a*q^16 + (a - 1)*q^25 + 2*a*q^37 - 2*q^43 - q^64 + (2*a -
        2)*q^67 - 2*a*q^79 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + (-a + 1)*q^16 - 2*q^22 - a*q^25 - 2*a*q^46 + (2*a - 2)*q^58 + 
        q^64 + 2*a*q^67 + (2*a - 2)*q^79 + O(q^82),
    q^2 + (a - 1)*q^11 - q^23 + a*q^29 + (-a + 1)*q^32 - q^44 - a*q^50 + (-a + 
        1)*q^53 - a*q^71 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^4 + q^16 + q^25 - 2*q^37 - 2*q^43 - q^64 + 2*q^67 + 2*q^79 + O(q^82),
    q^7 - q^28 - q^49 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
441
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
442
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
120
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
443
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
442
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
443
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
443
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
443
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
221*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^13 + q^16 - q^17 + q^25 - q^27 - q^39 + q^49 - q^51 - q^52 - 
        q^59 + q^64 - q^68 - q^71 + O(q^74),
    q^3 - q^9 + q^12 - q^13 - q^17 - q^36 + q^37 + q^41 + q^47 + q^48 - q^52 - 
        q^59 + q^61 + q^67 - q^68 - q^71 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^4*q^3 + (-a^5 - a^3 + a^2 + 1)*q^7 + (a^5 - a^2)*q^9 + (a^2 - 1)*q^13 
        + (a^4 - 2*a)*q^19 + (a^3 + a)*q^21 + a^5*q^25 - a^3*q^27 + (-a^4 - a^2 
        + a)*q^31 + (a^3 - 1)*q^37 + (-a^4 + a^3 - 1)*q^39 + (-a^5 - a^4)*q^43 +
        (-a^5 - a^4 - a^3 + a)*q^49 + (-a^5 - a^2)*q^57 + (a^5 + a^4 - a)*q^63 +
        (a^3 - a^2)*q^67 + (a^5 - a^4)*q^73 - q^75 + (a^3 + a^2)*q^79 + (-a^4 + 
        a)*q^81 + (a^3 + a - 1)*q^91 + (-a^3 + a^2 + 1)*q^93 + (a^5 + a^4 - a^2 
        - a)*q^97 + (-a^3 - 1)*q^103 + (a^4 - a^3 + 1)*q^109 - a*q^111 + (-a^5 +
        a^2 - a)*q^117 - a^3*q^121 + (a^4 + 1)*q^127 + (-a^5 + a^2 + 1)*q^129 + 
        (2*a^4 + a^3 - a - 2)*q^133 + (-a^3 + a + 1)*q^139 + O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 + a^2*q^4 + (a^4 + a^3 - 1)*q^5 - a^3*q^8 + (-a^4 + a)*q^9 + (-a^5
        - a^4 + a)*q^10 - a^2*q^13 + a^4*q^16 + (-a^3 + a^2)*q^17 + (a^5 - 
        a^2)*q^18 + (a^5 + a^3 - a^2 - 1)*q^20 + (a^5 - a^3 - a^2 - a)*q^25 + 
        a^3*q^26 + (-a^5 - a)*q^29 - a^5*q^32 + (a^4 - a^3)*q^34 + q^36 + 
        a^2*q^37 + (-a^4 + a + 1)*q^40 + (-a^4 + a^3 + a - 1)*q^41 + (a^4 + 
        a^2)*q^45 - a*q^49 + (a^4 + a^2 + 1)*q^50 - a^4*q^52 - a^4*q^53 + (a^3 +
        a^2 - 1)*q^58 + (a^4 + 1)*q^61 + (a^3 - 1)*q^64 + (-a^5 - a^3 + a^2 + 
        1)*q^65 + (-a^5 + a^4)*q^68 - a*q^72 - q^73 - a^3*q^74 + (a^5 - a^2 - 
        a)*q^80 - a^5*q^81 + (a^5 - a^4 - a^2 + a)*q^82 + (a^5 - a^4 + a^3 - a^2
        + a)*q^85 + (a^5 - a^2 + 1)*q^89 + (-a^5 - a^3)*q^90 + (a^5 + a^4 - 
        a^2)*q^97 + a^2*q^98 + (-a^5 - a^3 - a)*q^100 + (a^5 + a^4 - a^2)*q^101 
        + a^5*q^104 + a^5*q^106 + (-a^5 + a^3 - 1)*q^109 + a*q^113 + (-a^4 - a^3
        + a)*q^116 - q^117 + (a^3 - 1)*q^121 + (-a^5 - a)*q^122 + (-a^5 - a^4 - 
        a^3 + a + 1)*q^125 + (-a^4 + a)*q^128 + (a^4 - a - 1)*q^130 + (-a^5 + 
        a^3 - 1)*q^136 + (a^4 + a^2)*q^137 + O(q^142),
    q^3 - a*q^6 + a^2*q^12 + (a^4 + a^3 - 1)*q^15 - a^3*q^24 + (-a^4 + a)*q^27 +
        (-a^5 - a^4 + a)*q^30 - a^2*q^39 + a^4*q^48 + (-a^3 + a^2)*q^51 + (a^5 -
        a^2)*q^54 + (a^5 + a^3 - a^2 - 1)*q^60 + (a^5 - a^3 - a^2 - a)*q^75 + 
        a^3*q^78 + (-a^5 - a)*q^87 - a^5*q^96 + (a^4 - a^3)*q^102 + q^108 + 
        a^2*q^111 + (-a^4 + a + 1)*q^120 + (-a^4 + a^3 + a - 1)*q^123 + (a^4 + 
        a^2)*q^135 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^5 - a^2)*q^3 + (-a^4 - a^3 + a)*q^7 + (-a^4 + a)*q^9 + (a^4 + 1)*q^13
        + (-a^5 + a^2)*q^19 + (a^3 + a^2 - 1)*q^21 - a*q^25 + (a^3 - 1)*q^27 + 
        (-a^5 + a^4)*q^31 - a^3*q^37 + (a^5 - a^3 - a^2)*q^39 + (a^5 - a^2 - 
        a)*q^43 + (-a^5 + a^3 - a - 1)*q^49 + (a^4 - a)*q^57 + 2*a^2*q^61 + 
        (-a^5 - a)*q^63 + (a^4 + a^3 - 1)*q^67 + (a^5 - a^2 - a)*q^73 + q^75 + 
        (a^4 + a^3 - 1)*q^79 - a^5*q^81 + (-2*a^4 - a^3 + a^2 + 2*a)*q^91 + (a^4
        - a^3)*q^93 + (-a^5 - a^4 + a)*q^97 + a^3*q^103 + (a^5 - a^3 - 
        a^2)*q^109 + a^2*q^111 + (-a^4 + a^2 + a)*q^117 + (a^3 - 1)*q^121 + (a^5
        - a^2 + 1)*q^127 + (-a^4 + a + 1)*q^129 + (-a^3 - a^2 + 1)*q^133 + (-a^3
        + a^2)*q^139 + O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 - a*q^7 + (a - 1)*q^9 + (a - 2)*q^13 + (a - 1)*q^21 + (-a + 
        1)*q^25 + q^27 + (-2*a + 1)*q^31 + q^37 + (a + 1)*q^39 + (2*a - 1)*q^43 
        + q^63 - a*q^67 + q^73 - q^75 + (a - 2)*q^79 - a*q^81 + (a + 1)*q^91 + 
        (a - 2)*q^93 + (2*a - 1)*q^97 + (-a - 1)*q^109 - a*q^111 + (-2*a + 
        1)*q^117 + q^121 + (-a + 1)*q^127 + (-a + 2)*q^129 + (a - 1)*q^139 + 
        O(q^142),
    q^2 - a*q^6 + a*q^8 - a*q^14 + (a - 1)*q^18 + (-a + 1)*q^24 + (a - 2)*q^26 +
        (a - 1)*q^32 + (a - 1)*q^42 + (-a + 1)*q^50 + q^54 + (-a + 1)*q^56 + 
        (-2*a + 1)*q^62 - q^72 + q^74 + (a + 1)*q^78 + (2*a - 1)*q^86 + q^96 + 
        (-a - 1)*q^104 + q^126 - q^128 - a*q^134 + O(q^142),
    q^4 - a*q^12 + a*q^16 - a*q^28 + (a - 1)*q^36 + (-a + 1)*q^48 + (a - 2)*q^52
        + (a - 1)*q^64 + (a - 1)*q^84 + (-a + 1)*q^100 + q^108 + (-a + 1)*q^112 
        + (-2*a + 1)*q^124 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 + q^9 + a*q^11 + (a - 1)*q^17 + (-a + 1)*q^19 + (a - 1)*q^23 + 
        a*q^25 - a*q^27 + (-a - 1)*q^29 - a*q^37 - a*q^41 + q^47 + q^53 - q^63 +
        q^71 - a*q^73 - a*q^77 + (a - 1)*q^79 - q^83 + (-a - 1)*q^89 + a*q^99 + 
        a*q^101 + (a - 1)*q^109 + (a + 1)*q^113 + (-a + 1)*q^119 + q^127 + (a + 
        1)*q^131 + (a - 1)*q^133 + O(q^142),
    q^3 - a*q^9 - q^21 + a*q^33 + (a - 1)*q^51 + (-a + 1)*q^57 + a*q^63 + (a - 
        1)*q^69 + a*q^75 - a*q^81 + (-a - 1)*q^87 + q^99 - a*q^111 - a*q^123 + 
        q^141 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 + (a - 1)*q^4 + (-a + 1)*q^5 + q^8 - a*q^9 - q^10 + (2*a - 2)*q^13
        - a*q^16 + a*q^17 + (a - 1)*q^18 + a*q^20 + 2*q^26 - q^29 + (a - 1)*q^32
        + (-a + 1)*q^34 + q^36 + (a - 1)*q^37 + (-a + 1)*q^40 + (-a + 1)*q^41 - 
        q^45 - a*q^49 - 2*a*q^52 - 2*a*q^53 + a*q^58 + (-a + 1)*q^61 + q^64 + 
        2*a*q^65 - q^68 - a*q^72 + 2*q^73 + q^74 - q^80 + (a - 1)*q^81 - q^82 + 
        q^85 + a*q^89 + a*q^90 - q^97 + (a - 1)*q^98 - q^101 + (2*a - 2)*q^104 +
        (2*a - 2)*q^106 + a*q^109 - 2*a*q^113 + (-a + 1)*q^116 + 2*q^117 + q^121
        - q^122 + q^125 - a*q^128 + (-2*a + 2)*q^130 + a*q^136 - q^137 + 
        O(q^142),
    q^3 - a*q^6 + (a - 1)*q^12 + (-a + 1)*q^15 + q^24 - a*q^27 - q^30 + (2*a - 
        2)*q^39 - a*q^48 + a*q^51 + (a - 1)*q^54 + a*q^60 + 2*q^78 - q^87 + (a -
        1)*q^96 + (-a + 1)*q^102 + q^108 + (a - 1)*q^111 + (-a + 1)*q^120 + (-a 
        + 1)*q^123 - q^135 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^3 + (-a + 1)*q^7 - a*q^9 + (-a + 1)*q^13 + (2*a - 2)*q^19 + 
        a*q^21 - a*q^25 + q^27 - q^31 + q^37 + a*q^39 - q^43 - 2*a*q^57 + (2*a -
        2)*q^61 - q^63 + (-a + 1)*q^67 - q^73 + q^75 + (-a + 1)*q^79 + (a - 
        1)*q^81 - a*q^91 + (-a + 1)*q^93 - q^97 + 2*q^103 + a*q^109 + (a - 
        1)*q^111 - q^117 + q^121 + a*q^127 + (-a + 1)*q^129 + 2*a*q^133 + 
        a*q^139 + O(q^142),
    q^2 + (a - 1)*q^6 + (a - 1)*q^8 + (-a + 1)*q^14 - a*q^18 - a*q^24 + (-a + 
        1)*q^26 - a*q^32 + (2*a - 2)*q^38 + a*q^42 - a*q^50 + q^54 + a*q^56 - 
        q^62 + q^72 + q^74 + a*q^78 - q^86 + q^96 + a*q^104 - 2*a*q^114 + (2*a -
        2)*q^122 - q^126 + q^128 + (-a + 1)*q^134 + O(q^142),
    q^4 + (a - 1)*q^12 + (a - 1)*q^16 + (-a + 1)*q^28 - a*q^36 - a*q^48 + (-a + 
        1)*q^52 - a*q^64 + (2*a - 2)*q^76 + a*q^84 - a*q^100 + q^108 + a*q^112 -
        q^124 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
444
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 18*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^7 - q^9 + q^11 - q^25 + q^27 - 2*q^33 + q^37 - q^41 - q^47 - q^53 - 
        q^63 - 2*q^67 + q^71 + q^73 + q^77 - q^83 + q^99 + q^101 - 2*q^121 + 
        2*q^123 - q^127 - 2*q^139 + 2*q^141 + O(q^142),
    q^3 - q^9 + 2*q^11 + q^21 - q^33 - 2*q^41 - 2*q^47 - 2*q^53 - q^63 + 2*q^71 
        - q^75 + 2*q^77 + q^81 - 2*q^83 - q^99 + 2*q^101 + q^111 + q^123 + q^141
        + O(q^142)
]
;
Bo:=
[
    q - q^7 + q^9 - q^21 + q^49 - q^63 - q^67 - q^73 - q^75 + q^81 - q^85 + 
        q^111 + q^115 + q^121 + 2*q^127 - q^139 + O(q^142),
    q^2 - q^14 + q^18 - q^20 - q^24 - q^42 + q^56 + q^60 + q^68 - q^92 + q^96 + 
        q^98 + q^116 - q^126 - q^128 - q^134 + O(q^142),
    q^3 - q^7 - q^21 - q^25 + q^27 + q^37 + 2*q^49 - q^63 - q^67 - q^73 + q^85 -
        q^115 - q^139 + O(q^142),
    q^4 - q^28 + q^36 - q^40 - q^48 - q^84 + q^112 + q^120 + q^136 + O(q^142),
    q^5 - q^15 - q^17 + q^23 - q^29 + q^45 + q^51 - q^59 - q^69 + q^87 + q^89 + 
        q^113 - q^131 - q^135 + O(q^142),
    q^6 - q^14 - q^24 + q^32 - q^42 - q^50 + q^54 + q^56 + q^74 - q^80 + 2*q^98 
        - q^126 - q^128 - q^134 + O(q^142),
    q^8 - q^20 - q^24 + q^60 + q^68 + q^72 - q^80 - q^92 + q^116 - q^128 + 
        O(q^142),
    q^10 + q^16 - q^30 - q^34 - q^40 + q^46 - q^48 - q^58 + q^90 + q^102 - q^118
        + q^120 + q^136 - q^138 + O(q^142),
    q^12 - q^16 - q^28 + q^40 + q^64 - q^84 - q^100 + q^108 + q^112 - q^120 - 
        q^136 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
88
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
88
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
44
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
44
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
44
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
44
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 22*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 22*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
445
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 44*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a - 1)*q^2 + a*q^4 - a*q^5 - a*q^9 + (a - 1)*q^10 + q^16 + (-a - 
        1)*q^17 + (a - 1)*q^18 + q^20 - q^25 + (-a - 1)*q^32 + 2*a*q^34 + q^36 -
        q^45 + (a + 1)*q^47 + a*q^49 + (a + 1)*q^50 + (-a + 1)*q^53 + a*q^64 + 
        (a + 1)*q^67 + (-a + 1)*q^68 + 2*q^71 + (-a + 1)*q^73 - 2*a*q^79 - 
        a*q^80 - q^81 + (a - 1)*q^85 + O(q^88)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
446
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
222
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
446
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
74
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
446
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
37*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
446
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
111*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 + q^25 - q^28 - q^29 - q^31 - q^34 - q^38 - q^43 + q^58 + q^62 - 
        q^64 + q^68 - q^73 + q^76 + q^81 - q^83 + q^86 - q^94 + q^98 - q^106 + 
        O(q^110),
    q^2 + q^18 - q^28 - q^34 - q^38 + q^50 - q^56 - q^64 - q^94 + q^98 - q^106 +
        O(q^110),
    q^4 + q^17 + q^19 - q^28 - q^29 - q^31 - q^34 + q^36 - q^38 - q^43 + q^47 - 
        q^49 + q^53 - q^56 + q^58 + q^62 - q^64 - q^73 - q^83 + q^86 - q^94 + 
        q^98 + q^100 - q^106 + q^109 + O(q^110),
    q^7 + q^16 - q^17 - q^19 - q^28 - q^32 + q^37 + q^41 - q^47 - q^53 + q^63 + 
        q^68 + q^76 + q^89 + q^101 - q^109 + O(q^110),
    q^8 - q^16 + q^17 + q^19 - q^29 - q^31 + q^32 - q^43 + q^47 - q^49 + q^53 - 
        q^56 - q^64 - q^68 + q^72 - q^73 - q^76 - q^83 + q^109 + O(q^110),
    q^14 + q^17 + q^19 - q^29 - q^31 + q^32 - q^34 - q^38 - q^43 + q^47 - q^49 +
        q^53 - q^56 - q^64 - q^73 + q^74 + q^82 - q^83 - q^94 - q^106 + q^109 + 
        O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
447
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
447
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
148
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
447
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
74
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
447
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
74
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
447
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
37*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
447
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 74*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^28 - q^31 - q^33 - q^42 - q^46 + q^49 - q^61 - q^67 + 
        q^81 - q^88 - q^96 + O(q^98),
    q^2 - q^14 + q^18 - q^21 - q^23 - q^44 - q^48 + q^50 + q^57 + q^59 + q^71 + 
        q^77 - q^83 - q^89 + O(q^98),
    q^3 - q^11 - q^14 + q^27 - q^32 + q^38 - q^41 + q^44 + q^56 + q^74 + q^75 - 
        q^77 - q^84 - q^92 - q^93 + O(q^98),
    q^4 - q^7 - q^22 - q^24 + q^31 + q^33 + q^36 + q^61 - q^63 + q^67 - q^69 - 
        q^73 - q^76 - q^82 + O(q^98),
    q^6 - q^7 - q^16 + q^19 + q^37 - q^42 - q^46 + q^49 + q^54 - q^63 - q^69 - 
        q^73 + q^76 + q^88 + O(q^98),
    q^8 - q^11 - q^12 + q^21 + q^23 - q^38 - q^41 + q^62 + q^66 + q^72 - q^74 - 
        q^77 + q^83 + q^89 - q^93 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^5 - a*q^17 + a*q^21 + (a - 1)*q^33 + (a - 1)*q^37 - q^49 - 
        a*q^53 - q^57 + (a - 1)*q^61 - q^69 + a*q^73 - a*q^77 + a*q^81 - q^85 + 
        (-a + 1)*q^89 + (-a + 1)*q^93 + a*q^101 + q^105 + O(q^106),
    q^3 + (a - 1)*q^7 - q^11 + (-a + 1)*q^15 - a*q^19 - a*q^23 + (a - 1)*q^27 + 
        q^31 + a*q^35 + a*q^47 - a*q^51 + (a - 1)*q^55 + q^59 + q^67 - a*q^79 - 
        q^95 - a*q^103 + O(q^106)
]
;
Bo:=
[
    q + (a - 1)*q^5 - a*q^17 - a*q^21 + (a - 1)*q^33 + (-a + 1)*q^37 - q^49 + 
        a*q^53 - q^57 + (-a + 1)*q^61 + q^69 + a*q^73 + a*q^77 + a*q^81 + q^85 +
        (-a + 1)*q^89 + (a - 1)*q^93 - a*q^101 + q^105 + O(q^106),
    q^2 + (a - 1)*q^10 - a*q^34 - a*q^42 + (a - 1)*q^66 + (-a + 1)*q^74 - q^98 +
        O(q^106),
    q^3 + (-a + 1)*q^7 - q^11 + (a - 1)*q^15 - a*q^19 + a*q^23 + (a - 1)*q^27 - 
        q^31 + a*q^35 - a*q^47 - a*q^51 + (-a + 1)*q^55 + q^59 + q^67 + a*q^79 +
        q^95 + a*q^103 + O(q^106),
    q^6 + (-a + 1)*q^14 - q^22 + (a - 1)*q^30 - a*q^38 + a*q^46 + (a - 1)*q^54 -
        q^62 + a*q^70 - a*q^94 - a*q^102 + O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + a^2*q^4 + a^5*q^7 - a^3*q^8 + a^3*q^9 + (-a^7 + a^6)*q^11 - 
        a^6*q^14 + a^4*q^16 - a^4*q^18 + (-a^7 - 1)*q^22 + (a^4 - a^2)*q^23 + 
        a*q^25 + a^7*q^28 + (-a^6 - a^5)*q^29 - a^5*q^32 + a^5*q^36 + (a^7 + 
        a^2)*q^37 + (-a^4 + a)*q^43 + (a - 1)*q^44 + (-a^5 + a^3)*q^46 - 
        a^2*q^49 - a^2*q^50 + (-a^4 - a)*q^53 + q^56 + (a^7 + a^6)*q^58 - q^63 +
        a^6*q^64 + (-a^3 - 1)*q^67 + (a^7 + a^3)*q^71 - a^6*q^72 + (-a^3 + 
        1)*q^74 + (a^4 - a^3)*q^77 + (-a^3 - a)*q^79 + a^6*q^81 + (a^5 - 
        a^2)*q^86 + (-a^2 + a)*q^88 + (a^6 - a^4)*q^92 + a^3*q^98 + (a^2 - 
        a)*q^99 + a^3*q^100 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^7 + a^3*q^9 + (-a^3 - a^2)*q^11 + (a^2 - 1)*q^23 + a*q^25 + (-a^2 - 
        a)*q^29 + (-a^3 + a^2)*q^37 + (a - 1)*q^43 + a^2*q^49 + (a - 1)*q^53 + 
        q^63 + (a^3 + 1)*q^67 + (a^3 - 1)*q^77 + (a^3 + a)*q^79 - a^2*q^81 + 
        (a^2 + a)*q^99 + O(q^106),
    q^2 + a*q^4 + a^2*q^8 - a*q^14 + a^3*q^16 + a^3*q^18 + (-a^3 - a^2)*q^22 - 
        a^2*q^28 - q^32 - q^36 + (-a^3 + 1)*q^44 + (a^2 - 1)*q^46 + a*q^50 - 
        a^3*q^56 + (-a^2 - a)*q^58 - a*q^64 - a*q^72 + (-a^3 + a^2)*q^74 + (a - 
        1)*q^86 + (a + 1)*q^88 + (a^3 - a)*q^92 + a^2*q^98 + a^2*q^100 + 
        O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^7 - a*q^9 + (a + 1)*q^11 + a*q^25 + (a - 1)*q^29 + (-a - 1)*q^37 + 
        (-a - 1)*q^43 - q^49 + (a + 1)*q^53 - q^63 + (a - 1)*q^67 + 2*a*q^71 + 
        (-a + 1)*q^77 - q^81 + (-a + 1)*q^99 + O(q^106)
]
;
Bo:=
[
    q + a*q^7 - a*q^9 + (-a - 1)*q^11 + a*q^25 + (a - 1)*q^29 + (-a - 1)*q^37 + 
        (a + 1)*q^43 - q^49 + (a + 1)*q^53 + q^63 + (-a + 1)*q^67 - 2*a*q^71 + 
        (-a + 1)*q^77 - q^81 + (a - 1)*q^99 + O(q^106),
    q^2 + a*q^14 - a*q^18 + (-a - 1)*q^22 + a*q^50 + (a - 1)*q^58 + (-a - 
        1)*q^74 + (a + 1)*q^86 - q^98 + O(q^106),
    q^4 + a*q^8 - q^16 + a*q^28 - a*q^32 - a*q^36 + (-a - 1)*q^44 - q^56 + q^64 
        + q^72 + (-a + 1)*q^88 + a*q^100 + O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
448
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 - q^25 + q^49 + q^81 + O(q^106),
    q^2 - q^18 - q^50 + q^98 + O(q^106),
    q^4 - q^28 - q^36 + 2*q^92 - q^100 + O(q^106),
    q^7 - 2*q^23 - q^63 + 2*q^71 + 2*q^79 + O(q^106),
    q^8 - q^16 + q^32 - q^56 - q^64 - q^72 + O(q^106),
    q^14 - 2*q^46 + O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
449
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
448
);
qprec:=
75
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
449
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
64
);
qprec:=
75
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 - q^16 + 2*a*q^19 - 2*q^31 - a*q^49 + 2*q^61 + a*q^64 + 2*q^76 - 
        2*a*q^79 - 2*a*q^109 - q^121 + 2*a*q^124 + O(q^134),
    q^2 - a*q^8 - q^32 + 2*a*q^38 - 2*q^62 - a*q^98 + 2*q^122 + a*q^128 + 
        O(q^134)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
450
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - a*q^5 + a*q^9 + (-a - 1)*q^14 - q^16 - a*q^20 + (a + 1)*q^22 + 
        q^23 - q^31 + (a - 1)*q^34 + a*q^36 + q^37 + (a - 1)*q^38 + q^45 + (-a -
        1)*q^47 + (-a + 1)*q^53 + (-a - 1)*q^58 - q^59 - q^64 + (a - 1)*q^70 + 
        (a - 1)*q^71 - a*q^77 + a*q^80 - q^81 + O(q^82),
    q^2 + 1/2*(-a - 1)*q^7 - a*q^10 + 1/2*(a + 1)*q^11 + 1/2*(a - 1)*q^17 + 
        a*q^18 + 1/2*(a - 1)*q^19 + 1/2*(-a - 1)*q^28 + 1/2*(-a - 1)*q^29 - q^32
        + 1/2*(a - 1)*q^35 + 1/2*(-a + 1)*q^41 + 1/2*(a + 1)*q^44 + q^46 + 
        1/2*(-a + 1)*q^55 - q^62 + 1/2*(-a + 1)*q^63 + 1/2*(a - 1)*q^68 + q^73 +
        q^74 + 1/2*(a - 1)*q^76 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
451
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^5 + q^9 + q^16 - q^20 - q^23 - q^31 + q^36 - q^37 - q^45 - q^59 
        + q^64 - q^77 - q^80 + q^81 + O(q^82),
    q^7 - q^11 - 2*q^13 + q^17 + q^19 + q^28 + q^29 - q^35 - q^41 - q^44 - 
        2*q^52 + q^55 + q^63 + 2*q^65 + q^68 + q^76 - 2*q^79 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
452
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
452
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
112
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
452
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
56
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
452
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^6*q^2 + (a^10 - a^8 + a^6 - a^4 + a^2 - 1)*q^4 + (-a^8 + a^5)*q^5 + 
        a^4*q^8 + a*q^9 + (-a^11 - 1)*q^10 + (-a^5 + a^3)*q^13 - a^10*q^16 + 
        (-a^4 - a)*q^17 - a^7*q^18 + (a^6 - a^3)*q^20 + (-a^11 + a^10 + a^9 - 
        a^7 + a^5 - a^3 - a^2 + a)*q^25 + (a^11 - a^9)*q^26 + (-a^10 + a^8 + a^7
        - a^6 + a^4 - a^2 + 1)*q^29 - a^2*q^32 + (a^10 + a^7)*q^34 + (a^11 - a^9
        + a^7 - a^5 + a^3 - a)*q^36 + (a^9 + a^2)*q^37 + (-a^10 + a^9 + a^8 - 
        a^6 + a^4 - a^2 + 1)*q^40 + (-a^7 - a^3)*q^41 + (-a^9 + a^6)*q^45 + 
        a^8*q^49 + (a^8 - a^5 + a^2)*q^50 + (a^3 - a)*q^52 + (2*a^11 - a^9 + a^7
        - a^5 + a^3 - a)*q^53 + (-a^11 + a^9 - a^7 + a^5 - a^4 - a^3 + a)*q^58 +
        (a^4 - 1)*q^61 + a^8*q^64 + (-a^10 - a^9 + a^8 + a^7 - a^5 + a^3 - 
        a)*q^65 + (-a^11 + a^9 - a^7 + a^5 - a^3 + a^2 + a)*q^68 + a^5*q^72 + 
        (a^11 - a^10)*q^73 + (-a^8 + a)*q^74 + (-a^4 + a)*q^80 + a^2*q^81 + 
        (a^11 + a^7 - a^5 + a^3 - a)*q^82 + (a^10 - a^8 - a^4 + a^2 - 1)*q^85 + 
        (-a^11 + a^10 - a^8 + a^6 - a^4 + a^2 - 1)*q^89 + (-a^10 + a^8 - a^6 + 
        a^4 - a^2 - a + 1)*q^90 + (a^6 - 1)*q^97 + q^98 + (a^11 - a^8 + 1)*q^100
        + (-a^11 - a^10 + a^9 + a^8 - a^7 - a^6 + a^5 + a^4 - a^3 - a^2 + a + 
        1)*q^101 + (-a^9 + a^7)*q^104 + (a^5 + a^3)*q^106 + (a^7 - a^3)*q^109 + 
        O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
452
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
452
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^2 - a^5*q^4 + (a^5 - a)*q^5 + a^4*q^8 
        + a*q^9 + (-a^4 + 1)*q^10 + (a^5 + a^3)*q^13 - a^3*q^16 + (a^4 + a)*q^17
        - q^18 + (a^5 - a^4 + 2*a^3 - a^2 + a - 1)*q^20 + (-a^5 + a^4 - 2*a^3 + 
        2*a^2 - a + 1)*q^25 + (-a^4 - a^2)*q^26 + (-a^5 - 1)*q^29 + a^2*q^32 + 
        (-a^3 - 1)*q^34 + (-a^5 + a^4 - a^3 + a^2 - a + 1)*q^36 + (-a^5 - 
        a^2)*q^40 + (a^3 - 1)*q^41 + (a^5 - a^4 + a^3 - 2*a^2 + a - 1)*q^45 - 
        a*q^49 + (a^5 + a^2 - a)*q^50 + (a^3 + a)*q^52 + (-a^5 - a^3 + a^2 - a +
        1)*q^53 + (-a^5 + 2*a^4 - a^3 + a^2 - a + 1)*q^58 + (a^4 + 1)*q^61 - 
        a*q^64 + (-a^5 - 2*a^3 + a^2 - 2*a + 1)*q^65 + (-a^5 + a^4 - a^3 + 2*a^2
        - a + 1)*q^68 + a^5*q^72 + (-a^4 - a^3)*q^73 + (a^4 + a)*q^80 + a^2*q^81
        + (-a^5 + a^4 - a^3 - a + 1)*q^82 + (-a^4 + a^3 - 3*a^2 + a - 1)*q^85 + 
        (-a^5 - a^4)*q^89 + (-a^5 + a)*q^90 + (a^5 - a^4 + a^3 - a^2 + a)*q^97 +
        q^98 + (-a^4 - a + 1)*q^100 + (-2*a^5 + a^4 - a^3 + a^2 - a + 1)*q^101 +
        (-a^2 - 1)*q^104 + (a^5 + a^3)*q^106 + (a^3 - 1)*q^109 + O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
452
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
452
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 16*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^5*q^2 - a^3*q^4 + (-a^3 + a^2)*q^5 - a*q^8 + a^2*q^9 + (-a + 1)*q^10 +
        (a^5 - a^4 - a^2 + a - 1)*q^13 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^16 + 
        (a^2 - a)*q^17 + q^18 + (-a^4 + a^3 - a^2 + a - 1)*q^20 + (a^3 - a^2 + a
        - 1)*q^25 + (a^4 - a)*q^26 + (-a^3 + 1)*q^29 + a^4*q^32 + (a^5 - a^4 + 
        a^3 - a^2 + a)*q^34 - a^5*q^36 + 2*a^4*q^37 + (a^4 - a^3)*q^40 + (a^5 - 
        a^4 + a^3 - a^2 + a)*q^41 + (-a^5 + a^4)*q^45 + a^2*q^49 + (a^4 - a^3 + 
        a^2)*q^50 + (a^5 - a^4 + a^3 + a - 1)*q^52 + (-a^5 - a)*q^53 + (-a^5 - 
        a)*q^58 + (-a + 1)*q^61 + a^2*q^64 + (-a^4 + a^3 - 1)*q^65 + (-a^5 + 
        a^4)*q^68 - a^3*q^72 + (a^5 - a^4 + a^3 - a^2 - 1)*q^73 + 2*a^2*q^74 + 
        (a^2 - a)*q^80 + a^4*q^81 + (-a^5 + a^4)*q^82 + (-a^5 + 2*a^4 - 
        a^3)*q^85 + (-a^3 - a)*q^89 + (-a^3 + a^2)*q^90 + (-a^5 + 1)*q^97 + q^98
        + (a^2 - a + 1)*q^100 + (-a^5 - a^3)*q^101 + (a^4 + 1)*q^104 + (a^5 - 
        a^4 - a^2 + a - 1)*q^106 + (a^5 - a^4 + a^3 - a^2 + a)*q^109 + O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
452
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 28*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^2 + q^4 + (a - 1)*q^5 + q^8 + a*q^9 + (a - 1)*q^10 - 2*a*q^13 + q^16 +
        (-a - 1)*q^17 + a*q^18 + (a - 1)*q^20 - a*q^25 - 2*a*q^26 + (-a - 
        1)*q^29 + q^32 + (-a - 1)*q^34 + a*q^36 + (a - 1)*q^37 + (a - 1)*q^40 + 
        2*a*q^41 + (-a - 1)*q^45 + q^49 - a*q^50 - 2*a*q^52 + (-a - 1)*q^58 + 
        q^64 + (2*a + 2)*q^65 + (-a - 1)*q^68 + a*q^72 + (-a + 1)*q^73 + (a - 
        1)*q^74 + (a - 1)*q^80 - q^81 + 2*a*q^82 + 2*q^85 + (a + 1)*q^89 + (-a -
        1)*q^90 - 2*q^97 + q^98 - a*q^100 + (-a - 1)*q^101 - 2*a*q^104 + 
        O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
452
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 56*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^13 + q^16 - q^18 + q^25 - q^26 - q^41 + q^49 - q^52 - q^53 - 
        q^57 + q^64 - q^69 - q^72 - q^82 + q^100 - q^104 - q^106 - q^109 + 
        O(q^110),
    q^2 + q^8 - q^9 - q^13 - q^26 + q^32 - q^36 - q^41 + q^50 - q^52 - q^53 + 
        q^57 + 2*q^61 + q^69 + q^81 - q^82 + 2*q^97 + q^98 - q^104 - q^106 - 
        q^109 + O(q^110),
    q^3 - q^6 + q^12 - q^19 - q^23 - q^24 + q^38 + q^43 + q^46 - q^47 + q^48 + 
        q^59 - q^67 + q^71 + q^75 - q^76 - q^79 - q^86 - q^92 + q^94 - q^96 + 
        q^103 - q^107 + O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
150
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
150
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
50
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
50
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^6*q^3 - a^15*q^4 + (a^8 - a)*q^7 + a^12*q^9 + (-a^16 + a^11 - a^6 + 
        a)*q^12 + (a^4 - a^3)*q^13 - a^5*q^16 + (-a^17 - a^13)*q^19 + (a^14 - 
        a^7)*q^21 + (a^19 - a^14 + a^9 - a^4)*q^25 + a^18*q^27 + (-a^18 + a^16 +
        a^13 - a^8 + a^3)*q^28 + (a^15 - a^11 - a^10 + a^5 - 1)*q^31 + a^2*q^36 
        + (a^17 - a^12 + a^10 + a^7 - a^2)*q^37 + (a^10 - a^9)*q^39 + (-a^19 + 
        a^17 - a^12 + a^7 - a^2)*q^43 - a^11*q^48 + (a^16 - a^9 + a^2)*q^49 + 
        (-a^19 + a^18)*q^52 + (-a^19 - a^18 + a^13 - a^8 + a^3)*q^57 + (a^19 + 
        a^9 - a^4)*q^61 + (a^15 - a^13 - a^10 + a^5 - 1)*q^63 + (a^15 - a^10 + 
        a^5 - 1)*q^64 + (-a^17 - a^9)*q^67 + (-a^7 + a^2)*q^73 - a^5*q^75 + 
        (-a^7 - a^3)*q^76 + (-a^18 - a^16 + a^13 + a^11 - a^8 - a^6 + a^3 + 
        a)*q^79 + (a^19 - a^14 + a^9 - a^4)*q^81 + (a^17 - a^12 + a^7 + a^4 - 
        a^2)*q^84 + (a^12 - a^11 - a^5 + a^4)*q^91 + (-a^17 - a)*q^93 + (a^18 + 
        a^8)*q^97 + O(q^99)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
25*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 30*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + q^4 + (-a^3 - a)*q^7 + a^2*q^9 - a*q^12 + (-a^2 + a - 1)*q^13 + 
        q^16 + (-a^3 + a^2)*q^19 + (a^3 + a - 1)*q^21 + (a^3 - a^2 + a - 1)*q^25
        - a^3*q^27 + (-a^3 - a)*q^28 + (-a + 1)*q^31 + a^2*q^36 + (a^2 + 1)*q^37
        + (a^3 - a^2 + a)*q^39 + (a^3 + a - 1)*q^43 - a*q^48 + (a^3 - 1)*q^49 + 
        (-a^2 + a - 1)*q^52 + (-a^2 + a - 1)*q^57 + (2*a^3 - 2*a^2 + 2*a - 
        2)*q^61 + (-a^3 + 1)*q^63 + q^64 + (a^3 + a - 1)*q^67 + 2*a^2*q^73 + 
        q^75 + (-a^3 + a^2)*q^76 + (-a^3 - a)*q^79 + (a^3 - a^2 + a - 1)*q^81 + 
        (a^3 + a - 1)*q^84 + a^3*q^91 + (a^2 - a)*q^93 - 2*a^3*q^97 + O(q^99)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 50*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^3 - a*q^7 + q^9 + (-a + 1)*q^10 + (-a + 1)*q^13 + a*q^16 + a*q^21 + 
        (-a + 1)*q^22 - q^27 + (a - 1)*q^30 - a*q^31 + (a - 1)*q^34 - a*q^37 + 
        (a - 1)*q^39 + a*q^40 + (a - 1)*q^43 + (a - 1)*q^46 - a*q^48 + (-a + 
        1)*q^55 + 2*a*q^58 + (a - 1)*q^61 - a*q^63 - q^64 + (a - 1)*q^66 - q^70 
        + q^81 + (a - 1)*q^85 + a*q^88 + (-a + 1)*q^90 - q^91 + a*q^93 + q^94 - 
        a*q^97 + O(q^99),
    q^2 + q^5 - q^6 + (a - 1)*q^8 + q^11 - a*q^14 - q^15 - q^17 + q^18 - q^23 + 
        (-a + 1)*q^24 + (-a + 1)*q^26 + (2*a - 2)*q^29 - q^33 - a*q^35 + a*q^42 
        + q^45 + a*q^47 + q^51 - q^54 + q^56 - a*q^62 + (-a + 1)*q^65 + q^69 - 
        a*q^71 + (a - 1)*q^72 - a*q^74 - a*q^77 + (a - 1)*q^78 + a*q^80 + (2*a -
        2)*q^83 + (a - 1)*q^86 + (-2*a + 2)*q^87 + a*q^89 + O(q^99)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
453
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
75*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^10 - q^11 - q^17 - q^20 + q^25 - q^32 - q^37 + q^38 + q^40 + 
        q^44 + q^49 + q^50 - q^55 + q^58 - q^62 + q^68 + q^80 + q^81 - q^85 - 
        q^86 - q^88 - q^90 + q^94 - q^95 + O(q^99),
    q^2 - q^5 - q^10 - q^16 + q^18 + q^19 + q^25 + q^29 - q^31 - q^43 - q^44 - 
        q^45 + q^47 + q^50 + q^55 - q^59 - q^62 - q^68 + q^76 + q^80 + q^85 - 
        q^86 + q^88 - q^90 - q^95 + q^97 + q^98 + O(q^99),
    q^3 + q^27 - q^30 - q^33 - q^51 - q^60 + q^75 - q^96 + O(q^99),
    q^4 - q^5 - q^8 + q^11 + q^17 - q^22 - q^31 - q^34 + q^36 + q^37 + q^38 - 
        q^43 - q^45 + q^50 + q^55 + q^58 - q^59 - q^72 - q^74 - q^76 + q^85 + 
        q^94 + O(q^99),
    q^6 - q^15 - q^30 - q^48 + q^54 + q^57 + q^75 + q^87 - q^93 + O(q^99),
    q^12 - q^15 - q^24 + q^33 + q^51 - q^66 - q^93 + O(q^99)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
454
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
226
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
454
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
113*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^7 - q^11 + q^16 - q^21 + q^25 - q^27 - q^28 - q^33 - q^44 - q^47
        + q^49 - q^53 + q^57 + 2*q^59 + q^63 + q^64 + q^69 - q^73 + 2*q^77 - 
        q^79 - q^84 + q^87 + q^99 + q^100 - q^101 - q^103 - q^108 + O(q^112),
    q^2 + q^8 - q^14 - q^22 + q^32 - q^42 + q^50 - q^54 - q^56 - q^66 - q^88 - 
        q^94 + q^98 - q^106 + O(q^112),
    q^3 - q^7 - q^9 - q^11 + q^12 + q^19 + q^23 - q^28 + q^29 - q^36 + q^43 - 
        q^44 - q^47 + q^48 + q^49 - q^53 - q^57 - q^69 + q^71 - q^73 + q^75 + 
        q^76 + q^77 - q^79 - q^87 + q^89 + q^92 + q^97 - q^101 - q^103 + q^109 +
        O(q^112),
    q^6 - q^14 - q^18 - q^22 + q^24 + q^38 + q^46 - q^56 + q^58 - q^72 + q^86 - 
        q^88 - q^94 + q^96 + q^98 - q^106 + O(q^112)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 4*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 5*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 - 2*a*q^9 + (-a - 1)*q^15 + (a - 1)*q^16 + (2*a - 1)*q^21 - q^25 +
        (-a + 1)*q^29 + a*q^35 + (-2*a + 2)*q^36 + (2*a - 1)*q^39 + (-a + 
        1)*q^49 + 3*q^51 + (-2*a + 1)*q^60 - q^64 + a*q^65 + (a - 2)*q^71 - q^79
        + (a - 1)*q^81 + (a - 2)*q^84 + (-a + 2)*q^85 + (-a + 1)*q^91 - a*q^100 
        + O(q^106),
    q^3 + 1/3*(-a + 2)*q^5 + 1/3*(-a - 1)*q^7 + a*q^12 + 1/3*(-a - 1)*q^13 + (a 
        - 1)*q^17 + 1/3*(a + 1)*q^20 - a*q^27 + 1/3*(-2*a + 1)*q^28 + 1/3*(-2*a 
        - 2)*q^45 + 1/3*(-a + 2)*q^47 + (a - 1)*q^48 + 1/3*(-2*a + 1)*q^52 + 
        1/3*(4*a - 2)*q^63 - q^68 + 1/3*(a - 2)*q^73 - q^75 + 1/3*(2*a - 1)*q^80
        + 1/3*(-a + 2)*q^83 + (-a + 1)*q^87 + 1/3*(a + 1)*q^97 - a*q^103 + 
        a*q^105 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 3*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 - 2*a*q^11 + a*q^15 - a*q^16 - q^21 + q^25 + a*q^29 + (a - 
        1)*q^35 - q^39 + 2*q^44 - a*q^49 + q^51 - q^60 + q^64 + (a - 1)*q^65 + 
        (-a + 1)*q^71 - q^79 + a*q^81 + (-a + 1)*q^84 + (-a + 1)*q^85 - a*q^91 +
        (a - 1)*q^100 + O(q^106),
    q^3 + (-a + 1)*q^5 + a*q^7 + (a - 1)*q^12 + a*q^13 - a*q^17 + a*q^20 + (-a +
        1)*q^27 - q^28 - 2*a*q^33 + (a - 1)*q^47 - a*q^48 - q^52 - 2*q^55 + q^68
        + (a - 1)*q^73 + q^75 + (-2*a + 2)*q^77 - q^80 + (a - 1)*q^83 + a*q^87 -
        a*q^97 + (a - 1)*q^103 + (a - 1)*q^105 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
455
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - 1/3*q^14 + 1/3*q^16 + 1/3*q^25 + 1/3*q^29 - 2/3*q^30 - 1/3*q^35 - 
        1/3*q^36 - 1/3*q^39 + 1/3*q^49 - 2/3*q^51 - 2/3*q^56 - 2/3*q^64 - 
        1/3*q^65 - 2/3*q^74 + 1/3*q^79 + 1/3*q^81 - 1/3*q^91 - 1/3*q^95 + 
        2/3*q^100 - 1/3*q^105 + O(q^106),
    q^2 - q^15 - q^28 - q^37 + q^50 + q^63 + q^67 - q^72 + q^85 + q^93 + q^98 - 
        q^102 + O(q^106),
    q^3 - q^12 - q^13 + q^27 - q^35 - q^38 + q^40 + q^42 + q^62 + q^68 + q^75 - 
        q^82 - 2*q^87 - q^90 + O(q^106),
    q^4 - 2/3*q^14 - 1/3*q^16 + 2/3*q^25 - 1/3*q^29 - 1/3*q^30 + 1/3*q^35 - 
        2/3*q^36 + 1/3*q^39 + 2/3*q^49 - 1/3*q^51 - 1/3*q^56 - 1/3*q^64 + 
        1/3*q^65 - 1/3*q^74 - 4/3*q^79 - 1/3*q^81 + 1/3*q^91 - 2/3*q^95 + 
        1/3*q^100 + 1/3*q^105 + O(q^106),
    q^5 + q^8 + q^13 + q^15 - q^18 - q^20 - q^28 - q^32 + q^37 - q^45 - 2*q^47 -
        q^52 + q^57 + q^58 - q^60 - 2*q^63 - q^65 + q^72 + 2*q^73 + q^78 + q^80 
        - 2*q^83 - 2*q^93 + 2*q^97 + O(q^106),
    q^6 + q^8 + q^13 + q^15 - q^18 - q^20 + q^21 - q^24 - q^28 + q^31 - q^32 - 
        q^34 + q^37 - 2*q^45 - 2*q^47 - q^52 + q^57 + q^58 + q^59 - q^60 - 
        2*q^63 - q^65 + q^72 + 2*q^73 + q^76 + q^78 + q^80 - 2*q^83 - q^84 + 
        q^89 - q^91 - 2*q^93 + q^96 + 2*q^97 + q^104 + O(q^106),
    q^7 - q^8 - q^15 + q^18 + q^32 - q^37 - q^57 - q^58 + q^60 + q^63 + q^65 - 
        q^72 - q^78 + 2*q^93 + O(q^106),
    q^9 + 1/3*q^14 - 1/3*q^16 + 2/3*q^25 - 4/3*q^29 - 1/3*q^30 + 1/3*q^35 - 
        2/3*q^36 - 2/3*q^39 + 2/3*q^49 - 1/3*q^51 - 1/3*q^56 + 2/3*q^64 + 
        1/3*q^65 - 1/3*q^74 - 1/3*q^79 - 1/3*q^81 + 1/3*q^91 + 1/3*q^95 - 
        2/3*q^100 - 2/3*q^105 + O(q^106),
    q^10 - q^12 - q^13 + q^17 + q^27 - q^35 - 2*q^38 + q^40 + q^42 - q^52 + q^62
        + 2*q^68 - 2*q^82 - q^87 - q^90 + q^103 + O(q^106),
    q^19 - q^20 - q^21 + q^24 + q^26 - q^31 - q^34 + q^41 + q^45 - q^54 - q^59 +
        q^70 + q^76 - q^89 - q^96 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + 1/2*(-a^4 - a^3 + a + 1)*q^3 - a*q^4 + 1/2*(a^3 - a^2)*q^6 + 1/2*(-a^5 -
        a^3)*q^9 + 1/2*(a^5 + a^4 - a^2 - a)*q^12 + a^2*q^16 + 1/2*(a^5 - a^2 + 
        a)*q^18 + a*q^19 + (a^4 - 1)*q^22 + 1/2*(-a^4 + a^3)*q^24 + (a^4 - 
        a)*q^25 + 1/2*(-a^3 - 1)*q^27 + 1/2*(a^5 - a^3 + a^2 - a + 1)*q^33 + 
        (-2*a^4 + a)*q^34 + 1/2*(a^4 + a^3 - 1)*q^36 + (a^5 - a^2)*q^43 + 
        1/2*(-a^5 + a^2 + 1)*q^48 + (a^3 - 1)*q^49 + 1/2*(-2*a^5 + a^3 + a^2 - 
        2)*q^51 + 1/2*a^2*q^54 + 1/2*(-a^5 - a^4 + a^2 + a)*q^57 - a^3*q^64 + 
        1/2*(a^4 + a^3 + a^2 - 1)*q^66 + (-a^5 + a^3)*q^67 + 1/2*(-a^2 + 1)*q^72
        + (-a^4 - 1)*q^73 + 1/2*(a^5 + a^4)*q^75 - a^2*q^76 + 1/2*(a^3 - a - 
        1)*q^81 + (-a^5 - a^3 + a^2 + 1)*q^82 + (-a^5 + a)*q^88 + 1/2*(a^5 - 
        a^4)*q^96 + (a^4 - a^3 + 1)*q^97 + 1/2*(a^2 - a + 1)*q^99 + (-a^5 + 
        a^2)*q^100 + 1/2*(-a^5 - a^4 - a^2 - a)*q^102 + 1/2*(a^4 + a)*q^108 + 
        1/2*(a^4 - a^3)*q^114 + (a^5 - a^3 - a^2)*q^118 + (a^5 - a^4 + a^3 - a^2
        + a)*q^121 + 1/2*(a^5 - a^4 - a^2 + 1)*q^123 + 1/2*(a^5 + a^3 - 1)*q^129
        + 1/2*(a^4 - 2*a^3 + a^2 - a + 1)*q^132 + (2*a^5 - a^2)*q^136 + (a^5 + 
        a^3 - a^2 - 1)*q^139 + 1/2*(-a^5 - a^4 + a)*q^144 + O(q^146),
    q^2 + 1/2*(-a^2 + a)*q^3 + 1/2*(-a^4 - a^3 + a + 1)*q^6 - a*q^8 + 1/2*(-a^4 
        + a - 1)*q^9 + (-a^5 - a^3 + a^2)*q^11 + 1/2*(a^3 - a^2)*q^12 + (2*a^3 -
        1)*q^17 + 1/2*(-a^5 - a^3)*q^18 + 1/2*(a^5 + a^4 - a^2 - a)*q^24 - 
        1/2*a*q^27 + a^2*q^32 + 1/2*(-a^5 - a^3 - a)*q^33 + 1/2*(a^5 - a^2 + 
        a)*q^36 + a*q^38 + (a^5 + a^4 - a)*q^41 + (a^4 - 1)*q^44 + 1/2*(-a^4 + 
        a^3)*q^48 + (a^4 - a)*q^50 + 1/2*(a^4 + a^3 + a + 1)*q^51 + 1/2*(-a^3 - 
        1)*q^54 + 1/2*(-a^3 + a^2)*q^57 + (-a^4 + a^2 + a)*q^59 + 1/2*(a^5 - a^3
        + a^2 - a + 1)*q^66 + (-2*a^4 + a)*q^68 + 1/2*(a^4 + a^3 - 1)*q^72 + 
        1/2*(a^5 - a^2 + 1)*q^75 + 1/2*(a^5 - a)*q^81 + (a^5 - a^3 - a^2 + 
        1)*q^83 + (a^5 - a^2)*q^86 - a^2*q^89 + 1/2*(-a^5 + a^2 + 1)*q^96 + (a^3
        - 1)*q^98 + 1/2*(a^5 - a^4 + a^3 - 2*a^2 - 1)*q^99 + 1/2*(-2*a^5 + a^3 +
        a^2 - 2)*q^102 + (a^4 - a)*q^107 + 1/2*a^2*q^108 + (-a^3 - a^2 + 
        1)*q^113 + 1/2*(-a^5 - a^4 + a^2 + a)*q^114 + 1/2*(a^5 + a^4 + a^3 + 
        a^2)*q^123 - a^3*q^128 + 1/2*(a - 1)*q^129 + (-a^5 - a^4)*q^131 + 
        1/2*(a^4 + a^3 + a^2 - 1)*q^132 + (-a^5 + a^3)*q^134 + (a + 1)*q^137 + 
        1/2*(-a^2 + 1)*q^144 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 + a^2*q^4 - a^3*q^8 + (-a^5 + a^2)*q^9 + (a^5 - a^4 - a^2 + 
        a)*q^11 + a^4*q^16 + a*q^17 - q^18 + a^2*q^19 + (a^5 - a^2 + 1)*q^22 - 
        a^5*q^25 + (-a^4 - a^2)*q^27 - a^5*q^32 - a^2*q^34 + a*q^36 - a^3*q^38 +
        (a^3 + a^2 - 1)*q^41 + (a^4 - a)*q^43 + (-a + 1)*q^44 - a^3*q^49 + (a^3 
        - 1)*q^50 + (a^5 + a^3)*q^54 + (-a^5 + a^3 - 1)*q^59 + (a^3 - 1)*q^64 + 
        (a^3 - a - 1)*q^67 + a^3*q^68 - a^2*q^72 + (a^5 - a^2 + 1)*q^73 + 
        a^4*q^76 + (a^5 + a^4 - a - 1)*q^81 + (-a^4 - a^3 + a)*q^82 + (a^5 + a^4
        - a^2)*q^83 + (-a^5 + a^2)*q^86 + (a^2 - a)*q^88 + a^5*q^89 + (a^5 - a^3
        - a^2)*q^97 + a^4*q^98 + (a^4 - a^3 - a + 1)*q^99 + (-a^4 + a)*q^100 + 
        (-a^3 + 1)*q^107 + (-a^4 - a^3 + 1)*q^108 + (-a^5 + a^4)*q^113 + (-a^4 +
        a^3 + a - 1)*q^118 + (-a^5 - a^4 + a^3 + a - 1)*q^121 + (-a^4 + a)*q^128
        + (a^2 + 1)*q^131 + (-a^4 + a^2 + a)*q^134 - a^4*q^136 + (-a^3 - 
        a)*q^137 + (-a^4 - a^3 + a)*q^139 + a^3*q^144 + O(q^146),
    q^3 - a*q^6 + (-a^5 - a^3)*q^9 + a^2*q^12 + (a^4 + a^3 - 1)*q^18 - a^3*q^24 
        + (a^5 + a^3 - a^2 - a - 1)*q^27 + (a^5 - a^4 - a^2 + a)*q^33 + (-a^5 - 
        a^4 + a)*q^36 + a^4*q^48 + a*q^51 + (-a^4 + a^2 + a + 1)*q^54 + a^2*q^57
        + (a^5 - a^2 + 1)*q^66 + (a^5 + a^3 - a^2 - 1)*q^72 - a^5*q^75 + (a^4 + 
        a^3 + a^2)*q^81 - a^5*q^96 + (a^4 - a^3 + a^2 - a)*q^99 - a^2*q^102 + 
        (a^5 - a^3 - a^2 - a)*q^108 - a^3*q^114 + (a^3 + a^2 - 1)*q^123 + (a^4 -
        a)*q^129 + (-a + 1)*q^132 + (-a^4 + a + 1)*q^144 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a^4*q^3 + (a^2 - a)*q^7 + (a^5 - a^2)*q^9 + (-a^4 - a^3 + a)*q^13 + (a^3
        - 1)*q^19 + (-a^5 + a^3 - 1)*q^21 - a^5*q^25 - a^3*q^27 + (-a^5 - a^4 + 
        a)*q^31 + (a^5 - a^2 - a)*q^37 + (-a^4 + a^2 + a)*q^39 + (a^5 + a^3 - 
        a^2 - 1)*q^43 + (a^4 - a^3 + a^2)*q^49 - a*q^57 + (a^4 + 1)*q^61 + (-a +
        1)*q^63 + (a^4 - a^3)*q^67 + (a^3 + a^2 - 1)*q^73 + q^75 + (a^5 - a^2 + 
        1)*q^79 + (-a^4 + a)*q^81 + (a^4 - a^2 + 1)*q^91 + (a^2 + 1)*q^93 + 
        a*q^97 + (-a^5 - a)*q^103 + (a^4 - a)*q^109 + (-a^5 - a^3)*q^111 + (a^3 
        + a^2 - 1)*q^117 + (a^3 - 1)*q^121 + a^5*q^127 + (-a^3 - a)*q^129 + (a^5
        - a^4 - a^2 + a)*q^133 + (-a^4 - a^3 + a)*q^139 + O(q^146),
    q^2 + a^4*q^6 + (a^2 - a)*q^14 + (a^5 - a^2)*q^18 + (-a^4 - a^3 + a)*q^26 + 
        (a^3 - 1)*q^38 + (-a^5 + a^3 - 1)*q^42 - a^5*q^50 - a^3*q^54 + (-a^5 - 
        a^4 + a)*q^62 + (a^5 - a^2 - a)*q^74 + (-a^4 + a^2 + a)*q^78 + (a^5 + 
        a^3 - a^2 - 1)*q^86 + (a^4 - a^3 + a^2)*q^98 - a*q^114 + (a^4 + 1)*q^122
        + (-a + 1)*q^126 + (a^4 - a^3)*q^134 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + 1/2*(-a - 1)*q^3 - a*q^4 - 1/2*a*q^6 + 1/2*a*q^9 + 1/2*(2*a - 1)*q^12 + 
        (a - 1)*q^16 + 1/2*(2*a - 1)*q^18 + a*q^19 + (-a - 1)*q^22 + 1/2*(a - 
        1)*q^24 + a*q^25 + 1/2*(-a - 1)*q^33 + 1/2*(-a + 1)*q^36 + (-2*a + 
        2)*q^43 + 1/2*(-a + 2)*q^48 + q^49 + (-a + 1)*q^54 + 1/2*(-2*a + 1)*q^57
        + q^64 + 3/2*a*q^66 + (a - 2)*q^67 + 1/2*(-a + 2)*q^72 + (a - 1)*q^73 + 
        1/2*(-2*a + 1)*q^75 + (-a + 1)*q^76 + 1/2*(-a + 1)*q^81 - a*q^82 + (2*a 
        - 1)*q^88 + 1/2*q^96 + (-a - 1)*q^97 + 3/2*a*q^99 + (-a + 1)*q^100 + 
        1/2*(-a + 1)*q^114 + a*q^118 - 2*q^121 - 1/2*a*q^123 + (a - 2)*q^129 + 
        1/2*(2*a - 1)*q^132 + a*q^139 - 1/2*q^144 + O(q^146),
    q^2 + 1/2*q^3 + 1/2*(-a - 1)*q^6 - a*q^8 + 1/2*(-a - 1)*q^9 + (-a + 2)*q^11 
        - 1/2*a*q^12 + 1/2*a*q^18 + 1/2*(2*a - 1)*q^24 + a*q^27 + (a - 1)*q^32 -
        3/2*q^33 + 1/2*(2*a - 1)*q^36 + a*q^38 + q^41 + (-a - 1)*q^44 + 1/2*(a -
        1)*q^48 + a*q^50 + 1/2*a*q^57 - q^59 + 1/2*(-a - 1)*q^66 + 1/2*(-a + 
        1)*q^72 + 1/2*a*q^75 + 1/2*(-2*a + 1)*q^81 + (a - 2)*q^83 + (-2*a + 
        2)*q^86 + (2*a - 2)*q^89 + 1/2*(-a + 2)*q^96 + q^98 + 1/2*(a + 1)*q^99 -
        2*a*q^107 + (-a + 1)*q^108 - a*q^113 + 1/2*(-2*a + 1)*q^114 + 1/2*(-a - 
        1)*q^123 + q^128 + (-a + 1)*q^129 + (2*a - 1)*q^131 + 3/2*a*q^132 + (a -
        2)*q^134 + (a + 1)*q^137 + 1/2*(-a + 2)*q^144 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 6*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 + (a - 1)*q^4 + q^8 + (-a + 1)*q^9 - q^11 - a*q^16 - 2*a*q^17 - 
        q^18 + (a - 1)*q^19 + a*q^22 + (a - 1)*q^25 + q^27 + (a - 1)*q^32 + (2*a
        - 2)*q^34 + a*q^36 + q^38 + a*q^41 - 2*a*q^43 + (-a + 1)*q^44 + q^49 + 
        q^50 - a*q^54 + a*q^59 + q^64 + (-a + 1)*q^67 + 2*q^68 + (-a + 1)*q^72 +
        a*q^73 - a*q^76 + (-a + 1)*q^82 - q^83 + (2*a - 2)*q^86 - q^88 + (2*a - 
        2)*q^89 + a*q^97 - a*q^98 + (a - 1)*q^99 - a*q^100 + 2*q^107 + (a - 
        1)*q^108 - q^113 + (-a + 1)*q^118 - a*q^128 + a*q^131 - q^134 - 
        2*a*q^136 + (-a + 1)*q^137 + (-a + 1)*q^139 - q^144 + O(q^146),
    q^3 - a*q^6 + a*q^9 + (a - 1)*q^12 + (-a + 1)*q^18 + q^24 - q^33 - q^36 - 
        a*q^48 - 2*a*q^51 + (a - 1)*q^57 + a*q^66 + a*q^72 + (a - 1)*q^75 + q^81
        + (a - 1)*q^96 - a*q^99 + (2*a - 2)*q^102 + q^114 + a*q^123 - 2*a*q^129 
        + (-a + 1)*q^132 + (-a + 1)*q^144 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 6*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 - q^7 + (a - 1)*q^9 + (-a + 1)*q^13 + q^19 + a*q^21 + (a - 1)*q^25
        + q^27 - q^31 - q^37 - q^39 + a*q^43 - a*q^57 + (-a + 1)*q^61 + (-a + 
        1)*q^63 + (-a + 1)*q^67 + a*q^73 + q^75 + a*q^79 - a*q^81 + (a - 1)*q^91
        + a*q^93 - 2*a*q^97 - q^103 - 2*a*q^109 + a*q^111 + a*q^117 + q^121 + 
        (2*a - 2)*q^127 + (-a + 1)*q^129 - q^133 + (-a + 1)*q^139 + O(q^146),
    q^2 - a*q^6 - q^14 + (a - 1)*q^18 + (-a + 1)*q^26 + q^38 + a*q^42 + (a - 
        1)*q^50 + q^54 - q^62 - q^74 - q^78 + a*q^86 - a*q^114 + (-a + 1)*q^122 
        + (-a + 1)*q^126 + (-a + 1)*q^134 + O(q^146),
    q^4 - a*q^12 + (a - 1)*q^16 - q^28 + (a - 1)*q^36 + q^48 + (-a + 1)*q^52 - 
        a*q^64 + q^76 + a*q^84 + (a - 1)*q^100 + q^108 + (-a + 1)*q^112 - q^124 
        - a*q^144 + O(q^146),
    q^8 - a*q^24 + (a - 1)*q^32 - q^56 + (a - 1)*q^72 + q^96 + (-a + 1)*q^104 - 
        a*q^128 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 6*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 - q^7 + q^9 - q^11 - q^17 + q^19 + 2*q^23 + q^35 - q^43 - q^45 - 
        q^47 + q^55 - q^61 - q^63 - q^73 + q^77 + q^81 + 2*q^83 + q^85 - q^95 - 
        q^99 + 2*q^101 - 2*q^115 + q^119 + q^125 - q^131 - q^133 - q^137 - q^139
        + O(q^146),
    q^2 - q^10 - q^14 + q^18 - q^22 - q^34 + q^38 + 2*q^46 + q^70 - q^86 - q^90 
        - q^94 + q^110 - q^122 - q^126 + O(q^146),
    q^3 - q^15 - q^21 + q^27 - q^33 - q^51 + q^57 + 2*q^69 + q^105 - q^129 - 
        q^135 - q^141 + O(q^146),
    q^6 - q^30 - q^42 + q^54 - q^66 - q^102 + q^114 + 2*q^138 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 9*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^7 - q^9 + q^16 - q^17 - q^23 + q^25 - q^26 - q^28 - q^36 + q^38 
        + 2*q^47 + q^54 - q^58 + q^63 + q^64 - q^68 - q^73 + 2*q^74 - q^92 + 
        q^100 - q^104 - q^106 - q^112 - q^118 + q^119 + q^121 - q^134 - q^137 - 
        q^144 + O(q^146),
    q^2 + q^8 - q^13 - q^14 - q^18 + q^19 + q^27 - q^29 + q^32 - q^34 + 2*q^37 -
        q^46 + q^50 - q^52 - q^53 - q^56 - q^59 - q^67 - q^72 + q^76 + q^91 + 
        2*q^94 - q^107 + q^108 - q^109 - q^116 + q^117 + q^126 + q^128 - q^133 -
        q^136 + O(q^146),
    q^3 + q^12 - q^18 - q^21 + q^48 - q^51 - q^69 - q^72 + q^75 - q^78 - q^84 + 
        q^114 + q^117 + q^126 + 2*q^141 + O(q^146),
    q^6 - q^9 + q^24 - q^36 - q^39 - q^42 + q^57 + q^63 + q^81 - q^87 + q^96 - 
        q^102 + 2*q^111 - q^138 - q^144 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + 9*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
456
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + 9*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^6 + q^9 + q^16 - q^19 - q^24 - q^25 + q^36 - 2*q^43 + q^49 - 
        q^54 + q^64 - 2*q^73 - q^76 + q^81 - 2*q^82 - q^96 - q^100 + q^114 + 
        2*q^118 + q^121 + 2*q^123 + 2*q^139 + q^144 + O(q^146),
    q^2 - q^3 + q^8 - q^12 + q^18 - q^27 + q^32 - q^38 - 2*q^41 - q^48 - q^50 + 
        q^57 + 2*q^59 + q^72 + q^75 - 2*q^86 + 2*q^89 + q^98 + 2*q^107 - q^108 -
        2*q^113 + q^128 + 2*q^129 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
457
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
456
);
qprec:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
457
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
152
);
qprec:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
457
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
19*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
457
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
57*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
458
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
228
);
qprec:=
113
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
458
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
76
);
qprec:=
113
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
458
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
19*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
113
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
458
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
57*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
113
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^5 + (-a - 1)*q^6 + 1/2*(a - 1)*q^7 + 1/2*(a - 1)*q^8 - a*q^11 - 
        a*q^12 + 1/2*(-a - 1)*q^13 + q^14 + 1/2*(a - 1)*q^21 + 1/2*(a - 1)*q^24 
        + a*q^26 + 1/2*(a + 1)*q^28 + (-a + 1)*q^30 + 1/2*(-a - 1)*q^31 + (a + 
        1)*q^32 + (-a - 1)*q^34 + 1/2*(-a - 1)*q^35 + (a + 1)*q^38 + 1/2*(-a - 
        1)*q^39 + 1/2*(-a - 1)*q^40 + 1/2*(a - 1)*q^41 + q^42 - 2*a*q^46 + (a - 
        1)*q^47 - q^48 + q^51 + 1/2*(a - 1)*q^52 + q^53 + (a + 1)*q^54 + q^55 - 
        a*q^56 - q^57 + 1/2*(a + 1)*q^59 + q^60 - a*q^62 + a*q^64 + 1/2*(-a + 
        1)*q^65 + (a - 1)*q^66 + 1/2*(a - 1)*q^67 - a*q^68 + (a + 1)*q^69 + 
        a*q^70 - a*q^71 + a*q^76 + 1/2*(a + 1)*q^77 + a*q^78 - q^81 - q^82 + 
        1/2*(a + 1)*q^84 + (-a - 1)*q^86 + 1/2*(a + 1)*q^88 + q^91 + (-a + 
        1)*q^92 + 1/2*(a + 1)*q^93 - a*q^97 + (a - 1)*q^98 + 1/2*(-a - 1)*q^101 
        - a*q^103 + q^104 + 1/2*(-a - 1)*q^105 + (-a - 1)*q^106 + a*q^108 + (-a 
        + 1)*q^109 + 1/2*(-a + 1)*q^112 + O(q^113),
    q^2 + q^6 - a*q^8 + a*q^10 + (a - 1)*q^14 - a*q^22 - a*q^24 + (-a - 1)*q^26 
        + a*q^30 - q^32 + q^34 - q^38 + q^40 + (a - 1)*q^42 + (a + 1)*q^46 - 
        q^54 + (a + 1)*q^56 - a*q^66 + (-a - 1)*q^70 + (-a - 1)*q^78 + q^86 - 
        q^88 + (a - 1)*q^94 - q^96 - a*q^98 + q^102 + (a - 1)*q^104 + 2*q^106 + 
        q^110 + O(q^113),
    q^3 + 1/2*(a - 1)*q^7 + 1/2*(a - 1)*q^8 - a*q^12 + 1/2*(-a - 1)*q^13 + 
        a*q^15 - q^16 + q^17 - q^19 + 1/2*(a - 1)*q^21 + (a + 1)*q^23 + 1/2*(-a 
        + 1)*q^24 - q^27 + 1/2*(a + 1)*q^28 + 1/2*(a + 1)*q^31 - a*q^33 + 
        1/2*(-a - 1)*q^35 + 1/2*(-a - 1)*q^39 + 1/2*(-a - 1)*q^40 + 1/2*(-a + 
        1)*q^41 + q^43 - a*q^49 + 1/2*(a - 1)*q^52 + q^53 + 1/2*(-a - 1)*q^59 + 
        q^60 - q^61 + a*q^64 + 1/2*(-a + 1)*q^65 + 1/2*(-a + 1)*q^67 - a*q^68 + 
        a*q^76 + 1/2*(a + 1)*q^77 - a*q^80 - q^83 + 1/2*(a + 1)*q^84 + a*q^85 + 
        1/2*(a + 1)*q^88 + (a + 1)*q^89 + q^91 + (-a + 1)*q^92 + 1/2*(-a - 
        1)*q^93 - a*q^95 + 1/2*(a + 1)*q^101 + 1/2*(-a - 1)*q^105 + a*q^108 + 
        1/2*(-a + 1)*q^112 + O(q^113),
    q^4 + (a - 1)*q^6 + (a + 1)*q^8 - q^12 - a*q^14 + a*q^20 + q^26 + (-a - 
        1)*q^30 + (-a + 1)*q^32 + (a - 1)*q^34 + (-a + 1)*q^38 + (a - 1)*q^40 - 
        a*q^42 - a*q^44 - 2*q^46 + (-a + 1)*q^54 - q^56 - a*q^60 - q^62 + q^64 +
        (a + 1)*q^66 - q^68 + q^70 + q^76 + q^78 + a*q^82 + (a - 1)*q^86 + (-a +
        1)*q^88 + (-a - 1)*q^92 + (a + 1)*q^98 - a*q^104 + (a - 1)*q^106 + q^108
        + O(q^113)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
144
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
72
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
459
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^13 + q^16 - q^19 - q^43 + q^49 - q^52 - 2*q^55 + q^64 - q^67 - 
        q^76 - q^85 + O(q^98),
    q^5 - 2*q^11 - q^17 + q^20 + q^23 + q^29 + q^41 - 2*q^44 - q^65 - q^68 + 
        q^71 + q^80 + q^92 - q^95 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
44
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
44
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^4*q^4 - a*q^5 + (-a^9 - a^5)*q^6 + (a^9 - a^8 + a^7 + a^5 - a^4 - a^2 
        + a - 1)*q^9 + (-a^7 + a^2)*q^14 + a^8*q^16 - a^5*q^20 + (a^8 - a^7 - 
        a^3 - a)*q^21 + (-a^9 + a^2)*q^24 + a^2*q^25 + (a^8 + a^6)*q^29 + (a^9 -
        a^8 + a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^30 + (a^9 - a^8 - a^6 + a^5
        - a^4 - a^2 + a - 1)*q^36 + (-a^9 + a^4)*q^41 + (-a^7 + a^4 + 1)*q^45 + 
        a^4*q^46 + (a^9 - a^8 + a^7 - a^6 - a^4 + a^3 - a^2 + a)*q^49 + (a^8 + 
        a^4 - a + 1)*q^54 + (a^6 + 1)*q^56 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 
        + a^3 + a - 1)*q^61 - a*q^64 + (-a^9 - a^5)*q^69 + (a^8 - a^3)*q^70 - 
        a^9*q^80 + (-a^9 + a^6 - a^5 + a^2 - a)*q^81 + (-a^7 - a^5 - a + 1)*q^84
        + (-a^3 + 1)*q^86 + (-a^7 - a^3)*q^89 + (-a^3 - a)*q^94 + (a^6 + 
        a^2)*q^96 + a^6*q^100 + (-a^5 + a^4)*q^101 + (-a^9 + a^8 + a^4 + 
        a^2)*q^105 + (-a^9 - a^5)*q^109 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + 
        a^3 - a^2 - 1)*q^116 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 - a^2 + a - 
        1)*q^120 - a^7*q^121 - a^3*q^125 + (a^9 + a^7 - a^4 + a^3 - 1)*q^126 + 
        (a^8 - a^5 + a^4 - a)*q^129 + O(q^134),
    q^2 + (-a^5 - a)*q^3 + (-a^9 - a^3)*q^7 + a^4*q^8 - a*q^10 + (-a^9 - 
        a^5)*q^12 + (a^6 + a^2)*q^15 + (a^9 - a^8 + a^7 + a^5 - a^4 - a^2 + a - 
        1)*q^18 + q^23 + (a^8 - a^7 + a^4 + 1)*q^27 + (-a^7 + a^2)*q^28 + 
        a^8*q^32 + (a^9 - a^8 + a^7 - a^6 + a^5 + a^3 - a^2 + a - 1)*q^35 - 
        a^5*q^40 + (a^8 - a^7 - a^3 - a)*q^42 + (a^9 - a^8 - a^6 + a^5 - a^4 + 
        a^3 - a^2 + a - 1)*q^43 + (a^9 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a -
        1)*q^47 + (-a^9 + a^2)*q^48 + a^2*q^50 + (a^8 + a^6)*q^58 + (a^9 - a^8 +
        a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^60 + (-a^9 + a^8 + a^6 + a^4 + 
        a^2 - a)*q^63 + (a^6 - a^5)*q^67 + (a^9 - a^8 - a^6 + a^5 - a^4 - a^2 + 
        a - 1)*q^72 + (-a^7 - a^3)*q^75 + (-a^9 + a^4)*q^82 + (-a^3 + a^2)*q^83 
        + (-a^9 - a^7 + a^2 + 1)*q^87 + (-a^7 + a^4 + 1)*q^90 + a^4*q^92 + (a^9 
        - a^8 + a^7 - a^6 - a^4 + a^3 - a^2 + a)*q^98 + (a^8 + a^6)*q^103 + 
        (-a^5 - a^3)*q^107 + (a^8 + a^4 - a + 1)*q^108 + (a^6 + 1)*q^112 - 
        a*q^115 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 + a - 1)*q^122 + 
        (-a^8 + a^7 - a^6 - a^4 - a^2 + a - 1)*q^123 + (a^2 - a)*q^127 - a*q^128
        + O(q^134)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 - q^13 + q^23 + q^25 + q^27 - q^29 - q^31 + q^39 - q^41 - q^47 + 
        q^49 + 2*q^59 - q^69 - q^71 - q^73 - q^75 - q^81 + q^87 + q^93 + 2*q^101
        + q^121 + q^123 - q^127 - q^131 + O(q^134),
    q^2 - q^6 - q^8 + q^16 + q^24 - q^26 + q^46 - q^48 + q^50 + q^54 - q^58 - 
        q^62 - q^64 + q^78 - q^82 - q^94 + q^98 + q^104 + 2*q^118 + q^128 + 
        O(q^134),
    q^4 - q^8 - q^12 + q^24 + q^32 - q^52 - q^64 + q^92 - q^96 + q^100 + q^104 +
        q^108 - q^116 - q^124 + O(q^134),
    q^5 - q^15 - q^65 + q^115 + q^125 + O(q^134),
    q^10 - q^30 - q^40 + q^80 + q^120 - q^130 + O(q^134),
    q^20 - q^40 - q^60 + q^120 + O(q^134)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
460
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^29 - q^31 - q^35 - q^41 - q^59 - q^71 + q^81 - q^85 - 
        q^101 + q^115 + q^119 + q^121 + 2*q^131 + O(q^134),
    q^5 - q^7 - q^17 + q^23 - q^37 + 2*q^43 + q^45 - q^53 - q^63 - q^67 - q^83 +
        2*q^97 + 2*q^103 - q^107 - q^113 + q^125 + O(q^134)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
461
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
460
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
461
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
92
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
461
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
461
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
115*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a^2*q^4 + a^2*q^7 + (a - 1)*q^8 - a*q^9 + (a^3 - a^2 + a - 1)*q^11 + 
        (a^2 - a)*q^16 + (-a^3 + a^2)*q^23 - a^3*q^25 + (-a^3 + a^2 - a + 
        1)*q^28 + (-a^3 - a)*q^29 + q^32 + a^3*q^36 + (a^3 - a^2 + a)*q^37 + 
        (a^3 - a^2 - 1)*q^43 + a*q^44 + (a^3 - a^2 + a - 1)*q^49 + (a^2 + 
        1)*q^53 + (a^3 - a^2)*q^56 - a^3*q^63 + (a^3 - a^2 - 1)*q^67 + (-a^3 + 
        1)*q^71 + (-a^2 + a)*q^72 - a*q^77 + (a^2 + 1)*q^79 + a^2*q^81 + (-a^3 +
        a^2 - a)*q^88 + (-a^3 + a^2 - a)*q^92 + q^99 - q^100 + (-a + 1)*q^107 + 
        (-a^3 + a^2)*q^109 + (-a^2 + a - 1)*q^112 + (a^3 + a - 1)*q^113 + (a^3 -
        1)*q^116 - a^3*q^121 + (a^2 - a)*q^127 - a^2*q^128 + (a^2 - a)*q^137 + 
        (-a^3 + a^2)*q^144 + (-a^2 + a)*q^148 + (2*a^3 - 2*a^2 + 2*a - 2)*q^149 
        + (-a + 1)*q^151 + (a^3 - a^2 + a)*q^161 + (-a^2 + a - 1)*q^163 + 
        a^2*q^169 + (a^3 + a)*q^172 + q^175 + (-a + 1)*q^176 + O(q^178),
    q^2 + (-a^2 + a - 1)*q^4 + (-a^3 + a^2 - a)*q^8 + a^2*q^14 + a^3*q^16 - 
        a*q^18 + (a^3 - a^2 + a - 1)*q^22 + (-a + 1)*q^28 + (a^3 - a^2 + a)*q^36
        + (-a^3 + a^2)*q^44 + (-a^3 + a^2)*q^46 - a^3*q^50 + (-a^2 + a)*q^56 + 
        (-a^3 - a)*q^58 + q^64 + (a - 1)*q^72 + (a^3 - a^2 + a)*q^74 + (a^3 - 
        a^2 - 1)*q^86 + (a^2 - a + 1)*q^88 + (a^2 - 2*a + 1)*q^92 + (a^3 - a^2 +
        a - 1)*q^98 + (a^2 - a)*q^100 + (a^2 + 1)*q^106 - q^112 + a^3*q^116 - 
        a^3*q^126 + (-a^2 + a - 1)*q^128 + (a^3 - a^2 - 1)*q^134 + (-a^3 + 
        1)*q^142 + (-a^3 + a^2 - a + 1)*q^144 + (-a^3 + a - 1)*q^148 - a*q^154 +
        (a^2 + 1)*q^158 + a^2*q^162 + a*q^172 - a^2*q^176 + O(q^178),
    q^3 - a^2*q^12 + a^2*q^21 + (a - 1)*q^24 - a*q^27 + (a^3 - a^2 + a - 1)*q^33
        + (a^2 - a)*q^48 + (-a^3 + a^2)*q^69 - a^3*q^75 + (-a^3 + a^2 - a + 
        1)*q^84 + (-a^3 - a)*q^87 + q^96 + a^3*q^108 + (a^3 - a^2 + a)*q^111 + 
        (a^3 - a^2 - 1)*q^129 + a*q^132 + (a^3 - a^2 + a - 1)*q^147 + (a^2 + 
        1)*q^159 + (a^3 - a^2)*q^168 + O(q^178),
    q^6 + (-a^2 + a - 1)*q^12 + (-a^3 + a^2 - a)*q^24 + a^2*q^42 + a^3*q^48 - 
        a*q^54 + (a^3 - a^2 + a - 1)*q^66 + (-a + 1)*q^84 + (a^3 - a^2 + 
        a)*q^108 + (-a^3 + a^2)*q^132 + (-a^3 + a^2)*q^138 - a^3*q^150 + (-a^2 +
        a)*q^168 + (-a^3 - a)*q^174 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
462
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^15 - q^16 - q^22 - q^37 - q^42 + q^49 + q^58 + q^64 - q^67 + 
        q^70 + q^78 + q^81 + q^88 - q^91 + q^114 + q^121 - q^130 - q^133 - q^135
        - q^141 - q^144 - q^163 + q^168 - q^177 + O(q^178),
    q^2 + q^18 - q^30 - q^32 - q^44 - q^74 - q^84 + q^98 + q^116 + q^128 - q^134
        + q^140 + q^156 + q^162 + q^176 + O(q^178),
    q^3 - q^5 - q^14 + q^26 + q^27 + q^38 - q^45 - q^47 - q^48 + q^56 - q^59 - 
        q^66 + q^77 + q^80 + 2*q^89 - q^104 + q^110 - q^111 - 2*q^122 + q^125 - 
        q^126 - q^143 + q^146 + q^147 - q^152 + q^174 + O(q^178),
    q^4 - q^16 - q^22 + q^36 - q^42 + q^58 - q^60 + q^70 + q^78 + q^114 - q^130 
        - q^144 - q^148 + O(q^178),
    q^6 - q^10 - q^28 + q^52 + q^54 + q^76 - q^90 - q^94 - q^96 + q^112 - q^118 
        - q^132 + q^154 + q^160 + O(q^178),
    q^7 - q^13 - q^19 + q^24 - q^28 + q^33 - q^40 + q^52 - q^55 + 2*q^61 + q^63 
        - q^73 + q^76 - q^87 - q^96 - q^105 - q^117 - q^132 + 2*q^139 + q^145 + 
        q^160 - q^171 + O(q^178),
    q^8 + q^11 + q^21 - q^29 - q^32 - q^35 - q^39 - q^44 - q^57 + q^65 + q^72 - 
        q^84 + q^95 + q^99 - q^107 + q^116 - q^120 + q^140 - q^149 + q^156 - 
        q^165 + O(q^178),
    q^12 - q^14 - q^20 + q^26 + q^38 - q^48 - q^66 + q^80 + q^108 + q^110 - 
        2*q^122 - q^126 + q^146 + q^174 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
463
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
462
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
463
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
154
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
463
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
463
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
463
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
463
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
33*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
463
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
77*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
463
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
231*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^29 - q^32 - q^34 - q^43 - q^47 + q^49 - q^62 - q^68 + 
        O(q^77),
    q^2 - q^16 - q^17 + q^18 - q^31 - q^34 + q^50 + q^59 + q^61 - q^62 - q^67 + 
        q^73 + O(q^77),
    q^4 - q^8 - q^17 + q^29 - q^31 + q^36 + q^43 + q^47 - q^58 - q^67 - q^72 + 
        O(q^77)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^5 - a^4 + a^3 + a - 1)*q^5 + a^5*q^9 + (a^3 + a)*q^13 + (-a^4 - 
        a^3)*q^17 + (-a^5 + a^4 - a)*q^25 - a^2*q^29 + (-a^5 + 2*a^4 - a^3 + a^2
        - a + 1)*q^37 + (-a^5 + a^4 - a^3 + a^2 - 2*a + 1)*q^41 + (-a^4 - 
        1)*q^45 - a^5*q^49 + (a - 1)*q^53 + (-a^3 - a^2)*q^61 + (a^5 + a^3 - a^2
        - 1)*q^65 + (a^5 - a^4 + a^3 - a^2 + a - 2)*q^73 - a^3*q^81 + (-2*a^5 + 
        a^4 + 2*a^2 - a + 1)*q^85 + (-a^5 + a^4 - a^3 + 2*a^2 - a + 1)*q^89 + 
        (-a^2 + 1)*q^97 + (a^5 - a)*q^101 + (-a^5 + 1)*q^109 + O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^5 + a^4)*q^5 - a^3*q^9 + (a^5 - a^4 + a^3 + a - 1)*q^13 + (a^5 - a^4
        + a^3 - a^2 - 1)*q^17 + (-a^3 + a^2 - a)*q^25 + a^4*q^29 + (-a^5 - 
        a)*q^37 + (-a^5 + a^2)*q^41 + (-a + 1)*q^45 - a^3*q^49 + (a^2 + 1)*q^53 
        + (a^5 + a^3 - a^2 + a - 1)*q^61 + (a^5 - a^2 + a)*q^65 + (-a^5 + 
        1)*q^73 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^81 + (-a^2 + a - 1)*q^85 + 
        (-a^5 + a^4)*q^89 + (a^4 + 1)*q^97 + (-a^3 + a^2)*q^101 + (-a^3 + 
        1)*q^109 + O(q^110),
    q^2 + (-a^5 + a^4)*q^10 - a^3*q^18 + (a^5 - a^4 + a^3 + a - 1)*q^26 + (a^5 -
        a^4 + a^3 - a^2 - 1)*q^34 + (-a^3 + a^2 - a)*q^50 + a^4*q^58 + (-a^5 - 
        a)*q^74 + (-a^5 + a^2)*q^82 + (-a + 1)*q^90 - a^3*q^98 + (a^2 + 1)*q^106
        + O(q^110),
    q^4 - a*q^8 + a^2*q^16 + (-a^5 + a^4)*q^20 - a^3*q^32 - a^3*q^36 + (-a^4 + 
        a^3 - a^2 + a - 1)*q^40 + (a^5 - a^4 + a^3 + a - 1)*q^52 + a^4*q^64 + 
        (a^5 - a^4 + a^3 - a^2 - 1)*q^68 + a^4*q^72 + (a^5 - a^4 + a^3 - a^2 + 
        a)*q^80 + (-a^3 + a^2 - a)*q^100 + (-a^3 + 1)*q^104 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^29 - 2*q^33 - 2*q^45 + q^49 - 2*q^65 + q^81 - 2*q^93 + 
        O(q^110),
    q^3 - q^11 - q^15 + q^27 - q^31 + q^39 - q^43 + q^47 + q^55 + q^79 - q^87 - 
        2*q^99 + O(q^110),
    q^5 - q^9 - q^13 + q^25 + q^33 - q^53 - q^65 + q^93 + q^109 + O(q^110)
]
;
Bo:=
[
    q - q^5 - q^13 + q^29 + q^33 + q^49 - q^53 - 2*q^57 + q^65 - q^81 + q^93 - 
        q^109 + O(q^110),
    q^2 - q^10 - q^26 + q^58 + q^66 + q^98 - q^106 + O(q^110),
    q^3 + q^11 - q^15 - 2*q^19 - q^27 + q^31 - q^39 + q^43 + q^47 - q^55 + q^79 
        + q^87 + 2*q^95 + O(q^110),
    q^4 + q^16 - q^20 - q^24 - q^52 + q^64 - q^80 - q^88 - q^96 + O(q^110),
    q^6 + q^22 - q^30 - 2*q^38 - q^54 + q^62 - q^78 + q^86 + q^94 + O(q^110),
    q^8 - q^12 + q^32 - q^40 - q^44 - q^48 + q^60 + 2*q^76 - q^104 + q^108 + 
        O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
464
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^6 - a^4 - 2*a^3 - a^2 + 1)*q^4 + (a^5 + a^4 + a^3 - a^2 - a - 1)*q^6 
        + a^2*q^9 + (a^7 - a^2 - a)*q^10 + a^6*q^15 + (2*a^7 + 2*a^6 - 2*a^4 - 
        a^3 + a + 1)*q^16 + (-a^5 - a^3)*q^19 + (-a^7 - a^6 + a^4 + a + 1)*q^24 
        + (a^5 - 1)*q^25 + (-a^7 - a^6 + a^3 + a^2 - 1)*q^31 + (-a^7 - a^6 + a^4
        + 2*a^3 + a^2 - 1)*q^34 + (-a^7 - a^6 - a^5 + a^3 + a^2 - a - 1)*q^36 + 
        (-a^7 - a^6 + a^5 + 2*a^4 + a^3)*q^40 + (-a^7 - a^6 - a^5)*q^46 + (-a^6 
        + a)*q^49 + (a^7 - a^5 - a^4 - a^3 + a + 1)*q^51 + (a^7 + a^6 + a^5 - 
        a^4 - a^3 - a^2)*q^54 + (-a^6 - 2*a^5 - a^4 + a^3 + a^2 + a)*q^60 + 
        (-a^6 + a^4 + a)*q^61 + (a^7 - 2*a^5 - a^4 + a^3 + a^2)*q^64 + (a^5 - a 
        - 1)*q^69 + (a^6 + 2*a^5 + 2*a^4 + a^3 - a - 2)*q^76 + (-a^7 + a^6 + a^5
        + a^4 + a^3 - a - 1)*q^79 + a^4*q^81 + (-a^7 + a^2)*q^85 + (a^7 + a^6 - 
        a^4 - 2*a^3 - a^2 + 1)*q^90 + (-a^7 + a^3 + a^2 - 2)*q^94 + (a^6 + a^5 -
        a^4 - 2*a^3 - a^2 + a)*q^96 + (-a^6 - a^5 - a^4 + a^3 + 2*a^2 + a)*q^100
        + (-a^7 + a^4 - a^3 + 1)*q^106 + (a^7 - a^2 + 1)*q^109 + (a^7 - a^6 - 
        a^5 - a^4 + a^2 + 2*a + 2)*q^114 + (a^7 + a^6 - a^5 - a^4 - a^3 - a^2 + 
        1)*q^115 - a*q^121 + O(q^122),
    q^2 + (-2*a^6 + a^4 + a^2 + a - 2)*q^3 + (-a^7 + a^6 - a^4 + a^3 - a + 
        1)*q^5 + (a^6 - a^4 - a^3 - a^2 + 1)*q^8 + (-a^7 - 2*a^6 + 2*a^5 + 2*a^4
        + a^3 + a^2 - a - 3)*q^12 + (2*a^7 + 2*a^6 - 2*a^5 - a^4 - a^3 - 2*a^2 +
        a + 2)*q^17 + a^2*q^18 + (a^7 + 2*a^6 - a^5 - a^4 - 2*a^2 - a + 2)*q^20 
        + (-3*a^6 + a^5 + 2*a^4 + 2*a^2 + a - 3)*q^23 + (2*a^7 + a^6 - 2*a^5 - 
        a^4 - a^3 - 2*a^2 + 2*a + 2)*q^27 + a^6*q^30 + (2*a^7 + 2*a^6 - a^5 - 
        2*a^4 - a^3 - a^2 + a + 2)*q^32 + (-a^5 - a^3)*q^38 + (-2*a^7 - 2*a^6 + 
        2*a^5 + a^4 + a^3 + 2*a^2 - a - 2)*q^45 + (-5*a^7 + 3*a^5 + a^4 + 2*a^3 
        + 3*a^2 - 4*a - 2)*q^47 + (-3*a^7 - 2*a^6 + 2*a^5 + 2*a^4 + a^3 + 2*a^2 
        - a - 2)*q^48 + (a^5 - 1)*q^50 + (2*a^7 - a^5 - a^3 - a^2 + a + 1)*q^53 
        + (-a^7 + 2*a^6 + a^5 - a^4 + a^3 - a^2 - 2*a + 1)*q^57 + (-a^7 - a^6 + 
        a^3 + a^2 - 1)*q^62 + (2*a^7 - 2*a^5 - a^2 + 2*a + 1)*q^68 + (-a^7 - a^6
        + a^3 + a^2 - a - 1)*q^72 + (2*a^7 + 2*a^6 - 2*a^5 - a^4 - a^3 - 2*a^2 +
        a + 3)*q^75 + (a^7 + a^6 - a^5 - 2*a^2 + a + 2)*q^80 + (-4*a^7 - 2*a^6 +
        4*a^5 + a^4 + 2*a^3 + 3*a^2 - 3*a - 3)*q^83 + (-3*a^7 - 4*a^6 + 2*a^5 + 
        2*a^4 + a^3 + 3*a^2 - a - 4)*q^92 + (3*a^7 + a^6 - 2*a^5 - a^4 - 2*a^3 -
        2*a^2 + 2*a + 2)*q^93 + (3*a^7 - a^6 - a^5 - 2*a^3 - a^2 + 2*a)*q^95 + 
        (-a^6 + a)*q^98 + (a^7 - a^5 - a^4 - a^3 + a + 1)*q^102 + (4*a^7 + 3*a^6
        - 3*a^5 - 2*a^4 - 2*a^3 - 4*a^2 + 2*a + 4)*q^107 + (3*a^7 + a^6 - a^5 - 
        a^4 - 2*a^3 - 2*a^2 + 2*a + 1)*q^108 + (2*a^6 - a^5 - a^4 - a^2 + 
        2)*q^113 + (a^7 - 2*a^5 - a^4 + a + 1)*q^120 + O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 - a^3*q^4 + (a^3 + a - 1)*q^7 + a^2*q^9 + (a^3 - a^2 + a - 1)*q^12
        + (-a^2 + a - 1)*q^13 - a*q^16 + (a^2 - a)*q^19 + (-a^3 + 1)*q^21 + q^25
        - a^3*q^27 + (a^2 + 1)*q^28 - a*q^31 + q^36 + (a^3 - a^2 - 1)*q^37 + 
        (a^3 - a^2 + a)*q^39 + (-a^3 + 1)*q^43 + a^2*q^48 + (-a^2 - 1)*q^49 + 
        (a^2 - a)*q^52 + (-a^3 + a^2)*q^57 + (-a^3 + a^2)*q^61 + (a^3 - a^2 - 
        1)*q^63 + (a^3 - a^2 + a - 1)*q^64 + (-a^3 + a^2)*q^67 + (a^3 + a - 
        1)*q^73 - a*q^75 + (a^3 - a^2 + a)*q^76 + (a^3 - a^2 + a)*q^79 + (a^3 - 
        a^2 + a - 1)*q^81 + (-a^3 - a)*q^84 + (-a^3 + a^2 - a + 1)*q^91 + 
        a^2*q^93 + (-a + 1)*q^97 - a^3*q^100 + (-a^3 + 1)*q^103 - a*q^108 + (a^2
        + 1)*q^109 + (a^2 + 1)*q^111 + (-a^3 + 1)*q^112 + (-a + 1)*q^117 - 
        a*q^121 + O(q^122),
    q^5 - a*q^15 - a^3*q^20 + (a^3 + a - 1)*q^35 + a^2*q^45 + (a^3 - a^2 + a - 
        1)*q^60 + (-a^2 + a - 1)*q^65 - a*q^80 + (a^2 - a)*q^95 + (-a^3 + 
        1)*q^105 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 + (-a^3 + a^2)*q^6 + a^2*q^9 + (a^2 - a)*q^10 - a*q^15 + 
        (-a^3 + 1)*q^19 + a^3*q^24 + q^25 + (a^3 - a^2 + a - 1)*q^31 + (-2*a^2 +
        2*a - 2)*q^34 + (a^3 - a^2)*q^36 - a^2*q^40 + (a^2 - 2*a + 1)*q^46 - 
        a*q^49 - 2*a^3*q^51 + (a^3 - a^2 + a)*q^54 + (-a^2 + a)*q^60 + (a^3 - 
        a^2 - 1)*q^61 + (a^2 - a)*q^64 + (-a + 1)*q^69 + a^2*q^76 + (-a^3 - 
        a)*q^79 + (a^3 - a^2 + a - 1)*q^81 + 2*a^2*q^85 + (-a^2 + a - 1)*q^90 + 
        (a^3 - a^2 + 1)*q^94 - a*q^96 + (a - 1)*q^100 + a*q^106 + (a^2 + 
        1)*q^109 + (-a^3 + a^2 - a + 1)*q^114 + (a^3 - a^2 + a)*q^115 - a*q^121 
        + O(q^122),
    q^2 + (a^3 + a)*q^3 + (-a^2 - 1)*q^5 + (a^3 + a - 1)*q^8 - q^12 + (-2*a^3 - 
        2*a + 2)*q^17 + a^2*q^18 + (-a^3 + a^2 - a + 1)*q^20 - a^3*q^23 + (a^3 -
        1)*q^27 - a*q^30 + (-a^2 - 1)*q^32 + (-a^3 + 1)*q^38 + (-a^3 - a + 
        1)*q^45 + a^2*q^47 + q^50 + (2*a^3 + a - 1)*q^53 + (a^2 + a + 1)*q^57 + 
        (a^3 - a^2 + a - 1)*q^62 + 2*a*q^68 + (a^3 - a^2 - 1)*q^72 + (a^3 + 
        a)*q^75 + q^83 + (a^2 - a + 1)*q^92 + (-a^2 - 1)*q^93 + (a^3 - a^2 - 
        2)*q^95 - a*q^98 - 2*a^3*q^102 - a^3*q^107 - a^2*q^108 + (2*a^3 - 
        2)*q^113 + (-a^3 + 1)*q^120 + O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^6 + (a - 1)*q^9 + (-a + 1)*q^10 + q^15 - q^16 + a*q^19 - a*q^24 - 
        a*q^25 + q^31 - a*q^34 + (a - 1)*q^40 - 2*q^46 + (a - 1)*q^49 + (-a + 
        1)*q^51 - q^54 - q^61 + q^64 - 2*a*q^69 + a*q^79 - a*q^81 - q^85 + 
        a*q^90 + q^94 + (-2*a + 2)*q^106 + 2*q^109 + (a - 1)*q^114 + (2*a - 
        2)*q^115 - a*q^121 + O(q^122),
    q^2 + a*q^3 + (-a + 1)*q^5 - q^8 - a*q^17 + (a - 1)*q^18 - 2*q^23 - q^27 + 
        q^30 + a*q^38 + a*q^45 + q^47 - a*q^48 - a*q^50 + (-2*a + 2)*q^53 + (a -
        1)*q^57 + q^62 + (-a + 1)*q^72 + (-a + 1)*q^75 + (a - 1)*q^80 + (a - 
        1)*q^83 + a*q^93 + q^95 + (a - 1)*q^98 + (-a + 1)*q^102 + 2*a*q^107 + (a
        - 1)*q^113 - q^120 + O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 - q^7 + q^8 + q^9 + q^14 - q^16 - q^18 - q^19 - q^25 + q^31 + q^38 -
        q^41 + 2*q^47 + q^50 - q^56 - q^59 - q^62 - q^63 + q^64 + 2*q^67 - q^71 
        + q^72 + q^81 + q^82 - 2*q^94 - q^97 - q^101 - q^103 - q^107 - q^109 + 
        q^112 - q^113 + q^118 + q^121 + O(q^122),
    q^3 - q^6 - q^21 + q^24 + q^27 + q^42 - q^48 - q^54 - q^57 - q^75 + q^93 + 
        q^114 + O(q^122),
    q^5 - q^10 - q^25 - q^35 + q^40 + q^45 + q^50 + q^70 - q^80 - q^90 - q^95 + 
        O(q^122),
    q^15 - q^30 - q^75 - q^105 + q^120 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 15*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
465
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 15*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - 1/2*q^5 - q^9 - 1/2*q^10 + q^14 + q^16 - q^19 - q^20 + 1/2*q^25 - q^31 +
        1/2*q^35 + 1/2*q^40 + q^41 + 1/2*q^45 - 1/2*q^50 - q^56 + q^59 + q^64 + 
        1/2*q^70 - q^71 - 2*q^76 - 1/2*q^80 + q^81 + 1/2*q^90 + 3/2*q^95 + q^100
        - q^101 - q^109 + q^121 + O(q^122),
    q^2 + 1/2*q^5 - q^7 - q^8 + 1/2*q^10 - q^18 - q^20 + 1/2*q^25 + 2*q^28 - 
        1/2*q^35 + q^38 - 1/2*q^40 - 1/2*q^45 - 1/2*q^50 - q^62 + q^63 + 
        3/2*q^70 + q^72 + 1/2*q^80 - q^82 - 1/2*q^90 + 1/2*q^95 + q^97 - 2*q^98 
        - q^100 - q^103 + q^107 - q^112 + q^113 - q^118 + O(q^122),
    q^3 - 1/2*q^15 - q^27 - 1/2*q^30 + q^42 + q^48 - q^57 - q^60 + 1/2*q^75 - 
        q^93 + 1/2*q^105 + 1/2*q^120 + O(q^122),
    q^4 - 1/2*q^5 + 1/2*q^10 - q^14 - q^19 + 1/2*q^25 - 1/2*q^35 - q^36 - 
        1/2*q^40 + q^41 + 1/2*q^45 + q^49 + 1/2*q^50 + q^56 + q^59 - 1/2*q^70 - 
        q^71 - 1/2*q^80 - 1/2*q^90 + 1/2*q^95 - q^101 - q^109 + O(q^122),
    q^6 + 1/2*q^15 - q^21 - q^24 + 1/2*q^30 - q^54 - q^60 + 1/2*q^75 + 2*q^84 - 
        1/2*q^105 + q^114 - 1/2*q^120 + O(q^122),
    q^12 - 1/2*q^15 + 1/2*q^30 - q^42 - q^57 + 1/2*q^75 - 1/2*q^105 - q^108 - 
        1/2*q^120 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
466
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
232
);
qprec:=
115
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
466
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
29*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
115
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
467
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
466
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
467
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
233*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^13 + q^16 - q^21 - q^23 + q^25 - q^47 + q^49 - q^51 - q^52 - 
        q^59 - q^63 + q^64 + O(q^78),
    q^3 - q^9 + q^12 - q^13 - q^21 - q^23 + q^27 - q^36 + q^39 + q^41 + q^43 - 
        q^47 + q^48 + q^49 - q^51 - q^52 + q^53 - q^59 + q^69 + q^75 + O(q^78),
    q^7 - q^9 - q^13 + q^17 - q^23 + q^27 + q^28 - q^36 + q^39 - q^47 - q^52 - 
        q^59 + q^68 + q^69 + q^71 + O(q^78)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^3 + a^2)*q^7 + a*q^13 + (-a^2 - a + 1)*q^19 + a^3*q^25 + (a^3 + a^2 
        - a - 1)*q^31 + (-a^3 - a^2 + a)*q^37 + (-a^2 - 1)*q^43 + (-a^3 + a^2 + 
        a - 2)*q^49 + (2*a^3 - a)*q^61 + (-a - 1)*q^67 + (a^3 - a^2 - a + 
        1)*q^73 + (-a^3 + 2*a)*q^79 + (a^3 - a^2 + 1)*q^91 + (-a^3 - a^2)*q^97 +
        (2*a^2 - 1)*q^103 + (a^2 - a)*q^109 + a*q^121 + (-a^3 + a)*q^127 + (-a^3
        + a^2 - a)*q^133 + (-a^2 + 1)*q^139 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (a^2 - 2)*q^10 - a^2*q^13 + a^2*q^16 + 2*a^3*q^25 + (a^3 - a^2 -
        a + 1)*q^34 + (-a^3 - a^2 + 1)*q^37 + (-a^3 + 2*a)*q^40 + (-a^3 + 
        a)*q^49 + a^3*q^52 + (-a^3 - a^2)*q^58 + (a^2 - 1)*q^61 - a^3*q^64 + 
        (-a^3 + a^2 + a - 1)*q^73 + a*q^82 + (-a^3 + 2*a^2 - a - 1)*q^85 + (-a^2
        - a + 1)*q^97 + (-2*a^2 + 2)*q^100 + (a + 1)*q^106 + (a^3 - 1)*q^109 + 
        a*q^121 + (a^2 + 1)*q^130 + (a^3 - a + 1)*q^136 + (a^3 - a^2 - 2*a - 
        1)*q^145 + O(q^146),
    q^2 + (-2*a^3 + a)*q^5 - a*q^8 + (a^3 - a^2 + 1)*q^17 + (a^2 - 2)*q^20 - 
        a^2*q^26 + (a^2 + a)*q^29 + a^2*q^32 - q^41 + 2*a^3*q^50 + (a^3 - a - 
        1)*q^53 + (a^3 - 2*a)*q^65 + (a^3 - a^2 - a + 1)*q^68 + (-a^3 - a^2 + 
        1)*q^74 + (-a^3 + 2*a)*q^80 + (-a^3 + a)*q^98 + (-a^2 + a)*q^101 + 
        a^3*q^104 + (-a + 1)*q^113 + (-a^3 - a^2)*q^116 + (a^2 - 1)*q^122 + (a^2
        + 1)*q^125 - a^3*q^128 + (a^3 - a)*q^137 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + (-a + 1)*q^10 + (a - 1)*q^13 + (a - 1)*q^16 + (-2*a + 1)*q^34 + 
        (-a - 1)*q^37 + q^40 + (-a + 1)*q^49 - q^52 + (a - 2)*q^58 + a*q^61 - 
        q^64 + (-2*a + 1)*q^73 - a*q^82 + (a - 2)*q^85 + (a + 1)*q^106 + a*q^121
        + a*q^130 + (-a + 2)*q^136 + (a + 1)*q^145 + O(q^146),
    q^2 - a*q^5 + a*q^8 + (-a - 1)*q^17 + (-a + 1)*q^20 + (a - 1)*q^26 + (2*a - 
        1)*q^29 + (a - 1)*q^32 - q^41 + (-a + 2)*q^53 + q^65 + (-2*a + 1)*q^68 +
        (-a - 1)*q^74 + q^80 + 2*q^89 + (-a + 1)*q^98 + (2*a - 1)*q^101 - q^104 
        + (a + 1)*q^113 + (a - 2)*q^116 + a*q^122 - a*q^125 - q^128 + (a - 
        1)*q^137 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 2)*q^7 + a*q^13 - q^25 + (-2*a + 1)*q^31 + a*q^43 + (-2*a + 2)*q^49
        - a*q^61 + (a + 1)*q^67 + (-2*a + 1)*q^73 + q^79 + (-a - 1)*q^91 + (a - 
        2)*q^97 - q^103 + (2*a - 1)*q^109 + a*q^121 + (a - 1)*q^127 + a*q^139 + 
        O(q^146),
    q^3 + (-a + 1)*q^9 + (a - 2)*q^21 - a*q^27 + a*q^39 + (2*a - 1)*q^63 - q^75 
        - q^81 + (-2*a + 1)*q^93 + q^117 + a*q^129 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^7 + a*q^13 + (-a - 1)*q^19 - a*q^25 + (a + 1)*q^31 + (-a + 
        1)*q^37 - a*q^49 + (-a - 1)*q^67 + (a - 1)*q^73 + (-a - 1)*q^91 + (a + 
        1)*q^97 + (-a - 1)*q^109 + a*q^121 + 2*a*q^127 + 2*q^133 + 2*q^139 + 
        O(q^146),
    q^2 - a*q^8 + (a - 1)*q^14 + a*q^26 - q^32 + (-a - 1)*q^38 - a*q^50 + (a + 
        1)*q^56 + (a + 1)*q^62 + (-a + 1)*q^74 - a*q^98 + q^104 + a*q^128 + (-a 
        - 1)*q^134 + O(q^146),
    q^4 - a*q^16 + (a - 1)*q^28 + a*q^52 - q^64 + (-a - 1)*q^76 - a*q^100 + (a +
        1)*q^112 + (a + 1)*q^124 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + q^13 - q^16 + a*q^25 + (a - 1)*q^34 + (a - 1)*q^37 - a*q^49 - 
        a*q^52 + (a + 1)*q^58 - 2*q^61 + a*q^64 + (-a + 1)*q^73 - 2*a*q^82 + (-a
        - 1)*q^97 + q^100 + (a + 1)*q^106 + (-a - 1)*q^109 + a*q^121 + (a + 
        1)*q^136 + O(q^146),
    q^2 - a*q^8 + (-a - 1)*q^17 + q^26 + (a - 1)*q^29 - q^32 + 2*q^41 + a*q^50 +
        (a - 1)*q^53 + (a - 1)*q^68 + (a - 1)*q^74 - a*q^98 + (a + 1)*q^101 - 
        a*q^104 + (-a + 1)*q^113 + (a + 1)*q^116 - 2*q^122 + a*q^128 - 2*a*q^137
        + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 + (a - 1)*q^4 + q^5 - q^8 + a*q^10 - a*q^13 - a*q^16 + (a - 
        1)*q^17 + (a - 1)*q^20 + (-a + 1)*q^26 - a*q^29 + (-a + 1)*q^32 - q^34 +
        a*q^37 - q^40 - a*q^41 - a*q^49 + q^52 + q^53 + (-a + 1)*q^58 + (-a + 
        1)*q^61 + q^64 - a*q^65 - a*q^68 - q^73 + (a - 1)*q^74 - a*q^80 + (-a + 
        1)*q^82 + (a - 1)*q^85 + 2*a*q^89 + (2*a - 2)*q^97 + (-a + 1)*q^98 - 
        a*q^101 + a*q^104 + a*q^106 + 2*q^109 + (a - 1)*q^113 + q^116 + (a - 
        1)*q^121 + q^122 - q^125 + a*q^128 + (-a + 1)*q^130 + (-a + 1)*q^136 + 
        (a - 1)*q^137 - a*q^145 + O(q^146)
]
;
Bo:=
[
    q - a*q^2 + (a - 1)*q^4 - q^5 + q^8 + a*q^10 - a*q^13 - a*q^16 + (-a + 
        1)*q^17 + (-a + 1)*q^20 + (a - 1)*q^26 + a*q^29 + (a - 1)*q^32 - q^34 + 
        a*q^37 - q^40 + a*q^41 - a*q^49 + q^52 - q^53 + (-a + 1)*q^58 + (-a + 
        1)*q^61 + q^64 + a*q^65 + a*q^68 - q^73 + (-a + 1)*q^74 + a*q^80 + (-a +
        1)*q^82 + (a - 1)*q^85 - 2*a*q^89 + (2*a - 2)*q^97 + (a - 1)*q^98 + 
        a*q^101 - a*q^104 + a*q^106 + 2*q^109 + (-a + 1)*q^113 - q^116 + (a - 
        1)*q^121 - q^122 + q^125 - a*q^128 + (-a + 1)*q^130 + (-a + 1)*q^136 + 
        (-a + 1)*q^137 - a*q^145 + O(q^146),
    q^3 - a*q^6 + (a - 1)*q^12 - q^15 + q^24 + (a - 1)*q^27 + a*q^30 - a*q^39 - 
        a*q^48 + (-a + 1)*q^51 + q^54 + (-a + 1)*q^60 + (a - 1)*q^78 + a*q^87 + 
        (a - 1)*q^96 - q^102 - a*q^108 + a*q^111 - q^120 + a*q^123 + (-a + 
        1)*q^135 + O(q^146),
    q^9 - a*q^18 + (a - 1)*q^36 - q^45 + q^72 + (a - 1)*q^81 + a*q^90 - a*q^117 
        - a*q^144 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + (-a + 1)*q^5 - a*q^6 + a*q^9 - a*q^13 + (-a + 1)*q^14 + (a - 
        1)*q^16 + (a - 1)*q^17 + q^20 + (a - 1)*q^21 + (-a + 1)*q^24 - q^30 + (a
        - 1)*q^36 - a*q^37 + a*q^38 - q^41 + q^45 + (a - 1)*q^46 + (-a + 1)*q^52
        - 2*q^53 + (-a + 1)*q^54 + q^56 - a*q^57 + q^61 - a*q^62 - q^64 - q^65 -
        q^68 + (-a + 1)*q^69 - a*q^70 + (a - 1)*q^78 + a*q^80 + (a - 1)*q^81 - 
        q^84 + a*q^85 + (a - 1)*q^86 + a*q^89 + a*q^93 - q^94 + q^96 - q^97 + 
        q^102 + a*q^105 + (-a + 1)*q^117 - a*q^120 - a*q^121 + q^125 + q^126 + 
        (-a + 1)*q^129 + (-a + 1)*q^133 + (-a + 1)*q^134 + q^137 + q^141 + 
        a*q^142 - q^144 + O(q^146),
    q^2 - q^3 - a*q^7 + a*q^8 + (-a + 1)*q^10 - a*q^12 + (a - 1)*q^15 + a*q^18 +
        q^19 + a*q^23 - a*q^26 - a*q^27 + (-a + 1)*q^28 - q^31 + (a - 1)*q^32 + 
        (a - 1)*q^34 - q^35 + a*q^39 + q^40 + (a - 1)*q^42 + a*q^43 + (a - 
        1)*q^47 + (-a + 1)*q^48 + (-a + 1)*q^51 - q^60 + (-a + 1)*q^63 - a*q^67 
        + q^71 + (a - 1)*q^72 - a*q^74 + a*q^76 + (-a + 1)*q^79 - q^82 + (-a + 
        1)*q^83 + q^90 + (a - 1)*q^91 + (a - 1)*q^92 + (-a + 1)*q^95 + q^103 + 
        (-a + 1)*q^104 - 2*q^106 + (-a + 1)*q^107 + (-a + 1)*q^108 + a*q^111 + 
        q^112 - a*q^114 + q^115 + q^119 + q^122 + q^123 - a*q^124 + (a - 
        1)*q^127 - q^128 - q^130 - q^131 - q^135 - q^136 + (-a + 1)*q^138 + (2*a
        - 2)*q^139 - a*q^140 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^7 + (-a + 1)*q^13 - q^25 + q^31 + (a - 1)*q^43 - 2*a*q^55 + (a
        - 1)*q^61 - a*q^67 - q^73 - q^79 + a*q^91 + (-a + 1)*q^97 + q^103 + 
        q^109 + 2*a*q^115 + (-a + 1)*q^121 - a*q^127 + (a - 1)*q^139 + 2*a*q^145
        + O(q^146),
    q^5 + a*q^11 - a*q^23 - a*q^29 + (a - 1)*q^35 - q^47 + (a - 1)*q^59 + (-a + 
        1)*q^65 + (-a + 1)*q^71 - q^77 + a*q^101 - a*q^107 + (a - 1)*q^113 + 
        q^131 + q^143 + O(q^146)
]
;
Bo:=
[
    q + (-a + 1)*q^7 + (a - 1)*q^13 + (2*a - 2)*q^19 + q^25 - q^31 - 2*a*q^37 + 
        (-a + 1)*q^43 + (-a + 1)*q^61 + a*q^67 - q^73 - q^79 + a*q^91 + (-a + 
        1)*q^97 - q^103 - q^109 + (a - 1)*q^121 + a*q^127 + 2*a*q^133 + (-a + 
        1)*q^139 + O(q^146),
    q^3 - a*q^9 + (-a + 1)*q^21 + (a - 1)*q^27 + (a - 1)*q^39 + (2*a - 2)*q^57 -
        q^63 + q^75 + q^81 - q^93 - 2*a*q^111 + q^117 + (-a + 1)*q^129 + 
        O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 + a*q^5 + q^6 - q^9 + q^13 + a*q^14 + q^16 + (a - 1)*q^17 - a*q^20 -
        a*q^21 - q^24 + a*q^30 + q^36 - a*q^37 + (-a + 1)*q^38 + (-a + 1)*q^41 -
        a*q^45 + (a - 1)*q^46 - q^52 - 2*q^53 - q^54 - a*q^56 + (a - 1)*q^57 - 
        a*q^61 - a*q^62 - q^64 + a*q^65 + (-a + 1)*q^68 + (-a + 1)*q^69 + (a - 
        1)*q^70 + q^78 + a*q^80 + q^81 + a*q^84 - q^85 - a*q^86 + a*q^89 + 
        a*q^93 + (-a + 1)*q^94 + q^96 + a*q^97 + (a - 1)*q^102 + (-a + 1)*q^105 
        - q^117 - a*q^120 + q^121 + q^125 - a*q^126 + a*q^129 - q^133 + (-a + 
        1)*q^134 - a*q^137 + (a - 1)*q^141 + (-a + 1)*q^142 - q^144 + O(q^146),
    q^2 - q^3 - a*q^7 - q^8 + a*q^10 + q^12 - a*q^15 - q^18 + (a - 1)*q^19 + (-a
        + 1)*q^23 + q^26 + q^27 + a*q^28 + a*q^31 + q^32 + (a - 1)*q^34 + (-a + 
        1)*q^35 - q^39 - a*q^40 - a*q^42 + a*q^43 + (a - 1)*q^47 - q^48 + (-a + 
        1)*q^51 + a*q^60 + a*q^63 + (a - 1)*q^67 + (a - 1)*q^71 + q^72 - a*q^74 
        + (-a + 1)*q^76 + (-a + 1)*q^79 + (-a + 1)*q^82 + (-a + 1)*q^83 - a*q^90
        - a*q^91 + (a - 1)*q^92 - q^95 - a*q^103 - q^104 - 2*q^106 + a*q^107 - 
        q^108 + a*q^111 - a*q^112 + (a - 1)*q^114 + q^115 + q^119 - a*q^122 + (a
        - 1)*q^123 - a*q^124 - a*q^127 - q^128 + a*q^130 + a*q^131 + a*q^135 + 
        (-a + 1)*q^136 + (-a + 1)*q^138 + 2*q^139 + (a - 1)*q^140 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^10 + q^16 - q^22 - q^25 - q^40 - q^49 - q^52 - q^82 - q^88 - q^94 + 
        2*q^100 + q^118 + q^121 + q^130 + q^142 + O(q^146),
    q^2 + q^8 - 2*q^11 - q^26 + q^32 - 2*q^44 - 2*q^47 + q^50 + 2*q^59 + 2*q^71 
        + 2*q^83 - q^98 - q^104 - 2*q^122 + q^128 + 2*q^143 + O(q^146),
    q^4 - q^10 - q^13 - q^22 + 2*q^25 + q^40 - 2*q^61 + q^64 + q^82 - q^88 - 
        q^94 - q^100 + q^118 + 2*q^121 - q^130 + q^142 + O(q^146),
    q^5 + q^8 - q^11 - q^20 - q^26 - q^41 - q^44 - q^47 + 2*q^50 + q^59 + q^65 +
        q^71 + q^80 + q^83 - q^89 - 2*q^122 - 2*q^125 + q^128 + q^137 + q^143 + 
        O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^3 + (a - 1)*q^9 + a*q^13 + (-2*a + 1)*q^17 + (a - 2)*q^23 + (-a + 
        1)*q^25 - q^27 + (a - 1)*q^39 + (-a + 1)*q^43 - a*q^49 + (-a + 2)*q^51 +
        (-2*a + 1)*q^53 + (a - 1)*q^61 + (-a - 1)*q^69 + q^75 + (a - 1)*q^79 - 
        a*q^81 + (a + 1)*q^101 - 2*a*q^103 + (2*a - 1)*q^107 + (a - 2)*q^113 - 
        q^117 + a*q^121 - 2*q^127 + q^129 + (-a + 2)*q^131 + a*q^139 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
468
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^13 - q^25 + 2*q^43 + q^49 - 2*q^61 - 2*q^79 + 2*q^103 - q^121 - 
        2*q^127 + 2*q^139 + O(q^146),
    q^2 - q^8 - q^26 + q^32 - q^50 + 2*q^86 + q^98 + q^104 - 2*q^122 - q^128 + 
        O(q^146),
    q^3 - q^9 + q^27 - q^39 - q^75 - q^81 + q^117 + 2*q^129 + O(q^146),
    q^4 - q^16 - q^52 + q^64 - q^100 + O(q^146),
    q^6 - q^18 - q^24 + q^54 + q^72 - q^78 + q^96 + O(q^146),
    q^12 - q^36 - q^48 + q^108 + q^144 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^19 + a^16)*q^2 + (a^19 + a^18 - a^16 - a^15 + a^13 + a^12 - a^10 - 
        a^9 - a^8 + a^6 - a^3 + 1)*q^4 + (-a^12 + a)*q^7 + (-a^19 + a^16 - a^12 
        + a^9 + a^8 - a^6 - a^5 + a^3 - 1)*q^8 + a^12*q^9 + (-a^16 - a^14 + a^5 
        + a^3)*q^11 + (-a^9 + a^6)*q^14 + (a^19 - a^17 - a^16 + a^14 + a^13 - 
        a^11 + a^6 - a^3 + 1)*q^16 + (a^19 - a^16 + a^14 + a^13 - a^11 - a^10 + 
        a^7 - a^4 - a^3 + a + 1)*q^18 + (-a^13 - a^11 + a^10 + a^8)*q^22 + 
        (-a^19 + a^17 + a^16 - a^14 - a^13 + a^11 + a^10 + a^9 - a^7 - a^6 + a^4
        - a - 1)*q^23 + (a^19 - a^8)*q^25 + (a^17 - a^14 + a^11 - a^6 + a^3 - 
        1)*q^28 + (-a^19 - a^18 + a^16 + a^15 - a^13 - a^12 + a^9 + a^8 - a^6 - 
        a^5 + a^3 + a^2 - a - 1)*q^29 + (-a^19 - a^18 + a^16 + a^15 - a^13 - 
        a^12 + a^11 + a^10 + a^9 - a^6 + a^3 - 1)*q^32 + (-a^17 + a^14 - 
        a^11)*q^36 + (a^18 + a^15 - a^4)*q^37 + (-a^18 + a^11 + a^7 - 1)*q^43 + 
        (2*a^19 - 2*a^16 + 2*a^13 + a^12 - a^10 - a^9 - 2*a^8 + a^7 + a^6 + 
        2*a^5 - a^4 - a^3 - 2*a^2 + 1)*q^44 + (-a^19 + a^11 + a^6 - a^3 - 
        1)*q^46 - a^13*q^49 + (a^16 - a^13)*q^50 + (a^8 - a^7)*q^53 + (a^14 - 
        a^11 + a^8 - a^5)*q^56 + (-a^19 + a^16 - a^14 - a^13 + a^11 + a^10 + a^9
        - 2*a^7 - a^6 + 2*a^4 + a^3 - a - 1)*q^58 + a^2*q^63 + (a^19 - a^15 + 
        a^12 - a^9 - a^8 + a^6 - a^3 + 1)*q^64 + a^4*q^67 + (a^17 - a^9 - 
        a^6)*q^71 + (a^19 - a^16 - a^8 + a^5 - a^3 + 1)*q^72 + (a^12 - a^9 + a^4
        - a)*q^74 + (-a^17 - a^15)*q^77 + (a^14 + a^2)*q^79 + (a^13 - a^2)*q^81 
        + (-a^15 + a^12 + a^8 - a^5)*q^86 + O(q^88)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^8 - a^5)*q^2 + (a^9 - a^8 + a^7 - a^6 - a^4 + a^3 + a - 1)*q^4 - 
        a*q^7 + (a^9 - a^8 - a^6 + a^5 + a^3 + a - 1)*q^8 - a*q^9 + (-a^5 - 
        a^3)*q^11 + (-a^9 + a^6)*q^14 + (-a^8 - a^6 + a^5 + a^3 - a^2 - 1)*q^16 
        + (-a^9 + a^6)*q^18 + (a^9 + a^7 - a^6 + a^5 - a^4 + a^3 + a)*q^22 + 
        (-a^9 - a^3)*q^23 + a^8*q^25 + (a^6 - a^3 + 1)*q^28 + (a^9 - a^8 + a^7 -
        a^6 + a^5 - a^4 + a^3 - a^2 - 1)*q^29 + (-a^9 - a^7 + a^6 + a^4 - a^3 - 
        a)*q^32 + (a^6 - a^3 + 1)*q^36 + (-a^7 + a^4)*q^37 + (-a^7 + 1)*q^43 + 
        (a^9 - a^6 + a^3 + a - 1)*q^44 + (a^8 + a^6 - a^3 + 1)*q^46 + a^2*q^49 +
        (-a^5 + a^2)*q^50 + (a^8 - a^7)*q^53 + (a^8 - a^5 - a^3 + 1)*q^56 + 
        (-a^9 - a^7 + a^6 + a^4)*q^58 + a^2*q^63 + (-a^9 + a^8 + a^6 + a^4 - a^3
        - a + 1)*q^64 + a^4*q^67 + (-a^9 + a^6)*q^71 + (a^8 - a^5 - a^3 + 
        1)*q^72 + (-a^9 + a^4 - 2*a)*q^74 + (a^6 + a^4)*q^77 + (-a^3 + a^2)*q^79
        + a^2*q^81 + (a^8 - a^5 + a^4 - a)*q^86 + O(q^88)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 22*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 22*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - 2*a*q^2 + (3*a - 3)*q^4 + (a - 1)*q^7 + 4*q^8 + q^9 + (-a + 1)*q^11 + 
        2*q^14 - 5*a*q^16 - 2*a*q^18 - 2*q^22 + a*q^23 + q^25 - 3*a*q^28 + (-a +
        1)*q^29 + (6*a - 6)*q^32 + (3*a - 3)*q^36 + a*q^37 - q^43 + 3*a*q^44 + 
        (-2*a + 2)*q^46 - a*q^49 - 2*a*q^50 - q^53 + (4*a - 4)*q^56 - 2*q^58 + 
        (a - 1)*q^63 + 7*q^64 - a*q^67 + (-a + 1)*q^71 + 4*q^72 + (-2*a + 
        2)*q^74 + a*q^77 + (2*a - 2)*q^79 + q^81 + 2*a*q^86 + O(q^88)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 22*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
33*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
469
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 33*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
470
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
470
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
470
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
470
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
92
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
470
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^6 - q^7 + q^14 - q^16 + q^18 - q^21 + q^24 + q^25 - q^27 + q^32 - q^34
        + q^47 + q^49 + q^51 - q^53 - q^56 - q^59 - q^61 + q^63 - q^72 - q^74 + 
        2*q^83 - q^89 - q^97 - q^98 + q^102 + q^106 + q^111 + q^112 + q^118 - 
        q^119 + q^121 + q^122 - q^131 + q^136 + O(q^138),
    q^2 - q^6 - q^12 - q^16 + q^18 + q^24 + q^28 - q^34 + q^36 - q^42 + q^48 + 
        q^50 - q^54 - q^56 + q^64 - q^68 - q^72 - q^74 + q^94 + 2*q^102 + q^126 
        + q^136 + O(q^138),
    q^3 - q^7 + q^8 - q^9 - q^12 - q^16 + q^17 + q^28 + q^36 + q^37 + q^49 - 
        q^51 - q^53 - q^56 - q^59 - q^61 - q^68 + q^71 + q^75 + q^79 - q^89 + 
        q^96 - q^97 + q^101 + q^103 - q^111 + q^112 - q^131 + O(q^138),
    q^4 - q^6 - q^8 + q^14 + q^18 - q^28 - q^34 + q^48 + q^56 - q^74 - q^84 - 
        q^98 + q^100 + q^102 + q^106 - q^108 - q^112 + q^118 + q^122 + q^128 + 
        O(q^138),
    q^5 - q^30 - q^35 + q^70 - q^80 + q^90 - q^105 + q^120 + q^125 - q^135 + 
        O(q^138),
    q^10 - q^30 - q^60 - q^80 + q^90 + q^120 + O(q^138),
    q^15 - q^35 + q^40 - q^45 - q^60 - q^80 + q^85 + O(q^138),
    q^20 - q^30 - q^40 + q^70 + q^90 + O(q^138)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
470
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 23*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
156
);
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^3 + a^11*q^4 + (a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + 2*a^5 - a^4 
        + a^3 - a^2 + a - 1)*q^7 + a^4*q^9 - q^12 + (a^8 - a^5)*q^13 - a^9*q^16 
        + (-a^11 + a^10 - a^9 - a^7 + a^6 - a^5 + a^4 - a^3 + a^2 - a + 1)*q^19 
        + (a^7 - a)*q^21 + a*q^25 + a^6*q^27 + (-a^10 - a^3)*q^28 + (-a^6 - 
        a^4)*q^31 - a^2*q^36 + (a^9 + a^3)*q^37 + (a^10 - a^7)*q^39 + (-a^7 - 
        a^2)*q^43 - a^11*q^48 + (-a^11 + a^10 - a^4)*q^49 + (-a^6 + a^3)*q^52 + 
        (-a^10 + a)*q^57 + (-a^11 + a^9)*q^61 + (a^9 - a^3)*q^63 + a^7*q^64 + 
        (a^6 - a)*q^67 + (-a^9 - a^8)*q^73 + a^3*q^75 + (a^10 + a^6)*q^76 + 
        (-a^11 + a^10 - a^9 + a^8 - a^7 + a^6 - a^5 + a^4 - 2*a^3 + a^2 - a + 
        1)*q^79 + a^8*q^81 + (-a^11 + a^10 - a^9 + a^8 - a^7 + a^6 - 2*a^5 + a^4
        - a^3 + a^2 - a + 1)*q^84 + (-a^10 - a^7 + a^4 - 1)*q^91 + (-a^8 - 
        a^6)*q^93 + (-a - 1)*q^97 + (a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 -
        a^4 + a^3 - a^2 + a - 1)*q^100 + O(q^103)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^4*q^3 - a^9*q^4 + (-a^11 + a^10)*q^7 + a^8*q^9 + q^12 + (a^10 - 
        a^3)*q^13 - a^5*q^16 + (-a^11 - a^3)*q^19 + (a^2 - a)*q^21 + a^2*q^25 + 
        (a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 
        1)*q^27 + (-a^7 + a^6)*q^28 + (a^11 - a^10 + a^9 + a^7 - a^6 + a^5 - a^4
        + a^3 - a^2 + a - 1)*q^31 + a^4*q^36 + (a^6 - a^5)*q^37 + (-a^7 - 
        a)*q^39 + (a^4 - a)*q^43 - a^9*q^48 + (-a^9 + a^8 - a^7)*q^49 + (a^11 - 
        a^10 + a^9 - a^8 + a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^52 + (-a^7 + 
        a^2)*q^57 + (-a^9 - a^5)*q^61 + (a^6 - a^5)*q^63 - a*q^64 + (a^11 - a^10
        + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 + a - 1)*q^67 + (-a^5 - 
        a^3)*q^73 + a^6*q^75 + (a^11 - a^10 + a^9 - a^8 - a^6 + a^5 - a^4 + a^3 
        - a^2 + a - 1)*q^76 + (-a^11 + a^6)*q^79 - a^3*q^81 + (-a^11 + 
        a^10)*q^84 + (a^8 - a^7 - a + 1)*q^91 + (a^11 - a^10 + a^9 - a^8 + a^7 -
        a^6 + a^5 - a^4 - a^2 + a - 1)*q^93 + (a^2 + 1)*q^97 - a^11*q^100 + 
        O(q^103)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
39*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 52*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
471
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 78*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
103
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^30 - q^31 - q^37 - q^40 + q^49 - q^52 - q^57 - q^75 + 
        q^81 - q^82 + O(q^103),
    q^2 - q^15 + q^18 - q^20 - q^26 - q^41 + q^50 - q^53 + q^59 + q^65 + q^69 - 
        q^78 + q^87 + q^95 - q^96 + q^98 + O(q^103),
    q^3 - q^10 - q^19 - q^25 + q^27 + q^40 + q^46 - q^52 + q^58 - q^64 + q^75 + 
        q^76 - q^90 - q^93 + q^100 + O(q^103),
    q^4 - q^10 - q^13 + q^31 + q^36 + q^37 - q^39 - q^48 + q^57 - q^67 + q^75 - 
        q^76 - q^90 + O(q^103),
    q^5 - q^8 - q^15 + q^24 + q^38 - q^41 + q^45 + q^50 - q^53 - q^62 - q^72 - 
        q^74 + q^92 + q^95 + O(q^103),
    q^6 - q^8 - q^15 + q^23 + q^24 - q^26 + q^29 - q^32 + q^38 - q^41 + q^50 - 
        q^53 + q^54 - q^60 - q^62 + q^65 - q^72 - q^74 - q^78 + q^80 + q^83 + 
        2*q^92 + O(q^103),
    q^12 - q^13 - q^16 + q^19 + q^25 - q^30 - q^39 + q^46 + q^58 - q^67 - q^82 +
        q^93 + O(q^103)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
472
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
472
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
472
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
472
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
472
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
472
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + (-a^23 - a^19)*q^3 + a^2*q^4 + (a^24 + a^20)*q^6 - a^3*q^8 + 
        (-a^17 - a^13 - a^9)*q^9 + (a^16 - a^5)*q^11 + (-a^25 - a^21)*q^12 + 
        a^4*q^16 + (a^14 + a^8)*q^17 + (a^18 + a^14 + a^10)*q^18 + (a^26 - 
        a^21)*q^19 + (-a^17 + a^6)*q^22 + (a^26 + a^22)*q^24 + a^12*q^25 + (a^27
        - a^26 + a^25 - a^24 + a^23 - a^22 + a^21 - a^20 + a^19 - a^18 + a^17 - 
        a^16 + a^15 - a^14 + a^13 - a^12 - a^10 + a^9 - a^8 - a^6 + a^5 - a^4 - 
        a^2 + a - 1)*q^27 - a^5*q^32 + (a^27 - a^26 + a^25 + a^23 - a^22 + a^21 
        - a^20 + a^19 - a^18 + a^17 - a^16 + a^15 - a^14 + a^13 - a^12 + a^11 + 
        a^9 - a^8 + a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^33 + (-a^15 - 
        a^9)*q^34 + (-a^19 - a^15 - a^11)*q^36 + (-a^27 + a^22)*q^38 + (-a^27 - 
        a)*q^41 + (-a^25 + a^12)*q^43 + (a^18 - a^7)*q^44 + (-a^27 - a^23)*q^48 
        - a^7*q^49 - a^13*q^50 + (-a^27 + a^8 + a^4 + a^2)*q^51 + (a^12 + a^8 + 
        a^4 + 1)*q^54 + (a^20 + a^16 - a^15 - a^11)*q^57 - a^15*q^59 + a^6*q^64 
        + (-a^25 - a^11 - a^7 + 1)*q^66 + (a^22 - a^13)*q^67 + (a^16 + 
        a^10)*q^68 + (a^20 + a^16 + a^12)*q^72 + (a^20 + a^18)*q^73 + (a^6 + 
        a^2)*q^75 + (a^27 - a^26 + a^25 - a^24 - a^22 + a^21 - a^20 + a^19 - 
        a^18 + a^17 - a^16 + a^15 - a^14 + a^13 - a^12 + a^11 - a^10 + a^9 - a^8
        + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^76 + (a^26 + a^22 + a^18 
        - a^5 - a)*q^81 + (a^27 - a^26 + a^25 - a^24 + a^23 - a^22 + a^21 - a^20
        + a^19 - a^18 + a^17 - a^16 + a^15 - a^14 + a^13 - a^12 + a^11 - a^10 + 
        a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 + a - 1)*q^82 + (a^10 - 
        a^9)*q^83 + (a^26 - a^13)*q^86 + (-a^19 + a^8)*q^88 + (-a^23 + a^4)*q^89
        + (a^27 - a^26 + a^25 + a^23 - a^22 + a^21 - a^20 + a^19 - a^18 + a^17 -
        a^16 + a^15 - a^14 + a^13 - a^12 + a^11 - a^10 + a^9 - a^8 + a^7 - a^6 +
        a^5 - a^4 + a^3 - a^2 + a - 1)*q^96 + (-a^25 + a^24)*q^97 + a^8*q^98 + 
        (-a^25 + a^22 + a^18 + a^14 + a^4 + 1)*q^99 + a^14*q^100 + (a^27 - a^26 
        + a^25 - a^24 + a^23 - a^22 + a^21 - a^20 + a^19 - a^18 + a^17 - a^16 + 
        a^15 - a^14 + a^13 - a^12 + a^11 - a^10 - a^8 + a^7 - a^6 - a^4 - a^2 + 
        a - 1)*q^102 + (a^18 - a^3)*q^107 + (-a^13 - a^9 - a^5 - a)*q^108 + 
        (a^22 - a^19)*q^113 + O(q^114)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
472
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
29*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^15 - q^17 - q^21 + q^25 - q^27 - q^35 - q^45 + q^49 - q^57 + 
        q^59 + 2*q^63 - q^71 + 2*q^75 + q^81 - q^87 + 2*q^95 - q^105 + O(q^114),
    q^2 + q^18 - q^30 - q^34 - q^42 + q^50 - q^54 - q^70 - q^90 + q^98 + 
        O(q^114),
    q^3 - q^15 - q^17 + q^25 - q^35 + q^41 - q^45 + q^53 - q^57 - q^71 + q^75 + 
        q^79 + q^85 + q^95 + O(q^114),
    q^4 - q^12 + q^16 - q^20 - q^28 - q^48 + q^60 + q^64 + 2*q^68 - q^76 - q^80 
        + q^84 + q^108 - q^112 + O(q^114),
    q^5 - q^17 + q^19 - q^21 - q^27 - q^35 + q^49 + q^51 + q^63 - q^71 + q^81 - 
        q^87 + q^107 + O(q^114),
    q^6 - q^30 - q^34 + q^50 - q^70 + q^82 - q^90 + q^106 + O(q^114),
    q^7 + q^9 - q^15 - q^17 - q^21 - q^27 + q^29 + q^51 - q^57 + q^63 - q^71 + 
        q^75 + q^81 + q^85 - q^87 + O(q^114),
    q^8 - q^24 + q^32 - q^40 - q^56 - q^96 + O(q^114),
    q^10 - q^34 + q^38 - q^42 - q^54 - q^70 + q^98 + q^102 + O(q^114),
    q^14 + q^18 - q^30 - q^34 - q^42 - q^54 + q^58 + q^102 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
472
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 29*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^7 + q^9 + q^16 - q^17 - q^22 + q^25 - q^26 - q^28 + q^36 - q^41 
        - q^63 + q^64 - q^68 - q^71 - q^74 - q^79 + q^81 - q^86 - q^88 + q^100 -
        q^104 - q^112 + O(q^114),
    q^2 + q^8 - q^11 - q^13 - q^14 + q^18 + q^32 - q^34 - q^37 - q^43 - q^44 + 
        q^50 - q^52 - q^56 + q^59 + 2*q^61 + 2*q^67 + q^72 + q^77 - q^82 - q^83 
        + q^91 - q^99 - q^101 + 2*q^109 + O(q^114)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
210
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
210
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
473
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 - a*q^9 + q^11 + (a^2 + 1)*q^13 + (a^3 - a^2 + a - 1)*q^16 + 
        (a^2 - a)*q^17 + (a^3 - a^2 - 1)*q^23 - a^3*q^25 + (-a^2 + a - 1)*q^31 -
        a^3*q^36 - 2*a^3*q^41 + q^43 + a^2*q^44 + (-a + 1)*q^47 + (a^3 - a^2 + a
        - 1)*q^49 + (a^3 + a - 1)*q^52 + (-a^2 + a - 1)*q^53 + (-a^3 - a)*q^59 -
        a*q^64 + (a^3 - a^2 - 1)*q^67 + (-a^2 + a - 1)*q^68 + (-a^2 + a - 
        1)*q^79 + a^2*q^81 + (a^2 - a)*q^83 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
474
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
474
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
474
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
474
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
474
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 + a^8*q^4 + (-a^11 + a^4)*q^7 + a^2*q^9 - a^9*q^12 + (a^10 + 
        a^6)*q^13 - a^3*q^16 + (-a^7 - a^5)*q^19 + (a^11 - a^10 + a^9 - a^8 + 
        a^7 - a^6 - a^4 + a^3 - a^2 + a - 1)*q^21 - a^7*q^25 - a^3*q^27 + (a^11 
        - a^10 + a^9 - a^8 + a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^28 + (a^11 -
        a^10 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^31 + a^10*q^36
        + (a^10 + a^2)*q^37 + (-a^11 - a^7)*q^39 + (a^4 - a^3)*q^43 + a^4*q^48 +
        (-a^9 + a^8 + a^2)*q^49 + (-a^5 - a)*q^52 + (a^8 + a^6)*q^57 + (-a^11 - 
        a)*q^61 + (a^6 + 1)*q^63 - a^11*q^64 + (-a^5 + 1)*q^67 + (-a^9 - a)*q^73
        + a^8*q^75 + (a^2 + 1)*q^76 - a^3*q^79 + a^4*q^81 + (-a^7 + 1)*q^84 + 
        (a^10 + a^8 + a^4 - a)*q^91 + (a^10 + 1)*q^93 + (a^11 - a^10 + a^9 - a^8
        + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a)*q^97 + a^2*q^100 + (a^11 - a^10
        + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 - 1)*q^103 - a^11*q^108 
        + (-a^9 + a^8)*q^109 + (-a^11 - a^3)*q^111 + (-a^7 - a)*q^112 + (a^11 - 
        a^10 + a^9 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^117 + 
        a^6*q^121 + (-a^7 + a^4)*q^124 + (a^6 + a^2)*q^127 + (-a^5 + a^4)*q^129 
        + (-a^11 - a^9 - a^5 - a^3)*q^133 + (a^10 + a^2)*q^139 - a^5*q^144 + 
        (a^10 - a^9 - a^3)*q^147 + (a^10 - a^5)*q^148 + (-a^9 + a^6)*q^151 + 
        O(q^154),
    q^2 - a*q^6 + a^8*q^8 + (-a^11 + a^4)*q^14 + a^2*q^18 - a^9*q^24 + (a^10 + 
        a^6)*q^26 - a^3*q^32 + (-a^7 - a^5)*q^38 + (a^11 - a^10 + a^9 - a^8 + 
        a^7 - a^6 - a^4 + a^3 - a^2 + a - 1)*q^42 - a^7*q^50 - a^3*q^54 + (a^11 
        - a^10 + a^9 - a^8 + a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^56 + (a^11 -
        a^10 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^62 + a^10*q^72
        + (a^10 + a^2)*q^74 + (-a^11 - a^7)*q^78 + (a^4 - a^3)*q^86 + a^4*q^96 +
        (-a^9 + a^8 + a^2)*q^98 + (-a^5 - a)*q^104 + (a^8 + a^6)*q^114 + (-a^11 
        - a)*q^122 + (a^6 + 1)*q^126 - a^11*q^128 + (-a^5 + 1)*q^134 + (-a^9 - 
        a)*q^146 + a^8*q^150 + (a^2 + 1)*q^152 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
474
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
474
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
474
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
39*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^10 - q^11 - q^13 - q^16 + q^22 + q^26 - q^31 + q^32 - q^38 + 
        q^40 - q^46 + q^49 + q^50 - q^55 + q^62 - q^65 + q^79 + q^81 + 2*q^83 - 
        q^88 - q^89 - q^90 + q^95 - q^99 - q^101 - q^104 + q^115 - q^117 + q^121
        - q^125 - q^134 + 2*q^143 - q^144 - q^146 + q^152 + O(q^154),
    q^2 - q^10 - q^16 + q^18 - q^20 - q^38 + q^40 + q^44 - q^46 + q^50 + q^52 + 
        q^64 - q^76 + q^80 - q^88 - q^90 - q^92 + q^98 + q^100 - q^104 - q^110 +
        q^124 - q^130 - q^134 - q^144 - q^146 + q^152 + O(q^154),
    q^3 + q^27 - q^30 - q^33 - q^39 - q^48 + q^66 + q^78 - q^93 + q^96 - q^114 +
        q^120 - q^138 + q^147 + q^150 + O(q^154),
    q^4 - q^8 - q^10 + q^22 + q^26 + q^36 - q^38 - q^44 - q^46 + q^50 - q^52 + 
        q^62 - q^72 + q^80 + q^88 - q^90 + q^104 - q^124 + q^128 - q^134 - q^146
        + O(q^154),
    q^5 + q^8 - q^11 - q^13 - q^16 + q^19 - q^20 + q^23 - q^25 - q^31 + q^44 + 
        q^45 + q^52 + q^67 + q^72 + q^73 - q^76 - q^88 - q^89 - q^92 - q^95 + 
        q^97 - q^99 + q^100 - q^101 - q^104 - q^115 - q^117 + q^121 + q^124 + 
        q^131 + q^143 - q^144 + q^151 + O(q^154),
    q^6 - q^30 - q^48 + q^54 - q^60 - q^114 + q^120 + q^132 - q^138 + q^150 + 
        O(q^154),
    q^12 - q^24 - q^30 + q^66 + q^78 + q^108 - q^114 - q^132 - q^138 + q^150 + 
        O(q^154),
    q^15 + q^24 - q^33 - q^39 - q^48 + q^57 - q^60 + q^69 - q^75 - q^93 + q^132 
        + q^135 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
180
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^6 - q^11 + q^26 + q^36 + q^39 - q^44 - q^49 - q^61 + q^64 + q^74 - 
        q^76 + O(q^90),
    q^2 + q^3 - q^12 - q^13 - q^18 - q^32 - q^37 + q^38 - q^48 + q^52 + q^53 + 
        q^57 + q^67 + 2*q^78 + O(q^90),
    q^4 + q^6 + q^9 - q^11 + q^16 - q^19 - q^26 - q^39 - q^44 - q^61 - q^74 + 
        q^81 + O(q^90)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + a^2*q^5 + (-a^3 - a^2)*q^7 - a^2*q^9 + (a - 1)*q^11 + a^2*q^16 +
        (a^3 + 1)*q^17 + (a^3 - a^2 + a - 1)*q^19 + a^3*q^20 + (-a - 1)*q^23 + 
        (a^3 - a^2 + a - 1)*q^25 + (-2*a^3 + a^2 - a + 1)*q^28 + (-a^3 + a^2 - a
        + 2)*q^35 - a^3*q^36 + (-a^3 + a^2 - 2*a + 1)*q^43 + (a^2 - a)*q^44 + 
        (-a^3 + a^2 - a + 1)*q^45 + (a^3 - a^2 - 2)*q^49 + (a^3 - a^2)*q^55 + 
        (-a^3 - a + 1)*q^61 + (a^3 - a^2 + a - 2)*q^63 + a^3*q^64 + (a^3 - a^2 +
        2*a - 1)*q^68 - q^76 + (-a^3 + 2*a^2 - a + 1)*q^77 + (a^3 - a^2 + a - 
        1)*q^80 + (a^3 - a^2 + a - 1)*q^81 + (a^3 + 1)*q^83 + (a^2 - 1)*q^85 + 
        O(q^90)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 + (a^3 - a^2 + a - 1)*q^5 + (a^3 - a^2 - 1)*q^7 + (a^3 - a^2 + a
        - 1)*q^9 + (a^2 + 1)*q^11 + (a^3 - a^2 + a - 1)*q^16 + (-a + 1)*q^17 - 
        a^3*q^19 - a*q^20 + (a^2 + 1)*q^23 - a^3*q^25 + (-a^3 - a)*q^28 + (-a^3 
        + 1)*q^35 - a*q^36 + (-a^3 + a^2)*q^43 + (a^3 + a - 1)*q^44 - a^3*q^45 +
        2*a^2*q^47 + (-a^3 + a^2 + 1)*q^49 + (a^3 - a^2 - 1)*q^55 + (-a^2 + a - 
        1)*q^61 + (-a^3 + 1)*q^63 - a*q^64 + (-a^3 + a^2)*q^68 - 2*a*q^73 + q^76
        + (-a^2 - a - 1)*q^77 - a^3*q^80 - a^3*q^81 + (-a + 1)*q^83 + (a^3 - a^2
        + a)*q^85 + O(q^90)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
475
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^6 - q^11 + q^26 + q^36 - q^39 + q^44 + q^49 - q^61 - q^64 - q^74 - 
        q^76 + O(q^90),
    q^2 - q^3 - q^12 + q^13 + q^18 - q^32 - q^37 - q^38 + q^48 + q^52 - q^53 + 
        q^57 + q^67 - 2*q^78 + O(q^90),
    q^4 - q^6 + q^9 + q^11 - q^16 - q^19 + q^26 - q^39 - q^44 + q^61 - q^74 - 
        q^81 + O(q^90),
    q^5 - q^30 - q^55 + O(q^90),
    q^10 - q^15 - q^50 - q^60 + q^65 + q^75 + O(q^90),
    q^20 - q^25 - q^30 + q^45 + q^55 - q^80 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^2 - q^4 + (-a - 1)*q^5 - a*q^8 + a*q^9 + (-a + 1)*q^10 + q^16 - q^17
        - q^18 + (a + 1)*q^20 + a*q^25 + (a + 1)*q^29 + a*q^32 - a*q^34 - a*q^36
        + (-a - 1)*q^37 + (a - 1)*q^40 + (-a + 1)*q^41 + (-a + 1)*q^45 - a*q^49 
        - q^50 + (a - 1)*q^58 + (a - 1)*q^61 - q^64 + q^68 + q^72 + (a + 1)*q^73
        + (-a + 1)*q^74 + (-a - 1)*q^80 - q^81 + (a + 1)*q^82 + (a + 1)*q^85 + 
        (a + 1)*q^90 + (-a - 1)*q^97 + q^98 - a*q^100 + (a - 1)*q^109 + (a - 
        1)*q^113 + (-a - 1)*q^116 - a*q^121 + (-a - 1)*q^122 - a*q^128 + 
        O(q^134),
    q^7 + a*q^14 - q^28 + (-a - 1)*q^35 - a*q^56 + a*q^63 + (-a + 1)*q^70 + 
        q^112 - q^119 - q^126 + O(q^134)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 + q^4 - q^8 - q^9 - 2*q^13 + q^16 + q^17 + q^18 + q^25 + 2*q^26 - 
        q^32 - q^34 - q^36 - q^49 - q^50 - 2*q^52 + 2*q^53 + q^64 + q^68 + q^72 
        + q^81 - 2*q^89 + q^98 + q^100 - 2*q^101 + 2*q^104 - 2*q^106 + 2*q^117 -
        q^121 - q^128 + O(q^134),
    q^7 - q^14 + q^28 - q^56 - q^63 - 2*q^91 + q^112 + q^119 + q^126 + O(q^134)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (a - 1)*q^9 + (a - 1)*q^16 - a*q^17 + a*q^18 + (a - 1)*q^21 - 
        a*q^25 + (-a + 1)*q^26 + (-a + 1)*q^33 + q^36 + (a - 1)*q^42 + a*q^53 + 
        q^64 - 2*a*q^66 + (a - 1)*q^68 - q^69 + (-a + 1)*q^72 + q^77 + q^84 + 
        (-a + 1)*q^93 + (a - 1)*q^98 + (a - 1)*q^100 - q^104 + (a - 1)*q^117 + 
        (a - 1)*q^121 - q^132 + O(q^134),
    q^2 - a*q^8 - q^9 + a*q^13 + (a - 1)*q^18 - a*q^21 + (a - 1)*q^32 + 2*q^33 -
        a*q^34 + a*q^36 + (a - 1)*q^42 - a*q^49 - a*q^50 + (-a + 1)*q^52 + (-a +
        1)*q^66 + a*q^69 + q^72 + q^77 + (-a + 1)*q^81 + (a - 1)*q^84 - q^89 - 
        q^93 + (2*a - 2)*q^101 + a*q^106 - q^117 - q^121 + q^128 - 2*a*q^132 + 
        O(q^134),
    q^3 + 1/3*(-a + 2)*q^7 - a*q^12 + 1/3*(a + 1)*q^14 + (a - 1)*q^22 + a*q^23 +
        1/3*(-a - 1)*q^28 - q^31 - q^46 + (a - 1)*q^48 - a*q^51 + a*q^54 + 
        1/3*(-2*a + 1)*q^56 + (-a + 1)*q^62 + 1/3*(a - 2)*q^63 + (a - 1)*q^71 - 
        a*q^75 + (-a + 1)*q^78 + q^88 + 1/3*(2*a - 1)*q^91 + (-a + 1)*q^92 + (-a
        + 1)*q^99 - a*q^107 + 1/3*(2*a - 1)*q^112 + 1/3*(-a - 1)*q^119 + a*q^124
        + 1/3*(2*a - 1)*q^126 + a*q^131 + O(q^134),
    q^6 + 1/3*(a - 2)*q^7 - a*q^11 + 1/3*(-a + 2)*q^14 + (-a + 1)*q^23 - a*q^24 
        - q^27 + 1/3*(a + 1)*q^28 + a*q^31 + a*q^39 + (a - 1)*q^44 + a*q^46 + 
        1/3*(-a - 1)*q^56 - q^62 + 1/3*(-a - 1)*q^63 + (a - 1)*q^79 + 1/3*(a + 
        1)*q^91 - q^92 + (a - 1)*q^96 + q^99 - a*q^102 + a*q^108 + 1/3*(-2*a + 
        1)*q^112 + 1/3*(a + 1)*q^119 + (-a + 1)*q^124 + 1/3*(a - 2)*q^126 + (-a 
        + 1)*q^131 + O(q^134)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
476
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^15 + q^25 - q^35 + q^49 - q^53 - q^67 - q^85 - q^93 + q^119 + q^121 + 
        q^123 - q^127 + O(q^134),
    q^2 + q^18 - q^30 - q^32 - q^36 - q^42 + q^64 + q^84 - q^86 + q^98 + q^100 -
        q^102 + O(q^134),
    q^3 - q^7 - q^17 + q^27 + q^41 - q^45 + q^61 - q^63 + q^73 - q^75 + q^105 + 
        q^125 - 2*q^129 - 2*q^131 + O(q^134),
    q^4 - q^32 - q^60 - q^72 + q^100 + q^128 + O(q^134),
    q^5 - q^7 - q^17 + q^27 + q^31 - q^45 - q^75 + q^97 + q^105 + q^125 - q^129 
        - 2*q^131 + O(q^134),
    q^6 - q^14 - q^24 - q^34 + 2*q^48 + q^54 + q^56 - q^80 + q^82 - q^90 - 
        2*q^96 - q^112 + q^122 - q^126 + O(q^134),
    q^8 + q^18 - q^32 - q^36 - q^42 - q^50 + q^70 + q^84 - q^86 + q^100 - q^102 
        + q^106 - q^120 + O(q^134),
    q^9 - q^21 - q^25 + q^35 - q^43 - q^51 + q^53 + q^67 + q^85 + q^123 + q^127 
        + O(q^134),
    q^10 - q^14 - q^34 - q^40 + q^48 + q^54 + q^56 + q^62 - q^80 - q^90 - q^96 +
        O(q^134),
    q^12 - 2*q^24 - q^28 + q^40 + 2*q^48 + q^56 - q^68 - q^80 - q^96 + q^108 - 
        q^112 + O(q^134),
    q^16 + q^18 - q^32 - q^42 - q^50 + q^70 - q^72 - q^86 - q^102 + q^106 + 
        O(q^134),
    q^20 - q^24 - q^28 + q^40 + q^48 - q^68 - q^80 + q^108 + q^124 + O(q^134)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
156
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
477
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^10 - q^13 + q^25 - q^28 + q^40 - q^43 + q^46 + q^52 + q^82 - q^91 - 
        q^97 - q^100 + O(q^102),
    q^2 + q^8 - 2*q^14 - q^20 + q^23 + q^26 - q^32 + q^35 + q^41 - q^50 - q^53 -
        q^56 - q^65 - 2*q^74 + q^86 + 2*q^92 + 2*q^98 - 2*q^101 + O(q^102),
    q^3 + q^27 - q^30 - q^39 - q^45 - q^72 + q^75 - q^84 + O(q^102),
    q^4 - q^7 + q^13 - q^25 - q^28 - q^37 - q^40 + q^43 + q^46 + q^49 - q^64 + 
        q^70 + q^82 + q^97 + O(q^102),
    q^5 + q^8 - q^14 - q^20 + q^26 - q^32 + q^35 - q^50 - q^53 - 2*q^65 + q^71 -
        q^74 + q^83 + q^86 + q^92 + q^98 - 2*q^101 + O(q^102),
    q^6 - q^15 - q^36 - q^42 + q^54 + q^63 + q^69 + O(q^102),
    q^9 - q^15 - q^24 + q^42 + q^60 - q^78 + q^81 - q^90 + q^96 + O(q^102),
    q^12 - q^18 - q^21 + q^39 + q^45 - q^75 - q^84 + O(q^102)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
478
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
238
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
478
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
478
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
478
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
119*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^17 - q^18 - q^22 - 2*q^24 + q^25 - q^27 - q^29 + q^30 + q^32 - q^33 + 
        q^34 + q^36 - q^44 - q^48 + q^49 - q^50 - q^54 - q^55 + q^61 + q^62 + 
        q^64 + q^66 + q^67 - q^68 - q^71 + 2*q^72 - q^75 + q^80 - q^83 + q^93 + 
        q^99 - q^100 + q^102 + q^108 - q^109 - q^110 + q^116 + O(q^118),
    q^2 + q^18 - q^30 - q^36 - q^40 + q^50 - q^58 - q^66 - q^96 + q^98 - q^108 +
        O(q^118),
    q^3 + q^22 + q^24 + q^27 - q^30 - q^31 - q^33 - q^36 - q^40 + q^44 - q^45 + 
        q^50 - q^51 - q^58 - q^66 + q^81 + q^90 - q^96 + q^100 + q^101 - q^108 +
        q^113 + O(q^118),
    q^4 - q^18 - q^22 - q^24 + q^30 + q^34 + q^36 - q^44 - q^48 - q^50 - q^54 + 
        q^62 + q^64 + q^66 + q^72 + q^102 - q^110 + O(q^118),
    q^5 - q^17 + q^18 + q^24 + q^29 - q^30 - q^31 - q^36 + q^54 + q^55 - q^58 + 
        q^60 - q^61 - q^64 - q^66 - q^67 + q^68 - q^72 - q^80 + q^83 - q^85 + 
        q^87 - q^93 - q^108 + q^110 + O(q^118),
    q^6 + q^17 - q^18 - q^22 - q^24 - q^29 + q^30 - q^33 + q^34 - q^50 + q^61 + 
        q^64 + q^67 + q^72 - q^75 - q^83 + q^88 - q^90 + q^93 + q^99 - q^110 + 
        O(q^118),
    q^8 + q^17 - q^18 - q^22 - 2*q^24 - q^29 + 2*q^30 + q^32 - q^33 + q^34 + 
        q^36 - q^44 - q^48 - q^50 - q^54 + q^58 - q^60 + q^61 + q^64 + q^66 + 
        q^67 - q^68 + 2*q^72 - q^75 - q^83 - q^90 + q^93 + q^99 - q^100 + q^108 
        - q^110 + O(q^118),
    q^9 - q^17 + q^18 + q^22 + 2*q^24 + q^27 + q^29 - 2*q^30 - q^31 - q^32 - 
        q^34 - 2*q^36 - q^40 + q^44 - q^45 + q^48 + q^50 - q^51 + q^54 + q^55 - 
        q^58 + q^60 - q^61 - q^64 - q^66 - q^67 + q^68 + q^71 - q^72 + q^81 + 
        q^83 - q^85 + q^90 - q^93 - q^96 - q^99 + q^100 - 2*q^108 + q^109 + 
        q^110 + O(q^118),
    q^10 + q^17 - q^18 - q^22 - q^24 - q^29 + q^30 + q^32 - q^33 + q^34 + q^36 -
        q^44 - q^48 - q^50 - q^54 + q^61 + q^64 + q^67 + q^72 - q^75 - q^83 + 
        q^93 + q^99 - q^100 + q^102 + q^108 + O(q^118),
    q^11 - q^17 + q^18 + q^22 + q^24 + q^25 + q^29 - 2*q^30 - q^31 - q^34 - q^36
        + q^50 - q^51 + q^54 - q^58 + q^60 - q^61 - q^64 - q^66 - q^67 + q^68 - 
        q^72 + q^83 - q^85 + q^87 - q^88 + q^90 - q^96 - q^108 + q^110 + 
        O(q^118),
    q^12 + q^17 - q^18 - q^24 - q^29 + q^30 - q^33 + q^34 - q^40 - q^54 - q^60 +
        q^61 + q^64 + q^67 - q^68 + q^72 - q^75 + q^80 - q^83 + q^88 + q^93 + 
        q^99 + q^108 - q^110 + O(q^118),
    q^15 + q^18 + q^22 + q^24 + q^29 - 2*q^30 - q^31 - q^34 - q^36 - q^40 + q^44
        - q^45 + q^48 + q^50 - q^51 + q^54 - q^58 - q^64 - q^66 - q^72 + q^83 - 
        q^85 + q^90 - q^96 + q^100 - q^108 + q^110 + O(q^118),
    q^16 + q^17 - q^24 - q^29 - q^33 - q^40 + q^61 + q^64 + q^67 - q^68 + q^72 -
        q^75 + q^80 - q^83 + q^93 - q^96 + q^99 + q^116 + O(q^118),
    q^20 - q^22 - q^24 + q^30 + q^34 - q^44 - q^50 + q^64 + q^72 - q^90 - q^100 
        + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
479
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
478
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
479
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
239*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^11 + q^15 + q^16 - q^18 - q^21 - q^23 + q^25 - q^28 - q^35 - q^40 + 
        q^42 + q^45 + q^49 - q^50 - q^54 - q^55 - q^56 - q^60 - q^63 + q^64 - 
        q^69 + q^70 + q^73 - q^75 + q^77 + O(q^80),
    q^2 - q^15 + q^18 - q^22 - q^24 - q^45 - q^49 + q^50 + q^61 + q^63 + q^75 + 
        O(q^80),
    q^3 - q^11 - q^16 + q^27 - q^30 + q^40 - q^45 + q^50 + q^54 - q^73 + q^75 + 
        O(q^80),
    q^4 - q^11 - q^14 - q^15 + q^21 + q^23 + q^35 - q^42 - q^45 + q^50 + q^54 + 
        q^63 + q^69 - q^70 - q^72 - q^73 - q^77 + O(q^80),
    q^5 - q^11 - q^14 - q^15 - q^16 + 2*q^21 + q^22 + q^23 + q^24 - q^25 - q^27 
        + q^28 + q^32 - q^33 + q^35 - q^36 - q^42 - q^44 - q^48 + q^50 + q^54 + 
        q^55 + q^60 - q^64 + q^66 - q^70 - q^71 - q^73 - 2*q^77 + O(q^80),
    q^6 - q^11 - q^14 - q^15 - q^16 + 2*q^21 + q^22 + q^23 + q^24 - q^30 + q^32 
        - q^33 + q^35 - q^36 - q^42 - q^44 - q^45 - q^48 + q^50 + 2*q^54 + q^55 
        + q^60 - q^64 - q^70 - q^72 - q^73 - q^77 + O(q^80),
    q^7 - q^11 - q^14 - q^15 - q^16 + q^18 + 2*q^21 + q^22 + q^23 - q^25 - q^27 
        + q^28 + q^32 - q^33 + q^35 - 2*q^42 - q^44 - q^45 - q^46 - q^48 + q^50 
        + q^54 + q^55 + q^56 + q^60 + q^63 - q^64 + q^66 + q^69 - q^70 - q^71 - 
        q^73 - 2*q^77 + O(q^80),
    q^8 - q^11 - q^14 - q^16 + q^21 + q^22 + q^23 + q^24 - q^30 + q^32 - q^33 - 
        q^36 - q^42 - q^44 - q^48 + q^49 + q^50 + q^54 + q^60 - q^64 + q^66 - 
        q^73 - q^77 + O(q^80),
    q^9 - q^11 - q^15 - q^16 + q^18 + q^21 + q^23 + q^28 - q^30 - q^33 + q^40 - 
        q^42 - q^44 - q^45 - q^48 + q^50 + q^54 + q^55 + q^56 + q^60 - q^64 - 
        q^70 - q^73 + q^75 - q^77 + O(q^80),
    q^10 - q^11 - q^16 + q^21 + q^23 - q^30 + q^40 - q^42 - q^44 - q^45 + q^50 +
        q^54 + q^56 + q^60 - q^64 - q^70 - q^73 + O(q^80),
    q^12 - q^14 - q^15 + q^21 + q^23 - q^33 - q^36 + q^50 + q^54 - q^72 - q^77 +
        O(q^80),
    q^20 - q^21 - q^22 + q^25 + q^27 - q^32 - q^35 + q^42 + q^46 - q^55 - q^60 +
        q^71 + q^77 + O(q^80)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^5 + a*q^9 + (a - 1)*q^13 + (-a - 1)*q^17 - q^25 + (a + 1)*q^37 + 
        q^45 - a*q^49 + (-a + 1)*q^53 + (a + 1)*q^65 + (-a + 1)*q^73 - q^81 + (a
        - 1)*q^85 + (a + 1)*q^97 - 2*q^101 - 2*a*q^109 + (a - 1)*q^113 + (-a - 
        1)*q^117 - q^121 + a*q^125 + (a + 1)*q^137 + 2*a*q^149 + (-a + 1)*q^153 
        + (-a - 1)*q^157 + O(q^162),
    q^3 - a*q^15 + a*q^27 + (a - 1)*q^39 + (-a - 1)*q^51 - q^75 + (a + 1)*q^111 
        + q^135 - a*q^147 + (-a + 1)*q^159 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 - q^9 + q^25 + 2*q^29 - 2*q^41 + q^45 - q^49 - 2*q^61 + q^81 + 
        2*q^89 + 2*q^101 - 2*q^109 + q^121 - q^125 - 2*q^145 - 2*q^149 + 
        O(q^162),
    q^2 - q^10 - q^18 + q^50 + 2*q^58 - 2*q^82 + q^90 - q^98 - 2*q^122 + 
        O(q^162),
    q^3 - q^15 - q^27 + q^75 + 2*q^87 - 2*q^123 + q^135 - q^147 + O(q^162),
    q^6 - q^30 - q^54 + q^150 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^21 - q^25 - q^45 - q^49 - q^69 - q^81 + q^105 + q^121 + q^129 + q^141 
        + O(q^162),
    q^3 - q^15 - 2*q^23 - q^27 + 2*q^35 + 2*q^47 + 2*q^63 - q^75 - 2*q^83 - 
        2*q^107 + 2*q^123 - q^135 - q^147 + O(q^162),
    q^5 + q^9 - q^21 - 2*q^41 - q^69 + q^105 - q^125 - q^129 + q^141 + 2*q^149 +
        2*q^161 + O(q^162),
    q^7 - q^15 - q^23 - q^27 + q^35 + q^43 + q^47 + q^63 - q^67 - q^83 - q^103 -
        q^107 + q^115 + 2*q^123 - q^127 + O(q^162)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^3*q^4 - a*q^6 + a^3*q^9 - q^10 + a^2*q^15 - a^2*q^16 + (-a^2 + a)*q^19
        - q^24 + a*q^25 + (a^3 - a)*q^31 + (a^2 + a)*q^34 + a^2*q^36 + a^3*q^40 
        + (-a^3 - a^2)*q^46 + a^2*q^49 + (-a^3 + 1)*q^51 + q^54 + a*q^60 + (-a^3
        - 1)*q^61 - a*q^64 + (-a - 1)*q^69 + (-a + 1)*q^76 - a^2*q^81 + (-a^3 - 
        a^2)*q^85 - a^3*q^90 + (a^3 + 1)*q^94 + a^3*q^96 + q^100 + (a^3 + 
        a)*q^106 + (a^2 - a)*q^109 + (a^3 - a^2)*q^114 + (a^3 - 1)*q^115 - 
        a*q^121 + (a^2 - 1)*q^124 - a*q^135 + (a + 1)*q^136 + (-a^3 - a^2)*q^139
        + (-a^2 + a)*q^141 + a*q^144 - a^2*q^150 + (a^2 - 1)*q^151 + (-a^3 + 
        a)*q^159 + a^2*q^160 + O(q^162),
    q^2 - a^2*q^3 - a*q^5 - a^3*q^8 - a*q^12 + (a^3 + a^2)*q^17 + a^3*q^18 - 
        q^20 + (-a^3 + 1)*q^23 + a*q^27 + a^2*q^30 - a^2*q^32 + (-a^2 + a)*q^38 
        + q^45 + (a - 1)*q^47 - q^48 + a*q^50 + (a^2 - 1)*q^53 + (-a^3 - 1)*q^57
        + (a^3 - a)*q^62 + (a^2 + a)*q^68 + a^2*q^72 - a^3*q^75 + a^3*q^80 + 
        (a^3 - a)*q^83 + (-a^3 - a^2)*q^92 + (a^3 + a)*q^93 + (a^3 - a^2)*q^95 +
        a^2*q^98 + (-a^3 + 1)*q^102 + (a^2 - 1)*q^107 + q^108 + (-a + 1)*q^113 +
        a*q^120 + (-a^3 - 1)*q^122 - a^2*q^125 - a*q^128 + (-a^2 + a)*q^137 + 
        (-a - 1)*q^138 + q^147 + (-a + 1)*q^152 + (-a^2 - a)*q^153 + (a^2 + 
        1)*q^155 + O(q^162)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^9 - q^15 + (a - 1)*q^19 + a*q^25 - q^49 + (-a + 1)*q^51 + (-a + 
        1)*q^61 + (a + 1)*q^69 + 2*q^79 - q^81 + (-a - 1)*q^85 + (a - 1)*q^109 +
        (-a + 1)*q^115 + a*q^121 + a*q^135 + (-a - 1)*q^139 + (a - 1)*q^141 + 
        O(q^162),
    q^2 - a*q^8 + a*q^12 - a*q^18 + q^20 - q^30 - q^32 + (a - 1)*q^38 + q^48 + 
        a*q^50 + (a - 1)*q^68 - q^72 - a*q^80 + (-a - 1)*q^92 - q^98 + (-a + 
        1)*q^102 + q^108 + a*q^120 + (-a + 1)*q^122 + a*q^128 + (a + 1)*q^138 + 
        (a + 1)*q^152 + 2*q^158 + O(q^162),
    q^3 - a*q^5 + (a + 1)*q^17 + (a - 1)*q^23 - a*q^27 - q^45 + (-a - 1)*q^47 + 
        (a - 1)*q^57 + a*q^75 + (a + 1)*q^95 + (-a - 1)*q^113 + q^125 + (-a + 
        1)*q^137 - q^147 + (-a + 1)*q^153 + O(q^162),
    q^4 - q^6 + a*q^10 - a*q^16 + a*q^24 + (-a - 1)*q^34 - a*q^36 + q^40 + (-a +
        1)*q^46 + a*q^54 - q^60 - q^64 + (a - 1)*q^76 + q^90 + (a + 1)*q^94 + 
        q^96 + a*q^100 + (-a + 1)*q^114 + (a - 1)*q^136 - q^144 - a*q^150 - 
        a*q^160 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
480
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^9 - q^15 - q^25 + 2*q^31 + q^49 - 2*q^79 + q^81 - q^121 + q^135 - 
        2*q^151 + 2*q^159 + O(q^162),
    q^3 + q^5 - q^27 - q^45 - 2*q^53 - q^75 - 2*q^83 + 2*q^93 + 2*q^107 - q^125 
        + q^147 + 2*q^155 + O(q^162)
]
;
Bo:=
[
    q - q^9 + q^15 - q^25 - 2*q^31 + q^49 + 2*q^79 + q^81 - q^121 - q^135 + 
        2*q^151 - 2*q^159 + O(q^162),
    q^2 - q^18 + q^30 - q^50 - 2*q^62 + q^98 + 2*q^158 + O(q^162),
    q^3 - q^5 - q^27 + q^45 + 2*q^53 - q^75 - 2*q^83 - 2*q^93 + 2*q^107 + q^125 
        + q^147 + 2*q^155 + O(q^162),
    q^4 - q^16 - q^24 - q^36 + q^40 + q^60 + q^64 + q^96 - q^100 - 2*q^124 + 
        q^144 - q^160 + O(q^162),
    q^6 - q^10 - q^54 + q^90 + 2*q^106 - q^150 + O(q^162),
    q^8 + q^12 - q^20 - q^32 - q^48 - q^72 + q^80 - q^108 + q^120 + q^128 + 
        O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
481
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
482
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
240
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
482
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
80
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
482
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
482
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^9 + a^6)*q^2 + (-a^7 + a^4 - a)*q^4 + a^8*q^7 + (a^9 - a^8 - a^6 - 
        a^4 + a^3 + a - 1)*q^8 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 
        + a - 1)*q^9 + (a^4 - a^3)*q^11 + (a^6 - a^3)*q^14 + (a^8 - a^5 - a^3 + 
        a^2 + 1)*q^16 + (a^8 - a^5)*q^18 + (-a^8 + a^7 - a^6 + a^5 - a^4 + a^3 -
        1)*q^22 - a*q^23 + a^2*q^25 + (-a^9 + a^4 - a)*q^28 + (-a^9 - a^5)*q^29 
        + (-a^9 + a^8 + a^6 - a^3 - a + 1)*q^32 + (a^6 - a^3 + 1)*q^36 + (-a^7 +
        a^2)*q^37 + (a^6 + a^4)*q^43 + (a^9 - a^6 + a^3 - a^2 + a)*q^44 + (a^9 -
        a^8 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^46 - a^5*q^49 + (a^8 + 
        1)*q^50 + (a^9 - a^8 + a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^53 + (a^9 
        - a^8 - a^6 + a^5 + a^3 + a - 1)*q^56 + (-a^7 + a^4 - a^3 + 1)*q^58 - 
        a^7*q^63 + (-a^8 + a^5 - a^2 - 1)*q^64 + (-a^9 + a^6)*q^67 + (a^8 - 
        a^7)*q^71 + (-a^9 + a^6 + a^4 - a)*q^72 + (a^8 - a^5 + a^2 + 1)*q^74 + 
        (-a + 1)*q^77 + (-a^5 - a)*q^79 - a^9*q^81 + (a^9 - a^8 + a^7 - a^6 + 
        a^5 + a^3 - 1)*q^86 + (a^7 - a^4 + a)*q^88 + (a^8 - a^5 + a^2)*q^92 + 
        (-a^3 + 1)*q^98 + (-a^3 + a^2)*q^99 + (-a^9 + a^6 - a^3)*q^100 + (a^8 - 
        a^5 + a^4 - a)*q^106 + (-a^9 - a^3)*q^107 + (-a^3 + 1)*q^109 + (a^9 + 
        a^7 - a^6 - a^4 + a^3 + a)*q^112 + (-a^3 - a)*q^113 + (-a^8 + a^7 - a^4 
        + a^3 - 1)*q^116 + (a^8 - a^7 + a^6)*q^121 + O(q^122),
    q^3 + (-a^9 + a^6)*q^6 + (-a^7 + a^4 - a)*q^12 + a^8*q^21 + (a^9 - a^8 - a^6
        - a^4 + a^3 + a - 1)*q^24 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - 
        a^2 + a - 1)*q^27 + (a^4 - a^3)*q^33 + (a^6 - a^3)*q^42 + (a^8 - a^5 - 
        a^3 + a^2 + 1)*q^48 + (a^8 - a^5)*q^54 + (-a^8 + a^7 - a^6 + a^5 - a^4 +
        a^3 - 1)*q^66 - a*q^69 + a^2*q^75 + (-a^9 + a^4 - a)*q^84 + (-a^9 - 
        a^5)*q^87 + (-a^9 + a^8 + a^6 - a^3 - a + 1)*q^96 + (a^6 - a^3 + 
        1)*q^108 + (-a^7 + a^2)*q^111 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 + q^8 - q^9 - q^13 - q^16 + q^18 + q^23 + q^25 + q^26 + q^27 - q^29 
        - q^31 - q^41 - q^46 - q^47 + q^49 - q^50 - q^54 + q^58 + 2*q^59 + q^62 
        + q^64 - q^71 - q^72 - q^73 + q^82 + q^94 - q^98 + 2*q^101 - q^104 + 
        q^117 - 2*q^118 + q^121 + O(q^122),
    q^3 - q^6 - q^9 + q^18 + q^24 - q^39 - q^48 + q^69 - q^72 + q^75 + q^78 + 
        q^81 - q^87 - q^93 + q^117 + O(q^122),
    q^7 - q^14 + q^56 - q^63 - q^91 - q^112 + O(q^122),
    q^21 - q^42 - q^63 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
483
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
484
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^5 + q^9 + q^16 - q^20 - q^26 - q^34 + q^36 - q^37 - q^45 + q^49 
        - q^53 - q^58 + q^64 - q^80 + q^81 - q^82 - q^89 - q^97 + O(q^98),
    q^2 + q^8 - q^10 - q^13 - q^17 + q^18 - q^29 + q^32 - q^40 - q^41 - q^52 + 
        2*q^61 + q^65 - q^68 + q^72 + 2*q^73 - q^74 + q^85 - q^90 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
484
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
110
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
484
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
110
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
484
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
484
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
484
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^3 + a^2 - a + 1)*q^3 - a^2*q^5 - a*q^15 - q^23 + a^2*q^27 + a^3*q^31
        + a*q^37 + (2*a^3 - 2*a^2 + 2*a - 2)*q^47 + a^2*q^49 - 2*a^3*q^53 + 
        a*q^59 - q^67 + (a^3 - a^2 + a - 1)*q^69 - a^2*q^71 + a*q^81 - q^89 + 
        a^2*q^93 + a^3*q^97 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
484
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 22*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 + (-a^3 + a^2 - a + 1)*q^5 - a*q^9 + (a^3 - a^2 + a - 1)*q^16 + 
        a*q^20 - a^2*q^26 - q^34 - a^3*q^36 - a^2*q^37 - q^45 + (a^3 - a^2 + a -
        1)*q^49 + a*q^53 + a^3*q^58 - a*q^64 + a^3*q^80 + a^2*q^81 + (-a^3 + a^2
        - a + 1)*q^82 - q^89 + a*q^97 + O(q^98),
    q^2 + a^2*q^8 + (-a^3 + a^2 - a + 1)*q^10 - q^13 + a^3*q^17 - a*q^18 + 
        a*q^29 + (a^3 - a^2 + a - 1)*q^32 + a*q^40 - a^2*q^41 - a^2*q^52 - 
        2*a^3*q^61 + (a^3 - a^2 + a - 1)*q^65 - q^68 - a^3*q^72 - 2*a*q^73 - 
        a^2*q^74 + a^2*q^85 - q^90 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
484
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
55*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 - q^5 + q^15 - q^23 + q^27 - q^31 - q^37 + 2*q^47 + q^49 + 2*q^53 - 
        q^59 - q^67 + q^69 - q^71 - q^81 - q^89 + q^93 - q^97 + O(q^98),
    q^11 - q^33 - q^55 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
96
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
96
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
32
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
32
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 16*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 24*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 24*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 32*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
485
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 48*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
486
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
162
);
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
486
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
486
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
486
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + (-a + 1)*q^7 + a*q^13 + (a - 1)*q^16 - q^19 + (a - 1)*q^25 - 
        q^28 + a*q^31 - q^37 + (-a + 1)*q^43 + (-a + 1)*q^52 + (2*a - 2)*q^61 + 
        q^64 - 2*a*q^67 + 2*q^73 + a*q^76 + (-a + 1)*q^79 + q^91 + (-a + 1)*q^97
        + q^100 - 2*a*q^103 - q^109 + a*q^112 - a*q^121 + (-a + 1)*q^124 - q^127
        + O(q^128),
    q^2 - a*q^8 + (-a + 1)*q^14 + a*q^26 + (a - 1)*q^32 - q^38 + (a - 1)*q^50 - 
        q^56 + a*q^62 - q^74 + (-a + 1)*q^86 + (-a + 1)*q^104 + (2*a - 2)*q^122 
        + O(q^128)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
486
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
81*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^7 - q^13 + q^16 - q^19 + q^25 - q^28 - q^31 - q^37 - q^43 - q^52
        + 2*q^61 + q^64 + 2*q^67 + 2*q^73 - q^76 - q^79 + q^91 - q^97 + q^100 + 
        2*q^103 - q^109 - q^112 + q^121 - q^124 - q^127 + O(q^128),
    q^2 + q^8 - q^14 - q^26 + q^32 - q^38 + q^50 - q^56 - q^62 - q^74 - q^86 - 
        q^104 + 2*q^122 + O(q^128)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
487
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
486
);
qprec:=
81
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
487
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
162
);
qprec:=
81
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
487
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
81
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
487
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
81
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
487
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
81*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
81
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
487
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
243*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
81
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^31 - q^32 - q^38 - q^41 + q^49 - q^53 - q^58 - q^76 + 
        O(q^81),
    q^2 - q^16 + q^18 - q^19 - q^29 - q^38 + q^50 - q^58 + q^61 + q^67 + q^71 - 
        q^73 + O(q^81),
    q^4 - q^8 - q^19 - q^29 + q^31 + q^36 + q^41 + q^53 - q^62 - q^72 - q^73 + 
        O(q^81)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^7 - a^6 - a^5 + a^3 + a^2 - 1)*q^5 + (a^7 - a^2)*q^9 + (-a^5 - a^4 +
        a + 1)*q^13 + (-a^7 - a^6 + a^5 + a^4 + a^3 - 1)*q^17 + (a^7 + a^6 + a^5
        - a^4 - 2*a^3 - a^2)*q^25 + (a^6 + a^4)*q^29 + (a^7 + a^6 - a^3 - a^2 + 
        1)*q^37 + (a^2 - a)*q^41 + (a^6 + a^2)*q^45 + (-a^7 + a^5 + a^4 + a^3 - 
        a - 1)*q^49 + (-a^6 + a^5 + a - 1)*q^53 - a*q^61 + (-a^3 - a^2 - a)*q^65
        + (a^7 - a^5 - a^4 - a^3 + a + 1)*q^73 + (-a^7 - a^6 + a^3 + a^2 - 
        1)*q^81 + (a^7 - 2*a^5 - a^4 + a^2 + 1)*q^85 + (a^5 + a^2 - 1)*q^89 + 
        (-a^7 + a^6)*q^97 + (-a^5 + 1)*q^101 + (-a^7 - 2*a^6 + a^3 + a^2 + a - 
        1)*q^109 + (a^6 - a^3)*q^113 + (a^5 + a^4 - 1)*q^117 + O(q^118),
    q^2 - a*q^4 + a^2*q^8 + (-a^7 - a^6 - a^5 + a^3 + a^2 - 1)*q^10 - a^3*q^16 +
        (a^7 - a^2)*q^18 + (a^6 + a^5 - 1)*q^20 + (-a^5 - a^4 + a + 1)*q^26 + 
        a^4*q^32 + (-a^7 - a^6 + a^5 + a^4 + a^3 - 1)*q^34 + (a^7 - a^5 - a^4 + 
        a + 1)*q^36 + (-a^7 - a^6 + a)*q^40 + (a^7 + a^6 + a^5 - a^4 - 2*a^3 - 
        a^2)*q^50 + (a^6 + a^5 - a^2 - a)*q^52 + (a^6 + a^4)*q^58 - a^5*q^64 + 
        (-a^6 + a^3 - 1)*q^68 + (a^7 + a^6 - a^4 - a^3 - a^2 + 1)*q^72 + (a^7 + 
        a^6 - a^3 - a^2 + 1)*q^74 + (a^5 + a^4 + a^3 - a^2 - a - 1)*q^80 + (a^2 
        - a)*q^82 + (a^6 + a^2)*q^90 + (-a^7 + a^5 + a^4 + a^3 - a - 1)*q^98 + 
        (-a^6 + a^4 + a + 1)*q^100 + (-a^7 - a^6 + a^3 + a^2)*q^104 + (-a^6 + 
        a^5 + a - 1)*q^106 + (-a^7 - a^5)*q^116 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a^3 - a^2 + a)*q^5 + a^2*q^9 + (-a^3 + a^2)*q^13 + (-a^3 - a)*q^17 + 
        (-a^2 + a)*q^25 + (a^3 - a^2 - 1)*q^29 + (2*a^3 - 2*a^2 + 2*a - 2)*q^37 
        + (a^2 - a)*q^41 + (a^2 - a)*q^45 - a^3*q^49 + (-a + 1)*q^53 - a*q^61 + 
        (-a^3 + 2*a^2 - a)*q^65 - 2*a^3*q^73 + (a^3 - a^2 + a - 1)*q^81 + (-a^3 
        + a^2 - a + 1)*q^85 + (a^2 + 1)*q^89 + (a^2 - a)*q^97 + 2*q^101 + (a^3 -
        a^2 - 1)*q^109 + (-a^3 - a)*q^113 + (a^3 - a^2 + a)*q^117 + O(q^118),
    q^2 - a*q^4 + a^2*q^8 + (a^3 - a^2 + a)*q^10 - a^3*q^16 + a^2*q^18 + (-a + 
        1)*q^20 + (-a^3 + a^2)*q^26 + (a^3 - a^2 + a - 1)*q^32 + (-a^3 - a)*q^34
        - a^3*q^36 + (a^2 - a)*q^40 + (-a^2 + a)*q^50 + (-a^2 + a - 1)*q^52 + 
        (a^3 - a^2 - 1)*q^58 + q^64 + (a^3 + a - 1)*q^68 + (a^3 - a^2 + a - 
        1)*q^72 + (2*a^3 - 2*a^2 + 2*a - 2)*q^74 + (-a^3 + a^2)*q^80 + (a^2 - 
        a)*q^82 + (a^2 - a)*q^90 - a^3*q^98 + (a^3 - a^2)*q^100 + (a^3 - a^2 + 
        a)*q^104 + (-a + 1)*q^106 + (a^2 + 1)*q^116 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 15*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^5 + q^9 - 2*a*q^13 + (2*a - 2)*q^17 + (-a + 1)*q^29 - q^37 - q^41 + 
        a*q^45 + (a - 1)*q^49 - q^53 - a*q^61 + (-2*a + 2)*q^65 + (-a + 1)*q^73 
        + q^81 - 2*q^85 - q^89 + (-a + 1)*q^97 + a*q^101 + a*q^109 + 2*q^113 - 
        2*a*q^117 + O(q^118),
    q^2 - a*q^4 + (a - 1)*q^8 + a*q^10 + q^16 + q^18 + (-a + 1)*q^20 - 2*a*q^26 
        - a*q^32 + (2*a - 2)*q^34 - a*q^36 - q^40 + (2*a - 2)*q^52 + (-a + 
        1)*q^58 + (a - 1)*q^64 + 2*q^68 + (a - 1)*q^72 - q^74 + a*q^80 - q^82 + 
        a*q^90 + (a - 1)*q^98 + 2*q^104 - q^106 - q^116 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 20*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 30*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 + q^9 - q^13 - q^41 - q^45 + q^61 + q^65 - q^73 + q^77 + q^81 + 
        2*q^97 - q^109 - q^113 - q^117 + O(q^118),
    q^2 + q^8 - q^10 + q^18 - q^26 - q^28 + q^32 - q^40 - q^44 + q^72 - q^82 - 
        q^90 - q^92 - q^104 - q^112 + O(q^118),
    q^4 - q^14 + q^16 - q^20 - q^22 + q^36 - q^46 - q^52 - q^56 + 2*q^62 + q^64 
        + q^70 - q^80 + 2*q^86 - q^88 + q^110 + O(q^118),
    q^7 + q^11 + q^23 - 2*q^31 - q^35 - 2*q^43 - q^55 + q^59 + q^63 + q^67 - 
        2*q^71 + q^79 - q^91 + q^99 - q^115 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
488
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 30*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^14 + q^16 - q^19 + q^25 - q^27 - q^42 + q^49 - q^56 - q^57 - 
        q^58 + q^64 - q^73 - q^76 - q^83 + q^100 - q^107 - q^108 - q^113 + 
        O(q^118),
    q^2 - q^7 + q^8 - q^21 - q^28 - q^29 + q^32 - q^38 + q^50 - q^54 + q^61 + 
        q^63 + q^69 - q^71 + 2*q^79 - q^84 - q^87 + q^93 + q^98 + q^111 - q^112 
        - q^114 - q^116 + O(q^118),
    q^3 - q^9 + q^12 - q^14 - q^19 - q^36 + q^41 + q^46 + q^48 + q^49 - q^56 - 
        q^58 + q^62 - q^73 + q^74 + q^75 - q^76 - q^83 + q^97 + q^106 - q^107 - 
        q^113 + O(q^118),
    q^6 - q^7 - q^18 + q^23 + q^24 - q^28 - q^29 + q^31 + q^37 - q^38 + q^53 - 
        q^69 - q^71 - q^72 + q^82 + q^92 - q^93 + q^96 + q^98 + q^101 - q^111 - 
        q^112 - q^116 + O(q^118)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
489
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
107
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
489
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
162
);
qprec:=
107
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
489
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
162
);
qprec:=
107
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
489
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
107
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
489
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
107
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^11 - a^2)*q^3 + a^2*q^4 + (-a^17 - a^12 + a^3)*q^7 - a^13*q^9 + (a^13
        - a^4)*q^12 + (a^16 - a^5)*q^13 + a^4*q^16 + a^17*q^19 + (a^14 + 
        a^10)*q^21 - a^3*q^25 + a^6*q^27 + (-a^14 - a^10 + a^5 + a)*q^28 + (a^12
        + a^9 - 1)*q^31 - a^15*q^36 + (-a^11 - a)*q^37 + (-a^16 - a^9 + 
        a^7)*q^39 + (-a^16 + a^15 + a^7 - a^6)*q^43 + (a^15 - a^6)*q^48 + (-a^15
        - a^11 - a^7)*q^49 + (a^9 - a^7 - 1)*q^52 - a^10*q^57 + (a^12 - 
        a^9)*q^61 + (-a^7 - a^3)*q^63 + a^6*q^64 + (a^14 - a^9)*q^67 + (-a^14 + 
        a^8 + a^5)*q^73 + (-a^14 + a^5)*q^75 + (a^10 - a)*q^76 + (a^15 - a^6 + 
        a^4)*q^79 + (a^17 - a^8)*q^81 + (a^16 + a^12)*q^84 + (a^17 + a^13 + a^10
        - a^8 + a^6 - a^4)*q^91 + (-a^11 - a^5)*q^93 + (-a^15 - a^13)*q^97 - 
        a^5*q^100 + (-a^17 - a^3)*q^103 + O(q^107)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
489
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
107
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
489
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
107
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^3 + a^2*q^4 + (a^5 - a^3 - a^2)*q^7 + a^4*q^9 + a^4*q^12 + (-a^5 -
        a^4 + a)*q^13 + a^4*q^16 + (2*a^5 - 2*a^2)*q^19 + (-a^5 - a)*q^21 - 
        a^3*q^25 + (a^3 - 1)*q^27 + (-a^5 - a)*q^28 + (-a^3 + 1)*q^31 + (a^3 - 
        1)*q^36 + (a^2 - a)*q^37 + (-a^4 + a + 1)*q^39 + (-a^4 + a^3 + a - 
        1)*q^43 + (a^3 - 1)*q^48 + (-a^4 + a^3 + a^2 + a - 1)*q^49 + (-a^4 + a +
        1)*q^52 - 2*a*q^57 + (-a^3 + 1)*q^61 + (-a^4 - a^3 + a)*q^63 + (a^3 - 
        1)*q^64 + (-a^5 + 1)*q^67 - a^2*q^73 - a^5*q^75 - 2*a*q^76 + (a^4 + a^3 
        - 1)*q^79 + (a^5 - a^2)*q^81 + (-a^4 - a^3 + a)*q^84 + (a^5 + a^4 + a^3 
        - a^2 - a - 1)*q^91 + (-a^5 + a^2)*q^93 + (a^4 + a^3 - 1)*q^97 - 
        a^5*q^100 + (a^5 - a^3 - a^2)*q^103 + O(q^107)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
489
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
107
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
489
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 54*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
107
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^3 + (a - 1)*q^4 + a*q^7 - a*q^9 - a*q^12 - q^13 - a*q^16 + 
        (2*a - 2)*q^19 - q^21 + q^25 + q^27 - q^28 + 2*q^31 + q^36 - q^37 + (-a 
        + 1)*q^39 + (-a + 1)*q^43 + q^48 + (-a + 1)*q^52 - 2*a*q^57 + 2*q^61 + 
        (-a + 1)*q^63 + q^64 + a*q^67 + (2*a - 2)*q^73 + (a - 1)*q^75 - 2*a*q^76
        + (-a + 1)*q^79 + (a - 1)*q^81 + (-a + 1)*q^84 - a*q^91 + (2*a - 2)*q^93
        + (-a + 1)*q^97 + (a - 1)*q^100 + a*q^103 + O(q^107)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
489
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
81*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
107
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
84
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
490
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
491
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
490
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
491
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
98
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
491
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
491
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
35*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
491
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
49*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
491
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
245*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^12 - q^13 - q^14 - q^15 - q^17 + q^27 - q^33 + q^38 + q^41 + q^42 + 
        q^43 - q^44 - q^46 + q^48 + q^51 - q^58 - q^60 + q^64 + q^71 - q^81 + 
        O(q^82),
    q^2 - q^6 + q^7 - q^19 - q^21 + q^22 + q^23 - q^26 - q^28 + q^29 - q^32 - 
        q^34 - q^50 + q^54 + q^57 + q^59 + q^62 - q^66 - q^67 - q^69 - q^73 + 
        q^74 + q^76 + q^77 + q^78 + O(q^82),
    q^3 - q^11 + q^12 - q^13 - q^15 + q^27 - q^33 - q^39 + q^41 + q^43 - q^44 + 
        q^48 + q^51 - q^52 + q^55 - q^60 + q^65 + q^71 - q^81 + O(q^82),
    q^4 - q^12 + q^13 + q^14 + q^16 + q^25 - q^27 - q^31 + q^33 - q^37 - q^38 - 
        q^41 - q^42 - q^43 + q^44 + q^46 - q^48 + q^49 - q^51 - q^55 + q^58 - 
        q^65 - q^68 - q^71 - q^75 + q^81 + O(q^82),
    q^5 - q^11 - q^13 - q^15 + q^20 + q^25 + q^27 - q^44 + q^51 - q^52 - q^60 + 
        q^61 - q^75 + q^79 + q^80 - q^81 + O(q^82),
    q^9 - q^11 - q^13 + q^17 + q^31 - q^33 + q^36 + q^37 - q^39 - q^44 - q^45 - 
        q^52 + q^55 + q^65 + q^68 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a^3*q^2 - a*q^4 + (a^2 - a + 1)*q^5 + (a^3 - a^2 + a - 1)*q^8 - q^9 + 
        (-a^2 + a)*q^10 + (a^3 - 2*a^2 + a - 1)*q^13 + a^2*q^16 + (a^2 + a)*q^17
        + a^3*q^18 + (-a^3 + a^2 - a)*q^20 + (-a^3 + a^2 - a)*q^25 + (a^2 - 
        1)*q^26 + q^32 + (-a^3 + a^2 - a + 2)*q^34 + a*q^36 + (-a^2 - 1)*q^37 + 
        (a^3 - a^2)*q^40 - a^3*q^41 + (-a^2 + a - 1)*q^45 + (-a^3 + a^2 - a + 
        1)*q^49 + (a^3 - a^2)*q^50 + (a^3 + 1)*q^52 + (2*a^3 - a^2 + a - 1)*q^53
        + (-a^3 - a)*q^61 - a^3*q^64 + (a^3 - a^2 - a + 1)*q^65 + (-a^3 - 
        a^2)*q^68 + (-a^3 + a^2 - a + 1)*q^72 + (-a^3 + a^2 + 1)*q^73 + (a^3 - 
        1)*q^74 + (a - 1)*q^80 + q^81 - a*q^82 + (a^3 - a^2 + 2*a - 1)*q^85 + 
        (a^2 - a)*q^90 + (a^2 - 1)*q^97 - a^2*q^98 + (a - 1)*q^100 + (-a^3 + a^2
        - a + 2)*q^101 + (-a^3 + a)*q^104 + (a^2 + a)*q^106 + (a^3 + a^2)*q^109 
        + (a^3 - 1)*q^113 + (-a^3 + 2*a^2 - a + 1)*q^117 + a^3*q^121 + (a^3 - 
        a^2 - 1)*q^122 - a^3*q^125 - a*q^128 + (-a^2 + 2*a - 2)*q^130 + (-a - 
        1)*q^136 + (a^3 - a^2 + 2*a - 1)*q^137 - a^2*q^144 + (-a^3 - a + 
        1)*q^146 + (a^3 + a)*q^148 + (-a^2 + 1)*q^149 + (-a^2 - a)*q^153 + (a^3 
        - a)*q^157 + O(q^158),
    q^3 - a^3*q^6 - a*q^12 + (a^2 - a + 1)*q^15 + (a^3 - a^2 + a - 1)*q^24 - 
        q^27 + (-a^2 + a)*q^30 + (a^3 - 2*a^2 + a - 1)*q^39 + a^2*q^48 + (a^2 + 
        a)*q^51 + a^3*q^54 + (-a^3 + a^2 - a)*q^60 + (-a^3 + a^2 - a)*q^75 + 
        (a^2 - 1)*q^78 + q^96 + (-a^3 + a^2 - a + 2)*q^102 + a*q^108 + (-a^2 - 
        1)*q^111 + (a^3 - a^2)*q^120 - a^3*q^123 + (-a^2 + a - 1)*q^135 + (-a^3 
        + a^2 - a + 1)*q^147 + (a^3 - a^2)*q^150 + (a^3 + 1)*q^156 + O(q^158)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 + a^2*q^4 + (-a^3 - a)*q^5 - a^3*q^8 + q^9 + (a^3 + a - 1)*q^10 + 
        (-a^2 + a - 1)*q^13 + (a^3 - a^2 + a - 1)*q^16 + (a^3 + a - 1)*q^17 - 
        a*q^18 + (-a^3 + 1)*q^20 + (a^3 - 1)*q^25 + (a^3 - a^2 + a)*q^26 + 
        2*a^2*q^29 + q^32 + (-a^3 + 1)*q^34 + a^2*q^36 + (a^3 - a^2 + a)*q^37 + 
        (a^3 - a^2 - 1)*q^40 - a*q^41 + (-a^3 - a)*q^45 - a^3*q^49 + (-a^3 + a^2
        + 1)*q^50 + (-a + 1)*q^52 + (-a^3 - a)*q^53 - 2*a^3*q^58 + (a^2 - 
        a)*q^61 - a*q^64 + a^3*q^65 + (a^3 - a^2 - 1)*q^68 - a^3*q^72 + (-a^3 + 
        a^2)*q^73 + (-a + 1)*q^74 + (a^2 + 1)*q^80 + q^81 + a^2*q^82 + (-a^3 + 
        a^2 + 2)*q^85 + (2*a^3 - 2*a^2 + 2*a - 2)*q^89 + (a^3 + a - 1)*q^90 + 
        (a^3 - a^2 + a)*q^97 + (a^3 - a^2 + a - 1)*q^98 + (-a^2 - 1)*q^100 + 
        (-a^3 + 1)*q^101 + (a^2 - a)*q^104 + (a^3 + a - 1)*q^106 + (a^3 - a^2 - 
        1)*q^109 + (-a + 1)*q^113 + (2*a^3 - 2*a^2 + 2*a - 2)*q^116 + (-a^2 + a 
        - 1)*q^117 - a*q^121 + (-a^3 + a^2)*q^122 + a*q^125 + a^2*q^128 + (-a^3 
        + a^2 - a + 1)*q^130 + (a^2 + 1)*q^136 + (-a^3 + a^2)*q^137 + (a^3 - a^2
        + a - 1)*q^144 + (-2*a^3 + 2)*q^145 + (-a^2 + a - 1)*q^146 + (a^2 - 
        a)*q^148 + (a^3 - a^2 + a)*q^149 + (a^3 + a - 1)*q^153 + (a^2 - a)*q^157
        + O(q^158),
    q^3 - a*q^6 + a^2*q^12 + (-a^3 - a)*q^15 - a^3*q^24 + q^27 + (a^3 + a - 
        1)*q^30 + (-a^2 + a - 1)*q^39 + (a^3 - a^2 + a - 1)*q^48 + (a^3 + a - 
        1)*q^51 - a*q^54 + (-a^3 + 1)*q^60 + (a^3 - 1)*q^75 + (a^3 - a^2 + 
        a)*q^78 + 2*a^2*q^87 + q^96 + (-a^3 + 1)*q^102 + a^2*q^108 + (a^3 - a^2 
        + a)*q^111 + (a^3 - a^2 - 1)*q^120 - a*q^123 + (-a^3 - a)*q^135 - 
        a^3*q^147 + (-a^3 + a^2 + 1)*q^150 + (-a + 1)*q^156 + O(q^158)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^5 - q^10 + q^16 - q^18 - q^20 - q^21 + q^25 - q^33 - q^37 - q^40
        + q^41 + q^42 + q^45 + 2*q^50 + q^57 + q^64 + q^66 - q^72 - q^73 - q^74 
        + q^77 - q^80 - q^84 + q^90 - q^98 + q^100 - q^113 - q^114 + 2*q^122 - 
        2*q^125 - q^132 - q^133 + q^141 - q^146 - q^148 - q^154 + O(q^158),
    q^2 - q^5 + q^8 - q^10 - q^18 - q^20 + 2*q^25 + q^32 - q^37 - q^40 + q^45 - 
        q^49 + q^50 + 2*q^61 - q^72 - q^73 - q^74 - q^77 - q^80 + q^81 + q^82 + 
        q^90 + 2*q^100 - q^113 - q^121 - 2*q^125 + q^128 + q^133 - q^146 - q^148
        + q^154 + O(q^158),
    q^3 + q^12 - q^15 - q^30 + q^48 - q^54 - q^60 - q^63 + q^75 - q^99 - q^111 -
        q^120 + q^123 + q^126 + q^135 + 2*q^150 + O(q^158),
    q^6 - q^15 + q^24 - q^27 - q^30 - q^60 + q^63 + 2*q^75 + q^96 + q^99 - q^108
        - q^111 - q^120 - q^126 + q^135 - q^147 + q^150 + O(q^158),
    q^7 + q^11 - q^14 - q^19 - q^22 + q^27 + q^28 + q^38 + q^44 - q^47 - q^54 - 
        q^56 - q^63 + q^67 - q^71 - q^76 - q^79 - q^88 + q^94 - q^99 + q^108 + 
        q^112 + q^126 - q^134 + q^142 - q^151 + q^152 + O(q^158),
    q^9 - q^18 - q^21 - q^33 + q^36 + q^42 + q^57 + q^66 - q^72 - q^84 - q^114 -
        q^132 + q^141 + q^144 + O(q^158)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
492
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 20*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^31 - q^33 - q^37 - q^43 + q^49 - q^51 - q^61 - q^73 + 
        q^81 - q^87 - q^103 + q^123 + 2*q^127 + 2*q^139 - q^141 + O(q^158),
    q^3 - q^11 - q^17 + q^27 - q^29 + q^41 - q^47 + 2*q^53 - q^71 + q^75 + 
        2*q^89 - q^93 - q^99 - q^101 - q^111 - q^129 - q^137 + q^147 + 2*q^149 -
        q^153 + O(q^158)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
56
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
56
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
12*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
112
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
112
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
12*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
493
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
494
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^16 - q^17 - q^23 + q^25 - q^26 - q^38 - q^43 + q^49 - q^61 + 
        q^62 + q^64 + q^74 + q^81 + q^82 - q^101 + q^104 + q^118 + q^121 - q^131
        + O(q^134),
    q^2 + q^18 - q^32 - q^34 - q^46 + q^50 - q^52 - q^76 - q^86 + q^98 - q^122 +
        q^124 + q^128 + O(q^134),
    q^4 - q^16 - q^26 + q^36 - q^38 + q^62 - q^68 + q^74 + q^82 - q^92 + q^100 +
        q^118 + O(q^134),
    q^8 + q^13 + q^19 - q^31 - q^32 - q^37 - q^41 - q^52 - q^59 - q^67 + 2*q^71 
        + q^72 - q^76 + 2*q^89 - q^97 - q^109 + q^117 + q^124 + O(q^134)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^3 + (a - 1)*q^4 - a*q^9 - a*q^11 - a*q^12 - a*q^16 + (2*a - 
        2)*q^23 + a*q^25 + q^27 + (-a + 1)*q^31 + q^33 + q^36 - q^37 + q^44 + 
        a*q^47 + q^48 + (a - 1)*q^49 - q^53 + (-a + 1)*q^59 + q^64 + (-a + 
        1)*q^67 - 2*a*q^69 - q^71 - q^75 + (a - 1)*q^81 + 2*q^89 - 2*a*q^92 + 
        a*q^93 + a*q^97 + (a - 1)*q^99 - q^100 + (-a + 1)*q^103 + (a - 1)*q^108 
        + (-a + 1)*q^111 + (-a + 1)*q^113 + (a - 1)*q^121 + a*q^124 + q^125 + 
        O(q^130),
    q^5 + (a - 1)*q^15 + (a - 1)*q^20 + (-a + 1)*q^25 - a*q^45 - a*q^55 - a*q^60
        + a*q^75 - a*q^80 + a*q^100 + (2*a - 2)*q^115 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^3 - a)*q^4 + 1/2*(a^3 + a^2 + a)*q^5 - a*q^9 + (-a^2 + 1)*q^11 + 
        1/2*(a^2 + a - 1)*q^15 + (-a^2 + 1)*q^16 + 1/2*(-a^2 - a - 1)*q^20 + 
        (-a^3 + a^2 + a)*q^23 + 1/2*(2*a^3 + a^2 - a - 1)*q^25 + (-a^3 - 1)*q^27
        + (a^2 - 2)*q^31 + (-a^3 + 1)*q^33 + q^36 + (a^2 - a - 1)*q^37 + 
        a^3*q^44 + 1/2*(a^3 - 2*a^2 + 1)*q^45 + (-a^3 - a^2 + a)*q^47 + (-a^3 + 
        a)*q^49 + (a^3 - a^2 - a)*q^53 + 1/2*(-a^3 + 2*a - 1)*q^55 + (-a^3 + 
        a)*q^59 + 1/2*(-a^3 - 1)*q^60 + a^3*q^64 + (-a^2 + a + 1)*q^67 + 
        2*a*q^69 + (2*a^2 - 1)*q^71 + 1/2*(a^3 + 2*a^2 - 2*a - 1)*q^75 + 
        1/2*(-a^3 + 2*a + 1)*q^80 - a^2*q^81 + (a^2 - a - 1)*q^92 + (2*a^3 - a^2
        - a - 1)*q^93 + (-a^3 - 1)*q^97 + (-a^3 + a)*q^99 + 1/2*(-a^3 - 2*a^2 + 
        1)*q^100 + (-a^2 - a + 1)*q^103 + (-a^3 + a^2 + a)*q^108 + (a^2 - 
        2)*q^111 + (-a^2 - a + 1)*q^113 + (a^3 - a + 1)*q^115 + a^2*q^121 + 
        (-2*a^3 + a)*q^124 - q^125 + O(q^130),
    q^3 + 1/2*(-a^3 - 1)*q^5 + (-a^3 + a^2 + a)*q^9 + (a^3 + a^2 - a)*q^11 + 
        (a^3 - a)*q^12 + 1/2*(a^3 - a^2 + a)*q^15 + 1/2*(-a^3 + a^2 + a)*q^20 - 
        2*q^23 + 1/2*(-a^3 - a^2 - a + 2)*q^25 + a*q^27 + (-a^3 - 2*a^2 + 2*a + 
        1)*q^31 + (a^2 - 1)*q^33 + (a^2 - a - 1)*q^36 + (-2*a^3 + a)*q^37 + 
        (-a^2 - a + 1)*q^44 + 1/2*(2*a^3 + a^2 - a + 1)*q^45 + (a^3 - a)*q^47 + 
        (-a^2 + 1)*q^48 + (-a^2 + 1)*q^53 + 1/2*(2*a^3 - a^2 - a - 1)*q^55 + 
        (a^3 - 1)*q^59 + 1/2*(-a^2 + a - 1)*q^60 + (a^3 - 2*a)*q^67 + (a^3 - a^2
        - a)*q^69 + 1/2*(-2*a^3 + a^2 + a - 1)*q^75 + 1/2*(a^2 - a - 1)*q^80 + 
        (-2*a^3 + 2*a)*q^92 + (-a^2 + 2)*q^93 + (a^3 + a)*q^97 + 1/2*(2*a^3 + 
        a^2 - a + 1)*q^100 + (2*a^2 - 1)*q^103 - q^108 + (-a^3 - a^2 + a)*q^111 
        + q^113 + (-a^3 - a)*q^115 + (a^3 + a^2 + a - 2)*q^124 + (-a^2 + a + 
        1)*q^125 + O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 - q^16 - q^25 + (a + 1)*q^37 + a*q^49 + q^55 + a*q^64 + (-a - 
        1)*q^67 + (-a - 1)*q^97 + a*q^100 + (a - 1)*q^103 + (-a + 1)*q^115 - 
        q^121 + O(q^130),
    q^3 - a*q^12 + q^15 + a*q^27 - q^33 + (a - 1)*q^45 - q^48 - a*q^60 + (a - 
        1)*q^69 - q^75 + (-a - 1)*q^81 + (-a + 1)*q^99 + q^108 + (a + 1)*q^111 +
        O(q^130),
    q^5 - q^11 - a*q^20 + (a - 1)*q^23 + a*q^44 + (a + 1)*q^47 + (-a + 1)*q^53 -
        2*a*q^59 - q^80 + (a + 1)*q^92 + (a - 1)*q^113 - q^125 + O(q^130),
    q^9 + (a + 1)*q^15 + (a - 1)*q^27 + (-a - 1)*q^33 - a*q^36 - q^45 + (-a + 
        1)*q^60 - 2*q^69 - a*q^81 + q^99 + (a + 1)*q^108 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^11 + q^14 - q^20 + q^25 - q^26 - q^31 - q^34 - q^59 - q^64 - q^70 - 
        q^71 + q^80 - q^86 + 2*q^89 - q^91 - q^119 + q^121 + q^124 + O(q^130),
    q^2 - q^17 - q^32 - q^35 + q^50 + q^65 - q^68 + q^77 + q^83 + q^98 + q^107 -
        q^110 + O(q^130),
    q^4 - q^11 - q^14 - q^16 + q^20 + q^26 + q^31 - q^34 + q^49 - q^55 + q^59 - 
        q^70 + q^71 - q^80 + q^86 - 2*q^89 - q^91 + q^100 + q^119 - q^124 + 
        O(q^130),
    q^5 - q^11 - 2*q^14 + q^20 + 2*q^26 - q^44 - q^80 + 2*q^86 - 2*q^89 + 
        2*q^119 + q^125 + O(q^130),
    q^7 - q^10 - q^13 + q^22 + q^28 - q^43 - q^52 + q^73 + q^85 - q^112 - q^127 
        + O(q^130)
]
;
Bo:=
[
    q - q^4 - q^5 - q^11 + q^16 + q^20 + q^25 - 2*q^31 + q^44 - q^49 + q^55 + 
        2*q^59 - q^64 + 2*q^71 - q^80 - 2*q^89 - q^100 + q^121 + 2*q^124 - q^125
        + O(q^130),
    q^3 - q^12 - q^15 + q^27 - q^33 + q^48 + q^60 + q^75 - 2*q^93 - q^108 + 
        O(q^130),
    q^9 - q^36 - q^45 + q^81 - q^99 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
495
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 2*H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^4 + 1/2*(a - 1)*q^5 - a*q^9 + a*q^11 + 1/2*(a - 2)*q^15 - 
        a*q^16 + 1/2*a*q^20 + 1/2*a*q^25 + (a - 1)*q^31 - q^36 + q^44 + 1/2*q^45
        + (-a + 1)*q^49 - 1/2*q^55 + (-a + 1)*q^59 + 1/2*(2*a - 1)*q^60 - q^64 -
        q^71 + 1/2*(-2*a + 1)*q^75 + 1/2*q^80 + (a - 1)*q^81 - 2*q^89 + (-a + 
        1)*q^99 + 1/2*q^100 + (a + 1)*q^111 + (a - 1)*q^121 + a*q^124 - q^125 + 
        O(q^130),
    q^3 + 1/2*(-2*a + 1)*q^5 + (-a + 1)*q^12 + 1/2*(a - 1)*q^15 + 1/2*(-a - 
        1)*q^20 + 1/2*(a + 1)*q^25 - a*q^27 + a*q^33 + (a - 2)*q^37 + 1/2*(a - 
        2)*q^45 + (a + 1)*q^47 - a*q^48 + (a - 2)*q^53 + 1/2*(-a + 2)*q^55 + 
        1/2*a*q^60 + (2*a - 1)*q^67 + 1/2*a*q^75 + 1/2*(a - 2)*q^80 + (a - 
        1)*q^93 + (-a - 1)*q^97 + 1/2*(-a + 2)*q^100 + (-2*a + 1)*q^103 - q^108 
        + (-2*a + 1)*q^113 + O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^5 + (-a + 1)*q^13 - a*q^17 + (a - 1)*q^21 - q^33 - a*q^37 + (a
        - 1)*q^41 + (-a + 1)*q^53 + (-a + 1)*q^57 + a*q^65 + (a - 1)*q^73 + q^77
        + a*q^81 + q^85 + a*q^93 - a*q^105 + (-a + 1)*q^113 + O(q^118),
    q^2 + (a - 1)*q^10 + (-a + 1)*q^26 - a*q^34 + (a - 1)*q^42 - q^66 - a*q^74 +
        (a - 1)*q^82 + (-a + 1)*q^106 + (-a + 1)*q^114 + O(q^118),
    q^3 - q^7 - a*q^11 + (a - 1)*q^15 + q^19 + (a - 1)*q^27 + (a - 1)*q^31 + (-a
        + 1)*q^35 + (-a + 1)*q^39 + q^43 - a*q^51 + q^55 - q^59 - a*q^67 + 
        a*q^71 - q^79 + a*q^83 + (a - 1)*q^91 + (a - 1)*q^95 - a*q^103 + q^107 -
        a*q^111 + O(q^118),
    q^4 - q^16 + (a - 1)*q^20 - a*q^24 + (-a + 1)*q^52 + a*q^56 + q^64 - a*q^68 
        + (-a + 1)*q^80 + (a - 1)*q^84 + (a - 1)*q^88 + a*q^96 + O(q^118),
    q^6 - q^14 - a*q^22 + (a - 1)*q^30 + q^38 + (a - 1)*q^54 + (a - 1)*q^62 + 
        (-a + 1)*q^70 + (-a + 1)*q^78 + q^86 - a*q^102 + q^110 + O(q^118),
    q^8 + a*q^12 - a*q^28 - q^32 + (a - 1)*q^40 + (-a + 1)*q^44 - a*q^48 - q^60 
        + a*q^76 + (-a + 1)*q^104 - q^108 + a*q^112 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^5 + q^7 + q^9 + q^19 - q^31 - q^35 - q^41 - q^45 - 2*q^47 + q^59 + 
        q^63 - 2*q^67 + q^71 + q^81 - q^95 - q^97 - q^101 + q^103 + q^107 - 
        q^109 - q^113 + O(q^118)
]
;
Bo:=
[
    q - q^5 - q^7 + q^9 - q^19 + q^31 + q^35 - q^41 - q^45 + 2*q^47 - q^59 - 
        q^63 + 2*q^67 - q^71 + q^81 + q^95 - q^97 - q^101 - q^103 - q^107 - 
        q^109 - q^113 + O(q^118),
    q^2 - q^10 - q^14 + q^18 - q^38 + q^62 + q^70 - q^82 - q^90 + 2*q^94 + 
        O(q^118),
    q^4 - q^20 - q^28 + q^36 - q^76 + O(q^118),
    q^8 - q^32 - q^40 - q^56 + q^64 + q^72 + O(q^118),
    q^16 - q^32 - q^80 - q^112 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 15*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^8 - a*q^9 - q^10 + a*q^14 + a*q^20 + a*q^25 - a*q^28 + q^31 + (-a + 
        1)*q^35 - a*q^38 - q^49 + q^50 + q^64 + (a - 1)*q^67 - q^70 + a*q^72 - 
        q^76 + q^80 - q^81 - a*q^82 + a*q^90 - 2*q^95 + q^98 + q^100 - a*q^112 +
        O(q^118),
    q^2 - a*q^5 + a*q^7 - q^16 - a*q^18 + q^19 - q^20 - q^25 + a*q^28 + a*q^35 +
        a*q^40 - a*q^41 - q^45 + q^49 + a*q^50 - a*q^56 - q^59 + q^62 + q^63 + 
        (-a + 1)*q^70 - q^71 - a*q^76 - a*q^95 - a*q^97 - q^98 + q^100 + q^101 +
        q^103 + a*q^107 + a*q^109 + a*q^113 + O(q^118),
    q^4 + q^5 - a*q^7 - a*q^10 + a*q^14 + a*q^19 - q^25 - q^32 + q^35 - a*q^36 +
        q^38 - q^40 + a*q^41 - a*q^45 - q^49 - q^50 + a*q^56 + a*q^59 - q^63 + 
        a*q^70 - q^71 + a*q^80 - a*q^82 - q^90 - a*q^95 - a*q^97 + q^98 + 
        a*q^100 - a*q^101 + q^103 - q^107 + q^109 - a*q^112 + a*q^113 + O(q^118)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
496
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 15*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^33 - q^39 - q^47 + q^71 + q^87 + q^95 - q^103 + q^111 + O(q^118),
    q^2 + q^16 - q^18 + q^20 - q^28 - q^40 - q^50 - q^56 + q^62 - q^76 - 2*q^94 
        + q^98 + q^100 + O(q^118),
    q^3 - q^11 - q^13 + q^29 + q^37 - q^43 - q^53 + q^61 + q^75 + q^83 - q^93 - 
        q^99 - q^117 + O(q^118),
    q^4 - q^14 + q^16 - q^18 - q^28 - q^56 + q^62 + q^64 + q^66 - q^72 + q^78 - 
        q^82 - q^94 + 2*q^98 + q^100 - q^112 + O(q^118),
    q^5 - q^19 + q^35 - q^45 - q^59 - q^101 + q^107 + q^109 + O(q^118),
    q^6 - q^12 - q^22 + q^24 - q^26 + q^44 - q^48 + q^52 + q^58 + q^74 - q^86 - 
        q^88 + q^96 - q^104 - q^106 - q^116 + O(q^118),
    q^7 - q^25 + q^41 - q^49 - q^63 - q^71 + q^95 + q^97 - q^103 + q^113 + 
        O(q^118),
    q^8 - q^14 - q^16 + q^18 - q^20 + q^32 - q^36 + q^40 + 2*q^50 - q^62 - q^66 
        + q^76 - q^78 - q^82 + q^94 - q^100 - q^112 + O(q^118),
    q^9 + q^25 - q^31 - q^33 - q^39 + q^47 - q^49 + q^71 - q^81 + q^87 - q^95 - 
        q^103 + q^111 + O(q^118),
    q^10 + q^16 - q^18 - q^28 - q^32 + q^36 - q^38 - q^40 - q^50 + q^62 + q^64 +
        q^66 + q^70 - q^72 + q^78 + q^80 - q^90 - q^94 + q^98 + 2*q^100 + 
        O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
210
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
210
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^23 + a^22 - a^20 + a^16 + a^15 - a^10 - a^9 + a^5 + a^2 - 1)*q^2 + 
        (-a^15 + a^12 - a^9)*q^4 - a*q^7 + (2*a^23 + a^22 - a^19 - 2*a^18 - a^17
        - 2*a^16 - a^15 + a^14 + 2*a^13 + 2*a^12 + 2*a^11 + a^10 + a^9 - a^8 - 
        2*a^7 - 2*a^6 - 3*a^5 - a^4 + a^3 + a^2 + a + 2)*q^8 - a^17*q^9 + (a^23 
        - a^22 - a^21 - a^18 + a^15 + a^14 + a^13 - 2*a^8 - a^7 + a^3 + a + 
        1)*q^11 + (-2*a^23 + a^21 + a^19 + a^18 - a^14 - a^13 - a^12 + a^8 + a^7
        + a^5 - a^3 - 1)*q^14 + (-a^23 - a^22 - a^21 - a^20 + a^19 + 3*a^18 + 
        2*a^17 + a^16 + a^15 - a^14 - a^13 - 2*a^12 - 2*a^11 - 2*a^10 + a^8 + 
        2*a^7 + a^6 + 2*a^5 + a^4 - a^2 - a - 2)*q^16 + (-a^7 + a^4)*q^18 + 
        (-a^23 + a^20 - a^19 + a^16)*q^22 + (-a^23 + a^19 + a^18 + a^17 + a^16 -
        a^14 - a^13 - a^12 - a^11 - a^10 + a^8 + a^7 + 2*a^6 + a^5 - a - 1)*q^23
        - a^21*q^25 + (a^16 - a^13 + a^10)*q^28 + (a^21 - a^14 + a^7 - a^3 - 
        1)*q^29 + (a^20 - a^17 + a^14 - a^11 + a^8 - a^5)*q^32 + (-a^22 + a^21 +
        a^20 + a^19 - a^16 - a^14 - a^13 - a^12 + a^11 + a^10 + a^9 + a^7 - a^4 
        - a^3 - a^2 + a)*q^36 + (a^23 + a^20 - a^18 - a^16 - a^15 + a^11 + a^10 
        + a^9 + a^8 - a^5 - a^4 - a^2 + 1)*q^37 + (a^14 + a^12)*q^43 + (-a^13 + 
        a^10 - a^9 - a^7 + a^6 - a^3)*q^44 + (a^23 + a^21 - a^19 - a^18 - a^16 +
        a^14 + a^13 + a^12 - a^8 - a^6 - a^5 + a^3 + a)*q^46 + a^2*q^49 + (-a^11
        + a^8)*q^50 + (-a^23 - a^22 - a^20 - a^19 + a^18 + a^17 + a^16 + a^15 - 
        a^12 - a^11 - a^10 - a^9 + a^7 + a^5 + a^4 - 1)*q^53 + (a^23 + a^20 - 
        a^18 - a^16 - a^15 + a^11 + a^10 + a^9 + a^6 - a^5 - a^4 - a^3 - a^2 + 
        2)*q^56 + (-a^23 + a^21 - a^20 + a^18 + a^16 - a^14 - a^10 - a^9 + a^7 +
        a^5 + a^2 - 2)*q^58 + a^18*q^63 + (a^23 - a^22 - a^21 - a^20 + a^17 + 
        a^15 + a^14 + a^13 - a^12 - a^11 - a^8 - a^7 + a^5 + 2*a^4 + a^3 - a^2 -
        a)*q^64 + (a^20 + a^4)*q^67 - a^13*q^71 + (a^22 - a^19 + a^16 - 
        a^13)*q^72 + (2*a^23 + a^22 - a^21 - a^19 - a^18 - a^16 + a^14 + a^13 + 
        a^9 - a^8 - a^7 + a^3 - a^2 + 1)*q^74 + (2*a^23 + a^22 - a^18 - a^17 - 
        2*a^16 - a^15 + a^13 + a^12 + a^11 + a^10 + 2*a^9 - a^7 - a^6 - a^5 - 
        a^4 - a^2 + 1)*q^77 + (-a^23 + a^21 + a^19 + a^18 - a^14 - a^13 - a^12 +
        a^10 + a^8 + a^7 + a^5 - a^3 - 1)*q^79 + (a^23 + a^22 - a^18 - a^17 - 
        a^16 - a^15 + a^13 + a^12 + a^11 + a^10 + a^9 - a^7 - a^6 - a^5 - a^4 + 
        1)*q^81 + (a^23 + a^22 - a^18 - a^17 - a^16 - a^15 + a^13 + a^12 + a^11 
        + a^10 + a^9 - a^7 - a^6 - a^5 + a^2 - a + 1)*q^86 + (2*a^23 + a^21 - 
        a^19 - 3*a^18 - a^17 - 2*a^16 + 2*a^13 + 2*a^12 + 3*a^11 + a^10 + a^9 - 
        2*a^8 - a^7 - 2*a^6 - 2*a^5 - 2*a^4 + 2*a + 2)*q^88 + (a^23 - 2*a^21 - 
        a^15 + a^14 + a^13 - a^8 - a^7 + a^4 + a^3 - a + 1)*q^92 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^4 - a)*q^2 + (-a^5 + a^2 - a)*q^4 - a*q^7 + (-a^4 + a - 1)*q^8 - 
        a^3*q^9 + (-a^5 - a)*q^11 + (-a^5 + a^2)*q^14 + (a^5 + a)*q^16 + (a^4 + 
        1)*q^18 + (-a^4 + a^3 + a^2 + a - 1)*q^22 + (a^5 - a^4 - a^2 + a - 
        1)*q^23 + q^25 + (a^5 - a^4 + a - 1)*q^28 + (-a^3 + 1)*q^29 - a^2*q^32 +
        (-a^5 + a^4 - a)*q^36 + (a^4 - a)*q^37 + (-a^5 + 1)*q^43 + (2*a^5 - 
        2*a^4 - a^2 + 2*a - 1)*q^44 + (a^4 - a^3 + 2)*q^46 + a^2*q^49 + (a^4 - 
        a)*q^50 + (-a^4 + a^3 - a^2 + a - 1)*q^53 + (a^5 - a^2 + a)*q^56 + 
        (2*a^4 - a + 1)*q^58 + a^4*q^63 + (a^5 + a^3 - a^2 + a - 1)*q^67 + (a^5 
        - a^4 + a^3 - a^2 + a - 1)*q^71 + (-a^4 + a^3 - 1)*q^72 + (-2*a^5 + a^2 
        - a)*q^74 + (a^5 - a^4 + a^3 + a - 1)*q^77 + (-a^5 - a^3)*q^79 + (a^5 - 
        a^4 + a^3 - a^2 + a - 1)*q^81 + (a^5 + a^3 - 1)*q^86 + (a^5 + a^4 - a^3 
        - a^2 + 1)*q^88 + (-a^5 + 2*a^4 - 2*a + 1)*q^92 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^2 + 1)*q^2 + (a^3 + a)*q^4 - a*q^7 + a^3*q^8 + a^2*q^9 + (-a^2 + a - 
        1)*q^11 + (-a^3 - a)*q^14 + (a^3 + a - 1)*q^18 - a^2*q^22 + (a^3 - a^2 -
        1)*q^23 - a*q^25 + (-a^3 - a + 1)*q^28 - 2*a^3*q^29 + q^32 + (a^3 - 
        1)*q^36 + (-a^3 + a^2)*q^37 + (a^3 + a - 1)*q^43 - a^3*q^44 + (-a^2 - a 
        - 1)*q^46 + a^2*q^49 + (-a^3 - a)*q^50 + (a^3 + a - 1)*q^53 + (-a^3 + 
        a^2 - a + 1)*q^56 + (-2*a^3 + 2)*q^58 - a^3*q^63 + (a^2 + 1)*q^64 + (a^3
        - a^2 + a)*q^67 - a^3*q^71 - q^72 + a*q^74 + (a^3 - a^2 + a)*q^77 + (-a 
        + 1)*q^79 + (a^3 - a^2 + a - 1)*q^81 + (2*a^3 - a^2 + a - 2)*q^86 + 
        (-a^2 + a)*q^88 + (-a^3 - a^2 - a)*q^92 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
35*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 - q^6 + q^9 - q^12 - q^15 + q^18 + q^20 + q^24 + q^25 - q^27 + q^30 
        - q^32 + q^38 - q^40 - q^43 - q^45 + q^48 + q^49 - q^50 - q^54 - q^57 - 
        q^58 + q^60 + q^71 - q^73 + q^74 + 2*q^75 - q^79 + 2*q^87 + O(q^94),
    q^2 - q^4 - q^5 - q^6 + q^8 + q^9 + q^10 - q^16 + q^19 - q^20 - q^27 + q^36 
        + q^37 - q^38 + q^40 - q^43 + q^48 - q^57 - q^58 + q^60 - q^72 - q^73 - 
        q^74 + q^75 + 2*q^76 - q^79 - q^80 + q^83 + q^86 + q^87 - q^90 + 
        O(q^94),
    q^3 - q^4 - q^5 + q^8 + q^10 - q^15 - q^18 + q^25 + q^29 - q^38 - q^43 + 
        q^54 + q^60 - q^73 - q^74 + q^75 + q^76 - q^79 - q^80 - q^81 + q^86 + 
        q^89 + O(q^94),
    q^7 - q^35 - q^42 + q^63 - q^84 + O(q^94),
    q^14 - q^28 - q^35 - q^42 + q^56 + q^63 + q^70 + O(q^94),
    q^21 - q^28 - q^35 + q^56 + q^70 + O(q^94)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
497
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 35*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^2 + a*q^3 + (a - 1)*q^5 - q^6 - q^8 - a*q^10 - q^15 + (-a + 
        1)*q^16 + (-a + 1)*q^19 - a*q^24 + q^27 + (-a + 1)*q^30 + (a - 1)*q^37 +
        a*q^38 + (-a + 1)*q^40 + q^48 - q^49 + (a - 1)*q^54 + q^57 + q^64 - 
        a*q^73 - a*q^74 + a*q^77 + (-a + 1)*q^79 + a*q^80 + a*q^81 + (-a + 
        1)*q^89 + 2*q^91 + O(q^94),
    q^7 - a*q^11 - 2*q^13 + (a - 1)*q^14 + a*q^17 + a*q^21 + q^22 + (-a + 
        1)*q^23 + (-2*a + 2)*q^26 + a*q^31 + (-a + 1)*q^33 - q^34 + (a - 1)*q^35
        - 2*a*q^39 - q^42 + a*q^46 + (a - 1)*q^47 + (a - 1)*q^51 + a*q^53 + q^55
        - q^56 + a*q^59 + (-a + 1)*q^61 - q^62 + (-2*a + 2)*q^65 + a*q^66 - 
        a*q^67 + q^69 - a*q^70 - q^71 + 2*q^78 - q^85 + a*q^88 + (a - 1)*q^93 + 
        O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
498
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
498
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
82
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
498
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
82
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
498
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
41*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^7 - q^9 - q^11 + q^16 - q^17 + 2*q^23 + q^25 + q^27 - q^28 - 
        q^29 - q^31 - q^36 - q^37 + 2*q^41 - q^44 - q^59 - q^61 + q^63 + q^64 - 
        q^68 + q^77 + q^83 + 2*q^92 + q^99 + q^100 + q^108 - q^109 - q^112 - 
        q^113 - q^116 + q^119 - q^124 - q^127 + 2*q^131 - q^144 - q^148 - q^151 
        + q^153 - 2*q^161 + O(q^162),
    q^2 + q^8 - q^14 - q^18 - q^22 + q^32 - q^34 + 2*q^46 + q^50 + q^54 - q^56 -
        q^58 - q^62 - q^72 - q^74 + 2*q^82 - q^88 - q^118 - q^122 + q^126 + 
        q^128 - q^136 + q^154 + O(q^162),
    q^3 - q^9 + q^12 - q^21 - q^33 - q^36 + q^48 - q^51 + q^63 + 2*q^69 + q^75 +
        q^81 - q^84 - q^87 - q^93 + q^99 - q^111 + 2*q^123 - q^132 - q^144 + 
        q^153 + O(q^162),
    q^6 - q^18 + q^24 - q^42 - q^66 - q^72 + q^96 - q^102 + q^126 + 2*q^138 + 
        q^150 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
499
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
498
);
qprec:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
499
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
166
);
qprec:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
499
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
83*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
499
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
249*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^5 + q^9 + q^16 - q^20 - q^29 - q^31 + q^36 - q^43 - q^45 - q^47 
        + q^49 + q^64 - q^67 - q^73 - q^80 + q^81 + O(q^83)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
500
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 + q^14 + q^16 - q^21 - q^46 - q^49 + q^54 - q^56 - q^61 - q^64 + 
        q^69 + q^84 + q^89 - q^101 + q^121 + O(q^122),
    q^2 - q^7 - q^8 + q^23 - q^27 + q^28 + q^32 - q^42 - q^63 + 2*q^67 + q^83 + 
        q^87 - q^92 - q^98 - 2*q^103 + q^108 - q^112 + O(q^122),
    q^3 + q^7 - q^12 - q^18 - q^23 - q^28 + q^43 - q^47 + q^48 + q^58 + q^72 - 
        q^82 - q^83 + q^87 + q^92 + q^98 - q^107 + q^112 + O(q^122),
    q^6 + q^9 + q^14 - q^24 - q^29 - q^36 + q^41 - q^46 - q^49 - q^56 - q^61 + 
        q^86 + q^89 - q^94 + q^96 - q^101 - q^109 + q^116 + O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
500
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
100
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
500
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
50
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
500
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
50
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + a^2*q^4 + a^18*q^5 - a^3*q^8 + a^14*q^9 - a^19*q^10 + (a^17 - 
        a^12 + a^7 + a^6 - a^2)*q^13 + a^4*q^16 + (a^12 - a^9)*q^17 - a^15*q^18 
        + (a^15 - a^10 + a^5 - 1)*q^20 - a^11*q^25 + (-a^18 + a^13 - a^8 - a^7 +
        a^3)*q^26 + (a^16 + a^8)*q^29 - a^5*q^32 + (-a^13 + a^10)*q^34 + 
        a^16*q^36 + (-a^18 + a^13 + a^10 - a^8 + a^3)*q^37 + (-a^16 + a^11 - a^6
        + a)*q^40 + (-a^17 - a^16 + a^11 - a^6 + a)*q^41 - a^7*q^45 + (a^15 - 
        a^10 + a^5 - 1)*q^49 + a^12*q^50 + (a^19 - a^14 + a^9 + a^8 - a^4)*q^52 
        + (-a^5 + a^4)*q^53 + (-a^17 - a^9)*q^58 + (a^19 - a^14 - a^13 + a^9 - 
        a^4)*q^61 + a^6*q^64 + (a^19 - a^15 - a^14 + a^9 - a^4)*q^65 + (a^14 - 
        a^11)*q^68 - a^17*q^72 + (-a^19 - a^13)*q^73 + (a^19 - a^14 - a^11 + a^9
        - a^4)*q^74 + (a^17 - a^12 + a^7 - a^2)*q^80 - a^3*q^81 + (a^18 + a^17 -
        a^12 + a^7 - a^2)*q^82 + (-a^5 + a^2)*q^85 + (-a^17 - a^15)*q^89 + 
        a^8*q^90 + (-a^16 + a^11 - a^6 - a^3 + a)*q^97 + (-a^16 + a^11 - a^6 + 
        a)*q^98 - a^13*q^100 + (-a^19 - a)*q^101 + (-a^9 + 1)*q^104 + (a^6 - 
        a^5)*q^106 + (-a^7 - a)*q^109 + (a^10 + a^8)*q^113 + (a^18 + a^10)*q^116
        + (a^15 - a^11 - a^10 + a^5 - 1)*q^117 + a^2*q^121 + O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
500
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
500
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 - a^2*q^9 + a^2*q^16 + (a^3 - a^2 - 1)*q^26 + (a^2 - a + 1)*q^29 +
        (-a^3 + a^2 - a)*q^34 - a^3*q^36 + (-a^3 - a)*q^41 - q^49 + (a^3 + a - 
        1)*q^61 + a^3*q^64 + (a^3 - a^2)*q^74 + (a^3 - a^2 + a - 1)*q^81 + (a - 
        1)*q^89 + (-a^3 + a^2)*q^101 + (-a^2 - 1)*q^104 + (-a^3 + 1)*q^106 + 
        (a^3 + a)*q^109 + (a^3 - a^2 + a)*q^116 - a*q^121 + O(q^122),
    q^2 + a*q^8 + (a^3 - 1)*q^13 + (-a^2 + a - 1)*q^17 - a^2*q^18 + a^2*q^32 + 
        (a^2 - a)*q^37 + (a^3 - a^2 - 1)*q^52 + (-a^3 - a + 1)*q^53 + (a^2 - a +
        1)*q^58 + (-a^3 + a^2 - a)*q^68 - a^3*q^72 + (-a^3 + a^2 + 1)*q^73 + 
        (-a^3 - a)*q^82 + (-a + 1)*q^97 - q^98 + (-a^2 + a)*q^113 + (a^2 + 
        1)*q^117 + O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
500
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 + a^2*q^4 + a^3*q^8 + (a^3 - a^2 + a - 1)*q^9 + (-a^2 + a)*q^13 + 
        (a^3 - a^2 + a - 1)*q^16 + (-a^3 - a + 1)*q^17 - q^18 + (-a^3 + 
        a^2)*q^26 + (-a^3 - a)*q^29 - q^32 + (-a^3 + 1)*q^34 - a*q^36 + (a^3 - 
        1)*q^37 + (a^2 - a)*q^41 + q^49 + (a^2 - a + 1)*q^52 + (-a^3 + a^2 - 
        a)*q^53 + (-a^3 - a + 1)*q^58 + (-a^2 + a - 1)*q^61 - a*q^64 + (-a^3 + 
        a^2 + 1)*q^68 - a^2*q^72 + (a^2 - a + 1)*q^73 + (a^3 - a^2 - 1)*q^74 - 
        a^3*q^81 + (a^3 - a^2)*q^82 + (a^2 + 1)*q^89 + (a^3 + a)*q^97 + a*q^98 +
        (a^3 - a^2 - 1)*q^101 + (a^3 - a^2 + a)*q^104 + (-a + 1)*q^106 + (a^2 - 
        a)*q^109 + (a^3 - 1)*q^113 + (-a^3 + 1)*q^116 + (a - 1)*q^117 + 
        a^2*q^121 + O(q^122)
]
;
Bo:=
[
    q - a*q^2 + a^2*q^4 - a^3*q^8 + (a^3 - a^2 + a - 1)*q^9 + (a^2 - a)*q^13 + 
        (a^3 - a^2 + a - 1)*q^16 + (a^3 + a - 1)*q^17 + q^18 + (-a^3 + a^2)*q^26
        + (-a^3 - a)*q^29 + q^32 + (-a^3 + 1)*q^34 - a*q^36 + (-a^3 + 1)*q^37 + 
        (a^2 - a)*q^41 + q^49 + (-a^2 + a - 1)*q^52 + (a^3 - a^2 + a)*q^53 + 
        (a^3 + a - 1)*q^58 + (-a^2 + a - 1)*q^61 - a*q^64 + (a^3 - a^2 - 1)*q^68
        + a^2*q^72 + (-a^2 + a - 1)*q^73 + (a^3 - a^2 - 1)*q^74 - a^3*q^81 + 
        (-a^3 + a^2)*q^82 + (a^2 + 1)*q^89 + (-a^3 - a)*q^97 - a*q^98 + (a^3 - 
        a^2 - 1)*q^101 + (a^3 - a^2 + a)*q^104 + (-a + 1)*q^106 + (a^2 - 
        a)*q^109 + (-a^3 + 1)*q^113 + (-a^3 + 1)*q^116 + (-a + 1)*q^117 + 
        a^2*q^121 + O(q^122),
    q^5 - a*q^10 + a^2*q^20 - a^3*q^25 - a^3*q^40 + (a^3 - a^2 + a - 1)*q^45 + 
        (a^3 - a^2 + a - 1)*q^50 + (a^2 - a)*q^65 + (a^3 - a^2 + a - 1)*q^80 + 
        (a^3 + a - 1)*q^85 + q^90 + q^100 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
500
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
25*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
500
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 50*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^14 + q^16 - q^21 - q^46 + q^49 - q^54 - q^56 - q^61 + q^64 - 
        q^69 - q^84 - q^89 - q^101 + q^121 + O(q^122),
    q^2 - q^7 + q^8 - q^23 - q^27 - q^28 + q^32 - q^42 + q^63 + 2*q^67 - q^83 + 
        q^87 - q^92 + q^98 + 2*q^103 - q^108 - q^112 + O(q^122),
    q^3 - q^7 + q^12 - q^18 - q^23 - q^28 + q^43 + q^47 + q^48 + q^58 - q^72 + 
        q^82 - q^83 - q^87 - q^92 + q^98 + q^107 - q^112 + O(q^122),
    q^6 - q^9 - q^14 + q^24 + q^29 - q^36 + q^41 - q^46 + q^49 - q^56 - q^61 + 
        q^86 - q^89 + q^94 + q^96 - q^101 + q^109 + q^116 + O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
501
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
501
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
166
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
501
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
166
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
501
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
83*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^11 - q^18 - q^24 + q^25 - q^27 + q^36 - q^38 + q^42 + q^44 + q^48 + 
        q^49 + q^54 - q^56 - q^57 + q^62 - q^66 - q^94 - q^96 - q^97 + q^98 + 
        q^99 + O(q^110),
    q^2 - q^18 - q^19 - q^28 + q^31 - q^47 + q^49 + q^50 + q^54 - q^56 - q^77 + 
        q^81 + q^88 + q^98 + O(q^110),
    q^3 + q^27 - q^33 - q^36 - q^54 - q^63 + q^75 - q^99 + O(q^110),
    q^4 + q^11 - q^14 + q^27 - q^28 - q^36 - q^58 - q^61 + q^62 - q^77 - q^89 + 
        q^97 + q^98 - q^99 + q^100 + O(q^110),
    q^6 - q^18 - q^27 + q^54 - q^57 + q^63 + q^81 - q^84 + q^93 + O(q^110),
    q^7 - q^16 + q^27 + q^29 + q^32 - q^38 - q^44 - q^54 - q^61 - q^63 + q^76 - 
        q^77 + q^88 - q^89 - q^94 + q^107 + O(q^110),
    q^8 - q^14 - q^16 + q^19 + q^22 + q^27 + q^32 - q^38 - q^44 + q^47 - q^54 - 
        q^58 - q^61 - q^64 - q^72 + q^76 - q^81 + q^88 - q^89 - q^94 + q^108 + 
        O(q^110),
    q^9 - q^18 - q^24 - q^27 + q^36 + q^42 + q^48 + q^54 - q^57 - q^66 + q^81 - 
        q^96 - q^108 + O(q^110),
    q^12 - q^18 - q^24 - q^27 + q^33 + q^36 + q^48 + q^54 - q^57 + q^63 - q^66 -
        q^72 - q^84 - q^96 + q^99 + O(q^110),
    q^21 - q^24 - q^27 + q^36 + q^42 - q^57 - q^66 + q^87 + q^99 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
502
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
250
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
502
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
50
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
502
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
25*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
502
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
125*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^7 - q^15 + q^16 - q^17 + q^25 - q^28 - q^35 - q^39 - q^41 - q^45
        + q^49 - q^60 + q^63 + q^64 + 2*q^65 - q^68 + q^69 + q^75 + 2*q^83 - 
        q^85 - q^91 + q^93 + q^100 - q^103 + q^105 - q^112 - q^115 - q^117 + 
        2*q^119 + q^121 + O(q^124),
    q^2 + q^8 - q^14 - q^30 + q^32 - q^34 + q^50 - q^56 - q^70 - q^78 - q^82 - 
        q^90 + q^98 - q^120 + O(q^124),
    q^3 - q^7 - q^9 + q^12 - q^15 - q^17 + q^21 + q^23 + q^25 + q^27 - q^28 + 
        q^31 - q^36 - q^39 - q^41 + q^48 + q^51 - q^60 - q^63 + q^65 - q^68 - 
        q^69 + q^73 - q^81 + q^84 + q^89 + q^92 - q^93 + q^100 + q^101 - q^103 +
        q^108 - q^112 - q^115 + q^123 + O(q^124),
    q^5 - q^7 - q^9 + q^13 - q^17 + q^20 + q^21 + q^27 - q^28 - q^35 - q^36 - 
        q^41 + q^49 + q^51 + q^52 + q^67 - q^68 - q^69 - q^75 + q^79 + q^80 + 
        q^84 - q^85 - q^91 - q^93 - q^103 + q^108 - q^112 + q^113 + q^119 + 
        q^123 + O(q^124),
    q^6 - q^14 - q^18 + q^24 - q^30 - q^34 + q^42 + q^46 + q^50 + q^54 - q^56 + 
        q^62 - q^72 - q^78 - q^82 + q^96 + q^102 - q^120 + O(q^124),
    q^10 - q^14 - q^18 + q^26 - q^34 + q^40 + q^42 + q^54 - q^56 - q^70 - q^72 -
        q^82 + q^98 + q^102 + q^104 + O(q^124)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
503
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
502
);
qprec:=
84
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
503
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
251*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
84
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^12 + q^13 - q^22 - q^24 + q^25 - q^32 - q^33 + q^49 - q^54 - q^59 - 
        q^63 - q^67 - q^77 + q^83 + O(q^84),
    q^2 - q^16 + q^18 - q^22 - q^23 + q^26 - q^27 + q^28 - q^33 - q^36 - q^42 + 
        q^43 + q^47 + q^50 - q^54 - q^56 - q^61 + q^63 + q^69 + q^72 + q^73 + 
        q^78 - q^79 + O(q^84),
    q^3 - q^13 - q^14 + q^27 - q^36 - q^39 + q^44 + q^46 + q^66 + q^72 + q^75 - 
        q^83 + O(q^84),
    q^4 - q^12 - q^13 - q^14 + q^16 + q^32 + q^33 - q^48 - q^52 + q^54 - q^56 + 
        q^59 + q^64 + q^77 - q^83 + O(q^84),
    q^6 - q^12 - q^13 - q^14 + q^22 + q^23 + q^24 + q^33 - q^39 - q^42 - q^48 - 
        q^52 + q^54 + q^61 - q^83 + O(q^84),
    q^7 - q^12 - q^13 - q^14 + q^18 + q^24 + q^26 + q^28 - q^36 - q^39 - q^42 + 
        q^44 - q^52 - q^56 + q^63 + q^72 + q^77 + q^78 + q^81 - q^83 + O(q^84),
    q^8 - q^12 - q^13 - q^14 + q^16 + q^22 + q^23 - q^26 + q^27 - q^28 + q^32 + 
        q^33 - q^39 - q^43 - q^47 - q^48 - q^52 + q^54 + q^61 + q^64 + q^66 + 
        q^79 - q^83 + O(q^84),
    q^9 - q^12 - q^13 + q^22 + q^24 - q^39 - q^42 + q^63 + q^67 + q^81 - q^83 + 
        O(q^84),
    q^11 - q^13 - q^14 + q^18 + q^28 - q^36 - q^39 - q^42 + q^44 + q^46 + q^49 -
        q^52 - q^56 + q^66 + q^69 + q^72 - q^83 + O(q^84),
    q^21 - q^22 - q^23 + q^26 + q^28 - q^33 - q^36 + q^43 + q^47 - q^56 - q^61 +
        q^72 + q^78 + O(q^84)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 - a*q^3 + (a - 1)*q^4 + (a - 1)*q^6 + q^8 + (a - 1)*q^9 + a*q^11 +
        q^12 - a*q^16 - q^17 + q^18 - q^19 + (-a + 1)*q^22 - a*q^24 - a*q^25 + 
        q^27 + (a - 1)*q^32 + (-a + 1)*q^33 + a*q^34 - a*q^36 + a*q^38 + (-a + 
        1)*q^41 + a*q^43 - q^44 + (a - 1)*q^48 + (a - 1)*q^49 + (a - 1)*q^50 + 
        a*q^51 - a*q^54 + a*q^57 + (-a + 1)*q^59 + q^64 - q^66 + (-a + 1)*q^67 +
        (-a + 1)*q^68 + (a - 1)*q^72 - q^73 + (a - 1)*q^75 + (-a + 1)*q^76 - 
        a*q^81 - q^82 - 2*a*q^83 + (-a + 1)*q^86 + a*q^88 + 2*q^89 + q^96 + 
        a*q^97 + q^98 - q^99 + q^100 + (-a + 1)*q^102 - q^107 + (a - 1)*q^108 + 
        (2*a - 2)*q^113 + (-a + 1)*q^114 - q^118 - q^123 - a*q^128 + (-a + 
        1)*q^129 + (2*a - 2)*q^131 + a*q^132 - q^134 - q^136 + a*q^137 + (-a + 
        1)*q^139 + q^144 + a*q^146 + q^147 + q^150 - q^152 + (-a + 1)*q^153 + 
        O(q^162),
    q^7 - a*q^14 - a*q^21 + (a - 1)*q^28 + (a - 1)*q^42 + q^56 + (a - 1)*q^63 + 
        a*q^77 + q^84 - a*q^112 - q^119 + q^126 - q^133 + (-a + 1)*q^154 + 
        O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^7 + (-2*a + 1)*q^13 + (a - 2)*q^19 + (a - 1)*q^25 + (-a - 1)*q^31 - 
        a*q^37 + q^43 + (a - 1)*q^49 + (-a + 1)*q^67 + (a + 1)*q^73 + a*q^79 + 
        (-a + 2)*q^91 + (-a + 2)*q^103 + (a - 1)*q^109 + a*q^121 - q^127 + (-a -
        1)*q^133 + (2*a - 1)*q^139 + (-2*a + 2)*q^151 + O(q^162),
    q^2 + a*q^14 + (-2*a + 1)*q^26 + (a - 2)*q^38 + (a - 1)*q^50 + (-a - 1)*q^62
        - a*q^74 + q^86 + (a - 1)*q^98 + (-a + 1)*q^134 + (a + 1)*q^146 + 
        a*q^158 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^4 + (a - 1)*q^7 + (-a - 1)*q^10 - a*q^16 + q^22 + (2*a - 
        2)*q^25 + a*q^28 + (a + 1)*q^31 + (a - 2)*q^40 - a*q^49 + (-2*a + 
        1)*q^55 + a*q^58 - q^64 + (-a + 2)*q^70 - a*q^79 + (-a + 1)*q^88 + (-2*a
        + 1)*q^97 + 2*a*q^100 - q^106 + q^112 + (2*a - 1)*q^118 + (-a + 2)*q^124
        - q^127 + (-a + 2)*q^145 + (a - 1)*q^151 + (a - 1)*q^154 + (2*a - 
        1)*q^160 + O(q^162),
    q^2 + (-2*a + 1)*q^5 + (-a + 1)*q^8 + a*q^11 + (a - 1)*q^14 + (-a - 1)*q^20 
        + (a - 1)*q^29 - a*q^32 + (a + 1)*q^35 + q^44 + (2*a - 2)*q^50 - a*q^53 
        + a*q^56 + (a - 2)*q^59 + (a + 1)*q^62 - q^77 + (a - 2)*q^80 + (-a - 
        1)*q^83 - a*q^98 + q^107 + (-2*a + 1)*q^110 + a*q^116 + (a + 1)*q^125 - 
        q^128 + (2*a - 1)*q^131 + (-a + 2)*q^140 + 2*q^149 + (-3*a + 3)*q^155 - 
        a*q^158 + O(q^162)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 5*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^3 - q^4 + q^9 + a*q^10 + (-a + 1)*q^11 + q^12 + q^14 + q^16 + a*q^17 +
        (a - 1)*q^19 + (-a + 1)*q^26 - q^27 - a*q^30 + (a - 1)*q^33 - a*q^35 - 
        q^36 - a*q^40 + (-a + 1)*q^41 - q^42 + a*q^43 + (a - 1)*q^44 + a*q^46 - 
        q^48 - q^49 - a*q^51 - q^56 + (-a + 1)*q^57 + a*q^58 - q^64 - q^65 - 
        a*q^68 - a*q^73 + (-a + 1)*q^74 + (-a + 1)*q^76 + (a - 1)*q^78 + q^81 + 
        a*q^83 + (a - 1)*q^89 + a*q^90 + (a - 1)*q^91 - a*q^97 + (-a + 1)*q^99 +
        (a - 1)*q^104 + a*q^105 - a*q^106 + (-a + 1)*q^107 + q^108 + q^110 + (a 
        - 1)*q^113 + (-a + 1)*q^115 + a*q^120 + (a - 1)*q^123 + q^126 - a*q^129 
        + a*q^131 + (-a + 1)*q^132 + (a - 1)*q^137 - a*q^138 + (-a + 1)*q^139 + 
        a*q^140 + q^144 + (-a + 1)*q^145 + q^147 + a*q^153 + (-a + 1)*q^154 - 
        2*q^158 + a*q^160 - a*q^161 + O(q^162),
    q^2 - a*q^5 - q^6 - q^7 - q^8 + (a - 1)*q^13 + a*q^15 + q^18 + a*q^20 + q^21
        + (-a + 1)*q^22 - a*q^23 + q^24 + q^28 - a*q^29 + q^32 + a*q^34 + (a - 
        1)*q^37 + (a - 1)*q^38 + (-a + 1)*q^39 - a*q^45 + (-a + 1)*q^52 + a*q^53
        - q^54 - q^55 - a*q^60 - q^63 + (a - 1)*q^66 + a*q^69 - a*q^70 - q^72 + 
        (a - 1)*q^77 + 2*q^79 - a*q^80 + (-a + 1)*q^82 - q^84 + (-a + 1)*q^85 + 
        a*q^86 + a*q^87 + (a - 1)*q^88 + a*q^92 + q^95 - q^96 - q^98 + (-a + 
        1)*q^101 - a*q^102 + a*q^103 - a*q^109 + (-a + 1)*q^111 - q^112 + (-a + 
        1)*q^114 + a*q^116 + (a - 1)*q^117 - a*q^119 + q^125 - q^128 - q^130 + 
        (-a + 1)*q^133 + a*q^135 - a*q^136 + a*q^143 - a*q^146 + (-a + 1)*q^148 
        + a*q^149 + (a - 1)*q^151 + (-a + 1)*q^152 + (a - 1)*q^156 - a*q^159 + 
        O(q^162)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^7 - q^13 + (-a + 1)*q^19 + a*q^25 + a*q^31 + (a - 1)*q^37 - 
        q^43 - a*q^49 - 2*q^55 + a*q^67 - a*q^73 + (a - 1)*q^79 + (a - 1)*q^91 +
        (-a + 1)*q^103 + a*q^109 + (-a + 1)*q^121 + q^127 - a*q^133 + q^139 + 
        O(q^162),
    q^5 + (a - 1)*q^11 + (-a + 1)*q^35 - a*q^41 - q^47 - q^65 + a*q^71 + a*q^77 
        - a*q^83 + (-a + 1)*q^95 + (a - 1)*q^101 - a*q^113 + q^131 + (-a + 
        1)*q^143 + a*q^155 + O(q^162)
]
;
Bo:=
[
    q + (a - 1)*q^7 - q^13 + (-a + 1)*q^19 - a*q^25 + a*q^31 + (-a + 1)*q^37 - 
        q^43 - a*q^49 + (2*a - 2)*q^61 + a*q^67 + a*q^73 + (-a + 1)*q^79 + (-a +
        1)*q^91 + 2*q^97 + (-a + 1)*q^103 + a*q^109 + (a - 1)*q^121 - q^127 + 
        a*q^133 - q^139 - 2*a*q^151 - 2*a*q^157 + O(q^162),
    q^2 + (a - 1)*q^14 - q^26 + (-a + 1)*q^38 - a*q^50 + a*q^62 + (-a + 1)*q^74 
        - q^86 - a*q^98 + (2*a - 2)*q^122 + a*q^134 + a*q^146 + (-a + 1)*q^158 +
        O(q^162),
    q^3 - a*q^9 + (a - 1)*q^21 + (a - 1)*q^27 - q^39 + (-a + 1)*q^57 + q^63 - 
        a*q^75 + q^81 + a*q^93 + (-a + 1)*q^111 + a*q^117 - q^129 - a*q^147 + 
        O(q^162),
    q^6 - a*q^18 + (a - 1)*q^42 + (a - 1)*q^54 - q^78 + (-a + 1)*q^114 + q^126 -
        a*q^150 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 - a*q^7 + a*q^10 + (a - 1)*q^16 - q^22 + (a - 1)*q^28 + a*q^31 + 
        (-a + 1)*q^40 + (a - 1)*q^49 + q^55 + (-a + 1)*q^58 + q^64 + (-a + 
        1)*q^70 - 2*a*q^73 + (-a + 1)*q^79 + a*q^88 - q^97 + (2*a - 2)*q^103 - 
        q^106 + q^112 - q^118 + (-a + 1)*q^124 - q^127 + (a - 1)*q^145 + a*q^151
        + a*q^154 - q^160 + O(q^162),
    q^2 - q^5 - a*q^8 + (-a + 1)*q^11 - a*q^14 + a*q^20 + a*q^29 + (a - 1)*q^32 
        + a*q^35 - q^44 + (-a + 1)*q^53 + (a - 1)*q^56 + (-a + 1)*q^59 + a*q^62 
        - q^77 + (-a + 1)*q^80 + a*q^83 + (a - 1)*q^98 + (2*a - 2)*q^101 - q^107
        + q^110 + (-a + 1)*q^116 - a*q^125 + q^128 - q^131 + (-a + 1)*q^140 - 
        2*a*q^146 + 2*q^149 - a*q^155 + (-a + 1)*q^158 + O(q^162),
    q^3 - a*q^12 + q^18 - a*q^21 + (a - 1)*q^27 + a*q^30 - q^45 + (a - 1)*q^48 -
        q^66 - a*q^72 + (a - 1)*q^84 + a*q^93 + (-a + 1)*q^99 + q^108 + (-a + 
        1)*q^120 - a*q^126 + (a - 1)*q^147 + O(q^162),
    q^6 + (a - 1)*q^9 - q^15 - a*q^24 + (-a + 1)*q^33 + q^36 - a*q^42 + (a - 
        1)*q^54 + a*q^60 + q^63 - a*q^81 + a*q^87 - q^90 + (a - 1)*q^96 + 
        a*q^105 - q^132 + (-a + 1)*q^135 - a*q^144 + (-a + 1)*q^159 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 4*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^3 + (-a + 1)*q^4 - a*q^9 + a*q^10 - q^11 - a*q^12 + (a - 
        1)*q^14 - a*q^16 + a*q^17 + (a - 1)*q^19 + (-a + 1)*q^26 - q^27 + q^30 +
        (a - 1)*q^33 - a*q^35 - q^36 + q^40 + a*q^41 + a*q^42 + (-a + 1)*q^43 + 
        (a - 1)*q^44 + a*q^46 - q^48 + (-a + 1)*q^49 + q^51 + a*q^56 + a*q^57 - 
        q^58 - q^64 + a*q^65 + q^68 - a*q^73 - q^74 + a*q^76 - a*q^78 + (a - 
        1)*q^81 + (-a + 1)*q^83 + (a - 1)*q^89 + (-a + 1)*q^90 + (a - 1)*q^91 + 
        (a - 1)*q^97 + a*q^99 - a*q^104 - q^105 + (a - 1)*q^106 + (-a + 1)*q^107
        + (a - 1)*q^108 - a*q^110 - a*q^113 - q^115 + (-a + 1)*q^120 + q^123 + 
        q^126 - a*q^129 - q^131 + a*q^132 + q^137 + q^138 + a*q^139 - q^140 + (a
        - 1)*q^144 + (-a + 1)*q^145 - a*q^147 + (-a + 1)*q^153 + (-a + 1)*q^154 
        + (-2*a + 2)*q^158 + (-a + 1)*q^160 - a*q^161 + O(q^162),
    q^2 + (a - 1)*q^5 + (-a + 1)*q^6 - q^7 + (-a + 1)*q^8 + q^13 + a*q^15 - 
        a*q^18 + a*q^20 + (a - 1)*q^21 - q^22 + (a - 1)*q^23 - a*q^24 + (a - 
        1)*q^28 - a*q^29 - a*q^32 + a*q^34 - a*q^37 + (a - 1)*q^38 + (-a + 
        1)*q^39 + q^45 + (-a + 1)*q^52 - q^53 - q^54 + (-a + 1)*q^55 + q^60 + 
        a*q^63 + (a - 1)*q^66 + a*q^69 - a*q^70 - q^72 + q^77 + 2*q^79 + q^80 + 
        a*q^82 + a*q^84 - q^85 + (-a + 1)*q^86 - q^87 + (a - 1)*q^88 + a*q^92 - 
        a*q^95 - q^96 + (-a + 1)*q^98 + (-a + 1)*q^101 + q^102 + (-a + 1)*q^103 
        + q^109 - q^111 + a*q^112 + a*q^114 - q^116 - a*q^117 - a*q^119 + (a - 
        1)*q^125 - q^128 + a*q^130 + (-a + 1)*q^133 + (-a + 1)*q^135 + q^136 - 
        q^143 - a*q^146 - q^148 + (-a + 1)*q^149 + (a - 1)*q^151 + a*q^152 - 
        a*q^156 + (a - 1)*q^159 + O(q^162)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 5*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 + q^25 - 2*q^37 - 2*q^43 + q^49 + 2*q^67 + 2*q^79 - 2*q^109 - q^121 
        + 2*q^127 - 2*q^151 + O(q^162),
    q^2 - q^14 + q^50 - 2*q^74 - 2*q^86 + q^98 + 2*q^134 + 2*q^158 + O(q^162),
    q^4 - q^16 - q^28 + q^64 + q^100 + q^112 - 2*q^148 + O(q^162),
    q^8 - q^32 - q^56 + q^128 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^8 - q^11 - q^14 + q^16 - q^22 - q^23 - q^25 - q^28 + q^29 + q^44 - 
        q^46 + q^49 + q^53 + q^58 + q^71 - q^77 - 2*q^79 + q^88 - q^92 + q^106 +
        q^107 + q^113 - q^116 - q^121 + 2*q^127 + q^128 - q^137 + q^142 - q^149 
        - q^154 + q^161 + O(q^162),
    q^2 - q^8 + 2*q^11 + q^14 - 2*q^29 + q^32 - 2*q^44 - q^50 - 2*q^53 - q^56 + 
        2*q^77 + q^98 - 2*q^107 + 2*q^116 - q^128 + 2*q^149 - 2*q^158 + 
        O(q^162),
    q^4 - q^7 + q^8 - q^11 - q^14 + q^22 - q^23 + q^29 + q^44 - q^46 + q^53 - 
        q^58 + q^64 + q^71 - q^77 - q^88 - q^92 - q^100 - q^106 + q^107 - q^112 
        + q^113 - q^116 + 2*q^121 + q^128 - q^137 + q^142 - q^149 + 2*q^151 + 
        q^154 + q^161 + O(q^162)
]
;
Bo:=
[
    q - q^2 + q^4 - q^7 - q^8 + q^14 + q^16 + 2*q^23 - q^25 - q^28 - q^32 - 
        2*q^46 + q^49 + q^50 + q^56 + q^64 - 2*q^71 - 2*q^79 + 2*q^92 - q^98 - 
        q^100 - q^112 - 2*q^113 + q^121 + 2*q^127 - q^128 + 2*q^137 + 2*q^142 + 
        2*q^151 + 2*q^158 - 2*q^161 + O(q^162),
    q^3 - q^6 + q^12 - q^21 - q^24 - q^27 + q^42 + q^48 + q^54 + 2*q^69 - q^75 -
        q^84 - q^96 - q^108 - 2*q^138 + q^147 + q^150 + O(q^162),
    q^9 - q^18 + q^36 - q^63 - q^72 - q^81 + q^126 + q^144 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 + (a - 1)*q^14 + q^15 - a*q^16 - a*q^18 + (-a + 1)*q^23 - 
        a*q^25 + (a - 1)*q^30 + (a - 1)*q^39 + (a - 1)*q^49 + (-a + 1)*q^50 - 
        a*q^56 - a*q^57 + (a - 1)*q^60 - a*q^63 + q^64 + a*q^65 + q^72 + q^78 + 
        q^81 + a*q^92 + (2*a - 2)*q^95 + q^100 + (a - 1)*q^105 + q^114 - a*q^120
        + (a - 1)*q^121 - q^127 + (-a + 1)*q^130 - a*q^135 - 2*a*q^137 + a*q^142
        + a*q^151 - a*q^156 + (-a + 1)*q^158 + O(q^162),
    q^2 + q^7 + (a - 1)*q^8 + (a - 1)*q^9 + q^15 - q^25 + (a - 1)*q^28 + q^30 - 
        a*q^32 - a*q^36 - a*q^39 + (-a + 1)*q^46 - a*q^50 - a*q^57 + (a - 
        1)*q^60 - q^65 + (-a + 1)*q^71 + (a - 1)*q^78 - q^79 + a*q^95 + (a - 
        1)*q^98 + (-a + 1)*q^100 + q^105 - a*q^112 + a*q^113 - a*q^114 + (a - 
        1)*q^120 - a*q^126 + q^128 + a*q^130 + (a - 1)*q^135 + q^144 + q^156 + 
        (-a + 1)*q^161 + O(q^162),
    q^3 + (-a + 1)*q^6 + (-a - 1)*q^10 + (a - 1)*q^12 + (a - 2)*q^13 + (-a + 
        1)*q^21 + a*q^24 + (a + 1)*q^26 + a*q^27 + (-a - 1)*q^35 + (2*a - 
        1)*q^38 + (-a + 2)*q^40 + (a - 1)*q^42 + (-a + 2)*q^45 - a*q^48 + (-2*a 
        + 1)*q^52 - a*q^54 + (a - 2)*q^59 + (-a + 1)*q^69 - q^75 + (-2*a + 
        1)*q^83 + a*q^84 + (a + 1)*q^91 - q^96 + (2*a - 1)*q^101 + (a - 2)*q^104
        - q^108 + (a - 2)*q^117 + (a + 1)*q^118 + (-a + 2)*q^122 + (a + 1)*q^125
        + (-a + 2)*q^131 + (2*a - 1)*q^133 - a*q^138 + (-a + 2)*q^139 + (-a + 
        2)*q^140 + (a - 1)*q^147 - a*q^150 + (-a - 1)*q^152 + (2*a - 1)*q^160 + 
        O(q^162),
    q^5 - a*q^6 + (a - 1)*q^10 + (a - 1)*q^13 - a*q^19 + (a - 1)*q^20 - a*q^21 +
        q^24 + q^26 + q^27 + (a - 1)*q^35 + q^38 - a*q^40 - a*q^45 - a*q^52 + (a
        - 1)*q^59 + (a - 1)*q^61 + (a - 1)*q^70 + a*q^75 + q^76 - a*q^80 - 
        a*q^83 + q^84 - a*q^90 + q^91 + (a - 1)*q^96 + q^101 + (a - 1)*q^104 + 
        (a - 1)*q^108 + (-a + 1)*q^115 + (a - 1)*q^117 + q^118 - a*q^122 + (-a +
        1)*q^125 - a*q^131 + q^133 - q^138 - a*q^139 - a*q^140 + (a - 1)*q^150 +
        (a - 1)*q^152 + q^157 + q^160 + O(q^162)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^25 - q^49 + q^121 + O(q^162),
    q^2 - q^32 - q^44 - q^50 + q^56 + q^92 - q^98 + q^116 + O(q^162),
    q^4 - q^22 + q^46 - q^58 - q^64 - q^88 - q^100 + q^106 + q^112 + q^142 + 
        q^154 + O(q^162),
    q^7 - 2*q^43 + 2*q^151 + O(q^162),
    q^8 - q^14 - q^44 + 2*q^86 + q^92 - q^116 - q^128 + O(q^162),
    q^11 - q^23 - q^71 + q^107 + O(q^162),
    q^16 + q^22 - q^28 - q^46 - q^58 - q^88 + q^106 - q^142 + q^154 + O(q^162),
    q^29 - q^53 - q^77 - q^113 + q^137 + q^149 + q^161 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
504
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^16 + q^22 + q^25 - q^28 - q^46 - q^49 + q^58 - 2*q^67 + q^88 - q^106 -
        q^121 + q^142 + 2*q^148 + q^154 + O(q^162),
    q^2 - q^11 - q^23 + q^29 - q^32 + q^44 + q^50 - q^53 - q^56 + q^71 + q^77 - 
        q^92 - q^98 + q^107 + q^113 + q^116 - 2*q^134 + q^137 - q^149 - q^161 + 
        O(q^162),
    q^4 + q^7 - q^22 - 2*q^37 - q^46 + q^58 - q^64 + q^88 + q^100 - q^106 + 
        2*q^109 - q^112 + q^142 - 2*q^151 + q^154 + O(q^162),
    q^8 - q^11 + q^14 + q^23 - q^29 - q^44 + q^53 - q^71 - 2*q^74 - q^77 - q^92 
        + q^107 + q^113 + q^116 - q^128 + q^137 + q^149 - q^161 + O(q^162)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
100
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
100
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
100
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
100
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
25*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 25*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + q^5 + a*q^9 + (-a - 1)*q^11 - q^16 + a*q^20 + q^25 + (-a + 
        1)*q^29 - q^36 + (-a - 1)*q^41 + (-a + 1)*q^44 + a*q^45 + a*q^49 + (-a -
        1)*q^55 + (-a - 1)*q^59 + (-a - 1)*q^61 - a*q^64 + 2*q^71 - 2*q^79 - 
        q^80 - q^81 + (a + 1)*q^89 + (-a + 1)*q^99 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
505
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 50*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + q^5 - a*q^9 + (a - 1)*q^13 - q^16 + (a + 1)*q^17 - 2*a*q^19 + 
        a*q^20 + (a - 1)*q^23 + q^25 + q^36 + (-a - 1)*q^37 + (-a + 1)*q^43 - 
        a*q^45 + (-a - 1)*q^47 + a*q^49 + (-a - 1)*q^52 - a*q^64 + (a - 1)*q^65 
        + (a - 1)*q^68 - 2*q^71 + 2*q^76 - q^80 - q^81 + (a + 1)*q^85 + (-a - 
        1)*q^92 - 2*a*q^95 + (-a - 1)*q^97 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
506
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
506
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
506
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
506
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
110
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
506
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
110
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
506
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a^8 + a^2)*q^3 + a^4*q^4 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 - a^2 + a
        - 1)*q^5 + (a^9 - a^8 + a^7 - a^6 + a^3 - a^2 + a - 1)*q^9 - a^9*q^11 + 
        (a^6 - a)*q^12 + (-a^7 - a^5 - a + 1)*q^15 + a^8*q^16 + (-a^7 - 
        a^3)*q^20 - a^9*q^23 + (-a^9 + a^6 + a^2)*q^25 + (-a^7 + a^6 + a^2 - 
        a)*q^27 + (-a^7 - a^5)*q^31 + (a^6 + 1)*q^33 + (-a^9 + a^8 - a^3)*q^36 +
        (a^6 - a^3)*q^37 + a^2*q^44 + (-a^9 + a^8 - a^7 + a^4 - a^3 + a^2)*q^45 
        + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 - 1)*q^47 + (a^9 - a^8 
        + a^7 - a^6 - a^4 + a^3 - a^2 + a - 1)*q^48 - a^5*q^49 + (a^4 - a)*q^53 
        + (a^8 - a)*q^55 + (a^9 - a^8 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 
        1)*q^59 + (-a^9 - a^5 + a^4 + 1)*q^60 - a*q^64 + (a^9 - a^8 + a^7 - a^6 
        - a^4 + a^3 - a^2 + a - 1)*q^67 + (a^6 + 1)*q^69 + (a^4 + 1)*q^71 + (a^9
        + a^7 + a^5 - a^2 + a)*q^75 + (-a^7 + 1)*q^80 + (a^7 - a^6 + a^5 - a^2 +
        a - 1)*q^81 + (a^8 + a^2)*q^89 + a^2*q^92 + (-a^9 - a^7 + a^4 + 
        a^2)*q^93 + (a^2 + 1)*q^97 + (a^8 - a^3 + a^2)*q^99 + (a^9 - a^8 + a^7 +
        a^5 - a^4 + a^3 + a - 1)*q^100 + (a^4 - a^3)*q^103 + (a^9 - a^8 + a^7 - 
        a^4 + a^3 - a^2 + a)*q^108 + (a^8 - a^5 - a^3 + 1)*q^111 + (-a^3 - 
        a)*q^113 + (a^8 - a)*q^115 - a^7*q^121 + (-a^9 + 1)*q^124 + (-a^9 + a^8 
        - a^5 - a)*q^125 + (a^9 - a^8 + a^7 - a^6 + a^5 + a^3 - a^2 + a - 
        1)*q^132 + (-a^8 + a^7 - a^5 + a^3 - a^2)*q^135 + (a^6 - a^5)*q^137 + 
        O(q^138),
    q^2 + (a^8 + a^2)*q^6 + a^4*q^8 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 - a^2 +
        a - 1)*q^10 + (a^9 - a^8 + a^7 - a^6 + a^3 - a^2 + a - 1)*q^18 - 
        a^9*q^22 + (a^6 - a)*q^24 + (-a^7 - a^5 - a + 1)*q^30 + a^8*q^32 + (-a^7
        - a^3)*q^40 - a^9*q^46 + (-a^9 + a^6 + a^2)*q^50 + (-a^7 + a^6 + a^2 - 
        a)*q^54 + (-a^7 - a^5)*q^62 + (a^6 + 1)*q^66 + (-a^9 + a^8 - a^3)*q^72 +
        (a^6 - a^3)*q^74 + a^2*q^88 + (-a^9 + a^8 - a^7 + a^4 - a^3 + a^2)*q^90 
        + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 - 1)*q^94 + (a^9 - a^8 
        + a^7 - a^6 - a^4 + a^3 - a^2 + a - 1)*q^96 - a^5*q^98 + (a^4 - a)*q^106
        + (a^8 - a)*q^110 + (a^9 - a^8 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 
        1)*q^118 + (-a^9 - a^5 + a^4 + 1)*q^120 - a*q^128 + (a^9 - a^8 + a^7 - 
        a^6 - a^4 + a^3 - a^2 + a - 1)*q^134 + O(q^138)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
506
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 - q^4 + q^8 + q^12 - q^13 + q^23 - q^24 + q^25 + q^27 - q^29 - q^31 
        - q^32 + q^39 - q^41 - q^47 + q^49 + q^52 + 2*q^59 + q^64 - q^69 - q^71 
        - q^73 - q^75 - q^81 + q^87 - q^92 + q^93 + q^96 - q^100 + 2*q^101 - 
        q^104 - q^108 + q^116 + q^121 + q^123 + q^124 - q^127 - q^131 + 
        O(q^138),
    q^2 - q^4 - q^6 + q^12 + q^16 - q^26 - q^32 + q^46 - q^48 + q^50 + q^52 + 
        q^54 - q^58 - q^62 + q^78 - q^82 - q^92 - q^94 + q^96 + q^98 - q^100 - 
        q^108 + q^116 + 2*q^118 + q^124 + q^128 + O(q^138),
    q^11 - q^33 - q^44 + q^88 + q^132 + O(q^138),
    q^22 - q^44 - q^66 + q^132 + O(q^138)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
506
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^3 + q^4 + q^9 - q^12 + q^16 + q^25 - q^27 + q^36 - 2*q^43 - q^48 - 
        q^49 - 2*q^61 + q^64 - q^75 - 2*q^79 + q^81 + O(q^95)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
156
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^10*q^3 + a*q^4 + (a^11 - a^5)*q^7 - a^7*q^9 - a^11*q^12 - q^13 + 
        a^2*q^16 + (a^7 + a^6)*q^19 + (a^8 - a^2)*q^21 + a^9*q^25 - a^4*q^27 + 
        (a^11 - a^10 + a^9 - a^8 + a^7 - 2*a^6 + a^5 - a^4 + a^3 - a^2 + a - 
        1)*q^28 + (a^5 - a^3)*q^31 - a^8*q^36 + (-a^11 + a^10 - 2*a^9 + a^8 - 
        a^7 + a^6 - a^5 + a^4 - a^3 + a^2 - a + 1)*q^37 + a^10*q^39 + (a^4 - 
        a)*q^43 + (-a^11 + a^10 - a^9 + a^8 - a^7 + a^6 - a^5 + a^4 - a^3 + a^2 
        - a + 1)*q^48 + (a^10 - a^9 + a^3)*q^49 - a*q^52 + (a^4 + a^3)*q^57 + 
        (-a^6 - a^4)*q^61 + (a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + 2*a^5 - a^4 +
        a^3 - a^2 + a - 1)*q^63 + a^3*q^64 + (-a^8 - a^3)*q^67 + (-a^8 + 
        a^4)*q^73 + a^6*q^75 + (a^8 + a^7)*q^76 + (a^9 - a^2)*q^79 - a*q^81 + 
        (a^9 - a^3)*q^84 + (-a^11 + a^5)*q^91 + (a^2 - 1)*q^93 + O(q^95)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^7*q^3 + a^2*q^4 + (a^10 - a^9)*q^7 - a*q^9 - a^9*q^12 + q^13 + 
        a^4*q^16 + (a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 
        - 1)*q^19 + (a^4 - a^3)*q^21 - a^5*q^25 + a^8*q^27 + (-a^10 + a^9 - a^8 
        + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^28 + (a^10 + a^6)*q^31 - 
        a^3*q^36 + (-a^11 - a^5)*q^37 - a^7*q^39 + (a^8 + a^2)*q^43 - a^11*q^48 
        + (-a^7 + a^6 - a^5)*q^49 + a^2*q^52 + (a^8 + a^6)*q^57 + (a^11 - a^10 +
        a^9 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^61 + (-a^11 + 
        a^10)*q^63 + a^6*q^64 + (a^6 - a^3)*q^67 + (a^8 - a^3)*q^73 + (a^11 - 
        a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^75 + 
        (-a^3 - a)*q^76 + (-a^5 + a^4)*q^79 + a^2*q^81 + (a^6 - a^5)*q^84 + 
        (a^10 - a^9)*q^91 + (a^4 + 1)*q^93 + O(q^95)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^3 + a*q^4 - a*q^9 + q^12 + (a - 1)*q^16 - q^25 - q^27 + (-a +
        1)*q^36 - 2*a*q^43 + a*q^48 + (a - 1)*q^49 + 2*a*q^61 - q^64 + (a - 
        1)*q^75 - 2*q^79 + (a - 1)*q^81 + O(q^95)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
39*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 52*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^3 + (a - 1)*q^4 + (a - 1)*q^9 - q^12 - a*q^16 + q^25 - q^27 - a*q^36
        + (-2*a + 2)*q^43 + (-a + 1)*q^48 + a*q^49 + (-2*a + 2)*q^61 + q^64 + 
        a*q^75 - 2*q^79 - a*q^81 + O(q^95)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
507
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 78*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 - q^4 + q^9 + q^12 + q^16 - q^25 - q^27 - q^36 + 2*q^43 - q^48 + 
        q^49 - 2*q^61 - q^64 + q^75 - 2*q^79 + q^81 + O(q^95),
    q^13 - q^39 - q^52 + O(q^95)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
126
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
126
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 42*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
508
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
63*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
124
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^17 - q^19 + q^25 - q^31 - q^37 + q^49 - q^61 - q^71 + q^81 - 
        q^107 + O(q^124),
    q^2 + q^18 - q^32 - q^34 - q^38 - q^44 + q^50 - q^52 - q^62 + q^64 + q^68 - 
        q^74 + q^76 + q^98 - q^122 + O(q^124),
    q^4 - q^32 + q^36 - q^44 - q^52 - q^88 + q^100 - q^104 + O(q^124),
    q^8 + q^22 + q^26 - q^32 - q^34 - q^38 - q^44 - q^52 - q^62 + q^68 + q^72 - 
        q^74 + q^76 + q^82 - q^88 + q^94 - q^104 - q^122 + O(q^124),
    q^11 + q^13 - q^17 - q^19 - q^31 - q^37 + q^41 + q^47 - q^61 - q^71 + q^73 +
        q^79 + q^99 + q^103 - q^107 + q^113 + q^117 - q^121 + O(q^124),
    q^16 + q^22 + q^26 - q^32 - q^34 - q^38 - q^62 - q^74 + q^82 - q^88 + q^94 -
        q^104 - q^122 + O(q^124)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
509
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
508
);
qprec:=
85
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
509
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
127*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
85
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + 1/2*(a^3 - a^2 + a - 1)*q^6 + a*q^9 + 1/2*(-a^3 + a^2 + a - 1)*q^10 - 
        a^3*q^15 + q^16 + (a^2 - 1)*q^19 + 1/2*(a^3 - a^2 - a + 1)*q^24 - a*q^25
        + (a^3 - a^2)*q^31 + 1/2*(-a^3 + a^2 - a + 1)*q^34 + 1/2*(a^3 - a^2 + a 
        - 1)*q^40 + a^3*q^49 - a*q^51 + 1/2*(-a^3 + a^2 - a - 1)*q^54 + (-a^3 - 
        1)*q^61 + (-a^3 - a)*q^64 + (-a^2 + a)*q^79 + a^2*q^81 + a^3*q^85 + 
        1/2*(a^3 + a^2 - a + 1)*q^90 + (-a^2 + a - 1)*q^94 + 1/2*(a^3 + a^2 - a 
        - 1)*q^96 + a^2*q^106 + (-a^2 - a)*q^109 + (-a + 1)*q^114 - a^3*q^121 + 
        q^135 + 1/2*(-a^3 + a^2 + a - 1)*q^136 + (a + 1)*q^139 + (a - 1)*q^141 +
        a*q^144 + 1/2*(a^3 - a^2 + a + 1)*q^150 + (-a^3 + 1)*q^159 + 1/2*(a^3 + 
        a^2 + a + 1)*q^160 - a^2*q^166 - q^169 + (a^3 - a)*q^171 + (-a^3 + 
        1)*q^181 + (-a^3 + a - 1)*q^186 + (a^3 - a^2)*q^190 + (a^3 + a^2)*q^199 
        + O(q^202),
    q^2 + (-a^3 - a^2 - a)*q^8 + (a^3 - 1)*q^12 + a*q^18 + (a^2 + a)*q^20 - 
        a^3*q^30 + (a^3 - a - 1)*q^32 + (a^2 - 1)*q^38 + (a^3 + a^2 + a + 
        1)*q^48 - a*q^50 + (a^3 - a^2)*q^62 + (-a^3 + 1)*q^68 + (-a^3 - a^2 + 
        1)*q^72 + (-a^3 - a^2 + a + 1)*q^80 + a^3*q^98 - a*q^102 + (-a - 
        1)*q^108 + (-a^2 - a - 1)*q^120 + (-a^3 - 1)*q^122 + a^2*q^128 + (a^2 + 
        2*a + 1)*q^152 + (-a^2 + a)*q^158 + a^2*q^162 + a^3*q^170 + (a^3 + 
        a^2)*q^180 + (-a^2 - 1)*q^188 + (-a^3 + 1)*q^192 + (a^3 + a^2 - 1)*q^200
        + O(q^202),
    q^3 - a^2*q^5 + (-a - 1)*q^8 + a^2*q^12 - q^17 + q^20 + a*q^27 + (a^3 + a^2 
        + a - 1)*q^32 - a^3*q^45 + (a^3 + 1)*q^47 + (-a^3 + a + 1)*q^48 + (-a^3 
        - a^2)*q^53 + (a^2 - 1)*q^57 - a^2*q^68 + (-a^2 - a)*q^72 - a*q^75 + 
        (-a^3 - a^2 - a)*q^80 + (a^3 + a^2)*q^83 + (a^3 - a^2)*q^93 + (a^2 + 
        1)*q^95 + (-a^3 - a)*q^107 + a^3*q^108 + (a^2 - 1)*q^113 + (a^3 - 
        1)*q^120 + a^3*q^125 + (a + 1)*q^128 + (a^2 - a)*q^137 + a^3*q^147 + 
        (-a^3 - a^2 + a + 1)*q^152 - a*q^153 + (a - 1)*q^155 + (-a^3 + a)*q^167 
        + (-a^3 + a)*q^173 + a*q^180 + (-a^3 - 1)*q^183 + (a^2 - a)*q^188 + 
        (-a^3 - a^2 - a)*q^192 + (a^2 + a)*q^200 + O(q^202),
    q^4 + 1/2*(a^3 - a^2 - a + 1)*q^6 + 1/2*(a^3 - a^2 + a - 1)*q^10 + (-a^3 - 
        a)*q^16 + 1/2*(a^3 + a^2 - a - 1)*q^24 + 1/2*(-a^3 + a^2 + a - 1)*q^34 +
        a*q^36 + 1/2*(a^3 + a^2 + a + 1)*q^40 + 1/2*(-a^3 - a^2 + a - 1)*q^54 - 
        a^3*q^60 - q^64 + (a^2 - 1)*q^76 + 1/2*(-a^3 + a^2 - a - 1)*q^90 + (a^3 
        - a^2 + 1)*q^94 + 1/2*(a^3 + a^2 + a + 1)*q^96 - a*q^100 - q^106 + (-a^3
        + a^2)*q^114 + (a^3 - a^2)*q^124 + 1/2*(-a^3 - a^2 + a + 1)*q^136 + 
        (-a^2 + 1)*q^144 + 1/2*(a^3 + a^2 - a + 1)*q^150 + 1/2*(-a^3 - a^2 + a +
        1)*q^160 + q^166 + (a^3 - a^2 + a)*q^186 + (-a + 1)*q^190 + a^3*q^196 + 
        O(q^202)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + 1/2*(-a + 1)*q^6 + a*q^9 + 1/2*(a - 1)*q^10 - a*q^15 - q^16 + 1/2*(-a + 
        1)*q^24 + a*q^25 + (-a - 1)*q^31 + 1/2*(-a + 1)*q^34 + 1/2*(a - 1)*q^40 
        + (a + 1)*q^46 - a*q^49 + a*q^51 + 1/2*(a + 1)*q^54 + (-a + 1)*q^61 - 
        2*q^69 + (a - 1)*q^79 - q^81 - a*q^85 + 1/2*(-a - 1)*q^90 - a*q^94 + 
        1/2*(a - 1)*q^96 - q^106 + (a - 1)*q^109 + 2*q^115 - a*q^121 + q^135 + 
        1/2*(-a + 1)*q^136 + (a + 1)*q^139 + (a + 1)*q^141 - a*q^144 + 1/2*(a + 
        1)*q^150 + 2*a*q^151 + (-a + 1)*q^159 + 1/2*(-a + 1)*q^160 - q^166 + 
        q^169 + (-a + 1)*q^181 + (a + 1)*q^184 - q^186 + (-a - 1)*q^199 + 
        O(q^202),
    q^2 - q^8 + (-a + 1)*q^12 + a*q^18 + (a - 1)*q^20 - a*q^30 - q^32 + a*q^50 +
        (-a - 1)*q^62 + (-a + 1)*q^68 - a*q^72 + (2*a + 2)*q^92 - a*q^98 + 
        a*q^102 + (a + 1)*q^108 + a*q^120 + (-a + 1)*q^122 + q^128 - 2*q^138 + 
        (a - 1)*q^158 - q^162 - a*q^170 + (-a - 1)*q^180 - 2*a*q^188 + (a - 
        1)*q^192 - a*q^200 + O(q^202),
    q^3 - q^5 + (-a - 1)*q^8 + q^12 + q^17 - q^20 + 2*a*q^23 + a*q^27 - a*q^45 +
        (-a + 1)*q^47 - q^48 + (-a - 1)*q^53 + q^68 + (-a + 1)*q^72 + a*q^75 + 
        q^80 + (-a - 1)*q^83 + 2*a*q^92 + (-a - 1)*q^93 + a*q^108 + (a - 
        1)*q^120 - a*q^125 + (a + 1)*q^128 + (a - 1)*q^137 - a*q^147 + a*q^153 +
        (a + 1)*q^155 - a*q^180 + (-a + 1)*q^183 + (-a + 1)*q^188 - q^192 - 
        2*a*q^197 + (-a + 1)*q^200 + O(q^202),
    q^4 + 1/2*(a - 1)*q^6 + 1/2*(-a + 1)*q^10 + 1/2*(-a + 1)*q^24 + 1/2*(a - 
        1)*q^34 + a*q^36 + 1/2*(a - 1)*q^40 + (-a - 1)*q^46 + 1/2*(-a - 1)*q^54 
        - a*q^60 - q^64 + 1/2*(a + 1)*q^90 + a*q^94 + 1/2*(-a + 1)*q^96 + 
        a*q^100 + q^106 + (-a - 1)*q^124 + 1/2*(-a + 1)*q^136 + 1/2*(-a - 
        1)*q^150 + 1/2*(a - 1)*q^160 + q^166 + (a + 1)*q^184 + q^186 - a*q^196 +
        O(q^202)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
510
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
202
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - 1/2*q^16 + 1/2*q^17 - q^18 + 1/2*q^19 - 1/2*q^21 - 3/2*q^30 + 1/2*q^32 -
        1/2*q^33 - q^34 - 1/2*q^35 + q^36 + 3/2*q^38 + 1/2*q^42 - 1/2*q^47 - 
        1/2*q^49 - q^50 - 1/2*q^51 - 1/2*q^53 - 1/2*q^55 + 1/2*q^60 + q^66 + 
        q^69 + q^70 + q^72 - 3/2*q^76 + 1/2*q^77 + q^81 + q^83 - 1/2*q^84 - 
        1/2*q^85 - 1/2*q^87 + q^94 - 1/2*q^98 + q^100 - 1/2*q^102 + q^106 + 
        1/2*q^110 - 1/2*q^111 + q^115 + q^120 - 1/2*q^121 - 1/2*q^123 - q^128 + 
        q^135 + 1/2*q^136 - 1/2*q^137 + q^138 - 3/2*q^144 - 1/2*q^145 - 
        3/2*q^151 - 3/2*q^152 + 1/2*q^153 - q^154 - 2*q^166 - 1/2*q^168 + q^169 
        - 1/2*q^170 - 3/2*q^171 + q^174 - 1/2*q^185 - 1/2*q^189 + 1/2*q^196 + 
        q^200 + O(q^202),
    q^2 + q^18 - q^32 - q^38 - q^42 + q^50 - q^60 - q^68 - q^110 + q^128 + q^132
        + q^140 + q^162 + q^188 + O(q^202),
    q^3 + q^11 + q^14 + q^17 + q^20 + q^22 - 2*q^23 - 2*q^24 - q^27 - q^28 + 
        q^29 + q^34 - q^40 + q^41 - 2*q^44 - 2*q^45 - 2*q^46 - q^51 - 2*q^54 + 
        q^56 + 2*q^57 + q^58 - q^68 - 2*q^71 + q^74 - q^75 + q^82 - 2*q^90 + 
        2*q^92 + 3*q^95 + 3*q^96 + q^99 - q^102 + q^105 - 2*q^107 + 2*q^108 + 
        q^112 + 2*q^113 + 3*q^114 - 2*q^116 + q^119 - 2*q^125 + q^126 - 2*q^131 
        - q^136 + q^141 - 2*q^142 + q^146 - q^147 - q^148 - 2*q^150 - q^153 + 
        q^159 + 2*q^160 - 2*q^164 - 2*q^167 - q^170 - 2*q^173 + q^176 + 3*q^180 
        + 2*q^184 + 3*q^190 - q^192 - 2*q^194 - 2*q^197 + q^198 + O(q^202),
    q^4 - q^16 - q^30 - q^34 + q^36 + q^66 + q^70 - q^76 - q^84 + q^94 + q^100 +
        q^106 - q^144 - q^154 - 2*q^166 + q^174 + O(q^202),
    q^5 - q^11 - q^20 + q^24 - q^29 - q^41 + q^44 + q^45 + q^51 - q^56 + 2*q^71 
        - q^95 - q^96 - q^99 - q^105 + q^116 - q^119 + q^125 + 2*q^131 - q^141 -
        q^159 + q^164 - q^180 + O(q^202),
    q^6 - q^14 - q^20 + q^44 + q^54 - q^74 + q^80 - q^96 - q^114 + q^116 - q^126
        - q^146 + q^150 + q^164 + q^170 - q^176 - q^180 + 2*q^194 + O(q^202),
    q^7 + q^11 + q^17 - 2*q^23 - q^24 - 2*q^27 - q^28 + q^29 + q^37 - q^40 + 
        q^41 - q^44 - 2*q^45 + q^48 - q^51 + q^56 + 3*q^57 + q^63 - q^68 - 
        2*q^71 + q^73 - 2*q^75 + q^80 - q^85 + q^88 + 2*q^92 + 3*q^95 + q^96 - 
        2*q^97 + q^99 + q^105 - 2*q^107 + 2*q^108 + 2*q^113 - q^116 + q^119 - 
        2*q^125 - 2*q^131 - q^133 + q^141 - q^147 - q^148 - q^153 + q^159 + 
        q^160 + q^163 - q^164 + q^165 - 2*q^167 - 2*q^173 + q^175 + 2*q^180 + 
        q^187 - 2*q^192 - 2*q^193 - 2*q^197 + O(q^202),
    q^8 + 2*q^18 + q^30 - 2*q^32 - 3*q^38 - q^42 + 2*q^50 - q^60 - q^68 - q^72 +
        q^98 + q^102 - q^110 - q^120 + 2*q^128 + q^132 - 2*q^138 + q^140 + 
        2*q^152 + q^170 + q^188 - q^200 + O(q^202),
    q^9 - 1/2*q^16 - 1/2*q^17 + q^18 - 3/2*q^19 - 1/2*q^21 + q^25 + 1/2*q^30 - 
        1/2*q^32 + 1/2*q^33 + 1/2*q^35 - q^36 - 3/2*q^38 - 1/2*q^42 + 1/2*q^47 +
        1/2*q^49 + q^50 + 1/2*q^51 + 1/2*q^53 - 1/2*q^55 - 1/2*q^60 + q^64 - 
        q^69 - q^72 + 3/2*q^76 - 1/2*q^77 - q^83 + 1/2*q^84 + 1/2*q^85 + 
        1/2*q^87 + 1/2*q^98 - q^100 + 1/2*q^102 - 1/2*q^110 - 1/2*q^111 - q^115 
        + 1/2*q^121 + 1/2*q^123 + q^128 - q^135 + 1/2*q^136 + 1/2*q^137 - q^138 
        + 1/2*q^144 - 1/2*q^145 + 1/2*q^151 + 3/2*q^152 - 1/2*q^153 + 1/2*q^168 
        + 1/2*q^170 + 1/2*q^171 + 1/2*q^185 - 1/2*q^189 - 1/2*q^196 - q^200 + 
        O(q^202),
    q^10 + q^14 + q^20 - q^24 + q^34 - q^40 - q^44 - 2*q^46 - 2*q^54 + q^74 - 
        q^80 - q^90 + 2*q^96 + 3*q^114 - q^116 + q^126 - q^136 + q^146 - 2*q^150
        + q^160 - q^164 - q^170 + q^176 + q^180 + 2*q^184 + 2*q^190 - 2*q^194 + 
        O(q^202),
    q^12 + q^14 + q^20 + q^22 - q^24 - q^28 + q^34 - q^40 - q^44 - 2*q^46 - q^48
        - 2*q^54 + q^58 + q^74 - q^80 + q^82 - 2*q^90 + 2*q^96 - q^102 + q^108 +
        q^112 + 3*q^114 - q^116 + q^126 - q^136 - 2*q^142 + q^146 - q^148 - 
        2*q^150 + 2*q^160 - q^164 - q^170 + q^176 + q^180 + 2*q^184 + 3*q^190 - 
        2*q^194 + q^198 + O(q^202),
    q^15 + q^17 - 2*q^18 - q^30 + q^32 - q^33 - q^35 + 3*q^38 + q^42 - q^47 - 
        2*q^50 - q^53 + 2*q^72 + q^77 + 2*q^83 - q^87 - q^98 - q^102 + q^110 + 
        q^120 - q^123 - 2*q^128 + q^135 - q^137 + 2*q^138 - 3*q^152 + q^153 - 
        q^168 - q^170 - q^185 + 2*q^200 + O(q^202)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
72
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
72
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
72
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 24*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 24*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 24*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 36*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
511
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 36*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^32 - q^35 - q^37 - q^46 + q^49 - q^50 - q^65 - q^71 + 
        q^81 - q^92 + O(q^96),
    q^2 - q^16 + q^18 - q^23 - q^25 - q^46 + q^65 + q^67 + q^79 - q^91 + 
        O(q^96),
    q^4 - q^8 - q^23 - q^25 + q^35 + q^36 + q^37 + q^65 - q^70 + q^71 - q^72 - 
        q^74 - q^85 - q^91 + O(q^96),
    q^5 - q^10 - q^14 - q^17 + q^20 + q^26 + q^28 - q^31 + q^34 - q^40 + q^45 - 
        q^56 + q^62 - 2*q^68 + q^80 - q^83 - q^90 + q^94 + O(q^96),
    q^7 - q^10 - q^14 - q^17 + 2*q^20 + q^28 - q^31 + 2*q^34 - 2*q^40 - q^52 - 
        q^56 + 2*q^62 + q^63 - 2*q^68 + q^73 + q^80 - q^83 - q^90 + O(q^96),
    q^13 - q^14 - q^17 + q^20 + q^26 - q^31 - q^40 + q^47 + q^59 - q^68 - q^83 +
        q^94 + O(q^96)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
512
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^9 - q^25 - 2*q^33 + 2*q^41 + q^49 + 2*q^57 - q^81 + O(q^98),
    q^3 + q^11 - q^19 - q^43 - q^59 - q^67 - q^75 + q^83 + O(q^98)
]
;
Bo:=
[
    q + q^9 - 2*q^17 - q^25 - 2*q^41 + q^49 + 2*q^73 + q^81 + 2*q^89 - 2*q^97 + 
        O(q^98),
    q^2 + q^18 - 2*q^34 - q^50 - 2*q^82 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
512
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
128
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
512
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
64
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
512
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
32
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
512
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
512
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 16*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
512
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 32*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^9 + a*q^25 - q^49 - 2*q^65 + 2*a*q^73 - q^81 - 2*a*q^89 + O(q^98),
    q^5 + a*q^13 - a*q^29 - q^37 - a*q^45 - q^53 + a*q^61 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
512
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 64*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - 2*q^33 - 2*q^41 + q^49 - 2*q^57 - q^81 + O(q^98),
    q^3 - q^11 - q^19 + q^43 + q^59 - q^67 + q^75 + q^83 + O(q^98)
]
;
Bo:=
[
    q - q^9 - 2*q^17 + q^25 + 2*q^41 + q^49 - 2*q^73 + q^81 - 2*q^89 - 2*q^97 + 
        O(q^98),
    q^2 - q^18 - 2*q^34 + q^50 + 2*q^82 + O(q^98),
    q^4 - q^36 - 2*q^68 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (-a^4 - a^2)*q^7 + (-a^5 - 1)*q^13 + a^2*q^16 + (-a^3 + 1)*q^19 
        + (a^4 - a)*q^25 + (a^5 + a^3)*q^28 + (-a^5 - a^4 + a^2 + a)*q^31 + (a^5
        - a^2 + a)*q^37 + (a^4 - a^3)*q^43 + (a^5 + a^4 + a^3 - a^2 - 1)*q^49 + 
        (a^3 + a - 1)*q^52 + (-a^5 + a^3 + a^2)*q^61 - a^3*q^64 + (a^5 - 
        a^3)*q^67 + (-a^4 + a^3 + a - 1)*q^73 + (a^4 - a)*q^76 + (-a^4 - a^3 + a
        + 1)*q^79 + (2*a^4 + a^2 - a - 1)*q^91 + (-a^5 + a^2)*q^100 + (a^2 + 
        a)*q^103 + (-a^5 - a^2)*q^109 + O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
12*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
14*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
16*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 + (a^5 + a^4 - a^2)*q^7 + (-a + 1)*q^13 + a^4*q^16 - a^3*q^19 - 
        a^5*q^25 + (a^3 - a - 1)*q^28 + (-a^5 - a^4 + a)*q^31 + (-a^4 + a^2 + 
        a)*q^37 + (a^5 + a^3 - a^2 - 1)*q^43 + (a^5 - a^4 - a^3 - a^2 + a)*q^49 
        + (-a^3 + a^2)*q^52 + (-a^4 + a^3 + a - 1)*q^61 + (a^3 - 1)*q^64 + (a^3 
        - a - 1)*q^67 + (-a^5 - a^3)*q^73 - a^5*q^76 + (-a^5 - a^3)*q^79 + (a^4 
        - a^2 + 1)*q^91 - 2*a*q^97 + (-a^4 + a)*q^100 + (a^4 + a^2)*q^103 + (a^4
        - a)*q^109 + O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + q^7 + (a - 2)*q^13 + (a - 1)*q^16 - q^19 + a*q^25 - a*q^28 + 
        (-2*a + 1)*q^31 + (2*a - 1)*q^37 + (-a + 1)*q^43 + (a + 1)*q^52 - a*q^61
        + q^64 + (-a + 2)*q^67 + (-a + 1)*q^73 + a*q^76 + (-a - 1)*q^79 + (a - 
        2)*q^91 + (-a + 1)*q^100 + (2*a - 1)*q^103 + O(q^110),
    q^3 - a*q^12 + q^21 + (a - 2)*q^39 + (a - 1)*q^48 - q^57 + a*q^75 - a*q^84 +
        (-2*a + 1)*q^93 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
12*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^4 - q^7 + (-a + 1)*q^13 - a*q^16 + q^19 + (a - 1)*q^25 + (-a +
        1)*q^28 - q^31 - q^37 + a*q^43 + a*q^52 + (-a + 1)*q^61 + q^64 + (-a + 
        1)*q^67 + a*q^73 + (a - 1)*q^76 + a*q^79 + (a - 1)*q^91 - 2*a*q^97 - 
        a*q^100 - q^103 - 2*a*q^109 + O(q^110),
    q^3 + (a - 1)*q^12 - q^21 + (-a + 1)*q^39 - a*q^48 + q^57 + (a - 1)*q^75 + 
        (-a + 1)*q^84 - q^93 + O(q^110),
    q^9 - a*q^27 + (a - 1)*q^36 - q^63 + (a - 1)*q^81 + q^108 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - 2*q^7 + q^16 - q^19 - q^25 - 2*q^28 + 2*q^43 + 3*q^49 - 2*q^61 + 
        q^64 + 2*q^73 - q^76 - q^100 + O(q^110),
    q^3 + q^12 - 2*q^21 + q^48 - q^57 - q^75 - 2*q^84 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
513
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^5 - a*q^7 - a*q^11 + a*q^16 + (a - 1)*q^23 + q^26 - q^35 + 
        a*q^38 - a*q^43 + a*q^47 - q^55 + (a - 1)*q^58 + a*q^61 - q^62 - q^64 + 
        (a - 1)*q^77 + q^80 - q^82 - a*q^83 + a*q^101 + (a - 1)*q^104 + 
        O(q^110),
    q^2 + (a - 1)*q^8 + (-a + 1)*q^10 + a*q^13 - a*q^14 + (a - 1)*q^19 - a*q^22 
        - q^29 - a*q^31 + a*q^40 - a*q^41 + (a - 1)*q^46 + q^56 + a*q^59 + q^65 
        - a*q^67 - q^70 + q^79 - a*q^86 + q^88 + (-a + 1)*q^91 + a*q^94 + a*q^95
        - q^97 + a*q^103 + (-2*a + 2)*q^109 + O(q^110)
]
;
Bo:=
[
    q + (a - 1)*q^5 - a*q^7 + a*q^11 + a*q^16 + (-a + 1)*q^23 - q^26 + q^35 - 
        a*q^38 - a*q^43 - a*q^47 - q^55 + (a - 1)*q^58 + a*q^61 + q^62 - q^64 + 
        (-a + 1)*q^77 - q^80 - q^82 + a*q^83 - a*q^101 + (-a + 1)*q^104 + 
        O(q^110),
    q^2 + (a - 1)*q^8 + (a - 1)*q^10 - a*q^13 - a*q^14 + (-a + 1)*q^19 + a*q^22 
        - q^29 + a*q^31 - a*q^40 - a*q^41 + (-a + 1)*q^46 + q^56 + a*q^59 + q^65
        + a*q^67 + q^70 - q^79 - a*q^86 - q^88 + (a - 1)*q^91 - a*q^94 + a*q^95 
        + q^97 - a*q^103 + (2*a - 2)*q^109 + O(q^110),
    q^3 + (a - 1)*q^15 - a*q^18 - a*q^21 - q^27 + a*q^33 + a*q^48 + (-a + 
        1)*q^69 + q^72 - q^78 + q^90 + q^105 + O(q^110),
    q^6 + (-a + 1)*q^9 + (a - 1)*q^24 + (a - 1)*q^30 - a*q^39 - a*q^42 + a*q^45 
        - q^54 + (-a + 1)*q^57 - q^63 + a*q^66 + (a - 1)*q^81 - q^87 + a*q^93 + 
        q^99 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
514
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
256
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
102
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
102
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
204
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
68
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 17*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 34*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
51*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 - q^8 + q^9 - q^14 - q^17 + q^25 + q^26 + q^28 - q^29 + q^32 - q^34 
        + q^38 + q^46 + q^49 - q^52 + q^56 - q^58 - q^59 - q^61 - q^63 + q^68 - 
        q^72 - q^76 + q^81 + q^82 - q^83 - q^91 - q^92 - q^97 + q^98 + O(q^102),
    q^2 - q^4 - q^7 + q^13 - q^17 + q^18 + q^19 + q^23 - q^26 - q^29 - q^36 - 
        q^38 + q^41 - q^46 + q^49 + q^50 + q^52 + q^56 - q^59 - q^61 - q^63 + 
        q^64 + q^76 + q^79 - q^82 - q^83 + q^92 - q^97 - q^100 + O(q^102),
    q^5 - q^35 - q^40 + q^45 - q^70 - q^85 + O(q^102),
    q^10 - q^20 - q^35 + q^65 - q^85 + q^90 + q^95 + O(q^102)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
515
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 51*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^15 + q^16 - q^19 + q^25 - q^29 - q^41 + q^49 - q^59 - q^60 - 
        q^61 + q^64 - q^76 - q^79 - q^81 + q^100 + O(q^102),
    q^3 - q^5 + q^12 - q^20 - q^27 - 2*q^37 + q^43 + q^47 + q^48 + q^53 - q^57 +
        q^67 + q^73 + q^75 - q^80 - q^87 + q^95 + O(q^102)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + (a^11 + a^10 - a^4)*q^7 + a^2*q^9 + (a^9 + a^6 - a^2)*q^13 + 
        (-a^11 - a^10 + a^8 + a^7 - a^6 - a^5 + a^4 + a^3 + a^2 - 1)*q^19 + 
        (-a^9 - a^8 + a^6 + a^5 - a^4 - a^3 + a + 1)*q^21 + a^8*q^25 - a^3*q^27 
        + (-a^11 + a^9 + a^8 + a^7 - a^6 + a^4 + a^3 - a - 2)*q^31 + (-a^9 - 
        a^5)*q^37 + (-a^10 - a^7 + a^3)*q^39 + (-a^8 + a)*q^43 + (a^11 + a^10 - 
        2*a^8 - 2*a^7 + a^5 - a^3 - a^2 + a + 1)*q^49 + (a^7 - a^5 - 1)*q^57 + 
        (a^11 - a^8 - a^7 + a^5 - a^2 + 1)*q^61 + (a^10 + a^9 - a^7 - a^6 + a^5 
        + a^4 - a^2 - a)*q^63 + (-a^9 + a^8)*q^67 + (a^11 - a^9 - a^8 + a^6 + 
        a^5 - a^4 - 2*a^3 + a + 1)*q^73 - a^9*q^75 + (-a^11 - a^10 + a^3)*q^79 +
        a^4*q^81 + (-a^11 - a^10 + a^9 + a^8 + a^7 - a^6 - 2*a^5 - 1)*q^91 + 
        (-a^11 - a^10 + a^7 - a^6 - a^5 + a^3 + a^2 + a - 1)*q^93 + (-a^11 + a^9
        + a^8 + a^4 + a^3 - a - 1)*q^97 + (-a^11 + a^2)*q^103 + (-a^7 + 
        a^4)*q^109 + (a^10 + a^6)*q^111 + (a^11 + a^8 - a^4)*q^117 + (a^11 - 
        a^4)*q^121 + (a^11 - a^9 - a^8 + a^7 + a^6 + a^5 - a^4 - a^3 + a)*q^127 
        + (a^9 - a^2)*q^129 + (a^10 + a^7 + a^2 - a - 1)*q^133 + (a^11 - a^9 - 
        a^8 + a^6 + a^5 - a^4 - a^3 + 1)*q^139 + (a^9 + a^8 - a^2 + 1)*q^147 + 
        (-a^7 + a^2)*q^151 + (a^10 + 1)*q^157 + (a^4 + 1)*q^163 + O(q^166)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 + (a^4 - a^3)*q^7 + a^2*q^9 + (a^5 - a^4 + a^3 + a - 1)*q^13 + 
        (a^5 + a^3 - a^2 + a - 1)*q^19 + (-a^5 + a^4)*q^21 - a*q^25 - a^3*q^27 +
        (-a^5 + 1)*q^31 + (-a^5 + a^2)*q^37 + (-a^3 + 1)*q^39 - a*q^43 + (a^5 - 
        a^4 + a^3 - a^2)*q^49 + (-a^5 + 1)*q^57 + (a^5 - a^4 - a^2 + a - 1)*q^61
        + (-a^4 + a^3 - a^2 + a - 1)*q^63 + (a^2 - a)*q^67 + (-a^5 - a^3)*q^73 +
        a^2*q^75 + (a^4 - a^3)*q^79 + a^4*q^81 + (-a^4 + a - 1)*q^91 + (a^5 - 
        a^4 + a^3 - a^2 - 1)*q^93 + (-a^4 + a^3 - a^2 + a - 1)*q^97 + (a^4 + 
        a^2)*q^103 + (a^4 + 1)*q^109 + (a^5 - a^4 - a^2 + a - 1)*q^111 + (a^4 - 
        a)*q^117 + a^4*q^121 + (-a^5 + 1)*q^127 + a^2*q^129 + (-a^3 + a^2 - a + 
        1)*q^133 + (-a^5 - a)*q^139 + (a^2 - a + 1)*q^147 + (a^2 + 1)*q^151 + 
        (-a^3 + 1)*q^157 + (a^4 + 1)*q^163 + O(q^166),
    q^2 - a*q^6 - a^5*q^8 + (a^4 - a^3)*q^14 + a^2*q^18 + (a^5 - a^4 + a^3 - a^2
        + a - 1)*q^24 + (a^5 - a^4 + a^3 + a - 1)*q^26 - a^3*q^32 + (a^5 + a^3 -
        a^2 + a - 1)*q^38 + (-a^5 + a^4)*q^42 - a*q^50 - a^3*q^54 + (a^2 - 
        a)*q^56 + (-a^5 + 1)*q^62 + q^72 + (-a^5 + a^2)*q^74 + (-a^3 + 1)*q^78 -
        a*q^86 + a^4*q^96 + (a^5 - a^4 + a^3 - a^2)*q^98 + (a^4 + 1)*q^104 + 
        (-a^5 + 1)*q^114 + (a^5 - a^4 - a^2 + a - 1)*q^122 + (-a^4 + a^3 - a^2 +
        a - 1)*q^126 - a*q^128 + (a^2 - a)*q^134 + (-a^5 - a^3)*q^146 + 
        a^2*q^150 + (a^4 + a^2)*q^152 + (a^4 - a^3)*q^158 + a^4*q^162 + 
        O(q^166),
    q^4 - a*q^12 - a^5*q^16 + (a^4 - a^3)*q^28 + a^2*q^36 + (a^5 - a^4 + a^3 - 
        a^2 + a - 1)*q^48 + (a^5 - a^4 + a^3 + a - 1)*q^52 - a^3*q^64 + (a^5 + 
        a^3 - a^2 + a - 1)*q^76 + (-a^5 + a^4)*q^84 - a*q^100 - a^3*q^108 + (a^2
        - a)*q^112 + (-a^5 + 1)*q^124 + q^144 + (-a^5 + a^2)*q^148 + (-a^3 + 
        1)*q^156 + O(q^166)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + (-a + 1)*q^7 + (a - 1)*q^9 + (-a + 1)*q^13 - 2*a*q^19 - q^21 + 
        (a - 1)*q^25 + q^27 + a*q^31 + a*q^37 - q^39 + q^43 + (2*a - 2)*q^57 + 
        (2*a - 2)*q^61 + a*q^63 + a*q^67 + (-a + 1)*q^73 + q^75 + (2*a - 2)*q^79
        - a*q^81 - a*q^91 + (-a + 1)*q^93 + 2*q^97 + (2*a - 2)*q^103 - 2*a*q^109
        + (-a + 1)*q^111 + a*q^117 + q^121 - q^127 - a*q^129 - 2*q^133 - 
        2*a*q^139 - q^151 + (-a + 1)*q^157 + (-a + 1)*q^163 + O(q^166)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^11 - q^13 - q^17 - q^23 + q^25 - q^31 - q^41 + q^43 + 2*q^47 + 
        q^49 - q^53 + 2*q^59 - q^67 + 2*q^79 + q^81 - q^83 - q^97 - q^99 - q^101
        - q^103 + 2*q^107 - q^109 - q^117 - q^127 - q^139 + q^143 - q^153 + 
        O(q^166),
    q^3 + q^27 - q^33 - q^39 - q^51 - q^69 + q^75 - q^93 - q^123 + q^129 + 
        2*q^141 + q^147 - q^159 + O(q^166)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
516
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 21*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 + q^9 - q^10 - q^13 + q^16 - q^21 + q^36 - q^40 - q^52 - q^57 - q^58
        + q^64 - q^66 + q^81 - q^84 - q^90 - q^97 - q^109 - q^117 + q^129 + 
        q^130 + q^133 + 2*q^138 + q^144 + q^145 + q^154 - q^160 + q^165 + 
        O(q^166),
    q^2 - q^5 + q^8 + q^18 - q^20 - q^26 - q^29 + q^32 - q^33 - q^42 - q^45 + 
        q^65 + 2*q^69 + q^72 + q^77 - q^80 + 2*q^89 - q^104 + q^105 - q^113 - 
        q^114 - q^116 + q^125 + q^128 - q^132 - q^137 - q^141 + 2*q^149 - 
        2*q^161 + q^162 + O(q^166),
    q^3 - q^7 + q^12 - q^19 - q^22 + q^27 - q^28 - q^30 - q^39 + q^43 + 2*q^46 +
        q^48 + q^55 - q^63 + q^70 - q^76 - q^88 + q^91 - q^94 + q^108 - q^112 - 
        2*q^115 + 2*q^118 - q^120 + 2*q^151 - q^156 - q^163 + O(q^166),
    q^6 - q^11 - q^14 - q^15 + 2*q^23 + q^24 + q^35 - q^38 - q^44 - q^47 + q^54 
        - q^56 + 2*q^59 - q^60 - q^78 - q^83 + q^86 - q^87 + 2*q^92 + q^95 + 
        q^96 - q^99 - q^107 + q^110 - q^126 - q^135 + q^140 + q^143 - q^152 + 
        O(q^166)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
517
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
517
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
517
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
517
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
230
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
517
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
230
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
517
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^12 - a^5)*q^3 - a^13*q^4 + (-a^21 + a^4)*q^5 + (-a^17 + a^10 - a)*q^9
        - a^7*q^11 + (a^18 + a^2)*q^12 + (a^16 + a^10 - a^9 - a^3)*q^15 - 
        a^3*q^16 + (-a^17 - a^11)*q^20 + (a^6 + a^4)*q^23 + (-a^19 + a^8 + 
        a^2)*q^25 + (a^21 - a^20 + a^19 - a^18 + a^17 - a^16 - a^14 - a^12 + 
        a^11 - a^10 + a^9 - a^8 + a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^27 + 
        (a^20 - a^9)*q^31 + (-a^19 + a^12)*q^33 + (a^14 - a^7 + 1)*q^36 + (a^14 
        - a)*q^37 + a^20*q^44 + (-a^20 + a^19 - a^18 + a^17 - a^16 + a^13 - a^12
        + a^11 - a^10 + a^9 + a^7 - a^6 - a^4 + a^3 - a^2 + a - 1)*q^45 + 
        a^20*q^47 + (-a^15 + a^8)*q^48 + a^18*q^49 + (-a^19 - a^11)*q^53 + 
        (-a^11 - a^5)*q^55 + (-a^20 + a^19 - a^18 + a^17 - a^16 + a^15 - a^14 + 
        a^13 - a^12 + a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - 
        a^2 + a - 1)*q^59 + (a^21 - a^20 + a^19 - a^18 + a^17 + a^15 - a^14 + 
        a^13 - a^12 + a^11 - a^10 + a^9 - a^8 + a^7 + a^5 - a^4 + a^3 - a^2 + 
        a)*q^60 + a^16*q^64 + (a^16 + a^12)*q^67 + (a^18 + a^16 - a^11 - 
        a^9)*q^69 + (a^18 - a^15)*q^71 + (a^20 + a^14 - a^13 + a^8 - a^7 - 
        a)*q^75 + (-a^7 - a)*q^80 + (a^20 + a^18 - a^11 + a^4 + a^2)*q^81 + 
        (a^21 - a^20 + a^19 - a^18 + a^17 - a^16 + a^15 - a^14 + a^13 - a^12 + 
        a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 - a^2 + a - 1)*q^89 + 
        (-a^19 - a^17)*q^92 + (-a^21 + a^14 - a^9 + a^2)*q^93 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
517
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 - q^6 - q^8 + q^9 + q^12 + q^14 - q^17 + q^18 - q^21 + q^24 + q^25 -
        q^27 - q^28 + q^32 - q^34 - q^36 - q^37 + q^47 + 2*q^51 + q^63 + q^68 - 
        q^71 - q^72 - q^74 - q^75 - q^79 + 2*q^83 + O(q^94),
    q^2 - q^3 - q^4 + q^7 + q^9 - q^14 - q^17 + q^24 + q^28 - q^37 - q^42 - q^49
        + q^50 + q^51 + q^53 - q^54 - q^56 + q^59 + q^61 + q^64 - q^71 - q^72 - 
        q^75 - q^79 + q^84 + q^89 + O(q^94),
    q^11 - q^33 - q^66 - q^88 + O(q^94),
    q^22 - q^33 - q^44 + q^77 + O(q^94)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
517
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 23*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + (a^4 - a)*q^7 + (a^5 - a^4 - a^2)*q^8 + (a^5 - a^2)*q^9 + (-a^5 
        - a^4 + a^2)*q^11 + (-a^4 + a^3 - a^2 + a - 1)*q^16 + (a^4 - a^2)*q^23 +
        a^5*q^25 + (-a^5 + a^2)*q^28 + (a^2 + a)*q^29 + (-a^5 + a^4 + a - 
        1)*q^32 + q^36 - q^37 + (-2*a^3 + 1)*q^43 + (a^5 - 1)*q^44 - a^5*q^49 + 
        (a^3 + a)*q^53 + (-a^3 + a^2 + 1)*q^56 + (-a^3 + 1)*q^63 + (-a^5 + 2*a^4
        - a^3 + 2*a^2 - a)*q^64 + (a^4 - a)*q^67 - a^4*q^71 + (-a^4 + a^3 + 
        a)*q^72 + (a^3 + a^2 - 1)*q^77 + (-a^5 + a^3 + a^2 - 1)*q^79 + (-a^4 + 
        a)*q^81 + (a^5 + a^4 - a^2 - a)*q^88 + (-a^5 + a^3)*q^92 + (a^4 + a^3 - 
        a)*q^99 + (-a^3 + 1)*q^100 + (-a^5 + a^3 - 1)*q^107 + (-a - 1)*q^109 + 
        (a^5 - a^4 + 1)*q^112 + (-a^3 - a^2)*q^116 + (a^5 - a^4 - a^3 - a^2 + 
        a)*q^121 + (-a^4 - 1)*q^127 + (a^5 + a^4 - a^3 + a^2 - 2*a + 2)*q^128 + 
        (-a^3 + 1)*q^137 + (-a^5 + a^3 + a - 1)*q^144 + O(q^146),
    q^2 + (-a^4 + a^3 + a)*q^4 + (-a^5 + a^3 + a - 1)*q^8 + (a^4 - a)*q^14 + 
        (-a^5 + a^4 - a^3 + a^2 - 1)*q^16 + (a^5 - a^2)*q^18 + (-a^5 - a^4 + 
        a^2)*q^22 + (a^5 - a)*q^28 + (a^4 - 2*a^3 + a^2 - 2*a + 1)*q^32 + (a^3 -
        a^2 - 1)*q^36 + (-a^4 - a^3 + a + 1)*q^44 + (a^4 - a^2)*q^46 + a^5*q^50 
        + (a^5 - a^4 + a^3 - a^2)*q^56 + (a^2 + a)*q^58 + (2*a^5 - a^4 - a^3 - 
        a^2 - a + 2)*q^64 + (-a^5 + a^4 - 1)*q^72 - q^74 + (-2*a^3 + 1)*q^86 + 
        (-a^4 + a)*q^88 + (-a^5 + a^4 + a^2 - a - 1)*q^92 - a^5*q^98 + (a^5 + 
        a^3 - a^2)*q^100 + (a^3 + a)*q^106 + (-a^4 + a^3 - a^2 + 2*a - 1)*q^112 
        + (a^4 + a^2 + 1)*q^116 + (-a^3 + 1)*q^126 + (a^5 - 2*a^4 + 2*a^3 - 
        2*a^2 + a)*q^128 + (a^4 - a)*q^134 - a^4*q^142 + (-a^5 + a^4 - a^3 + 
        2*a^2 - a)*q^144 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a^2*q^4 - a^5*q^7 + (-a^5 + a^4 + a^2 - a)*q^8 + (-a^4 + a)*q^9 + (a^5 -
        a^4 - a^2 + a)*q^11 + (a^5 - a^4 + a^3)*q^16 + (a^5 + a^4 - a^2)*q^23 - 
        a*q^25 + (a^4 - a)*q^28 + (a^4 + a^2)*q^29 + (-a^5 + a - 1)*q^32 - q^36 
        + q^37 - q^43 + (a - 1)*q^44 - a*q^49 + (a^3 + a^2 - 1)*q^53 + (-a^4 + 
        a^3)*q^56 - a^3*q^63 + (-a^3 + a^2 - a + 1)*q^64 + a^5*q^67 + (-a^5 + 
        a^2)*q^71 + (a^5 - a^3 + 1)*q^72 + (a^4 - a^3)*q^77 + (-a^4 - a^3 + 
        a)*q^79 - a^5*q^81 + (a^5 + a^4 - 2*a^3 - a + 2)*q^88 + (-a^3 + a + 
        1)*q^92 + (-a^5 + a^3 - 1)*q^99 + a^3*q^100 + (-a^3 - a)*q^107 + (a^2 + 
        1)*q^109 + (-a^5 + a^2 + a - 1)*q^112 - 2*a*q^113 + (-a^4 - a^3 + 
        1)*q^116 + (-a^5 - a^4 + a^3 + a - 1)*q^121 + (a^5 - a^2 + 1)*q^127 + 
        (a^5 - a^4 + a^3 - a^2 + a - 1)*q^128 + a^3*q^137 + (a^3 - a^2 + 
        a)*q^144 + O(q^146),
    q^2 + (-a^5 + a^3 - 1)*q^4 + (-a^3 + a^2 - a)*q^8 - a^5*q^14 + (a^5 - a^4 + 
        a^3 - a^2 + a)*q^16 + (-a^4 + a)*q^18 + (a^5 - a^4 - a^2 + a)*q^22 + 
        (a^2 - a)*q^28 + (-a^5 + a^4 + a^2 - 1)*q^32 + (a^4 - a^3)*q^36 + (-a^5 
        + 2*a^4 - a^3)*q^44 + (a^5 + a^4 - a^2)*q^46 - a*q^50 + (a^5 - a^4 + a^3
        - a^2 + a - 1)*q^56 + (a^4 + a^2)*q^58 + (a^5 - a^4 - a^3 + 1)*q^64 + 
        (a^5 - a^2 - a + 1)*q^72 + q^74 - q^86 + (a^5 - 2*a + 2)*q^88 + (-a^5 + 
        a^4 - a + 1)*q^92 - a*q^98 + (-a^4 + a^3 + a - 1)*q^100 + (a^3 + a^2 - 
        1)*q^106 + (-a^5 + a^4 - a^3 + a^2)*q^112 + (a^5 - a^4 - a^2 + 1)*q^116 
        - a^3*q^126 + (-a^2 + a)*q^128 + a^5*q^134 + (-a^5 + a^2)*q^142 + (-a^5 
        + a^3 + a - 1)*q^144 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + a*q^7 + (2*a - 1)*q^8 + (a - 1)*q^9 + q^11 + (-2*a + 2)*q^16 + 
        (-2*a + 1)*q^23 + (-a + 1)*q^25 + (-a + 1)*q^28 + (2*a - 1)*q^29 + (a - 
        2)*q^32 + q^36 - q^37 - a*q^44 + (a - 1)*q^49 + (a - 1)*q^53 + (a - 
        2)*q^56 - q^63 + q^64 - 2*a*q^67 - 2*a*q^71 + (-a - 1)*q^72 + a*q^77 + 
        (-a + 2)*q^79 - a*q^81 + (2*a - 1)*q^88 + (a - 2)*q^92 + (a - 1)*q^99 - 
        q^100 + a*q^107 + (-a - 1)*q^109 + 2*q^112 + (-a + 2)*q^116 + (a - 
        1)*q^127 + 2*q^137 + 2*a*q^144 + O(q^146),
    q^2 + (-a - 1)*q^4 + 2*a*q^8 + a*q^14 + (-2*a + 1)*q^16 + (a - 1)*q^18 + 
        q^22 + (-2*a + 1)*q^28 + (a - 1)*q^32 + (-a + 2)*q^36 + (-a - 1)*q^44 + 
        (-2*a + 1)*q^46 + (-a + 1)*q^50 + (2*a - 2)*q^56 + (2*a - 1)*q^58 - 
        2*q^72 - q^74 + 2*a*q^88 + (3*a - 3)*q^92 + (a - 1)*q^98 + (a - 2)*q^100
        + (a - 1)*q^106 + (-a + 2)*q^112 + (-3*a + 3)*q^116 - q^126 + q^128 - 
        2*a*q^134 - 2*a*q^142 + (a + 1)*q^144 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a + 1)*q^4 + (a - 1)*q^7 + q^8 - a*q^9 - q^11 - q^23 - a*q^25 + a*q^28
        - q^29 + (-a + 1)*q^32 - q^36 + q^37 + 2*q^43 + (a - 1)*q^44 - a*q^49 + 
        a*q^53 + (a - 1)*q^56 + q^63 + q^64 + (2*a - 2)*q^67 + (2*a - 2)*q^71 - 
        a*q^72 + (-a + 1)*q^77 + (-a + 1)*q^79 + (a - 1)*q^81 - q^88 + (a - 
        1)*q^92 + a*q^99 - q^100 + (-a + 1)*q^107 + a*q^109 - 2*a*q^113 + (a - 
        1)*q^116 + a*q^127 + 2*q^137 + O(q^146),
    q^2 + a*q^4 + (a - 1)*q^14 + q^16 - a*q^18 - q^22 - q^28 + a*q^32 + (-a + 
        1)*q^36 - a*q^44 - q^46 - a*q^50 - q^58 + q^74 + 2*q^86 - a*q^92 - 
        a*q^98 + (-a + 1)*q^100 + a*q^106 + (a - 1)*q^112 - a*q^116 + q^126 + 
        q^128 + (2*a - 2)*q^134 + (2*a - 2)*q^142 - a*q^144 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
518
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^7 + q^9 - 2*q^11 + q^16 - q^25 - q^28 + q^36 - q^37 - 2*q^44 + 
        q^49 - 2*q^53 - q^63 + q^64 + 2*q^67 + 2*q^71 + 2*q^77 + q^81 - 2*q^99 -
        q^100 + 2*q^107 - q^112 + 3*q^121 - 2*q^127 + 2*q^137 + q^144 + 
        O(q^146),
    q^2 + q^8 - q^14 + q^18 - 2*q^22 + q^32 - q^50 - q^56 + q^72 - q^74 - 2*q^88
        + q^98 - 2*q^106 - q^126 + q^128 + 2*q^134 + 2*q^142 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
519
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
519
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
172
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
519
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
86
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
519
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
86
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
519
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
43*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
519
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 86*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^33 - q^34 - q^40 - q^43 + q^49 - q^55 - q^60 - q^78 + 
        q^81 - q^85 - q^109 + O(q^114),
    q^2 - q^17 + q^18 - q^20 - q^30 - q^39 + q^50 - q^59 + q^65 + q^71 - q^74 + 
        q^75 + q^93 + q^98 + q^101 - q^104 + O(q^114),
    q^3 - q^11 - q^20 - q^26 + q^27 + q^44 + q^50 - q^53 + q^62 - q^65 + q^75 + 
        q^80 - q^99 - q^102 + q^104 - q^110 + O(q^114),
    q^4 - q^10 - q^15 + q^33 + q^36 - q^37 + q^43 - q^52 + q^55 - q^73 + q^85 - 
        q^88 - q^90 - q^96 + q^100 + q^109 + O(q^114),
    q^5 - q^11 - q^12 + q^30 + q^32 + q^45 - q^50 - q^53 - q^62 - q^65 + q^68 + 
        q^74 - q^99 + q^107 - q^108 + q^111 + O(q^114),
    q^6 - q^10 - q^15 - q^16 + q^22 + q^24 + q^25 + q^31 - q^34 - q^37 + q^54 - 
        q^60 - q^64 + q^67 - q^73 - q^78 + q^85 + q^88 - q^90 + 2*q^100 + q^106 
        + O(q^114),
    q^8 - q^11 - q^12 + q^17 - q^26 + q^30 + q^32 + q^39 - q^44 - q^48 - q^50 - 
        q^53 + q^59 - q^62 - q^65 + q^66 + q^68 + q^72 + q^74 + q^86 - q^99 - 
        q^102 - q^108 + O(q^114),
    q^13 - q^15 - q^16 + q^22 + q^24 - q^34 - q^37 + q^51 + q^55 - q^73 - q^78 +
        q^100 + q^106 + O(q^114)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a^3 - a)*q^5 + a*q^9 + (-a^3 + a)*q^13 + (-a^3 - a^2)*q^17 + (-a^2 + 
        1)*q^25 + (a^3 - a)*q^29 + (a^2 - 2)*q^37 + (a^3 - a^2 + 1)*q^41 - q^45 
        + a^2*q^49 + (a^2 - a)*q^53 + (-2*a^3 + a)*q^61 + (a^2 - 1)*q^65 - q^73 
        + a^2*q^81 + (a^2 + a)*q^85 + (a^3 - a^2 - a)*q^89 + (a^2 - 2)*q^101 + 
        (-a^3 - 1)*q^109 + (a^3 - a + 1)*q^113 + q^117 - a*q^121 + a^3*q^125 + 
        a*q^137 + (-a^2 + 1)*q^145 + (-a^3 + a + 1)*q^149 + (-a^3 - a^2 + 
        1)*q^153 + O(q^154),
    q^2 + a^2*q^4 + (a^2 - 1)*q^8 + (a^3 - a)*q^10 - q^16 + a*q^18 - a*q^20 + 
        (-a^3 + a)*q^26 - a^2*q^32 + (-a^3 - a^2)*q^34 + a^3*q^36 - a^3*q^40 + 
        (-a^2 + 1)*q^50 + a*q^52 + (a^3 - a)*q^58 + (-a^2 + 1)*q^64 + (-a^3 - 
        a^2 + a + 1)*q^68 + (a^3 - a)*q^72 + (a^2 - 2)*q^74 + (-a^3 + a)*q^80 + 
        (a^3 - a^2 + 1)*q^82 - q^90 + a^2*q^98 + q^100 + a^3*q^104 + (a^2 - 
        a)*q^106 - a*q^116 + (-2*a^3 + a)*q^122 + q^128 + (a^2 - 1)*q^130 + (a +
        1)*q^136 - a*q^144 - q^146 + (-a^2 - 1)*q^148 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a^2 - 1)*q^5 - a*q^9 + a^2*q^13 + (a^3 - a - 1)*q^17 - a^2*q^25 + (-a^3
        + a)*q^29 + (a^3 + a)*q^37 + (a^3 - a^2 + 1)*q^41 + (-a^3 + a)*q^45 - 
        a^2*q^49 + (a^3 - a^2 - a + 1)*q^53 + (-2*a^3 + a)*q^61 - q^65 - 
        a^3*q^73 + a^2*q^81 + (-a^3 - a^2 + 1)*q^85 + (-a^3 + a^2 + a)*q^89 + 
        (a^2 - 2)*q^101 + (a^3 + 1)*q^109 + (a^3 - a^2)*q^113 - a^3*q^117 - 
        a*q^121 + q^125 + (-a^2 + 1)*q^137 + a^3*q^145 + (a^3 - a - 1)*q^149 + 
        (a + 1)*q^153 + O(q^154),
    q^2 + (-a^3 + a)*q^4 + (-a^2 + 1)*q^8 + (a^2 - 1)*q^10 - a^3*q^16 - a*q^18 +
        a^3*q^20 + a^2*q^26 - a^2*q^32 + (a^3 - a - 1)*q^34 - q^36 + a^2*q^40 - 
        a^2*q^50 + a*q^52 + (-a^3 + a)*q^58 - a*q^64 + (a^3 + a^2 - a - 1)*q^68 
        + (a^3 - a)*q^72 + (a^3 + a)*q^74 + a*q^80 + (a^3 - a^2 + 1)*q^82 + 
        (-a^3 + a)*q^90 - a^2*q^98 - a*q^100 + q^104 + (a^3 - a^2 - a + 1)*q^106
        + (-a^2 + 1)*q^116 + (-2*a^3 + a)*q^122 - q^128 - q^130 + (a^3 + a^2 - 
        1)*q^136 + (a^2 - 1)*q^144 - a^3*q^146 + (a^2 + 1)*q^148 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^9 + (a + 1)*q^13 - 3*a*q^17 + q^25 + (a - 1)*q^29 + (a + 1)*q^37 + 
        (-a - 1)*q^41 + (a - 1)*q^49 - 3*q^53 - a*q^61 + (-2*a + 2)*q^65 + (-2*a
        + 1)*q^73 + (a - 1)*q^81 + (2*a - 4)*q^85 + (2*a - 4)*q^97 + (-a + 
        1)*q^101 + 3*a*q^113 + (2*a - 1)*q^117 + a*q^121 + (-2*a + 1)*q^125 + 
        (-a + 2)*q^137 + (-a + 2)*q^149 + (-3*a + 3)*q^153 + O(q^154),
    q^2 - a*q^8 + 1/2*(-2*a + 1)*q^10 + a*q^18 + 1/2*(a - 1)*q^20 + (a - 1)*q^32
        + 1/2*(a - 2)*q^40 - 1/2*q^50 + a*q^52 + (a - 1)*q^58 + (-2*a + 1)*q^68 
        + (-a + 1)*q^72 + 1/2*q^80 + (-a - 1)*q^82 + 1/2*(-a + 2)*q^90 + (a - 
        1)*q^98 + 1/2*(a + 1)*q^100 - a*q^122 + q^128 + 1/2*(-a + 1)*q^130 + 
        a*q^148 + O(q^154),
    q^4 - 1/2*a*q^10 - a*q^16 + 1/2*(-2*a + 1)*q^20 - q^26 + (a + 1)*q^34 + 
        a*q^36 + 1/2*(a - 1)*q^40 + 1/2*(a - 2)*q^50 + (a - 1)*q^64 - q^74 + 
        1/2*(a - 2)*q^80 + 1/2*(-a + 1)*q^90 - 1/2*q^100 + a*q^104 + (-a + 
        2)*q^106 + (a - 1)*q^116 + 1/2*(2*a - 1)*q^130 + (-2*a + 1)*q^136 + (-a 
        + 1)*q^144 + a*q^146 + O(q^154),
    q^5 + (-2*a + 2)*q^13 + (2*a - 4)*q^17 + (-2*a + 1)*q^25 + (-2*a + 2)*q^37 +
        a*q^45 + (4*a - 2)*q^53 + (-a - 1)*q^65 - 2*q^73 + 3*a*q^85 + 4*a*q^97 +
        (-2*a + 4)*q^113 + 2*q^117 - 2*q^125 - 2*a*q^137 + (a - 1)*q^145 + (-2*a
        - 2)*q^153 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 - a*q^9 + (a - 1)*q^10 + (-a - 1)*q^11 + q^14 + (a - 1)*q^16 + (-a
        + 2)*q^19 - q^25 - q^26 + a*q^35 + (-a + 1)*q^36 - q^40 + (-2*a + 
        1)*q^44 + a*q^56 - q^64 - a*q^65 + a*q^74 + (a + 1)*q^76 + (a - 1)*q^81 
        + (a + 1)*q^89 + q^90 + (a - 1)*q^91 + (-a + 1)*q^94 + (2*a - 1)*q^99 - 
        a*q^100 - a*q^104 + (-a - 1)*q^106 + (-a + 2)*q^110 + 2*a*q^121 - 
        a*q^126 + q^131 - a*q^139 + (a - 1)*q^140 + q^144 + O(q^154),
    q^2 + a*q^5 + (-a + 1)*q^7 + a*q^8 + (a - 1)*q^13 - a*q^18 + (a - 1)*q^20 + 
        (-a - 1)*q^22 + q^28 + (a - 1)*q^32 + q^37 + (-a + 2)*q^38 + (-a + 
        1)*q^45 - a*q^47 - q^50 - q^52 + (a - 2)*q^53 + (-2*a + 1)*q^55 - q^63 +
        a*q^70 + (-a + 1)*q^72 + (a - 2)*q^77 - q^80 + (-2*a + 1)*q^88 + (a + 
        1)*q^95 + (a - 2)*q^103 + a*q^112 + q^117 - a*q^125 + (2*a - 1)*q^127 - 
        q^128 - a*q^130 + (-2*a + 1)*q^133 + (-a + 2)*q^143 + a*q^148 + (a + 
        1)*q^152 + O(q^154)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^5 - a*q^9 - q^13 + (a - 1)*q^17 + q^25 + 2*a*q^29 + (-a - 1)*q^41 - 
        a*q^45 + q^49 + (a - 1)*q^53 - q^65 - 2*a*q^73 - q^81 + (a - 1)*q^85 + 
        (-a - 1)*q^89 + (-a + 1)*q^109 + (-a + 1)*q^113 + a*q^117 - a*q^121 + 
        q^125 + 2*q^137 + 2*a*q^145 + (a - 1)*q^149 + (a + 1)*q^153 + O(q^154),
    q^2 - a*q^4 - q^8 + q^10 + a*q^16 - a*q^18 - a*q^20 - q^26 + q^32 + (a - 
        1)*q^34 - q^36 - q^40 + q^50 + a*q^52 + 2*a*q^58 - a*q^64 + (a + 1)*q^68
        + a*q^72 + a*q^80 + (-a - 1)*q^82 - a*q^90 + q^98 - a*q^100 + q^104 + (a
        - 1)*q^106 + 2*q^116 - q^128 - q^130 + (-a + 1)*q^136 + q^144 - 
        2*a*q^146 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + (-a - 1)*q^6 + q^9 + a*q^10 + (-a - 1)*q^15 - q^16 + (-a + 
        1)*q^24 + a*q^25 - q^26 + (a + 1)*q^31 + a*q^36 + (-a + 1)*q^39 - q^40 +
        (-a - 1)*q^41 - a*q^49 + (-a + 1)*q^60 - a*q^64 - q^65 + (a + 1)*q^71 + 
        2*q^74 - q^81 + (-a + 1)*q^86 + (a - 1)*q^89 + a*q^90 + (a + 1)*q^96 - 
        q^100 - a*q^104 + (a + 1)*q^106 + (2*a - 2)*q^111 - a*q^121 + (a - 
        1)*q^124 + 2*a*q^129 + 2*a*q^134 - q^144 + (-a + 1)*q^150 + (-a + 
        1)*q^151 + O(q^154),
    q^2 + (a - 1)*q^3 + q^5 + a*q^8 + (-a - 1)*q^12 + a*q^13 + q^18 + a*q^20 + 
        (-a - 1)*q^30 - q^32 - 2*a*q^37 + (-a - 1)*q^43 + q^45 + (-a + 1)*q^48 +
        a*q^50 - q^52 + (-a + 1)*q^53 + (a + 1)*q^62 + 2*q^67 + a*q^72 + (-a - 
        1)*q^75 + (-a + 1)*q^78 - q^80 + (-a - 1)*q^82 - 2*q^83 - 2*q^93 - 
        a*q^98 + (a - 1)*q^107 + a*q^117 + (-a + 1)*q^120 + 2*q^123 + a*q^125 - 
        a*q^128 - q^130 + (a + 1)*q^142 + (a + 1)*q^147 + 2*q^148 + O(q^154)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^5 + a*q^9 - a*q^13 + (a + 1)*q^17 - q^25 - 2*a*q^29 + (-a - 1)*q^41 
        - q^45 - q^49 + (-a - 1)*q^53 + q^65 + 2*q^73 - q^81 + (a - 1)*q^85 + (a
        + 1)*q^89 + (a - 1)*q^109 + (a + 1)*q^113 + q^117 - a*q^121 - a*q^125 - 
        2*a*q^137 + 2*q^145 + (-a + 1)*q^149 + (a - 1)*q^153 + O(q^154),
    q^2 - q^4 + q^8 + a*q^10 - q^16 + a*q^18 - a*q^20 - a*q^26 + q^32 + (a + 
        1)*q^34 - a*q^36 + a*q^40 - q^50 + a*q^52 - 2*a*q^58 - q^64 + (-a - 
        1)*q^68 + a*q^72 - a*q^80 + (-a - 1)*q^82 - q^90 - q^98 + q^100 - 
        a*q^104 + (-a - 1)*q^106 + 2*a*q^116 + q^128 + q^130 + (a + 1)*q^136 - 
        a*q^144 + 2*q^146 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^9 - a*q^13 + (-a + 1)*q^17 - q^25 + a*q^29 + a*q^37 + a*q^41 -
        a*q^49 - q^53 + (-a + 1)*q^61 - q^73 - a*q^81 - 2*a*q^89 + (2*a - 
        2)*q^97 + a*q^101 + 2*q^109 + (-a + 1)*q^113 + q^117 + (a - 1)*q^121 + 
        q^125 + (-a + 1)*q^137 + (-a + 1)*q^149 + a*q^153 + O(q^154),
    q^2 - a*q^4 + (a - 1)*q^8 + q^16 + (a - 1)*q^18 - a*q^26 - a*q^32 + (-a + 
        1)*q^34 + q^36 - q^50 + (a - 1)*q^52 + a*q^58 + (a - 1)*q^64 - q^68 - 
        a*q^72 + a*q^74 + a*q^82 - a*q^98 + a*q^100 + q^104 - q^106 + (-a + 
        1)*q^116 + (-a + 1)*q^122 + q^128 + a*q^136 + (a - 1)*q^144 - q^146 + 
        (-a + 1)*q^148 + O(q^154),
    q^5 - q^25 + (a - 1)*q^45 - a*q^65 + (-a + 1)*q^85 + a*q^145 + O(q^154),
    q^10 - a*q^20 + (a - 1)*q^40 - q^50 + q^80 + (a - 1)*q^90 + a*q^100 - 
        a*q^130 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 + (a - 1)*q^9 - a*q^10 + a*q^11 - q^14 - a*q^16 + (-a + 
        1)*q^19 + q^25 + q^26 + (-a + 1)*q^35 - a*q^36 + q^40 - 2*a*q^41 - q^44 
        + (2*a - 2)*q^46 + (-a + 1)*q^56 + (2*a - 2)*q^59 + q^64 + (a - 1)*q^65 
        + (-a + 1)*q^74 + a*q^76 - a*q^81 + a*q^89 + q^90 + a*q^91 + a*q^94 - 
        q^99 + (a - 1)*q^100 + (a - 1)*q^104 + a*q^106 + (-a + 1)*q^110 - 
        2*a*q^115 + (-a + 1)*q^126 - q^131 + (-a + 1)*q^139 + a*q^140 + q^144 + 
        O(q^154),
    q^2 + (a - 1)*q^5 + a*q^7 + (a - 1)*q^8 - a*q^13 + (a - 1)*q^18 - a*q^20 + 
        a*q^22 + 2*q^23 - q^28 - a*q^32 - q^37 + (-a + 1)*q^38 - a*q^45 + (-a + 
        1)*q^47 + q^50 + q^52 + (-a + 1)*q^53 - q^55 - q^63 + (-a + 1)*q^70 - 
        a*q^72 + (a - 1)*q^77 + q^80 - 2*a*q^82 - q^88 + (2*a - 2)*q^92 + a*q^95
        + (-a + 1)*q^103 + (-a + 1)*q^112 + q^117 + (2*a - 2)*q^118 + (a - 
        1)*q^125 - q^127 + q^128 + (a - 1)*q^130 + q^133 + (-a + 1)*q^143 + (-a 
        + 1)*q^148 + a*q^152 + O(q^154)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 6*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + q^4 - q^12 - q^14 + q^16 - q^17 - q^25 + q^26 + q^27 + q^42 - q^43
        - q^48 + q^51 - q^56 + 2*q^62 + q^64 - q^68 - q^74 + q^75 - q^78 - q^81 
        - q^91 - q^94 - q^100 + q^104 + 2*q^107 + q^108 + 2*q^113 + q^121 + 
        q^129 - q^131 - q^139 - q^142 + O(q^154),
    q^2 - q^6 - q^7 + q^8 + q^13 + q^21 - q^24 - q^28 + 2*q^31 + q^32 - q^34 - 
        q^37 - q^39 - q^47 - q^50 + q^52 + q^54 - q^71 + q^84 - q^86 - 2*q^93 - 
        q^96 + q^102 - q^109 + q^111 - q^112 + q^119 + 2*q^124 + q^125 + q^128 -
        q^136 + q^141 - q^148 + 2*q^149 + q^150 - q^151 + O(q^154),
    q^5 - q^15 + q^20 - q^50 - q^60 - q^70 + q^80 - q^85 + q^130 + q^135 + q^150
        + O(q^154),
    q^10 - q^25 - q^30 - q^35 + q^40 + q^65 + q^75 - q^100 + q^105 - q^120 - 
        q^140 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 6*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 6*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 - a*q^9 + a*q^10 - q^16 + (-a - 1)*q^17 + (-a - 1)*q^22 + (-a + 
        1)*q^23 + a*q^25 + q^26 + q^36 + (a - 1)*q^38 - q^40 + a*q^49 + (-a - 
        1)*q^55 - a*q^64 + q^65 + (-a + 1)*q^68 + 2*a*q^79 - q^81 + (-a + 
        1)*q^88 + q^90 + (a + 1)*q^92 + (a - 1)*q^95 - q^100 + (-a + 1)*q^103 + 
        a*q^104 + (a - 1)*q^113 + (-a + 1)*q^118 + q^121 + (a + 1)*q^127 - 
        2*a*q^134 + (a - 1)*q^143 + a*q^144 + (-a - 1)*q^152 + (a - 1)*q^153 + 
        O(q^154),
    q^2 + q^5 + a*q^8 + (a - 1)*q^11 - a*q^13 - a*q^18 + (a + 1)*q^19 + a*q^20 -
        q^32 + (-a - 1)*q^34 + (-a - 1)*q^44 - a*q^45 + (-a + 1)*q^46 + a*q^50 +
        q^52 + (-a - 1)*q^59 - 2*q^67 + q^72 + (a - 1)*q^76 - q^80 + (-a - 
        1)*q^85 + a*q^98 + (a + 1)*q^99 + (a + 1)*q^109 + (-a - 1)*q^110 + (-a +
        1)*q^115 - q^117 + a*q^125 - a*q^128 + q^130 + (-a + 1)*q^136 + (a + 
        1)*q^149 + O(q^154)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3 + 6*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 + q^25 - 2*q^29 + q^49 - 2*q^61 + q^65 + q^81 + 2*q^101 - q^121 + 
        O(q^154),
    q^2 + q^8 - q^18 - q^20 + q^32 + q^50 - q^52 - 2*q^58 - q^72 - q^80 + q^98 -
        2*q^122 + q^128 + q^130 + 2*q^148 + O(q^154),
    q^4 - q^10 + q^16 - q^26 - q^36 - q^40 + q^64 + 2*q^74 + q^90 + q^100 - 
        q^104 - 2*q^116 - q^144 + 2*q^146 + O(q^154),
    q^5 + q^13 - 2*q^37 - q^45 - 2*q^73 + 2*q^97 - q^117 + q^125 + 2*q^137 - 
        2*q^145 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
520
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3 + 6*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 + 1/2*q^10 - q^14 + q^16 - 1/2*q^25 - q^26 + 1/2*q^30 + 3/2*q^35 - 
        1/2*q^40 - 2*q^49 - q^51 + q^56 - q^64 + 1/2*q^65 + q^74 + 1/2*q^75 + 
        q^81 + q^90 - q^91 + q^94 + 1/2*q^100 + q^104 - 1/2*q^105 - 1/2*q^120 + 
        q^121 - 2*q^126 + q^129 - q^131 - q^139 - 3/2*q^140 + O(q^154),
    q^2 - q^8 + q^13 - q^15 - q^18 + q^32 - q^45 - q^52 + q^60 + 2*q^63 + q^70 +
        q^72 - q^85 - q^98 - 2*q^102 - q^117 + q^125 - q^128 + q^135 + q^150 + 
        O(q^154),
    q^3 - 1/2*q^10 - q^12 + q^17 - 1/2*q^25 - q^27 - 1/2*q^30 + 1/2*q^35 + 
        1/2*q^40 + q^42 - q^43 + q^48 - 1/2*q^65 - q^68 + 1/2*q^75 - q^78 + q^90
        + 1/2*q^100 + 1/2*q^105 + q^108 + 1/2*q^120 - 1/2*q^140 + q^142 - 
        2*q^153 + O(q^154),
    q^5 - 2*q^7 - q^15 - 2*q^18 - q^20 + 2*q^28 + 2*q^37 + 2*q^47 + q^50 + q^60 
        - q^70 + 2*q^72 + q^80 - q^85 + 2*q^98 - 2*q^102 - 2*q^112 - 2*q^117 - 
        q^130 + q^135 - 2*q^148 + q^150 + O(q^154),
    q^6 + q^7 + q^15 + q^18 - q^21 - q^24 - q^28 + q^34 - q^37 + q^39 - q^45 - 
        q^47 - q^50 - q^54 - q^60 + q^70 - q^71 - q^72 + q^84 + q^85 - q^86 + 
        q^96 - q^98 + q^102 - q^109 + q^111 + q^112 + q^117 - q^119 - q^135 - 
        q^136 + q^141 + q^148 + q^151 + O(q^154),
    q^9 + 1/2*q^10 - q^14 - 1/2*q^25 - 1/2*q^30 + 1/2*q^35 - q^36 - 1/2*q^40 - 
        q^49 + q^51 + q^56 + 1/2*q^65 + q^74 - 1/2*q^75 - q^91 + q^94 + 
        1/2*q^100 + 1/2*q^105 + 1/2*q^120 - q^129 - q^131 - q^139 - 1/2*q^140 + 
        q^144 + O(q^154)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
521
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
520
);
qprec:=
87
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
521
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
104
);
qprec:=
87
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
521
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
87
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
521
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
65*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
87
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
84
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 + (a - 1)*q^10 - a*q^13 + q^16 - a*q^22 - q^25 + a*q^34 + (a + 
        1)*q^40 + (a + 1)*q^43 + (-a - 1)*q^46 + (-a + 1)*q^55 - a*q^58 + (a + 
        1)*q^61 - a*q^64 + a*q^67 + (-a + 1)*q^70 + (a - 1)*q^73 + (-a - 1)*q^79
        + (a - 1)*q^85 - q^88 + a*q^91 - q^94 - a*q^109 - q^112 - 2*a*q^115 + (a
        + 1)*q^118 + (a + 1)*q^130 + q^136 + q^139 + (-a + 1)*q^145 + a*q^154 + 
        (a - 1)*q^163 + O(q^166),
    q^2 - q^14 + (a - 1)*q^20 - a*q^26 + q^32 - a*q^44 - q^50 + a*q^68 + (a + 
        1)*q^80 + (a + 1)*q^86 + (-a - 1)*q^92 + (-a + 1)*q^110 - a*q^116 + (a +
        1)*q^122 - a*q^128 + a*q^134 + (-a + 1)*q^140 + (a - 1)*q^146 + (-a - 
        1)*q^158 + O(q^166),
    q^4 + (a + 1)*q^10 - a*q^16 - q^22 - q^28 + q^34 + (a - 1)*q^46 - a*q^52 - 
        q^58 + (-a - 1)*q^70 + a*q^94 - q^100 + a*q^112 + (-a + 1)*q^118 + (-a +
        1)*q^130 + q^154 + (a + 1)*q^160 + O(q^166),
    q^5 + 1/2*(-a - 1)*q^8 + 1/2*(a - 1)*q^11 + 1/2*(-a + 1)*q^17 - a*q^20 + 
        a*q^23 + 1/2*(a - 1)*q^29 + 1/2*(a - 1)*q^32 - q^35 + 1/2*(a + 1)*q^44 +
        1/2*(a + 1)*q^47 + 1/2*(a + 1)*q^56 - a*q^59 - a*q^65 + 1/2*(-a - 
        1)*q^68 + 1/2*(-a + 1)*q^77 + 1/2*(a - 1)*q^89 + q^92 + 1/2*(-a + 
        1)*q^101 + 1/2*(a - 1)*q^104 - a*q^107 + 1/2*(a + 1)*q^113 + 1/2*(a + 
        1)*q^116 + 1/2*(a - 1)*q^119 + 1/2*(-a - 1)*q^131 + a*q^140 + 1/2*(a + 
        1)*q^143 - a*q^161 + O(q^166)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
522
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
166
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 - q^13 - q^16 + q^22 + q^25 + q^34 - q^58 + q^64 - q^67 - 2*q^82 - 
        q^88 + q^91 + q^94 + 2*q^103 - q^109 + q^112 - q^136 - q^139 + 2*q^151 -
        q^154 + O(q^166),
    q^2 - q^14 - q^26 - q^32 + q^44 + q^50 + q^68 - q^116 + q^128 - q^134 - 
        2*q^164 + O(q^166),
    q^3 - q^18 - q^21 + q^27 - q^39 - q^48 + q^66 + q^72 + q^75 - q^99 + q^102 +
        q^126 - q^153 - q^162 + O(q^166),
    q^4 - q^16 + q^22 - q^28 + q^34 - q^52 - q^58 - 2*q^82 + q^94 + q^100 + 
        q^112 - q^154 + O(q^166),
    q^6 - q^36 - q^42 + q^54 - q^78 - q^96 + q^132 + q^144 + q^150 + O(q^166),
    q^8 - q^11 - q^17 + q^29 - q^32 + 2*q^41 + q^44 - q^47 - q^56 + q^68 + q^77 
        - q^89 - q^101 - q^104 - q^113 - q^116 + q^119 - q^131 + 2*q^137 + q^143
        - 2*q^164 + O(q^166),
    q^9 + q^24 - q^33 - q^36 - q^51 - q^63 + q^81 + q^87 - q^96 - q^117 + 
        2*q^123 + q^132 - q^141 + O(q^166),
    q^12 - q^18 - q^48 + q^66 - q^84 + q^102 + q^108 + q^126 - q^156 - q^162 + 
        O(q^166)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
523
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
522
);
qprec:=
87
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
523
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
174
);
qprec:=
87
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
523
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
87
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
523
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
29*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
87
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
523
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
87*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
87
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
523
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
261*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
87
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 + q^9 - q^11 - q^13 + q^16 - q^17 + q^25 - q^31 + q^36 - q^43 - q^44
        - q^52 + q^64 - q^68 - q^71 - q^77 + q^81 + O(q^87),
    q^7 - q^11 - q^13 - q^17 + q^19 + q^23 + q^28 + q^29 - q^31 + q^41 - q^43 - 
        q^44 - q^49 - q^52 + q^53 + q^63 - q^68 - q^71 + q^73 + q^76 + O(q^87)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
524
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
524
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
130
);
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
524
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
130
);
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
524
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
524
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
524
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
524
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
524
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
65*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
128
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^33 - q^35 - q^39 - q^45 + q^49 - q^53 - q^63 - q^75 + 
        q^81 - q^89 - q^105 + q^121 - q^123 + O(q^128),
    q^3 - q^13 - q^15 + q^27 - q^35 - q^41 + q^45 + q^49 + q^65 + q^75 + q^77 - 
        q^81 - q^91 - q^99 - q^105 + q^109 - q^117 + O(q^128),
    q^5 - q^9 - q^15 + q^27 + q^39 - q^43 + q^45 + q^55 - q^59 - q^61 - q^77 - 
        q^81 + q^91 + q^105 - q^117 + q^121 + q^123 + q^125 + O(q^128),
    q^7 - q^9 - q^15 + q^21 + q^33 - q^43 - q^59 - q^61 + q^63 + q^65 + q^75 - 
        q^77 - q^81 + q^99 + q^101 + q^107 - q^117 + O(q^128),
    q^11 - q^13 - q^15 + q^21 + q^25 - q^35 - q^41 + q^55 + q^63 - q^81 - q^91 +
        q^113 + q^125 + O(q^128)
]
;
Bo:=
[
    q - q^5 - q^7 - q^15 - q^21 + q^25 - q^27 + q^33 + 2*q^35 + q^39 - q^43 + 
        q^45 + q^49 + 2*q^53 - q^55 - q^59 - q^61 + q^63 - q^65 + q^75 - q^77 + 
        2*q^89 - q^91 - q^99 - q^101 + q^105 - q^107 - q^117 + q^123 - q^125 + 
        O(q^128),
    q^2 + q^8 - q^10 - q^14 - q^30 + q^32 - q^40 - q^42 + q^50 - q^54 - q^56 + 
        q^66 + 2*q^70 + q^78 - q^86 + q^90 + q^98 + 2*q^106 - q^110 - q^118 - 
        q^120 - q^122 + q^126 + O(q^128),
    q^3 - q^5 - q^7 - q^9 + q^11 + q^13 + q^25 - q^33 + q^35 - q^39 + q^41 - 
        q^43 + q^49 - q^59 - q^61 + q^99 - q^101 + q^105 - q^107 + q^109 + q^113
        + q^117 - q^121 - q^123 + O(q^128),
    q^4 + q^16 - q^20 - q^28 - q^60 + q^64 - q^80 - q^84 + q^100 - q^108 - q^112
        + O(q^128),
    q^6 - q^10 - q^14 - q^18 + q^22 + q^24 + q^26 - q^40 + q^50 - q^56 - q^66 + 
        q^70 - q^72 - q^78 + q^82 - q^86 + q^88 + q^96 + q^98 + q^104 - q^118 - 
        q^122 + O(q^128),
    q^12 - q^20 - q^28 - q^36 + q^44 + q^48 + q^52 - q^80 + q^100 - q^112 + 
        O(q^128)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (-a^3 + a)*q^9 + a^2*q^16 + (a^3 + a)*q^19 - a^2*q^21 - q^36 - 
        a*q^39 + (a^3 - a)*q^49 + (a^2 - 2)*q^61 - a^3*q^64 + (-2*a^2 + 1)*q^76 
        + (-a^3 + a)*q^79 + (-a^2 + 1)*q^81 + a^3*q^84 + (a^2 - 1)*q^91 + 
        a*q^109 + (2*a^2 - 1)*q^111 - a^2*q^121 + O(q^138),
    q^3 - a^3*q^7 - a*q^12 - a^2*q^13 + (-a^3 + a)*q^27 + (a^2 - 1)*q^28 + 
        (2*a^3 - a)*q^37 + a^2*q^48 + a^3*q^52 + (a^3 + a)*q^57 - a^2*q^63 + 
        (-a^3 + 2*a)*q^67 - q^73 + (a^3 - a)*q^97 + (a^2 - 1)*q^103 - q^108 + 
        (-a^3 + a)*q^112 - a*q^117 + (-a^3 - a)*q^127 + (-a^2 + 2)*q^133 + 
        O(q^138)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (a - 1)*q^9 + (a - 1)*q^16 + (-a + 1)*q^19 + (a - 1)*q^21 - 
        2*a*q^31 + q^36 + a*q^39 + (a - 1)*q^49 + (-a + 1)*q^61 + q^64 - q^76 + 
        (-a + 1)*q^79 - a*q^81 + q^84 + a*q^91 + a*q^109 - q^111 + (a - 1)*q^121
        + (2*a - 2)*q^124 - 2*a*q^129 + O(q^138),
    q^3 + q^7 - a*q^12 + (-a + 1)*q^13 + (a - 1)*q^27 - a*q^28 + a*q^37 + (2*a -
        2)*q^43 + (a - 1)*q^48 - q^52 + (-a + 1)*q^57 + (a - 1)*q^63 - q^67 - 
        q^73 - 2*a*q^93 + (-a + 1)*q^97 + a*q^103 + q^108 + (a - 1)*q^112 + 
        a*q^117 + (-a + 1)*q^127 + (-a + 1)*q^133 + O(q^138)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + (-a + 1)*q^9 + (a - 1)*q^16 + (a - 1)*q^19 + (a - 1)*q^21 - 
        2*a*q^31 + q^36 - a*q^39 + (-a + 1)*q^49 + (-a + 1)*q^61 - q^64 - q^76 +
        (a - 1)*q^79 - a*q^81 - q^84 + a*q^91 - a*q^109 - q^111 + (a - 1)*q^121 
        + (-2*a + 2)*q^124 + 2*a*q^129 + O(q^138),
    q^3 - q^7 + a*q^12 + (-a + 1)*q^13 + (-a + 1)*q^27 - a*q^28 - a*q^37 + (2*a 
        - 2)*q^43 + (a - 1)*q^48 + q^52 + (a - 1)*q^57 + (a - 1)*q^63 + q^67 - 
        q^73 - 2*a*q^93 + (a - 1)*q^97 + a*q^103 + q^108 + (-a + 1)*q^112 - 
        a*q^117 + (a - 1)*q^127 + (-a + 1)*q^133 + O(q^138)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^11 - q^14 - q^16 - q^29 + q^46 + q^49 + q^56 + q^64 - q^71 + 
        q^74 - q^79 + q^81 + q^86 - q^99 - 2*q^106 - q^109 - q^126 + q^134 + 
        O(q^138),
    q^2 - q^7 - q^8 + q^18 - q^22 + q^23 + q^37 + q^43 - 2*q^53 - q^58 - q^63 + 
        q^67 - q^72 + q^77 + q^88 + q^98 - 2*q^107 + q^112 + q^113 + q^127 + 
        q^128 - 2*q^137 + O(q^138),
    q^3 + q^27 - q^33 - q^42 - q^48 - q^87 + O(q^138),
    q^6 - q^21 - q^24 + q^54 - q^66 + q^69 + q^111 + q^129 + O(q^138)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + a*q^9 - q^16 + q^21 - q^36 - 2*a*q^39 - a*q^49 - a*q^64 - 
        2*a*q^79 - q^81 + a*q^84 - 2*q^91 + 2*a*q^109 + q^121 + O(q^138),
    q^3 - a*q^7 + a*q^12 - 2*q^13 + a*q^27 + q^28 - q^48 - 2*a*q^52 + q^63 + 
        2*q^73 + 2*a*q^97 - 2*q^103 - q^108 + a*q^112 - 2*a*q^117 + O(q^138)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
525
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 - q^11 + q^14 - q^16 + q^29 + q^46 - q^49 + q^56 - q^64 - q^71 - 
        q^74 + q^79 + q^81 + q^86 + q^99 - 2*q^106 + q^109 - q^126 - q^134 + 
        O(q^138),
    q^2 - q^7 + q^8 - q^18 - q^22 - q^23 + q^37 - q^43 + 2*q^53 + q^58 + q^63 + 
        q^67 - q^72 + q^77 - q^88 - q^98 - 2*q^107 + q^112 - q^113 + q^127 - 
        q^128 - 2*q^137 + O(q^138),
    q^3 - q^27 - q^33 + q^42 - q^48 + q^87 + O(q^138),
    q^6 - q^21 + q^24 - q^54 - q^66 - q^69 + q^111 - q^129 + O(q^138)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
526
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
262
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
526
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
131*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^16 - q^18 - q^24 + q^25 - q^31 + q^32 + q^36 - q^44 + q^48 + q^49 - 
        q^51 - q^62 - q^64 + q^66 + q^78 - q^83 + q^86 + q^88 - q^102 - q^117 + 
        q^121 + q^122 + q^124 + q^128 + O(q^130),
    q^2 + q^18 - q^34 - q^36 - q^48 + q^50 - q^54 - q^78 - q^88 + q^98 - q^124 +
        O(q^130),
    q^3 + q^24 + q^26 + q^27 - q^33 - q^34 - q^36 - q^39 - q^43 + q^46 - q^48 + 
        q^52 - q^54 - q^61 - q^69 + q^75 - q^78 - q^88 + q^89 + q^92 + q^93 - 
        q^99 + q^102 + q^109 - q^111 + q^121 - q^124 + O(q^130),
    q^4 - q^18 - q^24 + q^36 - q^44 - q^62 + q^66 + q^78 + q^86 + q^100 - q^102 
        + q^122 + O(q^130),
    q^6 - q^16 - q^18 + q^48 + q^52 + q^54 - q^62 - q^68 + q^92 - q^102 + q^104 
        - q^108 + O(q^130),
    q^8 - q^16 - q^18 - q^24 + q^32 + q^34 + q^36 - q^44 + q^48 + q^54 - q^62 - 
        q^64 - q^68 + q^78 + q^88 - q^96 - q^102 - q^108 + q^124 + q^128 + 
        O(q^130),
    q^9 + q^16 + q^18 + q^24 + q^31 - q^32 - q^33 - q^34 - 2*q^36 - q^39 - q^43 
        + q^44 - 2*q^48 + q^51 - q^54 - q^61 + q^62 + q^64 + q^68 - q^69 + q^72 
        - q^78 + q^81 + q^83 - 2*q^88 + q^96 - q^99 + q^102 + q^108 - q^111 + 
        q^117 - 2*q^124 - q^128 + O(q^130),
    q^11 + q^16 + q^18 - q^34 - q^36 + q^37 - q^39 - q^43 - q^48 - q^54 - q^61 +
        q^62 + q^68 - q^69 - q^78 - q^88 + q^102 + q^103 + q^108 + q^117 - q^124
        + q^129 + O(q^130),
    q^12 - q^16 - q^18 + q^26 - q^44 + q^46 + q^48 + q^52 - q^62 - q^64 - q^68 -
        q^72 + q^88 + q^92 + q^104 + q^128 + O(q^130),
    q^13 + q^16 + q^18 + q^23 - q^33 - q^34 - q^36 - q^39 - q^43 + q^44 - 2*q^48
        + q^51 - q^52 - q^54 - q^61 + q^62 + q^64 + q^68 - q^69 + q^72 - q^78 + 
        q^81 - q^88 - q^92 + q^102 - q^104 + q^108 - q^111 + q^117 - q^124 + 
        q^129 + O(q^130),
    q^17 + q^18 + q^24 + q^27 - q^33 - q^34 - q^36 - q^43 + q^44 - q^48 - q^54 -
        q^61 + q^62 - q^78 - q^88 + q^93 - q^99 + q^102 - q^111 - q^124 + 
        O(q^130),
    q^22 - q^24 - q^26 + q^32 + q^36 - q^46 - q^52 + q^66 + q^74 - q^92 - q^102 
        + q^124 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
120
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
240
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
80
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 - q^5 - q^7 + q^8 + q^9 + q^10 + q^14 - q^16 - q^18 - q^19 + q^31 + 
        q^35 + q^38 - q^40 - q^41 - q^45 + 2*q^47 - q^56 - q^59 - q^62 - q^63 + 
        q^64 + 2*q^67 - q^70 - q^71 + q^72 + q^80 + q^81 + q^82 + q^90 + 
        O(q^94),
    q^17 - q^34 - q^85 + O(q^94)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + (-a - 1)*q^5 - a*q^8 + (a - 1)*q^10 - q^16 + a*q^25 + q^33 + (a 
        + 1)*q^39 + (a - 1)*q^40 + (-a + 1)*q^41 - q^47 + a*q^49 + q^50 + a*q^51
        + a*q^59 - q^64 - a*q^66 + q^67 - q^69 + (a + 1)*q^71 + (-a + 1)*q^78 + 
        (a + 1)*q^80 + q^81 + (-a - 1)*q^82 - a*q^93 + O(q^94),
    q^3 - a*q^6 + a*q^11 + (a - 1)*q^13 + (-a - 1)*q^15 - q^17 + q^22 - a*q^23 -
        a*q^24 + (a + 1)*q^26 + a*q^27 + (a - 1)*q^30 + q^31 + a*q^34 + q^37 + 
        (-a - 1)*q^43 - q^46 - q^48 + q^54 + (-a + 1)*q^55 - a*q^61 - a*q^62 + 
        2*q^65 - 2*q^73 - a*q^74 + a*q^75 + (a + 1)*q^85 + (a - 1)*q^86 + q^88 +
        O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
527
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^33 - q^36 - q^38 - q^47 + q^49 - q^51 - q^66 - q^72 + 
        q^81 - q^93 + O(q^94),
    q^2 - q^19 - q^33 - q^36 + q^50 - q^64 + q^67 + q^81 + q^87 + O(q^94),
    q^3 - q^12 - q^17 + q^27 - q^31 + q^44 - q^46 + q^54 + q^58 - q^74 + q^75 + 
        q^88 + O(q^94),
    q^4 - q^9 - q^18 - q^32 + q^33 + q^36 + q^47 + q^51 - q^59 - q^76 - q^81 - 
        q^87 + q^93 + O(q^94),
    q^6 - 2*q^12 - q^17 + q^23 + 2*q^24 - q^31 + q^34 + q^37 - 2*q^46 - 2*q^48 +
        q^54 + q^57 + q^62 - q^68 - 2*q^74 + q^88 + 2*q^92 + O(q^94),
    q^8 - q^9 - q^16 + q^19 + q^33 - q^38 - q^59 + q^69 + q^72 - q^81 - q^87 + 
        O(q^94),
    q^11 - q^12 - q^17 + q^23 + 2*q^24 - q^27 - q^29 - q^31 + q^34 + q^37 - 
        2*q^46 - 2*q^48 + q^54 + 2*q^57 + q^58 + q^61 + q^62 - q^68 - q^73 - 
        2*q^74 - q^79 + q^88 + q^92 + O(q^94),
    q^22 - q^23 - q^24 + q^27 + q^29 - q^34 - q^37 + q^44 + q^48 - q^57 - q^62 +
        q^73 + q^79 - q^92 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a^3*q^9 + 1/5*(-3*a^3 + a^2 + a - 3)*q^11 + 1/5*(-a^3 + 2*a^2 - 3*a + 
        4)*q^17 + (-a^3 - 1)*q^19 + (-a^3 + a^2 - a + 1)*q^25 + (a^3 - a^2 + 
        a)*q^27 + 1/5*(-2*a^3 + 4*a^2 - 6*a - 2)*q^33 + 1/5*(-4*a^3 + 3*a^2 + 
        3*a - 4)*q^41 + (a^3 + a^2)*q^43 - a^2*q^49 + 1/5*(-4*a^3 - 2*a^2 - 2*a 
        + 6)*q^51 + (-a^2 + 2*a - 1)*q^59 + (a^3 - a^2 - 1)*q^67 + (2*a^3 - a^2 
        + a - 1)*q^73 + (-a^2 + a - 1)*q^81 + 1/5*(a^3 + 3*a^2 - 7*a + 6)*q^83 +
        (a^3 - a^2)*q^89 + (a - 1)*q^97 + 1/5*(2*a^3 + a^2 - 4*a + 2)*q^99 + 
        1/5*(4*a^3 - 3*a^2 - 3*a + 4)*q^107 + (a^3 - 2*a^2 + 2*a - 1)*q^113 - 
        a^3*q^121 + 1/5*(-6*a^3 + 12*a^2 - 8*a + 4)*q^123 + 1/5*(a^3 + 3*a^2 - 
        2*a + 1)*q^131 + (-a^3 + a^2 - a)*q^137 + 1/5*(-a^3 - 3*a^2 + 2*a - 
        1)*q^153 + (-a^3 - a + 1)*q^163 + a*q^169 + O(q^170),
    q^2 + 1/2*(-a^2 + a)*q^6 - a*q^8 + 1/2*(a^3 - a^2 + a - 2)*q^12 + 1/2*(a^3 +
        a - 1)*q^18 + 1/2*(a^3 - a^2)*q^24 + a^2*q^32 + 1/2*(a^2 - 1)*q^36 + 
        (-a^3 - 1)*q^38 - a^2*q^44 + 1/2*(a + 1)*q^48 + (-a^3 + a^2 - a + 
        1)*q^50 + 1/2*(a^3 + a)*q^54 + 1/2*(-a - 1)*q^66 + (-a^3 + a^2 + 1)*q^68
        + 1/2*(-a^3 + 1)*q^72 + (a^3 + a^2)*q^86 + 1/2*(a^2 - a + 1)*q^96 - 
        a^2*q^98 + 1/2*(-2*a^3 - a + 2)*q^102 + 1/2*(-a^3 + a^2 - 2*a + 1)*q^108
        + 1/2*(-a^3 + 2*a^2 - 2*a)*q^114 - a^3*q^128 + 1/2*(-a^2 + a - 1)*q^132 
        + (a^3 - a^2 - 1)*q^134 + 1/2*(-a^3 + a)*q^144 + (2*a^3 - a^2 + a - 
        1)*q^146 + 1/2*(-a + 1)*q^150 + (a^3 - a^2 + 2*a - 1)*q^152 + 1/2*(-a^2 
        + a - 1)*q^162 + (a^3 - a^2 + a)*q^164 + O(q^170),
    q^3 + (-a^2 + a)*q^9 + 1/5*(2*a^3 + 6*a^2 - 4*a + 2)*q^11 + 1/5*(4*a^3 - 
        8*a^2 + 2*a - 6)*q^17 + (a - 1)*q^27 + 1/5*(3*a^3 - a^2 - a + 3)*q^33 + 
        1/5*(-4*a^3 + 8*a^2 - 12*a + 6)*q^41 + 1/5*(a^3 - 2*a^2 + 3*a - 4)*q^51 
        + (-a^3 - 1)*q^57 + (-2*a^3 + 2*a^2 - 2*a)*q^59 + (-a^3 + a^2 - a + 
        1)*q^75 + a^2*q^81 + 1/5*(6*a^3 - 12*a^2 + 8*a - 4)*q^83 + 2*a*q^89 + 
        1/5*(2*a^3 - 4*a^2 + a - 3)*q^99 + 1/5*(4*a^3 - 8*a^2 + 12*a - 6)*q^107 
        + (-2*a^3 + 2*a^2)*q^113 + 1/5*(4*a^3 - 3*a^2 - 3*a + 4)*q^123 + (a^3 + 
        a^2)*q^129 + 1/5*(-4*a^3 - 2*a^2 - 2*a + 6)*q^131 + 2*a^3*q^137 - 
        a^2*q^147 + 1/5*(-6*a^3 + 2*a^2 - 3*a + 4)*q^153 + O(q^170),
    q^4 + 1/2*(-2*a^3 + a^2 - a + 1)*q^6 + 1/2*(-a^2 + a)*q^12 - a*q^16 + 
        1/2*(-a^3 + a^2 - 2*a + 1)*q^18 + a*q^22 + 1/2*(a^3 - a^2 + a - 2)*q^24 
        + (a^3 - 1)*q^34 + 1/2*(a^3 + a - 1)*q^36 + 1/2*(a^3 - a^2)*q^48 + 
        1/2*(a^3 + 1)*q^54 + a^2*q^64 + 1/2*(-a^3 + a^2)*q^66 + 1/2*(a^2 - 
        1)*q^72 + (-a^3 - 1)*q^76 + (-a^2 + a - 1)*q^82 - a^2*q^88 + 1/2*(a + 
        1)*q^96 + (-a^3 + a^2 - a + 1)*q^100 + 1/2*a^3*q^102 + 1/2*(a^3 + 
        a)*q^108 + 1/2*(2*a^3 - 2*a^2 - 1)*q^114 + (a^3 - 2*a^2 + a - 1)*q^118 +
        1/2*(-a - 1)*q^132 + (-a^3 + a^2 + 1)*q^136 + 1/2*(-a^3 + 1)*q^144 + 
        1/2*(-a^3 - a^2)*q^150 + 1/2*(a + 1)*q^162 + (a^2 - a)*q^166 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^9 - a^3*q^11 + (a^2 - a)*q^17 + (-a + 1)*q^19 - a^3*q^25 + (a^3 - 
        1)*q^27 + (a^3 + a - 1)*q^41 + (a^3 - a^2 - 1)*q^43 + (a^3 - a^2 + a - 
        1)*q^49 + (a^3 - a^2 + a)*q^59 + (-a^3 + a^2)*q^67 + (-a^3 - a)*q^73 + 
        (-a^3 - a)*q^81 + (-a^3 + 1)*q^83 + (a^3 - a^2 - 1)*q^89 + (a^2 + 
        1)*q^97 + (-a^3 + a^2 - a + 1)*q^99 + (a^3 + a - 1)*q^107 + (-a + 
        1)*q^113 - a*q^121 + (-a^3 + a^2)*q^131 + (-a^3 + 1)*q^137 + 2*a^2*q^139
        + (a^3 - a^2)*q^153 + (-a^2 + a - 1)*q^163 + a^2*q^169 + O(q^170),
    q^2 - a*q^4 + a^2*q^8 - a^3*q^16 + a*q^18 - a^3*q^22 + (a^3 - a^2 + a - 
        1)*q^32 + (a^2 - a)*q^34 - a^2*q^36 + (-a + 1)*q^38 + (a^3 - a^2 + a - 
        1)*q^44 - a^3*q^50 + (a^3 - 1)*q^54 + q^64 + (-a^3 + a^2)*q^68 + 
        a^3*q^72 + (a^2 - a)*q^76 + (a^3 + a - 1)*q^82 + (a^3 - a^2 - 1)*q^86 + 
        q^88 + (a^3 - a^2 + a - 1)*q^98 + (a^3 - a^2 + a - 1)*q^100 + (-a^3 + 
        a^2 + 1)*q^108 + (a^3 - a^2 + a)*q^118 - a*q^128 + (-a^3 + a^2)*q^134 + 
        (-a^2 + a - 1)*q^136 + (-a^3 + a^2 - a + 1)*q^144 + (-a^3 - a)*q^146 + 
        (-a^3 + a^2)*q^152 + (-a^3 - a)*q^162 + (-a^3 + 1)*q^164 + (-a^3 + 
        1)*q^166 + O(q^170),
    q^3 + (a^3 + a - 1)*q^9 + (-a^2 - 1)*q^27 - a^3*q^33 + (a^2 - a)*q^51 + (-a 
        + 1)*q^57 - a^3*q^75 + (-a^3 + a^2 - a + 1)*q^81 + (a^2 + 1)*q^99 + (a^3
        + a - 1)*q^123 + (a^3 - a^2 - 1)*q^129 + (a^3 - a^2 + a - 1)*q^147 - 
        a^2*q^153 + O(q^170),
    q^6 - a*q^12 + (a^3 + a - 1)*q^18 + a^2*q^24 + (-a^3 + 1)*q^36 - a^3*q^48 + 
        (-a^2 - 1)*q^54 - a^3*q^66 + (a^3 - a^2 - 1)*q^72 + (a^3 - a^2 + a - 
        1)*q^96 + (a^2 - a)*q^102 + (a^3 + a)*q^108 + (-a + 1)*q^114 + (a^3 - 
        a^2 + a - 1)*q^132 + (a^2 + 1)*q^144 - a^3*q^150 + (-a^3 + a^2 - a + 
        1)*q^162 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^3 - a)*q^7 - a*q^9 + (a^3 - a^2 + a)*q^15 + (a - 1)*q^25 + (a^2 + 
        1)*q^31 - a^3*q^33 + (a^3 - 1)*q^49 + (a^2 - a)*q^55 + (a^3 + a - 
        1)*q^63 + (a^3 - a^2 + a)*q^73 + (-a^2 + a - 1)*q^79 + a^2*q^81 + (-a^3 
        + a^2)*q^87 + (-a^2 + a - 1)*q^97 + (-a^3 - a)*q^103 + (-a^3 + a^2 - a +
        1)*q^105 + q^121 + (2*a^3 - 2*a^2 + 2*a - 2)*q^127 + (-a + 1)*q^135 + 
        (a^2 - 2*a + 1)*q^145 + (-a + 1)*q^151 + (-a^3 + 1)*q^159 + a^2*q^169 + 
        O(q^170),
    q^2 + a^2*q^8 + (a^3 - a^2 + a - 1)*q^12 + (-a^3 - a)*q^14 - a*q^18 + (-a^3 
        + a^2)*q^20 + (a^3 - a^2 + a)*q^30 + (a^3 - a^2 + a - 1)*q^32 - a*q^44 -
        a*q^48 + (a - 1)*q^50 + (-a^3 + 1)*q^56 + (a^2 + 1)*q^62 - a^3*q^66 - 
        a^3*q^72 + (a^3 - a^2 + a)*q^80 + (a^2 + 1)*q^84 + (a^3 - 1)*q^98 + 
        q^108 + (a^2 - a)*q^110 + (-a + 1)*q^116 + (a^2 - a)*q^120 + (a^3 + a - 
        1)*q^126 - a*q^128 - a^2*q^140 + (a^3 - a^2 + a)*q^146 + (-a^2 + a - 
        1)*q^158 + a^2*q^162 + O(q^170),
    q^3 + (-a^2 + a - 1)*q^5 + a^2*q^11 + (-a^3 - a)*q^21 - a*q^27 + (a^2 - 
        a)*q^29 + a^3*q^35 + (a^3 - a^2 + a)*q^45 + (a^3 + a - 1)*q^53 + (-a^3 +
        1)*q^59 + (a - 1)*q^75 + (-a^3 + 1)*q^77 + (-a^2 + a - 1)*q^83 + (a^2 + 
        1)*q^93 - a^3*q^99 + (-a + 1)*q^101 + (a^3 - a^2 - 1)*q^107 + (-a^3 + 
        a^2 - a + 1)*q^125 + (-a^3 - a)*q^131 + (a^3 - 1)*q^147 + (a^2 + 
        1)*q^149 - a^2*q^155 + (a^2 - a)*q^165 + O(q^170),
    q^4 + a^2*q^6 + (-a + 1)*q^10 + a^2*q^16 + (a^3 - a^2 + a - 1)*q^22 + (a^3 -
        a^2 + a - 1)*q^24 + (-a^3 - a)*q^28 - a*q^36 + (-a^3 + a^2)*q^40 + (-a^3
        + 1)*q^42 - a^3*q^54 + (-a^2 + a - 1)*q^58 + (a^3 - a^2 + a)*q^60 + (a^3
        - a^2 + a - 1)*q^64 - q^70 - a*q^88 + (a^2 - a)*q^90 - a*q^96 + (a - 
        1)*q^100 + (a^3 - a^2 - 1)*q^106 + (-a^3 + 1)*q^112 + (a^2 + 1)*q^118 + 
        (a^2 + 1)*q^124 - a^3*q^132 - a^3*q^144 + (a^3 - a^2)*q^150 + (a^2 + 
        1)*q^154 + (a^3 - a^2 + a)*q^160 + (-a + 1)*q^166 + (a^2 + 1)*q^168 + 
        O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 - q^33 - q^37 + q^49 + 2*q^53 + q^69 - q^81 - q^89 + q^93 - q^97 - 
        q^113 + q^121 + q^125 - q^137 - 2*q^141 - q^157 + q^165 + q^169 + 
        O(q^170),
    q^2 - q^10 - q^18 + q^22 - q^46 + q^54 - q^62 - q^74 + q^90 + 2*q^94 + q^98 
        + 2*q^106 - q^110 - q^118 - q^134 - q^142 + O(q^170),
    q^3 - q^15 - q^99 - q^111 + q^147 + 2*q^159 + O(q^170),
    q^4 - q^20 - q^36 + q^44 - q^92 + q^108 - q^124 - q^148 + O(q^170),
    q^6 - q^18 - q^30 + q^66 + q^90 - q^138 + q^162 + O(q^170),
    q^9 - q^33 - q^45 + q^69 - q^81 + q^93 - 2*q^141 + q^165 + O(q^170),
    q^11 - q^23 + q^27 - q^31 + 2*q^47 - q^55 - q^59 - q^67 - q^71 - q^99 + 
        2*q^103 + q^115 - q^135 + q^155 + 2*q^163 + O(q^170),
    q^12 - q^36 - q^60 + q^132 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^25 + q^45 - q^49 - q^69 - q^93 + q^121 + q^165 + q^169 + O(q^170),
    q^3 - q^23 + q^31 - q^55 - q^59 - q^67 + q^71 - q^75 + q^115 + q^135 - q^147
        + q^155 + O(q^170),
    q^5 + q^25 - q^33 - q^37 - q^45 + q^81 - q^89 - q^97 + q^113 - q^125 - q^137
        + 2*q^141 + q^157 + O(q^170),
    q^9 + 2*q^25 - q^33 - 2*q^37 - q^45 - q^69 + q^81 + q^93 - 2*q^97 + 2*q^141 
        + 2*q^157 - q^165 + O(q^170),
    q^11 + q^23 - q^27 + q^31 - 2*q^47 - q^55 + q^59 - q^67 - q^71 - 2*q^75 + 
        q^99 + 2*q^111 + q^115 + q^135 + q^155 + O(q^170),
    q^15 - q^23 - q^31 + q^55 - q^59 + q^67 + q^71 + q^75 - q^99 - q^111 - q^115
        - q^135 + q^155 + O(q^170)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
528
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + H.3 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + q^9 - q^25 - q^27 - q^49 + 2*q^67 + q^75 + q^81 - 2*q^97 + q^121 +
        q^147 - 2*q^163 - q^169 + O(q^170),
    q^2 - q^6 + q^8 + q^18 - q^24 + q^32 - q^44 - q^50 - q^54 - 2*q^68 + q^72 - 
        q^96 - q^98 + q^128 + q^132 + 2*q^134 + q^150 + q^162 + 2*q^164 + 
        O(q^170),
    q^4 - q^12 + q^16 - q^22 - 2*q^34 + q^36 - q^48 + q^64 + q^66 + 2*q^82 - 
        q^88 - q^100 + 2*q^102 - q^108 - 2*q^136 + q^144 + 2*q^166 + O(q^170),
    q^11 + 2*q^17 - q^33 - 2*q^41 - 2*q^51 - 2*q^83 + q^99 + 2*q^107 + 2*q^123 -
        2*q^131 + 2*q^153 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
529
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
506
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
529
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
529
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 - a^8*q^3 - a^9*q^6 - a^3*q^8 + a^7*q^13 - a^4*q^16 - q^24 - 
        a*q^25 + a^8*q^26 + a^2*q^27 + a^9*q^29 + a^3*q^31 + a^4*q^39 - a^6*q^41
        - q^47 - a*q^48 + a^8*q^49 - a^2*q^50 + a^3*q^54 + (a^9 - a^8 + a^7 - 
        a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^58 - 2*a^7*q^59 + a^4*q^62 + 
        a^6*q^64 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
529
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
253*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 - q^3 + q^6 + q^8 - q^13 - q^16 - q^24 + q^25 + q^26 + q^27 - q^29 -
        q^31 + q^39 - q^41 - q^47 + q^48 + q^49 - q^50 - q^54 + q^58 + 2*q^59 + 
        q^62 + q^64 + O(q^70),
    q^23 - q^46 - q^69 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
530
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
156
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
530
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
156
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
530
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
156
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
530
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
156
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
530
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
156
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
530
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
156
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
530
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
156
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
530
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
156
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
531
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
531
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
531
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
531
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
174
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
531
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
174
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
531
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
531
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
29*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 + q^5 - q^7 + q^16 - 2*q^17 - q^19 + q^20 - q^28 + q^29 - q^35 + 
        q^41 + q^53 - q^59 + q^64 - 2*q^68 - 2*q^71 - q^76 - q^79 + q^80 - 
        2*q^85 - q^95 + q^107 - q^112 + O(q^114)
]
;
Bo:=
[
    q + q^4 - q^5 - q^7 + q^16 + 2*q^17 - q^19 - q^20 - q^28 - q^29 + q^35 - 
        q^41 - q^53 + q^59 + q^64 + 2*q^68 + 2*q^71 - q^76 - q^79 - q^80 - 
        2*q^85 + q^95 - q^107 - q^112 + O(q^114),
    q^3 + q^12 - q^15 - q^21 - q^27 + q^48 + 2*q^51 - q^57 - q^60 + q^81 - q^84 
        - q^87 + q^105 - q^108 + O(q^114),
    q^9 - q^27 + q^36 - q^45 - q^63 - q^108 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
531
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 29*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 - a*q^15 - a*q^16 - q^17 + q^21 - a*q^25 + (a - 1)*q^27 + 
        2*q^35 + (a - 1)*q^45 + (a - 1)*q^49 + q^57 + (a - 1)*q^59 + q^60 - 
        a*q^63 + q^64 + (-a + 1)*q^68 - q^71 + (a - 1)*q^75 + (a - 1)*q^84 - 
        a*q^87 + (-a + 1)*q^95 + q^100 - a*q^105 - a*q^108 + O(q^114),
    q^3 + a*q^9 + (a - 1)*q^12 + a*q^15 + (-a + 2)*q^19 - q^21 + (a + 1)*q^25 + 
        (-a - 1)*q^29 + (a - 2)*q^35 - q^36 + (-2*a + 1)*q^41 - a*q^45 - a*q^48 
        + (-2*a + 1)*q^49 - q^51 + (-a + 2)*q^53 + a*q^57 - q^60 + q^63 + (2*a -
        1)*q^76 + (-a - 1)*q^79 + (a - 1)*q^81 + (-a + 1)*q^84 + (-a + 1)*q^87 +
        (2*a - 1)*q^95 + (a - 2)*q^100 + q^105 + (a - 2)*q^107 + O(q^114),
    q^5 + (a - 1)*q^7 - a*q^9 - a*q^15 + (a - 1)*q^19 + (a - 1)*q^20 + q^21 - 
        a*q^25 - a*q^28 + q^29 + q^35 + q^36 + (a - 1)*q^41 + (a - 1)*q^49 + (a 
        - 1)*q^53 - a*q^57 + q^60 - a*q^75 - a*q^76 + q^79 - a*q^80 + (a - 
        1)*q^84 - q^85 + (a - 1)*q^87 - a*q^95 + q^100 + q^105 + q^107 + q^112 +
        O(q^114)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 + (-a + 1)*q^6 + (-a + 1)*q^13 + q^14 + q^16 + (-a + 1)*q^17 + (a - 
        1)*q^21 - a*q^22 + (a - 1)*q^24 - q^25 + (a - 1)*q^29 + q^33 + (a - 
        1)*q^37 + q^38 - a*q^41 + a*q^46 - q^49 + (a - 1)*q^52 - q^54 - q^56 + 
        (a - 1)*q^57 - a*q^61 + a*q^62 - q^64 + (a - 1)*q^68 - q^69 + (-a + 
        1)*q^73 + a*q^77 - a*q^78 + (-a + 1)*q^81 + (-a + 1)*q^84 + a*q^86 + 
        a*q^88 + a*q^89 - q^93 - a*q^94 + (-a + 1)*q^96 + a*q^97 + q^100 - 
        a*q^102 + (a - 1)*q^109 + 2*q^113 + (-a + 1)*q^116 + (a - 1)*q^118 - 
        q^129 - q^132 - q^133 + 2*q^137 + q^141 - a*q^142 + (-a + 1)*q^148 + 
        O(q^150),
    q^2 + (a - 1)*q^3 - q^7 - q^8 + a*q^11 + (-a + 1)*q^12 - q^19 - a*q^23 + (-a
        + 1)*q^26 + q^27 + q^28 - a*q^31 + q^32 + (-a + 1)*q^34 + a*q^39 + (a - 
        1)*q^42 - a*q^43 - a*q^44 + a*q^47 + (a - 1)*q^48 - q^50 + a*q^51 + (a -
        1)*q^58 + (-a + 1)*q^59 + q^66 + a*q^71 + (a - 1)*q^74 + (-a + 1)*q^75 +
        q^76 - a*q^82 - a*q^87 + (a - 1)*q^91 + a*q^92 - q^98 + (-a + 1)*q^103 +
        (a - 1)*q^104 + (-a + 1)*q^107 - q^108 - a*q^111 - q^112 + (a - 1)*q^114
        + (a - 1)*q^119 - a*q^122 + q^123 + a*q^124 + (a - 1)*q^127 - q^128 + (a
        - 1)*q^136 - q^138 + (a - 1)*q^139 + q^143 + (-a + 1)*q^146 + (-a + 
        1)*q^147 + O(q^150)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^15 + a*q^21 + (a - 1)*q^23 + (-a + 1)*q^29 - a*q^35 - q^39 - 
        a*q^43 - q^49 + (-a + 1)*q^51 + (-a + 1)*q^53 - a*q^57 + q^65 + (a - 
        1)*q^67 + a*q^71 - a*q^79 + a*q^81 + (a - 1)*q^85 + (-a + 1)*q^91 + 
        a*q^95 - a*q^109 + a*q^119 - q^121 + (-a + 1)*q^123 + (a - 1)*q^127 + 
        q^133 - a*q^135 + (-a + 1)*q^137 - q^141 + a*q^149 + O(q^150),
    q^2 + (-a + 1)*q^8 - q^16 + (a - 1)*q^30 + a*q^42 + (a - 1)*q^46 + (-a + 
        1)*q^58 + (a - 1)*q^64 - a*q^70 - q^78 - a*q^86 - q^98 + (-a + 1)*q^102 
        + (-a + 1)*q^106 - a*q^114 + a*q^120 + q^128 + q^130 + (a - 1)*q^134 + 
        a*q^142 + O(q^150),
    q^3 - q^5 + (a - 1)*q^7 - a*q^13 + q^17 + (-a + 1)*q^19 + (a - 1)*q^27 + 
        q^41 - a*q^47 - q^59 + a*q^61 + (a - 1)*q^69 - q^73 + (-a + 1)*q^87 + 
        a*q^89 + q^97 + a*q^101 - a*q^105 + (-a + 1)*q^115 + (-a + 1)*q^125 - 
        a*q^129 - q^131 + a*q^139 + (a - 1)*q^145 - q^147 + O(q^150),
    q^4 - a*q^8 - q^32 + (a - 1)*q^60 + a*q^64 + a*q^84 + (a - 1)*q^92 + (-a + 
        1)*q^116 + q^120 - a*q^140 + O(q^150),
    q^6 - q^10 + (a - 1)*q^14 + (-a + 1)*q^24 - a*q^26 + q^34 + (-a + 1)*q^38 + 
        (a - 1)*q^40 - q^48 + (a - 1)*q^54 + a*q^56 + q^80 + q^82 - a*q^94 - 
        q^104 + (-a + 1)*q^112 - q^118 + a*q^122 + (-a + 1)*q^136 + (a - 
        1)*q^138 - q^146 + O(q^150),
    q^12 - q^20 - a*q^24 + (a - 1)*q^28 + a*q^40 - a*q^52 + q^56 + q^68 + (-a + 
        1)*q^76 - q^96 + (a - 1)*q^104 + (a - 1)*q^108 - a*q^136 + O(q^150)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + (-a + 1)*q^6 + (-a + 1)*q^13 + (a - 1)*q^14 + (a - 1)*q^16 - 
        q^17 + q^21 - a*q^22 + q^24 + a*q^25 + (a - 1)*q^29 + (a - 1)*q^33 - 
        a*q^37 - a*q^38 - a*q^41 + (-a + 1)*q^46 - q^49 + q^52 + (-a + 1)*q^54 -
        q^56 + (a - 1)*q^57 + q^61 + a*q^62 - q^64 - a*q^68 - q^69 - q^73 + (-a 
        + 1)*q^77 - a*q^78 - q^81 + a*q^84 - q^86 + (-a + 1)*q^88 - q^89 + (-a +
        1)*q^93 + (a - 1)*q^94 + a*q^96 + a*q^97 + (a - 1)*q^100 + (a - 1)*q^102
        + q^109 + 2*q^113 - q^116 + (a - 1)*q^118 + a*q^129 - q^132 + (-a + 
        1)*q^133 - 2*a*q^137 + q^141 + q^142 + (-a + 1)*q^148 + O(q^150),
    q^2 - a*q^3 + a*q^7 + a*q^8 - q^11 + (-a + 1)*q^12 - q^19 - a*q^23 + (-a + 
        1)*q^26 - a*q^27 + (a - 1)*q^28 + q^31 + (a - 1)*q^32 - q^34 - q^39 + 
        q^42 + (a - 1)*q^43 - a*q^44 + a*q^47 + q^48 + a*q^50 + a*q^51 + (a - 
        1)*q^58 + a*q^59 + (a - 1)*q^66 + (-a + 1)*q^71 - a*q^74 + (-a + 1)*q^75
        - a*q^76 - a*q^82 + q^87 + q^91 + (-a + 1)*q^92 - q^98 + (-a + 1)*q^103 
        + q^104 + (-a + 1)*q^107 + (-a + 1)*q^108 + (a - 1)*q^111 - q^112 + (a -
        1)*q^114 - a*q^119 + q^122 + (a - 1)*q^123 + a*q^124 + q^127 - q^128 - 
        a*q^136 - q^138 + q^139 + (a - 1)*q^143 - q^146 + a*q^147 + O(q^150)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 + q^9 - q^11 - q^17 + q^19 + 2*q^23 - q^43 - q^45 - q^47 - q^49 + 
        q^55 - q^61 - q^73 + q^81 + 2*q^83 + q^85 - q^95 - q^99 + 2*q^101 - 
        2*q^115 + q^125 - q^131 - q^137 - q^139 - q^149 + O(q^150),
    q^7 - q^35 - q^49 + q^63 - q^77 - q^119 + q^133 + O(q^150)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + 1/3*(-a + 2)*q^7 + (a - 1)*q^9 - a*q^11 + a*q^17 + (a - 1)*q^19 + (-a + 
        1)*q^23 - a*q^25 + 1/3*(-2*a + 4)*q^35 + (a - 1)*q^47 + 1/3*(a + 1)*q^49
        - 2*q^55 + (a - 1)*q^61 + 1/3*(2*a - 1)*q^63 - a*q^73 + 1/3*(-5*a + 
        1)*q^77 - a*q^81 - q^83 + q^99 + a*q^101 + 1/3*(a + 1)*q^119 + (2*a - 
        2)*q^121 + 2*q^125 + (-a + 1)*q^131 + 1/3*(2*a - 1)*q^133 - a*q^137 + 
        q^139 + O(q^150),
    q^5 + 1/3*(2*a - 1)*q^7 + (-a + 1)*q^11 + (a - 1)*q^25 + 1/3*(-2*a + 1)*q^35
        - a*q^43 + (a - 1)*q^45 - q^47 + 1/3*(a + 1)*q^49 - q^61 + 1/3*(-a - 
        1)*q^63 + (-a + 1)*q^73 + 1/3*(-2*a + 1)*q^77 + a*q^85 + (a - 1)*q^95 + 
        a*q^99 + (-a + 1)*q^115 + 1/3*(a - 2)*q^119 - q^121 - a*q^125 + 1/3*(-a 
        - 1)*q^133 + (-a + 1)*q^137 + a*q^139 + q^149 + O(q^150)
]
;
Bo:=
[
    q + (-a + 1)*q^5 + (a - 1)*q^7 + (a - 1)*q^9 + a*q^11 - 2*a*q^17 + (a - 
        1)*q^19 + (-a + 1)*q^23 + a*q^35 - q^43 + a*q^45 + (-a + 1)*q^47 - 
        a*q^49 + q^55 + (-a + 1)*q^61 - a*q^63 + a*q^73 - q^77 - a*q^81 - q^83 -
        2*q^85 + a*q^95 - q^99 + a*q^101 - a*q^115 + 2*q^119 + q^125 + (2*a - 
        2)*q^131 - a*q^133 + a*q^137 - q^139 + (-a + 1)*q^149 + O(q^150),
    q^2 - a*q^8 + (-a + 1)*q^10 + (a - 1)*q^14 + (a - 1)*q^18 + a*q^22 + (a - 
        1)*q^32 - 2*a*q^34 + (a - 1)*q^38 - q^40 + (-a + 1)*q^46 + q^56 + a*q^70
        + q^72 - q^86 + (-a + 1)*q^88 + a*q^90 + (-a + 1)*q^94 - a*q^98 + q^110 
        + (-a + 1)*q^122 - a*q^126 + q^128 + (2*a - 2)*q^136 + a*q^146 + 
        O(q^150),
    q^4 - a*q^16 + (-a + 1)*q^20 + (a - 1)*q^28 + (a - 1)*q^36 + a*q^44 + (a - 
        1)*q^64 - 2*a*q^68 + (a - 1)*q^76 - q^80 + (-a + 1)*q^92 + q^112 + 
        a*q^140 + q^144 + O(q^150)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
532
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
150
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
120
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
120
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
533
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
534
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
534
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
88
);
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
534
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
44
);
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
534
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
534
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
534
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
534
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 22*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
534
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 44*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
535
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
535
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
106
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
535
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
106
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
535
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
212
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
535
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
53*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + q^4 - q^11 - q^12 - q^13 + q^16 - q^19 - q^23 + q^25 + q^27 + 
        2*q^29 + q^33 - q^37 + q^39 - q^41 - q^44 + 2*q^47 - q^48 + q^49 - q^52 
        - q^53 + q^57 - q^61 + q^64 + q^69 - q^75 - q^76 - q^79 - q^81 + 2*q^83 
        - 2*q^87 - q^89 - q^92 + q^100 - q^101 + O(q^106),
    q^5 - q^15 + q^20 - q^55 - q^60 - q^65 + q^80 - q^95 + O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
535
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 53*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^34 - q^35 - q^41 - q^44 + q^49 - q^56 - q^61 - q^79 + 
        q^81 - q^86 + O(q^106),
    q^2 - q^17 + q^18 - q^22 - q^28 - q^43 + q^50 - q^55 + q^67 + q^73 + q^77 - 
        q^80 + q^95 + q^103 + O(q^106),
    q^4 - q^11 - q^14 + q^35 + q^36 - q^40 + q^41 - q^49 + q^61 - q^76 + q^79 - 
        q^85 - q^99 + q^100 - q^101 + O(q^106),
    q^5 - q^8 - q^17 + q^20 - q^22 + q^28 - q^32 + 2*q^38 - q^43 + q^45 - q^55 +
        2*q^58 - q^68 - q^70 - q^72 - q^82 + q^88 - q^98 + O(q^106),
    q^7 - q^8 - q^17 + q^20 + q^38 - q^43 - q^55 + q^58 + q^63 - q^70 - q^72 + 
        q^77 - q^82 + q^97 + O(q^106),
    q^10 - q^11 - q^16 + q^19 + q^29 - q^34 - q^49 + q^56 + q^76 - q^85 - q^86 +
        q^89 + q^90 - q^99 - q^101 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + (-a^19 + a^17 + a^16 - 2*a^14 - a^13 + a^11 + a^10 + a^9 - a^7 -
        a^6 + a^4 + 2*a^3 - a - 1)*q^3 + a^2*q^4 + (-a^19 - a^18 + a^16 + 2*a^15
        - a^13 - a^12 + a^9 + a^8 - a^6 - a^5 - a^4 + a^3 + a^2 - 1)*q^6 - 
        a^3*q^8 + (-a^17 + a^12 - a^7)*q^9 + (-a^18 - a^12 + a^7 + a)*q^11 + 
        (-a^16 + a^11 + a^5 - 1)*q^12 + a^4*q^16 + (a^18 - a^11)*q^17 + (a^18 - 
        a^13 + a^8)*q^18 + (a^14 + a^6)*q^19 + (a^19 + a^13 - a^8 - a^2)*q^22 + 
        (a^17 - a^12 - a^6 + a)*q^24 + (a^19 - a^8)*q^25 + (a^19 + a^18 - 2*a^16
        - a^15 + a^13 + a^12 - a^10 - 2*a^9 - a^8 + a^6 + 2*a^5 + a^4 - a^3 - 
        a^2 + 1)*q^27 - a^5*q^32 + (-a^19 - a^18 + 2*a^16 - a^13 - a^12 + a^10 +
        a^9 + a^8 - a^6 - a^5 + a^3 + a^2 - 1)*q^33 + (-a^19 + a^12)*q^34 + 
        (-a^19 + a^14 - a^9)*q^36 + (-a^15 - a^7)*q^38 + (a^19 + a^18 - a^16 - 
        a^15 + a^13 + a^12 - a^10 - a^9 + a^6 + a^5 - a^3 - a^2 + 1)*q^41 + 
        (a^16 + a^2)*q^43 + (a^19 - a^17 - a^16 + a^13 - a^11 - a^10 + a^7 + a^6
        - a^4 + a + 1)*q^44 + (-a^18 + a^13 + a^7 - a^2)*q^48 - a^13*q^49 + 
        (a^19 - a^17 - a^16 + a^14 + a^13 - a^11 - a^10 + a^7 + a^6 - a^4 - a^3 
        + a + 1)*q^50 + (a^19 - a^17 - a^16 + a^14 + a^13 - a^11 + a^7 + a^6 - 
        a^5 - a^4 - 2*a^3 + a + 1)*q^51 + (a^17 + a^10 - a^6 - a^5 + 1)*q^54 + 
        (a^19 - a^17 - a^16 + a^15 + a^14 + a^13 - a^11 - a^10 + a^7 + 2*a^6 - 
        2*a^4 - a^3 + 1)*q^57 + (a^17 - a^11 - a^6)*q^59 + a^6*q^64 + (-a^17 + 
        a^16 - 1)*q^66 - a^15*q^67 + (-a^19 + a^17 + a^16 - a^14 - 2*a^13 + a^11
        + a^10 + a^9 - a^7 - a^6 + a^4 + a^3 - a - 1)*q^68 + (-a^19 + a^17 + 
        a^16 - a^15 - a^14 - a^13 + a^11 + 2*a^10 + a^9 - a^7 - a^6 + a^4 + a^3 
        - a - 1)*q^72 + (-a^9 - a^5)*q^73 + (-a^17 + a^11 - 1)*q^75 + (a^16 + 
        a^8)*q^76 + (-a^19 - a^18 + a^14 + a^13 + a^7 - a^2 - a)*q^81 + (-a^9 + 
        1)*q^82 + (-a^19 + a^11 - 1)*q^83 + (-a^17 - a^3)*q^86 + (a^19 + a^18 - 
        a^16 + a^13 + a^12 - a^10 - a^9 - a^8 + a^6 + a^5 - a^4 - a^3 - a^2 + 
        1)*q^88 + (a^17 + a^15 - a^6 - a^4)*q^89 + (a^19 - a^14 - a^8 + 
        a^3)*q^96 + (-a^19 + a^17 + a^16 - a^14 + a^11 + a^10 + a^9 - a^7 - a^6 
        + a^4 + a^3 - a^2 - a - 1)*q^97 + a^14*q^98 + (a^19 - a^13 - a^7 - a^3 +
        a^2)*q^99 + (a^19 + a^18 - a^16 - a^15 + a^13 + a^12 - a^10 - a^9 - a^8 
        + a^6 + a^5 - a^3 - a^2 + 1)*q^100 + (a^19 + a^18 - a^16 - a^15 + a^13 +
        a^12 - a^11 - a^10 - a^9 - a^8 + 2*a^6 + a^5 + a^4 - a^3 - a^2 + 
        1)*q^102 + (a^13 + a^12 - a^2)*q^107 + (-a^18 - a^11 + a^7 + a^6 - 
        a)*q^108 + (-a^19 - a^18 + a^16 + a^15 - a^13 - a^12 + a^9 + a^8 - a^6 -
        a^5 + a^4 + a^3 + a^2 - 1)*q^113 + (a^19 + a^18 - 2*a^16 - a^15 + a^13 +
        a^12 - a^10 - a^9 - a^8 - a^7 + a^6 + 2*a^5 - a^3 + 1)*q^114 + (-a^18 + 
        a^12 + a^7)*q^118 + (-a^19 - a^14 - a^13 + a^3)*q^121 + (-a^19 + a^17 + 
        a^13 - a^6 - a^2 + 1)*q^123 - a^7*q^128 + (-a^16 + a^11 + a^8 + a^5 - 
        a^3 - 1)*q^129 + O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + (-a^9 - a^3)*q^3 + a^2*q^4 + (a^9 - a^8 + a^7 - a^6 + a^5 + a^3 
        - a^2 + a - 1)*q^6 - a^3*q^8 + (-a^7 + a^6 - a)*q^9 + (-a^7 - a)*q^11 + 
        (-a^5 + 1)*q^12 + a^4*q^16 + (-a^7 + 1)*q^17 + (a^8 - a^7 + a^2)*q^18 + 
        (a^6 - a^3)*q^19 + (a^8 + a^2)*q^22 + (a^6 - a)*q^24 + a^8*q^25 + (-a^8 
        + a^7 - a^6 + a^3 - a^2 + a - 1)*q^27 - a^5*q^32 + (2*a^9 - 2*a^8 + 
        2*a^7 - 2*a^6 + a^5 - a^4 + 2*a^3 - 2*a^2 + 2*a - 2)*q^33 + (a^8 - 
        a)*q^34 + (-a^9 + a^8 - a^3)*q^36 + (-a^7 + a^4)*q^38 + (a^9 + a^7 - a^6
        + a^5 - a^4 + a^3 - a^2 + a - 1)*q^41 + (-a^5 + a^2)*q^43 + (-a^9 - 
        a^3)*q^44 + (-a^7 + a^2)*q^48 + a^2*q^49 - a^9*q^50 + (-a^8 + a^7 - a^6 
        - a^4 - a^2 + a - 1)*q^51 + (a^9 - a^8 + a^7 - a^4 + a^3 - a^2 + a)*q^54
        + (-a^9 + a^6 + a^4 - a)*q^57 + (a^6 + 1)*q^59 + a^6*q^64 + (a^6 - a^5 +
        2)*q^66 + a^4*q^67 + (-a^9 + a^2)*q^68 + (-a^8 + a^7 - a^6 + a^5 + a^3 -
        a^2 + a - 1)*q^72 + (-a^9 - a^5)*q^73 + (a^6 + 1)*q^75 + (a^8 - 
        a^5)*q^76 + (a^8 - a^7 - a^3 + a^2 - a)*q^81 + (-a^9 + 1)*q^82 + (a^8 + 
        1)*q^83 + (a^6 - a^3)*q^86 + (a^9 - a^8 + a^7 - a^6 + a^5 + a^3 - a^2 + 
        a - 1)*q^88 + (a^6 + a^4)*q^89 + (a^8 - a^3)*q^96 + (-a^9 + a^2)*q^97 - 
        a^3*q^98 + (2*a^8 - a^7 - a^3 + 2*a^2)*q^99 + (a^9 - a^8 + a^7 - a^6 + 
        a^5 - a^4 + a^3 - a^2 + a - 1)*q^100 + (a^9 - a^8 + a^7 + a^5 + a^3 - 
        a^2 + a)*q^102 + (a^2 - a)*q^107 + (-a^7 + a^6 - a + 1)*q^108 + (a^9 - 
        a^8 + a^7 - a^6 + a^5 + a^3 - a^2 + a - 1)*q^113 + (a^9 - a^8 - a^6 - 
        a^4 + a^3 + a - 1)*q^114 + (-a^7 - a)*q^118 + (a^8 - a^3 + a^2)*q^121 + 
        (a^8 + a^6 + a^2 + 1)*q^123 - a^7*q^128 + (a^8 - a^5 - a^3 + 1)*q^129 + 
        O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 22*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 22*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 - q^3 + (a - 1)*q^4 + a*q^6 + q^8 + (2*a - 2)*q^11 + (-a + 1)*q^12
        - a*q^16 + a*q^17 + a*q^19 + 2*q^22 - q^24 + q^25 + q^27 + (a - 1)*q^32 
        + (-2*a + 2)*q^33 + (-a + 1)*q^34 + (-a + 1)*q^38 + (2*a - 2)*q^41 - 
        q^43 - 2*a*q^44 + a*q^48 - a*q^49 - a*q^50 - a*q^51 - a*q^54 - a*q^57 - 
        q^59 + q^64 - 2*q^66 + q^67 - q^68 + a*q^73 - q^75 - q^76 - q^81 + 
        2*q^82 - 2*a*q^83 + a*q^86 + (2*a - 2)*q^88 - q^89 + (-a + 1)*q^96 + 
        a*q^97 + (a - 1)*q^98 + (a - 1)*q^100 + (a - 1)*q^102 + 2*q^107 + (a - 
        1)*q^108 + (-a + 1)*q^113 + (a - 1)*q^114 + a*q^118 - 3*a*q^121 + (-2*a 
        + 2)*q^123 - a*q^128 + q^129 + O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
33*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^17 - q^19 - q^23 + q^25 - q^29 - q^37 - q^47 + q^49 - q^59 + 
        q^67 + 2*q^71 - q^73 + q^81 + 2*q^83 - q^89 + 2*q^103 - q^107 + q^121 - 
        q^127 + O(q^130),
    q^2 + q^18 - q^34 - q^38 - q^46 + q^50 - q^58 - q^74 - q^94 + q^98 - q^118 +
        O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
536
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 33*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^15 + q^16 - q^22 + q^25 - q^26 - q^47 + q^49 - q^55 - q^60 + 
        q^64 - q^65 - q^73 - q^88 - q^90 + q^100 - q^102 - q^104 + q^121 - q^129
        + O(q^130),
    q^2 + q^8 - q^11 - q^13 - q^30 + q^32 - q^44 - q^45 + q^50 - q^51 - q^52 + 
        q^67 + q^69 + q^75 + 2*q^85 - q^94 + q^98 + q^99 - q^110 - q^115 + q^117
        - q^120 - q^125 + q^128 + O(q^130),
    q^3 - q^11 + q^12 - q^13 - q^18 + q^27 - q^30 - q^44 + q^46 + q^48 + q^50 - 
        q^51 - q^52 + q^53 + q^61 + q^66 - q^69 - q^72 + q^78 + q^85 - q^94 - 
        q^99 + q^101 + q^108 - q^115 - q^117 - q^120 - q^125 + O(q^130),
    q^5 - q^11 - q^13 - q^18 + q^20 + q^27 + q^34 + q^43 - q^44 - q^52 + q^66 - 
        q^69 - q^72 - q^75 + q^78 + q^80 - q^94 + q^108 + q^109 - q^110 + 
        O(q^130),
    q^6 - q^10 - q^15 - q^17 + q^23 + q^24 + q^25 - q^40 + q^55 - q^60 + q^65 - 
        q^68 - q^71 - q^81 - q^86 + q^89 + q^92 + q^96 + q^100 - q^102 + q^103 +
        q^106 - q^121 + q^122 - q^127 - q^129 + O(q^130),
    q^9 - q^10 - q^17 + q^22 + q^26 - q^33 + q^36 - q^39 - q^40 + q^47 - q^54 + 
        q^55 + q^65 - q^68 - q^71 + q^73 - q^86 + q^88 + q^104 - q^121 - q^127 +
        O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
537
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
537
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
178
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
537
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
178
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
537
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
89*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^15 + q^16 - q^17 - q^19 - q^29 - q^39 + 2*q^47 + q^49 + q^51 + 
        q^57 - q^59 - q^60 - q^61 + q^64 + q^65 - q^67 - q^68 + q^75 - q^76 - 
        q^81 - q^85 + q^87 - q^93 - q^95 + 2*q^101 - q^116 + O(q^118),
    q^3 + q^12 - q^15 - q^39 - q^45 + q^48 - q^60 + q^75 - q^81 - q^93 - q^117 +
        O(q^118),
    q^5 + q^13 - q^17 - q^19 + q^20 - q^25 + q^27 - q^29 + q^31 + q^43 - q^45 + 
        q^52 - q^59 - q^61 - q^65 - q^67 - q^68 - q^76 + q^80 - q^81 + q^83 + 
        q^89 - q^100 + q^107 + q^108 - q^116 - q^117 + O(q^118),
    q^9 - q^15 - q^27 + q^36 - q^39 + q^51 + q^57 - q^60 + q^75 + q^87 - q^93 - 
        q^108 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
538
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
268
);
qprec:=
133
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
538
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
67*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
133
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^3 - 2*a^2 + a - 1)*q^2 + (-a^2 + 2*a - 1)*q^4 + (-a^3 + a^2 + a - 
        1)*q^8 + a^3*q^9 + a^2*q^11 + (-2*a^3 + 2*a^2 - 2*a)*q^16 + (-a^2 + 
        1)*q^18 + (-a^3 + a^2 - 2*a + 1)*q^22 + (-a^3 + a^2 + 1)*q^23 + (-a^3 + 
        a^2 - a + 1)*q^25 + (2*a^3 - a^2 + a - 1)*q^29 + (2*a^2 - 2*a + 1)*q^32 
        + (a^3 - 2*a^2 + 2*a - 1)*q^36 + (a^2 + 1)*q^37 + (-a^3 - a^2)*q^43 + 
        (a^3 - a + 1)*q^44 + (-a - 1)*q^46 + (a^3 - a)*q^50 + (a - 1)*q^53 + 
        (-a^3 - a^2 + a + 1)*q^58 + (a^3 - a + 1)*q^64 + (a^3 - a^2)*q^67 + 
        (-a^3 + a^2 - a)*q^71 + (-a^2 + 2*a - 2)*q^72 + (-a^2 - a)*q^74 + (-a - 
        1)*q^79 - a*q^81 + (a^3 + 2*a - 2)*q^86 + (2*a^3 - 2*a^2 + a)*q^88 + 
        (a^2 - a + 1)*q^92 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
210
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
14*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^7 + a)*q^2 + (2*a^7 + a^6 - a^5 - 2*a^4 - 2*a^3 + a + 2)*q^4 + (-a^7
        + 2*a^3 + a^2 - 2)*q^8 - a^4*q^9 + (-a^6 + a)*q^11 + (2*a^7 - 2*a^5 + 
        2)*q^16 + (a^6 - a^5 - a)*q^18 + (-a^7 - a^3 + a^2)*q^22 + (a^5 + a^4 - 
        a - 1)*q^23 - a^2*q^25 + (2*a^7 + a^6 - a^3 - 2*a^2 + 1)*q^29 + (-2*a^7 
        - 2*a^6 + a^5 + 2*a^4 + 2*a^3 - 2)*q^32 + (a^7 - a^6 + a^3 - a^2)*q^36 +
        (a^5 - a - 1)*q^37 + (-a^7 - 2*a^6 + a^3 + a^2 - 1)*q^43 + (a^7 - 2*a^4 
        + a)*q^44 + (-a^7 + 2*a^5 + a^4 + a^3 - a - 1)*q^46 + (a^7 + a^6 - 2*a^3
        - a^2 + 1)*q^50 + (a^7 - a^4 - a^3 + a + 1)*q^53 + (-a^7 + 2*a^5 + 2*a^4
        - 2)*q^58 + (a^7 + a^6 - 2*a^3 - a^2 + 2)*q^64 + (-a^7 + a^4 + a^3 + a^2
        - a - 1)*q^67 + (-a^7 + a^2 - 1)*q^71 + (-2*a^7 + 2*a^4 - a)*q^72 + 
        (-a^7 + a^6 + a^5 + a^4 + a^3 - 2*a - 1)*q^74 + (a^7 - 2*a^5 - a^4 + a +
        2)*q^79 + (-a^7 + a^5 + a^4 + a^3 - a - 1)*q^81 + (-2*a^7 + a^4 - 
        2*a)*q^86 + (-a^7 - a^5 + a^4 + a^3 + 2*a^2 - a - 1)*q^88 + (a^6 - a^3 +
        1)*q^92 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
210
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^7 + a^6 - a^4 - a^3 + 1)*q^2 + (a^7 - a^5 + 1)*q^4 + (a^7 + a^6 - a^3
        - a^2 + 1)*q^8 + (-a^7 + a^5 + a^4 + a^3 - a - 1)*q^9 - a^7*q^11 + (-a^7
        + a^5 - 1)*q^18 + (-a^7 + a^3 + a^2 - 1)*q^22 + (a^7 - a^4 - a^3 - a^2 +
        a + 1)*q^23 + a^4*q^25 + (-a^7 - a^6 + a^2 - 1)*q^29 + (a^5 - 1)*q^32 + 
        (a^3 - 1)*q^36 + (-a^5 + a^2)*q^37 + (a^7 - a^3 - a^2)*q^43 + (-a^7 - 
        a^6 + a^4 + a^3 - 1)*q^44 + (2*a^7 - a^5 - 2*a^4 + a + 1)*q^46 + (a^6 - 
        a^3)*q^50 + (a^5 - a - 1)*q^53 + (-a^7 - a^6 + a^4 + a^3 + a^2 - 1)*q^58
        + (-a^6 + a^3 - 1)*q^64 + (-a^5 - a^4 + a + 1)*q^67 + (-a^7 - a^6 + a^3 
        + a^2)*q^71 - a^2*q^72 + (-a^7 + 2*a^4 - a)*q^74 + (-a^6 - a^5 + a)*q^79
        - a*q^81 + (a^7 - a^5 - a^4 - a^3 + a + 1)*q^86 + a*q^88 + (a^7 - a^6 - 
        a^2 + 1)*q^92 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^2 + a - 1)*q^2 + (-a^3 + a^2 - a)*q^4 + a^3*q^8 - a*q^9 + (a^3 - a^2
        + a - 1)*q^11 + (a^3 - a^2 + a)*q^18 + (-a^3 + a^2)*q^22 + (-a^3 + 
        a^2)*q^23 - a^3*q^25 + (-a^3 - a)*q^29 + q^32 + (a - 1)*q^36 + (a^3 - 
        a^2 + a)*q^37 + (a^3 - a^2 - 1)*q^43 + (a^2 - a + 1)*q^44 + (a^2 - 2*a +
        1)*q^46 + (a^2 - a)*q^50 + (a^2 + 1)*q^53 + a^3*q^58 + (-a^2 + a - 
        1)*q^64 + (a^3 - a^2 - 1)*q^67 + (-a^3 + 1)*q^71 + (-a^3 + a^2 - a + 
        1)*q^72 + (-a^3 + a - 1)*q^74 + (a^2 + 1)*q^79 + a^2*q^81 + a*q^86 - 
        a^2*q^88 + (a^3 - 2*a^2 + a)*q^92 + O(q^98),
    q^7 + (-a^2 + a - 1)*q^14 + (-a^3 + a^2 - a)*q^28 + a^2*q^49 + a^3*q^56 - 
        a*q^63 + (a^3 - a^2 + a - 1)*q^77 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^15 + q^16 - q^23 - q^53 - q^60 + q^64 - q^67 - q^71 - q^92 - 
        q^93 + O(q^98),
    q^3 - q^5 + q^12 - q^20 - q^31 - q^33 - q^45 + q^47 + q^48 + q^55 + q^59 + 
        q^75 - q^80 + q^89 + q^97 + O(q^98),
    q^9 - q^11 - q^15 + q^23 + q^25 + q^36 - 2*q^37 - q^44 + q^53 - q^60 + q^67 
        + q^71 - q^81 + q^92 - q^93 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
539
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
14*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 - q^15 + (a - 1)*q^16 + (-a + 1)*q^23 + a*q^53 + a*q^60 + q^64 + 
        a*q^67 - q^71 - q^92 + (-a + 1)*q^93 + O(q^98),
    q^3 + a*q^5 - a*q^12 + (-a + 1)*q^20 - q^31 + a*q^33 - q^45 - a*q^47 + (a - 
        1)*q^48 + (a - 1)*q^55 + q^59 - a*q^75 - q^80 - a*q^89 + (a - 1)*q^97 + 
        O(q^98),
    q^9 + (-a + 1)*q^11 + a*q^15 + q^23 + (a - 1)*q^25 - a*q^36 - 2*q^37 - q^44 
        + (a - 1)*q^53 + (-a + 1)*q^60 + (a - 1)*q^67 - a*q^71 + (-a + 1)*q^81 -
        a*q^92 - q^93 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 - q^13 - q^19 + q^25 + 2*q^31 - q^37 + 2*q^43 - q^61 - q^67 - q^73 -
        q^79 + q^91 - q^97 - q^103 + 2*q^109 + q^121 + 2*q^127 + q^133 - q^139 -
        q^151 + 2*q^157 - q^163 - q^175 - q^181 + O(q^182),
    q^5 - q^35 - q^65 - q^95 + q^125 + 2*q^155 + O(q^182)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 9*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + a*q^10 + (a - 1)*q^13 - q^16 - a*q^25 + (-a - 1)*q^37 + q^40 + 
        a*q^49 + (a + 1)*q^52 + (-a + 1)*q^58 + a*q^64 + (-a + 1)*q^73 + (-a - 
        1)*q^82 + (a + 1)*q^97 - q^100 - q^121 + (-a - 1)*q^130 + (a - 1)*q^145 
        + (a - 1)*q^148 + (a + 1)*q^157 - a*q^160 - a*q^169 + (a - 1)*q^178 + 
        O(q^182),
    q^2 - q^5 - a*q^8 + a*q^20 + (a - 1)*q^26 + (a + 1)*q^29 - q^32 + (-a + 
        1)*q^41 - a*q^50 + (-a + 1)*q^65 + (-a - 1)*q^74 + q^80 + (-a - 1)*q^89 
        + a*q^98 + (a - 1)*q^101 + (a + 1)*q^104 + 2*a*q^113 + (-a + 1)*q^116 + 
        a*q^125 + a*q^128 - 2*q^137 + (-a + 1)*q^146 + (-a - 1)*q^149 + (-a - 
        1)*q^164 - 2*a*q^173 + O(q^182),
    q^3 - a*q^12 + a*q^30 + (a - 1)*q^39 - q^48 - a*q^75 + (-a - 1)*q^111 + 
        q^120 + a*q^147 + (a + 1)*q^156 + (-a + 1)*q^174 + O(q^182),
    q^6 - q^15 - a*q^24 + a*q^60 + (a - 1)*q^78 + (a + 1)*q^87 - q^96 + (-a + 
        1)*q^123 - a*q^150 + O(q^182)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^10 - q^16 - q^19 - q^25 + q^31 + q^34 + q^40 - q^46 - q^49 + q^61 - 
        q^64 - 2*q^76 + q^79 - q^85 - q^106 - q^109 - q^115 + q^121 + 2*q^124 + 
        q^136 + q^166 + q^169 + q^181 + O(q^182),
    q^2 + q^20 - 2*q^23 - q^32 - q^38 - q^50 + q^62 + q^68 + q^80 + 2*q^83 - 
        q^92 + 2*q^95 - q^98 + q^122 - q^128 - 2*q^152 - 2*q^155 + q^158 + 
        2*q^167 - q^170 + O(q^182),
    q^4 - q^10 + q^16 + 2*q^19 - 2*q^31 - q^34 - q^46 + q^76 - 2*q^79 - q^100 + 
        q^106 + 2*q^115 - q^124 + q^160 + q^166 + O(q^182),
    q^5 - q^8 + q^17 + q^20 - q^23 - q^32 - 2*q^38 - q^53 + 2*q^62 + q^68 + q^83
        + q^92 + q^95 - 2*q^113 - q^125 - q^137 - q^152 - q^155 + 2*q^158 + 
        q^167 + q^173 + O(q^182)
]
;
Bo:=
[
    q - q^4 - q^10 + q^16 - q^25 + 2*q^34 + q^40 - q^49 - 2*q^61 - q^64 + 2*q^85
        + q^100 - 2*q^106 + 2*q^109 + q^121 - 2*q^136 - q^160 + q^169 - 2*q^181 
        + O(q^182),
    q^2 + q^5 - q^8 - 2*q^17 - q^20 + q^32 - q^50 + 2*q^53 + 2*q^68 + q^80 - 
        q^98 - 2*q^113 - 2*q^122 - q^125 - q^128 + 2*q^137 + 2*q^170 - 2*q^173 +
        O(q^182),
    q^3 - q^12 - q^30 + q^48 - q^75 + 2*q^102 + q^120 - q^147 + O(q^182),
    q^6 + q^15 - q^24 - 2*q^51 - q^60 + q^96 - q^150 + 2*q^159 + O(q^182)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 - a^5*q^5 + (a^3 - 1)*q^6 - a*q^9 + (a^4 - a^3)*q^14 + a^4*q^16 
        + (-a^4 + a)*q^20 + (a^5 - a^4 - a^2 + a)*q^21 + (a^5 - a^2)*q^24 - 
        a*q^25 + (a^5 - a^3 - a^2)*q^29 + a^2*q^30 - a^3*q^36 + (-a^4 + a + 
        1)*q^41 + (a^3 - 1)*q^45 + (-a^5 - a)*q^46 + (-a^5 + a^4 + a^3 - 1)*q^49
        + (-a^4 + a)*q^54 + (-a^5 + a^3 - 1)*q^56 + (-a^3 + a^2)*q^61 + (a^3 - 
        1)*q^64 + (-a^5 + 1)*q^69 + (a^5 - a^2 + 1)*q^70 + q^80 + a^2*q^81 + (-a
        + 1)*q^84 + a^5*q^86 + (a^4 + a^2)*q^89 + (-a^4 + a + 1)*q^94 - a*q^96 -
        a^3*q^100 + (a^4 - a)*q^101 + (a^4 - a^3)*q^105 + (-a^4 + a^2 + a)*q^109
        + (-a^5 - a)*q^116 + a^4*q^120 + (a^5 - a^2)*q^121 + (a^3 - 1)*q^125 + 
        (-a^5 + a^4)*q^126 - q^129 + (a^5 - a^2 - a)*q^134 + (a^4 + a^2)*q^141 -
        a^5*q^144 + (a^5 + a^4 - a^2)*q^145 + (a^3 - a - 1)*q^149 + (-a^4 + 
        a)*q^150 + (-a^4 + a^2 + a - 1)*q^161 + (a^2 + 1)*q^164 + (-a^3 - 
        a)*q^166 + (-a^4 + a)*q^169 + (-a^5 + 1)*q^174 + (a^5 - a^2)*q^180 + 
        (a^5 - a^4 - a^2 + a)*q^181 + O(q^182),
    q^2 + a^4*q^3 + (a^2 - a)*q^7 + a^2*q^8 - a^5*q^10 + (a^3 - 1)*q^12 + q^15 -
        a*q^18 + (a^5 - a^3 - a^2)*q^23 - a^5*q^27 + (a^4 - a^3)*q^28 + a^4*q^32
        + (-a^4 + a^3 + a - 1)*q^35 + (-a^4 + a)*q^40 + (a^5 - a^4 - a^2 + 
        a)*q^42 + a^3*q^43 + (-a^5 - a^4 + a)*q^47 + (a^5 - a^2)*q^48 - a*q^50 +
        (a^5 - a^3 - a^2)*q^58 + a^2*q^60 + (-a^3 + a^2)*q^63 + (a^5 + a^3 - a^2
        - 1)*q^67 - a^3*q^72 - a^5*q^75 + (-a^4 + a + 1)*q^82 + (a^5 - a^2 - 
        a)*q^83 + (-a^4 - a^3 + a)*q^87 + (a^3 - 1)*q^90 + (-a^5 - a)*q^92 + 
        (-a^5 + a^4 + a^3 - 1)*q^98 - a^4*q^103 + (a^4 - a^3)*q^107 + (-a^4 + 
        a)*q^108 + (-a^5 + a^3 - 1)*q^112 + (a^5 + a^4 - a^2)*q^115 + (-a^3 + 
        a^2)*q^122 + (a^4 + a^2)*q^123 + (a^4 + 1)*q^127 + (a^3 - 1)*q^128 - 
        a*q^135 + (-a^5 + 1)*q^138 + (a^5 - a^2 + 1)*q^140 + (a^5 - a^2 - a + 
        1)*q^147 + q^160 + a^2*q^162 + (-a^5 + a^2)*q^163 + (a^3 + a^2 - 
        1)*q^167 + (-a + 1)*q^168 + a^5*q^172 + (-a^3 + a^2)*q^175 + (a^4 + 
        a^2)*q^178 + O(q^182)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 + (-a + 1)*q^5 + (a - 1)*q^14 - a*q^16 + a*q^20 - a*q^25 - 
        a*q^29 + (a - 1)*q^41 - q^46 - a*q^56 + a*q^61 + q^64 + a*q^70 - q^80 + 
        (-2*a + 2)*q^86 + q^89 + (-a + 1)*q^94 + q^100 + 2*a*q^101 - q^109 + 
        q^116 + (a - 1)*q^121 - q^125 + q^134 - q^145 + (a - 1)*q^149 - q^161 - 
        a*q^164 + (-a + 1)*q^166 - a*q^169 - q^181 + O(q^182),
    q^2 + q^7 + (a - 1)*q^8 + (-a + 1)*q^10 + a*q^23 + (a - 1)*q^28 - a*q^32 + 
        (-a + 1)*q^35 + a*q^40 - 2*q^43 - q^47 - a*q^50 - a*q^58 - a*q^67 + (a -
        1)*q^82 - q^83 - q^92 + 2*a*q^103 + (-a + 1)*q^107 - a*q^112 + q^115 + 
        a*q^122 + (a - 1)*q^127 + q^128 + a*q^140 - q^160 + (-2*a + 2)*q^163 + 
        a*q^167 + (-2*a + 2)*q^172 - a*q^175 + q^178 + O(q^182)
]
;
Bo:=
[
    q + (a - 1)*q^4 + (a - 1)*q^5 + (-a + 1)*q^14 - a*q^16 - a*q^20 - a*q^25 + 
        a*q^29 + (-a + 1)*q^41 - q^46 + a*q^56 + a*q^61 + q^64 + a*q^70 + q^80 +
        (2*a - 2)*q^86 - q^89 + (-a + 1)*q^94 + q^100 - 2*a*q^101 - q^109 - 
        q^116 + (a - 1)*q^121 + q^125 - q^134 - q^145 + (-a + 1)*q^149 + q^161 +
        a*q^164 + (-a + 1)*q^166 - a*q^169 - q^181 + O(q^182),
    q^2 - q^7 + (a - 1)*q^8 + (a - 1)*q^10 + a*q^23 + (-a + 1)*q^28 - a*q^32 + 
        (-a + 1)*q^35 - a*q^40 + 2*q^43 - q^47 - a*q^50 + a*q^58 + a*q^67 + (-a 
        + 1)*q^82 - q^83 - q^92 - 2*a*q^103 + (-a + 1)*q^107 + a*q^112 - q^115 +
        a*q^122 + (-a + 1)*q^127 + q^128 + a*q^140 + q^160 + (2*a - 2)*q^163 + 
        a*q^167 + (2*a - 2)*q^172 + a*q^175 - q^178 + O(q^182),
    q^3 + (a - 1)*q^12 + (a - 1)*q^15 + q^18 - a*q^27 + (-a + 1)*q^42 - a*q^48 -
        a*q^60 - q^63 + (a - 1)*q^72 - a*q^75 + a*q^87 + (a - 1)*q^90 + q^108 + 
        (-a + 1)*q^123 + q^135 - q^138 - a*q^162 + a*q^168 + O(q^182),
    q^6 - a*q^9 - q^21 + (a - 1)*q^24 + (a - 1)*q^30 + q^36 + q^45 - a*q^54 + 
        a*q^69 + (a - 1)*q^81 + (-a + 1)*q^84 - a*q^96 + (-a + 1)*q^105 - 
        a*q^120 - q^126 + 2*q^129 - q^141 + (a - 1)*q^144 - a*q^150 + a*q^174 + 
        (a - 1)*q^180 + O(q^182)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
540
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^19 + q^25 - q^31 + q^49 - q^61 - q^79 - q^85 - q^109 - q^115 + q^121 +
        2*q^139 + 2*q^151 + q^169 - q^181 + O(q^182),
    q^2 - q^20 - q^32 - q^38 + q^50 - q^62 + q^68 + q^80 + q^92 + q^98 - q^122 +
        q^128 - q^158 - q^170 + O(q^182),
    q^4 - q^40 - q^64 - q^76 + q^100 - q^124 + q^136 + q^160 + O(q^182),
    q^5 - q^17 - q^23 + 2*q^47 - q^53 - q^83 - q^95 + 2*q^107 + 2*q^113 + q^125 
        - q^137 - q^155 - q^167 - q^173 + O(q^182),
    q^8 - q^20 - q^32 + q^68 + q^92 - q^152 + O(q^182),
    q^10 + q^16 - q^34 - q^40 - q^46 - q^64 + 2*q^94 - q^106 + q^136 - q^166 + 
        O(q^182)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
541
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
540
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
541
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
180
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
541
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
108
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
541
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
541
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
541
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
541
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
45*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
541
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
135*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
542
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
270
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
542
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
542
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
542
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
542
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
542
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
542
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
45*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
542
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
135*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 + q^25 - q^34 - q^35 - q^37 - q^40 - q^44 - q^55 - q^62 + q^68 + 
        q^74 - q^79 + q^80 + q^81 + q^88 - q^89 + q^98 - q^100 + q^110 - q^112 +
        q^121 + q^124 - q^125 + O(q^134),
    q^2 + q^18 - q^34 - q^40 - q^44 + q^50 - q^62 - q^70 + q^98 - q^100 - q^112 
        + O(q^134),
    q^4 - q^20 - q^22 + q^36 - q^50 - q^56 + q^70 + q^74 + q^98 + q^100 + q^110 
        - q^112 - q^122 + O(q^134),
    q^5 + q^16 + q^22 - q^34 - q^35 - q^37 - q^40 - q^44 + q^45 - q^49 + q^50 - 
        q^62 + q^67 + q^68 - q^70 - q^79 + q^83 - q^89 - q^100 - q^112 + q^119 +
        q^122 + q^124 + O(q^134),
    q^7 + q^16 + q^20 + q^22 - q^28 - q^34 - q^35 - q^37 - 2*q^40 + q^41 - q^44 
        - q^49 + q^50 + q^53 - q^55 - q^62 + q^63 + q^64 + q^68 - q^70 - q^79 + 
        q^85 + q^88 - q^89 - q^100 - q^112 + q^121 + q^122 + q^124 - q^125 - 
        q^128 + O(q^134),
    q^8 - q^16 - q^20 - q^22 + q^32 + q^34 + q^40 + q^44 - q^50 - q^56 + q^62 - 
        q^64 - q^68 + q^70 + q^72 - q^80 - q^88 + q^100 - q^122 - q^124 + q^128 
        + O(q^134),
    q^10 - q^16 - q^20 - q^22 + q^28 + q^32 + q^40 + q^44 - q^50 - q^64 - q^68 -
        q^88 + q^90 + q^100 + q^110 - q^122 - q^124 + q^128 + O(q^134),
    q^11 + q^16 + q^20 + q^22 + q^25 - q^32 - q^34 - q^35 - q^37 - 2*q^40 - 
        2*q^44 - q^49 + q^50 - q^55 + q^56 + q^61 - q^62 + q^64 + q^68 - q^70 + 
        q^77 - q^79 + q^80 + q^88 - q^89 + q^99 - 2*q^100 + q^103 - q^112 + 
        q^119 + q^122 + q^124 - q^125 - q^128 + O(q^134),
    q^14 - q^16 - q^22 + q^28 + q^40 - q^50 - q^68 + q^82 + q^106 - q^122 - 
        q^124 + q^126 + q^128 + O(q^134),
    q^17 + q^20 + q^22 + q^31 - q^34 - q^37 - q^40 - q^44 - q^49 + q^50 - q^55 +
        q^56 - q^62 - q^70 + q^77 - q^79 + q^85 - q^89 - q^100 + q^122 - q^125 +
        O(q^134)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
180
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^7 + a^5 + a^4 - a - 1)*q^3 + a*q^4 + (-a^7 - 2*a^6 + a^3 + a^2 - 
        1)*q^7 + (-a^6 + a)*q^9 + (a^7 + a^6 - a^4 - a^3 - a^2 + 1)*q^12 + (a^7 
        - a^5 - a^4 + 1)*q^13 + a^2*q^16 + (2*a^5 - 1)*q^19 + (a^7 + a^4)*q^21 +
        a^6*q^25 + (a^7 + a^6 - a^3 - a^2 + 1)*q^27 + (-a^7 - a^5 + 1)*q^28 + 
        (-a^5 - a^4)*q^31 + (-a^7 + a^2)*q^36 + (a^7 - a^5 - a^4 + a + 1)*q^37 +
        (-a^7 + a^4 + a^3 + a^2 - a - 1)*q^39 + (a^5 + a^4 + a^3 - a^2 - a - 
        1)*q^43 - q^48 + (a^7 - a^3 - a^2 - 1)*q^49 + (-a^7 - a^6 + a^4 + a^3 - 
        1)*q^52 + (a^7 - a^5 - a^4 - 2*a^3 + a + 1)*q^57 + (-2*a^7 + a^5 + a^4 +
        a^3 + a^2 - a - 1)*q^61 + (-a^5 - a^2)*q^63 + a^3*q^64 + (-a^5 - a^2 + 
        1)*q^67 + (a^7 + 2*a^6 - a^3 - a^2 - a + 1)*q^73 - a^4*q^75 + (2*a^6 - 
        a)*q^76 + (a^4 - a^3)*q^79 - a^7*q^81 + (-a^7 + 2*a^5 + a^4 + a^3 - a - 
        1)*q^84 + (a^5 - a^4 - 1)*q^91 + (a^3 + a^2)*q^93 + (a^7 - a^5 - a^4 + 
        a)*q^97 + a^7*q^100 + (a^6 - a^4 - a^3 + 1)*q^103 + (a^5 - 1)*q^108 + 
        (a^7 + a^6 - a^3 - a^2 - a + 1)*q^109 + (a^6 - a)*q^111 + (a^7 - a^6 - 
        a^5 - a^4 - a^3 + 2*a + 1)*q^112 + (-a^6 + a^3 - 1)*q^117 + O(q^119)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^6 + a)*q^3 + a^2*q^4 + (a^7 - a^3 - a^2)*q^7 - a^7*q^9 + (a^7 - a^5 
        - a^4 + a + 1)*q^12 + (-a^6 + a^2 + a)*q^13 + a^4*q^16 - q^19 + (a^6 + 
        a^5 - a^2 - a)*q^21 + (a^7 - a^2)*q^25 - a^3*q^27 + (a^7 + a^6 - a^5 - 
        a^4 - a^3 - a^2 + 1)*q^28 + (-a^7 + 2*a^5 + a^4 + a^3 - a - 2)*q^31 + 
        (-a^7 - a^6 + a^3 + a^2 - 1)*q^36 + (a^6 - a)*q^37 + (-a^5 - a^4 + a + 
        1)*q^39 + (-a^7 - a^6 + a^3 + a^2 - a - 1)*q^43 + q^48 + (-a^7 + a^3 + 
        a^2)*q^49 + (a^7 - a^5 + a + 1)*q^52 + (a^6 - a)*q^57 + (-a^7 - a^6 + 
        a^3 + a^2 - a - 1)*q^61 + (a^5 + a^4 - 1)*q^63 + a^6*q^64 + (-a^5 + 
        a^4)*q^67 + (-a^7 - a^3)*q^73 + (-a^7 + a^5 + a^4 + a^3 - a - 1)*q^75 - 
        a^2*q^76 + (-a^7 + a^6 + a^5 + a^4 + a^3 - a - 1)*q^79 + (a^7 + a^6 - 
        a^4 - a^3 - a^2 + 1)*q^81 + (a^5 - a - 1)*q^84 + (a^7 + 2*a^6 - a^4 - 
        a^3 - 2*a^2 - a + 1)*q^91 + (a^6 + a^4)*q^93 + (-a^6 + a + 1)*q^97 + 
        (a^7 + a^6 - a^4 - a^3 - a^2 + 1)*q^100 + (-a^6 - a^5 - a^4 + a^3 + a^2 
        + a)*q^103 - a^5*q^108 + (-a^3 + a^2)*q^109 + a^7*q^111 + (-a^7 - 
        a)*q^112 + (-a^7 - a^6 + a^2 - 1)*q^117 + O(q^119)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^3*q^3 + a*q^4 + (a^3 - a^2 + 2*a - 1)*q^7 - a*q^9 + (a^3 - a^2 + a - 
        1)*q^12 + (-a^3 - a)*q^13 + a^2*q^16 + (a^3 - 2*a^2 + a - 1)*q^21 - 
        a*q^25 + (-a^3 + a^2 - a + 1)*q^27 + (a^2 - 1)*q^28 + (-a^3 + a^2 - a + 
        2)*q^31 - a^2*q^36 + 2*a^3*q^37 + (-a^3 + a^2 + 1)*q^39 + (-a^3 + 
        a^2)*q^43 - q^48 + (-a^3 + a^2 - 1)*q^49 + (-a^3 - a + 1)*q^52 + (-a^3 -
        a^2)*q^61 + (-a^2 + 1)*q^63 + a^3*q^64 + (-a^2 - 1)*q^67 + (-a^3 + a^2 +
        1)*q^73 + (-a^3 + a^2 - a + 1)*q^75 + (-a^2 + a - 1)*q^79 + a^2*q^81 + 
        (-a^3 - 1)*q^84 + (-a^3 + a^2 - a + 2)*q^91 + (a^3 + a^2)*q^93 + (-a^3 -
        1)*q^97 - a^2*q^100 + (a^3 - 2*a^2 + a - 1)*q^103 + q^108 + (-a^3 + a^2 
        - 2*a + 1)*q^109 - 2*a*q^111 + (a^3 - a)*q^112 + (a^3 + a - 1)*q^117 + 
        O(q^119)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 30*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^3 + a*q^4 + (a - 1)*q^9 + (a - 1)*q^12 - 2*a*q^13 + (a - 1)*q^16 + 
        (-2*a + 1)*q^19 + q^25 - q^27 + (2*a - 1)*q^31 - q^36 - a*q^37 + (-2*a +
        2)*q^39 + a*q^43 - q^48 + q^49 + (-2*a + 2)*q^52 + (-a + 2)*q^57 + (a - 
        2)*q^61 - q^64 + q^67 - a*q^73 + a*q^75 + (-a + 2)*q^76 + (-a + 1)*q^79 
        - a*q^81 + (a - 2)*q^93 + (-a - 1)*q^97 + a*q^100 + (a - 2)*q^103 - 
        a*q^108 + (-a - 1)*q^109 + (-a + 1)*q^111 + 2*q^117 + O(q^119)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 36*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + a^2*q^4 + (-a^3 + a^2)*q^7 + a^2*q^9 - a^3*q^12 + (a^2 - a)*q^13
        + (a^3 - a^2 + a - 1)*q^16 + 2*q^19 + (-a^2 + a - 1)*q^21 + a^2*q^25 - 
        a^3*q^27 + (a^3 - a^2 + a)*q^28 + (-a^3 + 1)*q^31 + (a^3 - a^2 + a - 
        1)*q^36 - 2*a*q^37 + (-a^3 + a^2)*q^39 + (a^3 - a^2 - 1)*q^43 + q^48 + 
        (a^3 - a^2)*q^49 + (-a^2 + a - 1)*q^52 - 2*a*q^57 + (a^3 - a^2 - 1)*q^61
        + (a^3 - a^2 + a)*q^63 - a*q^64 + (a^3 - a^2 + a)*q^67 + (-a^3 + 
        a^2)*q^73 - a^3*q^75 + 2*a^2*q^76 + (-a^3 - a)*q^79 + (a^3 - a^2 + a - 
        1)*q^81 + (-a + 1)*q^84 + (a^3 - 2*a^2 + 2*a - 1)*q^91 + (a^3 - a^2 - 
        1)*q^93 + (-a + 1)*q^97 + (a^3 - a^2 + a - 1)*q^100 + (-a^2 + a - 
        1)*q^103 + q^108 + (-a^3 + a^2)*q^109 + 2*a^2*q^111 + (a^2 - a)*q^112 + 
        (-a^2 + a - 1)*q^117 + O(q^119)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
45*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 60*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^3 + (a - 1)*q^4 + 2*q^7 - a*q^9 - a*q^12 + (2*a - 2)*q^13 - 
        a*q^16 - q^19 + (2*a - 2)*q^21 + q^25 + q^27 + (2*a - 2)*q^28 - q^31 + 
        q^36 + (-a + 1)*q^37 - 2*a*q^39 + (-a + 1)*q^43 + q^48 + 3*q^49 - 
        2*a*q^52 + (-a + 1)*q^57 + (-a + 1)*q^61 - 2*a*q^63 + q^64 - q^67 + (-a 
        + 1)*q^73 + (a - 1)*q^75 + (-a + 1)*q^76 + a*q^79 + (a - 1)*q^81 - 
        2*a*q^84 + (4*a - 4)*q^91 + (-a + 1)*q^93 + a*q^97 + (a - 1)*q^100 + (-a
        + 1)*q^103 + (a - 1)*q^108 + a*q^109 + a*q^111 - 2*a*q^112 + 2*q^117 + 
        O(q^119)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
543
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 90*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^34 - q^37 - q^39 - q^48 + q^49 - q^52 - q^67 - q^73 + 
        q^81 - q^94 - q^102 + O(q^119),
    q^2 - q^17 + q^18 - q^24 - q^26 - q^47 + q^50 - q^51 + q^69 + q^71 + q^83 - 
        q^86 + q^89 - q^92 + q^98 + q^113 + O(q^119),
    q^3 - q^13 - q^16 + q^27 - q^34 - q^43 + q^46 + q^52 + q^64 + q^75 - q^79 + 
        q^82 - q^94 - q^102 + q^106 - q^111 - q^117 + O(q^119),
    q^4 - q^12 - q^13 + q^36 + q^37 + q^39 - q^43 - q^46 + q^67 + q^73 - q^79 - 
        q^82 + q^100 - q^106 - q^108 - q^111 - q^117 + O(q^119),
    q^6 - q^8 - q^17 + q^23 + q^41 - q^47 - q^51 + q^53 + q^54 - q^72 - q^74 - 
        q^78 + q^92 + q^104 + q^107 + O(q^119)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^3 - a^2)*q^5 - a*q^9 + (a^7 - a^5)*q^13 - a^6*q^17 + (a^6 + a^5 + 
        a^4)*q^25 + (-a^4 + a)*q^29 + (-a^7 + a^2)*q^37 + (-a^7 - a^4)*q^41 + 
        (a^4 + a^3)*q^45 + a^3*q^49 + (a^6 - 1)*q^53 + (-a^6 + a^5)*q^61 + (a^7 
        + a^2 + a - 1)*q^65 + (-a^5 - 1)*q^73 + a^2*q^81 + (-a - 1)*q^85 + (-a^3
        + a)*q^89 + (a^3 - a^2)*q^97 + (a^5 + a^3)*q^101 + (a^2 - a)*q^109 + 
        (-a^5 - a^2)*q^113 + (a^6 + 1)*q^117 - a^7*q^121 + (-a^7 - a^6 + a + 
        1)*q^125 + O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a^3 + a^2)*q^5 + a*q^9 + (-a^3 - a)*q^13 - a^2*q^17 + (-a^2 - a - 
        1)*q^25 + (a - 1)*q^29 + (-a^3 + a^2)*q^37 + (-a^3 - 1)*q^41 + (a^3 - 
        1)*q^45 + a^3*q^49 + (-a^2 + 1)*q^53 + (-a^2 - a)*q^61 + (-a^3 + a^2 + a
        + 1)*q^65 + (-a + 1)*q^73 + a^2*q^81 + (a + 1)*q^85 + (a^3 + a)*q^89 + 
        (a^3 + a^2)*q^97 + (a^3 - a)*q^101 + (a^2 + a)*q^109 + (a^2 - a)*q^113 +
        (-a^2 + 1)*q^117 - a^3*q^121 + (-a^3 - a^2 + a + 1)*q^125 + O(q^130),
    q^2 + (a^3 + a^2)*q^10 + a*q^18 + (-a^3 - a)*q^26 - a^2*q^34 + (-a^2 - a - 
        1)*q^50 + (a - 1)*q^58 + (-a^3 + a^2)*q^74 + (-a^3 - 1)*q^82 + (a^3 - 
        1)*q^90 + a^3*q^98 + (-a^2 + 1)*q^106 + (-a^2 - a)*q^122 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^3 - a^2)*q^3 + (-a^2 + a - 1)*q^9 + (-a^3 + 1)*q^11 - a^3*q^17 - 
        a*q^25 + (-a^3 + a^2 + a - 1)*q^27 + (a^3 - a)*q^33 + (a^2 + a)*q^41 + 
        (-a^2 - 1)*q^43 + a^3*q^49 + (a^2 - a)*q^51 + (a^2 + 1)*q^59 + (a^3 - 
        a)*q^67 + (a^3 + a^2)*q^73 + (a^3 + 1)*q^75 + (-a^3 + a^2 - a)*q^81 + 
        (a^2 - 1)*q^83 + (-a^3 - a)*q^89 + (a - 1)*q^97 + (a^3 - a^2)*q^99 + (a 
        - 1)*q^107 + (-a^2 + a)*q^113 + (-a^3 - a^2 + 1)*q^121 + (-a^3 - 
        a)*q^123 + (-a^3 + a^2 + a - 1)*q^129 + O(q^130)
]
;
Bo:=
[
    q + (-a^3 + a^2)*q^3 + (-a^2 + a - 1)*q^9 + (a^3 - 1)*q^11 - a^3*q^17 - 
        a*q^25 + (a^3 - a^2 - a + 1)*q^27 + (a^3 - a)*q^33 + (a^2 + a)*q^41 + 
        (a^2 + 1)*q^43 + a^3*q^49 + (-a^2 + a)*q^51 + (-a^2 - 1)*q^59 + (-a^3 + 
        a)*q^67 + (a^3 + a^2)*q^73 + (-a^3 - 1)*q^75 + (-a^3 + a^2 - a)*q^81 + 
        (-a^2 + 1)*q^83 + (-a^3 - a)*q^89 + (a - 1)*q^97 + (-a^3 + a^2)*q^99 + 
        (-a + 1)*q^107 + (-a^2 + a)*q^113 + (-a^3 - a^2 + 1)*q^121 + (a^3 + 
        a)*q^123 + (-a^3 + a^2 + a - 1)*q^129 + O(q^130),
    q^2 + (-a^3 + a^2)*q^6 + (-a^2 + a - 1)*q^18 + (a^3 - 1)*q^22 - a^3*q^34 - 
        a*q^50 + (a^3 - a^2 - a + 1)*q^54 + (a^3 - a)*q^66 + (a^2 + a)*q^82 + 
        (a^2 + 1)*q^86 + a^3*q^98 + (-a^2 + a)*q^102 + (-a^2 - 1)*q^118 + 
        O(q^130),
    q^4 + a^3*q^8 + (-a^3 + a^2)*q^12 - a^2*q^16 + (a^2 - a)*q^24 + a*q^32 + 
        (-a^2 + a - 1)*q^36 + (a^3 - 1)*q^44 + (-a + 1)*q^48 - q^64 - a^3*q^68 +
        (-a^3 + a - 1)*q^72 + (-a^3 - a^2)*q^88 + (a^3 + 1)*q^96 - a*q^100 + 
        (a^3 - a^2 - a + 1)*q^108 - a^3*q^128 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 7*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a - 1)*q^5 + a*q^9 - q^17 + a*q^25 + (a + 1)*q^29 + (-a - 1)*q^37 + 
        (-a + 1)*q^41 + (-a + 1)*q^45 - a*q^49 + (a - 1)*q^61 + (a + 1)*q^73 - 
        q^81 + (a + 1)*q^85 + (-a - 1)*q^97 + (a - 1)*q^109 + (a - 1)*q^113 - 
        a*q^121 + O(q^130),
    q^2 + (-a - 1)*q^10 + a*q^18 - q^34 + a*q^50 + (a + 1)*q^58 + (-a - 1)*q^74 
        + (-a + 1)*q^82 + (-a + 1)*q^90 - a*q^98 + (a - 1)*q^122 + O(q^130),
    q^4 + (-a - 1)*q^20 + a*q^36 - q^68 + a*q^100 + (a + 1)*q^116 + O(q^130),
    q^8 + a*q^16 - q^32 + (-a - 1)*q^40 - a*q^64 + a*q^72 + (-a + 1)*q^80 + 
        q^128 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a + 1)*q^3 + a*q^9 + (a - 1)*q^11 - a*q^17 - 2*a*q^19 + a*q^25 - 2*q^33
        + (a - 1)*q^41 - a*q^49 + (-a + 1)*q^51 + (-2*a + 2)*q^57 + (-a - 
        1)*q^73 + (a - 1)*q^75 + q^81 + (a + 1)*q^97 + (-a - 1)*q^99 + (-a - 
        1)*q^107 + (a - 1)*q^113 - a*q^121 - 2*q^123 + O(q^130)
]
;
Bo:=
[
    q + (-a - 1)*q^3 + a*q^9 + (-a + 1)*q^11 - a*q^17 + 2*a*q^19 + a*q^25 - 
        2*q^33 + (a - 1)*q^41 - a*q^49 + (a - 1)*q^51 + (-2*a + 2)*q^57 + (-a - 
        1)*q^73 + (-a + 1)*q^75 + q^81 + (a + 1)*q^97 + (a + 1)*q^99 + (a + 
        1)*q^107 + (a - 1)*q^113 - a*q^121 + 2*q^123 + O(q^130),
    q^2 + (-a - 1)*q^6 + a*q^18 + (-a + 1)*q^22 - a*q^34 + 2*a*q^38 + a*q^50 - 
        2*q^66 + (a - 1)*q^82 - a*q^98 + (a - 1)*q^102 + (-2*a + 2)*q^114 + 
        O(q^130),
    q^4 - a*q^8 + (-a - 1)*q^12 - q^16 + (a - 1)*q^24 + a*q^32 + a*q^36 + (-a + 
        1)*q^44 + (a + 1)*q^48 + q^64 - a*q^68 + q^72 + 2*a*q^76 + (-a - 1)*q^88
        + (-a + 1)*q^96 + a*q^100 - a*q^128 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^13 - q^21 + q^25 - q^33 + q^69 + q^77 - q^89 + q^93 - q^101 + q^117 + 
        O(q^130),
    q^2 - q^26 - q^42 + q^50 - q^66 + O(q^130),
    q^3 - q^7 - q^11 + q^23 + q^31 - q^51 - q^63 - q^71 + q^75 + q^79 - q^99 + 
        q^107 + q^119 + O(q^130),
    q^4 - q^36 - 2*q^52 + q^68 + q^100 + O(q^130),
    q^6 - q^14 - q^22 + q^46 + q^62 - q^102 - q^126 + O(q^130),
    q^8 - q^16 + q^32 - q^64 - q^72 - 2*q^104 + q^128 + O(q^130),
    q^9 + q^13 - q^17 - q^21 - q^33 + q^49 - 2*q^53 + q^69 + q^77 - q^81 + q^89 
        + q^93 + q^101 - q^117 + q^121 + O(q^130),
    q^18 + q^26 - q^34 - q^42 - q^66 + q^98 - 2*q^106 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
544
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^17 + 2*q^19 - q^25 - 2*q^43 - q^49 - 2*q^59 + 2*q^67 + q^81 - 
        2*q^83 - 2*q^89 + q^121 + O(q^130)
]
;
Bo:=
[
    q + q^9 - q^17 - 2*q^19 - q^25 + 2*q^43 - q^49 + 2*q^59 - 2*q^67 + q^81 + 
        2*q^83 - 2*q^89 + q^121 + O(q^130),
    q^2 + q^18 - q^34 - 2*q^38 - q^50 + 2*q^86 - q^98 + 2*q^118 + O(q^130),
    q^4 - q^8 + q^16 - q^32 + q^36 + q^64 - q^68 - q^72 - 2*q^76 - q^100 - q^128
        + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
108
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
108
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
108
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
108
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 27*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 36*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
545
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 54*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a^3*q^3 + (a^3 - a)*q^4 + (a^2 - 1)*q^7 - q^9 - a^2*q^12 + (-a^3 + 
        a)*q^13 + (-a^2 + 1)*q^16 + (a^2 + a)*q^19 - a*q^21 - a*q^25 - a^3*q^27 
        - a^3*q^28 + (-a^2 + a + 1)*q^31 + (-a^3 + a)*q^36 + (-a^3 + a^2)*q^37 +
        a^2*q^39 + (-a^2 - 1)*q^43 + a*q^48 - a^2*q^49 + (a^2 - 1)*q^52 + (a^3 +
        a^2 - a - 1)*q^57 - a^3*q^61 + (-a^2 + 1)*q^63 + a^3*q^64 + (a^3 - 
        1)*q^67 + (a^3 - a + 1)*q^73 + (-a^2 + 1)*q^75 + (-a - 1)*q^76 + q^81 + 
        q^84 + a^3*q^91 + (a^2 + a - 1)*q^93 + (a^3 - a^2)*q^97 + q^100 + 
        a^2*q^103 + a^2*q^108 + (-a^3 - a^2)*q^109 + (a^3 - a + 1)*q^111 + 
        a^2*q^112 + (a^3 - a)*q^117 + a^3*q^121 + (a^3 - 1)*q^124 + (-a^3 + 
        a)*q^127 + (-2*a^3 + a)*q^129 + (a^3 - a - 1)*q^133 + (a^2 - 1)*q^144 + 
        (-a^3 + a)*q^147 + (a^2 - a)*q^148 + (-a^2 + a + 1)*q^151 - a*q^156 + 
        (-a^2 - 1)*q^157 + (-a^2 - a)*q^163 + (-a^2 + 1)*q^169 + (-a^2 - 
        a)*q^171 + (-a^3 + 2*a)*q^172 + (-a^3 + a)*q^175 + q^181 + q^183 + 
        a*q^189 - q^192 + (-a^3 + a^2 + a - 1)*q^193 + a*q^196 + (-a^3 - 
        a)*q^199 + (-a^3 - 1)*q^201 - a^3*q^208 + O(q^210),
    q^2 + a^3*q^6 + (a^3 - a)*q^8 + (a^2 - 1)*q^14 - q^18 - a^2*q^24 + (-a^3 + 
        a)*q^26 + (-a^2 + 1)*q^32 + (a^2 + a)*q^38 - a*q^42 - a*q^50 - a^3*q^54 
        - a^3*q^56 + (-a^2 + a + 1)*q^62 + (-a^3 + a)*q^72 + (-a^3 + a^2)*q^74 +
        a^2*q^78 + (-a^2 - 1)*q^86 + a*q^96 - a^2*q^98 + (a^2 - 1)*q^104 + (a^3 
        + a^2 - a - 1)*q^114 - a^3*q^122 + (-a^2 + 1)*q^126 + a^3*q^128 + (a^3 -
        1)*q^134 + (a^3 - a + 1)*q^146 + (-a^2 + 1)*q^150 + (-a - 1)*q^152 + 
        q^162 + q^168 + a^3*q^182 + (a^2 + a - 1)*q^186 + (a^3 - a^2)*q^194 + 
        q^200 + a^2*q^206 + O(q^210)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^3 - a^3*q^4 - a*q^7 + a^2*q^9 + (-a^2 + 1)*q^12 + (a^3 - a)*q^13 - 
        q^16 + (a^3 + a^2 - 1)*q^19 - a^2*q^21 + (-a^3 + a)*q^25 + a^3*q^27 + 
        (a^2 - 1)*q^28 + (-a^3 - a^2 + a)*q^31 + (-a^3 + a)*q^36 + (a^3 - a^2 - 
        a + 1)*q^37 - q^39 + (-a^2 - 1)*q^43 - a*q^48 + a^2*q^49 + a^2*q^52 + 
        (a^3 + a^2 - a - 1)*q^57 + (-a^3 + a)*q^61 - a^3*q^63 + a^3*q^64 + (-a^2
        - a + 1)*q^67 + (a^3 - a^2 + 1)*q^73 + q^75 + (a + 1)*q^76 + (a^2 - 
        1)*q^81 + (a^3 - a)*q^84 + q^91 + (-a^3 + 1)*q^93 + (-a^3 + a^2)*q^97 - 
        a^2*q^100 + (a^2 - 1)*q^103 + q^108 + (a + 1)*q^109 + (-a^3 + a - 
        1)*q^111 + a*q^112 - a*q^117 + (-a^3 + a)*q^121 + (a^3 - a^2 - a)*q^124 
        + (-a^3 + a)*q^127 + (-a^3 - a)*q^129 + (-a^3 - a^2 + a + 1)*q^133 - 
        a^2*q^144 + a^3*q^147 + (a^2 - a)*q^148 + (a^3 + a^2 - a)*q^151 + 
        a^3*q^156 + (a^2 - 2)*q^157 + (a^3 + a^2 - 1)*q^163 + (-a^2 + 1)*q^169 +
        (a^3 - a - 1)*q^171 + (2*a^3 - a)*q^172 - q^175 - q^181 + q^183 + (-a^2 
        + 1)*q^189 + (a^2 - 1)*q^192 + (a^3 - a^2)*q^193 + (-a^3 + a)*q^196 + 
        (a^3 - 2*a)*q^199 + (-a^3 - a^2 + a)*q^201 + (-a^3 + a)*q^208 + 
        O(q^210),
    q^2 + a*q^6 - a^3*q^8 - a*q^14 + a^2*q^18 + (-a^2 + 1)*q^24 + (a^3 - a)*q^26
        - q^32 + (a^3 + a^2 - 1)*q^38 - a^2*q^42 + (-a^3 + a)*q^50 + a^3*q^54 + 
        (a^2 - 1)*q^56 + (-a^3 - a^2 + a)*q^62 + (-a^3 + a)*q^72 + (a^3 - a^2 - 
        a + 1)*q^74 - q^78 + (-a^2 - 1)*q^86 - a*q^96 + a^2*q^98 + a^2*q^104 + 
        (a^3 + a^2 - a - 1)*q^114 + (-a^3 + a)*q^122 - a^3*q^126 + a^3*q^128 + 
        (-a^2 - a + 1)*q^134 + (a^3 - a^2 + 1)*q^146 + q^150 + (a + 1)*q^152 + 
        (a^2 - 1)*q^162 + (a^3 - a)*q^168 + q^182 + (-a^3 + 1)*q^186 + (-a^3 + 
        a^2)*q^194 - a^2*q^200 + (a^2 - 1)*q^206 + O(q^210)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + (-a + 1)*q^4 - a*q^7 + q^9 + (a - 1)*q^12 + (-a + 1)*q^13 - a*q^16
        + (2*a - 1)*q^19 + a*q^21 + a*q^25 - q^27 - q^28 + (-a + 1)*q^36 + (a - 
        2)*q^37 + (a - 1)*q^39 + a*q^43 + a*q^48 + (a - 1)*q^49 - a*q^52 + (-2*a
        + 1)*q^57 + q^61 - a*q^63 - q^64 + (-a + 2)*q^73 - a*q^75 + (a + 1)*q^76
        + (-2*a + 2)*q^79 + q^81 + q^84 - q^91 + (a - 2)*q^97 + q^100 + (-a + 
        1)*q^103 + (a - 1)*q^108 + (a - 2)*q^109 + (-a + 2)*q^111 + (a - 
        1)*q^112 + (-a + 1)*q^117 - q^121 + (a - 1)*q^127 - a*q^129 + (-a + 
        2)*q^133 - 2*a*q^139 - a*q^144 + (-a + 1)*q^147 + (2*a - 1)*q^148 + 
        a*q^156 + a*q^157 + (2*a - 1)*q^163 - a*q^169 + (2*a - 1)*q^171 + q^172 
        + (-a + 1)*q^175 - q^181 - q^183 + a*q^189 + q^192 + (-2*a + 1)*q^193 + 
        a*q^196 + (a - 1)*q^199 - q^208 + O(q^210),
    q^2 - q^6 + (-a + 1)*q^8 - a*q^14 + q^18 + (a - 1)*q^24 + (-a + 1)*q^26 - 
        a*q^32 + (2*a - 1)*q^38 + a*q^42 + a*q^50 - q^54 - q^56 + (-a + 1)*q^72 
        + (a - 2)*q^74 + (a - 1)*q^78 + a*q^86 + a*q^96 + (a - 1)*q^98 - a*q^104
        + (-2*a + 1)*q^114 + q^122 - a*q^126 - q^128 + (-a + 2)*q^146 - a*q^150 
        + (a + 1)*q^152 + (-2*a + 2)*q^158 + q^162 + q^168 - q^182 + (a - 
        2)*q^194 + q^200 + (-a + 1)*q^206 + O(q^210)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^3 - q^4 + a*q^7 + (a - 1)*q^9 - a*q^12 + (-a + 1)*q^13 + q^16 + (-a 
        - 1)*q^19 + (a - 1)*q^21 + (-a + 1)*q^25 - q^27 - a*q^28 + (-a + 1)*q^36
        + (-2*a + 1)*q^37 + q^39 + a*q^43 + a*q^48 + (a - 1)*q^49 + (a - 1)*q^52
        + (-2*a + 1)*q^57 + (a - 1)*q^61 - q^63 - q^64 + (-a - 1)*q^73 + q^75 + 
        (a + 1)*q^76 + 2*a*q^79 - a*q^81 + (-a + 1)*q^84 + q^91 + (a - 2)*q^97 +
        (a - 1)*q^100 + a*q^103 + q^108 + (a + 1)*q^109 + (-a + 2)*q^111 + 
        a*q^112 + a*q^117 + (-a + 1)*q^121 + (a - 1)*q^127 + (a - 1)*q^129 + 
        (-2*a + 1)*q^133 - 2*a*q^139 + (a - 1)*q^144 - q^147 + (2*a - 1)*q^148 -
        q^156 + (-a + 1)*q^157 + (-a - 1)*q^163 - a*q^169 + (-a + 2)*q^171 - 
        a*q^172 + q^175 - q^181 - q^183 - a*q^189 - a*q^192 + (a - 2)*q^193 + 
        (-a + 1)*q^196 + q^199 + (-a + 1)*q^208 + O(q^210),
    q^2 + a*q^6 - q^8 + a*q^14 + (a - 1)*q^18 - a*q^24 + (-a + 1)*q^26 + q^32 + 
        (-a - 1)*q^38 + (a - 1)*q^42 + (-a + 1)*q^50 - q^54 - a*q^56 + (-a + 
        1)*q^72 + (-2*a + 1)*q^74 + q^78 + a*q^86 + a*q^96 + (a - 1)*q^98 + (a -
        1)*q^104 + (-2*a + 1)*q^114 + (a - 1)*q^122 - q^126 - q^128 + (-a - 
        1)*q^146 + q^150 + (a + 1)*q^152 + 2*a*q^158 - a*q^162 + (-a + 1)*q^168 
        + q^182 + (a - 2)*q^194 + (a - 1)*q^200 + a*q^206 + O(q^210)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^4 + 1/2*(-a + 1)*q^7 - q^9 - q^16 + 1/2*(-a + 1)*q^21 - a*q^25 + 
        1/2*(a + 1)*q^28 - a*q^36 + (a - 1)*q^37 - q^39 + (a + 1)*q^57 + 1/2*(a 
        - 1)*q^63 - a*q^64 + (-a - 1)*q^67 + q^81 + 1/2*(a + 1)*q^84 + 1/2*(-a +
        1)*q^91 + (a + 1)*q^93 + q^100 + (a + 1)*q^109 + 1/2*(a - 1)*q^112 - 
        a*q^121 + 2*a*q^127 - q^133 + q^144 - a*q^147 + (-a - 1)*q^148 + (a - 
        1)*q^151 - a*q^156 + (-a + 1)*q^163 - q^169 + 1/2*(-a - 1)*q^175 - 
        2*q^183 + 1/2*(a - 1)*q^189 + (-a + 1)*q^193 + O(q^210),
    q^2 + a*q^8 + 1/2*(-a + 1)*q^14 - q^18 - q^32 + 1/2*(-a + 1)*q^42 - a*q^50 +
        1/2*(a + 1)*q^56 - a*q^72 + (a - 1)*q^74 - q^78 + (a + 1)*q^114 + 1/2*(a
        - 1)*q^126 - a*q^128 + (-a - 1)*q^134 + q^162 + 1/2*(a + 1)*q^168 + 
        1/2*(-a + 1)*q^182 + (a + 1)*q^186 + q^200 + O(q^210),
    q^3 + 1/2*(a - 1)*q^7 + a*q^12 + q^13 + (-a - 1)*q^19 + 1/2*(-a + 1)*q^21 - 
        q^27 + 1/2*(-a - 1)*q^28 + (-a - 1)*q^31 - q^48 + a*q^49 + a*q^52 + 
        2*q^61 + 1/2*(-a + 1)*q^63 + (a - 1)*q^73 - a*q^75 + (-a + 1)*q^76 + 
        1/2*(a + 1)*q^84 + 1/2*(-a + 1)*q^91 + (a + 1)*q^97 + 2*a*q^103 - 
        a*q^108 + (a - 1)*q^111 + 1/2*(-a + 1)*q^112 - q^117 + (-a + 1)*q^124 - 
        q^133 + (a + 1)*q^171 + 1/2*(a + 1)*q^175 - 2*a*q^181 + 1/2*(a - 
        1)*q^189 - a*q^192 - q^196 + (-a - 1)*q^201 - q^208 + O(q^210),
    q^6 + 1/2*(a - 1)*q^14 + a*q^24 + q^26 + (-a - 1)*q^38 + 1/2*(-a + 1)*q^42 -
        q^54 + 1/2*(-a - 1)*q^56 + (-a - 1)*q^62 - q^96 + a*q^98 + a*q^104 + 
        2*q^122 + 1/2*(-a + 1)*q^126 + (a - 1)*q^146 - a*q^150 + (-a + 1)*q^152 
        + 1/2*(a + 1)*q^168 + 1/2*(-a + 1)*q^182 + (a + 1)*q^194 + 2*a*q^206 + 
        O(q^210)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^7 - q^8 + a*q^9 + (-a + 1)*q^10 + (a - 1)*q^12 - q^13 + (-2*a + 
        1)*q^14 - a*q^15 - q^16 + 2*a*q^18 + (-a + 1)*q^20 + (a - 1)*q^26 - 
        a*q^30 + a*q^31 - 2*q^32 + q^34 + q^37 - a*q^38 + (-a + 1)*q^40 + (a + 
        1)*q^42 + (a - 1)*q^43 + q^46 + (a - 1)*q^48 + (a - 1)*q^49 + a*q^50 + 
        (-a + 1)*q^51 - 2*q^54 + (-a + 1)*q^56 - a*q^58 + 3*a*q^62 + (-a + 
        1)*q^63 - q^64 + q^68 + (-a + 1)*q^69 - q^70 + a*q^72 - a*q^73 + 2*q^74 
        - a*q^78 + (a - 1)*q^79 + (-a + 1)*q^80 + (a - 1)*q^81 + a*q^82 + q^84 +
        (a - 1)*q^85 + (2*a - 2)*q^86 - q^87 + q^90 + a*q^91 + q^92 + (-a + 
        1)*q^94 + (-a + 1)*q^96 + (-a + 1)*q^97 + (2*a - 1)*q^98 + (-a + 
        1)*q^102 + (a - 1)*q^103 + a*q^104 + (a - 1)*q^105 + a*q^106 - q^108 - 
        a*q^109 + a*q^112 + q^114 + (a - 1)*q^115 - a*q^116 - a*q^117 - q^118 - 
        a*q^121 - a*q^122 + q^123 - a*q^126 + a*q^127 - 2*q^128 + (a - 1)*q^130 
        + (-2*a + 2)*q^134 + (-a + 1)*q^135 + q^136 + (-a + 1)*q^138 + (-a + 
        1)*q^139 - q^140 - a*q^141 + (a - 1)*q^142 - a*q^144 + q^145 - 2*a*q^146
        - q^150 - a*q^151 - a*q^152 + (-a + 1)*q^156 - a*q^157 + (-a + 1)*q^158 
        + q^159 + a*q^164 + (a + 1)*q^168 + q^169 + (a - 1)*q^170 - q^174 + (a -
        1)*q^177 - q^178 + q^180 + (a - 1)*q^182 + q^184 - 3*q^186 + (-a + 
        1)*q^188 + a*q^195 + q^199 + a*q^200 - q^205 + (2*a - 2)*q^206 + q^208 +
        O(q^210),
    q^2 + (a - 1)*q^12 - a*q^14 + a*q^18 + (-a + 1)*q^20 - q^26 - a*q^30 - q^32 
        + (a - 1)*q^48 + a*q^62 + q^68 + q^74 + (-a + 1)*q^80 + q^84 + (a - 
        1)*q^86 + q^92 + (a - 1)*q^98 + (-a + 1)*q^102 - q^108 - a*q^116 + (-a +
        1)*q^126 - q^128 + (-a + 1)*q^138 - q^140 - a*q^146 + (-a + 1)*q^156 + 
        (a - 1)*q^158 + (a - 1)*q^162 + a*q^164 + (a - 1)*q^170 - q^174 + q^180 
        + a*q^182 + (-a + 1)*q^188 + (-a + 1)*q^194 + (a - 1)*q^206 + O(q^210),
    q^3 + (-a + 2)*q^7 + (2*a - 2)*q^9 + q^12 - q^13 + (-a + 1)*q^15 - a*q^16 + 
        (-a + 1)*q^19 + (a - 1)*q^21 - q^24 + (a - 1)*q^25 - a*q^27 + (-a + 
        2)*q^28 + (3*a - 3)*q^31 + (2*a - 2)*q^36 + 2*a*q^37 - a*q^39 + q^40 - 
        2*q^43 + q^48 + (a - 2)*q^49 + q^51 - q^52 + a*q^57 + (-a + 1)*q^60 + 
        (-a + 1)*q^61 + (-a + 1)*q^63 - 2*a*q^64 + 2*q^67 + q^69 + (-2*a + 
        2)*q^73 - a*q^75 + (-a + 1)*q^76 + q^79 + (a - 1)*q^84 - q^85 - a*q^87 -
        q^91 - 2*a*q^93 - q^96 + (a - 1)*q^100 - 2*q^103 - q^105 - a*q^108 + 
        (-2*a + 2)*q^109 - q^111 + q^112 - q^115 + (-a + 2)*q^117 + a*q^123 + 
        (3*a - 3)*q^124 + (-a + 1)*q^129 + a*q^133 + q^135 + a*q^136 + 3*q^139 +
        (-a + 1)*q^141 + (a - 1)*q^144 + a*q^145 - a*q^147 + 2*a*q^148 + (a - 
        1)*q^151 - a*q^156 + (-2*a + 2)*q^157 + a*q^159 + q^160 + (-a + 1)*q^163
        + a*q^168 + (a + 1)*q^169 - q^171 - 2*q^172 - a*q^175 - q^177 + a*q^181 
        + a*q^183 + a*q^184 + q^189 + q^192 - q^193 + (a - 1)*q^195 + (a - 
        2)*q^196 + 2*a*q^199 + (2*a - 2)*q^201 + q^204 - a*q^205 + (a - 1)*q^208
        + O(q^210),
    q^4 + q^8 + (a - 1)*q^10 + (-a + 1)*q^12 + (2*a - 1)*q^14 + q^16 - 2*a*q^18 
        + (a - 1)*q^20 + (a - 1)*q^24 + (-a + 1)*q^26 - a*q^28 + a*q^30 + 2*q^32
        - q^34 + a*q^36 + a*q^38 + (-a - 1)*q^42 - q^46 + (-a + 1)*q^48 - a*q^50
        - q^52 + 2*q^54 + (a - 1)*q^56 + a*q^58 - a*q^60 - 3*a*q^62 - q^68 + 
        q^70 - a*q^72 - 2*q^74 + a*q^78 + (a - 1)*q^80 - a*q^82 - q^84 + (-2*a +
        2)*q^86 - q^90 - q^92 + (a - 1)*q^94 + (2*a - 2)*q^96 + (-2*a + 1)*q^98 
        + (a - 1)*q^102 - a*q^104 - a*q^106 + q^108 - a*q^112 - q^114 + a*q^116 
        + q^118 + a*q^122 + a*q^124 + a*q^126 + 2*q^128 + (-a + 1)*q^130 + (2*a 
        - 2)*q^134 + (a - 1)*q^138 + q^140 + (-a + 1)*q^142 + a*q^144 + 
        2*a*q^146 + q^148 + q^150 + a*q^152 + (a - 1)*q^156 + (a - 1)*q^158 + 
        (-a + 1)*q^160 - a*q^164 - a*q^168 + (-a + 1)*q^170 + (a - 1)*q^172 + 
        q^174 + q^178 - q^180 + (-a + 1)*q^182 + 3*q^186 + (a - 1)*q^188 + (a - 
        1)*q^196 - a*q^200 + (-a + 1)*q^204 + (-2*a + 2)*q^206 - q^208 + 
        O(q^210),
    q^5 + (-a + 2)*q^7 - a*q^8 + (2*a - 2)*q^9 - q^13 + (-a + 1)*q^15 - a*q^16 +
        a*q^17 + (-a + 1)*q^19 + q^20 + (2*a - 1)*q^21 + a*q^23 - q^24 + (a - 
        1)*q^25 - 2*a*q^27 + (-a + 2)*q^28 + (-a + 1)*q^29 + (3*a - 3)*q^31 - 
        a*q^32 - a*q^35 + (2*a - 2)*q^36 + 2*a*q^37 + (-a + 1)*q^39 + q^40 + (a 
        - 1)*q^41 - 2*q^43 + a*q^45 + q^47 + q^48 + (a - 2)*q^49 + q^51 - q^52 +
        (a - 1)*q^53 + (a - 1)*q^56 + a*q^57 - a*q^59 + (-a + 1)*q^60 + (-a + 
        1)*q^61 + (-a + 1)*q^63 - 2*a*q^64 - q^65 + 2*q^67 + a*q^68 + q^69 - 
        q^71 + (-a + 1)*q^72 + (-2*a + 2)*q^73 - a*q^75 + (-a + 1)*q^76 + q^79 +
        (2*a - 1)*q^84 - q^85 - a*q^87 - a*q^89 - q^91 + a*q^92 - 3*a*q^93 - 
        q^96 + (a - 1)*q^100 - 2*q^103 + a*q^104 - q^105 - a*q^107 - 2*a*q^108 +
        (-2*a + 2)*q^109 - 2*q^111 + q^112 + q^113 - q^115 + (-a + 1)*q^116 + 
        (-a + 2)*q^117 + (-a + 1)*q^119 + (a - 1)*q^120 + a*q^123 + (3*a - 
        3)*q^124 - a*q^125 + (-2*a + 2)*q^129 - q^131 + a*q^133 + q^135 + 
        a*q^136 + a*q^137 + 3*q^139 - a*q^140 + (-a + 1)*q^141 + (a - 1)*q^144 +
        a*q^145 + (-2*a + 1)*q^147 + 2*a*q^148 + (a - 1)*q^151 + (a - 1)*q^153 +
        a*q^155 + (-a + 1)*q^156 + (-2*a + 2)*q^157 + a*q^159 + q^160 + (-a + 
        1)*q^161 + (-a + 1)*q^163 + (a - 1)*q^164 + (-a + 1)*q^167 + a*q^168 + 
        (a + 1)*q^169 - q^171 - 2*q^172 - a*q^175 - q^177 + a*q^180 + a*q^181 + 
        a*q^183 + a*q^184 + q^185 + q^188 + a*q^189 + (2*a - 2)*q^191 + 2*q^192 
        - q^193 + (a - 1)*q^195 + (a - 2)*q^196 + (a - 1)*q^197 + 2*a*q^199 + 
        (2*a - 2)*q^201 - q^203 + q^204 - a*q^205 + (a - 1)*q^207 + (a - 
        1)*q^208 + O(q^210),
    q^6 - a*q^8 - q^12 + (-a + 2)*q^14 + (2*a - 2)*q^18 + q^20 + q^24 - q^26 + 
        (-a + 1)*q^30 - 2*a*q^32 + (-a + 1)*q^38 + (a - 1)*q^42 - q^48 + (a - 
        1)*q^50 - a*q^54 + q^56 + (3*a - 3)*q^62 + a*q^68 + (a - 1)*q^72 + 
        2*a*q^74 - a*q^78 + q^80 + a*q^84 - 2*q^86 + a*q^92 + q^96 + (a - 
        2)*q^98 + q^102 + (a - 1)*q^104 - a*q^108 + a*q^114 + (-a + 1)*q^116 + 
        (-a + 1)*q^122 + (-a + 1)*q^126 - 2*a*q^128 + 2*q^134 + q^138 - a*q^140 
        + (-2*a + 2)*q^146 - a*q^150 + (-a + 1)*q^152 + q^156 + q^158 + (a - 
        1)*q^164 + (a - 1)*q^168 - q^170 - a*q^174 + a*q^180 - q^182 - 2*a*q^186
        + q^188 + (a - 1)*q^200 - 2*q^206 + O(q^210)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^7 - q^8 - q^9 - q^10 - a*q^12 - q^13 + (2*a - 1)*q^14 - a*q^15 + (-a +
        1)*q^16 + (-2*a + 2)*q^18 + (-a + 1)*q^20 - a*q^26 + q^30 + (-a + 
        1)*q^31 + 2*a*q^32 + q^34 + (a - 1)*q^37 + (a - 1)*q^38 + a*q^40 + (2*a 
        - 1)*q^42 + (a - 1)*q^43 - a*q^46 + (a - 1)*q^48 + q^49 + a*q^50 + 
        a*q^51 + (-2*a + 2)*q^54 + (-a + 1)*q^56 + q^58 + 3*a*q^62 - q^63 - q^64
        + (a - 1)*q^68 + (-a + 1)*q^69 - q^70 - q^72 + (a - 1)*q^73 - 2*a*q^74 -
        a*q^78 - a*q^79 - q^80 + q^81 - q^82 - a*q^84 + (a - 1)*q^85 - 2*a*q^86 
        + a*q^87 + q^90 - q^91 + q^92 - q^94 + a*q^96 + (-a + 1)*q^97 + (a - 
        2)*q^98 - q^102 - a*q^103 + a*q^104 - a*q^105 + a*q^106 + a*q^108 + (a -
        1)*q^109 + (-a + 1)*q^112 + (a - 1)*q^114 + q^115 + (a - 1)*q^116 + 
        q^117 - q^118 + q^121 + (a - 1)*q^122 - a*q^123 + q^126 + a*q^127 + 
        (-2*a + 2)*q^128 + q^130 + (-2*a + 2)*q^134 + a*q^135 - a*q^136 + 
        a*q^138 + (-a + 1)*q^139 + (-a + 1)*q^140 - a*q^141 - a*q^142 + (a - 
        1)*q^144 + (a - 1)*q^145 - 2*a*q^146 + a*q^150 + (a - 1)*q^151 + q^152 +
        a*q^156 + (a - 1)*q^157 - q^158 + (a - 1)*q^159 + (-a + 1)*q^164 + (-a +
        2)*q^168 + q^169 - a*q^170 - q^174 - a*q^177 + a*q^178 + (a - 1)*q^180 +
        (-2*a + 2)*q^182 + (a - 1)*q^184 + 3*a*q^186 + (-a + 1)*q^188 + a*q^195 
        - a*q^199 + (-a + 1)*q^200 + (-a + 1)*q^205 + 2*q^206 + (a - 1)*q^208 + 
        O(q^210),
    q^2 + (a - 1)*q^12 + q^14 - q^18 - q^20 - q^26 - a*q^30 + (-a + 1)*q^32 + 
        q^48 + (-a + 1)*q^62 + q^68 + (a - 1)*q^74 + a*q^80 + (a - 1)*q^84 + (a 
        - 1)*q^86 - a*q^92 + q^98 + a*q^102 + (-a + 1)*q^108 + q^116 - q^126 - 
        q^128 + (-a + 1)*q^138 - q^140 + (a - 1)*q^146 + (-a + 1)*q^156 - 
        a*q^158 + q^162 - q^164 + (a - 1)*q^170 + a*q^174 + q^180 - q^182 - 
        q^188 + (-a + 1)*q^194 - a*q^206 + O(q^210),
    q^3 + (a - 2)*q^7 + 2*q^9 - a*q^12 + (-a + 1)*q^13 + a*q^15 + (a - 1)*q^16 -
        q^19 + (a - 1)*q^21 - q^24 + (a - 1)*q^25 + q^27 + (a + 1)*q^28 + (3*a -
        3)*q^31 - 2*a*q^36 + (-2*a + 2)*q^37 - a*q^39 - a*q^40 + (-2*a + 2)*q^43
        + (a - 1)*q^48 + (-a - 1)*q^49 - a*q^51 - q^52 - q^57 + (-a + 1)*q^60 - 
        q^61 + a*q^63 + 2*q^64 + 2*q^67 + (a - 1)*q^69 + (-2*a + 2)*q^73 + (a - 
        1)*q^75 + a*q^76 - a*q^79 + q^84 + (-a + 1)*q^85 - a*q^87 + 2*q^91 + 
        (2*a - 2)*q^93 + a*q^96 + q^100 + 2*a*q^103 + a*q^105 - a*q^108 + (-2*a 
        + 2)*q^109 + (-a + 1)*q^111 - a*q^112 - q^115 + (-a - 1)*q^117 + a*q^123
        + 3*q^124 + (-a + 1)*q^129 + (-a + 1)*q^133 - a*q^135 + a*q^136 + (3*a -
        3)*q^139 + a*q^141 + (a - 1)*q^144 + (-a + 1)*q^145 - a*q^147 - 2*q^148 
        + (a - 1)*q^151 + (a - 1)*q^156 + (-2*a + 2)*q^157 + (-a + 1)*q^159 + (a
        - 1)*q^160 - q^163 - q^168 + (a - 2)*q^169 - q^171 - 2*q^172 - a*q^175 +
        a*q^177 - q^181 - q^183 + (-a + 1)*q^184 + (a - 1)*q^189 + q^192 - q^193
        - a*q^195 + (2*a - 1)*q^196 + 2*a*q^199 + 2*q^201 + (a - 1)*q^204 + (a -
        1)*q^205 + q^208 + O(q^210),
    q^4 + (a - 1)*q^8 + (a - 1)*q^10 - q^12 + (a + 1)*q^14 - a*q^16 - 2*a*q^18 -
        a*q^20 + (a - 1)*q^24 - q^26 + q^28 + (-a + 1)*q^30 + 2*q^32 + (-a + 
        1)*q^34 - q^36 + a*q^38 + (a + 1)*q^42 - q^46 + a*q^48 + q^50 - q^52 - 
        2*a*q^54 - a*q^56 + (-a + 1)*q^58 - a*q^60 + 3*q^62 + a*q^68 + (a - 
        1)*q^70 + (a - 1)*q^72 - 2*q^74 - q^78 + (a - 1)*q^80 + (a - 1)*q^82 - 
        q^84 - 2*q^86 + (-a + 1)*q^90 + (-a + 1)*q^92 + (a - 1)*q^94 + 2*q^96 + 
        (2*a - 1)*q^98 + (a - 1)*q^102 + q^104 + q^106 + q^108 - a*q^112 + 
        a*q^114 + a*q^116 + (a - 1)*q^118 + a*q^122 + (-a + 1)*q^124 + (-a + 
        1)*q^126 - 2*a*q^128 + (-a + 1)*q^130 - 2*a*q^134 + q^138 - a*q^140 - 
        q^142 + a*q^144 - 2*q^146 + (a - 1)*q^148 + q^150 + (-a + 1)*q^152 + 
        q^156 + (a - 1)*q^158 + a*q^160 - a*q^164 - a*q^168 - q^170 + (a - 
        1)*q^172 + (a - 1)*q^174 + q^178 + a*q^180 - 2*a*q^182 + 3*q^186 - 
        a*q^188 + q^196 - a*q^200 + a*q^204 + (-2*a + 2)*q^206 + a*q^208 + 
        O(q^210),
    q^5 + (-2*a + 1)*q^7 + (a - 1)*q^8 + (2*a - 2)*q^9 + a*q^13 - q^15 - a*q^16 
        - q^17 + (-a + 1)*q^19 - a*q^20 + (-2*a + 1)*q^21 + a*q^23 + (-a + 
        1)*q^24 - a*q^25 + (2*a - 2)*q^27 + (a - 2)*q^28 - q^29 - 3*a*q^31 + 
        q^32 + q^35 + 2*q^36 + 2*a*q^37 + a*q^39 + q^40 + q^41 + 2*a*q^43 - q^45
        + q^47 - a*q^48 + (-a + 2)*q^49 + q^51 + (-a + 1)*q^52 - a*q^53 + (a - 
        1)*q^56 + (-a + 1)*q^57 + q^59 + a*q^60 + (-a + 1)*q^61 - q^63 + (2*a - 
        2)*q^64 - q^65 + (2*a - 2)*q^67 + a*q^68 - a*q^69 + a*q^71 + (-a + 
        1)*q^72 + 2*a*q^73 - a*q^75 - q^76 + q^79 + (a - 2)*q^84 + a*q^85 + q^87
        - a*q^89 + (2*a - 2)*q^91 + (-a + 1)*q^92 - 3*a*q^93 - q^96 + (a - 
        1)*q^100 - 2*q^103 + (-a + 1)*q^104 - q^105 - a*q^107 + 2*q^108 + 
        2*a*q^109 + 2*a*q^111 + q^112 - a*q^113 + (-a + 1)*q^115 + a*q^116 + (-a
        + 2)*q^117 - q^119 + q^120 - q^123 + (3*a - 3)*q^124 + (a - 1)*q^125 + 
        2*a*q^129 - q^131 + a*q^133 + q^135 - q^136 - q^137 - 3*a*q^139 - 
        a*q^140 - q^141 - a*q^144 + a*q^145 + (-a + 2)*q^147 + (-2*a + 2)*q^148 
        - a*q^151 + q^153 + (-a + 1)*q^155 + (-a + 1)*q^156 + 2*a*q^157 + 
        a*q^159 - a*q^160 + a*q^161 + (-a + 1)*q^163 - a*q^164 - q^167 + (-a + 
        1)*q^168 + (-2*a + 1)*q^169 + (-a + 1)*q^171 + (-2*a + 2)*q^172 + q^175 
        - q^177 + a*q^180 + (-a + 1)*q^181 + (-a + 1)*q^183 + a*q^184 + (a - 
        1)*q^185 - a*q^188 - q^189 + (2*a - 2)*q^191 + (2*a - 2)*q^192 + (-a + 
        1)*q^193 + q^195 + (-a - 1)*q^196 + q^197 - 2*q^199 + (2*a - 2)*q^201 - 
        q^203 - a*q^204 - a*q^205 - a*q^207 + (a - 1)*q^208 + O(q^210),
    q^6 - a*q^8 + (-a + 1)*q^12 + (a - 2)*q^14 + 2*q^18 + q^20 - a*q^24 + (-a + 
        1)*q^26 + a*q^30 + (2*a - 2)*q^32 - q^38 + (a - 1)*q^42 - q^48 + (a - 
        1)*q^50 + q^54 + q^56 + (3*a - 3)*q^62 - q^68 - a*q^72 + (-2*a + 2)*q^74
        - a*q^78 - a*q^80 + (-a + 1)*q^84 + (-2*a + 2)*q^86 + a*q^92 + (a - 
        1)*q^96 + (-a - 1)*q^98 - a*q^102 + (a - 1)*q^104 + (a - 1)*q^108 - 
        q^114 - q^116 - q^122 + a*q^126 + 2*q^128 + 2*q^134 + (a - 1)*q^138 + 
        q^140 + (-2*a + 2)*q^146 + (a - 1)*q^150 + a*q^152 + (a - 1)*q^156 - 
        a*q^158 + q^164 + q^168 + (-a + 1)*q^170 - a*q^174 - q^180 + 2*q^182 + 
        (2*a - 2)*q^186 + q^188 + q^200 + 2*a*q^206 + O(q^210)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 - q^4 + q^9 + q^12 - q^13 + q^16 - q^25 - q^27 - q^36 + q^39 + 
        2*q^43 - q^48 + q^49 + q^52 - 2*q^61 - q^64 + q^75 - 2*q^79 + q^81 + 
        q^100 + 2*q^103 + q^108 - q^117 - q^121 - 2*q^127 - 2*q^129 + 2*q^139 + 
        q^144 - q^147 - q^156 + 2*q^157 + q^169 - 2*q^172 + 2*q^181 + 2*q^183 + 
        q^192 - q^196 - 2*q^199 - q^208 + O(q^210),
    q^2 - q^6 - q^8 + q^18 + q^24 - q^26 + q^32 - q^50 - q^54 - q^72 + q^78 + 
        2*q^86 - q^96 + q^98 + q^104 - 2*q^122 - q^128 + q^150 - 2*q^158 + q^162
        + q^200 + 2*q^206 + O(q^210),
    q^7 - q^21 - q^28 + q^63 + q^84 - q^91 + q^112 - q^175 - q^189 + O(q^210),
    q^14 - q^42 - q^56 + q^126 + q^168 - q^182 + O(q^210)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
546
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
210
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
547
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
546
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
547
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
182
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
547
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
547
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
547
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
547
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
39*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
547
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
91*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
547
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
273*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
91
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 + q^9 - q^11 - q^13 + q^16 - q^19 + q^25 - q^29 + q^36 - q^44 - q^47
        + q^49 - q^52 - q^53 + q^64 - q^67 - q^73 - q^76 + q^81 + O(q^91)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
548
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
548
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
136
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
548
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
68
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
548
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^5*q^2 + a^10*q^4 + (a^15 - a^9)*q^5 - a^15*q^8 + a*q^9 + (a^14 + 
        a^3)*q^10 + (-a^14 - a^11)*q^13 - a^3*q^16 + (-a^4 - 1)*q^17 - a^6*q^18 
        + (-a^8 + a^2)*q^20 + (-a^13 + a^7 - a)*q^25 + (a^15 - a^14 + a^13 - 
        a^12 + a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - 2*a^2 + a
        - 1)*q^26 + (-a^15 + a^14 - a^13 + a^12 - a^11 + a^10 - a^9 + a^8 - 
        2*a^7 + a^6 - a^5 + a^4 - a^3 + a^2 - a + 1)*q^29 + a^8*q^32 + (a^9 + 
        a^5)*q^34 + a^11*q^36 + (-a^12 + a^5)*q^37 + (a^13 - a^7)*q^40 + (a^11 +
        a^6)*q^41 + (a^15 - a^14 + a^13 - a^12 + a^11 - 2*a^10 + a^9 - a^8 + a^7
        - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^45 + a^8*q^49 + (-a^12 + a^6 - 
        a)*q^50 + (a^7 + a^4)*q^52 + (-a^8 + a^4)*q^53 + (a^12 - a^4)*q^58 + 
        (a^13 - a^2)*q^61 - a^13*q^64 + (a^12 + a^9 - a^6 - a^3)*q^65 + (-a^14 -
        a^10)*q^68 + (-a^15 + a^14 - a^13 + a^12 - a^11 + a^10 - a^9 + a^8 - a^7
        + a^6 - a^5 + a^4 - a^3 + a^2 - a + 1)*q^72 + (a^14 + a^12)*q^73 + 
        (-a^10 - 1)*q^74 + (a^12 + a)*q^80 + a^2*q^81 + (-a^15 + a^14 - a^13 + 
        a^12 - 2*a^11 + a^10 - a^9 + a^8 - a^7 + a^6 - a^5 + a^4 - a^3 + a^2 - a
        + 1)*q^82 + (-a^15 + a^13 + a^9 + a^2)*q^85 + (a^4 + a^3)*q^89 + (a^15 +
        a^4)*q^90 - a^13*q^98 + (-a^11 + a^6 - 1)*q^100 + (a^3 - a^2)*q^101 + 
        (-a^12 - a^9)*q^104 + (a^13 - a^9)*q^106 + (a^6 - a^5)*q^109 + (a^8 - 
        a^6)*q^113 + (a^9 + 1)*q^116 + (-a^15 - a^12)*q^117 - a^3*q^121 + (a^7 +
        a)*q^122 + (-a^15 + a^14 - a^13 + a^12 + 2*a^10 - a^9 + a^8 - a^7 + a^6 
        - 2*a^5 + a^4 - a^3 + a^2 - a + 1)*q^125 - a*q^128 + (-a^14 + a^11 + a^8
        + 1)*q^130 + O(q^134)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
548
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^10*q^2 - a^3*q^4 + (-a^13 - a)*q^5 - a^13*q^8 + a^2*q^9 + (-a^11 + 
        a^6)*q^10 + (-a^11 - a^5)*q^13 + a^6*q^16 + (a^8 + 1)*q^17 + a^12*q^18 +
        (a^15 - a^14 + a^13 - a^12 + a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 +
        a^3 - a^2 + a - 1)*q^20 + (a^14 - a^9 + a^2)*q^25 + (-a^15 + a^4)*q^26 +
        (-a^15 + a^14)*q^29 + (a^15 - a^14 + a^13 - a^12 + a^11 - a^10 + a^9 - 
        a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^32 + (a^10 - a)*q^34 
        - a^5*q^36 + (a^10 - a^7)*q^37 + (a^14 - a^9)*q^40 + (a^12 - a^5)*q^41 +
        (-a^15 - a^3)*q^45 + (a^15 - a^14 + a^13 - a^12 + a^11 - a^10 + a^9 - 
        a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^49 + (a^12 - a^7 + 
        a^2)*q^50 + (a^14 + a^8)*q^52 + (a^15 - a^14 + a^13 - a^12 + a^11 - a^10
        + a^9 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^53 + (a^8 - 
        a^7)*q^58 + (-a^9 + a^4)*q^61 - a^9*q^64 + (a^12 - a^7 + a^6 - a)*q^65 +
        (-a^11 - a^3)*q^68 - a^15*q^72 + (-a^11 - a^7)*q^73 + (-a^3 + 1)*q^74 + 
        (-a^7 + a^2)*q^80 + a^4*q^81 + (-a^15 - a^5)*q^82 + (-a^13 - a^9 + a^4 -
        a)*q^85 + (a^8 + a^6)*q^89 + (-a^13 + a^8)*q^90 - 2*a^3*q^97 - a^9*q^98 
        + (a^12 - a^5 + 1)*q^100 + (a^6 + a^4)*q^101 + (-a^7 - a)*q^104 + (-a^9 
        - a)*q^106 + (a^12 + a^10)*q^109 + (a^15 - a^14 + a^13 + a^11 - a^10 + 
        a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^113 + (-a + 
        1)*q^116 + (-a^13 - a^7)*q^117 + a^6*q^121 + (a^14 + a^2)*q^122 + (-a^15
        + a^10 - a^5 - a^3)*q^125 + a^2*q^128 + (a^15 - a^14 + a^13 - a^12 - 
        a^10 + a^9 - a^8 + a^7 - a^6 - a^4 + a^3 - a^2 + a)*q^130 + O(q^134)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
548
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
548
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 34*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
548
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 68*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
134
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 + q^16 - q^17 - q^18 + q^25 - q^34 - q^37 + q^49 - q^61 + q^64 - 
        q^68 - q^69 - q^72 - q^74 - q^93 + q^100 - q^101 + q^121 - q^122 - q^129
        + O(q^134),
    q^2 + q^8 - q^9 - q^17 + q^32 - q^34 - q^36 - q^37 + q^50 - q^61 - q^68 + 
        q^69 + 2*q^73 - q^74 + q^81 + q^93 + q^98 - q^101 + 2*q^109 - q^122 + 
        q^128 + q^129 + O(q^134),
    q^3 - q^6 + q^12 - q^23 - q^24 - q^31 - q^43 + q^46 + q^47 + q^48 + q^62 + 
        q^67 - q^71 + q^75 + q^79 - q^83 + q^86 - q^92 - q^94 - q^96 - q^124 - 
        q^127 + q^131 + O(q^134)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (a^5 + a^4)*q^7 + (-a^7 + a^3)*q^13 + a^2*q^16 + (a^5 - a^3 + 
        a)*q^19 - a^2*q^25 + (-a^6 - a^5)*q^28 + (a^6 - a^3)*q^31 + (-a^6 + a^4 
        - a^2 + a + 1)*q^37 + (a^7 - a^5 - a^4 + a^3 - a)*q^43 + (a^7 + a^6 - 
        a^5 - a^4 + a^3 + a^2 - a - 2)*q^49 + (a^6 - 2*a^4 + a^2 - 1)*q^52 - 
        q^61 - a^3*q^64 + (a^6 + a)*q^67 + (-a^6 - a^2)*q^73 + (-a^6 + a^4 - 
        a^2)*q^76 + (-a^6 - a^5 + a^4 - a^2 + 1)*q^79 + (a^7 + a^6 - a^4 + 2*a^2
        + a - 1)*q^91 + (-a^7 - a^3 + a)*q^97 + a^3*q^100 + (-2*a^7 + a^5 - a^3 
        + a)*q^103 + (-a^6 - a^4)*q^109 + (a^7 + a^6)*q^112 + O(q^118)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^4 + (a^3 - a^2 + a - 2)*q^7 + (a^3 - a^2)*q^13 + a^2*q^16 + (-a^3 - 
        a + 1)*q^19 + a^2*q^25 + (-a - 1)*q^28 + (a^3 - a)*q^31 + (-a^3 + 
        a)*q^37 + (-2*a^3 + a^2 - a + 2)*q^49 + (-a^2 + a - 1)*q^52 + q^61 + 
        a^3*q^64 + (a^2 - a)*q^73 + (-a^3 + 1)*q^76 + (-a^3 - 1)*q^79 + (-a^3 + 
        a)*q^91 + (-a^3 + a^2 - a)*q^97 + a^3*q^100 + (-a^3 - a + 1)*q^103 + 
        (a^3 - a^2 - 1)*q^109 + (-a^2 - a)*q^112 + O(q^118),
    q^3 - a^3*q^9 + a*q^12 + (a^3 - a^2 + a - 2)*q^21 - a*q^27 + (-a^3 + a^2 - a
        + 1)*q^36 + (a^3 - a^2)*q^39 + a^2*q^48 + (-a^3 - a + 1)*q^57 + (a^3 + 
        a^2)*q^63 + a^2*q^75 + (a^3 - a^2 + a - 1)*q^81 + (-a - 1)*q^84 + (a^3 -
        a)*q^93 - a^2*q^108 + (-a^3 + a)*q^111 + (a - 1)*q^117 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a^2*q^4 + (-a^3 + 1)*q^7 + (a^3 - a^2 - 1)*q^13 + (a^3 - a^2 + a - 
        1)*q^16 + (-a^2 + a - 1)*q^19 + (a^3 - a^2 + a - 1)*q^25 + (a^2 + 
        1)*q^28 + (a^2 - a)*q^31 + (a^2 - a)*q^37 - 2*a^3*q^43 + (-a^3 - a + 
        1)*q^49 + (-a^3 - a)*q^52 + q^61 - a*q^64 + 2*a^2*q^67 + (a^3 + a - 
        1)*q^73 + (-a + 1)*q^76 + (-a + 1)*q^79 + (2*a^3 - a^2 + a - 2)*q^91 + 
        (-a^3 + 1)*q^97 - a*q^100 + (-a^2 + a - 1)*q^103 + (-a^3 + a^2)*q^109 + 
        (a^3 + a - 1)*q^112 + O(q^118),
    q^3 - a*q^9 + a^2*q^12 + (-a^3 + 1)*q^21 + a^2*q^27 - a^3*q^36 + (a^3 - a^2 
        - 1)*q^39 + (a^3 - a^2 + a - 1)*q^48 + (-a^2 + a - 1)*q^57 + (a^3 - a^2 
        - 1)*q^63 + (a^3 - a^2 + a - 1)*q^75 - a^3*q^81 + (a^2 + 1)*q^84 + (a^2 
        - a)*q^93 + (a^3 - a^2 + a - 1)*q^108 + (a^2 - a)*q^111 + (a^2 + 
        1)*q^117 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (a + 1)*q^7 - q^16 - 2*a*q^19 + q^25 + (-a + 1)*q^28 + (a - 
        1)*q^31 + (a - 1)*q^37 + (a - 1)*q^43 + a*q^49 - q^61 + a*q^64 + (a - 
        1)*q^67 + 2*q^73 - 2*q^76 + (-a - 1)*q^79 - 2*a*q^97 - a*q^100 + (-a - 
        1)*q^112 + O(q^118)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 30*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
549
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 30*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^13 - q^19 - q^22 + q^25 - q^34 + q^46 + q^49 + q^52 + q^58 - q^64 + 
        q^76 - q^97 - q^103 - q^106 + O(q^118),
    q^2 - q^11 - q^17 + q^23 + q^29 - q^32 - q^44 + q^50 - q^53 + q^59 - q^68 - 
        q^71 + q^89 + q^92 + q^98 + q^101 + q^116 + O(q^118),
    q^3 + q^27 - q^36 - q^39 - q^57 - q^66 + q^75 - q^102 - q^117 + O(q^118),
    q^4 + q^13 - q^16 + q^19 - q^22 - q^34 + q^46 - q^52 + q^58 - q^61 - 2*q^73 
        - q^76 + q^97 + q^100 + q^103 - q^106 - 2*q^109 + O(q^118),
    q^6 - q^18 - q^33 - q^51 + q^54 + q^69 + q^87 - q^96 + q^99 + O(q^118),
    q^9 - q^12 - q^39 + q^48 - q^57 + q^66 + q^81 + q^102 - q^108 - q^117 + 
        O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
12*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
14*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
16*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
18*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^9 - q^11 + q^16 - 2*q^31 - q^36 - q^44 + q^49 - 2*q^59 + q^64 + 
        2*q^71 + q^81 + 2*q^89 + q^99 + q^121 - 2*q^124 - q^144 + O(q^158),
    q^2 + q^8 - q^18 - q^22 + q^32 - 2*q^62 - q^72 - q^88 + q^98 - 2*q^118 + 
        q^128 + 2*q^142 + O(q^158)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (2*a^3 - a^2 + a - 1)*q^3 + a*q^4 - q^5 + (-a^3 - a^2 - a)*q^9 + 
        a^3*q^11 + (a^3 - a^2 + a - 2)*q^12 + (-2*a^3 + a^2 - a + 1)*q^15 + 
        a^2*q^16 - a*q^20 + (-a^3 + 2*a^2 - a + 1)*q^23 + q^25 + (-a^3 + 2*a^2 +
        2)*q^27 + (-a^2 + a)*q^31 + (-a^2 - a)*q^33 + (-2*a^3 - a + 1)*q^36 + 
        (a^3 - a^2 + a - 1)*q^44 + (a^3 + a^2 + a)*q^45 + (-a - 1)*q^48 - q^49 +
        (-2*a^3 + a^2 - a + 1)*q^53 - a^3*q^55 + (a^3 - a^2 + a)*q^59 + (-a^3 + 
        a^2 - a + 2)*q^60 + a^3*q^64 + (-a^3 - 1)*q^67 + (a^3 + a^2 - a - 
        1)*q^69 + (-a^2 + a - 1)*q^71 + (2*a^3 - a^2 + a - 1)*q^75 - a^2*q^80 + 
        (2*a^3 - 2)*q^81 + (-a^3 - a + 1)*q^89 + (a^3 + 1)*q^92 + (a^3 - a^2 + 
        2*a - 1)*q^93 + (2*a^3 - a^2 + a - 1)*q^97 + (-a^3 + a^2 + 2)*q^99 + 
        a*q^100 + (-a^2 + 1)*q^103 + (a^3 + a^2 + a + 1)*q^108 + (-a^3 + 
        a)*q^113 + (a^3 - 2*a^2 + a - 1)*q^115 - a*q^121 + (-a^3 + a^2)*q^124 - 
        q^125 + (-a^3 - a^2)*q^132 + (a^3 - 2*a^2 - 2)*q^135 + (a^3 - a)*q^137 +
        (-2*a^3 + a^2 - a + 2)*q^144 + (-2*a^3 + a^2 - a + 1)*q^147 + (a^2 - 
        a)*q^155 + (-a^3 + a^2 - 2*a + 1)*q^157 + O(q^158),
    q^2 + (2*a^3 - a^2 + a - 1)*q^6 + a*q^8 - q^10 + (-a^3 - a^2 - a)*q^18 + 
        a^3*q^22 + (a^3 - a^2 + a - 2)*q^24 + (-2*a^3 + a^2 - a + 1)*q^30 + 
        a^2*q^32 - a*q^40 + (-a^3 + 2*a^2 - a + 1)*q^46 + q^50 + (-a^3 + 2*a^2 +
        2)*q^54 + (-a^2 + a)*q^62 + (-a^2 - a)*q^66 + (-2*a^3 - a + 1)*q^72 + 
        (a^3 - a^2 + a - 1)*q^88 + (a^3 + a^2 + a)*q^90 + (-a - 1)*q^96 - q^98 +
        (-2*a^3 + a^2 - a + 1)*q^106 - a^3*q^110 + (a^3 - a^2 + a)*q^118 + (-a^3
        + a^2 - a + 2)*q^120 + a^3*q^128 + (-a^3 - 1)*q^134 + (a^3 + a^2 - a - 
        1)*q^138 + (-a^2 + a - 1)*q^142 + (2*a^3 - a^2 + a - 1)*q^150 + O(q^158)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^3 - a)*q^3 + a^2*q^4 + q^5 + (a^3 - 1)*q^9 - a*q^11 + (-a^3 + 
        1)*q^12 + (-a^3 - a)*q^15 + (a^3 - a^2 + a - 1)*q^16 + a^2*q^20 + (-a^2 
        + a - 1)*q^23 + q^25 + a*q^27 + (a^3 + a - 1)*q^31 + (a^3 + a - 1)*q^33 
        + (-a^2 - 1)*q^36 + (2*a^3 - 2*a^2 + 2*a - 2)*q^37 - a^3*q^44 + (a^3 - 
        1)*q^45 + 2*a^2*q^47 + (a^2 + 1)*q^48 + q^49 + (-a^3 - a)*q^53 - a*q^55 
        + (-a^3 + 1)*q^59 + (-a^3 + 1)*q^60 - a*q^64 + (-a + 1)*q^67 + a^3*q^69 
        + (-a^3 - a)*q^71 + (-a^3 - a)*q^75 + (a^3 - a^2 + a - 1)*q^80 + (-a^2 +
        a - 1)*q^89 + (-a + 1)*q^92 + (-a^3 + a^2 + 2)*q^93 + (-a^3 - a)*q^97 + 
        (-a^3 + a^2 + 1)*q^99 + a^2*q^100 + (a^3 - a^2 + a)*q^103 + a^3*q^108 + 
        (2*a^2 + 2)*q^111 + (a^2 - a)*q^113 + (-a^2 + a - 1)*q^115 + a^2*q^121 +
        (a^3 - a^2 - 1)*q^124 + q^125 + (a^3 - a^2 - 1)*q^132 + a*q^135 + (a^2 -
        a)*q^137 + (-2*a^3 + 2)*q^141 + (-a^3 - a + 1)*q^144 + (-a^3 - a)*q^147 
        - 2*a*q^148 + (a^3 + a - 1)*q^155 + (-a^3 + a^2)*q^157 + O(q^158),
    q^2 + (-a^3 - a)*q^6 + a^2*q^8 + q^10 + (a^3 - 1)*q^18 - a*q^22 + (-a^3 + 
        1)*q^24 + (-a^3 - a)*q^30 + (a^3 - a^2 + a - 1)*q^32 + a^2*q^40 + (-a^2 
        + a - 1)*q^46 + q^50 + a*q^54 + (a^3 + a - 1)*q^62 + (a^3 + a - 1)*q^66 
        + (-a^2 - 1)*q^72 + (2*a^3 - 2*a^2 + 2*a - 2)*q^74 - a^3*q^88 + (a^3 - 
        1)*q^90 + 2*a^2*q^94 + (a^2 + 1)*q^96 + q^98 + (-a^3 - a)*q^106 - 
        a*q^110 + (-a^3 + 1)*q^118 + (-a^3 + 1)*q^120 - a*q^128 + (-a + 1)*q^134
        + a^3*q^138 + (-a^3 - a)*q^142 + (-a^3 - a)*q^150 + O(q^158)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
550
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^4 + q^9 - q^11 + q^16 - 2*q^31 - q^36 + q^44 - q^49 + 2*q^59 - q^64 + 
        2*q^71 + q^81 - 2*q^89 - q^99 + q^121 + 2*q^124 + q^144 + O(q^158),
    q^2 - q^8 + q^18 - q^22 + q^32 - 2*q^62 - q^72 + q^88 - q^98 + 2*q^118 - 
        q^128 + 2*q^142 + O(q^158),
    q^5 - q^20 - q^25 + q^45 - q^55 + q^80 + q^100 + q^125 - 2*q^155 + O(q^158),
    q^10 - q^40 - q^50 + q^90 - q^110 + O(q^158)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
252
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
84
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
126
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
126
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
551
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^35 - q^36 - q^42 - q^45 + q^49 - q^57 - q^62 - q^80 + 
        q^81 - q^87 + O(q^98),
    q^2 - q^21 - q^31 - q^40 + q^50 - q^60 + q^69 + q^79 + q^97 + O(q^98),
    q^3 - 2*q^15 - q^18 + q^21 + 2*q^27 - q^32 - q^37 - q^40 - q^41 + 2*q^48 + 
        q^50 + q^60 - q^69 + q^70 + q^75 + q^76 - 2*q^84 - q^89 + q^95 + 
        O(q^98),
    q^4 - q^9 - q^20 - q^30 + q^35 + q^36 + q^45 + q^57 - q^63 - q^81 - q^82 - 
        q^83 + q^87 + O(q^98),
    q^5 - q^9 - q^16 + q^28 + q^45 + q^54 - q^62 - q^63 - q^81 - q^83 + q^96 + 
        O(q^98),
    q^6 - q^9 - q^16 - q^20 + 2*q^24 + q^25 - q^30 + q^35 - q^36 + q^38 - q^42 +
        q^54 + q^58 - q^62 - q^64 - q^80 - q^81 - q^82 - q^83 + q^92 + q^93 + 
        2*q^96 + O(q^98),
    q^7 - q^9 - q^16 + q^24 + q^28 - q^36 + q^54 - q^62 - q^64 + q^74 - q^82 - 
        q^83 + q^92 + q^93 + q^96 + O(q^98),
    q^8 - 4*q^15 - q^18 + q^19 + 3*q^21 + 2*q^27 + q^29 + q^31 - q^32 - 2*q^37 -
        q^40 - 2*q^41 - 2*q^46 + 2*q^48 + 2*q^50 - 2*q^56 + q^60 - 2*q^69 + 
        3*q^70 + 2*q^72 + q^75 + q^76 - 3*q^84 - 2*q^89 - q^90 + 2*q^95 + 
        O(q^98),
    q^10 - 3*q^15 - q^18 + q^19 + 2*q^21 + 2*q^27 + q^29 - q^32 - 2*q^37 - q^40 
        - q^41 - 2*q^46 + 2*q^48 + 2*q^50 - q^56 + q^60 - q^69 + 2*q^70 + q^72 +
        q^76 - 2*q^84 - 2*q^89 - q^90 + 2*q^95 + O(q^98),
    q^12 - 2*q^15 - q^18 + q^19 + q^21 + q^27 + q^29 - q^32 - q^37 - q^40 - q^41
        - q^46 + 2*q^48 + 2*q^50 - q^56 - q^69 + 2*q^70 + q^76 - 2*q^84 - q^89 -
        q^90 + q^95 + O(q^98),
    q^14 - q^15 - q^18 + q^21 + q^27 - q^32 - q^41 + q^48 + q^60 - q^69 - q^84 +
        q^95 + O(q^98),
    q^23 - q^24 - q^25 + q^28 + q^30 - q^35 - q^38 + q^45 + q^49 - q^58 - q^63 +
        q^74 + q^80 - q^93 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 - q^13 + q^23 + q^25 + q^27 - q^29 - q^31 - q^41 - q^47 + q^49 + 
        2*q^59 - q^71 - q^73 + 2*q^101 + q^117 + q^121 - q^127 - q^131 - q^139 -
        q^151 - q^163 + 2*q^167 + 2*q^173 + O(q^178),
    q^2 - q^18 - q^26 + q^46 + q^50 + q^54 - q^58 - q^62 - q^82 - q^94 + q^98 + 
        2*q^118 - q^142 - q^146 + O(q^178),
    q^3 - q^9 - q^39 + q^69 + q^75 + q^81 - q^87 - q^93 + q^117 - q^123 - q^141 
        + q^147 + 2*q^177 + O(q^178),
    q^4 - q^16 + q^32 - q^36 - q^52 + q^92 + q^100 + q^108 - q^116 - q^124 - 
        q^128 + q^144 - q^164 + O(q^178),
    q^6 - q^18 - q^78 + q^138 + q^150 + q^162 - q^174 + O(q^178),
    q^8 - q^16 + q^64 - q^72 - q^104 - q^128 + q^144 + O(q^178),
    q^12 - q^36 - q^48 + q^96 + q^144 - q^156 + O(q^178),
    q^24 - q^48 - q^72 + q^144 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 11*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^8 + q^12 - q^18 - q^23 - q^25 - q^26 + q^27 + q^39 + q^49 - q^52 + 
        q^58 + q^62 + q^64 + q^78 + q^82 - q^87 - q^93 - q^94 - q^96 + q^116 - 
        q^117 - q^121 - q^123 - q^124 + q^141 - q^142 + q^144 + q^146 - q^164 + 
        2*q^167 - q^169 - q^174 + O(q^178),
    q^2 + q^13 - q^16 + q^18 - q^27 - q^29 + q^31 + q^41 - q^46 - q^47 - q^50 - 
        q^52 - q^71 + q^73 - q^81 + q^98 - q^104 + q^108 + q^116 + q^117 + q^124
        - q^127 + q^128 + q^131 - q^139 - q^144 + q^151 - q^162 + q^163 + q^164 
        - q^169 + O(q^178),
    q^3 + q^18 - q^24 - q^27 + q^36 - q^54 - q^69 - q^75 - q^78 + q^108 + 
        2*q^117 - q^144 + q^147 - q^156 - q^162 + q^174 + O(q^178),
    q^4 + q^13 + q^26 - q^27 - q^29 - q^31 - q^32 + q^36 - q^41 + q^47 - q^54 - 
        q^58 + q^62 + q^71 - q^73 + q^81 + q^82 - q^92 - q^94 - q^100 - q^104 + 
        q^117 + q^127 + q^131 - q^139 - q^142 + q^146 - q^151 - q^162 + q^163 + 
        q^169 + O(q^178),
    q^6 - q^12 + q^18 - 2*q^27 + q^36 - q^48 - q^78 + 2*q^93 + q^96 + 2*q^117 + 
        2*q^123 - q^138 - 2*q^141 - q^144 - q^150 - q^156 - q^162 + q^174 + 
        O(q^178),
    q^9 - q^12 + q^18 - q^27 - q^39 + q^54 - q^72 - q^78 - q^81 + q^87 + q^93 + 
        q^96 + q^108 + q^117 + q^123 - q^141 - q^144 - q^162 + q^174 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + 11*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^25 - q^49 + q^93 - q^117 + q^121 - q^141 + q^169 + O(q^178),
    q^2 - q^26 + q^32 - q^48 - q^50 + q^52 + q^58 + q^62 - q^64 + q^72 - q^78 - 
        q^82 - q^92 - q^94 + q^96 - q^98 - 2*q^104 - q^108 - q^116 - q^124 + 
        q^128 + q^138 + q^142 - q^144 + q^146 + 2*q^156 + q^162 + q^164 + q^174 
        + O(q^178),
    q^3 - q^39 - 2*q^47 + 2*q^71 - q^75 + q^87 - q^123 + 2*q^131 - q^147 + 
        O(q^178),
    q^4 - q^18 - q^24 + q^26 - q^32 + q^58 - q^62 + q^78 - q^82 + q^92 + q^94 - 
        q^100 + q^104 + q^108 - q^142 + q^144 - q^146 - q^156 - q^174 + 
        O(q^178),
    q^6 - q^18 - q^24 + 2*q^26 - 2*q^32 + q^48 - 2*q^62 - q^72 + q^78 + 2*q^92 +
        2*q^104 + 2*q^108 - q^138 + q^144 - 2*q^146 - q^150 - 2*q^156 - q^162 - 
        q^174 + O(q^178),
    q^8 + q^18 + q^24 - 3*q^26 + 2*q^32 - q^36 - 2*q^48 + q^52 + q^58 + q^62 - 
        q^64 + q^72 - q^78 - q^82 - 2*q^92 - q^94 - 2*q^104 - 2*q^108 + q^116 - 
        q^124 + 2*q^138 + q^142 - q^144 + 3*q^146 + 3*q^156 + 2*q^162 - q^164 + 
        q^174 + O(q^178),
    q^9 - 2*q^29 + 2*q^41 - q^69 - q^81 - q^93 + q^117 - q^141 + 2*q^177 + 
        O(q^178),
    q^12 + q^24 - 2*q^26 + 2*q^32 - q^36 - 2*q^48 + 2*q^52 + 2*q^58 + 2*q^62 - 
        2*q^64 + q^72 - 2*q^78 - 2*q^82 - 2*q^92 - 2*q^94 + q^96 - 2*q^104 - 
        2*q^108 - 2*q^124 + 2*q^138 + 2*q^142 - 2*q^144 + 2*q^146 + 3*q^156 + 
        2*q^162 + 2*q^174 + O(q^178),
    q^13 - q^29 + q^41 - q^69 - q^73 - q^81 + q^117 - q^169 + 2*q^177 + 
        O(q^178),
    q^16 - q^24 + q^26 - q^32 + q^36 - q^46 + q^48 - 2*q^52 - q^54 - q^58 - q^62
        + q^64 - q^72 + 2*q^78 + q^82 + q^92 + q^94 - q^96 + q^104 + q^108 + 
        2*q^118 - q^138 - q^142 + q^144 - q^146 - q^156 - q^162 + O(q^178),
    q^23 + q^27 - q^39 - 2*q^59 - q^87 + q^123 + 2*q^167 + O(q^178),
    q^31 - q^39 - q^47 + q^71 + q^87 - q^123 - q^127 + q^131 + q^139 - q^151 - 
        q^163 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
552
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + 11*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^12 + q^13 + q^16 - q^18 + q^24 + q^25 - q^26 - q^27 + q^29 - 
        q^31 - q^32 + q^36 - q^41 - q^46 + q^47 - q^48 - q^49 - q^58 + q^62 + 
        q^64 - q^69 - q^71 - q^73 - q^78 + q^82 + q^92 - q^94 + q^104 - q^117 - 
        q^121 - q^127 - q^131 + q^138 + q^139 + q^142 + q^146 + q^151 + q^156 + 
        q^163 + q^174 + O(q^178),
    q^2 + q^9 - q^12 + q^13 + q^16 - q^29 - q^31 + q^39 - q^41 - q^46 - q^47 + 
        q^50 - q^52 - q^54 + q^71 + q^72 - q^73 - q^78 + q^87 - q^93 - q^96 - 
        q^98 + q^104 - q^116 - q^123 + q^124 - q^127 + q^128 - q^131 + q^139 + 
        q^141 + q^151 + q^163 + q^164 + q^169 + q^174 + O(q^178),
    q^3 - q^9 + q^12 - 2*q^13 - 2*q^16 - q^24 + 2*q^31 - q^36 - q^39 + 2*q^46 + 
        2*q^52 + q^69 - q^72 + 2*q^73 + q^75 + 2*q^78 - q^81 - q^87 + q^93 + 
        q^96 + q^117 + q^123 - 2*q^124 + 2*q^127 - 2*q^139 - q^141 - q^147 - 
        2*q^151 + q^156 - 2*q^163 - 2*q^169 - 2*q^174 + O(q^178),
    q^4 - q^9 + q^12 - 3*q^13 - 2*q^16 + q^18 - 2*q^24 + q^26 - q^29 + 3*q^31 + 
        q^32 - q^36 - q^39 + q^41 + 2*q^46 - q^47 + 2*q^52 - q^58 - q^62 + 
        2*q^69 + q^71 - q^72 + q^73 + 3*q^78 - q^82 - q^87 - q^92 + q^93 - q^94 
        + q^96 + q^100 - q^104 - q^108 + 2*q^117 + q^123 - 2*q^124 + 3*q^127 + 
        q^131 - q^139 - q^141 + q^142 + q^144 - q^146 - 3*q^151 - q^163 - q^169 
        - q^174 + O(q^178),
    q^6 + 2*q^9 - q^12 + 2*q^13 + 2*q^16 - q^18 + 2*q^24 - 2*q^26 + 2*q^29 - 
        2*q^31 - 2*q^32 + q^36 - 2*q^41 - 2*q^46 + 2*q^47 - q^48 - 2*q^52 + 
        2*q^62 - 2*q^69 - 2*q^71 - 2*q^73 - 3*q^78 + 2*q^92 - q^96 + 2*q^104 - 
        2*q^117 - 2*q^123 + 2*q^124 - 2*q^127 - 2*q^131 + q^138 + 2*q^139 - 
        q^144 + 2*q^146 + q^150 + 2*q^151 + q^156 - q^162 + 2*q^163 + 2*q^169 + 
        q^174 + O(q^178),
    q^8 + q^9 + q^13 + q^16 - q^23 + q^24 - 2*q^26 + q^29 - q^31 - q^32 + q^36 -
        q^39 - q^41 - q^46 + q^47 - q^48 - q^52 + 2*q^62 - q^69 - q^71 - q^73 - 
        2*q^78 + q^87 + q^92 + q^93 - q^96 + 2*q^101 + q^104 - q^116 - 2*q^117 -
        q^123 + q^124 - q^127 - q^131 + q^138 + q^139 + q^141 - q^144 + q^151 + 
        q^156 + q^163 - q^164 + 2*q^167 + q^169 - 2*q^173 + O(q^178)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^18 - a^16 + a^3)*q^2 + (a^23 - a^19 - a^10 + a^8)*q^4 + a^14*q^7 + 
        (a^23 - a^21 - a^20 + a^18 + a^17 - 2*a^15 - a^14 + a^13 + a^12 + a^11 -
        a^10 - 2*a^9 + a^7 + a^6 - a^4 - a^3 + a)*q^8 + a^2*q^9 + (-a^13 + 
        a^6)*q^11 + (a^19 - a^6 + a^4)*q^14 + (a^23 + a^22 - 2*a^20 - a^19 + 
        a^17 + 2*a^16 - 2*a^14 - a^13 + a^11 - a^9 - a^8 + a^7 + a^6 - a^3 - a^2
        + a + 1)*q^16 + (a^20 - a^18 + a^5)*q^18 + (-a^23 - a^22 + a^21 + a^20 -
        2*a^18 - a^17 + a^15 + a^14 - a^12 + a^10 + 2*a^9 - a^7 - a^6 + a^5 + 
        a^4 - a - 1)*q^22 + (a^22 + a^17 - a^4)*q^23 - a^7*q^25 + (a^22 - a^20 -
        a^11 + a^7)*q^28 + (-a^17 - a^5)*q^29 + (-a^23 + a^21 - a^17 + a^15 + 
        a^12 - a^8 + a^6 - a^2)*q^32 + (a^23 + a^22 - a^21 - a^20 - a^19 + a^17 
        + a^16 - a^14 - a^13 + a^11 + a^10 - a^9 - a^8 + a^6 + a^5 - a^3 - a^2 +
        1)*q^36 + (a^23 - a^21 - a^20 + a^18 + a^17 - a^15 - a^14 + a^12 + a^11 
        - a^10 - a^9 + a^7 + a^6 - a^4 - a^3 + 1)*q^37 + (-a^23 - a^22 + a^21 + 
        a^20 + a^19 - a^17 - a^16 + a^14 + a^13 - a^12 - a^11 + a^9 - a^6 - a^5 
        + a^3 + a^2 - 1)*q^43 + (-a^23 - a^22 - a^21 + a^20 + 2*a^19 - a^17 - 
        a^16 + 2*a^14 + a^13 - a^12 - a^11 + a^10 + a^9 + a^8 - 2*a^6 - a^5 + 
        a^2 - 1)*q^44 + (a^20 + a^12 - a^9 - a)*q^46 + (a^15 - a^2)*q^49 + 
        (-a^22 + a^20 + a^19 - a^17 - a^16 + a^14 + a^13 - a^12 - a^11 - a^10 + 
        a^9 + a^8 - a^6 - a^5 + a^3 + a^2 - 1)*q^50 + (a^13 - a^11 - 1)*q^53 + 
        (-a^23 - a^16 + a^12 + a^3 - a)*q^56 + (-a^23 - a^22 + a^21 + a^9 - a^8 
        - a^7)*q^58 + a^16*q^63 + (-a^23 - a^22 + a^21 + a^20 + a^15 + a^14 - 
        a^13 - a^12 + a^10 + 2*a^9 - 2*a^7 - a^6 + a^3 + a^2 - a - 1)*q^64 + 
        (a^10 + a^8)*q^67 + (-a^21 - a^3)*q^71 + (-a^17 + a^15 - a^11 - a^2 + 
        1)*q^72 + (-a^19 + a^17 + a^16 - a^14 - a^4 + a)*q^74 + (a^20 - a^14 + 
        a)*q^77 + (-a^23 + a^21 + a^20 - a^18 - a^17 + a^15 + a^14 - a^12 + a^10
        + a^9 - a^7 - a^6 + a^4 + a^3 - a - 1)*q^79 + a^4*q^81 + (-a^23 + a^21 +
        a^20 - a^18 - a^17 + a^14 - a^13 - a^12 + a^10 + a^9 - a^7 - a^6 + 2*a^4
        + a^3 - a - 1)*q^86 + (a^22 - a^21 + a^19 - a^11 - a^6 + a^4 - a^2 + 
        1)*q^88 + (a^23 + a^22 - a^20 - 2*a^19 + 2*a^17 + a^16 - 2*a^14 - a^13 +
        a^11 + a^10 - a^9 - a^8 + a^6 + a^5 - a^4 - a^3 + a + 1)*q^92 + (a^18 - 
        a^7)*q^98 + (-a^15 + a^8)*q^99 + (-a^15 + a^13 + a^4 - 1)*q^100 + 
        O(q^104)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^5 - a^3)*q^2 + (a^10 + a^8 + a^6)*q^4 - a*q^7 + (-a^11 - a^9 + a^2 +
        1)*q^8 + a^2*q^9 + (a^6 + 1)*q^11 + (a^6 + a^4)*q^14 + (a^11 - a^10 + 
        a^9 - a^8 - a^6 - a^4 - a^2 - 1)*q^16 + (-a^7 - a^5)*q^18 + (-a^11 - a^9
        - a^5 - a^3)*q^22 + (-a^9 + a^4)*q^23 - a^7*q^25 + (-a^11 - a^9 - 
        a^7)*q^28 + (-a^5 + a^4)*q^29 + (a^11 + a^9 + a^7 + a^5 + a^3 + a - 
        1)*q^32 + (a^11 + a^9 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^36 
        + (-a^11 - a)*q^37 + (a^11 - a^10 + a^9 + a^7 - a^6 + a^5 - a^4 + a^3 - 
        a^2 + a - 1)*q^43 + (a^11 + a^9 + a^7 + a^5 - a^4 - a^2 - 1)*q^44 + 
        (a^11 - a^10 - a^8 - a^6 + a^5 - a^4 + a^3 - a^2 - 1)*q^46 + a^2*q^49 + 
        (a^11 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^50 + 
        (-a^11 + 1)*q^53 + (a^11 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 - a^2 - 
        1)*q^56 + (a^10 - a^9 + a^8 - a^7)*q^58 - a^3*q^63 + (-a^11 - a^9 - a^7 
        - a^5 + a^4 + a^2 + 1)*q^64 + (a^10 + a^8)*q^67 + (a^8 - a^3)*q^71 + 
        (-a^11 + a^4 + a^2 + 1)*q^72 + (a^6 + a^4 - a^3 - a)*q^74 + (-a^7 - 
        a)*q^77 - a^11*q^79 + a^4*q^81 + (-a^11 + a^4 + a^2 + 1)*q^86 + (-a^11 -
        a^9 + a^8 + a^6 + a^4 + 2*a^2 + 1)*q^88 + (a^11 + a^9 - a^8 + a^7 + a^5 
        + a^3 - 1)*q^92 + (-a^7 - a^5)*q^98 + (a^8 + a^2)*q^99 + (a^4 + a^2 + 
        1)*q^100 + O(q^104)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^14 + a*q^16 - q^18 + q^22 + (-a + 1)*q^23 - a*q^25 + (a - 1)*q^29 - 
        a*q^37 + (a - 1)*q^39 - a*q^43 - a*q^49 + a*q^51 + (a - 1)*q^53 + (a - 
        1)*q^56 + q^57 - q^58 - a*q^63 + q^64 - q^67 + q^71 + (a - 1)*q^72 + (-a
        + 1)*q^74 + a*q^77 + q^78 + q^79 + (-a + 1)*q^86 + (-a + 1)*q^88 + 
        a*q^99 + (-a + 1)*q^102 + O(q^104),
    q^2 + a*q^7 + (-a + 1)*q^8 + a*q^9 - a*q^11 + a*q^29 - q^37 - a*q^39 - q^43 
        + (-a + 1)*q^46 - a*q^50 - q^51 + a*q^53 + (a - 1)*q^57 + (a - 1)*q^58 +
        (-a + 1)*q^71 - a*q^74 + (a - 1)*q^78 - q^81 - a*q^86 - a*q^98 + a*q^102
        + O(q^104),
    q^3 - a*q^6 - q^13 + (a - 1)*q^17 + a*q^19 + (-a + 1)*q^21 - q^24 + a*q^26 +
        (a - 1)*q^33 + q^34 + (-a + 1)*q^38 - q^42 - a*q^47 + a*q^48 + (-a + 
        1)*q^61 + q^66 + (-a + 1)*q^69 - a*q^73 - a*q^75 + (-a + 1)*q^89 + (a - 
        1)*q^91 + (a - 1)*q^94 + (a - 1)*q^97 + (a - 1)*q^101 + q^103 + O(q^104)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
39*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 - q^8 + q^9 - q^10 - q^19 + q^20 + q^22 - q^23 + q^25 + q^26 + q^32 
        - q^38 + q^40 - q^44 - q^45 - q^46 + q^49 + q^50 - q^52 - q^55 + q^62 - 
        q^65 - q^67 - q^72 - q^73 + q^76 + q^79 + q^81 + 2*q^83 - q^90 + q^92 + 
        2*q^95 - q^97 - q^100 + O(q^104),
    q^2 - q^4 - q^5 + q^11 + q^13 + q^18 - q^19 - q^22 - q^23 + q^25 - q^26 + 
        q^31 - q^36 + q^40 + q^44 - q^45 + q^52 - q^62 + q^64 - q^67 - q^73 - 
        q^88 + q^89 + q^95 - q^97 + q^98 + q^99 + q^101 + O(q^104),
    q^7 - q^35 - q^56 + q^63 - q^70 + O(q^104),
    q^14 - q^28 - q^35 + q^77 + q^91 + O(q^104)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
553
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 39*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
554
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
276
);
qprec:=
137
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
554
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
92
);
qprec:=
137
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
554
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
137
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
554
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
69*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
137
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 + a*q^4 - a*q^7 + (a - 1)*q^9 + (-a + 1)*q^12 + (a - 2)*q^13 + (a 
        - 1)*q^16 + (a - 1)*q^21 + (-a + 1)*q^25 + q^27 + (-a + 1)*q^28 + (-2*a 
        + 1)*q^31 - q^36 + q^37 + (a + 1)*q^39 + (2*a - 1)*q^43 + q^48 + (-a - 
        1)*q^52 + q^63 - q^64 - a*q^67 + q^73 - q^75 + (a - 2)*q^79 - a*q^81 - 
        q^84 + (a + 1)*q^91 + (a - 2)*q^93 + (2*a - 1)*q^97 + q^100 + a*q^108 + 
        (-a - 1)*q^109 - a*q^111 + q^112 + (-2*a + 1)*q^117 + q^121 + (-a + 
        2)*q^124 + (-a + 1)*q^127 + (-a + 2)*q^129 + (a - 1)*q^139 - a*q^144 + 
        O(q^146),
    q^5 - a*q^15 + a*q^20 - a*q^35 + (a - 1)*q^45 + (-a + 1)*q^60 + (a - 2)*q^65
        + (a - 1)*q^80 + (a - 1)*q^105 + (-a + 1)*q^125 + q^135 + (-a + 1)*q^140
        + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^3 + (a - 1)*q^4 + (-a + 1)*q^7 - a*q^9 - a*q^12 + (-a + 
        1)*q^13 - a*q^16 + (2*a - 2)*q^19 + a*q^21 - a*q^25 + q^27 + a*q^28 - 
        q^31 + q^36 + q^37 + a*q^39 - q^43 + q^48 + a*q^52 - 2*a*q^57 + (2*a - 
        2)*q^61 - q^63 + q^64 + (-a + 1)*q^67 - q^73 + q^75 - 2*a*q^76 + (-a + 
        1)*q^79 + (a - 1)*q^81 - q^84 - a*q^91 + (-a + 1)*q^93 - q^97 + q^100 + 
        2*q^103 + (a - 1)*q^108 + a*q^109 + (a - 1)*q^111 - q^112 - q^117 + 
        q^121 + (-a + 1)*q^124 + a*q^127 + (-a + 1)*q^129 + 2*a*q^133 + a*q^139 
        + (a - 1)*q^144 + O(q^146),
    q^5 + (a - 1)*q^15 + (a - 1)*q^20 + (-a + 1)*q^35 - a*q^45 - a*q^60 + (-a + 
        1)*q^65 - a*q^80 + (2*a - 2)*q^95 + a*q^105 - a*q^125 + q^135 + a*q^140 
        + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 + q^9 - q^12 - q^21 - q^25 + q^28 + q^34 - q^46 + q^48 + q^49 + q^58
        - q^63 - q^64 - q^67 - q^73 + q^81 + q^84 - q^102 - q^108 + q^111 - 
        q^112 + q^118 + q^121 + 2*q^127 + q^138 - q^139 + O(q^146),
    q^2 - q^6 + q^17 + q^18 - q^23 + q^29 - q^32 - q^50 - q^51 - q^54 + q^59 + 
        q^68 + q^69 - q^74 - q^87 - q^89 - q^92 + q^96 - q^98 - q^113 + q^116 + 
        q^125 + q^131 + O(q^146),
    q^3 - q^4 - q^7 + q^16 - q^21 + q^27 + q^28 - q^34 - q^36 + q^37 + q^46 + 
        2*q^49 - q^58 - q^63 - q^67 - q^73 - q^75 + q^84 + q^100 + q^102 - q^112
        - q^118 - q^138 - q^139 + q^144 + O(q^146),
    q^5 - q^35 + q^45 - q^50 - q^60 - q^105 + q^140 + O(q^146),
    q^10 - q^25 - q^30 + q^75 + q^85 + q^90 - q^100 - q^115 + q^145 + O(q^146),
    q^15 - q^20 - q^35 + q^50 + q^80 - q^105 - q^125 + q^135 + q^140 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 18*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
555
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 18*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^9 - 1/2*q^10 + q^21 - 1/2*q^25 - 1/2*q^30 + q^34 - q^40 + q^46 - q^49 
        - q^64 - 1/2*q^75 + q^81 + q^84 + 1/2*q^85 + 1/2*q^90 - 1/2*q^100 - 
        q^111 + 3/2*q^115 + q^121 - q^139 - 1/2*q^145 + O(q^146),
    q^2 - q^8 + 1/2*q^15 - q^17 - q^18 + 1/2*q^20 + q^32 + 1/2*q^35 - q^42 + 
        1/2*q^50 - q^60 + 2*q^68 + q^72 - 1/2*q^80 - q^92 - q^98 + 1/2*q^105 - 
        1/2*q^125 - 1/2*q^135 - 3/2*q^140 + O(q^146),
    q^3 + q^10 - q^12 - q^27 - 2*q^28 + q^37 - q^40 + q^48 + q^70 - q^85 - q^90 
        + q^100 + 2*q^102 + q^108 + 2*q^112 - q^120 - q^145 + O(q^146),
    q^4 - 1/2*q^10 - q^16 + q^21 - 1/2*q^25 + 1/2*q^30 - q^34 - q^36 + q^46 + 
        q^70 - 1/2*q^75 - q^84 + 1/2*q^85 + 1/2*q^90 + 1/2*q^100 + 1/2*q^115 - 
        q^120 + 2*q^136 - q^139 + q^144 - 1/2*q^145 + O(q^146),
    q^5 + 2*q^8 - 2*q^23 - q^35 + 2*q^42 - q^45 - q^50 + q^60 - 2*q^68 - 2*q^72 
        - 2*q^87 + q^105 + 2*q^113 + q^140 + O(q^146),
    q^6 + q^8 + 1/2*q^15 + 1/2*q^20 - q^23 + q^29 - 3/2*q^35 + q^42 - 1/2*q^50 -
        q^51 - q^54 - 2*q^56 - q^59 + q^60 - q^68 - q^69 - q^72 + q^74 - 
        1/2*q^80 - q^87 + q^89 + q^96 + 1/2*q^105 + q^113 + q^116 + 1/2*q^125 - 
        q^131 - 1/2*q^135 + 1/2*q^140 + O(q^146),
    q^7 + 1/2*q^10 - q^12 - 1/2*q^25 - q^28 + 1/2*q^30 - q^40 + q^48 + q^58 - 
        q^63 - q^67 + q^73 + 1/2*q^75 - 1/2*q^85 - 1/2*q^90 + 1/2*q^100 + q^102 
        + q^108 + q^112 + 1/2*q^115 - q^118 - q^138 + 1/2*q^145 + O(q^146),
    q^14 - 1/2*q^15 + 1/2*q^20 - q^24 - q^29 + 1/2*q^35 - 1/2*q^50 + q^59 + q^69
        - 1/2*q^80 + 1/2*q^105 - q^119 - 1/2*q^125 - q^126 + q^131 - q^134 + 
        1/2*q^135 + 1/2*q^140 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
556
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
136
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
556
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
138
);
qprec:=
136
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
556
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
138
);
qprec:=
136
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
556
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
136
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
556
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
136
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
556
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
136
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
556
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 46*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
136
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
556
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
69*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
136
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^35 - q^37 - q^41 - q^47 + q^49 - q^55 - q^65 - q^77 + 
        q^81 - q^91 - q^107 + q^121 - q^125 + O(q^136),
    q^5 - q^11 - q^13 + q^31 + q^35 + q^45 - q^49 - q^55 - q^65 + q^67 - q^71 + 
        q^79 - q^99 + q^113 - q^117 + q^121 + q^125 - q^127 + O(q^136),
    q^7 - q^11 - q^13 + q^25 + q^29 - q^49 - q^55 + q^63 - q^65 - q^71 + q^77 + 
        q^83 + q^89 + q^91 - q^99 - q^117 - q^127 + q^131 + O(q^136)
]
;
Bo:=
[
    q - q^5 - q^7 + q^9 - q^11 - q^13 - q^29 - q^31 + q^35 + 2*q^37 + 2*q^41 - 
        q^45 + 2*q^47 + q^55 - q^63 + q^65 - q^67 - q^71 + q^77 - q^79 + q^81 - 
        q^83 - q^89 + q^91 - q^99 + 2*q^107 - q^113 - q^117 + q^125 - q^127 - 
        q^131 + O(q^136),
    q^2 + q^8 - q^10 - q^14 + q^18 - q^22 - q^26 + q^32 - q^40 - q^56 - q^58 - 
        q^62 + q^70 + q^72 + 2*q^74 + 2*q^82 - q^88 - q^90 + 2*q^94 - q^104 + 
        q^110 - q^126 + q^128 + q^130 - q^134 + O(q^136),
    q^4 + q^16 - q^20 - q^28 + q^36 - q^44 - q^52 + q^64 - q^80 - q^112 - q^116 
        - q^124 + O(q^136)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
557
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
556
);
qprec:=
93
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
557
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
139*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
93
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^3 + a^2 - a + 1)*q^4 + (a^2 - a)*q^7 + (a^3 - 2*a^2 + a - 1)*q^13 - 
        a^3*q^16 + (a^3 + a)*q^19 - q^25 + (a - 1)*q^28 + a^3*q^31 + (-a^3 - 
        a^2)*q^37 + (a^3 - a^2 + a - 2)*q^43 + (a - 1)*q^49 + (a^3 - a)*q^52 + 
        (-a^3 + a^2 - 2*a + 1)*q^61 - a^2*q^64 + (-a^3 + a^2 + 1)*q^67 + (a^2 + 
        a)*q^73 + (a^2 + 1)*q^76 + (-a^2 + 1)*q^79 + (a^2 - 2*a + 2)*q^91 + 
        (-a^3 + 1)*q^97 + (a^3 - a^2 + a - 1)*q^100 + (-a^3 + a^2 - a)*q^103 + 
        (-a + 1)*q^109 + (a^3 - a^2 + a)*q^112 - a^3*q^121 + a^2*q^124 + (-a^3 +
        2*a^2 - a + 1)*q^127 - a*q^133 + (-a - 1)*q^139 + (-a^2 - a)*q^148 + 
        (a^2 + a)*q^151 + (a^3 + a)*q^157 + (-a^2 + a - 1)*q^163 + (-a^2 + 2*a -
        1)*q^169 + (2*a^3 - a^2 + a - 1)*q^172 + (-a^2 + a)*q^175 + O(q^178),
    q^2 + (-a^3 + a^2 - a + 1)*q^8 + (a^2 - a)*q^14 + (a^3 - 2*a^2 + a - 1)*q^26
        - a^3*q^32 + (a^3 + a)*q^38 - q^50 + (a - 1)*q^56 + a^3*q^62 + (-a^3 - 
        a^2)*q^74 + (a^3 - a^2 + a - 2)*q^86 + (a - 1)*q^98 + (a^3 - a)*q^104 + 
        (-a^3 + a^2 - 2*a + 1)*q^122 - a^2*q^128 + (-a^3 + a^2 + 1)*q^134 + (a^2
        + a)*q^146 + (a^2 + 1)*q^152 + (-a^2 + 1)*q^158 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a^3*q^4 + (a^3 + a - 1)*q^7 + (-a^2 + a - 1)*q^13 - a*q^16 + (a^2 - 
        a)*q^19 + q^25 + (a^2 + 1)*q^28 - a*q^31 + (a^3 - a^2 - 1)*q^37 + (-a^3 
        + 1)*q^43 + (-a^2 - 1)*q^49 + (a^2 - a)*q^52 + (-a^3 + a^2)*q^61 + (a^3 
        - a^2 + a - 1)*q^64 + (-a^3 + a^2)*q^67 + (a^3 + a - 1)*q^73 + (a^3 - 
        a^2 + a)*q^76 + (a^3 - a^2 + a)*q^79 + (-a^3 + a^2 - a + 1)*q^91 + (-a +
        1)*q^97 - a^3*q^100 + (-a^3 + 1)*q^103 + (a^2 + 1)*q^109 + (-a^3 + 
        1)*q^112 - a*q^121 + (a^3 - a^2 + a - 1)*q^124 + (-a^2 + a - 1)*q^127 - 
        a^2*q^133 + (a^2 + 1)*q^139 + (a^3 + a - 1)*q^148 + (a^3 + a - 1)*q^151 
        + (a^2 - a)*q^157 + (-a^3 - a)*q^163 + (-a^3 + a^2 - a)*q^169 + (-a^3 - 
        a)*q^172 + (a^3 + a - 1)*q^175 + O(q^178),
    q^2 - a^3*q^8 + (a^3 + a - 1)*q^14 + (-a^2 + a - 1)*q^26 - a*q^32 + (a^2 - 
        a)*q^38 + q^50 + (a^2 + 1)*q^56 - a*q^62 + (a^3 - a^2 - 1)*q^74 + (-a^3 
        + 1)*q^86 + (-a^2 - 1)*q^98 + (a^2 - a)*q^104 + (-a^3 + a^2)*q^122 + 
        (a^3 - a^2 + a - 1)*q^128 + (-a^3 + a^2)*q^134 + (a^3 + a - 1)*q^146 + 
        (a^3 - a^2 + a)*q^152 + (a^3 - a^2 + a)*q^158 + O(q^178),
    q^3 - a*q^9 - a^3*q^12 + (a^3 + a - 1)*q^21 + a^2*q^27 + (a^3 - a^2 + a - 
        1)*q^36 + (-a^2 + a - 1)*q^39 - a*q^48 + (a^2 - a)*q^57 + (-a^3 + 
        1)*q^63 + q^75 - a^3*q^81 + (a^2 + 1)*q^84 - a*q^93 + q^108 + (a^3 - a^2
        - 1)*q^111 + (a^3 - a^2 + a)*q^117 + (-a^3 + 1)*q^129 + a^2*q^144 + 
        (-a^2 - 1)*q^147 + (a^2 - a)*q^156 + (-a^3 + a^2)*q^171 + O(q^178),
    q^6 - a*q^18 - a^3*q^24 + (a^3 + a - 1)*q^42 + a^2*q^54 + (a^3 - a^2 + a - 
        1)*q^72 + (-a^2 + a - 1)*q^78 - a*q^96 + (a^2 - a)*q^114 + (-a^3 + 
        1)*q^126 + q^150 - a^3*q^162 + (a^2 + 1)*q^168 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^19 - q^28 - q^40 + q^49 + q^76 + q^82 - q^94 + q^100 - q^103 + q^112 +
        q^121 - q^133 + q^142 - q^157 + q^169 - q^175 + O(q^178),
    q^2 - q^38 - q^56 - q^80 + q^98 + q^152 + q^164 + O(q^178),
    q^3 - q^12 - q^15 - q^21 + q^24 + q^27 - q^57 + q^60 + q^84 + q^93 - q^96 + 
        q^105 - q^108 - q^120 - q^123 - q^135 + 2*q^141 - q^168 - q^177 + 
        O(q^178),
    q^4 - q^28 - q^40 + q^82 - q^94 + q^100 + q^142 - q^160 + O(q^178),
    q^5 + 1/2*q^32 - q^35 - 1/2*q^38 - 1/2*q^41 - 1/2*q^47 - 1/2*q^50 + q^59 + 
        1/2*q^62 - 1/2*q^71 - q^80 + 1/2*q^95 - 1/2*q^101 + q^107 - 1/2*q^113 + 
        1/2*q^125 + 1/2*q^128 - 1/2*q^131 + q^134 - 1/2*q^149 + 1/2*q^152 - 
        1/2*q^155 - 1/2*q^173 + O(q^178),
    q^6 - q^12 - q^30 - q^42 + q^48 + q^54 + q^60 + q^84 - q^96 - q^108 - q^114 
        + O(q^178),
    q^7 - q^28 - q^31 + q^40 + q^49 - q^64 - 2*q^67 + q^97 + q^109 + q^112 + 
        q^124 - 2*q^133 + q^163 - q^175 + O(q^178),
    q^8 - q^41 + q^47 - q^56 - q^71 - q^80 + q^95 - q^101 - q^113 + q^125 + 
        q^131 + q^149 - q^155 + q^164 + q^173 + O(q^178),
    q^9 - q^36 - q^45 - q^63 + q^72 + q^81 - q^171 + O(q^178),
    q^10 - q^19 - q^25 + q^31 - q^40 + q^64 + 2*q^67 - q^70 - q^94 - q^103 + 
        q^118 + q^133 - q^157 - q^160 + q^175 + O(q^178),
    q^14 + 1/2*q^32 - 1/2*q^38 - 1/2*q^41 + 1/2*q^47 - 1/2*q^50 - q^56 - 
        1/2*q^62 - 1/2*q^71 + 1/2*q^95 + q^98 - 1/2*q^101 - 1/2*q^113 + 
        1/2*q^125 - 1/2*q^128 + 1/2*q^131 - q^134 + 1/2*q^149 + 1/2*q^152 - 
        1/2*q^155 + 1/2*q^173 + O(q^178),
    q^16 - q^19 - q^25 + q^31 - 2*q^40 + q^64 + 2*q^67 + q^76 + q^100 - q^103 - 
        q^112 - q^124 + q^133 - q^157 - q^160 + q^175 + O(q^178),
    q^18 - q^36 - q^90 - q^126 + q^144 + q^162 + O(q^178),
    q^20 - 1/2*q^32 - 1/2*q^38 - 1/2*q^41 + 1/2*q^47 - 1/2*q^50 + 1/2*q^62 - 
        1/2*q^71 + 1/2*q^95 - 1/2*q^101 - 1/2*q^113 + 1/2*q^125 + 1/2*q^128 + 
        1/2*q^131 + q^134 - q^140 + 1/2*q^149 - 1/2*q^152 - 1/2*q^155 + 
        1/2*q^173 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
558
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
84
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
84
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
84
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
84
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 - a*q^9 + (a + 1)*q^11 - a*q^13 + (a - 1)*q^16 + a*q^17 + (a - 
        1)*q^23 - q^25 + (-2*a + 1)*q^31 + (-a + 1)*q^36 - a*q^43 + (2*a - 
        1)*q^44 + (-a + 1)*q^49 + (-a + 1)*q^52 - 2*q^53 + (-a + 2)*q^59 - q^64 
        + (a - 1)*q^68 - q^79 + (a - 1)*q^81 + (-2*a + 1)*q^83 - q^92 + (a - 
        2)*q^97 + (-2*a + 1)*q^99 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 + (a - 1)*q^9 + a*q^11 + (a - 1)*q^13 - a*q^16 + (-a + 
        1)*q^17 + a*q^23 + q^25 - q^31 - a*q^36 - 2*a*q^41 + (a - 1)*q^43 - q^44
        + 2*q^47 - a*q^49 - a*q^52 + 2*q^53 + (-a + 1)*q^59 + q^64 - 2*a*q^67 + 
        a*q^68 - q^79 - a*q^81 - q^83 - q^92 + (-a + 1)*q^97 - q^99 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
559
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^35 - q^38 - q^40 - q^53 - q^68 - q^74 + q^81 - q^95 + 
        O(q^100),
    q^2 + q^18 - q^19 - q^20 - q^34 - q^37 + q^50 - q^65 - q^70 + q^71 + q^73 + 
        q^85 + q^91 + q^98 + O(q^100),
    q^4 - q^13 - q^16 - 2*q^17 + 2*q^23 + 2*q^25 - q^35 + q^36 - q^38 - q^40 - 
        q^43 + q^49 + q^52 + q^53 + q^64 + q^68 - q^74 - 2*q^79 - 2*q^92 - q^95 
        + O(q^100),
    q^5 - q^8 - q^19 + q^28 - q^37 + q^45 + q^46 + q^50 - q^65 - q^70 - q^72 - 
        q^98 + O(q^100),
    q^7 - q^8 - q^19 + q^26 + 2*q^28 - q^32 - q^34 - q^37 + q^46 + q^50 + q^63 -
        q^65 - 2*q^70 - q^72 - q^76 + q^80 + q^85 + q^86 + q^89 - q^98 + 
        O(q^100),
    q^10 - q^13 - q^16 - q^17 + 2*q^23 + 2*q^25 - q^35 - q^38 - q^40 - q^43 + 
        q^52 + q^56 + q^64 + q^68 - q^74 - q^79 + q^90 - q^92 - 2*q^95 + 
        O(q^100),
    q^14 - q^16 - q^17 + q^23 + q^25 - q^35 - q^38 + q^52 + q^56 - q^74 - q^79 +
        O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 - q^9 + q^25 + 2*q^29 - 2*q^41 + q^45 - q^49 - 2*q^61 + q^81 + 
        2*q^89 + 2*q^101 - 2*q^109 + q^121 - q^125 - 2*q^145 - 2*q^149 + q^169 +
        O(q^170),
    q^7 - q^35 - q^63 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 2*H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^5 + (2*a - 2)*q^9 + (-a - 1)*q^21 - a*q^25 - q^29 + q^41 + 
        2*a*q^45 + (-a + 1)*q^49 + (a - 1)*q^61 + 3*q^69 - a*q^81 + (-a + 
        1)*q^89 + a*q^101 + (a - 2)*q^105 - a*q^109 + (a - 1)*q^121 - q^125 - 
        3*a*q^129 + (a - 1)*q^145 + (a - 1)*q^149 + (2*a - 1)*q^161 + q^169 + 
        O(q^170),
    q^3 + 1/3*(2*a - 1)*q^7 + (-a + 1)*q^15 - a*q^23 + (a - 1)*q^27 + 1/3*(a + 
        1)*q^35 + (a - 1)*q^43 + 1/3*(-2*a - 2)*q^63 - q^67 - a*q^75 + (-a + 
        1)*q^83 - q^87 + a*q^103 + a*q^107 - q^115 + q^123 + a*q^135 + (-a + 
        1)*q^147 + (-a + 1)*q^167 + O(q^170)
]
;
Bo:=
[
    q + (a - 1)*q^5 + (-a + 1)*q^21 - a*q^25 - q^29 - q^41 + (a - 1)*q^49 + (-a 
        + 1)*q^61 + q^69 + a*q^81 + (-a + 1)*q^89 + a*q^101 + a*q^105 + a*q^109 
        + (a - 1)*q^121 + q^125 - a*q^129 - 2*q^141 + (-a + 1)*q^145 + (-a + 
        1)*q^149 - q^161 + q^169 + O(q^170),
    q^2 + (a - 1)*q^10 + (-a + 1)*q^42 - a*q^50 - q^58 - q^82 + (a - 1)*q^98 + 
        (-a + 1)*q^122 + q^138 + a*q^162 + O(q^170),
    q^3 - q^7 + (a - 1)*q^15 - a*q^23 + (-a + 1)*q^27 + (-a + 1)*q^35 + (a - 
        1)*q^43 + 2*a*q^47 + q^67 - a*q^75 + (a - 1)*q^83 - q^87 - a*q^103 - 
        a*q^107 + q^115 - q^123 + (-2*a + 2)*q^127 + a*q^135 + (a - 1)*q^147 + 
        2*a*q^163 + (a - 1)*q^167 + O(q^170),
    q^4 - a*q^16 + (a - 1)*q^20 - q^24 + q^56 + (a - 1)*q^64 + q^80 + (-a + 
        1)*q^84 + a*q^96 - a*q^100 - q^116 + (-a + 1)*q^120 - q^164 + O(q^170),
    q^6 - q^14 + (a - 1)*q^30 - a*q^46 + (-a + 1)*q^54 + (-a + 1)*q^70 + (a - 
        1)*q^86 + 2*a*q^94 + q^134 - a*q^150 + (a - 1)*q^166 + O(q^170),
    q^8 + (-a + 1)*q^12 + (a - 1)*q^28 - a*q^32 + (a - 1)*q^40 - q^48 + a*q^60 -
        q^92 - a*q^108 + q^112 + (a - 1)*q^128 - a*q^140 + q^160 + (-a + 
        1)*q^168 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^9 + a*q^11 + (-a + 1)*q^19 - a*q^25 + (a - 1)*q^35 - q^41 + 
        q^49 - 2*a*q^59 + (-a + 1)*q^65 - a*q^81 + (2*a - 2)*q^89 - q^91 - q^99 
        + a*q^115 + (-a + 1)*q^131 + 2*q^139 + (-a + 1)*q^161 + O(q^170),
    q^2 - a*q^8 + (a - 1)*q^18 - a*q^20 + a*q^22 + (a - 1)*q^28 + (a - 1)*q^32 +
        (-a + 1)*q^38 - a*q^50 + (-a + 1)*q^52 + (a - 1)*q^70 + q^72 + (a - 
        1)*q^80 - q^82 + (-a + 1)*q^88 + a*q^92 + q^98 + q^112 - 2*a*q^118 + 
        q^128 + (-a + 1)*q^130 + a*q^148 - q^152 - a*q^162 + O(q^170),
    q^4 + q^10 - a*q^14 - a*q^16 + a*q^26 + (a - 1)*q^36 - a*q^40 + a*q^44 - 
        q^46 + (a - 1)*q^56 + (a - 1)*q^64 - q^74 + (-a + 1)*q^76 + (a - 1)*q^90
        - q^94 - a*q^100 + (-a + 1)*q^104 + (-a + 1)*q^106 + a*q^110 + q^126 + 
        (a - 1)*q^140 + q^144 + (-a + 1)*q^154 + (a - 1)*q^160 - q^164 + 
        O(q^170),
    q^5 - a*q^7 + a*q^13 - q^23 - q^37 + (a - 1)*q^45 - q^47 + (-a + 1)*q^53 + 
        a*q^55 + q^63 + (-a + 1)*q^77 + (-a + 1)*q^95 + 2*q^103 - q^117 - 
        a*q^125 + a*q^127 - q^133 + (a - 1)*q^143 + (-a + 1)*q^157 + a*q^167 + 
        O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^2 - q^4 + a*q^7 - a*q^8 - a*q^9 + (-a - 1)*q^11 - q^14 + q^16 + q^18
        + (-a + 1)*q^22 + a*q^25 - a*q^28 + (a - 1)*q^29 + a*q^32 + a*q^36 + (-a
        - 1)*q^37 + (a + 1)*q^43 + (a + 1)*q^44 - q^49 - q^50 + (a + 1)*q^53 + 
        q^56 + (-a - 1)*q^58 + q^63 - q^64 + (-a + 1)*q^67 - 2*a*q^71 - q^72 + 
        (-a + 1)*q^74 + (-a + 1)*q^77 - q^81 + (a - 1)*q^86 + (a - 1)*q^88 - 
        a*q^98 + (a - 1)*q^99 - a*q^100 + (a - 1)*q^106 + (a + 1)*q^107 + (-a + 
        1)*q^109 + a*q^112 + (-a + 1)*q^116 + a*q^121 + a*q^126 - 2*q^127 - 
        a*q^128 + (a + 1)*q^134 + 2*q^142 - a*q^144 + (a + 1)*q^148 + (a + 
        1)*q^149 + (a + 1)*q^154 - a*q^162 + (a - 1)*q^163 - a*q^169 + O(q^170),
    q^5 + a*q^10 - q^20 + a*q^35 - a*q^40 - a*q^45 + (-a - 1)*q^55 - q^70 + q^80
        + q^90 + (-a + 1)*q^110 + a*q^125 - a*q^140 + (a - 1)*q^145 + a*q^160 + 
        O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 - q^9 + 2*q^23 - q^25 + q^49 + q^63 - 2*q^71 - 2*q^79 + q^81 - 
        2*q^113 + q^121 + 2*q^127 + 2*q^137 + 2*q^151 - 2*q^161 - q^169 + 
        O(q^170),
    q^2 - q^4 + q^8 - q^14 - q^16 - q^18 + q^28 + q^32 + q^36 + 2*q^46 - q^50 - 
        q^56 - q^64 - q^72 - 2*q^92 + q^98 + q^100 + q^112 + q^126 + q^128 - 
        2*q^142 + q^144 - 2*q^158 + q^162 + O(q^170),
    q^5 - q^35 - q^45 + 2*q^115 - q^125 + O(q^170),
    q^10 - q^20 + q^40 - q^70 - q^80 - q^90 + q^140 + q^160 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^11 + q^15 - q^21 + q^25 - q^29 - q^35 - q^39 + q^49 - q^51 - q^65 - 
        2*q^71 + q^79 - q^81 - q^85 + q^91 - q^109 + q^119 - q^135 + q^141 + 
        2*q^149 + q^151 + q^165 + O(q^170),
    q^3 + q^5 - q^7 - q^13 - q^17 - q^27 + q^33 + q^47 + q^55 + 2*q^73 + q^75 - 
        q^77 - 2*q^83 - q^87 - q^97 + q^103 - q^105 + q^125 - q^143 - q^145 + 
        q^147 + 2*q^157 + q^167 + O(q^170)
]
;
Bo:=
[
    q - q^11 - q^15 - q^21 + q^25 - q^29 + q^35 + q^39 + q^49 + q^51 - q^65 + 
        2*q^71 - q^79 - q^81 - q^85 - q^91 - q^109 - q^119 + q^135 + q^141 + 
        2*q^149 - q^151 + q^165 + O(q^170),
    q^2 - q^22 - q^30 - q^42 + q^50 - q^58 + q^70 + q^78 + q^98 + q^102 - q^130 
        + 2*q^142 - q^158 - q^162 + O(q^170),
    q^3 - q^5 - q^7 + q^13 + q^17 - q^27 - q^33 + q^47 + q^55 - 2*q^73 + q^75 + 
        q^77 - 2*q^83 - q^87 + q^97 + q^103 + q^105 - q^125 - q^143 + q^145 + 
        q^147 - 2*q^157 + q^167 + O(q^170),
    q^4 - q^44 - q^60 - q^84 + q^100 - q^116 + q^140 + q^156 + O(q^170),
    q^6 - q^10 - q^14 + q^26 + q^34 - q^54 - q^66 + q^94 + q^110 - 2*q^146 + 
        q^150 + q^154 - 2*q^166 + O(q^170),
    q^12 - q^20 - q^28 + q^52 + q^68 - q^108 - q^132 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
560
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 2*H.3 + 3*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 - q^15 + 2*q^39 - q^49 + q^65 - q^81 - q^95 + q^105 + q^121 - 
        2*q^151 - q^169 + O(q^170),
    q^2 - q^8 - q^18 + q^28 - q^30 + q^32 - q^60 + q^72 + 2*q^78 - q^98 - q^100 
        - q^112 + q^120 - q^128 + q^130 - q^162 + O(q^170),
    q^3 - q^13 + q^19 - q^21 - q^35 - q^59 + q^61 + q^75 - q^83 + q^91 + q^101 +
        q^117 + q^125 - q^131 + q^133 - q^139 - q^147 - q^157 + O(q^170),
    q^4 - q^14 - q^16 + q^30 - q^36 + q^50 + q^56 - q^60 + q^64 - 2*q^114 - 
        q^120 + q^126 - q^130 + q^144 + 2*q^156 + O(q^170),
    q^5 - 2*q^19 + 2*q^21 + q^35 - q^45 + 2*q^59 - 2*q^61 - 2*q^75 - 2*q^91 - 
        2*q^101 - q^125 + 2*q^131 + 2*q^139 + O(q^170),
    q^6 + q^12 + q^20 - q^24 - q^26 + q^38 - q^42 - q^48 - q^52 - q^70 - q^76 - 
        q^80 + q^84 + q^96 + q^104 - q^118 + q^122 + q^150 - q^152 - q^166 + 
        q^168 + O(q^170),
    q^7 - q^15 - q^25 + 2*q^57 - q^63 + q^65 + q^95 - q^105 - 2*q^113 + 
        O(q^170),
    q^10 - 2*q^12 - q^20 - 2*q^38 - q^40 + 2*q^42 + 2*q^48 + 2*q^52 + q^70 + 
        q^80 - q^90 + 2*q^118 - 2*q^122 + q^140 - 2*q^150 + 2*q^152 + q^160 - 
        2*q^168 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
80
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
80
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 - a*q^9 + (-a^2 + a - 1)*q^13 + (-a^3 - a)*q^15 + (a^3 - a^2 + a
        - 1)*q^16 + (a^3 + a - 1)*q^19 + (-a^3 - a + 1)*q^25 + a^2*q^33 - 
        a^3*q^36 + 2*q^43 + (a^3 - a^2 + a - 1)*q^49 + a^2*q^51 + (-a + 1)*q^52 
        + (a^3 + a - 1)*q^55 + (-a^3 + 1)*q^60 - a*q^64 + (-a^3 + a^2)*q^67 + 
        (-a + 1)*q^69 + (a^3 - a^2 - 1)*q^76 + a^2*q^81 + (a^3 + a - 1)*q^85 + 
        (a^3 - a^2 - 1)*q^87 + (-a^3 + a^2 + 1)*q^100 + (-a^3 - a)*q^103 + (-a^3
        + a^2 - a + 1)*q^115 + (a^3 - a^2 + a)*q^117 - a^3*q^121 + (-a^2 + a - 
        1)*q^123 + (-a^3 + 1)*q^127 + (a^3 - a^2 + a - 1)*q^132 + (a^3 + a - 
        1)*q^135 + O(q^138),
    q^3 + (a^2 + 1)*q^5 - a*q^11 + a^2*q^12 - a*q^17 + (a^3 + a - 1)*q^20 + (a^3
        - a^2 + a)*q^23 - a*q^27 + (-a^3 + 1)*q^29 + (-a^2 + a - 1)*q^39 + (-a^3
        + a^2)*q^41 - a^3*q^44 + (-a^3 - a)*q^45 + (a^3 - a^2 + a - 1)*q^48 + 
        (a^3 + a - 1)*q^57 - a^2*q^65 - a^3*q^68 + (-a^2 + a - 1)*q^71 + (-a^3 -
        a + 1)*q^75 + (a^3 - a^2 - 1)*q^80 + (a^2 - a)*q^92 + (2*a^3 - a^2 + a -
        2)*q^95 + a^2*q^99 + (a^3 - a^2 - 1)*q^107 - a^3*q^108 + (-a^3 + 
        a^2)*q^113 + (a^2 + 1)*q^116 + (-a^3 + a^2 - a + 1)*q^125 + 2*q^129 + 
        (-a^3 - a)*q^131 + O(q^138)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
561
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
562
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
280
);
qprec:=
139
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
562
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
56
);
qprec:=
139
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
562
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
139
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
562
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
35*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
139
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
563
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
562
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
563
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
281*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^10 + q^12 - q^17 - q^21 - q^23 + q^27 - q^28 + q^30 - q^33 - q^39 + 
        q^47 + q^48 + q^49 + q^51 + q^61 + q^62 - q^63 + q^64 - q^70 + q^71 + 
        q^75 - q^76 - q^81 - q^86 + O(q^94),
    q^2 + q^5 - q^6 + q^14 - q^15 - q^20 - q^31 - q^32 - q^34 + q^35 + q^38 - 
        q^42 + q^43 - q^46 - q^50 + q^53 + q^54 + q^60 + q^79 - q^80 - q^83 - 
        q^85 - q^89 + q^93 + O(q^94),
    q^3 - q^11 + q^12 - q^13 - q^21 - q^44 + q^47 + q^48 + q^49 - q^52 + q^61 - 
        q^63 - q^69 + q^71 + q^75 + q^77 - q^84 + q^91 + O(q^94),
    q^4 + q^10 - q^12 + q^16 - q^19 + q^21 + q^23 + q^25 - q^27 + q^28 - q^30 - 
        q^47 - q^48 - q^51 - q^61 - q^62 - q^67 - q^68 + q^70 - q^71 - q^75 - 
        q^77 + q^81 + q^86 - q^91 + O(q^94),
    q^7 - q^11 - q^13 + q^23 - q^27 + q^28 + q^33 + q^39 - q^44 - q^51 - q^52 - 
        q^57 + q^59 + q^81 + q^92 + O(q^94),
    q^9 - q^11 - q^13 + q^17 + q^19 - q^21 - q^27 + q^33 + q^36 + q^39 - q^44 - 
        q^51 - q^52 - q^57 + q^67 + q^68 - q^69 + q^76 + q^77 + q^81 - q^84 + 
        q^91 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
564
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
564
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
564
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
564
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
564
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
564
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
564
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^17 - q^21 + q^25 - q^37 + q^47 + q^51 - q^71 - q^79 - q^81 + 2*q^83 - 
        q^101 - q^103 + q^111 - q^119 + q^121 + q^147 - q^149 - q^159 + q^169 - 
        q^177 + O(q^182),
    q^2 - q^16 + q^28 - q^34 - q^42 + q^48 + q^50 - q^56 + q^64 - q^68 - q^72 - 
        q^74 + q^94 - q^96 + q^102 + q^108 + q^136 - q^142 + q^144 - q^148 - 
        q^158 - q^162 + 2*q^166 + q^168 + O(q^182),
    q^3 - q^21 - q^63 + q^75 - q^81 + q^141 + q^147 + q^153 - q^159 - q^177 + 
        O(q^182),
    q^4 - q^32 - q^36 + q^56 - q^68 + q^100 + q^108 - q^112 + q^128 - q^136 - 
        q^148 + O(q^182),
    q^6 - q^36 - q^42 + q^84 - q^96 + q^108 - q^126 + q^144 + q^150 - q^162 + 
        O(q^182),
    q^7 - q^17 + q^27 - q^37 - q^49 + q^53 + q^59 + q^61 - q^63 - q^71 - q^79 - 
        q^81 + q^89 + q^97 - q^101 - q^103 + q^131 - q^149 + q^153 + q^157 + 
        q^173 + q^175 + O(q^182),
    q^8 - q^16 + q^28 - q^56 - q^68 - q^72 + q^108 + q^112 + q^144 - q^148 + 
        O(q^182),
    q^9 - q^21 - q^27 + q^51 + q^111 + q^147 - q^153 - q^159 - q^177 + O(q^182),
    q^12 - q^36 - q^72 - q^96 + q^108 + q^144 + q^168 + O(q^182),
    q^14 - q^16 + q^32 - q^34 + q^54 - q^56 - q^74 - q^98 + q^106 + q^112 + 
        q^118 + q^122 - q^126 + q^136 - q^142 + q^144 - q^158 - q^162 + q^178 + 
        O(q^182),
    q^18 - q^42 + q^48 - q^54 - q^72 - q^96 + q^102 + q^168 + O(q^182),
    q^24 - q^36 - q^48 + q^84 + q^108 - q^168 + O(q^182)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
564
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 23*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
182
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - 1/4*q^16 - 3/4*q^17 + 5/4*q^18 - 1/2*q^21 - 3/4*q^24 - q^25 - 1/4*q^27 +
        q^28 + 3/4*q^32 - q^34 + 1/4*q^36 - 3/4*q^37 + 1/2*q^42 - 3/4*q^47 - 
        1/4*q^48 - 1/4*q^49 - 1/2*q^51 + 1/2*q^53 - 1/2*q^54 - 1/4*q^56 - 
        1/2*q^59 + 1/2*q^61 - 1/4*q^64 + 1/4*q^68 + 3/4*q^71 + 3/4*q^72 - 
        1/2*q^74 + 3/4*q^79 + 3/2*q^83 - 1/4*q^84 - 1/2*q^89 + 1/4*q^94 - 
        3/4*q^96 + 1/2*q^97 + 1/2*q^98 + 3/4*q^101 + 3/4*q^102 - 3/4*q^103 + 
        q^106 - 1/2*q^108 + q^111 + 1/4*q^112 - q^118 - 1/4*q^119 + q^121 - 
        3/2*q^122 - 3/4*q^126 + 3/4*q^128 + 1/2*q^131 - 5/4*q^136 + 3/4*q^141 + 
        1/2*q^142 + 1/2*q^144 - q^147 - 3/4*q^148 + 3/4*q^149 + 5/4*q^153 - 
        1/2*q^157 + 1/2*q^158 + 1/2*q^159 - 1/4*q^162 - 1/2*q^166 + 3/4*q^168 + 
        q^169 - 1/2*q^173 - 1/2*q^177 - q^178 + O(q^182),
    q^2 + 1/2*q^16 + 1/2*q^17 - 1/2*q^18 + q^21 + 1/2*q^24 - 1/2*q^27 - q^28 - 
        1/2*q^32 + q^34 + 1/2*q^36 + 1/2*q^37 - q^42 + 1/2*q^47 - 1/2*q^48 - 
        1/2*q^49 - q^50 + q^51 - q^53 + 1/2*q^56 - q^59 - q^61 + 1/2*q^64 - 
        1/2*q^68 - 1/2*q^71 - 1/2*q^72 - 1/2*q^79 - q^83 - 1/2*q^84 + q^89 - 
        1/2*q^94 + 1/2*q^96 - q^97 - q^98 - 1/2*q^101 - 1/2*q^102 + 1/2*q^103 + 
        1/2*q^112 + 3/2*q^119 + q^122 + 1/2*q^126 - 1/2*q^128 + q^131 + 
        1/2*q^136 - 1/2*q^141 - 1/2*q^148 - 1/2*q^149 - 3/2*q^153 + q^157 - 
        q^159 + 1/2*q^162 + q^166 - 1/2*q^168 + q^173 + q^177 + O(q^182),
    q^3 - 1/2*q^16 + 1/2*q^17 - 1/2*q^18 - 2*q^21 + 1/2*q^24 - 1/2*q^27 + 2*q^28
        - 1/2*q^32 - 2*q^34 + 1/2*q^36 - 3/2*q^37 + 1/2*q^47 + 1/2*q^48 + 
        3/2*q^49 + q^51 + q^53 + 3/2*q^56 - q^59 + q^61 - q^63 - 1/2*q^64 - 
        3/2*q^68 - 1/2*q^71 + 1/2*q^72 - q^74 - q^75 + 3/2*q^79 + q^81 - q^83 + 
        3/2*q^84 - q^89 + 1/2*q^94 - 1/2*q^96 + q^97 + q^98 - 1/2*q^101 + 
        1/2*q^102 - 3/2*q^103 - q^108 - 3/2*q^112 + 3/2*q^119 + q^122 - 
        3/2*q^126 - 1/2*q^128 + q^131 - 1/2*q^136 + 1/2*q^141 + q^142 + q^144 - 
        q^147 + 1/2*q^148 - 1/2*q^149 + 3/2*q^153 - q^157 + q^158 - 1/2*q^162 - 
        q^166 + 1/2*q^168 - q^173 + O(q^182),
    q^4 - 1/4*q^16 + 1/4*q^17 - 3/4*q^18 - 3/2*q^21 + 1/4*q^24 - 1/4*q^27 + q^28
        - 1/4*q^32 - q^34 + 1/4*q^36 - 7/4*q^37 + 1/2*q^42 + 1/4*q^47 + 3/4*q^48
        + 7/4*q^49 + 1/2*q^51 + 1/2*q^53 - 1/2*q^54 + 3/4*q^56 - 1/2*q^59 + 
        1/2*q^61 - 1/4*q^64 - 3/4*q^68 - 1/4*q^71 + 3/4*q^72 - 1/2*q^74 - 
        1/4*q^79 + q^81 - 1/2*q^83 + 3/4*q^84 - 1/2*q^89 + 1/4*q^94 - 3/4*q^96 +
        1/2*q^97 + 1/2*q^98 - q^100 - 1/4*q^101 + 3/4*q^102 + 1/4*q^103 - q^106 
        - 1/2*q^108 - 3/4*q^112 - q^118 + 3/4*q^119 + 1/2*q^122 - 3/4*q^126 - 
        1/4*q^128 + 1/2*q^131 - 1/4*q^136 + 3/4*q^141 + 1/2*q^142 + 1/2*q^144 + 
        1/4*q^148 - 1/4*q^149 + 5/4*q^153 - 1/2*q^157 + 1/2*q^158 - 1/2*q^159 - 
        1/4*q^162 - 1/2*q^166 - 1/4*q^168 - 1/2*q^173 + 1/2*q^177 + q^178 + 
        O(q^182),
    q^6 - 1/2*q^16 + 1/2*q^17 - 1/2*q^18 - q^21 + 1/2*q^24 - 1/2*q^27 - 1/2*q^32
        - 1/2*q^36 + 1/2*q^37 - q^42 + 1/2*q^47 + 1/2*q^48 - 1/2*q^49 + q^51 + 
        q^53 + 3/2*q^56 - q^59 + q^61 - 1/2*q^64 - 3/2*q^68 - 1/2*q^71 + 
        1/2*q^72 - q^74 - 1/2*q^79 - q^83 + 1/2*q^84 - q^89 + 1/2*q^94 + 
        1/2*q^96 + q^97 + q^98 - 1/2*q^101 + 1/2*q^102 + 1/2*q^103 + 1/2*q^112 +
        3/2*q^119 + q^122 - 1/2*q^126 - 1/2*q^128 + q^131 - 1/2*q^136 - 
        1/2*q^141 - q^142 + 1/2*q^148 - 1/2*q^149 - q^150 + 1/2*q^153 - q^157 + 
        q^158 - q^159 + 1/2*q^162 - q^166 + 1/2*q^168 - q^173 - q^177 + 
        O(q^182),
    q^7 - 1/2*q^16 - 1/2*q^17 + 1/2*q^18 - 1/2*q^24 - 1/2*q^27 + 1/2*q^32 - q^34
        + 1/2*q^36 - 1/2*q^37 + q^42 - 1/2*q^47 - 1/2*q^48 + 1/2*q^49 - q^51 - 
        1/2*q^56 + 1/2*q^64 + 1/2*q^68 + 1/2*q^71 + 1/2*q^72 + 1/2*q^79 + q^83 +
        1/2*q^84 - 1/2*q^94 - 1/2*q^96 + 1/2*q^101 - 1/2*q^102 - 1/2*q^103 - 
        1/2*q^112 - 1/2*q^119 - q^122 + 1/2*q^126 + 1/2*q^128 + 1/2*q^136 + 
        1/2*q^141 + 1/2*q^148 + 1/2*q^149 + 1/2*q^153 - 1/2*q^162 + q^166 - 
        1/2*q^168 - q^175 + O(q^182),
    q^8 - 1/2*q^16 + 3/2*q^17 - 1/2*q^18 - 2*q^21 + 1/2*q^24 - 1/2*q^27 + q^28 -
        1/2*q^32 - q^34 - 1/2*q^36 - 1/2*q^37 - q^42 + 1/2*q^47 + 1/2*q^48 + 
        1/2*q^49 + q^51 + q^53 + 3/2*q^56 - q^59 + q^61 - q^63 - 1/2*q^64 - 
        3/2*q^68 + 1/2*q^71 + 1/2*q^72 - 2*q^74 + 1/2*q^79 + q^81 - q^83 + 
        3/2*q^84 - q^89 + 1/2*q^94 + 1/2*q^96 + q^97 + 2*q^98 - 3/2*q^101 + 
        1/2*q^102 - 1/2*q^103 - q^108 - 1/2*q^112 + 1/2*q^119 + q^122 - 
        1/2*q^126 - 1/2*q^128 + q^131 - 1/2*q^136 - 1/2*q^141 + q^144 + 
        1/2*q^148 - 3/2*q^149 + 1/2*q^153 - q^157 + 1/2*q^162 - q^166 + 
        1/2*q^168 - q^173 + O(q^182),
    q^9 + q^16 + q^17 - q^18 + q^21 - 2*q^28 - q^32 + 2*q^34 + q^37 - 2*q^42 + 
        q^47 - q^49 + q^51 + q^56 - 2*q^61 + q^64 - q^68 - q^71 - q^72 - q^79 - 
        2*q^83 - q^94 + q^96 - 2*q^97 - q^101 - q^102 + q^103 + q^108 - q^111 + 
        q^112 + q^119 + 2*q^122 + q^126 - q^128 + q^136 - q^141 + q^147 - q^148 
        - q^149 - 2*q^153 + 2*q^157 - q^159 + q^162 + 2*q^166 + q^177 + 
        O(q^182),
    q^12 + 1/2*q^16 + 3/2*q^17 - 3/2*q^18 + q^21 + 1/2*q^24 + 1/2*q^27 - 2*q^28 
        - 3/2*q^32 + 2*q^34 - 1/2*q^36 + 3/2*q^37 - 2*q^42 + 3/2*q^47 + 1/2*q^48
        - 3/2*q^49 + q^51 - q^53 + 1/2*q^56 + q^59 - q^61 + 1/2*q^64 - 1/2*q^68 
        - 3/2*q^71 - 3/2*q^72 + q^74 - 3/2*q^79 - 3*q^83 - 1/2*q^84 + q^89 - 
        1/2*q^94 + 3/2*q^96 - q^97 - q^98 - 3/2*q^101 - 1/2*q^102 + 3/2*q^103 + 
        q^108 - 2*q^111 + 3/2*q^112 + 1/2*q^119 + 3*q^122 + 3/2*q^126 - 
        3/2*q^128 - q^131 + 1/2*q^136 - 3/2*q^141 - q^142 + 2*q^147 - 1/2*q^148 
        - 3/2*q^149 - 5/2*q^153 + q^157 - q^158 - q^159 + 1/2*q^162 + q^166 - 
        1/2*q^168 + q^173 + q^177 + O(q^182),
    q^14 - 1/4*q^16 - 3/4*q^17 + 1/4*q^18 - 1/2*q^21 + 1/4*q^24 - 1/4*q^27 + 
        q^28 - 1/4*q^32 - q^34 + 1/4*q^36 - 3/4*q^37 + 1/2*q^42 + 1/4*q^47 - 
        1/4*q^48 + 3/4*q^49 + 1/2*q^51 + 1/2*q^53 - 1/2*q^54 - 1/4*q^56 - 
        1/2*q^59 + 1/2*q^61 - q^63 - 1/4*q^64 - 3/4*q^68 + 3/4*q^71 + 3/4*q^72 -
        1/2*q^74 + 3/4*q^79 - 1/2*q^83 + 3/4*q^84 - 1/2*q^89 + 1/4*q^94 - 
        3/4*q^96 + 1/2*q^97 + 1/2*q^98 + 3/4*q^101 - 1/4*q^102 - 3/4*q^103 - 
        1/2*q^108 - 3/4*q^112 - 1/4*q^119 - 1/2*q^122 - 3/4*q^126 + 3/4*q^128 + 
        1/2*q^131 - 1/4*q^136 + 3/4*q^141 + 1/2*q^142 + 1/2*q^144 + 1/4*q^148 + 
        3/4*q^149 + 5/4*q^153 - 1/2*q^157 + 1/2*q^158 + 1/2*q^159 - 1/4*q^162 - 
        1/2*q^166 + 3/4*q^168 - 1/2*q^173 - 1/2*q^177 + O(q^182)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
112
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
112
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
56
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
56
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 16*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 28*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 28*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
565
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 56*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
112
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
566
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
282
);
qprec:=
140
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
566
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
94
);
qprec:=
140
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
566
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
47*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
140
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
566
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
141*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
140
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^6 - q^7 + q^10 - q^15 - q^23 - q^29 + q^36 - q^38 - q^42 - q^44 - q^52
        + q^57 + q^60 - q^62 + q^64 + q^66 - q^70 + q^71 + q^73 + q^78 - q^86 - 
        q^89 - q^90 + q^93 + q^94 + q^95 - q^96 - q^99 + q^100 + q^101 - q^103 +
        q^105 + q^110 + q^113 - q^117 + q^127 + q^129 + q^130 - q^138 + 
        O(q^140),
    q^2 + q^12 - q^14 + q^20 - q^30 - q^46 - q^58 + q^72 - q^76 - q^84 - q^88 - 
        q^104 + q^114 + q^120 - q^124 + q^128 + q^132 + O(q^140),
    q^3 + q^5 + q^18 - q^19 - q^21 - q^22 - q^26 + q^30 - q^31 + q^32 + q^33 - 
        q^35 + q^39 - q^43 - q^45 + q^47 - q^48 + q^50 + q^55 + q^65 - q^69 + 
        q^72 - q^75 - q^80 - q^82 - q^87 - q^88 - q^104 + q^109 - q^114 - q^115 
        - q^118 + q^120 - q^122 + q^123 - q^126 + q^128 + q^133 + q^139 + 
        O(q^140),
    q^4 - q^6 - q^10 + q^24 - q^28 - q^36 + q^38 + q^40 + q^42 + q^44 + q^52 - 
        2*q^60 + q^62 - q^64 - q^66 + q^70 - q^78 + q^86 + q^90 - q^92 - q^94 + 
        q^96 - q^100 - q^110 - q^116 - q^130 + q^138 + O(q^140),
    q^8 - q^12 + q^18 - q^20 - q^22 - q^26 + q^30 + q^32 + q^50 - q^56 + q^76 - 
        q^82 + q^84 - q^114 - q^118 - q^120 - q^122 + q^124 - q^126 - q^132 + 
        O(q^140),
    q^9 - q^11 - q^13 + q^15 + q^16 - q^24 + q^25 + q^36 - q^40 - q^41 - q^44 - 
        q^52 - q^57 - q^59 + q^60 - q^61 - q^63 + q^64 + q^71 + q^73 + q^77 + 
        q^81 + 2*q^83 + q^91 - q^93 - q^95 - q^97 + q^100 + q^101 - q^105 - 
        q^112 + q^113 + q^127 - q^129 - q^137 + O(q^140)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a + 1)*q^4 - q^7 + (2*a - 1)*q^13 - a*q^16 + (a - 1)*q^25 + (a - 
        1)*q^28 + (-a - 1)*q^31 - a*q^37 + q^43 + q^49 + (a + 1)*q^52 + (-a + 
        2)*q^61 - q^64 + (-a + 1)*q^67 + a*q^79 + (-2*a + 1)*q^91 + (-2*a + 
        1)*q^97 + a*q^100 + (a - 2)*q^103 + (a - 1)*q^109 + a*q^112 + a*q^121 + 
        O(q^122),
    q^3 + (-a + 1)*q^12 - q^21 + (2*a - 1)*q^39 - a*q^48 + (a - 1)*q^75 + (a - 
        1)*q^84 + (-a - 1)*q^93 - a*q^111 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
12*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
18*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + a*q^7 + (-a - 1)*q^13 + (a - 1)*q^16 + q^25 + (a - 1)*q^28 + (-a
        + 2)*q^31 - a*q^37 - a*q^43 + (a - 1)*q^49 + (-2*a + 1)*q^52 + (-a - 
        1)*q^61 - q^64 + a*q^67 + (-a + 1)*q^79 + (-2*a + 1)*q^91 + (a - 2)*q^97
        + a*q^100 + (-2*a + 1)*q^103 + (a - 1)*q^109 - q^112 - q^121 + O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
36*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 + (-a + 1)*q^7 + (-a + 2)*q^13 + q^16 - a*q^25 + (a - 1)*q^28 + (2*a
        - 1)*q^31 - a*q^37 + (a - 1)*q^43 - a*q^49 + (a - 2)*q^52 + (2*a - 
        1)*q^61 - q^64 - q^67 - q^79 + (-2*a + 1)*q^91 + (a + 1)*q^97 + a*q^100 
        + (a + 1)*q^103 + (a - 1)*q^109 + (-a + 1)*q^112 + (-a + 1)*q^121 + 
        O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 + (a - 1)*q^7 + a*q^13 - a*q^16 + (2*a - 2)*q^19 + q^25 - 
        a*q^28 + (-a + 1)*q^31 + (-a + 1)*q^37 + (-a + 1)*q^43 - a*q^49 - q^52 +
        a*q^61 + q^64 + (-a + 1)*q^67 - 2*a*q^73 - 2*a*q^76 + a*q^79 - q^91 + 
        (-a + 1)*q^97 + (a - 1)*q^100 - q^103 + a*q^109 + q^112 + q^121 + 
        O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + q^7 - q^13 + (a - 1)*q^16 + (2*a - 2)*q^19 - a*q^25 - a*q^28 + 
        a*q^31 + (-a + 1)*q^37 - q^43 + q^49 + a*q^52 + (-a + 1)*q^61 + q^64 + 
        a*q^67 - 2*a*q^73 + 2*q^76 + (-a + 1)*q^79 - q^91 - q^97 + (a - 1)*q^100
        + (-a + 1)*q^103 + a*q^109 + (a - 1)*q^112 + (a - 1)*q^121 + O(q^122),
    q^3 - a*q^12 + q^21 - q^39 + (a - 1)*q^48 + (2*a - 2)*q^57 - a*q^75 - a*q^84
        + a*q^93 + (-a + 1)*q^111 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
45*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - a*q^7 + (-a + 1)*q^13 + q^16 + (2*a - 2)*q^19 + (a - 1)*q^25 - 
        a*q^28 - q^31 + (-a + 1)*q^37 + a*q^43 + (a - 1)*q^49 + (-a + 1)*q^52 - 
        q^61 + q^64 - q^67 - 2*a*q^73 + (2*a - 2)*q^76 - q^79 - q^91 + a*q^97 + 
        (a - 1)*q^100 + a*q^103 + a*q^109 - a*q^112 - a*q^121 + O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^7 - q^16 + q^22 + q^25 - q^37 - q^43 - 2*q^46 + q^49 - 2*q^58 + q^64 -
        q^67 - q^79 - q^88 + q^106 + 2*q^109 - q^112 + O(q^122),
    q^2 - q^23 - q^29 - q^44 + q^50 - q^56 + q^71 + q^77 + q^98 + q^107 + 
        O(q^122),
    q^4 - q^7 + q^16 - 2*q^22 - q^28 + q^37 + q^43 + q^46 + q^58 - q^64 - q^88 +
        q^100 - 2*q^106 - 2*q^109 + q^121 + O(q^122),
    q^8 - q^11 - q^14 + q^23 + q^29 - q^44 - q^53 + q^74 + q^86 - q^113 + 
        O(q^122)
]
;
Bo:=
[
    q - q^4 - q^7 + q^16 + q^25 + q^28 - 2*q^37 - 2*q^43 + q^49 - q^64 + 2*q^67 
        + 2*q^79 - q^100 - 2*q^109 - q^112 - q^121 + O(q^122),
    q^3 - q^12 - q^21 + q^48 + q^75 + q^84 - 2*q^111 + O(q^122),
    q^9 - q^36 - q^63 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
567
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
18*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^25 - q^37 + a*q^43 - q^46 + (a - 1)*q^49 + (-a + 1)*q^58 + a*q^88 + 
        (-a + 1)*q^112 + O(q^122),
    q^2 + a*q^23 - q^29 + (-a + 1)*q^44 - a*q^50 - q^56 + (a - 1)*q^71 - a*q^77 
        + (a - 1)*q^98 + (a - 1)*q^107 + O(q^122),
    q^4 - q^22 + a*q^28 - a*q^37 + (a - 1)*q^43 - q^67 + (-a + 1)*q^79 + (-a + 
        1)*q^88 - a*q^100 + (-a + 1)*q^106 + q^121 + O(q^122),
    q^7 - q^16 - a*q^22 + (-a + 1)*q^46 + a*q^58 + (a - 1)*q^64 + a*q^67 - q^79 
        + q^106 + (2*a - 2)*q^109 + O(q^122),
    q^8 + a*q^11 + (-a + 1)*q^14 + (a - 1)*q^23 - a*q^29 - q^44 - q^53 - a*q^74 
        + (a - 1)*q^86 + (-a + 1)*q^113 + O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
35*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^15 - q^19 + q^25 - q^37 - q^45 + q^49 + q^71 + q^75 - q^83 + q^87 - 
        q^95 - q^101 + 2*q^107 + q^121 - q^125 - q^129 + q^135 + O(q^138),
    q^2 - q^30 - q^38 + q^50 - q^74 - q^90 + q^98 + O(q^138),
    q^3 - q^9 - q^15 - q^19 + q^25 + q^27 + q^29 - q^37 + q^57 - q^81 - q^83 - 
        q^87 + q^89 - q^101 + q^103 + q^109 + q^111 - q^125 - q^129 + O(q^138),
    q^4 - q^40 - q^48 - q^60 + q^72 - q^76 + q^80 + q^100 + O(q^138),
    q^5 - q^9 - q^19 + q^27 - q^37 + q^43 + q^57 + q^73 - q^75 + q^79 - q^83 - 
        q^87 - q^95 - q^101 + q^111 + q^131 + O(q^138),
    q^6 - q^18 - q^30 - q^38 + q^50 + q^54 + q^58 - q^74 + q^114 + O(q^138),
    q^8 - q^40 - q^48 + q^72 - q^96 - q^120 + O(q^138),
    q^10 - q^18 - q^38 + q^54 - q^74 + q^86 + q^114 + O(q^138),
    q^12 + q^32 - q^36 - q^48 - q^60 - q^76 - q^96 + q^100 + q^108 + q^116 + 
        O(q^138),
    q^16 - q^32 - q^40 - q^48 + q^64 + q^72 + q^80 - q^128 + O(q^138),
    q^20 + q^32 - q^36 - q^64 - q^76 - q^80 - q^96 + q^108 + q^128 + O(q^138),
    q^24 - q^32 - q^40 + q^64 + q^80 - q^120 + O(q^138)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
568
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 35*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^10 + q^12 - q^15 - q^18 - q^19 + q^20 - q^25 + q^37 + q^38 + q^45 - 
        q^48 + q^49 - q^54 + q^60 + q^64 - q^71 - q^74 - q^75 - q^80 + q^83 + 
        q^86 + q^87 + q^95 + q^100 - q^101 - q^114 - q^116 - q^121 - q^125 - 
        q^128 + q^129 - q^135 + O(q^138),
    q^2 - q^10 + q^12 - q^18 - 2*q^19 + q^24 - q^30 - q^36 + 2*q^37 + q^40 + 
        2*q^45 - q^48 - q^50 - q^54 + q^60 + q^64 - 2*q^75 + q^76 - q^80 + 
        2*q^83 + q^86 + q^90 - q^96 + q^98 + q^100 - 2*q^101 - q^108 - q^114 - 
        q^116 + q^120 - 2*q^125 + O(q^138),
    q^3 + q^8 - q^10 - q^25 - q^27 - q^29 + q^30 - q^36 + q^45 - q^54 + q^57 + 
        q^60 - q^72 - q^75 - q^76 + q^86 + q^89 + q^90 + q^95 + q^103 + q^109 - 
        q^111 + q^114 - q^135 + O(q^138),
    q^4 - q^8 + q^10 - q^12 + 2*q^15 + q^16 - q^18 - q^20 + 2*q^25 - q^32 - q^38
        + q^40 - 2*q^50 + q^54 - q^72 - 2*q^73 + q^74 + q^76 - 2*q^79 + q^80 + 
        2*q^81 - q^86 - 2*q^89 - 2*q^95 - q^96 - 2*q^103 + q^114 + q^116 + q^120
        - 2*q^129 + O(q^138),
    q^5 - q^8 + q^10 - q^12 + q^15 + q^16 - q^20 + 2*q^25 + q^27 - q^30 - q^32 +
        q^36 + q^40 - q^43 - q^45 - 2*q^50 + q^54 - q^57 - q^73 + q^76 - q^79 + 
        q^81 - q^86 - 2*q^89 - q^90 - 2*q^95 + q^100 - 2*q^103 + q^111 + q^114 +
        q^116 - q^125 - q^129 + q^131 + q^135 + O(q^138),
    q^6 - q^8 + q^10 + q^16 - q^20 + 2*q^25 - q^30 + q^36 - q^50 - 2*q^57 - q^58
        + q^76 - q^86 - 2*q^89 - 2*q^95 - 2*q^103 - q^108 + 2*q^111 + q^120 + 
        2*q^135 + O(q^138),
    q^9 - q^10 + q^12 - q^15 - q^19 + q^24 - q^30 + q^37 + q^45 - q^54 + q^64 - 
        q^75 - q^80 - q^81 + q^83 + q^86 - q^87 + q^90 + q^95 + q^100 - q^101 - 
        q^108 - q^114 - q^116 - q^125 + q^129 + q^135 + O(q^138)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
569
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
568
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
569
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
71*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^5 + a - 1)*q^6 + (a^5 - a^2)*q^9 + (a^5 - a^4 + a^3 - a^2)*q^10 + 
        a^2*q^15 - a^4*q^16 + a^4*q^19 + (a^4 - a^3 + a^2 - a)*q^24 - a^5*q^25 +
        (a^2 - a)*q^31 + (a^4 - 2*a^3 + a^2 - 2*a + 1)*q^34 + (-a^5 + a^3 + a - 
        1)*q^40 + (a^5 - a^4 + a^3 - a^2 + a)*q^46 - a^3*q^49 + (a^4 + a^3 - 
        1)*q^51 + (-a^5 + a^4 + a^2 - 1)*q^54 - a^2*q^61 + (-a^2 + a)*q^64 + 
        (-a^3 + 1)*q^69 - a^4*q^79 + (-a^4 + a)*q^81 + (-a^4 + a + 1)*q^85 + 
        (-a^4 + a^3 - a^2 + a)*q^90 + q^94 + (a^5 - a^2 - a + 1)*q^96 + (-a^5 + 
        2*a^4 - a^3 + 2*a^2 - a)*q^106 + (a^5 + a^3 - a^2 - 1)*q^109 + (a^5 - 
        a^4 + 1)*q^114 - q^115 + (a^3 - 1)*q^121 - a*q^135 + (2*a^5 - a^4 + a^3 
        - a^2 + 1)*q^136 + (a^4 + a^3 - 1)*q^139 + (-a^5 - a)*q^141 + a^3*q^144 
        + (a^5 - a^3 - a + 1)*q^150 + (-a^4 + a^2 + a)*q^151 + (-a^5 - a^4 + 
        a)*q^159 + (a^4 - a^3 + a^2)*q^160 + (-a^5 + 2*a^4 - 2*a^3 + 2*a^2 - 2*a
        + 1)*q^166 - a*q^169 - a^3*q^171 + (a^4 - a^3)*q^181 + (-a^5 + a - 
        1)*q^184 + (-a^4 + 2*a^3 - 2*a^2 + 2*a - 1)*q^186 + (-a^5 + a^4 - a^3 + 
        a^2 - a)*q^190 + (-a^5 + a^2)*q^199 + (a^5 - a^3 - a^2)*q^211 + (a^5 - 
        a^4 + 2*a^3 - 2*a^2 + a - 1)*q^214 + (-a^3 + a^2 - a + 1)*q^216 + 
        a^4*q^225 + O(q^226),
    q^2 + (-a^4 + a^3 + a^2 + a - 1)*q^8 + (-a^4 - a^3 + a)*q^12 + (a^5 - 
        a^2)*q^18 + (a^3 - a - 1)*q^20 + a^2*q^30 + (a^4 - a^3 - a^2 + 1)*q^32 +
        a^4*q^38 + (-a^5 + a^4 - a + 1)*q^48 - a^5*q^50 + (a^2 - a)*q^62 + (-a^3
        - a^2 - a)*q^68 + (-a^5 + a^3 - a - 1)*q^72 + (a^5 - a^3 - a^2 + a)*q^80
        + (a^5 + a)*q^92 - a^3*q^98 + (a^4 + a^3 - 1)*q^102 + (a^3 + a^2 - 
        1)*q^108 + (a^5 + a^4 - a^2 + 1)*q^120 - a^2*q^122 + (-a^5 - a^4 + 
        a^2)*q^128 + (-a^3 + 1)*q^138 + (a^3 + a^2 - a - 1)*q^152 - a^4*q^158 + 
        (-a^4 + a)*q^162 + (-a^4 + a + 1)*q^170 + (-a^5 + 1)*q^180 + (-a^5 + a^4
        + 2)*q^188 + (a^5 - a^4 - 1)*q^192 + (-a^4 - a^3 + a^2 + a)*q^200 + (a^4
        + a^3 + a^2)*q^212 + (a^5 + a^3 - a^2 - 1)*q^218 + O(q^226),
    q^3 - a^3*q^5 + (-a^3 + a + 1)*q^8 - a^2*q^12 + (-a^5 - a^4 + a)*q^17 + 
        a^5*q^20 + (a^4 - a)*q^23 + (a^5 - a^2)*q^27 + (-a^5 + a^3 + a^2 - 
        a)*q^32 + a^2*q^45 + (a^3 + a^2 - 1)*q^47 + (-a^5 - a^4 + a^2 - 1)*q^48 
        + (a^5 + a^3 - a^2 - 1)*q^53 + a^4*q^57 + (a^4 - a - 1)*q^68 + (a^5 - 
        1)*q^72 - a^5*q^75 + (a^4 + a^3 - a^2 - a)*q^80 + (-a^4 + a^3 + a - 
        1)*q^83 + q^92 + (a^2 - a)*q^93 + (-a^4 + a)*q^95 + (-a^3 - a)*q^107 + 
        a*q^108 + (-a + 1)*q^113 + (-a^5 + a^3 + a^2)*q^120 + (a^5 - a^2)*q^125 
        + (a^5 - a^4 - a^3 - a^2 + a)*q^128 + (-a^5 + 1)*q^137 - a^3*q^147 + 
        (a^5 + a)*q^152 + (a^4 + a^3 - 1)*q^153 + (-a^5 + a^4)*q^155 + (-a^3 + 
        a^2)*q^167 + (-a^3 + 1)*q^173 - a^4*q^180 - a^2*q^183 + (-a^5 - a^4 + 
        a^2)*q^188 + (a^5 + a^4 - a^3 - a^2 + 1)*q^192 + (a^4 + 1)*q^197 + (-a^3
        - a^2 + 1)*q^200 + (-a^3 + 1)*q^207 + (-a^5 + a^2 + a)*q^212 + O(q^226),
    q^4 + (-a^5 + a^4 - a^3 + a^2 - a)*q^6 + (a^3 - a^2 + a - 1)*q^10 + (-a^4 + 
        a^3 + a - 1)*q^16 + (a^5 - a^4 - a^3 + 1)*q^24 + (2*a^5 - a^4 - a^2 - a 
        + 1)*q^34 + (a^5 - a^2)*q^36 + (-a^5 + a^4 + a^2 - a - 1)*q^40 + (-a^5 +
        a^3 + a - 1)*q^46 + (a^4 - a^3 + a^2 - a + 1)*q^54 + a^2*q^60 + (-a^5 + 
        a^4 - a^3)*q^64 + a^4*q^76 + (-a^5 + a - 1)*q^90 + (-a^4 + a)*q^94 + 
        (a^3 - a^2)*q^96 - a^5*q^100 + (a^5 - a^3 + a^2 - a + 2)*q^106 + (-a^4 +
        a^3 - a^2 + a)*q^114 + (a^2 - a)*q^124 + (-a^4 + a^3 - 2*a^2 + a - 
        1)*q^136 + (-a^5 + a^3 - 1)*q^144 + (a^5 - a^4 + a^3 - a^2)*q^150 + (a^5
        - a^3 + 1)*q^160 + (2*a^5 - a^4 - a^3 - a + 2)*q^166 + (a^4 - a^3 + 
        a^2)*q^184 + (-2*a^5 + a^4 + a^2 + a - 2)*q^186 + (a^5 - a^3 - a + 
        1)*q^190 - a^3*q^196 + (a^4 + a^3 - 1)*q^204 + (-a^5 + a^4 + a^3 + a - 
        2)*q^214 + (a^5 - a^4 + a^3)*q^216 + O(q^226)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 + (a - 1)*q^4 - q^7 + (a - 1)*q^9 + q^12 + (-a + 1)*q^13 - a*q^16 
        + q^19 + a*q^21 + (a - 1)*q^25 + q^27 + (-a + 1)*q^28 - q^31 - a*q^36 - 
        q^37 - q^39 + a*q^43 + (a - 1)*q^48 + a*q^52 - a*q^57 + (-a + 1)*q^61 + 
        (-a + 1)*q^63 + q^64 + (-a + 1)*q^67 + a*q^73 + q^75 + (a - 1)*q^76 + 
        a*q^79 - a*q^81 - q^84 + (a - 1)*q^91 + a*q^93 - 2*a*q^97 - a*q^100 - 
        q^103 + (a - 1)*q^108 - 2*a*q^109 + a*q^111 + a*q^112 + a*q^117 + q^121 
        + (-a + 1)*q^124 + (2*a - 2)*q^127 + (-a + 1)*q^129 - q^133 + (-a + 
        1)*q^139 + q^144 + (-a + 1)*q^148 + 2*q^151 + (-a + 1)*q^156 + a*q^157 -
        q^163 + (a - 1)*q^171 - q^172 + (-a + 1)*q^175 + (2*a - 2)*q^181 - q^183
        - q^189 - a*q^192 + a*q^193 + (-a + 1)*q^199 - q^201 - q^208 + a*q^211 +
        q^217 + (-a + 1)*q^219 + a*q^223 - a*q^225 + O(q^226),
    q^2 - a*q^6 + (a - 1)*q^8 - q^14 + (a - 1)*q^18 + q^24 + (-a + 1)*q^26 - 
        a*q^32 + q^38 + a*q^42 + (a - 1)*q^50 + q^54 + (-a + 1)*q^56 - q^62 - 
        a*q^72 - q^74 - q^78 + a*q^86 + (a - 1)*q^96 + a*q^104 - a*q^114 + (-a +
        1)*q^122 + (-a + 1)*q^126 + q^128 + (-a + 1)*q^134 + a*q^146 + q^150 + 
        (a - 1)*q^152 + a*q^158 - a*q^162 - q^168 + (a - 1)*q^182 + a*q^186 - 
        2*a*q^194 - a*q^200 - q^206 + (a - 1)*q^216 - 2*a*q^218 + a*q^222 + 
        a*q^224 + O(q^226),
    q^5 - a*q^15 + (a - 1)*q^20 - q^35 + (a - 1)*q^45 + q^60 + (-a + 1)*q^65 - 
        a*q^80 + q^95 + a*q^105 + (a - 1)*q^125 + q^135 + (-a + 1)*q^140 - q^155
        - a*q^180 - q^185 - q^195 + a*q^215 + O(q^226),
    q^10 - a*q^30 + (a - 1)*q^40 - q^70 + (a - 1)*q^90 + q^120 + (-a + 1)*q^130 
        - a*q^160 + q^190 + a*q^210 + O(q^226)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a + 1)*q^6 + (a - 1)*q^9 + (-a + 1)*q^10 + (a - 1)*q^15 + a*q^16 - 
        a*q^19 - a*q^24 + (a - 1)*q^25 - q^31 + (a - 1)*q^34 - a*q^40 - 2*q^46 +
        q^49 + (-a + 1)*q^51 + a*q^54 + (2*a - 2)*q^61 + q^64 + 2*q^69 - 
        2*a*q^79 - a*q^81 + (-a + 1)*q^85 + a*q^90 + q^94 + q^106 + a*q^109 - 
        q^114 + 2*q^115 + q^121 - a*q^135 + a*q^136 + (-a + 1)*q^139 - q^141 - 
        q^144 + a*q^150 - q^151 - q^159 - a*q^166 - a*q^169 + q^171 + (-a + 
        1)*q^181 + (2*a - 2)*q^184 + (a - 1)*q^186 - q^190 + (2*a - 2)*q^199 + 
        a*q^211 - a*q^214 + q^216 - a*q^225 + O(q^226),
    q^2 + (-a + 1)*q^12 + (a - 1)*q^18 + (-a + 1)*q^20 + (a - 1)*q^30 + a*q^32 -
        a*q^38 - a*q^48 + (a - 1)*q^50 - q^62 + (a - 1)*q^68 - a*q^80 - 2*q^92 +
        q^98 + (-a + 1)*q^102 + a*q^108 + (2*a - 2)*q^122 + q^128 + 2*q^138 - 
        2*a*q^158 - a*q^162 + (-a + 1)*q^170 + a*q^180 + q^188 + q^212 + a*q^218
        + O(q^226),
    q^3 + q^5 + (a - 1)*q^8 + (-a + 1)*q^12 - q^17 + (-a + 1)*q^20 - 2*a*q^23 + 
        (a - 1)*q^27 + a*q^32 + (a - 1)*q^45 + a*q^47 + a*q^53 - a*q^57 + (a - 
        1)*q^68 - a*q^72 + (a - 1)*q^75 + (-a + 1)*q^83 - 2*q^92 - q^93 - a*q^95
        + (-a + 1)*q^107 + a*q^108 + (-a + 1)*q^113 - a*q^120 + (a - 1)*q^125 + 
        a*q^137 + q^147 + q^152 + (-a + 1)*q^153 - q^155 + a*q^167 + 2*q^173 + 
        a*q^180 + (2*a - 2)*q^183 + q^188 + q^192 + (-a + 1)*q^197 - a*q^200 + 
        2*q^207 + q^212 + O(q^226),
    q^4 - q^6 - q^10 + (-a + 1)*q^16 + q^34 + (a - 1)*q^36 + 2*a*q^46 + (-a + 
        1)*q^54 + (a - 1)*q^60 - a*q^76 + (-a + 1)*q^90 - a*q^94 - a*q^96 + (a -
        1)*q^100 - a*q^106 + a*q^114 - q^124 + a*q^144 + (-a + 1)*q^150 - 
        a*q^160 + (a - 1)*q^166 + q^186 + a*q^190 + q^196 + (-a + 1)*q^204 + (a 
        - 1)*q^214 + O(q^226)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
570
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
226
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^11 - q^20 + q^25 + q^26 + q^30 - q^39 + q^44 - q^45 + q^49 - q^55 - 
        q^61 - q^64 - q^66 - q^74 - q^76 + q^80 + q^95 + q^96 + q^99 - q^101 - 
        q^106 + q^111 + q^114 - q^120 + q^121 - q^130 + 2*q^131 + q^134 - q^139 
        - q^144 - q^149 + q^159 - q^171 - q^176 + q^180 - q^194 + q^195 - q^201 
        + q^206 - q^209 + q^214 + q^216 + q^220 + O(q^226),
    q^2 - q^18 - q^22 - q^40 + q^50 + q^52 + q^88 + q^98 + q^108 - q^110 - q^122
        - q^128 - q^148 - q^152 + q^160 + q^190 + q^198 - q^202 - q^212 + 
        O(q^226),
    q^3 - q^18 - q^33 - q^60 + q^75 + q^78 + q^90 + q^108 - q^117 + q^132 - 
        q^135 + q^147 - q^165 - q^183 - q^192 - q^222 + O(q^226),
    q^4 - q^20 + q^26 - q^36 + q^54 - q^64 - q^74 - q^76 + q^100 + q^104 - q^106
        - q^130 + q^134 + q^180 - q^194 + q^196 + q^206 + q^214 + q^216 + 
        O(q^226),
    q^5 - q^11 + q^16 + q^19 - q^20 + q^44 - q^45 - q^55 - q^61 - q^64 - q^76 + 
        q^81 + q^99 - q^101 + q^104 + 2*q^121 + q^125 - q^139 - q^144 - q^149 - 
        q^169 - q^171 - q^176 + q^180 + 2*q^191 + 2*q^199 - q^209 + q^216 + 
        q^220 + O(q^226),
    q^6 - q^36 - q^66 - q^120 + q^150 + q^156 + q^180 + q^216 + O(q^226),
    q^8 - q^13 - q^27 + q^37 - q^40 + q^52 + q^53 + q^65 - q^67 - q^72 + q^97 - 
        q^103 - q^107 + q^108 - q^113 + q^117 + q^127 - q^128 + q^135 - q^148 - 
        q^152 + q^167 - q^173 - q^185 + q^193 + q^200 + q^208 - q^212 + q^223 + 
        O(q^226),
    q^9 + q^30 - q^39 - q^45 - q^54 - q^66 + q^96 + q^111 + q^114 - q^120 - 
        q^144 + q^159 - q^171 + q^195 - q^201 + q^216 + q^225 + O(q^226),
    q^10 - q^13 - q^22 - q^27 + q^32 + q^37 + q^38 - q^40 + q^53 + q^65 - q^67 +
        q^88 - q^90 + q^97 - q^103 - q^107 - q^110 - q^113 + q^117 - q^122 + 
        q^127 - q^128 + q^135 - q^152 + q^162 + q^167 - q^173 - q^185 + q^193 + 
        q^198 - q^202 + q^208 + q^223 + O(q^226),
    q^12 - q^18 - q^60 - q^72 + q^78 + q^90 + q^108 - q^192 - q^222 + O(q^226),
    q^15 - q^27 - q^33 + q^48 + q^57 - q^60 - q^72 + q^108 + q^117 + q^132 - 
        q^165 - q^183 - q^192 + O(q^226),
    q^24 - q^30 - q^36 + q^54 + q^66 - q^96 - q^114 + q^156 + q^180 + O(q^226)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
571
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
570
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
571
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
190
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
571
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
114
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
571
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
38
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
571
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
19*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
571
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
57*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
571
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
95*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
571
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
285*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 + q^9 - q^11 - q^13 + q^16 - q^23 + q^36 - q^44 + q^49 - q^52 - q^55
        - q^59 - q^61 + q^64 - q^65 + q^81 - q^92 + O(q^95),
    q^5 - q^11 - q^13 + q^20 - q^23 - q^25 + q^29 + q^31 + q^37 + q^43 - q^44 + 
        q^45 - q^52 - q^59 - q^61 + q^80 + q^83 - q^92 + O(q^95)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 - q^5 + q^11 + q^15 - q^23 + q^27 - q^31 - q^33 - q^37 + 2*q^47 + 
        q^49 + 2*q^53 - q^55 - q^59 - q^67 + q^69 - q^71 - q^81 - q^89 + q^93 - 
        q^97 + 2*q^103 + q^111 - q^113 + q^115 + q^121 + q^125 - q^135 - q^137 -
        2*q^141 - q^147 + q^155 - q^157 + O(q^158),
    q^13 - q^39 - q^65 + q^143 + O(q^158)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 5*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 + (a - 1)*q^4 - q^5 + q^8 + (a - 1)*q^9 + a*q^10 - a*q^13 - a*q^16
        + (-a + 1)*q^17 + q^18 + (-a + 1)*q^20 + (a - 1)*q^26 + a*q^29 + (a - 
        1)*q^32 - q^34 - a*q^36 + a*q^37 - q^40 + a*q^41 + (-a + 1)*q^45 - 
        a*q^49 + q^52 - q^53 + (-a + 1)*q^58 + (-a + 1)*q^61 + q^64 + a*q^65 + 
        a*q^68 + (a - 1)*q^72 - q^73 + (-a + 1)*q^74 + a*q^80 - a*q^81 + (-a + 
        1)*q^82 + (a - 1)*q^85 - 2*a*q^89 - q^90 + (2*a - 2)*q^97 + (a - 1)*q^98
        + a*q^101 - a*q^104 + a*q^106 + 2*q^109 + (-a + 1)*q^113 - q^116 + q^117
        + (a - 1)*q^121 - q^122 + q^125 - a*q^128 + (-a + 1)*q^130 + (-a + 
        1)*q^136 + (-a + 1)*q^137 + q^144 - a*q^145 + a*q^146 - q^148 + (-a + 
        1)*q^149 + a*q^153 - q^157 + O(q^158),
    q^11 - a*q^22 + (a - 1)*q^44 - q^55 + q^88 + (a - 1)*q^99 + a*q^110 - 
        a*q^143 + O(q^158)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 - a*q^9 - a*q^13 + (a^3 + a - 1)*q^14 + (a^3 - a^2 + a - 1)*q^16
        + (-a^3 + 1)*q^17 - a^3*q^22 - a^3*q^25 + (a^3 - a^2 + a)*q^29 - 
        a^3*q^36 + (a^2 - a)*q^38 + (a^3 - 1)*q^49 - a^3*q^52 + (-a^2 + a - 
        1)*q^53 + (a^3 - a^2 - 1)*q^56 + (a^2 - a)*q^61 + (a^3 - a^2 + a)*q^62 -
        a*q^64 + (a^2 + 1)*q^68 + (-a^3 + 1)*q^77 + a^2*q^81 + q^88 + (-a^3 + 
        1)*q^94 + q^100 + (a^2 + 1)*q^101 + (a^3 + a - 1)*q^113 + (a^2 - 
        a)*q^116 + a^2*q^117 + (-a + 1)*q^118 + (a^3 - a^2 + a - 1)*q^121 + 
        (-a^3 + 1)*q^126 - q^133 - 2*a*q^134 + (a^3 - a^2 - 1)*q^142 + q^144 + 
        (-a^2 + a - 1)*q^152 + (a^3 - a^2 - 1)*q^153 + (a^3 + a - 1)*q^157 + 
        O(q^158),
    q^2 + (a^2 + 1)*q^7 + a^2*q^8 - a*q^11 - a*q^18 + (a^3 - a^2 + a)*q^19 - 
        a*q^26 + (a^3 + a - 1)*q^28 + (-a^3 + a^2)*q^31 + (a^3 - a^2 + a - 
        1)*q^32 + (-a^3 + 1)*q^34 - a^3*q^44 + (-a^3 - a)*q^47 - a^3*q^50 + (a^3
        - a^2 + a)*q^58 + (-a^2 + a - 1)*q^59 + (-a^3 - a)*q^63 + (2*a^3 - 2*a^2
        + 2*a - 2)*q^67 + (a^3 + a - 1)*q^71 - a^3*q^72 + (a^2 - a)*q^76 + (-a +
        1)*q^83 + (-a^3 - a)*q^91 + (a^3 - 1)*q^98 + a^2*q^99 - a^3*q^104 + 
        (-a^2 + a - 1)*q^106 + (a^3 - a^2 - 1)*q^112 + (-a^3 + a^2 + 2)*q^119 + 
        (a^2 - a)*q^122 + (a^3 - a^2 + a)*q^124 - a*q^128 + (a^2 + 1)*q^136 + 
        a^2*q^143 + (a^3 - a^2 + a)*q^151 + (-a^3 + 1)*q^154 + O(q^158)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
572
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
158
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^23 + q^25 - q^27 + q^49 - q^69 - q^77 - q^91 - q^103 + q^121 - q^133 +
        q^143 + q^147 - q^157 + O(q^158),
    q^2 - 2*q^28 - q^32 + q^44 - q^46 + q^50 + q^52 - q^54 + q^76 - q^84 + q^98 
        + 2*q^112 + q^128 + q^132 - q^138 - q^154 + q^156 + O(q^158),
    q^3 - q^9 - q^23 + q^49 + q^53 + q^75 - q^77 - q^91 - q^103 + q^113 - q^157 
        + O(q^158),
    q^4 - q^48 - q^56 - q^92 + q^100 - q^108 + q^144 + q^152 + O(q^158),
    q^6 - q^18 - q^28 + q^44 - q^46 + q^52 - q^84 - q^96 + q^98 + q^106 + q^112 
        + q^128 + q^150 - q^154 + O(q^158),
    q^7 - q^19 - q^33 - q^39 + q^41 + q^57 - q^73 + q^83 + q^99 - q^109 + q^117 
        + q^149 + O(q^158),
    q^8 - 2*q^28 - q^32 + q^44 + q^52 + q^76 - q^84 - q^96 + q^112 + q^128 + 
        q^132 + q^156 + O(q^158),
    q^11 + q^13 - q^19 - q^21 - q^33 - q^39 + 2*q^57 + q^63 - q^73 + q^99 - 
        q^109 + q^117 - q^123 + 2*q^151 + O(q^158),
    q^12 + q^22 + q^26 - q^36 - q^38 - q^42 - q^48 + q^64 - q^66 - q^78 - q^92 +
        2*q^114 + q^126 + q^144 - q^146 + O(q^158),
    q^14 - q^22 - q^26 + q^42 + q^48 - q^56 - q^64 + q^82 + q^88 + q^104 - q^114
        - q^126 - q^144 + O(q^158),
    q^16 + q^22 + q^26 - q^38 - q^42 - 2*q^48 + q^64 - q^66 - q^78 - q^88 - 
        q^104 + 2*q^114 + q^126 + 2*q^144 - q^146 + q^152 + O(q^158),
    q^24 - q^28 - q^32 + q^44 + q^52 - q^72 - q^84 + q^112 + q^128 + O(q^158)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
573
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
573
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
190
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
573
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
190
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
573
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
38
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
573
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
38
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
573
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
19*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
573
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 38*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
573
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
95*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
126
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^17 - q^18 + q^25 - q^26 - q^27 - q^30 + q^36 + q^48 + q^49 + q^50 + 
        q^54 + q^68 - q^69 - q^72 + q^78 - q^80 + q^90 - q^96 + q^104 - q^107 - 
        q^109 - q^115 - q^118 + q^121 + O(q^126),
    q^2 - q^13 - q^18 + q^25 - q^40 + q^50 + q^54 - q^59 - q^65 + q^79 - q^80 - 
        q^92 + q^98 + q^100 + q^115 + q^117 + O(q^126),
    q^3 + q^27 - q^36 - q^45 - q^51 + q^75 - q^78 - q^90 + O(q^126),
    q^4 + q^17 - q^20 + q^27 - q^36 - q^40 - q^46 + q^50 - q^65 - q^85 - q^86 - 
        q^97 + q^100 + q^107 + q^109 + q^115 + O(q^126),
    q^5 - q^23 - q^32 - q^43 - q^45 + q^46 - q^52 + q^54 + q^64 + q^67 + q^81 - 
        q^85 + q^86 + q^103 + q^104 - q^108 + O(q^126),
    q^6 - q^18 - q^39 - q^45 + q^54 + q^75 + q^81 - q^108 + q^117 - q^120 + 
        O(q^126),
    q^8 + q^13 - q^16 - q^20 - q^26 + q^27 + q^32 + q^34 - q^46 + q^52 - q^54 + 
        q^59 - q^64 - q^68 - q^72 - q^85 - q^86 + q^92 - q^97 + q^100 - q^104 + 
        q^108 - q^117 - q^118 + O(q^126),
    q^9 - q^18 - q^27 - q^30 + q^36 + q^48 + q^54 - q^69 - q^72 + q^78 + q^81 + 
        q^90 - q^96 - q^108 + O(q^126),
    q^10 - q^16 + q^23 - q^26 + q^27 + q^32 + q^43 - q^46 + q^52 - q^54 - q^64 -
        q^65 - q^68 - q^81 - q^86 - q^90 + q^92 - q^97 - q^104 + q^108 - q^118 +
        q^125 + O(q^126),
    q^12 - q^18 - q^27 - q^30 + q^36 + q^45 + q^48 + q^51 - q^60 - q^69 - q^72 +
        q^78 + q^90 - q^96 - q^120 + O(q^126),
    q^15 - q^18 - q^27 + q^36 + q^54 - q^69 - q^96 + q^117 + O(q^126),
    q^24 - q^27 - q^30 + q^39 + q^45 - q^60 - q^69 + q^90 + q^102 + O(q^126)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
120
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
574
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 20*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^16 + q^21 + q^23 + q^25 + q^32 - q^37 - 2*q^39 - q^42 - q^43 - q^46 + 
        q^49 - q^64 + q^74 + q^78 - q^81 - q^91 - q^107 + q^113 - q^119 + q^121 
        + q^123 - q^127 + q^128 - q^133 - 2*q^141 + O(q^162),
    q^2 - q^21 - q^23 - q^32 - q^36 + q^37 + q^39 + q^50 - q^78 + q^81 - q^86 + 
        q^91 + q^98 - q^113 - q^123 + q^127 + q^141 + q^144 + q^148 + O(q^162),
    q^3 - q^14 - q^17 - q^19 + q^27 + q^34 + q^38 + q^48 - 2*q^52 - q^56 - q^63 
        + 2*q^68 - q^69 + q^75 + 2*q^76 - q^82 - q^96 + q^97 + q^101 - 2*q^108 -
        q^111 + q^129 + q^136 - q^138 + q^147 + q^152 - q^153 - q^157 + q^161 + 
        O(q^162),
    q^4 + q^21 + q^23 - q^37 - q^39 - q^42 - q^46 - q^64 - q^72 + q^74 + q^78 - 
        q^81 - q^91 + q^100 + q^113 + q^123 - q^127 - q^141 - q^156 + O(q^162),
    q^6 - q^14 - q^26 - q^28 + q^34 + q^38 - q^52 + 2*q^68 + 2*q^76 - q^82 - 
        q^94 - q^104 - q^108 + q^136 - q^138 + q^150 + q^152 + O(q^162),
    q^7 - q^17 - q^19 + q^26 - q^34 - q^38 + q^41 + q^54 + q^69 + q^94 + q^96 - 
        q^104 - q^111 - q^112 - q^117 - q^126 + q^136 - q^138 + q^152 + q^153 - 
        q^157 + O(q^162),
    q^8 - q^16 + q^21 + q^23 + q^32 - q^37 - q^39 - q^64 - q^81 - q^84 - q^91 - 
        q^92 + q^113 + q^123 - q^127 - q^141 - q^144 + q^148 + q^156 + O(q^162),
    q^9 + q^16 - q^21 - q^23 - q^32 - q^36 + q^39 + q^43 - q^51 - q^57 + q^81 + 
        q^84 + q^92 + q^107 - q^113 + q^119 - q^123 + q^133 + q^141 + q^144 - 
        q^156 + O(q^162),
    q^12 - q^14 - q^26 - q^28 + 2*q^34 + 2*q^38 - 2*q^52 - q^54 - q^56 + 2*q^68 
        + 2*q^76 - q^82 - q^94 - q^96 - q^108 + q^112 + q^126 + q^136 + q^152 + 
        O(q^162),
    q^13 - q^17 - q^19 + q^27 + q^47 + q^48 - q^52 - q^56 - q^63 + q^68 - q^69 +
        q^76 + q^89 - q^96 - q^108 + q^129 + q^136 + q^152 - q^157 + O(q^162),
    q^18 + q^21 + q^23 + q^32 - q^37 - q^39 - q^42 - q^46 - q^64 - q^72 + q^78 -
        q^81 + q^86 - q^91 - q^102 + q^113 - q^114 + q^123 - q^127 - q^141 + 
        O(q^162),
    q^24 - q^26 - q^28 + q^34 + q^38 - q^48 - q^54 + q^68 + q^76 - q^94 - q^104 
        + q^126 + q^138 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
110
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
110
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
220
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
44
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^24 - q^26 + q^29 + q^31 - 2*q^36 - 2*q^39 - q^41 + q^46 + q^49 -
        q^54 - q^59 - q^64 - q^69 + 2*q^81 - q^94 - q^96 - q^101 - q^104 + 
        O(q^110),
    q^2 - q^24 + q^26 - q^27 - q^29 - q^31 + q^36 + q^39 - q^46 - q^48 - q^52 + 
        q^59 + q^64 + q^73 - q^81 + q^94 + q^98 + q^101 + O(q^110),
    q^3 - q^13 - q^18 + q^27 - q^32 - q^47 + q^48 + q^58 + q^62 + q^92 - q^108 +
        O(q^110),
    q^4 - q^9 - q^24 - q^26 + q^36 + q^39 + q^41 + q^69 - q^71 - q^81 - q^94 + 
        O(q^110),
    q^6 - q^9 - q^16 + q^24 - q^26 + q^29 + q^31 - q^36 + q^46 - q^64 - q^71 - 
        q^94 + q^96 + O(q^110),
    q^8 - 2*q^13 - q^18 + q^23 + 2*q^24 - 2*q^26 + q^27 + 2*q^29 + 2*q^31 - q^32
        - 2*q^36 - 2*q^39 + 2*q^46 - 2*q^47 + q^48 - q^52 + 2*q^58 - 2*q^59 + 
        2*q^62 - 2*q^64 - q^78 + 2*q^81 + q^82 + q^87 + q^92 + q^93 - 2*q^94 - 
        2*q^101 - q^108 + O(q^110),
    q^12 - q^13 - q^18 + q^23 + q^24 - q^26 + q^29 + q^31 - q^32 - q^36 - q^39 +
        q^46 - q^47 + q^48 - q^52 + 2*q^58 - q^59 + 2*q^62 - q^64 - q^72 - q^78 
        + q^81 + q^92 - q^94 - q^101 + O(q^110)
]
;
Bo:=
[
    q - q^2 - q^3 + q^6 + q^8 - q^13 - q^16 + q^23 - q^24 + q^26 + q^27 - q^29 -
        q^31 + q^39 - q^41 - q^46 - q^47 + q^48 + q^49 - q^54 + q^58 + 2*q^59 + 
        q^62 + q^64 - q^69 - q^71 - q^73 - q^78 - q^81 + q^82 + q^87 + q^93 + 
        q^94 - q^98 + 2*q^101 - q^104 + O(q^110),
    q^5 - q^10 - q^15 + q^30 + q^40 - q^65 - q^80 + O(q^110),
    q^25 - q^50 - q^75 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
575
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^9 - q^36 + q^39 - q^41 - q^49 + q^54 + q^69 + q^81 - q^96 + q^104 + 
        O(q^110),
    q^2 - q^27 + q^48 - q^52 - q^73 - q^98 + O(q^110),
    q^3 - q^13 - q^18 - q^27 + q^32 + q^47 + q^48 + q^58 - q^62 - q^92 - q^108 +
        O(q^110),
    q^4 - q^9 + 2*q^26 + q^29 - q^31 - q^41 - q^46 - q^59 - q^64 + q^69 + q^71 -
        2*q^94 + q^101 + O(q^110),
    q^6 + q^9 - q^16 - q^39 - q^59 - q^71 - q^81 + q^96 + q^101 + O(q^110),
    q^8 - 2*q^13 - q^18 + q^23 - q^27 + q^32 + 2*q^47 + q^48 + q^52 + 2*q^58 - 
        2*q^62 - q^78 - q^82 - q^87 - q^92 + q^93 - q^108 + O(q^110),
    q^12 + q^13 + q^18 - q^23 - q^32 - q^47 - q^48 - q^52 - 2*q^58 + 2*q^62 - 
        q^72 + q^78 + q^92 + O(q^110),
    q^24 + q^26 + q^29 - q^31 + q^36 - q^39 - q^46 - q^59 - q^64 - q^81 - q^94 +
        q^101 + O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + 2*q^13 - q^25 - 2*q^37 + q^49 - 2*q^61 - 2*q^73 - 2*q^97 + 2*q^109 + 
        q^121 + O(q^146)
]
;
Bo:=
[
    q - 2*q^13 - q^25 + 2*q^37 + q^49 + 2*q^61 - 2*q^73 - 2*q^97 - 2*q^109 + 
        q^121 + O(q^146),
    q^2 - 2*q^26 - q^50 + 2*q^74 + q^98 + 2*q^122 + O(q^146),
    q^4 - 2*q^52 - q^100 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^25 - 3*q^49 - 2*q^73 + 2*q^97 - q^121 + O(q^146),
    q^7 - q^31 - q^79 - q^103 + q^127 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^9 + (-2*a + 1)*q^17 + (-a + 1)*q^25 + (a - 2)*q^33 + (a - 2)*q^41 + 
        a*q^49 + (-a + 1)*q^57 - q^73 + (a - 1)*q^81 + (a - 1)*q^97 - 2*a*q^121 
        - a*q^129 + (a + 1)*q^137 + O(q^146),
    q^3 + (2*a - 1)*q^11 - a*q^19 + a*q^27 - q^43 + (-2*a + 1)*q^51 + (-a - 
        1)*q^59 + (-a + 1)*q^67 + (-a + 1)*q^75 + (a - 2)*q^99 + (-a + 2)*q^107 
        + (a - 2)*q^123 + (a - 1)*q^139 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^5 - q^9 + (-a + 1)*q^13 - a*q^21 + a*q^29 - a*q^33 + (a - 
        1)*q^41 + (-a + 1)*q^45 + a*q^61 + a*q^65 + (a - 1)*q^69 + (-a + 1)*q^77
        + q^81 + (a - 1)*q^93 - a*q^97 - a*q^101 + q^105 + (-a + 1)*q^113 + (a -
        1)*q^117 - q^125 + a*q^129 - a*q^137 - a*q^141 - q^145 + O(q^146),
    q^3 + a*q^7 + a*q^11 + (a - 1)*q^15 + (-a + 1)*q^23 - q^27 + (-a + 1)*q^31 -
        q^35 + (-a + 1)*q^39 - a*q^43 + a*q^47 - q^55 + (-a + 1)*q^59 - a*q^63 +
        (a - 1)*q^67 - 2*q^71 - a*q^79 - a*q^83 + a*q^87 + q^91 - a*q^99 + (a - 
        1)*q^103 + a*q^115 + (a - 1)*q^123 + (-a + 1)*q^131 + (-a + 1)*q^135 + 
        (-a + 1)*q^139 + q^143 + O(q^146)
]
;
Bo:=
[
    q + (-a + 1)*q^5 - q^9 + (a - 1)*q^13 + a*q^21 - a*q^29 - a*q^33 + (a - 
        1)*q^41 + (a - 1)*q^45 - a*q^61 + a*q^65 + (-a + 1)*q^69 + (a - 1)*q^77 
        + q^81 + (-a + 1)*q^93 - a*q^97 + a*q^101 + q^105 + (-a + 1)*q^113 + (-a
        + 1)*q^117 + q^125 + a*q^129 - a*q^137 + a*q^141 - q^145 + O(q^146),
    q^2 + (-a + 1)*q^10 - q^18 + (a - 1)*q^26 + a*q^42 - a*q^58 - a*q^66 + (a - 
        1)*q^82 + (a - 1)*q^90 - a*q^122 + a*q^130 + (-a + 1)*q^138 + O(q^146),
    q^3 - a*q^7 + a*q^11 + (-a + 1)*q^15 + (a - 1)*q^23 - q^27 + (a - 1)*q^31 - 
        q^35 + (a - 1)*q^39 - a*q^43 - a*q^47 + q^55 + (-a + 1)*q^59 + a*q^63 + 
        (a - 1)*q^67 + 2*q^71 + a*q^79 - a*q^83 - a*q^87 + q^91 - a*q^99 + (-a +
        1)*q^103 + a*q^115 + (a - 1)*q^123 + (-a + 1)*q^131 + (a - 1)*q^135 + 
        (-a + 1)*q^139 - q^143 + O(q^146),
    q^6 - a*q^14 + a*q^22 + (-a + 1)*q^30 + (a - 1)*q^46 - q^54 + (a - 1)*q^62 -
        q^70 + (a - 1)*q^78 - a*q^86 - a*q^94 + q^110 + (-a + 1)*q^118 + a*q^126
        + (a - 1)*q^134 + 2*q^142 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^9 - q^17 - a*q^25 + (-a + 1)*q^33 + (-a + 1)*q^41 + (a - 
        1)*q^49 + a*q^57 - q^73 - a*q^81 + 2*q^89 + a*q^97 + (2*a - 2)*q^113 + 
        (-a + 1)*q^129 + a*q^137 + O(q^146),
    q^2 + (a - 1)*q^18 - q^34 - a*q^50 + (-a + 1)*q^66 + (-a + 1)*q^82 + (a - 
        1)*q^98 + a*q^114 + O(q^146),
    q^3 - q^11 + (-a + 1)*q^19 + (a - 1)*q^27 - q^43 - q^51 + a*q^59 + a*q^67 - 
        a*q^75 + 2*q^83 + (-a + 1)*q^99 + (-a + 1)*q^107 + (-a + 1)*q^123 - 
        2*a*q^131 + a*q^139 + O(q^146),
    q^4 - a*q^12 + (a - 1)*q^36 + a*q^44 - q^68 - q^76 - a*q^100 + q^108 + (-a +
        1)*q^132 + O(q^146),
    q^6 - q^22 + (-a + 1)*q^38 + (a - 1)*q^54 - q^86 - q^102 + a*q^118 + a*q^134
        + O(q^146),
    q^8 - a*q^16 - a*q^24 + (a - 1)*q^32 + (a - 1)*q^48 + q^64 + (a - 1)*q^72 + 
        a*q^88 + q^96 - a*q^128 - q^136 + q^144 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^25 + 2*q^37 - q^49 - 2*q^61 - 2*q^85 + q^121 + 2*q^145 + O(q^146),
    q^5 + q^17 - q^29 - q^41 - q^53 - q^89 + q^101 - q^113 + q^137 + O(q^146)
]
;
Bo:=
[
    q - q^25 - 2*q^37 - q^49 + 2*q^61 + 2*q^85 + q^121 + 2*q^145 + O(q^146),
    q^2 - q^50 - 2*q^74 - q^98 + 2*q^122 + O(q^146),
    q^5 - q^17 - q^29 + q^41 - q^53 + q^89 + q^101 + q^113 - q^137 + O(q^146),
    q^10 - q^34 - q^58 + q^82 - q^106 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
576
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^25 - q^49 + 2*q^73 - 2*q^97 - q^121 + O(q^146),
    q^3 - q^27 - q^75 + O(q^146),
    q^9 - 2*q^57 - q^81 + 2*q^129 + O(q^146),
    q^19 - q^43 - q^67 + q^139 + O(q^146)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
577
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
576
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
577
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
192
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
577
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
64
);
qprec:=
96
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
578
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
272
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
578
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
119
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
192
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
96
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
64
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
32
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^10*q^3 + a^2*q^4 + (a^15 - a^9)*q^7 - a^4*q^9 - a^12*q^12 + (-a^13 - 
        1)*q^13 + a^4*q^16 + (a^12 + a^5)*q^19 + (a^9 - a^3)*q^21 + a*q^25 + 
        a^14*q^27 + (-a^11 - a)*q^28 + (a^11 + a^7)*q^31 - a^6*q^36 + (a^13 - 
        a^8)*q^37 + (a^10 - a^7)*q^39 + (-a^5 + a^3)*q^43 - a^14*q^48 + (-a^14 +
        a^8 - a^2)*q^49 + (-a^15 - a^2)*q^52 + (-a^15 + a^6)*q^57 + (-a^8 - 
        a^7)*q^61 + (a^13 + a^3)*q^63 + a^6*q^64 + (a^10 + a^8)*q^67 + (a^6 - 
        a^5)*q^73 - a^11*q^75 + (a^14 + a^7)*q^76 + (-a^6 - a)*q^79 + a^8*q^81 +
        (a^11 - a^5)*q^84 + (-a^15 + a^12 + a^9 - a^6)*q^91 + (a^5 + a)*q^93 + 
        (a^11 - a^3)*q^97 + a^3*q^100 + (a^10 + a)*q^103 - q^108 + (-a^12 + 
        a^4)*q^109 + (a^7 - a^2)*q^111 + (-a^13 - a^3)*q^112 + (a^4 - a)*q^117 -
        a^7*q^121 + (a^13 + a^9)*q^124 + O(q^127)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^2*q^3 + a^2*q^4 + (-a^7 - a)*q^7 + a^4*q^9 - a^4*q^12 + (-a^5 + 
        1)*q^13 + a^4*q^16 + (a^5 - a^4)*q^19 + (a^3 - a)*q^21 + a*q^25 - 
        a^6*q^27 + (-a^3 + a)*q^28 + (a^7 - a^3)*q^31 + a^6*q^36 + (-a^5 - 
        1)*q^37 + (a^7 - a^2)*q^39 + (a^5 + a^3)*q^43 - a^6*q^48 + (-a^6 + a^2 -
        1)*q^49 + (-a^7 + a^2)*q^52 + (-a^7 + a^6)*q^57 + (a^7 - 1)*q^61 + (-a^5
        + a^3)*q^63 + a^6*q^64 + (-a^2 - 1)*q^67 + (a^6 + a^5)*q^73 - a^3*q^75 +
        (a^7 - a^6)*q^76 + (a^6 + a)*q^79 - q^81 + (a^5 - a^3)*q^84 + (-a^7 + 
        a^6 - a^4 - a)*q^91 + (a^5 + a)*q^93 + a^3*q^100 + (-a^2 + a)*q^103 + 
        q^108 + (a^7 + a^2)*q^111 + (-a^5 + a^3)*q^112 + (a^4 + a)*q^117 + 
        a^7*q^121 + (-a^5 - a)*q^124 + O(q^127)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 16*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 24*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^3 + a^2*q^4 + (-a^3 + a)*q^7 - q^9 - q^12 + (-a + 1)*q^13 - q^16 +
        (-a - 1)*q^19 + (a^3 + a)*q^21 + a*q^25 - a^2*q^27 + (a^3 + a)*q^28 - 
        a^2*q^36 + (-a + 1)*q^37 + (-a^3 + a^2)*q^39 + (a^3 - a)*q^43 - a^2*q^48
        + q^49 + (-a^3 + a^2)*q^52 + (-a^3 - a^2)*q^57 + (-a^3 + 1)*q^61 + (a^3 
        - a)*q^63 - a^2*q^64 + (a^2 + 1)*q^67 + (-a^2 - a)*q^73 + a^3*q^75 + 
        (-a^3 - a^2)*q^76 + (-a^2 + a)*q^79 + q^81 + (a^3 - a)*q^84 + (-a^3 - 
        a^2 + a - 1)*q^91 + 2*a^3*q^97 + a^3*q^100 + (a^2 + a)*q^103 + q^108 - 
        2*q^109 + (-a^3 + a^2)*q^111 + (a^3 - a)*q^112 + (a - 1)*q^117 - 
        a^3*q^121 + O(q^127)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 32*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 48*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^3 - q^4 + q^9 + q^12 + (a + 1)*q^13 + q^16 + (a + 1)*q^19 + a*q^25 - 
        q^27 - 2*a*q^31 - q^36 + (a + 1)*q^37 + (-a - 1)*q^39 - q^48 - q^49 + 
        (-a - 1)*q^52 + (-a - 1)*q^57 + (-a + 1)*q^61 - q^64 + (a - 1)*q^73 - 
        a*q^75 + (-a - 1)*q^76 + (a - 1)*q^79 + q^81 + 2*a*q^93 - 2*a*q^97 - 
        a*q^100 + (a - 1)*q^103 + q^108 + 2*q^109 + (-a - 1)*q^111 + (a + 
        1)*q^117 - a*q^121 + 2*a*q^124 + O(q^127)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 64*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^3 + (a - 1)*q^7 + q^9 + (a - 1)*q^10 + a*q^16 + a*q^19 + (-a + 1)*q^21
        - q^27 + (-a + 1)*q^30 + a*q^31 + (a - 1)*q^34 + (-a + 1)*q^37 - a*q^40 
        - a*q^48 - a*q^57 - 2*a*q^58 + (-a + 1)*q^61 + (a - 1)*q^63 - q^64 - 
        a*q^70 + a*q^73 + (-a + 1)*q^79 + q^81 + (-a + 1)*q^82 + (-a + 1)*q^85 +
        (a - 1)*q^90 - a*q^93 - q^94 + (a - 1)*q^97 + (-a + 1)*q^102 + (-a + 
        1)*q^103 + q^106 - a*q^109 + (a - 1)*q^111 - q^112 + (a - 1)*q^118 + 
        a*q^120 + q^121 + O(q^127),
    q^2 - q^5 - q^6 + (a - 1)*q^8 + (a - 1)*q^14 + q^15 - q^17 + q^18 + (-a + 
        1)*q^24 + (-2*a + 2)*q^29 + (-a + 1)*q^35 + a*q^38 + q^41 + (-a + 
        1)*q^42 - q^45 - a*q^47 + q^51 + a*q^53 - q^54 - a*q^56 - q^59 + a*q^62 
        + (2*a - 2)*q^71 + (a - 1)*q^72 + (-a + 1)*q^74 - a*q^80 + a*q^83 + (2*a
        - 2)*q^87 - a*q^95 + a*q^101 + (a - 1)*q^105 + q^107 + a*q^113 - a*q^114
        + (-a + 1)*q^119 + (-a + 1)*q^122 - q^123 + (-a + 1)*q^125 + (a - 
        1)*q^126 + O(q^127)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
579
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 96*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
127
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^7 + q^9 + q^16 - q^21 - q^28 - q^31 + q^36 - q^43 + q^49 - q^55 
        - q^63 + q^64 - q^75 + q^81 - q^84 - q^85 - q^93 - q^97 - q^112 - q^124 
        + O(q^127),
    q^3 - q^7 + q^12 - q^21 - q^25 + q^27 - q^28 - q^31 - q^43 + q^48 + 2*q^49 +
        q^55 - q^63 + 2*q^67 - q^84 + q^85 - q^93 - q^97 - q^100 + q^108 + 
        2*q^109 - q^112 - q^121 - q^124 + O(q^127),
    q^5 - q^11 - q^15 - q^17 + q^20 + q^29 + q^33 - q^41 - q^44 + q^45 + q^47 + 
        q^51 - q^53 - q^60 - q^68 + q^71 + q^80 - q^87 - q^89 - q^99 + q^113 + 
        q^116 + q^123 + O(q^127)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^4*q^2 + a^8*q^4 - a^9*q^5 + (a^10 - a^8 + a^6 - a^4 + a^2 - 1)*q^8 + 
        (-a^10 + a^8 - a^6 + a^4 - a^2 + 1)*q^9 + (-a^11 + a^9 - a^7 + a^5 - a^3
        + a)*q^10 + (a^10 + a)*q^13 - a^2*q^16 + (a^11 - a^3)*q^17 + a^2*q^18 + 
        a^3*q^20 - a^4*q^25 + (a^5 - 1)*q^26 + a^9*q^29 - a^6*q^32 + (-a^7 - 
        a)*q^34 + a^6*q^36 + (-a^9 + a^7 - a^5 + a^3 - a)*q^37 + a^7*q^40 + 
        (-a^6 - a)*q^41 - a^7*q^45 - a^5*q^49 - a^8*q^50 + (a^9 - a^4)*q^52 + 
        (-a^8 + a^7)*q^53 + (a^11 - a^9 + a^7 - a^5 + a^3 - a)*q^58 + (a^3 + 
        a^2)*q^61 - a^10*q^64 + (-a^10 + a^5)*q^65 + (-a^11 - a^5)*q^68 + 
        a^10*q^72 + (a^6 - 1)*q^73 + (-a^3 + a)*q^74 + a^11*q^80 - a^10*q^81 + 
        (-a^10 - a^5)*q^82 + (a^10 - a^8 + 2*a^6 - a^4 + a^2 - 1)*q^85 + (-a^11 
        + a^9 - a^7 + a^5 - a^3 - a^2 + a)*q^89 - a^11*q^90 + (-a^2 - 1)*q^97 - 
        a^9*q^98 + (-a^10 + a^8 - a^6 + a^4 - a^2 + 1)*q^100 + (-a^8 - 
        a^5)*q^101 + (a^11 - a^9 - a^8 + a^7 - a^5 + a^3 - a)*q^104 + (a^11 - 
        a^10 + a^8 - a^6 + a^4 - a^2 + 1)*q^106 + (a^7 + a^5)*q^109 + (a^8 + 
        a^4)*q^113 - a^3*q^116 + (-a^11 + a^9 + a^8 - a^7 + a^5 - a^3 + a)*q^117
        - a^11*q^121 + (a^7 + a^6)*q^122 + (a^11 - a^9 + a^7 - a^5 + a^3 - 
        a)*q^125 + q^128 + (a^9 + 1)*q^130 + (-a^9 + a)*q^136 + (-a^7 + 
        a^3)*q^137 - q^144 + a^4*q^145 + (a^10 - a^4)*q^146 + (-a^7 + a^5)*q^148
        + (a^10 - a^8 + a^6 + a^2 - 1)*q^149 + (a^9 - a)*q^153 + (a^10 - a^8 + 
        a^6 - a^4 + 2*a^2 - 1)*q^157 - a*q^160 + q^162 + (-a^9 + 1)*q^164 + 
        (a^11 - a^6 + a^2)*q^169 + O(q^170)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^11*q^2 - a^8*q^4 + (-a^11 + a^9 - a^7 + a^5 - a^3 + a)*q^5 - a^5*q^8 +
        (a^10 - a^8 + a^6 - a^4 + a^2 - 1)*q^9 - a^10*q^10 + (a^8 - a^3)*q^13 - 
        a^2*q^16 + (a^10 + a^4)*q^17 + a^9*q^18 - a^7*q^20 + (-a^10 + a^8 - a^6 
        + a^4 - a^2 + 1)*q^25 + (a^5 - 1)*q^26 - a^9*q^29 + (a^11 - a^9 + a^7 - 
        a^5 + a^3 - a)*q^32 + (a^7 + a)*q^34 + a^6*q^36 + (a^6 - a^4)*q^37 - 
        a^4*q^40 + (-a^6 - a)*q^41 + a^11*q^45 + a^5*q^49 - a^9*q^50 + (a^11 + 
        a^2)*q^52 + (a - 1)*q^53 - a^6*q^58 + (a^3 + a^2)*q^61 + a^10*q^64 + 
        (a^7 - a^2)*q^65 + (-a^10 + a^8 - a^6 + 2*a^4 - a^2 + 1)*q^68 + a^3*q^72
        + (a^11 - a^9 - a^5 + a^3 - a)*q^73 + (a^3 - a)*q^74 - a*q^80 - 
        a^10*q^81 + (a^10 - a^8 + a^6 - a^4 - a^3 + a^2 - 1)*q^82 + (a^9 + 
        a^3)*q^85 + (a^11 - a^9 + a^7 - a^5 + a^3 + a^2 - a)*q^89 + a^8*q^90 + 
        (a^9 + a^7)*q^97 + a^2*q^98 - a^6*q^100 + (-a^8 - a^5)*q^101 + (-a^11 + 
        a^9 + a^8 - a^7 + a^5 - a^3 + a)*q^104 + (a^11 - a^10 + a^8 - a^6 + a^4 
        - a^2 + 1)*q^106 + (-a^7 - a^5)*q^109 + (a^11 - a)*q^113 - a^3*q^116 + 
        (-a^6 + a)*q^117 - a^11*q^121 + (-a^11 + a^9 - a^7 + a^5 - a^3 + a + 
        1)*q^122 - a^11*q^125 + a^7*q^128 + (a^11 - a^9 + a^7 - a^5 + a^4 + a^3 
        - a)*q^130 + (-a^9 + a)*q^136 + (-a^10 - 1)*q^137 + q^144 - a^8*q^145 + 
        (a^10 - a^4)*q^146 + (a^10 - a^8 + a^6 - a^4 + a^2)*q^148 + (-a^10 + a^8
        - a^6 - a^2 + 1)*q^149 + (-a^8 - a^2)*q^153 + (-a^9 + a^5)*q^157 + (a^10
        - a^8 + a^6 - a^4 + a^2 - 1)*q^160 - a^7*q^162 + (a^9 - 1)*q^164 + 
        (-a^11 + a^6 - a^2)*q^169 + O(q^170)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + 1/4*(-a^5 + 3*a^4 - a^3 - a + 1)*q^5 + 1/2*(-a^5 + a^4 - a^3 + a^2 - 
        a)*q^6 + 1/2*(-a^5 - a^3 + a^2 - a + 1)*q^9 + 1/4*(-a^5 + a^4 - 2*a^3 + 
        a^2 - a + 1)*q^10 + 1/2*(a^4 - a^2)*q^14 + a^2*q^16 + 1/4*(2*a^5 + a^3 -
        1)*q^20 + 1/2*(-a^3 + a^2 + a - 1)*q^21 + 1/2*(-a + 1)*q^24 + 1/4*(-a^5 
        + a^4 - 2*a)*q^25 + 1/2*(a^5 + 1)*q^26 + 1/2*(a^5 - a^4 + a^3 - 2*a^2 + 
        a - 1)*q^29 + 1/2*(-a^4 + a^3)*q^30 + 1/2*(a - 1)*q^34 + 1/2*(a^5 - 
        2*a^4 + 2*a^3 - 2*a^2 + 2*a - 1)*q^36 + 1/4*(a^4 - 1)*q^40 + 1/2*(-a^4 +
        a^3 - 2*a^2 + 2*a - 1)*q^41 + 1/4*(-a^4 + 2*a^3 - 2*a^2 + 2*a - 1)*q^45 
        + 1/2*(-a^4 - a^3)*q^46 + 1/2*(a^3 - 1)*q^49 + 1/4*(-a^2 - a)*q^50 + 
        1/2*(-a^2 + a - 1)*q^54 + 1/2*(a^5 - a^3)*q^56 + 1/2*(a^3 + a^2)*q^61 + 
        1/4*(a^5 - a^3 + a^2 - 1)*q^65 + 1/2*(a^3 - a)*q^69 + 1/2*(-a^5 + a^4 - 
        a^3 + a^2 - 2*a + 1)*q^70 + 1/2*(a^3 + a)*q^74 + 1/4*(2*a^5 - 3*a^4 + 
        2*a^3 - 2*a^2 + 3*a - 2)*q^80 + 1/2*(-a^5 + a^4 - 2*a^3 + a^2 - a)*q^81 
        + 1/2*(-a^4 + a^3 + a^2 - a)*q^84 + 1/4*(-a^4 + 2*a^3 - 2*a^2 + a - 
        1)*q^85 + 1/2*(-a^5 + a^2)*q^86 + 1/2*(a^4 - 2*a^3 + 2*a^2 - a + 1)*q^89
        + 1/4*(-a^4 - a)*q^90 + 1/2*(a^5 - 1)*q^94 + 1/2*(-a^2 + a)*q^96 + 
        1/4*(-a^4 + a^3 - 3*a^2 + a - 1)*q^100 + 1/2*(2*a^5 - a^4 + a^3 - a^2 - 
        2)*q^101 + 1/2*(-a^5 + a^4 - a^3 + a^2 - 2*a + 1)*q^104 + 1/2*(2*a^5 - 
        2*a^4 + a^3 - a^2 + a)*q^105 + 1/2*(-a^5 - a^4)*q^106 + 1/2*(a^5 - a^4 +
        a - 1)*q^109 + 1/2*(a^3 - 1)*q^116 + 1/2*(-a^5 + a^4)*q^120 - a^4*q^121 
        + 1/4*(-3*a^5 - a^3 + a^2 - a + 1)*q^125 + 1/2*(a^5 - a^4 + 2*a^3 - 
        2*a^2 + a)*q^126 + 1/2*(a^4 - a^3 - a + 1)*q^129 + 1/4*(-a^5 + 2*a^4 - 
        a^3 - a + 2)*q^130 + 1/2*(-a^2 + a)*q^136 + 1/2*(a^2 - a + 1)*q^141 + 
        1/2*(-a^5 + a^4 - a^3 + a^2 + 1)*q^144 + 1/4*(a^4 - 2*a^3 - a)*q^145 + 
        1/2*(a^4 - a^3)*q^146 + 1/2*(-a^5 + a^4 + a^2 + 1)*q^149 + 1/2*(a - 
        1)*q^150 + 1/4*(-a^5 + a)*q^160 + 1/2*(2*a^4 - a^3 + a^2 - a + 2)*q^161 
        + 1/2*(-a^5 + a^4 - 2*a^3 - a + 2)*q^164 + 1/2*(a^3 + 1)*q^166 + 
        1/2*(a^5 - a^4 + a^3 + a - 1)*q^169 + O(q^170),
    q^2 + 1/2*(a^5 + a^2)*q^5 - a*q^8 + 1/2*(-a^5 + a^4 - a^3 - a + 1)*q^10 + 
        (a^5 - 2*a^4 + a^3 - a^2 + a - 1)*q^13 + (-a^5 + a^4 - a^3 + a^2 - 
        a)*q^17 - a^5*q^18 + 1/2*(-a^5 + a^4 - 2*a^3 + a^2 - a + 1)*q^20 + 
        1/2*(a + 1)*q^25 + a^2*q^32 + (-a^2 - 1)*q^37 + 1/2*(a^3 - 1)*q^40 + 
        1/2*(a^3 + 1)*q^45 + 1/2*(-a^5 + a^4)*q^50 + (a^5 + 1)*q^52 + (a^4 + 
        a^3)*q^53 - a^2*q^58 + 1/2*(2*a^5 - a^4 - a^2 + 2*a - 1)*q^65 + (a - 
        1)*q^68 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^72 + (-a^3 + a^2)*q^73 + 
        1/2*(a^4 - 1)*q^80 + (a^5 - a^4 + a^3 - a^2 + 2*a - 1)*q^82 + 1/2*(-a^4 
        + a^3 - 1)*q^85 + 1/2*(-a^4 - 1)*q^90 + (-a^5 - a^3)*q^97 + a^5*q^98 + 
        1/2*(-a^2 - a)*q^100 + (a^4 + 1)*q^113 + (a^4 - a^2)*q^117 + (a^3 + 
        a^2)*q^122 + 1/2*(-a^2 + 1)*q^125 - a^3*q^128 + 1/2*(a^5 - a^3 + a^2 - 
        1)*q^130 + (-a^5 + a^4 + a^2 - a + 1)*q^137 + 1/2*(-a^4 + 1)*q^145 + 
        (a^3 + a)*q^148 + (a^5 - a^4)*q^153 + (-a^5 - a)*q^157 + 1/2*(-a^4 + 
        a)*q^160 - a^3*q^162 + O(q^170),
    q^3 + 1/2*(a^3 + a^2 + a + 1)*q^5 + (-a^4 - a^3)*q^7 + (2*a^5 + 2*a^3 - 
        2*a^2 - 2)*q^8 + 1/2*(-2*a^4 - a^3 - 3*a^2 - a - 2)*q^10 + a*q^12 + (a^5
        - a^4 + a^3 - a^2 + a - 2)*q^13 + a^4*q^15 - a*q^17 + (-a^5 + a^4 - a^3 
        + a^2 - a)*q^18 + 1/2*(-a^4 - a^3 - a^2 - a)*q^20 + (-2*a^5 + a^4 + 
        2*a^2 + 2)*q^23 + 1/2*(-2*a^5 - 2*a^3 + a^2 + 2)*q^25 + (-a^5 - a^3 + 
        a^2 - a + 1)*q^27 + (-a^5 - a^4)*q^28 + (a + 1)*q^35 + (2*a^5 + a^3 - 
        a^2 - 2)*q^37 + 1/2*(-2*a^5 + a^4 - a^3 + a^2 - 2*a)*q^40 + (a^4 - 
        a^2)*q^42 + (a^5 + a^4 + a^3)*q^43 + 1/2*(-2*a^5 + a^4 - a^3 + a^2 + 
        2)*q^45 + (-a^5 - a^4 - a^3 - a^2 - a)*q^47 + a^2*q^48 + 1/2*(-3*a^5 + 
        a^4 - 3*a^3 + 3*a^2 - a + 3)*q^50 + (a + 1)*q^52 + (-a^5 + 2*a^4 + 2*a^2
        + 2)*q^53 + (-a^3 - a^2 - a)*q^58 + a^5*q^60 + (-a^3 - 1)*q^63 + 
        1/2*(2*a^5 - a^4 + a^3 + 2*a - 1)*q^65 + a^2*q^68 + (2*a^5 + 2*a^3 + a -
        1)*q^72 - a^4*q^73 - a*q^75 + 1/2*(a^5 + a^4 + a^3 + a^2)*q^80 + (a^3 + 
        2*a^2 + 2*a + 1)*q^82 + (2*a^5 + a^3 - a^2 + a - 2)*q^83 + 1/2*(a^3 - 
        1)*q^85 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^87 + 1/2*(3*a^5 - 3*a^4 + 
        3*a^3 - 3*a^2 - 4)*q^90 + (-a^5 + 2*a^4 + 2*a^2 + 2)*q^92 + (-a^4 - a^3 
        - a^2 - a - 1)*q^97 + (2*a^5 - a^4 + a^3 - a^2 + 2*a)*q^98 + 1/2*(2*a^5 
        + a^3 - 2*a^2 - 2)*q^100 + (2*a^5 - a^4 + a^3 - a^2 - 2)*q^103 + (-a^5 -
        a^4 - a^3 - a^2 - a - 1)*q^107 + (-a^5 + 1)*q^108 + (-2*a^5 + a^4 - a^3 
        + a^2 - a + 1)*q^112 + (-a^5 + a^4 - a^3 + a^2 + 2)*q^113 + (2*a^5 + 
        2*a^3 + a - 2)*q^115 + (a^5 + a^4)*q^117 + (-2*a^5 + a^4 + 2*a^2 + 
        2)*q^122 + (-a^5 - a^2)*q^123 + 1/2*(-a^3 - a^2)*q^125 + (a^5 + a^4 + 
        a^3 + a^2 + a)*q^127 + (2*a^5 - 2*a^4 - 2*a^2 - 2)*q^128 + 1/2*(2*a^5 - 
        a^4 + 2*a^3 + a - 1)*q^130 + (a^3 + a)*q^135 + (-2*a^5 + a^4 - a^3 + a^2
        - a + 2)*q^137 + (-a^4 - a^3)*q^138 + (a^2 + a)*q^140 + 1/2*(-a^5 - a^4 
        - a^3 - a^2)*q^145 + (-a^5 + a^3 - 1)*q^147 + (-2*a^5 + a^4 - a^3 + 
        2*a^2 + 2)*q^148 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^153 + (-a^2 - a - 
        1)*q^157 + 1/2*(-3*a^5 - a^4 - 3*a^3 - 2*a + 2)*q^160 + (a^5 - a^4 - a^2
        + a - 1)*q^162 + (-a^4 - a^3 - a^2)*q^163 + (a^5 + a^4 + a^3 + 
        a^2)*q^167 + (a^5 - a^3)*q^168 + O(q^170),
    q^4 + 1/4*(a^5 + 2*a^3 + a)*q^5 + 1/2*(-a^4 + a^3 - a^2 + a - 1)*q^6 + 
        1/2*(-a^5 + 2*a^4 - a^3)*q^9 + 1/4*(a^5 + a^2)*q^10 + 1/2*(a^3 - a)*q^14
        + 1/4*(-a^5 + 3*a^4 - a^3 - a + 1)*q^20 + 1/2*(a^5 - a^4 + a^3 - 2*a^2 +
        2*a)*q^21 + 1/2*(-a^5 + a^4 - a^3 + a^2 - a)*q^24 + 1/4*(a^4 - a^3 - 
        2)*q^25 + 1/2*(a^5 - 2*a^4 + a^3 - a^2 + a - 1)*q^26 + 1/2*(a^5 + 
        a)*q^29 + 1/2*(-a^3 + a^2)*q^30 + 1/2*(-a^5 + a^4 - a^3 + a^2 - a)*q^34 
        + 1/2*(-a^5 - a^3 + a^2 - a + 1)*q^36 + 1/4*(-a^5 + a^4 - 2*a^3 + a^2 - 
        a + 1)*q^40 + 1/2*(-a^5 - a^4 - a - 1)*q^41 + 1/4*(-a^5 + a^4 + 3*a^2 - 
        3*a + 3)*q^45 + 1/2*(-a^3 - a^2)*q^46 + 1/2*(a^5 - 3*a^4 + a^3 + a - 
        1)*q^49 + 1/4*(a + 1)*q^50 + 1/2*(a^5 - a^4 + a^3 - a^2)*q^54 + 1/2*(a^4
        - a^2)*q^56 + 1/2*(-a^2 - a)*q^61 + a^2*q^64 + 1/4*(-a^5 - a^3 + 2*a^2 -
        2*a + 1)*q^65 + 1/2*(a^2 - 1)*q^69 + 1/2*(-a^5 - 1)*q^70 + 1/2*(-a^2 - 
        1)*q^74 + 1/4*(2*a^5 + a^3 - 1)*q^80 + 1/2*(-a^4 + a^3 + a - 1)*q^81 + 
        1/2*(-a^3 + a^2 + a - 1)*q^84 + 1/4*(-a^5 + a^4 - a^2 + a)*q^85 + 
        1/2*(-a^4 + a)*q^86 + 1/2*(a^5 + a^4 - a^2 - a)*q^89 + 1/4*(a^3 + 
        1)*q^90 + 1/2*(a^5 + a^3 - a^2 + a - 1)*q^94 + 1/2*(-a + 1)*q^96 + 
        1/4*(-a^5 + a^4 - 2*a)*q^100 + 1/2*(2*a^5 - 2*a^4 + a^3 - a^2 + a)*q^101
        + 1/2*(a^5 + 1)*q^104 + 1/2*(2*a^4 - 2*a^3 + a^2 - a + 1)*q^105 + 
        1/2*(a^4 + a^3)*q^106 + 1/2*(-a^5 - 2*a^3 + a^2 - a + 2)*q^109 + 
        1/2*(a^5 - a^4 + a^3 - 2*a^2 + a - 1)*q^116 + 1/2*(-a^4 + a^3)*q^120 + 
        1/4*(a^5 - 2*a^4 + a^3)*q^125 + 1/2*(a^4 - a^3 + 2*a^2 - 2*a + 1)*q^126 
        + 1/2*(-a^5 + a^4 - a)*q^129 + 1/4*(2*a^5 - a^4 - a^2 + 2*a - 1)*q^130 +
        1/2*(a - 1)*q^136 + 1/2*(-a^5 + a^4 - a^3 + a^2)*q^141 + 1/2*(a^5 - 
        2*a^4 + 2*a^3 - 2*a^2 + 2*a - 1)*q^144 + 1/4*(-a^3 - 2*a^2 + 1)*q^145 + 
        1/2*(-a^3 + a^2)*q^146 + 1/2*(-a^5 + 2*a^4 - 2*a^3 + a^2 + 1)*q^149 + 
        1/2*(a^5 - a^4 + a^3 - a^2 + a)*q^150 + 1/4*(a^4 - 1)*q^160 + 
        1/2*(-2*a^5 + 2*a^4 + a^2 - a + 1)*q^161 + 1/2*(-a^4 + a^3 - 2*a^2 + 2*a
        - 1)*q^164 + 1/2*(-a^5 + a^4 - a^3 + 2*a^2 - a + 1)*q^166 + 1/2*(-a^5 + 
        2*a^3 - a)*q^169 + O(q^170)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 + a^2*q^4 - a^3*q^8 - a^3*q^9 + (a^5 - a^4 + a^3 + a - 1)*q^13 + 
        a^4*q^16 + (a^5 - a^4 + a^3 - a^2 - 1)*q^17 + a^4*q^18 - a^2*q^25 + 
        (-a^3 + 1)*q^26 + a^4*q^29 - a^5*q^32 + (a^2 + 1)*q^34 - a^5*q^36 + 
        (-a^5 - a)*q^37 + (-a^5 + a^2)*q^41 - a^3*q^49 + a^3*q^50 + (a^4 - 
        a)*q^52 + (a^2 + 1)*q^53 - a^5*q^58 + (a^5 + a^3 - a^2 + a - 1)*q^61 + 
        (a^5 - a^4 + a^3 - a^2 + a - 1)*q^64 + (-a^3 - a)*q^68 + (a^5 - a^4 + 
        a^3 - a^2 + a - 1)*q^72 + (-a^5 + 1)*q^73 + (a^5 - a^4 + a^3 + a - 
        1)*q^74 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^81 + (a^5 - a^4 - a^2 + a - 
        1)*q^82 + (-a^5 + a^4)*q^89 + (a^4 + 1)*q^97 + a^4*q^98 - a^4*q^100 + 
        (-a^3 + a^2)*q^101 + (-a^5 + a^2)*q^104 + (-a^3 - a)*q^106 + (-a^3 + 
        1)*q^109 + (a^2 - a)*q^113 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^116 + 
        (-a^5 + a^2)*q^117 - a*q^121 + (-a^5 + 1)*q^122 + (-a^5 + a^4 - a^3 + 
        a^2 - a)*q^125 + q^128 + (a^4 + a^2)*q^136 + (a^5 - a^4 + a^3 - a^2 + 
        a)*q^137 + q^144 + (a^5 - a^4 + a^3 - a^2 - 1)*q^146 + (-a^3 + 1)*q^148 
        + (-a^3 - a)*q^149 + (a^4 + a^2)*q^153 + (a^4 - a^3)*q^157 + q^162 + 
        (a^4 + 1)*q^164 + (-a^5 + a^4 - a)*q^169 + O(q^170),
    q^5 - a*q^10 + a^2*q^20 + (-a^5 + a^4)*q^25 - a^3*q^40 - a^3*q^45 + (-a^4 + 
        a^3 - a^2 + a - 1)*q^50 + (a^5 - a^4 + a^3 + a - 1)*q^65 + a^4*q^80 + 
        (a^5 - a^4 + a^3 - a^2 - 1)*q^85 + a^4*q^90 + (a^5 - a^4 + a^3 - a^2 + 
        a)*q^100 + (-a^3 + a^2 - a)*q^125 + (-a^3 + 1)*q^130 + a^4*q^145 - 
        a^5*q^160 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 - a*q^5 + (-a^5 + 1)*q^6 + (-a^5 - a^3 - a)*q^9 + (a^4 - a)*q^14
        + a^4*q^16 - a^3*q^20 + (a^5 + a^3 + a)*q^21 + (a^2 + 1)*q^24 + a^2*q^25
        - a^5*q^29 + (a^5 - a^4 + a^3 - a^2 - 1)*q^30 + (-a^5 - a^3 + 1)*q^36 + 
        (a^4 - a^3)*q^41 + (a^5 + a^3 + a - 1)*q^45 + (a^5 - a^4 + a^3 - a^2 - 
        1)*q^46 + (a^5 - a^4 - a^2 + a)*q^49 + (-a^4 - a^2 - 1)*q^54 + (a^5 - 
        a^4 - a^2 + a - 1)*q^56 - 2*a^5*q^61 + (a^5 - a^4 + a^3 - a^2 + a - 
        1)*q^64 + (a^5 + a^4 + a^3 + a - 1)*q^69 + (-a^5 + a^2)*q^70 - a^5*q^80 
        + (a^5 - 1)*q^81 + (a^5 + a^3 - 1)*q^84 + (a^4 - a^3)*q^86 + (a^5 - a^4 
        - a^2 + a - 1)*q^89 + (-a^3 + 1)*q^94 + (a^4 + a^2)*q^96 + a^4*q^100 + 
        (-a^5 + 1)*q^101 + (-a^5 - a^3 - a + 1)*q^105 + (a^2 - a)*q^109 + q^116 
        + (-a^3 - a)*q^120 - a*q^121 - a^3*q^125 + (a^3 + a^2 + a)*q^126 + (a^5 
        - a^4 + a^3)*q^129 + 2*a^4*q^134 + (-a^4 - a^2 - 1)*q^141 + (-a^5 + a^2 
        + 1)*q^144 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^145 + (a^4 + 1)*q^149 + 
        (a^2 + 1)*q^150 + (-a^5 - a^3 - a + 1)*q^161 + (-a^4 + a^3 - a^2 + a - 
        1)*q^164 + (a^5 - a^4 + a^3 - a^2 + a)*q^166 - a*q^169 + O(q^170),
    q^2 + (-a^5 - a^3)*q^3 + (a^5 - a^4 + a^3 + a - 1)*q^7 + a^2*q^8 - a*q^10 + 
        (-a^5 + 1)*q^12 + (a^5 + a^3 - a^2 + a - 1)*q^15 + (-a^5 - a^3 - a)*q^18
        + (a^5 + a^3 - a^2 + a - 1)*q^23 + (a^5 - a^2 - 1)*q^27 + (a^4 - a)*q^28
        + a^4*q^32 + (-a^3 + 1)*q^35 - a^3*q^40 + (a^5 + a^3 + a)*q^42 + (a^2 - 
        a)*q^43 + (-a^5 - a)*q^47 + (a^2 + 1)*q^48 + a^2*q^50 - a^5*q^58 + (a^5 
        - a^4 + a^3 - a^2 - 1)*q^60 + (-a^5 + a^4 - a^3 + a^2 + 2)*q^63 + 
        2*a^2*q^67 + (-a^5 - a^3 + 1)*q^72 + (-a^5 + 1)*q^75 + (a^4 - a^3)*q^82 
        + (-a^5 + a^4)*q^83 + (-a^3 - a)*q^87 + (a^5 + a^3 + a - 1)*q^90 + (a^5 
        - a^4 + a^3 - a^2 - 1)*q^92 + (a^5 - a^4 - a^2 + a)*q^98 + (a^5 - a^4 + 
        a^3 - a^2 + a)*q^103 + (-a^3 - a)*q^107 + (-a^4 - a^2 - 1)*q^108 + (a^5 
        - a^4 - a^2 + a - 1)*q^112 + (-a^5 + 1)*q^115 - 2*a^5*q^122 + (a^5 - a^4
        + a^3)*q^123 + (-a^5 - a)*q^127 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^128 
        + (-a^5 + a^4 + a^2 + 1)*q^135 + (a^5 + a^4 + a^3 + a - 1)*q^138 + (-a^5
        + a^2)*q^140 - q^147 - a^5*q^160 + (a^5 - 1)*q^162 + (a^5 - a^4 + a^3 - 
        a^2 + a)*q^163 + (-a + 1)*q^167 + (a^5 + a^3 - 1)*q^168 + O(q^170)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 - q^4 - a*q^5 - a*q^8 + q^9 + q^10 + (a + 1)*q^13 + q^16 + a*q^18 
        + a*q^20 - q^25 + (a - 1)*q^26 - a*q^29 + a*q^32 - q^36 - 2*q^37 - q^40 
        + (-a + 1)*q^41 - a*q^45 + a*q^49 - a*q^50 + (-a - 1)*q^52 + (a - 
        1)*q^53 + q^58 + (-a - 1)*q^61 - q^64 + (-a + 1)*q^65 - a*q^72 + 
        2*a*q^73 - 2*a*q^74 - a*q^80 + q^81 + (a + 1)*q^82 + (a - 1)*q^89 + q^90
        - q^98 + q^100 + (-a - 1)*q^101 + (-a + 1)*q^104 + (-a - 1)*q^106 - 
        2*a*q^113 + a*q^116 + (a + 1)*q^117 + a*q^121 + (-a + 1)*q^122 + a*q^125
        - a*q^128 + (a + 1)*q^130 + q^144 - q^145 - 2*q^146 + 2*q^148 - 2*q^149 
        + q^160 + a*q^162 + (a - 1)*q^164 + a*q^169 + O(q^170)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^5 + a*q^9 + (-a - 1)*q^11 + (-a - 1)*q^19 - q^25 + a*q^29 + (a + 
        1)*q^31 + (-a + 1)*q^41 + q^45 + q^49 + (a - 1)*q^55 + (a + 1)*q^61 + 
        2*a*q^71 + (-a - 1)*q^79 - q^81 + (-a - 1)*q^89 + (a - 1)*q^95 + (-a + 
        1)*q^99 + (-a - 1)*q^101 + a*q^121 + a*q^125 + (a - 1)*q^131 + 2*q^139 +
        q^145 - 2*a*q^151 + (-a + 1)*q^155 - q^169 + O(q^170),
    q^2 + a*q^8 - a*q^10 + a*q^18 + (-a - 1)*q^22 - q^32 + (-a - 1)*q^38 + q^40 
        - q^50 + a*q^58 + (a + 1)*q^62 - q^72 + (-a + 1)*q^82 + (-a + 1)*q^88 + 
        q^90 + q^98 + (a - 1)*q^110 + (a + 1)*q^122 - a*q^128 + 2*a*q^142 + (-a 
        + 1)*q^152 + (-a - 1)*q^158 + a*q^160 - q^162 + O(q^170),
    q^4 + a*q^16 - a*q^20 + a*q^36 + (-a - 1)*q^44 - q^64 + (-a - 1)*q^76 + q^80
        - q^100 + a*q^116 + (a + 1)*q^124 - q^144 + (-a + 1)*q^164 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^2 + q^4 - a*q^5 + q^8 - q^9 - a*q^10 + (a - 1)*q^13 + q^16 - q^18 - 
        a*q^20 - q^25 + (a - 1)*q^26 + a*q^29 + q^32 - q^36 + 2*a*q^37 - a*q^40 
        + (-a + 1)*q^41 + a*q^45 - a*q^49 - q^50 + (a - 1)*q^52 + (-a - 1)*q^53 
        + a*q^58 + (-a - 1)*q^61 + q^64 + (a + 1)*q^65 - q^72 - 2*q^73 + 
        2*a*q^74 - a*q^80 + q^81 + (-a + 1)*q^82 + (-a + 1)*q^89 + a*q^90 - 
        a*q^98 - q^100 + (-a - 1)*q^101 + (a - 1)*q^104 + (-a - 1)*q^106 + 
        2*q^113 + a*q^116 + (-a + 1)*q^117 + a*q^121 + (-a - 1)*q^122 + a*q^125 
        + q^128 + (a + 1)*q^130 - q^144 + q^145 - 2*q^146 + 2*a*q^148 + 2*q^149 
        - a*q^160 + q^162 + (-a + 1)*q^164 - a*q^169 + O(q^170)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^6 - q^13 + q^16 - q^22 - q^24 - q^25 + q^29 + q^33 + 2*q^38 + 
        q^49 - q^52 - q^53 + q^54 - 2*q^57 - q^62 + q^64 + q^78 - q^81 - q^86 - 
        q^88 + q^93 - q^94 - q^96 - q^100 - q^109 + q^116 + q^125 + q^129 + 
        q^132 + q^141 - q^149 + q^150 + 2*q^152 - q^158 + O(q^170),
    q^2 - q^3 + q^8 - q^11 - q^12 + 2*q^19 - q^26 + q^27 - q^31 + q^32 + q^39 - 
        q^43 - q^44 - q^47 - q^48 - q^50 + q^58 + q^66 + q^75 + 2*q^76 - q^79 - 
        q^87 + q^98 - q^104 - q^106 + q^108 - 2*q^114 - q^124 + 2*q^127 + q^128 
        + 2*q^131 + q^143 - q^147 + q^156 + q^159 - q^162 - q^163 + O(q^170),
    q^5 + q^20 - q^25 - q^30 - q^65 + q^80 - q^100 - q^110 - q^120 + q^145 + 
        q^150 + q^165 + O(q^170),
    q^10 - q^15 + q^40 - q^50 - q^55 - q^60 + q^75 + 2*q^95 - q^130 + q^135 - 
        q^155 + q^160 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^5 + (-a - 1)*q^7 - a*q^9 + (-a + 1)*q^13 + (a - 1)*q^23 - q^25 + 
        a*q^29 + (-a + 1)*q^35 + q^45 + a*q^49 + (a - 1)*q^53 - 2*a*q^59 + (a - 
        1)*q^63 + (a + 1)*q^65 + (a + 1)*q^67 - q^81 + (-a + 1)*q^83 - 2*q^91 + 
        (a - 1)*q^103 + (a + 1)*q^107 + (-a - 1)*q^115 + (-a - 1)*q^117 + q^121 
        - a*q^125 - q^145 + 2*q^161 + (a + 1)*q^167 - a*q^169 + O(q^170),
    q^2 + a*q^8 + a*q^10 + (-a - 1)*q^14 - a*q^18 + (-a + 1)*q^26 - q^32 - q^40 
        + (a - 1)*q^46 - q^50 + (-a + 1)*q^56 + a*q^58 + (-a + 1)*q^70 + q^72 + 
        q^90 + a*q^98 + (a + 1)*q^104 + (a - 1)*q^106 - 2*a*q^118 + (a - 
        1)*q^126 - a*q^128 + (a + 1)*q^130 + (a + 1)*q^134 - a*q^160 - q^162 + 
        (-a + 1)*q^166 + O(q^170),
    q^4 + a*q^16 + a*q^20 + (-a - 1)*q^28 - a*q^36 + (-a + 1)*q^52 - q^64 - q^80
        + (a - 1)*q^92 - q^100 + (-a + 1)*q^112 + a*q^116 + (-a + 1)*q^140 + 
        q^144 + O(q^170)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
580
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
170
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^13 + q^16 - q^20 + q^22 - q^33 - q^34 + q^36 - q^45 - q^49 - q^52 - 
        q^53 + q^54 - q^62 - q^65 - q^74 + q^78 + q^81 - q^88 + q^93 + q^100 - 
        q^109 - q^110 - q^116 + q^129 + q^132 - q^136 - q^141 + q^145 + q^146 + 
        q^149 - q^150 - q^158 + q^165 + O(q^170),
    q^2 - q^11 - q^17 + q^26 - q^27 + q^31 + q^32 - q^37 - q^39 - q^40 + q^44 + 
        q^55 - q^66 - q^68 + q^72 + q^73 + q^75 + q^79 + q^85 - q^90 + q^97 - 
        q^98 - q^104 - q^106 + q^108 + q^113 - q^124 - q^127 - q^130 - q^135 - 
        q^137 + q^143 - q^148 - q^153 - q^155 + q^156 + q^157 + q^159 + q^162 + 
        O(q^170),
    q^3 + q^11 - q^12 + q^15 - q^18 - q^26 - q^27 - q^31 + q^39 - q^43 - q^44 + 
        q^47 + q^48 + q^50 - q^55 - q^60 + q^66 + q^72 - q^79 + q^87 - q^90 + 
        q^104 + q^106 + q^108 + q^124 + q^130 - q^135 - q^143 - q^147 + q^155 - 
        q^156 - q^159 + 2*q^162 - q^163 + O(q^170),
    q^4 + q^9 + q^13 - q^20 + q^22 - q^29 + q^30 - q^33 - q^34 - q^52 - q^53 - 
        q^54 - q^62 + q^64 - q^74 + q^78 - q^88 + q^93 + q^100 - q^109 - q^120 -
        q^121 - q^125 - q^129 + q^132 - q^136 + q^141 + q^144 + q^145 + q^146 + 
        q^149 - q^158 + q^169 + O(q^170),
    q^5 + 2*q^13 - q^20 + 2*q^22 - q^25 + q^30 - 2*q^33 - 2*q^52 - 2*q^53 - 
        2*q^62 - q^65 + 2*q^78 + q^80 - 2*q^88 + 2*q^93 + q^100 - q^110 - q^120 
        + 2*q^132 + q^145 - q^150 - 2*q^158 + q^165 + O(q^170),
    q^6 + q^9 + q^13 + q^22 - q^24 - q^25 + q^30 - q^33 - q^36 + q^45 - q^52 - 
        q^53 - q^54 - q^62 - q^65 + q^78 - 2*q^81 - q^86 - q^88 + q^93 + q^94 + 
        q^96 + q^100 + q^109 - q^110 - q^120 + q^121 - q^129 + q^132 + q^141 + 
        q^144 - q^149 - q^158 + q^165 - q^169 + O(q^170),
    q^8 - q^11 - q^15 - q^17 + q^18 + q^26 + q^27 + q^31 - q^37 - q^39 - q^40 + 
        q^44 - q^58 + q^60 - q^66 - q^68 + q^73 + q^79 + q^85 + q^97 - q^104 - 
        q^106 - q^108 + q^113 - q^124 + q^127 + q^128 - q^137 - q^143 - q^148 - 
        q^153 + q^156 + q^157 + q^159 + O(q^170),
    q^10 - 2*q^11 - q^15 + 2*q^26 + 2*q^31 - 2*q^39 - q^40 + 2*q^44 - q^50 + 
        q^55 + q^60 - 2*q^66 + q^75 + 2*q^79 - 2*q^104 - 2*q^106 - 2*q^124 - 
        q^130 - q^135 - q^155 + 2*q^156 + 2*q^159 + q^160 + O(q^170)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
581
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
581
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
581
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
82
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
581
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
246
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
581
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
246
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
581
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
82
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
581
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
41*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + q^4 - q^11 - q^12 + q^16 - q^17 + 2*q^23 + q^25 + q^27 - q^29 - 
        q^31 + q^33 - q^37 + 2*q^41 - q^44 - q^48 - q^49 + q^51 - q^59 - q^61 + 
        q^64 - q^68 - 2*q^69 - q^75 - q^81 + q^83 + q^87 + 2*q^92 + q^93 + q^100
        + q^108 - q^109 + O(q^110),
    q^7 - q^21 + q^28 - q^49 - q^77 - q^84 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
581
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 41*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-3*a + 1)*q^9 + a*q^10 - 2*a*q^11 + (a - 1)*q^12 + (-a + 1)*q^16 + (-a 
        - 2)*q^17 - 2*q^21 + (a - 1)*q^23 + (2*a - 2)*q^26 + 2*q^27 - a*q^28 + 
        (-2*a + 2)*q^29 + (a - 1)*q^30 + 2*q^31 + (-4*a + 2)*q^33 + (2*a - 
        3)*q^36 + (3*a - 1)*q^37 - a*q^38 + (-a + 1)*q^40 + (a - 1)*q^44 + 
        2*q^48 + (a + 2)*q^49 + (a + 1)*q^51 + (2*a + 2)*q^59 + (a + 1)*q^61 - 
        a*q^63 - q^64 + (2*a - 2)*q^65 + 2*a*q^68 - 2*q^69 - a*q^70 + (a - 
        1)*q^75 + (2*a - 2)*q^77 - 2*q^78 + 2*a*q^81 + (a + 1)*q^84 - 2*q^87 + 
        a*q^94 - a*q^95 + 2*q^99 + 2*q^104 + q^106 - a*q^108 + O(q^110),
    q^2 + q^5 + a*q^6 - a*q^8 + 2*a*q^13 - q^14 + a*q^15 - q^19 - a*q^22 + (-a +
        1)*q^24 - a*q^34 - q^35 + (2*a - 2)*q^39 - a*q^42 + (a - 1)*q^46 + q^47 
        + (-a + 1)*q^53 + q^54 - a*q^55 + a*q^56 - a*q^57 - a*q^62 + (-a + 
        1)*q^66 + (-a + 1)*q^67 + (a - 1)*q^73 + (a - 1)*q^74 - q^79 + (-a + 
        1)*q^80 + a*q^83 - a*q^85 + (a - 1)*q^88 + q^89 - 2*a*q^91 + q^98 + (a -
        1)*q^101 + (-a + 1)*q^102 - q^103 - a*q^105 - q^107 + O(q^110),
    q^3 + q^9 + q^11 - a*q^12 - a*q^17 - a*q^21 + (a - 1)*q^27 + q^29 + (a - 
        1)*q^31 + q^33 - a*q^36 + (a - 1)*q^37 - a*q^44 + (a - 1)*q^48 + (a - 
        1)*q^49 + (a - 1)*q^51 + (a - 1)*q^59 + (a - 1)*q^61 + q^63 + (a - 
        1)*q^68 + (-a + 1)*q^69 - a*q^75 - a*q^77 - q^81 + (a - 1)*q^84 - a*q^87
        - a*q^93 + (2*a - 2)*q^99 + q^108 + q^109 + O(q^110),
    q^4 + (-2*a - 2)*q^9 + q^10 - 2*q^11 + a*q^12 - 2*a*q^16 + (2*a - 3)*q^17 + 
        (3*a - 3)*q^21 + 2*a*q^23 + q^25 + 2*a*q^26 + (-3*a + 3)*q^27 - q^28 - 
        2*a*q^29 + a*q^30 + (-2*a + 2)*q^31 + (-4*a - 2)*q^33 + (4*a - 2)*q^36 +
        (a + 2)*q^37 - q^38 - a*q^40 + (-a + 1)*q^41 + a*q^44 + (-2*a + 2)*q^48 
        + (-2*a + 3)*q^49 + 2*q^51 + (-2*a + 4)*q^59 + (-a + 2)*q^61 + (a - 
        2)*q^63 + (2*a - 2)*q^64 + 2*a*q^65 + 2*q^68 + (2*a - 2)*q^69 - q^70 + 
        a*q^75 + (3*a - 1)*q^77 + (2*a - 2)*q^78 + 3*q^81 + (a - 1)*q^83 + (-a +
        3)*q^84 + (2*a - 3)*q^87 + (-a + 1)*q^92 + a*q^93 + q^94 - q^95 + (-3*a 
        + 3)*q^99 - a*q^100 + (-2*a + 2)*q^104 + (-a + 1)*q^106 - 2*q^108 + 
        O(q^110),
    q^7 + (-2*a + 1)*q^9 + (-a - 1)*q^17 - q^21 - a*q^28 + (-a + 2)*q^29 + (a + 
        1)*q^31 + (-2*a + 1)*q^33 + (a - 2)*q^36 + (2*a - 1)*q^37 + a*q^49 + 
        (2*a - 1)*q^51 + (a + 1)*q^59 + (2*a - 1)*q^61 + (2*a - 1)*q^68 - q^77 +
        a*q^84 + (-a - 1)*q^87 + O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
96
);
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
32
);
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a^3*q^3 + a^2*q^4 + (-a^4 + a^3)*q^7 + a^6*q^9 - a^5*q^12 + (-a^7 - 
        a^2)*q^13 + a^4*q^16 + (-a - 1)*q^19 + (a^7 - a^6)*q^21 + a*q^25 + 
        a*q^27 + (-a^6 + a^5)*q^28 + (a^5 - a)*q^31 - q^36 + (a^7 + a^4)*q^37 + 
        (a^5 - a^2)*q^39 + (a^7 - a^5)*q^43 - a^7*q^48 + (-a^7 + a^6 - 1)*q^49 +
        (-a^4 + a)*q^52 + (a^4 + a^3)*q^57 + (-a^5 + a^3)*q^61 + (a^2 - a)*q^63 
        + a^6*q^64 + (-a^6 - a^3)*q^67 - a^4*q^75 + (-a^3 - a^2)*q^76 + (-a^6 + 
        1)*q^79 - a^4*q^81 + (-a + 1)*q^84 + (a^6 - a^5 - a^3 + a^2)*q^91 + (a^4
        + 1)*q^93 + a*q^97 + a^3*q^100 + a^3*q^108 + (-a^7 - a^3)*q^109 + (-a^7 
        + a^2)*q^111 + (a^7 + 1)*q^112 + (a^5 + 1)*q^117 + a^6*q^121 + (a^7 - 
        a^3)*q^124 + (-a^5 - a^4)*q^127 + (a^2 - 1)*q^129 + (a^5 - a^3)*q^133 + 
        (a^5 + a^2)*q^139 - a^2*q^144 + (a^3 - a^2 + a)*q^147 + (a^6 - a)*q^148 
        + (a^3 + a)*q^151 + (a^7 - a^4)*q^156 + (-a^6 - a^5)*q^157 + (a^6 - 
        1)*q^163 + (-a^6 + a^4 - a)*q^169 + (-a^7 - a^6)*q^171 + (-a^7 - 
        a)*q^172 + (-a^5 + a^4)*q^175 + (-a^7 - a^2)*q^181 + (-a^6 - 1)*q^183 + 
        (-a^5 + a^4)*q^189 + O(q^190),
    q^2 - a^3*q^6 + a^2*q^8 + (-a^4 + a^3)*q^14 + a^6*q^18 - a^5*q^24 + (-a^7 - 
        a^2)*q^26 + a^4*q^32 + (-a - 1)*q^38 + (a^7 - a^6)*q^42 + a*q^50 + 
        a*q^54 + (-a^6 + a^5)*q^56 + (a^5 - a)*q^62 - q^72 + (a^7 + a^4)*q^74 + 
        (a^5 - a^2)*q^78 + (a^7 - a^5)*q^86 - a^7*q^96 + (-a^7 + a^6 - 1)*q^98 +
        (-a^4 + a)*q^104 + (a^4 + a^3)*q^114 + (-a^5 + a^3)*q^122 + (a^2 - 
        a)*q^126 + a^6*q^128 + (-a^6 - a^3)*q^134 - a^4*q^150 + (-a^3 - 
        a^2)*q^152 + (-a^6 + 1)*q^158 - a^4*q^162 + (-a + 1)*q^168 + (a^6 - a^5 
        - a^3 + a^2)*q^182 + (a^4 + 1)*q^186 + O(q^190)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a^3*q^3 + a^2*q^4 + (a^3 - 1)*q^7 - a^2*q^9 - a*q^12 + (-a^3 + a^2)*q^13
        - q^16 + (a + 1)*q^19 + (-a^3 - a^2)*q^21 + a*q^25 + a*q^27 + (-a^2 - 
        a)*q^28 + q^36 + (-a^3 - 1)*q^37 + (a^2 - a)*q^39 + (-a^3 - a)*q^43 - 
        a^3*q^48 + (-a^3 - a^2 + 1)*q^49 + (a - 1)*q^52 + (a^3 - 1)*q^57 + (a^3 
        - a)*q^61 + (a^2 + a)*q^63 - a^2*q^64 + (a^3 - a^2)*q^67 + 2*a^2*q^73 - 
        q^75 + (a^3 + a^2)*q^76 + (-a^2 + 1)*q^79 - q^81 + (a + 1)*q^84 + (a^3 -
        a)*q^91 + a*q^97 + a^3*q^100 + 2*q^103 + a^3*q^108 + (-a^3 + a^2)*q^111 
        + (-a^3 + 1)*q^112 + (-a + 1)*q^117 - a^2*q^121 + (-a - 1)*q^127 + (a^2 
        + 1)*q^129 + (a^3 - a - 2)*q^133 + (a^2 - a)*q^139 + a^2*q^144 + (a^3 + 
        a^2 + a)*q^147 + (-a^2 + a)*q^148 + (a^3 + a)*q^151 + (-a^3 - 1)*q^156 +
        (-a^2 - a)*q^157 + (-a^2 + 1)*q^163 + (-a^2 + a - 1)*q^169 + (-a^3 - 
        a^2)*q^171 + (-a^3 + a)*q^172 + (-a - 1)*q^175 + (-a^3 + a^2)*q^181 + 
        (-a^2 + 1)*q^183 + (-a - 1)*q^189 + O(q^190),
    q^2 + a^3*q^6 + a^2*q^8 + (a^3 - 1)*q^14 - a^2*q^18 - a*q^24 + (-a^3 + 
        a^2)*q^26 - q^32 + (a + 1)*q^38 + (-a^3 - a^2)*q^42 + a*q^50 + a*q^54 + 
        (-a^2 - a)*q^56 + q^72 + (-a^3 - 1)*q^74 + (a^2 - a)*q^78 + (-a^3 - 
        a)*q^86 - a^3*q^96 + (-a^3 - a^2 + 1)*q^98 + (a - 1)*q^104 + (a^3 - 
        1)*q^114 + (a^3 - a)*q^122 + (a^2 + a)*q^126 - a^2*q^128 + (a^3 - 
        a^2)*q^134 + 2*a^2*q^146 - q^150 + (a^3 + a^2)*q^152 + (-a^2 + 1)*q^158 
        - q^162 + (a + 1)*q^168 + (a^3 - a)*q^182 + O(q^190)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 16*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 24*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 - q^4 + (-a + 1)*q^7 - q^9 + a*q^12 + (-a - 1)*q^13 + q^16 + (a + 
        1)*q^19 + (-a - 1)*q^21 + a*q^25 + a*q^27 + (a - 1)*q^28 + 2*a*q^31 + 
        q^36 + (-a + 1)*q^37 + (a - 1)*q^39 - a*q^48 - a*q^49 + (a + 1)*q^52 + 
        (-a + 1)*q^57 + (a - 1)*q^63 - q^64 + (-a - 1)*q^67 - 2*q^73 + q^75 + 
        (-a - 1)*q^76 + q^81 + (a + 1)*q^84 - 2*q^91 + 2*q^93 + a*q^97 - a*q^100
        + 2*q^103 - a*q^108 - 2*a*q^109 + (-a - 1)*q^111 + (-a + 1)*q^112 + (a +
        1)*q^117 - q^121 - 2*a*q^124 + (a + 1)*q^127 + 2*q^133 + (a - 1)*q^139 -
        q^144 - q^147 + (a - 1)*q^148 + (-a + 1)*q^156 + (a - 1)*q^157 + a*q^169
        + (-a - 1)*q^171 + (a + 1)*q^175 + (-a - 1)*q^181 + (a + 1)*q^189 + 
        O(q^190),
    q^2 - a*q^6 - q^8 + (-a + 1)*q^14 - q^18 + a*q^24 + (-a - 1)*q^26 + q^32 + 
        (a + 1)*q^38 + (-a - 1)*q^42 + a*q^50 + a*q^54 + (a - 1)*q^56 + 2*a*q^62
        + q^72 + (-a + 1)*q^74 + (a - 1)*q^78 - a*q^96 - a*q^98 + (a + 1)*q^104 
        + (-a + 1)*q^114 + (a - 1)*q^126 - q^128 + (-a - 1)*q^134 - 2*q^146 + 
        q^150 + (-a - 1)*q^152 + q^162 + (a + 1)*q^168 - 2*q^182 + 2*q^186 + 
        O(q^190)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 32*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
582
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 48*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
190
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + q^4 + q^9 - q^12 + q^16 - q^25 - q^27 - 2*q^31 + q^36 - 2*q^43 - 
        q^48 + q^49 - 2*q^61 + q^64 + 2*q^73 + q^75 + 2*q^79 + q^81 + 2*q^93 - 
        q^97 - q^100 + 2*q^103 - q^108 - 2*q^109 + q^121 - 2*q^124 + 2*q^129 + 
        q^144 - q^147 - 2*q^151 + 2*q^163 + q^169 - 2*q^172 + 2*q^183 + 
        O(q^190),
    q^2 - q^6 + q^8 + q^18 - q^24 + q^32 - q^50 - q^54 - 2*q^62 + q^72 - 2*q^86 
        - q^96 + q^98 - 2*q^122 + q^128 + 2*q^146 + q^150 + 2*q^158 + q^162 + 
        2*q^186 + O(q^190)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
260
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
130
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^11 - a^6)*q^3 + a*q^4 + (a^6 - a^2)*q^5 + (a^11 - a^10 - a^8 + a^7 -
        a^6 + a^5 - 2*a^4 + a^3 - a^2 + a - 1)*q^9 - a^3*q^11 + (-a^11 + a^10 - 
        a^9 + a^8 - 2*a^7 + a^6 - a^5 + a^4 - a^3 + a^2 - a + 1)*q^12 + (-a^11 +
        a^10 - a^9 + 2*a^8 - a^7 + a^6 - a^5 + 2*a^4 - a^3 + a^2 - a)*q^15 + 
        a^2*q^16 + (a^7 - a^3)*q^20 + (a^10 + a^3)*q^23 + (a^11 - a^10 + a^9 - 
        2*a^8 + a^7 - a^6 + a^5 + a^3 - a^2 + a - 1)*q^25 + (a^10 - a^7 + a^5 - 
        a^2)*q^27 + (-a^11 + a^9)*q^31 + (a^9 - a)*q^33 + (-a^10 - a^5 - 1)*q^36
        + (a^11 - a^6)*q^37 - a^4*q^44 + (a^11 - a^10 + a^6 - a^5 + a^2 + 
        a)*q^45 + (a^11 + a^7)*q^47 + (-a^8 + 1)*q^48 - a*q^49 - a^5*q^53 + 
        (-a^9 + a^5)*q^55 + (-a^10 - a^8)*q^59 + (a^9 + a^5 - a + 1)*q^60 + 
        a^3*q^64 + (a^8 + a^7)*q^67 + (-a^9 + a^8 + a^3 + a)*q^69 + (a^6 + 
        a^3)*q^71 + (-a^6 + a^5 + a^2 - a)*q^75 + (a^8 - a^4)*q^80 + (-a^11 + 
        a^8 - a^5 + a^3 - 1)*q^81 + (-a^8 - a^2)*q^89 + (a^11 + a^4)*q^92 + 
        (-a^9 + a^7 - a^4 + a^2)*q^93 + (-a^7 - a)*q^97 + (a^11 - a^10 + a^9 - 
        a^8 + 2*a^7 - a^6 + a^5 - a^4 + a^3 + a - 1)*q^99 + (-a^9 + a^5 - 
        1)*q^100 + (-a^10 - a^7)*q^103 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
130
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^11 - a^10 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^3 + 
        a^2*q^4 + (a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 + a^3 - a^2 + a - 
        1)*q^5 + (-a^11 + a^8 - a^5)*q^9 + a^6*q^11 + (-a^11 - a)*q^12 + (-a^11 
        + a^8 - a^3 + 1)*q^15 + a^4*q^16 + (a^6 - a)*q^20 + (-a^7 + a^6)*q^23 + 
        (-a^11 + a^8 - a^3)*q^25 + (a^10 - a^7 + a^4 - a)*q^27 + (-a^9 - 
        a^5)*q^31 + (-a^5 + a^2)*q^33 + (a^10 - a^7 + 1)*q^36 + (a^11 - a^10 - 
        a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^37 + a^8*q^44 + (a^11
        - a^8 - a^6 + a^5 + a^3 + a - 1)*q^45 + (-a^9 - a)*q^47 + (-a^3 + 
        1)*q^48 + a^2*q^49 + a^10*q^53 + (a^10 - a^5)*q^55 + (-a^7 - a^3)*q^59 +
        (a^10 - a^5 + a^2 + 1)*q^60 + a^6*q^64 + (-a^3 - a)*q^67 + (a^6 - a^5 - 
        a^3 + a^2)*q^69 + (a^11 - a^10 + a^9 - a^8 + a^7 + a^5 - a^4 + a^3 - a^2
        + a - 1)*q^71 + (a^11 + a^9 - a^8 - a^7 - a^6 + a^5 + a^3 + a - 1)*q^75 
        + (a^8 - a^3)*q^80 + (a^10 - a^9 + a^6 - a^3 + 1)*q^81 + (a^4 - 
        a^3)*q^89 + (-a^9 + a^8)*q^92 + (a^8 - a^5 + a^4 - a)*q^93 + (a^2 - 
        a)*q^97 + (-a^11 + a^4 - a)*q^99 + (a^10 - a^5 + 1)*q^100 + (-a^7 - 
        a)*q^103 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 13*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
583
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^37 - q^38 - q^44 - q^47 + q^49 - q^59 - q^64 + q^81 - 
        q^82 - q^89 + O(q^106),
    q^2 + q^18 - q^19 - q^22 - q^32 - q^41 + q^50 - q^61 + q^73 - q^76 + q^79 + 
        q^83 + q^98 + q^101 + O(q^106),
    q^4 - q^11 - q^16 + q^36 + q^37 - q^38 + q^47 - q^53 + q^59 - q^82 + q^89 - 
        2*q^97 - q^99 + q^100 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
72
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
72
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^4*q^2 + (-a^5 - a)*q^3 + a^8*q^4 + (a^9 + a^5)*q^6 + (-a^6 + 1)*q^8 + 
        (a^10 + a^6 + a^2)*q^9 + (a^7 + a^6 - 1)*q^11 + (-a^9 - a^7 + a)*q^12 + 
        (a^10 - a^4)*q^16 + (a^3 - 1)*q^17 + (-a^10 - a^8 - a^6 + a^2)*q^18 + 
        (-2*a^10 + a^4)*q^19 + (-a^11 - a^10 + a^4)*q^22 + (a^11 + a^7 - a^5 - 
        a)*q^24 + a*q^25 + (-a^11 - a^9 - a^7)*q^27 + a^2*q^32 + (-a^11 - a^8 - 
        a^7 - a^6 + a^5 + a + 1)*q^33 + (-a^7 + a^4)*q^34 + (a^10 + a^8 - a^2 - 
        1)*q^36 + (a^8 - 2*a^2)*q^38 + (-a^9 + a^7 - a)*q^41 + (a^11 + a^4)*q^43
        + (a^9 - a^3 - a^2)*q^44 + (-a^11 + a^5 + a^3)*q^48 + (-a^9 + a^3)*q^49 
        - a^5*q^50 + (-a^8 + a^5 - a^4 + a)*q^51 + (a^11 + a^9 + a^7 - a^3 - 
        a)*q^54 + (2*a^11 + a^9 - a^5 - 2*a^3)*q^57 + (a^9 - a^8 + a^2)*q^59 - 
        a^6*q^64 + (a^11 + a^10 + a^6 - a^5 - a^4 - a^3 - 1)*q^66 + (-a^11 + a^9
        + a^5 - a^3)*q^67 + (a^11 - a^8)*q^68 + (-a^8 + a^4 + a^2 + 1)*q^72 + 
        a^8*q^73 + (-a^6 - a^2)*q^75 + (a^6 + 1)*q^76 + (a^10 + a^8 + a^6 - a^2 
        - 1)*q^81 + (-a^11 + a^7 + a^5 - a)*q^82 + (a^6 + a^3)*q^83 + (-a^9 - 
        a^8 + a^3)*q^86 + (a^6 + a)*q^88 + (-a^7 - a^3)*q^96 + (a^10 + a^8 - a^4
        - a^2)*q^97 - a*q^98 + (a^11 + a^9 + a^8 + a^7 - a^5 - a^4 - a^2 - a - 
        1)*q^99 + a^9*q^100 + (-a^9 + a^8 + a^6 - a^5 - 1)*q^102 + (-a^6 + 
        a^5)*q^107 + (-a^11 - a^9 + a^5 + a^3 + a)*q^108 + (-a^11 - a^8 + 
        a^2)*q^113 + (-a^9 + a^7 + 2*a^3 + a)*q^114 + (-a^7 + a - 1)*q^118 + 
        (a^8 - a^6 - a^2 - a)*q^121 + (a^10 + 1)*q^123 + a^10*q^128 + (-a^10 - 
        a^9 - a^6 - a^5 + a^4 + 1)*q^129 + (a^10 - a^9 - a^4)*q^131 + (-a^10 + 
        a^7 + a^4 + a^3 + a^2)*q^132 + (-a^3 + a)*q^134 + (-a^9 + a^6 + a^3 - 
        1)*q^136 + (a^11 - a^7 - a^5 + a)*q^137 + (-a^7 + a^2 + a)*q^139 + 
        O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^5 + 2*a^2)*q^5 + (a^3 - 1)*q^9 + (-a^5 - 1)*q^13 + (-a^2 - a)*q^17 +
        2*a*q^25 + (a^5 - a^3)*q^29 + (a^4 + a^3 - a)*q^37 + (a^4 - a^3 - a + 
        1)*q^41 + (2*a^5 - a^2)*q^45 + (-a^3 + 1)*q^49 + (a^3 + a)*q^61 + (a^5 -
        2*a^4 - 2*a^2 + a)*q^65 - a^5*q^73 - a^3*q^81 + (-a^4 - a^3 - a - 
        1)*q^85 + (a^5 + a^3 - a^2 - 1)*q^89 + (-a^5 - a^4 + a^2)*q^97 + (a^3 - 
        a)*q^101 + a^5*q^109 + (-a^4 + a - 1)*q^113 + (-a^3 + a^2 + 1)*q^117 + 
        a*q^121 + (a^3 + 1)*q^125 + (-a^3 + 1)*q^137 + O(q^142),
    q^2 - a^4*q^4 + (a^5 - a^2)*q^8 + (-a^5 + 2*a^2)*q^10 + a^3*q^16 + (a^3 - 
        1)*q^18 + (-2*a^3 + 1)*q^20 + (-a^5 - 1)*q^26 + (-a^4 + a)*q^32 + (-a^2 
        - a)*q^34 + a*q^36 + (a^4 - 2*a)*q^40 + 2*a*q^50 + (a^4 - 1)*q^52 + (a^5
        - a^3)*q^58 - a^2*q^64 + (a^5 + a^3 - 1)*q^68 - a^5*q^72 + (a^4 + a^3 - 
        a)*q^74 + (a^5 + a^2)*q^80 + (a^4 - a^3 - a + 1)*q^82 + (2*a^5 - 
        a^2)*q^90 + (-a^3 + 1)*q^98 - 2*a^5*q^100 + (-a^5 + a^4 + a^2)*q^104 + 
        (a^4 - a + 1)*q^116 + (a^3 + a)*q^122 + (a^3 - 1)*q^128 + (a^5 - 2*a^4 -
        2*a^2 + a)*q^130 + (a + 1)*q^136 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^4*q^2 + (a^5 + a)*q^3 + (a^5 - a^2)*q^4 + (a^5 - 1)*q^6 - a^3*q^8 + 
        (a^3 + a^2 - a - 1)*q^9 + (a^4 - a^3 - a)*q^11 + (-a^4 - 1)*q^12 + (-a^4
        + a)*q^16 + (a^3 + 1)*q^17 + (-a^5 + a^3 - a - 1)*q^18 - a^4*q^19 + 
        (-a^4 - a^2 + a)*q^22 + (-a^5 - a^4 + a^2)*q^24 + a*q^25 + (a^4 - a^2 - 
        a + 1)*q^27 + a^2*q^32 + (-a^4 - a^3)*q^33 + (2*a^4 - a)*q^34 + (-a^5 - 
        a + 1)*q^36 + (-a^5 + a^2)*q^38 + (-a^4 - 1)*q^41 + (a^4 - a^2)*q^43 + 
        (-a^3 + a^2 + 1)*q^44 + (-a^5 + a^3 + a^2)*q^48 + (-a^3 + 1)*q^49 + 
        a^5*q^50 + (2*a^5 + a^4 - a^2 + a)*q^51 + (a^4 - a^3 - a^2 + 1)*q^54 + 
        (-a^5 + 1)*q^57 + (-a^5 - 1)*q^59 + (a^3 - 1)*q^64 + (-a^5 - a^4 + a^2 +
        a)*q^66 + (-a^5 - a^3 + a^2 + 1)*q^67 + (a^5 - 2*a^2)*q^68 + (-a^5 + a^4
        + 1)*q^72 + (a^5 - a^2)*q^73 + (a^3 + a^2 - 1)*q^75 + a^3*q^76 + (a^5 - 
        a^3 + a)*q^81 + (-a^5 - a^4 + a^2)*q^82 + (2*a^3 - 1)*q^83 + (a^5 - a^3 
        - a^2 + 1)*q^86 + (a^3 + a - 1)*q^88 + (2*a^4 - 2*a)*q^89 + (a^4 + a^3 -
        a)*q^96 + (-a^5 - a^4 + a)*q^97 + a*q^98 + (-2*a^5 + a^2)*q^99 - q^100 +
        (2*a^5 - a^3 - a^2 - 1)*q^102 + (a^5 + a^3 - 1)*q^107 + (a^5 - a^3 - a^2
        + a + 1)*q^108 + (-a^5 - a^2)*q^113 + (a^4 + 1)*q^114 + (-a^4 + 1)*q^118
        + (-a^5 + a^3 + a - 1)*q^121 + (-2*a^5 - a + 1)*q^123 - a*q^128 + (a^5 -
        a^4 - a^3 + a - 1)*q^129 + (-a^4 + a - 1)*q^131 + (a^3 + a^2)*q^132 + 
        (a^3 + a)*q^134 + (-2*a^3 + 1)*q^136 + (-a^5 - a^4 + a^2)*q^137 + (-a^4 
        + a^2)*q^139 + O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^2 + 1)*q^2 - a^3*q^3 - a^2*q^4 - a*q^6 - q^8 + (-a + 1)*q^11 + (a^3 
        - a)*q^12 + (a^2 - 1)*q^16 + (a^3 - 1)*q^17 + (a^3 - a^2 - a + 1)*q^22 +
        a^3*q^24 + a*q^25 - a^3*q^27 + a^2*q^32 + (-a^3 + a^2 - 1)*q^33 + (a^2 +
        a - 1)*q^34 + (a^3 + a)*q^41 + (-a^3 + a^2 + a - 1)*q^43 + (a^3 - 
        a^2)*q^44 + a*q^48 - a^3*q^49 + (-a^3 + a)*q^50 + (a^3 + 1)*q^51 - 
        a*q^54 + (-a^3 - a^2)*q^59 + q^64 + (a^2 - a)*q^66 + a*q^67 + (-a^3 + 
        a^2 + a)*q^68 - a^2*q^73 + (-a^2 + 1)*q^75 - q^81 + (-a^3 + 2*a)*q^82 + 
        (a^3 - 1)*q^83 + (-a^3 + a^2)*q^86 + (a - 1)*q^88 + (-a^3 + a)*q^96 + 
        (2*a^2 - 1)*q^97 - a*q^98 - a^3*q^100 + (-a^2 + a + 1)*q^102 + (a^3 - a 
        + 1)*q^107 + (a^3 - a)*q^108 + (a^3 - a^2 - a)*q^113 + (-a - 1)*q^118 + 
        (a^2 - a + 1)*q^121 + (-a^2 + 2)*q^123 + (-a^2 + 1)*q^128 + (-a^2 + 
        a)*q^129 + (a^3 + a^2 - 1)*q^131 + (a^3 - a + 1)*q^132 + (-a^3 + 
        a)*q^134 + (-a^3 + 1)*q^136 + (a^3 - 2*a)*q^137 + (a^2 - a)*q^139 + 
        O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^5 - a^3*q^9 + (-a + 1)*q^13 + (a^4 + a^2)*q^17 + (a^3 - a - 1)*q^29 
        + (-a^5 + a^3 - 1)*q^37 + (-a^5 - a^3)*q^41 - a^4*q^45 - a^3*q^49 + 
        (2*a^5 - 2*a^2)*q^53 + (a^3 + a^2 - 1)*q^61 + (-a^2 + a)*q^65 - a*q^73 +
        (a^3 - 1)*q^81 + (a^5 + a^3)*q^85 + (-a^4 - a^3 + a)*q^89 + (a^5 - a^4 -
        a^2 + a)*q^97 + (a^3 + a^2 - 1)*q^101 + a*q^109 + (-a^5 + 1)*q^113 + 
        (a^4 - a^3)*q^117 + a^2*q^121 - a^3*q^125 + a^3*q^137 + O(q^142),
    q^2 + (a^5 - a^2)*q^4 + (-a^4 + a)*q^8 + a*q^10 + (a^3 - 1)*q^16 - a^3*q^18 
        - q^20 + (-a + 1)*q^26 - a^5*q^32 + (a^4 + a^2)*q^34 + a^2*q^36 + (-a^5 
        + a^2)*q^40 + (a^5 - a^2 + 1)*q^52 + (a^3 - a - 1)*q^58 + a^4*q^64 + 
        (-a^3 - a)*q^68 - a*q^72 + (-a^5 + a^3 - 1)*q^74 + (a^4 - a)*q^80 + 
        (-a^5 - a^3)*q^82 - a^4*q^90 - a^3*q^98 + (a^5 - a^4 - a^2 + a)*q^104 + 
        (2*a^5 - 2*a^2)*q^106 + (-a^5 + 1)*q^116 + (a^3 + a^2 - 1)*q^122 - 
        a^3*q^128 + (-a^2 + a)*q^130 + (a^2 + 1)*q^136 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^5 - a^2)*q^2 + (a^2 - a)*q^3 + (-a^4 + a)*q^4 + (-a + 1)*q^6 + (a^3 -
        1)*q^8 + (a^4 - a^3 + a^2)*q^9 + (-a^5 + a^3 - 1)*q^11 + (a^5 - a^2 + 
        1)*q^12 - a^5*q^16 + a^3*q^17 + (-a^3 + a^2 - a)*q^18 + (-a^5 + 
        a^2)*q^19 + (-a^5 + a^4)*q^22 + (a^5 - a^4 - a^2 + a)*q^24 + a^2*q^25 + 
        (-a^5 + a^4 - 1)*q^27 + a^4*q^32 + (a^5 - 2*a^4 + a^3 - a^2 + 2*a - 
        1)*q^33 - a^2*q^34 + (a^2 - a + 1)*q^36 + (a^4 - a)*q^38 + (a^5 - a^2 + 
        1)*q^41 + (a^5 + a^4 - a^2)*q^43 + (a^4 - a^3)*q^44 + (-a^4 + a^3 + a - 
        1)*q^48 - a^3*q^49 - a*q^50 + (a^5 - a^4)*q^51 + (-a^5 + a^4 - a^3 + 
        a^2)*q^54 + (a - 1)*q^57 + (-a + 1)*q^59 - a^3*q^64 + (-a^5 - a^4 + 
        2*a^3 + a - 2)*q^66 + (-a^4 - a^3 + a)*q^67 + a*q^68 + (a^5 - a^2 - a + 
        1)*q^72 + (-a^4 + a)*q^73 + (a^4 - a^3)*q^75 + (-a^3 + 1)*q^76 + (a^3 - 
        a^2 + a - 1)*q^81 + (a^5 - a^4 - a^2 + a)*q^82 - q^83 + (-a^4 - a^3 + 
        a)*q^86 + (-a^3 + a^2)*q^88 - 2*a^5*q^89 + (-a^5 + a^3 - 1)*q^96 + (-a^5
        - a)*q^97 + a^2*q^98 + (2*a^5 - a^4 - 2*a^2 + 2)*q^99 + q^100 + (-a^4 + 
        a^3)*q^102 + (-a^3 - a)*q^107 + (a^4 - a^3 + a^2 - a)*q^108 + (a^4 - 
        a)*q^113 + (-a^5 + a^2 - 1)*q^114 + (a^5 - a^2 + 1)*q^118 + (-a^3 + a^2 
        - a)*q^121 + (a^2 - 2*a + 1)*q^123 + a^2*q^128 + (-a^5 + a^3 - a)*q^129 
        + (-a^5 + 1)*q^131 + (-2*a^5 + a^4 + a^3 - 1)*q^132 + (a^3 + a^2 - 
        1)*q^134 - q^136 + (a^5 - a^4 - a^2 + a)*q^137 + (a^5 + a^4 - a^2)*q^139
        + O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 + (a - 2)*q^13 + (-2*a + 1)*q^17 - a*q^25 + (-a + 2)*q^29 + (a - 
        1)*q^37 + (a - 1)*q^41 - q^49 + (a - 1)*q^61 + (a - 1)*q^73 + q^81 + 
        a*q^89 + q^97 + (-a - 1)*q^101 + (2*a - 2)*q^109 + (-a - 1)*q^113 + (a -
        2)*q^117 + a*q^121 + 2*q^137 + O(q^142),
    q^2 + a*q^4 + (a - 1)*q^8 - q^16 + q^18 + (a - 2)*q^26 - a*q^32 + (-2*a + 
        1)*q^34 + a*q^36 - a*q^50 + (-a - 1)*q^52 + (-a + 2)*q^58 + (-a + 
        1)*q^64 + (-a + 2)*q^68 + (a - 1)*q^72 + (a - 1)*q^74 + (a - 1)*q^82 - 
        q^98 + (-a + 1)*q^100 + (-2*a + 1)*q^104 + (a + 1)*q^116 + (a - 1)*q^122
        + q^128 + (a + 1)*q^136 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + q^3 + (a - 1)*q^4 - a*q^6 + q^8 + (a + 1)*q^11 + (a - 1)*q^12 - 
        a*q^16 - 2*a*q^19 + (-2*a + 1)*q^22 + q^24 + a*q^25 - q^27 + (a - 
        1)*q^32 + (a + 1)*q^33 + (2*a - 2)*q^38 + (a - 1)*q^41 + (-2*a + 1)*q^43
        + (a - 2)*q^44 - a*q^48 - q^49 + (-a + 1)*q^50 + a*q^54 - 2*a*q^57 + (a 
        - 2)*q^59 + q^64 + (-2*a + 1)*q^66 - a*q^67 + (a - 1)*q^73 + a*q^75 + 
        2*q^76 - q^81 + q^82 + (a - 2)*q^86 + (a + 1)*q^88 + 2*a*q^89 + (a - 
        1)*q^96 - q^97 + a*q^98 - q^100 + (-a + 2)*q^107 + (-a + 1)*q^108 + (2*a
        - 2)*q^114 + (a + 1)*q^118 + 2*a*q^121 + (a - 1)*q^123 - a*q^128 + (-2*a
        + 1)*q^129 + (-a - 1)*q^131 + (a - 2)*q^132 + (a - 1)*q^134 + q^137 + 
        (2*a - 1)*q^139 + O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 18*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^2 - 2*a*q^3 + q^4 + 2*a*q^6 - q^8 - 3*q^9 + (-a + 1)*q^11 - 2*a*q^12 +
        q^16 + (-a - 1)*q^17 + 3*q^18 + (a - 1)*q^22 + 2*a*q^24 + a*q^25 + 
        4*a*q^27 - q^32 + (-2*a - 2)*q^33 + (a + 1)*q^34 - 3*q^36 + (-a + 
        1)*q^43 + (-a + 1)*q^44 - 2*a*q^48 + a*q^49 - a*q^50 + (2*a - 2)*q^51 - 
        4*a*q^54 + (a + 1)*q^59 + q^64 + (2*a + 2)*q^66 - 2*a*q^67 + (-a - 
        1)*q^68 + 3*q^72 + q^73 + 2*q^75 + 5*q^81 + (-a - 1)*q^83 + (a - 1)*q^86
        + (a - 1)*q^88 + 2*a*q^96 - a*q^98 + (3*a - 3)*q^99 + a*q^100 + (-2*a + 
        2)*q^102 + (a + 1)*q^107 + 4*a*q^108 + (a + 1)*q^113 + (-a - 1)*q^118 - 
        a*q^121 - q^128 + (-2*a - 2)*q^129 + (-a + 1)*q^131 + (-2*a - 2)*q^132 +
        2*a*q^134 + (a + 1)*q^136 + (-a - 1)*q^139 + O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 24*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - 2*a*q^5 + q^9 + (-a + 1)*q^13 - q^17 + (3*a - 3)*q^25 + (-a + 1)*q^29 + 
        a*q^37 + a*q^41 - 2*a*q^45 + q^49 + (2*a - 2)*q^53 + a*q^61 - 2*q^65 - 
        a*q^73 + q^81 + 2*a*q^85 + (-a + 1)*q^89 - q^97 + a*q^101 - 2*a*q^109 + 
        a*q^113 + (-a + 1)*q^117 + (a - 1)*q^121 + 4*q^125 + 2*q^137 + O(q^142),
    q^2 + (a - 1)*q^4 - a*q^8 - 2*a*q^10 + q^16 + q^18 + 2*q^20 + (-a + 1)*q^26 
        + (a - 1)*q^32 - q^34 + (a - 1)*q^36 + (2*a - 2)*q^40 + (3*a - 3)*q^50 +
        a*q^52 + (-a + 1)*q^58 - a*q^64 + (-a + 1)*q^68 - a*q^72 + a*q^74 - 
        2*a*q^80 + a*q^82 - 2*a*q^90 + q^98 - 3*a*q^100 - q^104 + (2*a - 
        2)*q^106 + a*q^116 + a*q^122 + q^128 - 2*q^130 + a*q^136 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 24*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^2 - q^3 - a*q^4 + (-a + 1)*q^6 + q^8 + a*q^11 + a*q^12 + (a - 
        1)*q^16 + 2*q^17 + (2*a - 2)*q^19 - q^22 - q^24 + (a - 1)*q^25 + q^27 - 
        a*q^32 - a*q^33 + (2*a - 2)*q^34 - 2*a*q^38 + a*q^41 - q^43 + (-a + 
        1)*q^44 + (-a + 1)*q^48 + q^49 - a*q^50 - 2*q^51 + (a - 1)*q^54 + (-2*a 
        + 2)*q^57 + (-a + 1)*q^59 + q^64 + q^66 + (-a + 1)*q^67 - 2*a*q^68 - 
        a*q^73 + (-a + 1)*q^75 + 2*q^76 - q^81 - q^82 + 2*q^83 + (-a + 1)*q^86 +
        a*q^88 + (2*a - 2)*q^89 + a*q^96 - q^97 + (a - 1)*q^98 + q^100 + (-2*a +
        2)*q^102 + (-a + 1)*q^107 - a*q^108 - 2*a*q^113 + 2*a*q^114 + a*q^118 - 
        a*q^123 + (a - 1)*q^128 + q^129 + a*q^131 + (a - 1)*q^132 + a*q^134 + 
        2*q^136 - q^137 - q^139 + O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 36*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 + q^25 - 2*q^37 - 2*q^41 - q^49 - 2*q^61 + q^73 + q^81 + 2*q^89 - 
        2*q^97 + 2*q^109 - q^121 + 2*q^137 + O(q^142),
    q^2 - q^4 + q^8 - q^16 + q^18 + q^32 - q^36 + q^50 - q^64 + q^72 - 2*q^74 - 
        2*q^82 - q^98 - q^100 - 2*q^122 + q^128 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
584
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 36*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 + q^16 - q^18 - q^19 + q^25 - q^35 - q^38 + q^49 + q^64 - q^65 - 
        q^70 - q^72 - q^75 - q^76 - q^97 + q^100 - q^105 + q^121 - q^123 - q^130
        - q^140 + O(q^142),
    q^2 + q^8 - q^9 - q^19 + q^32 - q^35 - q^36 - q^38 + q^50 - q^65 - q^70 + 
        q^73 + q^75 - q^76 + q^81 + 2*q^91 - q^97 + q^98 + q^105 + q^123 + q^128
        - q^130 - q^140 + O(q^142),
    q^3 - q^9 + q^12 - q^18 - q^19 + q^27 - q^35 - q^36 - q^38 + q^48 + q^49 + 
        q^50 + q^54 + q^57 - q^72 - q^76 - q^81 + q^82 + q^89 - q^97 + q^108 + 
        q^114 - q^123 - q^130 + q^134 - q^140 + O(q^142),
    q^5 - q^13 - q^14 - q^15 + q^20 + q^30 + q^31 - q^52 - q^56 + q^58 - q^60 + 
        q^63 + q^80 + q^87 - q^90 - q^93 + q^94 - q^95 - q^101 - q^103 - q^106 +
        q^120 + q^124 + q^125 + q^133 + q^141 + O(q^142),
    q^6 - q^9 - q^18 - q^19 + q^24 + q^25 + q^27 - q^36 - q^38 + q^41 + q^54 + 
        q^57 - q^65 + q^67 - q^70 - q^72 - q^75 - q^76 - q^81 + q^91 + q^96 - 
        q^97 + q^98 + q^100 + q^108 + q^114 - q^123 + q^137 + O(q^142),
    q^7 - q^13 - q^14 - q^15 + q^21 + q^26 + q^28 + q^30 - q^39 - q^42 - q^52 + 
        q^53 - q^56 - q^60 + q^63 + q^78 + q^84 + q^87 - q^93 - q^101 - q^103 + 
        q^104 - q^106 + q^112 - q^117 + q^120 + q^125 - q^126 + q^141 + 
        O(q^142),
    q^10 - q^13 - q^14 + q^21 + q^29 - q^39 + q^40 - q^42 - q^45 + q^47 - q^52 -
        q^56 + q^62 + q^63 + q^78 + q^84 - q^95 - q^101 - q^103 - q^106 + q^116 
        + q^133 + O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + (a - 1)*q^7 + a*q^13 - q^16 + (-a - 1)*q^19 - a*q^25 + (a + 
        1)*q^28 + (a + 1)*q^31 + (-a + 1)*q^37 - a*q^49 + q^52 + a*q^64 + (-a - 
        1)*q^67 + (a - 1)*q^73 + (a - 1)*q^76 + (-a - 1)*q^91 + (a + 1)*q^97 - 
        q^100 + (-a - 1)*q^109 + (-a + 1)*q^112 + a*q^121 + (-a + 1)*q^124 + 
        2*a*q^127 + 2*q^133 + 2*q^139 + (-a - 1)*q^148 + (-a + 1)*q^151 + 
        O(q^154),
    q^5 - a*q^20 + (a - 1)*q^35 + a*q^65 - q^80 + (-a - 1)*q^95 - a*q^125 + (a +
        1)*q^140 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 3*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^4 - q^13 + q^16 - q^25 + 2*q^43 + q^49 + q^52 - 2*q^61 - q^64 - 2*q^79
        + q^100 + 2*q^103 - q^121 - 2*q^127 + 2*q^139 + O(q^154),
    q^3 - q^9 - q^12 + q^27 + q^36 - q^39 + q^48 - q^75 - q^81 - q^108 + q^117 +
        2*q^129 - q^144 + q^147 + O(q^154),
    q^5 - q^20 - q^65 + q^80 - q^125 + O(q^154),
    q^15 - q^45 - q^60 + q^135 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + 1/2*(-a - 1)*q^10 + 1/2*(a - 1)*q^13 + 1/2*(-a - 1)*q^25 + q^40 + (a - 
        1)*q^43 + a*q^49 + 1/2*(-a - 1)*q^52 + 1/2*(-a - 1)*q^55 + q^61 + a*q^64
        - a*q^79 + (-a - 1)*q^82 + (-a + 1)*q^88 + a*q^94 + 1/2*(-a + 1)*q^100 +
        (-a + 1)*q^103 + (a - 1)*q^118 + (a + 1)*q^127 + 1/2*(a + 1)*q^130 + (a 
        + 1)*q^142 + O(q^154),
    q^2 + (-a - 1)*q^8 + a*q^11 + (a - 1)*q^20 - a*q^26 - q^32 + q^41 + (a + 
        2)*q^44 - a*q^47 + q^50 - a*q^59 - q^65 - q^71 + (a + 1)*q^80 + q^83 + 
        (a - 1)*q^86 - q^89 + a*q^98 + (-a - 1)*q^104 - 2*a*q^110 + (a - 
        1)*q^122 - a*q^125 + q^137 + a*q^143 + a*q^149 + O(q^154),
    q^4 + 1/2*(-a - 1)*q^10 + 1/2*(a + 1)*q^13 - a*q^16 + (a - 1)*q^22 + 1/2*(a 
        - 1)*q^25 - q^40 + 1/2*(-a + 1)*q^52 + 1/2*(a + 1)*q^55 - a*q^61 - q^79 
        + (a + 1)*q^88 + q^94 + 1/2*(a + 1)*q^100 - a*q^121 + (-a + 1)*q^127 + 
        1/2*(-a - 1)*q^130 + O(q^154),
    q^5 + 2*a*q^8 + (-a + 1)*q^11 + q^20 + (a - 1)*q^26 + (-a + 1)*q^41 + (-a - 
        1)*q^44 - 2*q^47 + (-a - 1)*q^50 + (-a - 1)*q^59 + a*q^65 + (a - 1)*q^71
        - a*q^80 - 2*a*q^83 + (a + 1)*q^89 + (a - 1)*q^110 + 2*q^122 - q^125 + 
        (a + 1)*q^149 + O(q^154)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
585
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^4 - q^13 - q^16 + 2*q^22 + q^25 - q^49 + q^52 - 2*q^55 + q^64 - 2*q^82
        + 2*q^94 - q^100 + 2*q^118 + q^121 + 2*q^127 - 2*q^130 + 2*q^139 - 
        2*q^142 + O(q^154),
    q^2 - q^11 - q^26 - q^32 + q^41 + q^44 - q^47 + q^50 - q^59 + q^65 + q^71 + 
        q^83 + q^89 - q^98 - 2*q^110 - q^125 + q^137 - q^143 - q^149 + O(q^154),
    q^3 - q^12 - q^27 + q^30 - q^48 + q^90 + q^108 + q^117 - q^147 + O(q^154),
    q^5 - 2*q^11 - q^20 - 2*q^26 + 2*q^41 + 2*q^44 + 2*q^50 - 2*q^59 + q^65 + 
        2*q^71 - q^80 + 2*q^89 - 2*q^110 - q^125 - 2*q^149 + O(q^154),
    q^6 + q^18 - q^33 - q^45 - q^54 - q^78 - q^96 + q^99 + q^123 + q^132 - q^141
        + q^150 + O(q^154),
    q^9 - q^30 - q^36 - q^39 + 2*q^66 + q^75 - q^81 + q^90 - q^144 + O(q^154),
    q^10 + q^13 - 2*q^22 - q^25 - q^52 + q^55 + 2*q^82 + q^100 - 2*q^118 - 
        2*q^127 + q^130 + 2*q^142 + O(q^154),
    q^15 + 2*q^18 - 2*q^33 - q^45 - q^60 - 2*q^78 + 2*q^123 + 2*q^132 - q^135 + 
        2*q^150 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
586
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
292
);
qprec:=
145
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
586
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
73*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
145
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
587
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
586
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
587
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
293*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 + q^16 - q^17 - q^21 + q^25 - q^31 - q^43 + q^49 - q^63 + q^64 - 
        q^67 - q^68 - q^83 - q^84 - q^87 + O(q^98),
    q^3 - q^9 + q^12 - q^17 - q^21 + q^27 - q^31 - q^36 - q^43 + q^48 + q^49 + 
        q^51 + q^53 + q^59 - q^67 - q^68 + q^73 + q^75 + q^79 - q^81 - q^83 - 
        q^84 - q^87 + q^93 + O(q^98),
    q^7 - q^9 - q^17 + q^27 + q^28 + q^29 - q^31 - q^36 - q^43 + q^47 + q^51 - 
        q^67 - q^68 - q^83 + q^89 + q^93 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 + q^4 - q^8 + q^9 + q^16 - q^18 - q^25 - 2*q^29 - q^32 + q^36 - 
        2*q^37 + q^50 + 2*q^53 + 2*q^58 + q^64 - q^72 + 2*q^74 + q^81 - q^100 - 
        2*q^106 - 2*q^109 + 2*q^113 - 2*q^116 + q^121 - q^128 - 2*q^137 + q^144 
        - 2*q^148 + 2*q^149 - q^162 - q^169 + O(q^178),
    q^3 - q^6 + q^12 - q^24 + q^27 + q^48 - q^54 - q^75 - 2*q^87 - q^96 + q^108 
        - 2*q^111 + q^150 + 2*q^159 + 2*q^174 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^37 - q^39 - q^43 - q^57 - q^67 - q^79 + q^81 - q^93 - 
        q^109 + q^121 - q^127 + 2*q^151 + 2*q^163 + O(q^178),
    q^3 - q^13 - q^19 + q^27 - q^31 + 2*q^61 - q^73 + q^75 + 2*q^97 - q^103 - 
        q^111 - q^117 - q^129 - q^139 + 2*q^157 - q^171 + O(q^178)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 - a^5*q^7 + a^2*q^9 + (-2*a^11 - a^10 + a^8 + a^7 - a^6 - a^5 + 
        a^3 + a^2 - 1)*q^13 + (a^11 - 2*a^9 - a^8 + a^6 + a^5 - a^4 - a^3 + a + 
        1)*q^19 + a^6*q^21 + (a^9 - a^2)*q^25 - a^3*q^27 + (a^11 - a^10 - a^4 + 
        a^3)*q^31 + (-a^8 - a^7 + a)*q^37 + (-a^11 + a^9 + a^8 + a^7 - a^6 + a^4
        + a^3 - a - 2)*q^39 + (a^8 + a^4)*q^43 + a^10*q^49 + (a^11 + 2*a^10 - 
        a^8 - a^7 + a^5 - a^3 - a^2 + 1)*q^57 + (a^8 + a^7 - 1)*q^61 - a^7*q^63 
        + (a^11 + a^10 - 2*a^8 - a^7 + a^5 - a^3 - a^2 + a + 1)*q^67 + (a^10 + 
        a^9 - a^7 - a^6 + a^5 + a^4 - a^2 - a)*q^73 + (-a^10 + a^3)*q^75 + (a^4 
        - a^3)*q^79 + a^4*q^81 + (a^11 + a^9 - a^4 - a^2)*q^91 + (2*a^11 - a^9 -
        a^8 + a^6 + a^5 - 2*a^4 - a^3 + a + 1)*q^93 + (-a^11 + a^8 - a^6 + a^4 +
        a^3 - a - 1)*q^97 + (a^10 + a^6)*q^103 + (-a^11 + a^6)*q^109 + (a^9 + 
        a^8 - a^2)*q^111 + (-a^11 - a^10 + a^7 - a^6 - a^5 + a^3 + a^2 + a - 
        1)*q^117 + (-a^10 + a^3)*q^121 + (-a^11 - a^10 + a^8 + a^7 - a^6 - a^5 +
        a^3 + 2*a^2 - 1)*q^127 + (-a^9 - a^5)*q^129 + (a^7 - a^3 - 1)*q^133 + 
        (-a^7 + a^2)*q^139 - a^11*q^147 + (a^11 - a^9 - a^8 + a^6 + a^5 - a^4 - 
        a^3 + 1)*q^151 + (a^11 - a^9 - a^8 - a^7 + a^6 + a^5 - a^4 - a^3 + a + 
        1)*q^157 + (a^7 - a^5 - 1)*q^163 + (-a^5 - a^3 - a)*q^169 + (-a^11 + 
        1)*q^171 + q^175 + O(q^178)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 - a^5*q^7 + a^2*q^9 + (a^5 + a^3 - a^2 + a - 1)*q^13 + (-a^5 + 
        a^2)*q^19 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^21 + a^2*q^25 - a^3*q^27 +
        (a^4 - a^3)*q^31 + (-a + 1)*q^37 + (-a^5 + 1)*q^39 + (a^4 - a)*q^43 - 
        a^3*q^49 + (a^5 - a^4 - a^2 + a - 1)*q^57 + (-a + 1)*q^61 + q^63 + (a^5 
        - a^4 + a^3 - a^2 - 1)*q^67 + (-a^4 + a^3 - a^2 + a - 1)*q^73 - a^3*q^75
        + (a^4 - a^3)*q^79 + a^4*q^81 + (a^4 + a^2)*q^91 + (-a^5 + a^4)*q^93 + 
        (-a^5 + a^2)*q^97 + (a^5 - a^4 - a^2 + a - 1)*q^103 + (a^5 + a^3 - a^2 +
        a - 1)*q^109 + (a^2 - a)*q^111 + (a^5 - a^4 + a^3 - a^2 - 1)*q^117 - 
        a^3*q^121 + (a^5 - a^4 + a^3 + a - 1)*q^127 + (-a^5 + a^2)*q^129 + (-a^3
        + 1)*q^133 + (a^2 + 1)*q^139 + a^4*q^147 + (-a^5 - a)*q^151 + (-a^5 + 
        1)*q^157 + (-a^5 + 1)*q^163 + (-a^5 - a^3 - a)*q^169 + (a^4 + 1)*q^171 +
        q^175 + O(q^178),
    q^2 - a*q^6 - a^3*q^8 - a^5*q^14 + a^2*q^18 + a^4*q^24 + (a^5 + a^3 - a^2 + 
        a - 1)*q^26 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^32 + (-a^5 + a^2)*q^38 +
        (a^5 - a^4 + a^3 - a^2 + a - 1)*q^42 + a^2*q^50 - a^3*q^54 - a*q^56 + 
        (a^4 - a^3)*q^62 - a^5*q^72 + (-a + 1)*q^74 + (-a^5 + 1)*q^78 + (a^4 - 
        a)*q^86 + q^96 - a^3*q^98 + (a^2 + 1)*q^104 + (a^5 - a^4 - a^2 + a - 
        1)*q^114 + (-a + 1)*q^122 + q^126 + a^2*q^128 + (a^5 - a^4 + a^3 - a^2 -
        1)*q^134 + (-a^4 + a^3 - a^2 + a - 1)*q^146 - a^3*q^150 + (-a^5 - 
        a)*q^152 + (a^4 - a^3)*q^158 + a^4*q^162 + a^2*q^168 + O(q^178),
    q^4 - a*q^12 - a^3*q^16 - a^5*q^28 + a^2*q^36 + a^4*q^48 + (a^5 + a^3 - a^2 
        + a - 1)*q^52 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^64 + (-a^5 + a^2)*q^76
        + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^84 + a^2*q^100 - a^3*q^108 - a*q^112
        + (a^4 - a^3)*q^124 - a^5*q^144 + (-a + 1)*q^148 + (-a^5 + 1)*q^156 + 
        (a^4 - a)*q^172 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 7*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a + 1)*q^2 - a*q^4 - q^8 + (a - 1)*q^9 + (a - 1)*q^16 + a*q^18 + 
        a*q^25 - 2*q^29 + a*q^32 + q^36 + (-2*a + 2)*q^37 + q^50 - 2*a*q^53 + 
        (2*a - 2)*q^58 + q^64 + (-a + 1)*q^72 - 2*a*q^74 - a*q^81 + (-a + 
        1)*q^100 - 2*q^106 + 2*a*q^109 + 2*q^113 + 2*a*q^116 + (a - 1)*q^121 + 
        (-a + 1)*q^128 + 2*a*q^137 - a*q^144 - 2*q^148 + (2*a - 2)*q^149 - q^162
        - q^169 + O(q^178),
    q^3 + (-a + 1)*q^6 - a*q^12 - q^24 + (a - 1)*q^27 + (a - 1)*q^48 + a*q^54 + 
        a*q^75 - 2*q^87 + a*q^96 + q^108 + (-2*a + 2)*q^111 + q^150 - 2*a*q^159 
        + (2*a - 2)*q^174 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^3 + (a - 1)*q^9 + q^13 + (a - 1)*q^19 - a*q^25 - q^27 - a*q^31 + (-a
        + 1)*q^37 + a*q^39 - q^43 - q^57 + (-2*a + 2)*q^61 + a*q^67 - a*q^73 + 
        (-a + 1)*q^75 + (-a + 1)*q^79 - a*q^81 + (-a + 1)*q^93 - 2*q^97 + (a - 
        1)*q^103 + a*q^109 + q^111 + (a - 1)*q^117 + (a - 1)*q^121 - q^127 - 
        a*q^129 + q^139 - 2*a*q^151 + 2*a*q^157 + (2*a - 2)*q^163 - a*q^171 + 
        O(q^178)
]
;
Bo:=
[
    q - a*q^3 + (a - 1)*q^9 - q^13 + (-a + 1)*q^19 - a*q^25 + q^27 + a*q^31 + 
        (-a + 1)*q^37 + a*q^39 - q^43 - q^57 + (2*a - 2)*q^61 + a*q^67 + a*q^73 
        + (a - 1)*q^75 + (-a + 1)*q^79 - a*q^81 + (-a + 1)*q^93 + 2*q^97 + (-a +
        1)*q^103 + a*q^109 - q^111 + (-a + 1)*q^117 + (a - 1)*q^121 - q^127 + 
        a*q^129 - q^139 - 2*a*q^151 - 2*a*q^157 + (2*a - 2)*q^163 + a*q^171 + 
        O(q^178),
    q^7 - a*q^21 + (a - 1)*q^49 + (a - 1)*q^63 - q^91 + (-a + 1)*q^133 + q^147 -
        a*q^175 + O(q^178)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
588
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 21*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
178
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
12*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
12*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1 + 10*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 - q^5 - q^7 + q^8 + q^9 + q^10 + q^14 - q^16 - q^18 + q^31 + q^35 - 
        q^40 - q^41 - q^45 + 2*q^47 - q^56 - q^59 - q^62 - q^63 + q^64 + 2*q^67 
        - q^70 - q^71 + q^72 + q^80 + q^81 + q^82 + q^90 - 2*q^94 - q^97 - q^101
        - q^103 + O(q^104),
    q^19 - q^38 - q^95 + O(q^104)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^5 - 1)*q^5 + (a^5 + a^4 - a^3 - a^2 + 1)*q^7 + (-a^5 - a)*q^8 + (a^5 
        - a^2)*q^9 + (a^5 + a^4 - a^3 - a^2)*q^10 + (a^4 + a^3 - a^2 - a)*q^14 +
        a^4*q^16 + 1/3*(-a^5 - 2*a^4 + 2*a^3 + 2*a^2 + a - 1)*q^19 + (-a^4 + a^2
        + a)*q^20 + (-2*a^5 - a + 1)*q^25 + (-a^4 + a + 1)*q^28 + (a^3 - 1)*q^31
        + (-a^5 - 2*a^4 + a^2 - 1)*q^35 + 1/3*(a^5 - a^4 + a^3 + a^2 + 2*a - 
        2)*q^38 + a*q^40 + (a^3 + a^2 - 1)*q^41 + (-a^5 - a^4 + a^2)*q^45 + (a^4
        - a^3)*q^47 - a^3*q^49 + (-a^5 - a^4 + a^2)*q^50 + (a^4 - a^2 - a + 
        1)*q^56 + (-a^5 + a^3 - a - 1)*q^59 + (a^5 - a^4 - a^3 + a)*q^63 + (a^3 
        + a^2 - a - 1)*q^64 + (-a^5 + a^2)*q^67 + (a^5 - a^4 - a^3 + a)*q^70 + 
        (a^4 - a)*q^71 + (a^4 + 1)*q^72 - a^5*q^76 + (a^4 - a^2 + 1)*q^80 + 
        (-a^4 + a)*q^81 + a^5*q^82 + (-a^4 - a^3 + a^2 + a)*q^90 + 1/3*(4*a^5 + 
        2*a^4 - 2*a^3 - 5*a^2 - a + 1)*q^95 + (-a^5 + a^3 + a^2)*q^97 + a^4*q^98
        + (a^5 + a^3 - a^2 - 1)*q^100 + (-a^5 + a^4 + a^3 - a)*q^101 + (a^5 - 
        a^3 + a)*q^103 + O(q^104),
    q^2 + (-a^3 + 1)*q^5 + (-a^5 + a^4 + a^3 - a)*q^7 + a^2*q^8 + (-a^5 + 
        1)*q^10 + (-a^5 - a^4 + a^3 + a^2 - 1)*q^14 + (-a^5 - a)*q^16 + (a^5 - 
        a^2)*q^18 + 1/3*(2*a^5 + a^4 - a^3 - a^2 + a - 1)*q^19 + (a^4 - 
        a^3)*q^20 + (-a^4 + a^3 + a^2 - 1)*q^25 + (a^5 + a^3 - a^2 - 1)*q^28 + 
        (a^5 + a)*q^35 + 1/3*(a^5 + 2*a^4 - 2*a^3 - 2*a^2 - a + 1)*q^38 + (a^5 -
        a^4 - a^3 - a^2 + a)*q^41 + a^5*q^45 + a^2*q^49 + (a - 1)*q^50 + (-a^5 -
        a^4 + a^3 + a^2)*q^56 + (-a^4 + a^2 + a - 1)*q^59 + (a^3 - 1)*q^62 + 
        (a^4 - a^3 - a^2 + 1)*q^63 + (-a^4 - a^3 + a)*q^64 + (a^5 - a^2 + 
        1)*q^70 - a*q^72 + (a^3 - 1)*q^76 + (-a^5 + a^3 - a - 1)*q^80 + (-a^3 - 
        a^2 + 1)*q^82 + (a^5 + a^4 - a^2)*q^90 + (a^4 - a^3)*q^94 + 1/3*(-2*a^5 
        + 2*a^4 + a^3 + a^2 - a + 1)*q^95 - q^97 - a^3*q^98 + (-a^3 + 1)*q^100 +
        (-a^5 - a^4 + a^2 - 1)*q^101 + (a^4 - a^3 - a^2 - a + 1)*q^103 + 
        O(q^104),
    q^4 + (-a^4 - a^3 + a)*q^5 + (a^4 - a^3 - a^2 + 1)*q^7 + (-a^3 + 1)*q^10 + 
        (-a^5 + a^4 + a^3 - a)*q^14 + 1/3*(a^5 - a^4 + a^3 + a^2 - a - 2)*q^19 +
        (-a^5 + a^4 + a^3 + a^2 - a)*q^25 + (-a^5 - a)*q^32 + (-a^4 + a^3 + a^2 
        + a - 1)*q^35 + (a^5 - a^2)*q^36 + 1/3*(2*a^5 + a^4 - a^3 - a^2 + a - 
        1)*q^38 + (a^5 + a^4 - a^3 - a^2)*q^40 + (-a^4 - 1)*q^41 + (a^3 + a^2 - 
        1)*q^45 + (-a^4 + a^3 + a^2 - 1)*q^50 + (a^4 + a^3 - a^2 - a)*q^56 + 
        (-a^5 - a^4 + a^3 + a^2)*q^59 + (a^5 - a^3 + a)*q^63 + (a^5 + a)*q^70 - 
        a^5*q^71 + (a^5 - a^4 - a^3 - a^2 + a)*q^82 + a^5*q^90 + 1/3*(-a^5 + a^4
        - a^3 - a^2 + a + 2)*q^95 + (a^3 - a - 1)*q^97 + a^2*q^98 - a^5*q^100 + 
        (-a^5 + a^3 - a)*q^101 + (a^5 - a^3 - a^2 + a)*q^103 + O(q^104)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
589
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
104
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^5 + q^7 - q^8 + (a - 1)*q^9 - a*q^16 + 1/3*(-a - 1)*q^19 - q^20 + (a
        - 1)*q^25 + (-a + 1)*q^28 + q^31 - 2*a*q^35 + 1/3*(a + 1)*q^38 + a*q^40 
        + a*q^41 + q^45 + (-a + 1)*q^47 + q^49 + q^50 - q^56 + (a - 1)*q^63 + 
        (2*a - 2)*q^67 + (a - 1)*q^70 + a*q^71 + (-a + 1)*q^72 + (a - 1)*q^76 + 
        (a - 1)*q^80 - a*q^81 + (-a + 1)*q^82 + 1/3*(4*a - 2)*q^95 - a*q^97 - 
        a*q^98 + a*q^100 + (-a + 1)*q^101 - q^103 + O(q^104),
    q^2 - q^5 + (-a + 1)*q^7 + (a - 1)*q^8 + a*q^10 - q^14 - q^16 + (a - 1)*q^18
        + 1/3*(-a - 1)*q^19 + (-a + 1)*q^20 - a*q^25 + a*q^28 + q^35 + 1/3*(a + 
        1)*q^38 + (-a + 1)*q^45 + (a - 1)*q^49 + (a - 1)*q^50 + q^59 + q^62 + 
        a*q^63 + (-a + 1)*q^64 - 2*a*q^70 - a*q^72 + q^76 - a*q^82 - q^90 + (-a 
        + 1)*q^94 + 1/3*(-2*a + 1)*q^95 - q^97 + q^98 + 2*q^100 + O(q^104),
    q^4 + (-a + 1)*q^5 + a*q^7 - q^10 + (-a + 1)*q^14 + 1/3*(-2*a + 1)*q^19 - 
        q^32 + (a - 1)*q^36 + 1/3*(-a - 1)*q^38 + (a - 1)*q^41 + a*q^45 - a*q^50
        - q^63 + q^70 + (a - 1)*q^71 + (-a + 1)*q^90 + 1/3*(2*a - 1)*q^95 + (-a 
        + 1)*q^97 + (a - 1)*q^98 + (a - 1)*q^100 + q^101 - a*q^103 + O(q^104)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
590
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
590
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
590
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
590
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
116
);
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
590
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
29*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + q^4 - q^7 - q^12 + q^16 + 2*q^17 - q^19 + q^21 - q^25 + q^27 - 
        q^28 - q^29 - q^41 - q^48 - 2*q^51 - q^53 + q^57 + q^59 + q^64 + 2*q^68 
        + 2*q^71 + q^75 - q^76 - q^79 - q^81 + q^84 + q^87 - q^100 - q^107 + 
        q^108 - q^112 - q^116 - 2*q^119 + q^121 + q^123 + q^125 - q^127 + q^133 
        - q^137 + 2*q^139 + q^159 + 2*q^163 - q^164 - q^167 + q^169 + O(q^174),
    q^2 - q^6 + q^8 - q^14 - q^24 + q^32 + 2*q^34 - q^38 + q^42 - q^50 + q^54 - 
        q^56 - q^58 - q^82 - q^96 - 2*q^102 - q^106 + q^114 + q^118 + q^128 + 
        2*q^136 + 2*q^142 + q^150 - q^152 - q^158 - q^162 + q^168 + O(q^174),
    q^5 - q^15 + q^20 - q^25 - q^35 - q^60 + q^75 + q^80 + 2*q^85 - q^95 - q^100
        + q^105 + q^135 - q^140 - q^145 + O(q^174),
    q^10 - q^30 + q^40 - q^50 - q^70 - q^120 + q^150 + q^160 + 2*q^170 + 
        O(q^174)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
590
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 29*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
174
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + 1/2*q^15 + 1/2*q^16 - 1/2*q^19 - q^20 - q^21 + 1/2*q^25 - q^26 - 
        1/2*q^29 + 1/2*q^35 + q^36 - 1/2*q^41 + 1/2*q^45 - q^46 + 1/2*q^59 - 
        1/2*q^60 - 3/2*q^64 - 3/2*q^71 + q^74 - 1/2*q^75 + 1/2*q^76 + 1/2*q^80 +
        q^81 + q^84 + q^86 + q^94 - q^95 + 1/2*q^100 - 1/2*q^104 + 1/2*q^105 + 
        1/2*q^116 + q^121 + 1/2*q^125 + q^130 - q^134 - 1/2*q^135 + q^139 - 
        1/2*q^140 - 1/2*q^144 - q^145 + q^146 + q^159 + 1/2*q^164 - q^166 - 
        1/2*q^169 - 3/2*q^171 + O(q^174),
    q^2 + q^18 - q^38 - q^40 + q^50 - q^52 - q^58 - q^82 - q^92 + q^98 - q^128 -
        q^142 + q^148 + q^152 + q^160 + q^162 + q^172 + O(q^174),
    q^3 + q^7 - q^12 - 1/2*q^15 + 1/2*q^16 - 1/2*q^19 + 1/2*q^25 - q^27 - q^28 -
        1/2*q^29 - 1/2*q^35 - 1/2*q^41 + 3/2*q^45 + q^48 - q^53 + q^57 + 
        1/2*q^59 + 1/2*q^60 - 2*q^63 - 1/2*q^64 - 1/2*q^71 - 1/2*q^75 + 1/2*q^76
        + q^79 - 1/2*q^80 + q^87 - q^95 - 1/2*q^100 - 1/2*q^104 + 3/2*q^105 + 
        q^107 + q^108 + q^112 + 1/2*q^116 + q^123 + 1/2*q^125 - q^127 + q^133 + 
        1/2*q^135 - q^137 + q^139 + 1/2*q^140 + 1/2*q^144 - q^145 - 2*q^147 + 
        1/2*q^164 - q^167 - 1/2*q^169 - 1/2*q^171 + O(q^174),
    q^4 - q^20 - q^26 + q^36 - q^46 - q^64 + q^74 + q^86 + q^94 + q^100 - q^104 
        + q^130 - q^134 + q^146 - q^166 + O(q^174),
    q^5 + q^16 - q^19 - q^20 - q^29 - q^41 + q^45 + q^59 - q^64 - q^71 + q^76 + 
        2*q^79 - q^95 - q^104 + q^116 + q^125 + 2*q^139 + q^144 - q^145 + q^164 
        - q^169 - q^171 + O(q^174),
    q^6 + q^14 + q^18 - q^24 - q^30 - q^38 + q^42 + q^50 - q^54 - q^56 - q^58 - 
        q^70 - q^72 - q^82 + q^90 + q^96 + q^98 - q^106 + q^114 + q^120 - 
        2*q^126 + q^152 + q^158 - q^168 + O(q^174),
    q^8 + 2*q^18 - q^30 - q^32 - q^38 - q^40 + 2*q^42 + q^50 - q^52 - q^58 - 
        q^70 - q^72 - q^82 - q^90 - q^92 + 2*q^98 - q^118 + q^120 + q^142 + 
        q^148 + q^150 + q^152 + q^160 - 2*q^168 + q^172 + O(q^174),
    q^9 - 1/2*q^15 - 1/2*q^16 - 1/2*q^19 + q^21 + 1/2*q^25 - 1/2*q^29 - 1/2*q^35
        - q^36 - 1/2*q^41 - 1/2*q^45 + q^49 - 1/2*q^59 + 1/2*q^60 + 1/2*q^64 + 
        1/2*q^71 + 1/2*q^75 + 1/2*q^76 + 1/2*q^80 - q^84 - 1/2*q^100 + 1/2*q^104
        - 1/2*q^105 + 1/2*q^116 - 1/2*q^125 + 1/2*q^135 - q^139 + 1/2*q^140 + 
        1/2*q^144 - q^159 + 1/2*q^164 + 1/2*q^169 + 1/2*q^171 + O(q^174),
    q^10 + 2*q^18 - q^30 - 2*q^38 - q^40 + 2*q^42 + q^50 - 2*q^58 - q^70 - 
        2*q^72 - 2*q^82 + 2*q^98 + q^120 + q^150 + 2*q^152 + 2*q^158 + q^160 - 
        2*q^168 + O(q^174),
    q^13 - 2*q^18 + q^23 + q^30 + q^32 - q^37 + q^38 - 2*q^42 - q^43 - q^47 - 
        q^50 + q^58 - q^65 + q^67 + q^70 + 2*q^72 - q^73 + q^82 + q^83 + q^90 + 
        q^97 - 2*q^98 - q^103 + q^113 - q^115 + q^117 + q^118 - q^120 - q^128 - 
        q^142 - q^150 - q^152 - q^157 - q^160 + 2*q^168 - q^173 + O(q^174)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
591
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
591
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
196
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
591
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
98
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
591
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
98
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
591
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
591
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
591
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 28*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
591
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
49*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
591
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 98*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 + q^25 - q^37 - q^40 - q^42 + q^49 - q^51 - q^55 - q^70 - q^76 + 
        q^81 - q^97 - q^105 + q^121 + O(q^130),
    q^2 + q^18 - q^20 - q^21 - q^35 - q^38 + q^50 - q^66 - q^71 + q^75 + q^77 + 
        q^89 + q^95 + q^98 - q^113 + q^119 - q^120 + q^129 + O(q^130),
    q^3 - q^14 - q^17 + q^27 - q^35 - q^44 + q^50 + q^56 + q^68 + q^75 - q^80 + 
        q^86 - q^95 + q^110 - q^111 - q^120 - q^126 + O(q^130),
    q^4 - q^10 - q^19 - q^33 + q^36 + q^37 + q^51 + q^55 - q^60 - q^85 - q^88 - 
        q^90 + q^97 + q^100 + q^105 - q^112 - q^127 + O(q^130),
    q^5 - q^12 - q^14 - q^17 + q^20 + q^30 + q^32 - q^35 + q^38 + q^45 - q^48 - 
        q^50 + q^66 - q^68 + q^84 - q^86 - q^95 + q^98 - q^108 - q^110 - q^111 +
        q^119 + q^122 + q^125 - q^126 + q^128 + O(q^130),
    q^6 - q^10 - q^16 - q^19 + q^24 + q^25 + q^28 - q^33 + q^34 - q^40 - q^42 + 
        q^43 + q^54 + q^55 - q^60 - q^64 - q^76 - q^85 - q^90 + q^96 + 2*q^100 +
        q^109 + q^112 - q^127 + O(q^130),
    q^7 - q^10 - q^16 - q^19 + q^22 + q^24 + q^28 - q^33 + q^34 - q^42 + q^63 - 
        q^64 - q^76 - q^90 + q^96 + q^100 + q^105 + q^114 + q^121 - q^127 + 
        O(q^130),
    q^8 - q^12 - q^14 - q^17 + q^20 + q^21 + q^32 + q^38 - q^44 - q^48 - q^50 - 
        q^56 + q^66 - q^68 + q^71 + q^72 + q^74 + q^84 - q^86 - q^95 + q^102 - 
        q^108 - q^111 + q^113 - q^126 + q^128 + O(q^130),
    q^11 - q^12 - q^17 + q^20 + q^30 - q^35 - q^50 + q^57 + q^77 - q^86 - q^95 +
        q^98 + q^99 - q^108 - q^110 - q^111 + q^122 + q^125 + q^128 + O(q^130),
    q^15 - q^16 - q^19 + q^22 + q^28 - q^33 - q^42 + q^49 + q^61 - q^70 - q^85 +
        q^96 + q^114 - q^127 + O(q^130)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^3 - a^2)*q^5 + (a^5 - a^2)*q^9 + (-2*a^4 + a)*q^13 + (-a^3 - a + 
        1)*q^17 + (a^5 + a^4 + a^3 - 1)*q^25 + (-a^5 + a^4 - a)*q^29 + a*q^37 + 
        (-a^5 + a^3 + a^2)*q^41 + (a^2 + a)*q^45 - a^5*q^49 + a^2*q^53 + (a^2 - 
        1)*q^61 + (a^4 + a^3 - 2*a - 2)*q^65 + q^73 + (-a^4 + a)*q^81 + (a^5 + 
        a^4 + a^3 - a^2 - 1)*q^85 + (a^4 - 1)*q^89 + (-a^4 + a^2)*q^97 + (-a^4 -
        a^2)*q^101 + (a^4 - a^3 - a)*q^109 + (-a^5 + 2*a^2)*q^113 + (2*a^3 - 
        1)*q^117 - a^3*q^121 + (-a^5 - a^4 - a^3 + a^2 + a + 2)*q^125 + (-a^2 + 
        a)*q^137 + O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a^4 + a^3 - 1)*q^5 + (-a^4 + a)*q^9 - a^2*q^13 + (-a^3 + a^2)*q^17 + 
        (a^5 - a^3 - a^2 - a)*q^25 + (-a^5 - a)*q^29 + a^2*q^37 + (-a^4 + a^3 + 
        a - 1)*q^41 + (a^4 + a^2)*q^45 - a*q^49 - a^4*q^53 + (a^4 + 1)*q^61 + 
        (-a^5 - a^3 + a^2 + 1)*q^65 - q^73 - a^5*q^81 + (a^5 - a^4 + a^3 - a^2 +
        a)*q^85 + (a^5 - a^2 + 1)*q^89 + (a^5 + a^4 - a^2)*q^97 + (a^5 + a^4 - 
        a^2)*q^101 + (-a^5 + a^3 - 1)*q^109 + a*q^113 - q^117 + (a^3 - 1)*q^121 
        + (-a^5 - a^4 - a^3 + a + 1)*q^125 + (a^4 + a^2)*q^137 + O(q^142),
    q^2 + (a^4 + a^3 - 1)*q^10 + (-a^4 + a)*q^18 - a^2*q^26 + (-a^3 + a^2)*q^34 
        + (a^5 - a^3 - a^2 - a)*q^50 + (-a^5 - a)*q^58 + a^2*q^74 + (-a^4 + a^3 
        + a - 1)*q^82 + (a^4 + a^2)*q^90 - a*q^98 - a^4*q^106 + (a^4 + 1)*q^122 
        + (-a^5 - a^3 + a^2 + 1)*q^130 + O(q^142),
    q^4 - a*q^8 + a^2*q^16 + (a^4 + a^3 - 1)*q^20 - a^3*q^32 + (-a^4 + a)*q^36 +
        (-a^5 - a^4 + a)*q^40 - a^2*q^52 + a^4*q^64 + (-a^3 + a^2)*q^68 + (a^5 -
        a^2)*q^72 + (a^5 + a^3 - a^2 - 1)*q^80 + (a^5 - a^3 - a^2 - a)*q^100 + 
        a^3*q^104 + (-a^5 - a)*q^116 - a^5*q^128 + (a^4 - a^3)*q^136 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 2)*q^5 + (a - 1)*q^9 + (-a - 1)*q^17 + (-2*a + 2)*q^25 + (2*a - 
        1)*q^29 + a*q^37 - a*q^41 + (2*a - 1)*q^45 + (a - 1)*q^49 + (-2*a + 
        2)*q^53 + (a - 2)*q^61 - 2*q^73 - a*q^81 - 3*q^85 + (-a - 1)*q^89 + (2*a
        - 1)*q^97 + q^101 + (a + 1)*q^109 + q^121 + (-2*a + 1)*q^125 + q^137 + 
        O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 6*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + 1/2*(a - 1)*q^5 + q^7 - a*q^11 + 1/2*(-a + 1)*q^13 + 1/2*(a + 1)*q^15 + 
        1/2*(a - 1)*q^17 + 1/2*(a - 1)*q^19 + 1/2*(a - 1)*q^35 + 1/2*(-a - 
        1)*q^37 + 1/2*(-a - 1)*q^39 - a*q^41 + 1/2*(a - 1)*q^43 + 1/2*(-a - 
        1)*q^51 + 1/2*(a + 1)*q^55 + 1/2*(-a - 1)*q^57 + a*q^65 + a*q^67 + (a + 
        1)*q^69 - q^71 - q^75 - a*q^77 + 1/2*(-a + 1)*q^79 - q^81 + q^83 + (-a +
        1)*q^87 + 1/2*(-a - 1)*q^89 + 1/2*(-a + 1)*q^91 + a*q^101 + 1/2*(-a - 
        1)*q^103 + 1/2*(a + 1)*q^105 + 1/2*(a - 1)*q^109 + 1/2*(a + 1)*q^111 - 
        a*q^115 + 1/2*(a - 1)*q^119 - q^127 + 1/2*(a + 1)*q^129 + 1/2*(-a - 
        1)*q^131 + 1/2*(a - 1)*q^133 + 1/2*(a + 1)*q^135 - a*q^141 + O(q^142),
    q^3 + 1/2*(-a - 1)*q^5 + 1/2*(a + 1)*q^13 + 1/2*(a - 1)*q^15 + 1/2*(a + 
        1)*q^17 + 1/2*(a + 1)*q^19 + q^21 + (-a - 1)*q^23 + q^25 + q^27 + (a - 
        1)*q^29 - a*q^33 + 1/2*(-a - 1)*q^35 + 1/2*(-a - 1)*q^37 + 1/2*(-a + 
        1)*q^39 + 1/2*(-a - 1)*q^43 + a*q^47 + 1/2*(a - 1)*q^51 - a*q^53 + 
        1/2*(a - 1)*q^55 + 1/2*(a - 1)*q^57 - q^65 - q^67 - q^73 + 1/2*(-a - 
        1)*q^79 + 1/2*(a - 1)*q^89 + 1/2*(a + 1)*q^91 + 1/2*(-a + 1)*q^103 + 
        1/2*(a - 1)*q^105 + 1/2*(a + 1)*q^109 + 1/2*(-a - 1)*q^111 + (-a + 
        1)*q^113 + q^115 + 1/2*(a + 1)*q^119 - a*q^123 + 1/2*(a - 1)*q^129 + 
        1/2*(a - 1)*q^131 + 1/2*(a + 1)*q^133 + 1/2*(a - 1)*q^135 + O(q^142)
]
;
Bo:=
[
    q + 1/2*(a - 1)*q^5 - q^7 + a*q^11 + 1/2*(-a + 1)*q^13 + 1/2*(-a - 1)*q^15 +
        1/2*(a - 1)*q^17 + 1/2*(-a + 1)*q^19 + 1/2*(-a + 1)*q^35 + 1/2*(-a - 
        1)*q^37 + 1/2*(a + 1)*q^39 - a*q^41 + 1/2*(-a + 1)*q^43 + 1/2*(a + 
        1)*q^51 + 1/2*(-a - 1)*q^55 + 1/2*(-a - 1)*q^57 + a*q^65 - a*q^67 + (a +
        1)*q^69 + q^71 + q^75 - a*q^77 + 1/2*(a - 1)*q^79 - q^81 - q^83 + (a - 
        1)*q^87 + 1/2*(-a - 1)*q^89 + 1/2*(a - 1)*q^91 + a*q^101 + 1/2*(a + 
        1)*q^103 + 1/2*(a + 1)*q^105 + 1/2*(a - 1)*q^109 + 1/2*(-a - 1)*q^111 + 
        a*q^115 + 1/2*(-a + 1)*q^119 + q^127 + 1/2*(a + 1)*q^129 + 1/2*(a + 
        1)*q^131 + 1/2*(a - 1)*q^133 + 1/2*(-a - 1)*q^135 - a*q^141 + O(q^142),
    q^2 + 1/2*(a - 1)*q^10 - q^14 + a*q^22 + 1/2*(-a + 1)*q^26 + 1/2*(-a - 
        1)*q^30 + 1/2*(a - 1)*q^34 + 1/2*(-a + 1)*q^38 + 1/2*(-a + 1)*q^70 + 
        1/2*(-a - 1)*q^74 + 1/2*(a + 1)*q^78 - a*q^82 + 1/2*(-a + 1)*q^86 + 
        1/2*(a + 1)*q^102 + 1/2*(-a - 1)*q^110 + 1/2*(-a - 1)*q^114 + a*q^130 - 
        a*q^134 + (a + 1)*q^138 + O(q^142),
    q^3 + 1/2*(a + 1)*q^5 + 1/2*(-a - 1)*q^13 + 1/2*(a - 1)*q^15 + 1/2*(-a - 
        1)*q^17 + 1/2*(a + 1)*q^19 - q^21 + (-a - 1)*q^23 - q^25 + q^27 + (-a + 
        1)*q^29 + a*q^33 + 1/2*(-a - 1)*q^35 + 1/2*(a + 1)*q^37 + 1/2*(-a + 
        1)*q^39 + 1/2*(-a - 1)*q^43 + a*q^47 + 1/2*(a - 1)*q^51 + a*q^53 + 
        1/2*(a - 1)*q^55 + 1/2*(-a + 1)*q^57 + q^65 - q^67 + q^73 + 1/2*(-a - 
        1)*q^79 + 1/2*(-a + 1)*q^89 + 1/2*(a + 1)*q^91 + 1/2*(-a + 1)*q^103 + 
        1/2*(-a + 1)*q^105 + 1/2*(-a - 1)*q^109 + 1/2*(-a - 1)*q^111 + (a - 
        1)*q^113 + q^115 + 1/2*(a + 1)*q^119 - a*q^123 + 1/2*(-a + 1)*q^129 + 
        1/2*(a - 1)*q^131 + 1/2*(-a - 1)*q^133 + 1/2*(a - 1)*q^135 + O(q^142),
    q^4 - a*q^12 - q^28 + a*q^44 + (a - 1)*q^68 + (-a + 1)*q^76 + a*q^84 + (a - 
        1)*q^92 + a*q^100 - a*q^108 + (-a - 1)*q^116 + q^132 + O(q^142),
    q^6 + 1/2*(a + 1)*q^10 + 1/2*(-a - 1)*q^26 + 1/2*(a - 1)*q^30 + 1/2*(-a - 
        1)*q^34 + 1/2*(a + 1)*q^38 - q^42 + (-a - 1)*q^46 - q^50 + q^54 + (-a + 
        1)*q^58 + a*q^66 + 1/2*(-a - 1)*q^70 + 1/2*(a + 1)*q^74 + 1/2*(-a + 
        1)*q^78 + 1/2*(-a - 1)*q^86 + a*q^94 + 1/2*(a - 1)*q^102 + a*q^106 + 
        1/2*(a - 1)*q^110 + 1/2*(-a + 1)*q^114 + q^130 - q^134 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^5 + a*q^9 + a*q^17 - q^29 + (-2*a + 2)*q^33 + (-a + 1)*q^37 + 
        (a - 1)*q^41 - q^45 - a*q^49 - 2*a*q^57 + (-a + 1)*q^61 + (2*a - 2)*q^69
        + (-a + 1)*q^81 - q^85 + a*q^89 + (-2*a + 2)*q^93 - q^97 - q^101 + 
        a*q^109 - q^121 - q^125 + q^137 + (-2*a + 2)*q^141 + O(q^142),
    q^3 - a*q^11 + (a - 1)*q^15 - q^19 + a*q^23 - a*q^31 - a*q^47 + a*q^51 + 
        q^55 + q^67 + q^79 + (a - 1)*q^83 - q^87 + (-a + 1)*q^95 + (-a + 1)*q^99
        + (-a + 1)*q^111 - q^115 + (a - 1)*q^123 + (a - 1)*q^127 + (a - 1)*q^131
        + (a - 1)*q^139 + O(q^142)
]
;
Bo:=
[
    q + (-a + 1)*q^5 - a*q^9 + (2*a - 2)*q^13 + a*q^17 - q^29 + (a - 1)*q^37 + 
        (-a + 1)*q^41 - q^45 - a*q^49 - 2*a*q^53 + (-a + 1)*q^61 + 2*a*q^65 + 
        2*q^73 + (a - 1)*q^81 + q^85 + a*q^89 - q^97 - q^101 + a*q^109 - 
        2*a*q^113 + 2*q^117 + q^121 + q^125 - q^137 + O(q^142),
    q^2 + (-a + 1)*q^10 - a*q^18 + (2*a - 2)*q^26 + a*q^34 - q^58 + (a - 1)*q^74
        + (-a + 1)*q^82 - q^90 - a*q^98 - 2*a*q^106 + (-a + 1)*q^122 + 2*a*q^130
        + O(q^142),
    q^4 - a*q^8 + (a - 1)*q^16 + (-a + 1)*q^20 + q^32 - a*q^36 - q^40 + (2*a - 
        2)*q^52 - a*q^64 + a*q^68 + (a - 1)*q^72 + a*q^80 + 2*q^104 - q^116 + (a
        - 1)*q^128 + (-a + 1)*q^136 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 12*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^21 + q^25 + q^33 - q^37 - q^41 - q^53 - q^73 + q^77 + q^81 - q^101 - 
        2*q^137 - q^141 + O(q^142),
    q^3 + q^7 - q^11 - q^27 + q^47 - 2*q^63 - q^71 + q^75 - q^83 + 2*q^99 - 
        q^111 + q^123 - q^127 + O(q^142),
    q^9 + q^21 - q^33 - q^41 + q^49 - q^53 - q^73 - q^77 - q^101 + q^121 + q^141
        + O(q^142)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 18*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
592
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 18*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
142
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^11 + q^25 - q^27 - q^33 + q^49 - q^65 - q^67 - q^73 + q^75 + 2*q^83 + 
        q^99 - q^115 + q^121 + q^123 - q^137 + O(q^142),
    q^2 + q^8 - q^20 - q^22 + q^32 + q^50 - q^54 - q^60 - q^66 - q^80 - q^88 + 
        q^98 - q^124 + q^128 - q^130 - q^134 + O(q^142),
    q^3 - q^9 - q^11 + q^25 + q^41 - q^67 - q^73 + q^107 + q^121 - q^123 - q^137
        + q^139 + O(q^142),
    q^4 - q^12 + q^16 - q^26 - q^30 + q^36 - q^46 - q^48 - q^58 + q^64 + q^74 + 
        2*q^78 + q^90 - q^104 - q^108 + q^110 - q^120 - q^132 + 2*q^138 + 
        O(q^142),
    q^5 + q^15 + q^31 - q^37 - q^39 - q^45 - 2*q^55 + q^61 - q^69 - q^87 + q^93 
        + q^103 - 2*q^109 + q^117 + q^125 - q^135 + O(q^142),
    q^6 - q^18 - q^20 - q^22 + q^24 + q^50 + q^52 - q^72 - q^80 + q^82 - q^88 + 
        q^92 + q^96 + q^116 - q^124 - q^134 + O(q^142),
    q^10 - q^12 - q^26 + q^36 + q^40 + q^44 - q^46 - q^48 - q^58 + q^62 + q^78 -
        q^100 - q^104 - q^110 + q^122 + q^138 + O(q^142),
    q^13 + q^15 + q^23 + q^29 - q^37 - 2*q^39 - q^45 - q^55 - 2*q^69 + q^79 - 
        2*q^87 + q^93 - 2*q^109 + q^111 + 2*q^117 + q^125 + O(q^142)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
593
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
592
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
593
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
37*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
99
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
90
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a^5 - a^2)*q^3 + a^2*q^4 + (-a^4 - a^3 + a)*q^5 + (-a^4 + a)*q^9 + 
        a^4*q^11 - a*q^12 + (a^3 + a^2 - 1)*q^15 + a^4*q^16 + (-a^5 + 1)*q^20 - 
        a^2*q^23 + (-a^5 + a^3 - a - 1)*q^25 + (a^3 - 1)*q^27 + (-a^3 - a)*q^31 
        - a^3*q^33 + q^36 + (a^5 + a^4 - a^2)*q^37 + (a^3 - 1)*q^44 + (-a^5 - 
        a)*q^45 + (-a^3 + a^2)*q^47 - a^3*q^48 - a^5*q^49 + (a^5 - a^2 - a)*q^53
        + (-a^4 + a^2 + a)*q^55 + (a^4 + a^3 - 1)*q^59 + (a^5 + a^4 - a^2)*q^60 
        + (a^3 - 1)*q^64 + (-a^4 + a + 1)*q^67 + a*q^69 + (a^2 - a)*q^71 + (-a^5
        + a^4 + 1)*q^75 + (-a^4 + a^2 + a)*q^80 - a^5*q^81 + a^3*q^89 - a^4*q^92
        + (a^2 + 1)*q^93 + (a^5 - a^2 + 1)*q^97 + a^2*q^99 + (a^5 - a^4 - a^3 - 
        a^2 + a)*q^100 + (-a^4 - a^3 + a)*q^103 + (a^5 - a^2)*q^108 + (-a^4 - 
        a^3 + a)*q^111 + (-a + 1)*q^113 + (a^5 - 1)*q^115 + (a^5 - a^2)*q^121 + 
        (-a^5 - a^3)*q^124 + (a^5 + a^4 - a^3 - a^2 + 1)*q^125 - a^5*q^132 + 
        (a^4 + 1)*q^135 + (a^2 + 1)*q^137 + (a^2 - a)*q^141 + a^2*q^144 + 
        a^4*q^147 + (a^3 - a - 1)*q^148 + (a^5 + a^4 + a^3 - a^2 - a - 1)*q^155 
        + (a^4 + a^3 - 1)*q^157 + (-a^4 + a + 1)*q^159 + (-a^5 + a^4)*q^163 + 
        (a^3 - a - 1)*q^165 + (-a^4 + a)*q^169 + (a^5 - a^2)*q^176 + (-a^5 - 
        a^3)*q^177 + (-a^5 - a^4 + a)*q^179 + (-a^4 - a^3 + a)*q^180 + (-a^5 - 
        a)*q^181 + (-a^4 + a^3 + 2*a^2 + a - 1)*q^185 + (-a^5 + a^4)*q^188 + 
        (-a^5 + a^3 - 1)*q^191 - a^5*q^192 + O(q^194),
    q^2 + (a^5 - a^2)*q^6 + a^2*q^8 + (-a^4 - a^3 + a)*q^10 + (-a^4 + a)*q^18 + 
        a^4*q^22 - a*q^24 + (a^3 + a^2 - 1)*q^30 + a^4*q^32 + (-a^5 + 1)*q^40 - 
        a^2*q^46 + (-a^5 + a^3 - a - 1)*q^50 + (a^3 - 1)*q^54 + (-a^3 - a)*q^62 
        - a^3*q^66 + q^72 + (a^5 + a^4 - a^2)*q^74 + (a^3 - 1)*q^88 + (-a^5 - 
        a)*q^90 + (-a^3 + a^2)*q^94 - a^3*q^96 - a^5*q^98 + (a^5 - a^2 - 
        a)*q^106 + (-a^4 + a^2 + a)*q^110 + (a^4 + a^3 - 1)*q^118 + (a^5 + a^4 -
        a^2)*q^120 + (a^3 - 1)*q^128 + (-a^4 + a + 1)*q^134 + a*q^138 + (a^2 - 
        a)*q^142 + (-a^5 + a^4 + 1)*q^150 + (-a^4 + a^2 + a)*q^160 - a^5*q^162 +
        a^3*q^178 - a^4*q^184 + (a^2 + 1)*q^186 + O(q^194)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
594
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^4 - a*q^16 + (-a + 1)*q^31 - q^37 + (a - 1)*q^49 - q^55 + q^64
        + (-a + 1)*q^67 + a*q^97 + (-a + 1)*q^103 + 2*a*q^115 + (a - 1)*q^121 + 
        a*q^124 + (-a + 1)*q^148 + (-a + 1)*q^157 - q^163 - a*q^169 - q^181 + 
        O(q^194),
    q^2 + (a - 1)*q^8 - a*q^32 + (-a + 1)*q^62 - q^74 + (a - 1)*q^98 - q^110 + 
        q^128 + (-a + 1)*q^134 + O(q^194),
    q^3 + (a - 1)*q^9 + (a - 1)*q^12 + (-a + 1)*q^15 - a*q^27 - a*q^33 - a*q^36 
        + a*q^45 - a*q^48 + a*q^60 + (2*a - 2)*q^69 + q^81 + (-a + 1)*q^93 + 
        q^99 + q^108 - q^111 + q^132 - q^135 + a*q^141 + q^144 + (a - 1)*q^147 -
        q^159 - q^165 + (-a + 1)*q^177 - q^180 + q^192 + O(q^194),
    q^5 + (-a + 1)*q^11 + (a - 1)*q^20 - 2*q^23 + a*q^44 + (a - 1)*q^47 - a*q^53
        + q^59 - a*q^71 - a*q^80 + 2*a*q^89 + (-2*a + 2)*q^92 + q^113 + a*q^125 
        + (a - 1)*q^137 + (-a + 1)*q^155 - q^176 - a*q^179 - q^185 - a*q^188 + 
        (a - 1)*q^191 + O(q^194),
    q^6 + (a - 1)*q^18 + (a - 1)*q^24 + (-a + 1)*q^30 - a*q^54 - a*q^66 - a*q^72
        + a*q^90 - a*q^96 + a*q^120 + (2*a - 2)*q^138 + q^162 + (-a + 1)*q^186 +
        O(q^194),
    q^10 + (-a + 1)*q^22 + (a - 1)*q^40 - 2*q^46 + a*q^88 + (a - 1)*q^94 - 
        a*q^106 + q^118 - a*q^142 - a*q^160 + 2*a*q^178 + (-2*a + 2)*q^184 + 
        O(q^194)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 2*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 3*H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2 + 2*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^2*q^4 + a*q^9 + (a^2 - a)*q^11 + (a^2 - 1)*q^15 - q^16 + (a^3 + 
        a)*q^21 - a*q^25 + (-a^3 - a^2)*q^29 - q^35 - a^3*q^36 + (-a^3 - a^2 - a
        + 1)*q^39 + (a^3 + 1)*q^44 + a^3*q^49 + (a^2 - 1)*q^51 + (a^2 + 1)*q^60 
        + a^2*q^64 + (a + 1)*q^65 + (a^3 - a^2)*q^71 + (-a^2 + a)*q^79 - 
        a^2*q^81 + (-a^3 + a)*q^84 - a*q^85 + (-a^3 + 1)*q^91 + (a^3 - a^2)*q^99
        + a^3*q^100 + (a^2 + a)*q^109 + (-a - 1)*q^116 - q^119 + (-a^3 + a^2 - 
        1)*q^121 + O(q^138),
    q^3 + 1/2*(a^3 + a)*q^5 + 1/2*(a^2 + 1)*q^7 - a^2*q^12 + 1/2*(-a^3 - a^2 - a
        - 1)*q^13 + 1/2*(a^3 + a)*q^17 + 1/2*(-a^3 + a)*q^20 + 1/2*(-a^2 + 
        1)*q^28 + (a^2 - a)*q^33 + 1/2*(a^2 - 1)*q^45 + 1/2*(-a^3 + a^2 + a - 
        1)*q^47 - q^48 + 1/2*(a^3 + a^2 - a - 1)*q^52 + 1/2*(a^3 - a^2 - a + 
        1)*q^55 + 1/2*(a^3 + a)*q^63 + 1/2*(-a^3 + a)*q^68 - a*q^75 + 1/2*(-a^3 
        + a^2 - a - 1)*q^77 + 1/2*(-a^3 - a)*q^80 + 1/2*(a^3 + a^2 + a - 1)*q^83
        + (-a^3 - a^2)*q^87 + a^2*q^97 + 1/2*(a^3 - a^2 + a - 1)*q^103 - q^105 +
        1/2*(-a^2 - 1)*q^112 + 1/2*(-a^3 - a^2 - a + 1)*q^117 + 1/2*(-a^2 + 
        1)*q^125 + (a^3 + 1)*q^132 + O(q^138)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2 + 4*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 - a*q^9 + (a - 1)*q^11 + q^16 + a*q^25 + (-a - 1)*q^29 + q^35 + 
        a*q^36 + (-a + 1)*q^44 - a*q^49 - q^64 + (a + 1)*q^65 + (-a - 1)*q^71 + 
        (a - 1)*q^79 - q^81 + a*q^85 + (-a + 1)*q^91 + (a + 1)*q^99 - a*q^100 + 
        (a - 1)*q^109 + (a + 1)*q^116 + q^119 - a*q^121 + O(q^138),
    q^5 - a*q^7 + (-a + 1)*q^13 + q^17 - q^20 + a*q^28 - a*q^45 + (a - 1)*q^47 +
        (a - 1)*q^52 + (a - 1)*q^55 - q^63 - q^68 - 2*q^73 + (a + 1)*q^77 + q^80
        + (a + 1)*q^83 + (-a + 1)*q^103 - a*q^112 + (-a - 1)*q^117 + a*q^125 + 
        O(q^138)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^8 - q^18 - q^30 + q^32 - q^35 + q^36 + q^42 + q^49 + q^50 - q^53 + 
        q^60 - q^67 - q^84 - q^85 + q^86 - q^93 - q^100 + q^102 - q^106 + q^119 
        + q^121 + q^123 - q^127 - q^134 + q^135 + O(q^138),
    q^2 - q^4 - q^9 + q^18 + q^21 - q^36 - q^42 + q^43 - q^50 + q^51 - q^53 + 
        q^64 - q^67 + q^72 + q^84 - q^86 + q^98 + q^100 - q^102 - q^123 - q^127 
        - q^128 + q^137 + O(q^138),
    q^3 + q^7 + q^14 + q^17 - q^24 - q^27 - q^28 - 2*q^31 + q^34 + q^41 - q^54 -
        q^56 + q^61 - q^62 - q^63 - q^68 + q^73 - q^75 + q^96 - 2*q^97 + q^108 +
        q^124 + 2*q^125 + 2*q^131 - q^136 + O(q^138),
    q^5 - q^40 - q^75 - q^90 + q^125 + O(q^138),
    q^6 + q^7 - q^12 + q^17 - q^27 - q^31 - q^56 - q^62 + q^82 - q^97 + q^122 + 
        q^124 + q^125 - q^126 + q^129 + 2*q^131 - q^136 + O(q^138),
    q^10 - q^20 - q^45 + q^90 + q^105 + q^125 + O(q^138),
    q^15 - 2*q^30 - q^35 + q^50 + 2*q^60 + q^70 - q^85 - q^100 - q^120 + q^135 +
        O(q^138),
    q^25 - q^30 - q^35 + q^50 + q^60 - q^85 - q^100 + q^135 + O(q^138)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
595
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 3*H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
138
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - 2*q^9 - q^16 + q^21 + 1/2*q^25 + 3/2*q^30 + 1/2*q^35 - q^49 + 1/2*q^50 -
        q^51 + 1/2*q^60 - q^70 + q^81 - q^84 - 1/2*q^85 - q^86 - 1/2*q^100 + 
        2*q^106 + q^119 + q^120 + q^121 - 2*q^134 - 1/2*q^135 + O(q^138),
    q^2 + 2*q^16 - q^18 - 2*q^21 - 3/2*q^25 - 3/2*q^30 + 1/2*q^35 - 2*q^36 + 
        q^42 + q^43 + 1/2*q^50 + 2*q^51 - q^53 + 3/2*q^60 + q^67 + q^70 - q^72 +
        2*q^81 - 1/2*q^85 + 2*q^93 - q^98 + 1/2*q^100 - q^102 - 2*q^106 - q^120 
        + q^123 - q^127 - q^128 + 2*q^134 - 3/2*q^135 - q^137 + O(q^138),
    q^3 + q^14 - q^20 - q^24 - q^27 - q^34 - q^40 + q^41 + q^45 + q^54 - q^56 - 
        q^61 + q^62 - q^73 + q^80 + q^90 + q^96 - q^108 + q^112 + q^124 + q^136 
        + O(q^138),
    q^4 - q^9 - 2*q^16 + q^21 + 1/2*q^25 + 1/2*q^30 + 1/2*q^35 + q^36 - 1/2*q^50
        - q^51 - 1/2*q^60 + q^64 - q^70 - q^84 - 1/2*q^85 + q^86 - 1/2*q^100 + 
        2*q^106 + q^120 - 2*q^134 + 1/2*q^135 + O(q^138),
    q^5 - 2*q^12 + 2*q^14 - 2*q^20 - 2*q^24 + 2*q^27 - 2*q^28 - 2*q^34 - q^40 + 
        2*q^41 + 2*q^54 - 2*q^56 - 2*q^61 + 2*q^62 + 2*q^63 + 2*q^68 + q^75 + 
        4*q^80 - 2*q^82 + q^90 + 2*q^96 - 2*q^97 - 2*q^105 + 2*q^112 + 2*q^122 +
        2*q^124 - q^125 + 2*q^136 + O(q^138),
    q^6 + q^12 - 2*q^14 + q^20 + 2*q^24 - q^27 + q^28 - q^31 + 2*q^34 + q^40 - 
        2*q^41 - q^45 - 2*q^54 + q^56 + 2*q^61 - q^62 - q^63 - q^68 - q^75 - 
        3*q^80 + q^82 - q^90 - 2*q^96 + q^97 + 2*q^105 - q^112 - q^122 - q^124 +
        q^125 + q^126 + q^129 - q^136 + O(q^138),
    q^7 - q^17 - q^20 - q^28 + q^40 + q^45 + 2*q^48 - q^63 + q^68 - q^75 + q^80 
        - 2*q^82 - q^90 - 2*q^108 + q^112 + 2*q^122 + O(q^138),
    q^8 + q^16 - q^18 - q^21 - 1/2*q^25 - 1/2*q^30 - q^32 + 1/2*q^35 - q^36 + 
        q^42 + 1/2*q^50 + q^51 - q^53 + 1/2*q^60 + q^67 + q^70 + q^81 - 1/2*q^85
        + q^93 - 1/2*q^100 - q^102 - q^106 - q^120 + q^123 - q^127 + q^134 - 
        1/2*q^135 + O(q^138),
    q^10 + 2*q^14 - q^20 - 2*q^24 - 2*q^34 - 2*q^40 + 2*q^41 + q^45 + 2*q^54 - 
        2*q^56 - 2*q^61 + 2*q^80 + q^90 + 2*q^96 - q^105 + 2*q^124 - q^125 + 
        2*q^136 + O(q^138),
    q^15 + 2*q^16 - 2*q^21 - q^25 - q^30 - 2*q^36 + 2*q^51 + q^60 + q^70 + 
        2*q^81 - 2*q^106 - q^120 + 2*q^134 - 2*q^135 + O(q^138)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
596
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
596
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
148
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
596
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
74
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
596
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
74
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + a^2*q^4 + (a^16 - a^7)*q^5 - a^3*q^8 + a^26*q^9 + (-a^17 + 
        a^8)*q^10 + (a^20 + a^12)*q^13 + a^4*q^16 + (a^34 - a^29)*q^17 - 
        a^27*q^18 + (a^18 - a^9)*q^20 + (a^32 - a^23 + a^14)*q^25 + (-a^21 - 
        a^13)*q^26 + (-a^31 + a^24)*q^29 - a^5*q^32 + (-a^35 + a^30)*q^34 + 
        a^28*q^36 + (a^22 - a^11)*q^37 + (-a^19 + a^10)*q^40 + (-a^35 + 
        a^10)*q^41 + (-a^33 - a^5)*q^45 - a^25*q^49 + (-a^33 + a^24 - a^15)*q^50
        + (a^22 + a^14)*q^52 + (a^30 + a^6)*q^53 + (a^32 - a^25)*q^58 + (-a^21 +
        a^18)*q^61 + a^6*q^64 + (a^35 - a^34 + a^33 - a^32 + a^31 - a^30 + a^29 
        - a^26 + a^25 - a^24 + a^23 - a^22 + a^21 - a^20 - a^18 + a^17 - a^16 + 
        a^15 - a^14 + a^13 - a^12 + a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - 
        a^4 + a^3 - a^2 + a - 1)*q^65 + (a^35 - a^34 + a^33 - a^32 - a^30 + a^29
        - a^28 + a^27 - a^26 + a^25 - a^24 + a^23 - a^22 + a^21 - a^20 + a^19 - 
        a^18 + a^17 - a^16 + a^15 - a^14 + a^13 - a^12 + a^11 - a^10 + a^9 - a^8
        + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^68 - a^29*q^72 + (-a^15 -
        a^9)*q^73 + (-a^23 + a^12)*q^74 + (a^20 - a^11)*q^80 - a^15*q^81 + (a^35
        - a^34 + a^33 - a^32 + a^31 - a^30 + a^29 - a^28 + a^27 - a^26 + a^25 - 
        a^24 + a^23 - a^22 + a^21 - a^20 + a^19 - a^18 + a^17 - a^16 + a^15 - 
        a^14 + a^13 - a^12 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - 
        a^2 + a - 1)*q^82 + (a^35 - a^34 + a^33 - a^32 + a^31 - a^30 + a^29 - 
        a^28 + a^27 - a^26 + a^25 - a^24 + a^23 - a^22 + a^21 - a^20 + a^19 - 
        a^18 + a^17 - a^16 + a^15 - a^14 - a^12 + a^11 - a^10 + a^9 + a^7 - a^6 
        + a^5 + a^3 - a^2 + a - 1)*q^85 + (-a^13 - a^3)*q^89 + (a^34 + a^6)*q^90
        + (-a^19 - a^17)*q^97 + a^26*q^98 + (a^34 - a^25 + a^16)*q^100 + (a^28 +
        a^6)*q^101 + (-a^23 - a^15)*q^104 + (-a^31 - a^7)*q^106 + (-a^25 + 
        a^4)*q^109 + (-a^17 + a^2)*q^113 + (-a^33 + a^26)*q^116 + (-a^9 - 
        a)*q^117 - a^33*q^121 + (a^22 - a^19)*q^122 + (a^30 - a^21 - a^11 + 
        a^2)*q^125 - a^7*q^128 + (-a^29 + a^28 + a^20 + 1)*q^130 + (a^32 + 
        1)*q^136 + (a^22 + a^8)*q^137 + a^30*q^144 + (-a^31 + a^10 - a^3 - 
        a)*q^145 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
596
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
37*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
596
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 74*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
146
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 + q^16 - q^17 - q^22 + q^25 - q^30 - q^45 + q^49 - q^61 + q^64 - 
        q^68 - q^69 - q^85 - q^86 - q^88 + q^100 - q^110 - q^120 + q^121 - q^125
        - q^145 + O(q^146),
    q^2 + q^8 - q^11 - q^15 + q^32 - q^34 - q^43 - q^44 + q^50 - q^55 - q^60 + 
        q^75 + 2*q^79 + q^87 - q^90 + q^98 + q^99 - q^111 + 2*q^115 - q^122 + 
        q^128 - q^131 + q^135 - q^136 - q^138 + O(q^146),
    q^3 - q^11 + q^12 - q^15 - q^18 + q^27 - q^34 - q^43 - q^44 + q^48 + q^50 + 
        q^51 + q^58 - q^60 + q^66 + q^71 - q^72 + q^83 - q^87 - q^99 + q^106 + 
        q^108 - q^111 + q^115 - q^122 - q^131 - q^136 - q^138 + O(q^146),
    q^5 - q^9 - q^17 + q^20 - q^22 + q^33 - q^36 + q^37 + q^46 + q^54 - q^61 - 
        q^68 + q^80 - q^85 - q^86 - q^88 + q^102 - q^110 + q^118 + q^121 + q^129
        + q^132 - q^144 + O(q^146),
    q^6 - q^9 - q^17 - q^22 + q^24 + q^25 + q^29 - q^30 + q^33 - q^36 + q^53 + 
        q^54 - q^61 - q^68 - q^69 + q^73 - q^81 - q^86 - q^88 + q^96 + q^100 + 
        q^102 + q^113 + q^116 - q^120 - q^125 + q^129 + q^132 + q^142 - q^144 - 
        q^145 + O(q^146),
    q^10 - q^11 - q^18 + q^23 + q^27 - q^34 + q^40 - q^43 - q^44 + q^51 - q^55 +
        q^59 + q^66 - q^72 + q^74 - q^75 - q^87 + q^92 + q^108 - q^122 - q^131 -
        q^136 + q^139 + O(q^146)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
198
);
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
198
);
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + a^14*q^4 + (a^19 - a^12 - a^8 + a)*q^7 + a^2*q^9 - a^15*q^12 + 
        (a^8 + a^6)*q^13 + (a^17 - a^6)*q^16 + (a^18 + a^15 - a^4)*q^19 + (a^19 
        - a^17 - a^16 + a^14 + 2*a^13 - a^11 - a^10 + a^7 + a^6 - a^4 - a^3 - 
        a^2 + a + 1)*q^21 + a^12*q^25 - a^3*q^27 + (-a^11 + a^4)*q^28 + (-a^19 -
        a^18 + a^16 + a^15 - a^13 - a^12 + a^10 + a^9 + a^8 - a^6 - a^5 + a^3 + 
        a^2 - 1)*q^31 + a^16*q^36 + (-a^17 - a^5)*q^37 + (-a^9 - a^7)*q^39 + 
        (-a^19 - a^14 + a^3)*q^43 + (-a^18 + a^7)*q^48 + (-a^19 + a^17 - a^14 - 
        2*a^13 + a^11 + a^10 + a^9 - a^7 - a^6 + a^5 + a^4 + a^3 - a - 1)*q^49 +
        (-a^19 + a^17 + a^16 - a^14 - a^13 + 2*a^11 + a^10 + a^9 - a^7 - a^6 + 
        a^4 + a^3 - a - 2)*q^52 + (-a^19 - a^16 + a^5)*q^57 + (a^19 + a^18 - 
        a^16 - a^15 + a^13 + a^12 + a^11 - a^10 - a^9 - a^8 + a^6 + a^5 - a^3 - 
        a^2)*q^61 + (a^19 + a^18 - a^16 - a^15 - a^14 + a^13 + a^12 - a^10 - a^9
        - a^8 + a^6 + a^5 - a^2 + 1)*q^63 - a^9*q^64 + (-a^18 + a^16 + a^7)*q^67
        + (-a^19 - a^18 - a^17 + a^16 + a^15 - a^13 - a^12 + a^9 + a^8 - a^6 - 
        a^5 + a^3 + a^2 - 1)*q^73 - a^13*q^75 + (a^19 + a^18 - a^16 - a^15 + 
        a^13 + a^12 - a^10 - a^9 - a^8 - a^7 + a^6 + a^5 - a^3 - a^2 + 1)*q^76 +
        (-a^13 + a^10)*q^79 + a^4*q^81 + (a^12 - a^5)*q^84 + (a^19 - a^18 - a^17
        - a^16 + a^14 + a^13 - a^11 - a^10 + 2*a^7 + a^6 - a^5 - a^4 - 2*a^3 + a
        + 1)*q^91 - q^93 + (a^13 - a^7 - a^2)*q^97 + (a^15 - a^4)*q^100 + (a^17 
        - a^11 - a^6)*q^103 - a^17*q^108 + (-a^16 + a^5 - a^3)*q^109 + (a^18 + 
        a^6)*q^111 + (a^18 - a^14 + a^3)*q^112 + (a^10 + a^8)*q^117 - a^15*q^121
        + a^13*q^124 + (-a^9 + a^4)*q^127 + (-a^19 + a^17 + a^16 + a^15 - a^14 -
        a^13 + a^11 + a^10 + a^9 - a^7 - a^6 + a^3 - a - 1)*q^129 + O(q^131)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 - a^3*q^4 + (a^8 - a)*q^7 + a^2*q^9 + a^4*q^12 + (a^8 + a^6)*q^13 
        + a^6*q^16 + (-a^7 + a^4)*q^19 + (-a^9 + a^2)*q^21 - a*q^25 - a^3*q^27 +
        (a^4 + 1)*q^28 + (2*a^9 - 2*a^8 + 2*a^7 - 2*a^6 + 2*a^5 - 2*a^4 + 2*a^3 
        - 2*a^2 + 2*a - 2)*q^31 - a^5*q^36 + (a^6 - a^5)*q^37 + (-a^9 - 
        a^7)*q^39 + (a^8 - a^3)*q^43 - a^7*q^48 + (-a^9 - a^5 + a^2)*q^49 + 
        (-a^9 + 1)*q^52 + (a^8 - a^5)*q^57 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 
        + a^3 - a^2 + a)*q^61 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 - a^2 + a - 
        1)*q^63 - a^9*q^64 + (-a^7 - a^5)*q^67 + (a^9 - a^8 + a^7 + a^5 - a^4 + 
        a^3 - a^2 + a - 1)*q^73 + a^2*q^75 + (a^9 - a^8 - a^6 + a^5 - a^4 + a^3 
        - a^2 + a - 1)*q^76 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 + a - 
        1)*q^79 + a^4*q^81 + (-a^5 - a)*q^84 + (-a^9 - a^7 - a^5 - a^3)*q^91 + 
        2*q^93 + (-a^7 + a^2)*q^97 + a^4*q^100 + (a^6 + 1)*q^103 + a^6*q^108 + 
        (-a^5 - a^3)*q^109 + (-a^7 + a^6)*q^111 + (-a^7 - a^3)*q^112 + (a^9 + 
        a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^117 + a^4*q^121 + 
        2*a^2*q^124 + (-a^9 + a^4)*q^127 + (-a^9 + a^4)*q^129 + O(q^131)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 22*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
33*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 66*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + (a - 1)*q^4 + a*q^7 + (a - 1)*q^9 + q^12 + a*q^13 - a*q^16 + 
        a*q^19 + (-a + 1)*q^21 + q^25 + q^27 - q^28 + (-a + 1)*q^31 - a*q^36 + 
        (2*a - 2)*q^37 + (-a + 1)*q^39 - 2*a*q^43 + (a - 1)*q^48 - q^52 + (-a + 
        1)*q^57 - q^61 - q^63 + q^64 - q^67 + a*q^73 - a*q^75 - q^76 - 2*a*q^79 
        - a*q^81 + a*q^84 + (a - 1)*q^91 - q^93 + (-a + 1)*q^97 + (a - 1)*q^100 
        - q^103 + (a - 1)*q^108 + 2*q^109 + 2*q^111 + (-a + 1)*q^112 - q^117 + 
        q^121 + a*q^124 + (-a + 1)*q^127 + (2*a - 2)*q^129 + O(q^131)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
597
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
99*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
131
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^13 - q^14 - q^20 - q^23 + q^25 - q^35 - q^40 + q^49 + q^50 + 
        q^52 + q^56 - q^58 + q^62 - q^65 + q^70 + q^80 + q^81 - q^89 + q^92 - 
        q^98 + q^106 - q^112 - q^115 - q^117 + q^121 + q^122 - q^126 - q^128 - 
        q^130 + O(q^131),
    q^2 - q^7 - q^10 + q^18 - q^20 + q^25 - q^29 + q^31 + q^35 - q^49 + q^50 + 
        q^53 - q^56 + q^61 - q^63 - q^64 - q^65 - q^86 - q^90 + q^91 - q^94 + 
        q^98 + q^100 + q^103 + q^104 + q^112 - q^115 + q^124 - q^125 + O(q^131),
    q^3 + q^27 - q^39 - q^42 - q^60 - q^69 + q^75 - q^105 - q^120 + O(q^131),
    q^4 - q^7 - q^8 - q^10 + q^13 + q^14 + q^16 + q^23 - q^26 - q^28 - q^29 - 
        q^32 + q^35 + q^36 - q^46 - q^49 + q^50 + q^52 + q^58 + q^62 - q^63 - 
        q^72 - q^86 + q^89 - q^90 + q^92 - q^94 + q^98 - q^104 + q^106 - q^116 +
        q^117 + q^122 - q^124 - q^125 + q^126 + O(q^131),
    q^5 - q^7 - q^8 + q^14 + q^16 - q^26 - q^29 + q^43 + q^45 - q^46 + q^47 - 
        q^49 + q^52 + q^58 - q^63 - q^65 - q^70 - q^72 + q^79 + q^91 + q^92 + 
        q^98 - q^100 - q^115 - q^124 + q^126 + O(q^131),
    q^6 - q^21 - q^30 + q^54 - q^60 + q^75 - q^87 + q^93 + q^105 + O(q^131),
    q^12 - q^21 - q^24 - q^30 + q^39 + q^42 + q^48 + q^69 - q^78 - q^84 - q^87 -
        q^96 + q^105 + q^108 + O(q^131),
    q^15 - q^21 - q^24 + q^42 + q^48 - q^78 - q^87 + q^129 + O(q^131)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
132
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 2*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
44
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 - q^4 + q^8 + q^12 + q^23 - q^24 + q^25 + q^27 - q^29 - q^31 - q^32 
        - q^41 - q^47 + q^49 + 2*q^59 + q^64 - q^69 - q^71 - q^73 - q^75 - q^81 
        + q^87 - q^92 + q^93 + q^96 - q^100 + 2*q^101 - q^108 + q^116 + q^121 + 
        q^123 + q^124 - q^127 - q^131 - q^139 + q^141 - q^147 - q^151 + 
        O(q^162),
    q^2 - q^4 - q^6 + q^12 + q^16 - q^32 + q^46 - q^48 + q^50 + q^54 - q^58 - 
        q^62 - q^82 - q^92 - q^94 + q^96 + q^98 - q^100 - q^108 + q^116 + 
        2*q^118 + q^124 + q^128 - q^138 - q^142 - q^146 - q^150 + O(q^162),
    q^13 - q^39 - q^52 + q^104 + q^156 + O(q^162),
    q^26 - q^52 - q^78 + q^156 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - 4*a*q^9 + 2*q^12 + (-a + 2)*q^13 + (-3*a + 3)*q^16 + (2*a - 1)*q^18 + (a
        - 1)*q^23 + (2*a + 2)*q^24 - q^25 - q^26 + q^27 + (-3*a + 3)*q^29 + (4*a
        - 2)*q^31 + (a - 2)*q^32 + (4*a - 4)*q^36 + (-a - 2)*q^39 + (-a - 
        1)*q^41 + (2*a - 1)*q^47 - 2*a*q^48 + (-a + 1)*q^49 - 2*a*q^52 + (a - 
        2)*q^58 + (-2*a + 2)*q^62 + q^64 + (a - 2)*q^71 + (a - 2)*q^72 + (2*a - 
        1)*q^73 + a*q^78 + (a - 1)*q^81 + a*q^82 + a*q^87 + (a + 1)*q^93 + (-a +
        1)*q^94 + (2*a - 1)*q^96 + (a - 1)*q^101 + (-a + 2)*q^104 - 2*a*q^108 - 
        4*q^116 - a*q^117 + a*q^121 + (-2*a + 4)*q^123 + (-2*a + 4)*q^124 + (3*a
        - 3)*q^127 + (-3*a - 3)*q^128 - 3*q^131 + 3*a*q^139 + (3*a + 3)*q^141 + 
        q^142 - 2*q^144 + (-a + 1)*q^146 + (-2*a + 1)*q^151 + 2*a*q^156 + 
        O(q^162),
    q^2 + (a + 1)*q^9 + (a - 2)*q^12 + (a - 1)*q^13 - a*q^18 - q^24 + (2*a - 
        1)*q^29 - 2*a*q^31 + (-2*a + 1)*q^36 + q^39 + q^41 + (a - 1)*q^46 - 
        a*q^47 - q^50 + a*q^52 + q^54 + (-a + 1)*q^71 + (-2*a + 2)*q^72 - a*q^73
        - q^78 - q^93 + a*q^96 + (-a + 1)*q^98 + a*q^104 + (a + 1)*q^108 + (-a +
        2)*q^116 + (a - 1)*q^123 + (a - 1)*q^124 + (-2*a + 1)*q^127 + q^128 + 
        (-a + 2)*q^131 + (-a - 1)*q^139 - 2*q^141 + a*q^151 - q^156 + O(q^162),
    q^3 + (2*a - 2)*q^9 - a*q^12 - a*q^13 - q^16 + (-2*a + 1)*q^24 - a*q^27 - 
        2*q^29 + (-a + 2)*q^31 + 2*q^36 + a*q^39 + (2*a - 1)*q^41 + (a - 1)*q^52
        + (a - 1)*q^69 + (a + 1)*q^71 + (a + 1)*q^72 + (-a + 2)*q^73 - q^75 + 
        q^81 + (-a + 1)*q^87 - q^104 + (a - 1)*q^108 + 2*a*q^116 - q^117 + (-a -
        1)*q^123 + (-a - 1)*q^124 + q^127 + (2*a - 1)*q^128 + a*q^131 + (-2*a + 
        2)*q^139 + (-2*a + 1)*q^141 + a*q^144 + (-a + 1)*q^147 + (a - 2)*q^151 +
        (-a + 1)*q^156 + O(q^162),
    q^4 - 3*q^9 + (-2*a + 2)*q^12 + (-2*a + 1)*q^13 - 2*a*q^16 + (a + 1)*q^18 + 
        (-a + 2)*q^24 + (a - 1)*q^26 - 3*a*q^29 + (2*a + 2)*q^31 + 3*a*q^36 + (a
        - 2)*q^39 + (a - 2)*q^41 + (a + 1)*q^47 - q^48 - 2*q^52 + (2*a - 1)*q^58
        - 2*a*q^62 + (2*a - 1)*q^71 + (2*a - 1)*q^72 + (a + 1)*q^73 + q^78 + 
        q^82 + (a - 1)*q^92 + (-a + 2)*q^93 - a*q^94 - q^100 - a*q^104 - q^108 +
        (4*a - 4)*q^116 + (-2*a + 1)*q^123 + (-4*a + 2)*q^124 + 3*a*q^127 + (2*a
        - 4)*q^128 + (3*a - 3)*q^131 + 3*q^139 + (-2*a + 4)*q^141 + (-a + 
        1)*q^142 - a*q^146 + (-a - 1)*q^151 + q^156 + O(q^162),
    q^6 + (-2*a + 1)*q^9 + (a + 1)*q^12 + q^13 + (-a + 2)*q^16 + (2*a - 2)*q^18 
        + 2*a*q^24 - a*q^26 + (-a + 2)*q^29 + (2*a - 2)*q^31 - q^32 + (2*a - 
        4)*q^36 - a*q^39 - a*q^41 + (a - 1)*q^47 + (-2*a + 1)*q^48 + (-2*a + 
        1)*q^52 - a*q^54 - 2*q^58 + (-a + 2)*q^62 - q^71 - q^72 + (a - 1)*q^73 +
        a*q^78 + (2*a - 1)*q^82 + a*q^93 + q^104 + (-2*a + 1)*q^108 + (-2*a - 
        2)*q^116 + q^123 + 3*q^124 + (a - 2)*q^127 - 3*a*q^128 + (-a - 1)*q^131 
        + (a - 1)*q^138 + (2*a - 1)*q^139 + 2*a*q^141 + (a + 1)*q^142 + (-a + 
        2)*q^146 - q^150 + (-a + 1)*q^151 + (2*a - 1)*q^156 + O(q^162),
    q^8 + (a - 2)*q^9 - a*q^13 + (-a - 1)*q^16 + (-2*a + 2)*q^24 + (-a - 1)*q^29
        + 2*q^31 + a*q^32 + (a + 1)*q^36 + (a - 1)*q^39 + (a - 1)*q^41 + q^47 + 
        (a - 2)*q^48 + (a - 1)*q^52 + (-2*a + 1)*q^64 + a*q^71 + q^73 + (-a + 
        1)*q^93 + 2*q^96 - a*q^104 + (2*a - 1)*q^116 - a*q^123 - 2*a*q^124 + (a 
        + 1)*q^127 + (3*a - 3)*q^128 + (2*a - 1)*q^131 + (-a + 2)*q^139 + (-2*a 
        + 2)*q^141 + (2*a - 1)*q^144 - q^151 + q^156 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + 1/3*(-a - 1)*q^13 + a*q^16 + q^18 - a*q^23 + q^25 + 1/3*(-2*a + 1)*q^26 
        - q^27 + a*q^29 + (a - 1)*q^32 + 1/3*(a + 1)*q^39 - a*q^41 - q^47 - 
        a*q^49 + (a - 1)*q^58 + (2*a - 2)*q^59 - q^64 + (a - 1)*q^71 + (-a + 
        1)*q^72 + q^73 + 1/3*(-a - 1)*q^78 - a*q^81 + (-a + 1)*q^82 + (-a + 
        1)*q^87 - a*q^93 - a*q^94 + q^96 + a*q^101 + 1/3*(-a - 1)*q^104 + (a - 
        1)*q^117 + (a - 1)*q^121 - a*q^127 - a*q^128 + q^131 + (-a + 1)*q^139 + 
        a*q^141 - q^142 + a*q^146 + q^151 + O(q^162),
    q^2 - a*q^9 + (-a + 1)*q^12 + 1/3*(a - 2)*q^13 + (a - 1)*q^18 - q^24 + q^29 
        + q^36 + 1/3*(2*a - 1)*q^39 - q^41 - a*q^46 + (a - 1)*q^47 + q^50 + 
        1/3*(-a - 1)*q^52 - q^54 + a*q^71 + (-a + 1)*q^73 + q^78 + q^93 + (a - 
        1)*q^96 - a*q^98 + 1/3*(a + 1)*q^104 + a*q^108 + (a - 1)*q^116 + (2*a - 
        2)*q^118 + a*q^123 + a*q^124 - q^127 - q^128 + (-a + 1)*q^131 - a*q^139 
        + (-a + 1)*q^151 + 1/3*(-2*a + 1)*q^156 + O(q^162),
    q^3 + (-a + 1)*q^12 + 1/3*(-a - 1)*q^13 + q^16 - q^24 + (a - 1)*q^27 + (a - 
        1)*q^31 + 1/3*(a + 1)*q^39 - q^41 + 1/3*(a - 2)*q^52 - a*q^69 + a*q^71 -
        a*q^72 + (-a + 1)*q^73 + q^75 - q^81 - a*q^87 + 1/3*(2*a - 1)*q^104 + 
        a*q^108 + q^117 + a*q^123 + a*q^124 - q^127 - q^128 + (-a + 1)*q^131 + 
        q^141 + (a - 1)*q^144 - a*q^147 + (-a + 1)*q^151 + 1/3*(-a + 2)*q^156 + 
        O(q^162),
    q^4 - q^9 + 1/3*(2*a - 1)*q^13 - a*q^18 + (-a + 1)*q^24 + 1/3*(a - 2)*q^26 +
        (-a + 1)*q^29 + (a - 1)*q^36 + 1/3*(a + 1)*q^39 + (a - 1)*q^41 + a*q^47 
        - q^48 + q^58 + q^71 + q^72 - a*q^73 + 1/3*(2*a - 1)*q^78 - q^82 - 
        a*q^92 + (-a + 1)*q^93 + (a - 1)*q^94 + q^100 + 1/3*(-a - 1)*q^104 - 
        q^108 + q^123 + (a - 1)*q^127 - a*q^131 - q^139 + a*q^142 + (-a + 
        1)*q^146 - a*q^151 + q^156 + O(q^162),
    q^6 - q^9 - a*q^12 + 1/3*(2*a - 1)*q^13 + (-a + 1)*q^16 + 1/3*(-a - 1)*q^26 
        + (-a + 1)*q^29 + q^32 + 1/3*(a + 1)*q^39 + (a - 1)*q^41 + a*q^47 - q^48
        + 1/3*(2*a - 1)*q^52 + (a - 1)*q^54 + (a - 1)*q^62 + q^71 - q^72 - 
        a*q^73 + 1/3*(a + 1)*q^78 - q^82 + (-a + 1)*q^93 + 1/3*(2*a - 1)*q^104 +
        q^108 + q^123 + q^124 + (a - 1)*q^127 + (a - 1)*q^128 - a*q^131 - 
        a*q^138 - q^139 + a*q^142 + (-a + 1)*q^146 + q^150 - a*q^151 + 1/3*(-2*a
        + 1)*q^156 + O(q^162),
    q^8 + (-a + 1)*q^9 + 1/3*(-a - 1)*q^13 + a*q^16 + a*q^29 + (a - 1)*q^32 - 
        a*q^36 + 1/3*(a - 2)*q^39 - a*q^41 - q^47 + (-a + 1)*q^48 + 1/3*(a - 
        2)*q^52 - q^64 + (a - 1)*q^71 + q^73 + a*q^93 + 1/3*(-a - 1)*q^104 + 
        q^116 + (a - 1)*q^123 - a*q^127 - a*q^128 + q^131 + (-a + 1)*q^139 + 
        q^144 + q^151 + 1/3*(2*a - 1)*q^156 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
598
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
6*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
162
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^12 + q^16 - q^18 - q^27 + q^31 + q^32 - q^35 - q^41 - q^46 - q^47 + 
        q^50 + q^54 - q^55 + q^62 + q^64 - q^70 + q^71 - q^72 - q^73 + q^77 + 
        q^78 + q^81 - q^82 + q^87 - q^92 + q^93 - q^94 + q^95 + q^96 + q^98 + 
        q^100 - q^101 - q^104 - q^110 - q^116 + q^117 - q^123 + q^131 - q^133 - 
        q^140 - q^141 + q^142 - q^146 + q^151 + q^154 + O(q^162),
    q^2 - q^24 - 1/2*q^26 + q^32 + 1/2*q^52 - q^54 - q^70 - 1/2*q^78 - q^110 + 
        q^124 + q^128 + q^154 + 1/2*q^156 + O(q^162),
    q^3 + q^12 - 2*q^16 + q^23 - q^25 + q^29 + q^35 - q^48 - q^49 + q^55 + q^69 
        - q^75 - q^77 - 2*q^81 + q^92 - q^95 - q^100 - q^101 + q^104 + q^116 - 
        q^117 - q^121 + q^127 - 2*q^131 + q^133 + q^139 + q^140 - q^147 + 
        O(q^162),
    q^4 + q^12 - q^16 - 1/2*q^26 - q^48 - 1/2*q^52 - q^62 - 1/2*q^78 + q^82 + 
        q^92 + q^94 - q^100 + q^104 - q^108 + q^116 - q^142 + q^146 - 1/2*q^156 
        + O(q^162),
    q^5 - q^7 - q^11 + q^19 + q^20 - q^28 + q^37 - q^44 - q^45 + q^63 - q^65 + 
        q^67 + q^76 + q^80 - q^83 - q^89 + q^91 - q^97 + q^99 - q^109 - q^112 - 
        q^115 + q^137 + q^143 + q^148 + q^149 + q^161 + O(q^162),
    q^6 - 2*q^18 + q^24 - q^26 - q^46 + q^50 + 2*q^54 + q^58 - q^70 - 2*q^72 + 
        q^78 + q^96 + q^98 - q^104 - q^110 + q^138 - q^150 + q^154 + O(q^162),
    q^8 - q^18 + q^24 - 1/2*q^26 - q^46 + q^50 - 1/2*q^52 + q^54 - q^70 - q^72 +
        1/2*q^78 + q^98 - q^104 - q^110 - q^124 + q^154 - 1/2*q^156 + O(q^162),
    q^9 - q^16 + q^18 + q^23 - q^25 + 1/2*q^26 - q^27 - q^31 - q^32 + q^35 + 
        q^36 - q^39 + q^41 + q^46 + q^47 - q^48 - q^49 - q^50 + 1/2*q^52 - q^54 
        + q^55 + q^70 - q^71 + q^72 + q^73 - q^77 - 1/2*q^78 + q^87 + q^92 - 
        q^93 - q^95 - q^96 - q^98 - q^100 - q^101 + q^104 - q^108 + q^110 - 
        q^121 + q^123 - q^131 + q^133 + q^140 + q^141 + q^144 - q^151 - q^154 - 
        1/2*q^156 + O(q^162),
    q^10 - q^14 - q^22 + q^38 + q^40 - q^56 + q^74 - q^88 - q^90 + q^126 - q^130
        + q^134 + q^152 + q^160 + O(q^162),
    q^13 - 2*q^18 - q^26 + 2*q^31 + 2*q^32 + q^39 - 2*q^41 - 2*q^46 - 2*q^47 + 
        2*q^50 + 2*q^54 - 2*q^70 + 2*q^71 - 2*q^72 - 2*q^73 + q^78 + 2*q^93 + 
        2*q^96 + 2*q^98 - q^104 - 2*q^110 - 2*q^123 - 2*q^141 + 2*q^151 + 
        2*q^154 + O(q^162)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
599
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
598
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
599
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
599
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
599
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
299*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^12 + q^16 + q^17 - q^20 - q^24 + q^27 - q^30 - q^32 - q^34 + q^37 + 
        q^41 - q^45 - q^47 + q^49 + q^50 - q^51 - q^53 - q^57 + q^60 + q^64 - 
        q^67 - q^68 - q^72 + q^75 - q^76 - q^78 - q^82 - q^83 + q^85 + q^94 + 
        O(q^100),
    q^2 + q^18 - q^19 - q^24 - q^30 - q^45 + q^50 - q^57 + q^75 + q^81 - q^82 + 
        q^85 + q^98 + O(q^100),
    q^3 - q^16 - q^17 - q^18 + q^24 + q^26 + q^27 - q^36 - q^38 - q^39 - q^41 + 
        q^52 + q^53 + q^54 + q^57 + q^74 - q^85 - q^90 + O(q^100),
    q^4 - q^12 - q^17 - q^18 + q^24 + q^26 - q^41 + q^45 - q^50 + q^53 + q^57 + 
        q^65 - q^75 - q^80 + q^83 - q^85 - q^94 + O(q^100),
    q^5 - q^12 - q^16 - q^17 - q^18 + q^20 + q^24 + q^26 + q^30 + q^34 - q^38 - 
        q^39 - q^41 + q^45 - q^50 + q^52 + q^53 + q^57 - q^60 - q^64 + q^72 - 
        q^75 + q^78 - q^85 - q^90 - q^94 + O(q^100),
    q^6 - q^12 - q^16 - q^17 - q^18 + 2*q^24 + 2*q^26 + q^27 - q^36 + q^37 - 
        q^38 - q^39 + q^40 - q^41 - q^48 - q^50 + q^53 + q^54 + q^57 - q^64 + 
        q^65 - q^75 - q^80 - q^85 - q^90 - q^94 + q^95 + q^96 + O(q^100),
    q^8 - q^12 - q^16 - q^17 - q^18 + q^19 + 2*q^24 + q^26 + q^30 + q^32 - q^36 
        - q^38 - q^39 - q^41 + q^45 - q^48 - q^50 + q^53 + 2*q^57 - q^60 - q^64 
        + q^72 - q^75 + q^76 + q^78 - q^80 + q^82 - q^85 - q^94 + q^96 + 
        O(q^100),
    q^9 - q^12 - q^16 - q^17 + q^20 + q^24 + q^26 + q^34 - q^38 - q^39 + q^40 - 
        q^41 - q^48 - q^50 + q^53 + q^57 - q^60 - q^64 + q^67 + q^68 + q^72 - 
        q^75 + q^78 + q^81 - q^85 - q^90 - q^94 + q^95 + O(q^100),
    q^10 - q^12 - q^16 + q^24 + q^26 - q^38 + q^40 - q^41 - q^48 - q^50 + q^53 +
        q^57 - q^64 + q^68 + q^72 - q^85 - q^94 + q^96 + O(q^100),
    q^13 - q^16 - q^17 - q^18 + q^20 + q^24 + q^26 + q^30 - q^36 - q^38 - q^39 -
        q^41 - q^50 + q^51 + q^52 + q^53 + q^54 + q^57 - q^60 - q^64 + q^71 + 
        q^74 - q^75 - q^85 - q^90 - q^94 + O(q^100),
    q^15 - q^17 - q^18 + q^24 + q^26 - q^36 - q^39 + q^53 + q^57 - q^75 - q^80 +
        O(q^100),
    q^25 - q^26 - q^27 + q^30 + q^32 - q^37 - q^40 + q^47 + q^51 - q^60 - q^65 +
        q^76 + q^82 - q^95 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^9 - q^11 + q^16 - q^19 - q^34 - q^36 - q^41 - q^44 + q^49 + q^54
        + 2*q^59 + q^64 - q^76 + 2*q^86 - q^89 + q^99 + 2*q^131 - q^134 - q^136 
        - q^139 - q^144 - q^146 - q^164 - q^166 + q^169 + q^171 - q^176 - q^179 
        + O(q^194),
    q^2 + q^8 - q^17 - q^18 - q^22 + q^27 + q^32 - q^38 + 2*q^43 - q^67 - q^68 -
        q^72 - q^73 - q^82 - q^83 - q^88 + 2*q^97 + q^98 - q^107 + q^108 - q^113
        + 2*q^118 + q^128 - q^137 - q^152 + q^153 - q^163 + 2*q^172 - q^178 + 
        q^187 - q^193 + O(q^194),
    q^3 + q^12 - q^18 - q^33 + q^48 - q^57 - q^72 - q^102 - q^123 - q^132 + 
        q^147 + q^153 + q^162 + 2*q^177 + q^192 + O(q^194),
    q^6 - q^9 + q^24 - q^36 - q^51 - q^66 + q^81 + q^96 + q^99 - q^114 + 2*q^129
        - q^144 + q^171 + O(q^194)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^19 - q^21 - q^31 - q^39 - q^61 + 2*q^79 + q^81 + q^91 - q^109 + 
        2*q^111 + q^121 - q^129 + 2*q^139 - q^151 - q^171 - q^181 - q^189 + 
        O(q^194),
    q^2 + q^18 - q^38 - q^42 - q^62 - q^78 - q^122 + 2*q^158 + q^162 + q^182 + 
        O(q^194),
    q^3 - q^7 - q^13 + q^27 + 2*q^37 - q^43 - q^57 - q^63 - q^67 + 2*q^73 - q^93
        - q^97 + 2*q^103 - q^117 + 2*q^127 + q^133 - q^157 - q^163 - q^183 - 
        q^193 + O(q^194),
    q^6 - q^14 - q^26 + q^54 + 2*q^74 - q^86 - q^114 - q^126 - q^134 + 2*q^146 -
        q^186 + O(q^194)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^6 + q^9 + q^16 - q^24 - 2*q^31 + q^36 - q^49 - q^54 + q^64 - 
        2*q^79 + q^81 - q^96 - 2*q^106 - q^121 - 2*q^124 + q^144 + 2*q^151 + 
        2*q^159 + 2*q^166 + q^169 + 2*q^186 + O(q^194),
    q^2 - q^3 + q^8 - q^12 + q^18 - q^27 + q^32 - q^48 - 2*q^53 - 2*q^62 + q^72 
        + 2*q^83 + 2*q^93 - q^98 + 2*q^107 - q^108 + q^128 + q^147 - 2*q^158 + 
        q^162 + 2*q^173 - q^192 + O(q^194)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 2*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + (-a^3 + a^2 - a + 1)*q^6 + (-a^3 + a^2 - 2*a + 1)*q^7 - a^2*q^9 
        - a*q^10 + (a^3 - a^2 + a - 1)*q^15 + a^2*q^16 + (2*a^3 - a^2 + a - 
        1)*q^22 + q^24 + a*q^25 + (-a^2 + 1)*q^28 + (a^3 - 1)*q^31 + (a^2 + 
        a)*q^33 - a^3*q^36 - a^2*q^40 + (-a^3 - 1)*q^42 + (-a^3 + a^2 - 1)*q^49 
        - a*q^54 + (-2*a^3 + a^2 - a + 1)*q^55 - q^60 + (a^3 - a)*q^63 + 
        a^3*q^64 + (a^2 - 1)*q^70 + (-a^2 + a - 1)*q^79 + (a^3 - a^2 + a - 
        1)*q^81 + (a^3 - a^2 + a - 2)*q^88 + a^3*q^90 + a*q^96 + (-a^2 + 1)*q^97
        + a^2*q^100 + (a^2 - 1)*q^103 + (a^3 + 1)*q^105 + (-a^2 + a)*q^106 + 
        (-a^3 + a)*q^112 + (-a^3 - a^2)*q^118 + (-a^2 - a - 1)*q^121 + (a^3 - 
        a^2 - 1)*q^124 + (a + 1)*q^127 + (a^3 + a^2)*q^132 + a*q^135 + (-a^3 + 
        a^2 - a + 1)*q^144 + q^150 + (a^3 - a^2 - 1)*q^151 + (2*a^2 - a + 
        2)*q^154 + (-a^3 + a^2 - a)*q^159 - a^3*q^160 + (-a^3 - a)*q^166 + (-a^3
        + a^2 - 2*a + 1)*q^168 + (-a^3 + a^2 - a + 1)*q^169 + (-a^2 + 1)*q^175 +
        (-a - 1)*q^177 + (a^3 + a - 1)*q^186 + (-a^3 + a^2 - 2*a + 1)*q^193 + 
        O(q^194),
    q^2 - a^3*q^3 - q^5 + a*q^8 + (a^3 + a^2)*q^11 + (-a^3 + a^2 - a + 1)*q^12 +
        (-a^3 + a^2 - 2*a + 1)*q^14 - a^2*q^18 - a*q^20 + (a^3 - 2*a^2 + a - 
        1)*q^21 - q^27 + (a^3 - a^2 + a - 1)*q^30 + a^2*q^32 + (a^3 - a^2 + 2*a 
        - 1)*q^35 + (2*a^3 - a^2 + a - 1)*q^44 + a^2*q^45 + q^48 + a*q^50 + (-a 
        + 1)*q^53 + (-a^2 + 1)*q^56 + (-a^2 - a)*q^59 + (a^3 - 1)*q^62 + (a^2 + 
        a)*q^66 - a^3*q^72 + (-a^3 + a^2 - a + 1)*q^75 + (-2*a^3 + 2*a^2 + 
        1)*q^77 - a^2*q^80 + (-a^2 - 1)*q^83 + (-a^3 - 1)*q^84 + (a^3 + a)*q^93 
        + (-a^3 + a^2 - 1)*q^98 + (-a^3 + a^2 - a + 2)*q^99 + (-a^3 + a^2 - a + 
        2)*q^101 + (a^3 - a^2 + a)*q^107 - a*q^108 + (-2*a^3 + a^2 - a + 
        1)*q^110 - q^120 - a*q^125 + (a^3 - a)*q^126 + a^3*q^128 + (a^2 - 
        1)*q^140 + (a^3 - a + 1)*q^147 + (a^3 - a^2 + a - 2)*q^149 + (-a^3 + 
        1)*q^155 + (-a^2 + a - 1)*q^158 + (a^3 - a^2 + a - 1)*q^162 + (-a^2 - 
        a)*q^165 + (-a^3 + a^2 + 1)*q^173 + (a^3 - a^2 + a - 2)*q^176 + (-a^3 + 
        2*a^2 - a + 1)*q^179 + a^3*q^180 + (a^3 - a^2 + 2*a - 1)*q^189 + a*q^192
        + O(q^194)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a^3*q^5 + (a^3 - a^2 + a - 1)*q^9 + (a^2 - a)*q^13 + (a^3 + a - 1)*q^17 
        - a*q^25 + (-a^3 - a)*q^29 + (-a^3 + 1)*q^37 + (a^2 - a)*q^41 + a^2*q^45
        + q^49 + (a^3 - a^2 + a)*q^53 + (-a^2 + a - 1)*q^61 + (a^3 - a^2 + 
        a)*q^65 + (-a^2 + a - 1)*q^73 - a^3*q^81 + (a^2 + 1)*q^85 + (a^2 + 
        1)*q^89 + (-a^3 - a)*q^97 + (a^3 - a^2 - 1)*q^101 + (a^2 - a)*q^109 + 
        (-a^3 + 1)*q^113 + (-a + 1)*q^117 + a^2*q^121 + (a^3 - a^2 + a - 
        1)*q^125 + (a^2 - a)*q^137 + (a^3 - a^2 - 1)*q^145 + (-a^3 + a^2)*q^149 
        + (-a^3 - a)*q^153 + (a^3 - a^2 - 1)*q^157 + (a - 1)*q^169 + (a^2 + 
        1)*q^173 + (a^3 + a - 1)*q^181 + (-a^3 - a)*q^185 + (-a^3 + a^2)*q^193 +
        O(q^194),
    q^2 - a*q^4 + a^2*q^8 - a^3*q^10 - a^3*q^16 + (a^3 - a^2 + a - 1)*q^18 + 
        (a^3 - a^2 + a - 1)*q^20 + (a^2 - a)*q^26 + (a^3 - a^2 + a - 1)*q^32 + 
        (a^3 + a - 1)*q^34 + q^36 + q^40 - a*q^50 + (-a^3 + a^2)*q^52 + (-a^3 - 
        a)*q^58 + q^64 + (-a^3 + 1)*q^68 - a*q^72 + (-a^3 + 1)*q^74 - a*q^80 + 
        (a^2 - a)*q^82 + a^2*q^90 + q^98 + a^2*q^100 + (-a^2 + a - 1)*q^104 + 
        (a^3 - a^2 + a)*q^106 + (a^3 + a - 1)*q^116 + (-a^2 + a - 1)*q^122 - 
        a*q^128 + (a^3 - a^2 + a)*q^130 + (a^3 - a^2 - 1)*q^136 + a^2*q^144 + 
        (-a^2 + a - 1)*q^146 + (a^3 - a^2 - 1)*q^148 + a^2*q^160 - a^3*q^162 + 
        (-a^3 + a^2)*q^164 + (a^2 + 1)*q^170 + (a^2 + 1)*q^178 - a^3*q^180 + 
        O(q^194),
    q^3 - a^3*q^15 + (a^3 - a^2 + a - 1)*q^27 + (a^2 - a)*q^39 + (a^3 + a - 
        1)*q^51 - a*q^75 + (-a^3 - a)*q^87 + (-a^3 + 1)*q^111 + (a^2 - a)*q^123 
        + a^2*q^135 + q^147 + (a^3 - a^2 + a)*q^159 + (-a^2 + a - 1)*q^183 + 
        O(q^194),
    q^6 - a*q^12 + a^2*q^24 - a^3*q^30 - a^3*q^48 + (a^3 - a^2 + a - 1)*q^54 + 
        (a^3 - a^2 + a - 1)*q^60 + (a^2 - a)*q^78 + (a^3 - a^2 + a - 1)*q^96 + 
        (a^3 + a - 1)*q^102 + q^108 + q^120 - a*q^150 + (-a^3 + a^2)*q^156 + 
        (-a^3 - a)*q^174 + q^192 + O(q^194)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 4*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 - a^3*q^6 + (-a^3 + a^2)*q^7 + (a^3 - a^2 + a - 1)*q^9 + 
        a^2*q^10 - a^3*q^15 + (a^3 - a^2 + a - 1)*q^16 + (-a^3 - a)*q^22 + q^24 
        + a^2*q^25 + (a^3 - a^2 + a)*q^28 + (-a + 1)*q^31 + (a^3 + a - 1)*q^33 -
        a*q^36 + (a^3 - a^2 + a - 1)*q^40 + (-a + 1)*q^42 + (a^3 - a^2)*q^49 + 
        a^2*q^54 + (-a^3 - a)*q^55 - 2*a^3*q^58 + q^60 + (a^2 - a)*q^63 - a*q^64
        + (a^3 - a^2 + a)*q^70 - 2*a*q^73 + (-a^3 - a)*q^79 - a^3*q^81 + (2*a^3 
        - 2*a^2 + 2*a - 2)*q^87 + (-a^3 + 1)*q^88 - a*q^90 + a^2*q^96 + (a^3 - 
        a^2 + a)*q^97 + (a^3 - a^2 + a - 1)*q^100 + (a^3 - a^2 + a)*q^103 + (-a 
        + 1)*q^105 + (a^3 + a - 1)*q^106 + (a^2 - a)*q^112 + (a^3 - a^2 - 
        1)*q^118 + (a^3 + a)*q^121 + (-a^3 + a^2)*q^124 + (a^2 + 1)*q^127 + (a^3
        - a^2 - 1)*q^132 + a^2*q^135 - a^3*q^144 - 2*a^3*q^145 + q^150 + (-a^3 +
        a^2)*q^151 - a^2*q^154 + (-a^3 + 1)*q^159 - a*q^160 + (a^2 - a)*q^166 + 
        (-a^3 + a^2)*q^168 - a^3*q^169 + (a^3 - a^2 + a)*q^175 + (a^2 + 1)*q^177
        + (-a^2 + a - 1)*q^186 + (-a^3 + a^2)*q^193 + O(q^194),
    q^2 - a*q^3 + q^5 + a^2*q^8 + (a^3 - a^2 - 1)*q^11 - a^3*q^12 + (-a^3 + 
        a^2)*q^14 + (a^3 - a^2 + a - 1)*q^18 + a^2*q^20 + (-a^2 + a - 1)*q^21 + 
        q^27 - 2*a*q^29 - a^3*q^30 + (a^3 - a^2 + a - 1)*q^32 + (-a^3 + 
        a^2)*q^35 + (-a^3 - a)*q^44 + (a^3 - a^2 + a - 1)*q^45 + q^48 + a^2*q^50
        + (a^2 + 1)*q^53 + (a^3 - a^2 + a)*q^56 + (a^3 + a - 1)*q^59 + (-a + 
        1)*q^62 + (a^3 + a - 1)*q^66 - a*q^72 - a^3*q^75 - q^77 + (a^3 - a^2 + a
        - 1)*q^80 + (a^3 - a^2 + a)*q^83 + (-a + 1)*q^84 + (a^2 - a)*q^93 + (a^3
        - a^2)*q^98 + (-a^3 + 1)*q^99 + (-a^3 + 1)*q^101 + (-a^3 + 1)*q^107 + 
        a^2*q^108 + (-a^3 - a)*q^110 - 2*a^3*q^116 + q^120 + a^2*q^125 + (a^2 - 
        a)*q^126 - a*q^128 + 2*a^2*q^131 + (a^3 - a^2 + a)*q^140 - 2*a*q^146 + 
        (a^2 - a + 1)*q^147 + (-a^3 + 1)*q^149 + (-a + 1)*q^155 + (-a^3 - 
        a)*q^158 - a^3*q^162 + (a^3 + a - 1)*q^165 + (-a^3 + a^2)*q^173 + (2*a^3
        - 2*a^2 + 2*a - 2)*q^174 + (-a^3 + 1)*q^176 + (-a^2 + a - 1)*q^179 - 
        a*q^180 + (-a^3 + a^2)*q^189 + a^2*q^192 + O(q^194)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.3 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^9 + a*q^49 - 2*q^61 + 2*a*q^69 - q^81 - 2*a*q^109 - q^121 + 2*q^141 
        + a*q^169 + 2*q^181 + O(q^194),
    q^2 + a*q^8 - q^12 - a*q^18 - q^32 - a*q^48 + q^72 + 2*q^92 + a*q^98 + 
        a*q^108 - 2*q^122 - a*q^128 + 2*a*q^138 - q^162 - 2*a*q^188 + q^192 + 
        O(q^194),
    q^3 - 2*q^23 - a*q^27 + 2*a*q^47 + 2*q^83 - 2*a*q^107 + a*q^147 - 2*a*q^167 
        - 2*q^183 + O(q^194),
    q^4 + a*q^6 + a*q^16 - q^24 - a*q^36 - 2*a*q^46 + q^54 - q^64 - 2*q^94 - 
        a*q^96 + q^144 + 2*a*q^166 + 2*q^184 + O(q^194)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + H.3 + 5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 - q^16 + a*q^49 - q^51 + a*q^54 + a*q^64 + q^66 - a*q^99 - a*q^114
        - q^121 - a*q^169 + q^171 + O(q^194),
    q^2 - a*q^8 - q^27 - q^32 + a*q^33 + q^57 + a*q^98 - q^102 + a*q^108 - 
        a*q^123 + a*q^128 + q^132 - a*q^153 + O(q^194),
    q^3 - a*q^12 - q^18 + 2*a*q^22 + q^33 - q^48 + a*q^57 - 2*a*q^67 + a*q^72 - 
        2*q^73 - 2*a*q^82 + 2*q^88 - a*q^102 - q^123 - a*q^132 + a*q^147 - q^153
        + a*q^162 - 2*q^163 + 2*q^178 + 2*a*q^187 + a*q^192 + 2*q^193 + 
        O(q^194),
    q^6 - q^11 - a*q^19 - a*q^24 + a*q^34 + q^41 + a*q^44 - q^76 - q^81 + a*q^89
        - q^96 + a*q^99 + q^121 - a*q^134 + q^136 + a*q^139 - q^146 - a*q^164 - 
        q^166 + q^171 + q^176 - a*q^179 + O(q^194),
    q^9 - a*q^11 - q^19 + q^34 - a*q^36 + a*q^41 - q^44 + a*q^51 + a*q^66 + 
        a*q^76 - q^89 - q^114 - a*q^121 + q^134 - a*q^136 + q^139 - q^144 - 
        a*q^146 + q^164 + a*q^166 + a*q^176 + q^179 + O(q^194),
    q^17 - a*q^18 - q^22 + a*q^33 + a*q^38 - q^57 + q^67 - a*q^68 - q^72 - 
        a*q^73 + q^82 + a*q^83 + a*q^88 + q^102 - q^107 - a*q^113 - a*q^123 + 
        q^132 - q^137 + q^152 - a*q^163 + a*q^178 - q^187 + a*q^193 + O(q^194)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2 + 10*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^4 + q^9 - q^11 + q^16 + q^19 + q^34 - q^36 - q^41 + q^44 - q^49 - q^54
        - 2*q^59 - q^64 - q^76 + 2*q^86 + q^89 - q^99 + 2*q^131 + q^134 - q^136 
        + q^139 + q^144 - q^146 + q^164 - q^166 - q^169 + q^171 - q^176 + q^179 
        + O(q^194),
    q^2 - q^8 - q^17 + q^18 - q^22 + q^27 + q^32 + q^38 - 2*q^43 - q^67 + q^68 -
        q^72 + q^73 - q^82 + q^83 + q^88 + 2*q^97 - q^98 - q^107 - q^108 + q^113
        - 2*q^118 - q^128 - q^137 - q^152 - q^153 + q^163 + 2*q^172 + q^178 + 
        q^187 + q^193 + O(q^194),
    q^3 - q^12 - q^18 - q^33 + q^48 + q^57 + q^72 + q^102 - q^123 + q^132 - 
        q^147 + q^153 - q^162 - 2*q^177 - q^192 + O(q^194),
    q^6 + q^9 - q^24 - q^36 - q^51 - q^66 + q^81 + q^96 - q^99 + q^114 - 2*q^129
        + q^144 + q^171 + O(q^194)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 10*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 + q^19 - q^21 - q^31 + q^39 - q^61 - 2*q^79 + q^81 + q^91 + q^109 + 
        2*q^111 + q^121 + q^129 - 2*q^139 - q^151 - q^171 - q^181 + q^189 + 
        O(q^194),
    q^2 - q^18 + q^38 - q^42 - q^62 + q^78 - q^122 - 2*q^158 + q^162 + q^182 + 
        O(q^194),
    q^3 + q^7 - q^13 - q^27 - 2*q^37 - q^43 + q^57 - q^63 + q^67 + 2*q^73 - q^93
        + q^97 + 2*q^103 + q^117 - 2*q^127 + q^133 + q^157 - q^163 - q^183 - 
        q^193 + O(q^194),
    q^6 + q^14 - q^26 - q^54 - 2*q^74 - q^86 + q^114 - q^126 + q^134 + 2*q^146 -
        q^186 + O(q^194)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
600
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3 + 10*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
194
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^4 - q^6 - q^9 + q^16 + q^24 - 2*q^31 + q^36 + q^49 + q^54 - q^64 + 
        2*q^79 + q^81 - q^96 - 2*q^106 - q^121 + 2*q^124 - q^144 + 2*q^151 - 
        2*q^159 + 2*q^166 - q^169 + 2*q^186 + O(q^194),
    q^2 + q^3 - q^8 - q^12 - q^18 - q^27 + q^32 + q^48 + 2*q^53 - 2*q^62 + q^72 
        - 2*q^83 - 2*q^93 + q^98 + 2*q^107 + q^108 - q^128 + q^147 + 2*q^158 + 
        q^162 - 2*q^173 - q^192 + O(q^194),
    q^5 - q^20 - q^30 - q^45 + q^50 + q^75 + q^80 + q^120 - q^125 - 2*q^155 + 
        q^180 + O(q^194),
    q^10 + q^15 - q^25 - q^40 - q^60 - q^90 + q^100 - q^135 + q^150 + q^160 + 
        O(q^194)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
