Qx<x>:=PolynomialRing(Rationals());
basis_list:=[**];
G:=FullDirichletGroup(
201
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
43
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
201
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
43
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
201
);
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:=
43
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
201
);
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:=
43
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
201
);
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:=
43
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^43)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
201
);
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:=
43
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
201
);
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:=
43
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + 
        O(q^43),
    q^2 + (-a + 1)*q^3 + (a - 1)*q^8 - a*q^11 + (a - 1)*q^14 + q^17 - q^18 + 
        a*q^21 - q^23 - a*q^26 + (a - 1)*q^27 - a*q^29 + a*q^38 - q^39 + a*q^41 
        + O(q^43)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
201
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
33*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
43
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
202
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
100
);
qprec:=
49
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
202
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
49
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
202
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
25*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
49
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^5 + a^3)*q^2 + (a^5 - a^4 - a^2 + 2*a - 1)*q^4 + (-a^5 + a^4 - a^3 +
        a^2 - a + 1)*q^7 + (-a^5 + 2*a^4 - a^3 - 2*a + 1)*q^8 + a^5*q^9 + (a^4 -
        1)*q^11 + (-a^4 + a^2)*q^14 + (-2*a^4 + a^3 + a - 2)*q^16 + (a^3 - 
        a)*q^18 + (a^5 - a^3 + a^2 - 1)*q^22 + (-a^4 - a^2)*q^23 - a*q^25 + (a^5
        - a^2 + 1)*q^28 + a*q^29 + (a^5 + a^4 - a^3 - a^2 + a + 1)*q^32 + (a^5 -
        2*a^4 + a^3 - a^2 + 2*a - 1)*q^36 + (a^2 + a)*q^37 + O(q^38)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^5 - a^4 - a^2 + a - 1)*q^2 + (-a^4 + a^3 + a - 1)*q^4 - a^5*q^7 + 
        (-a^5 + a^4 + a^2 - a)*q^8 - a^3*q^9 + (-a + 1)*q^11 + (a^4 - a)*q^14 + 
        (-a^5 + a^4 - a^3 - a + 1)*q^16 + (a^5 - a^4 + a^3 + a - 1)*q^18 + (a^5 
        - a^2 + a)*q^22 + (a^4 - a)*q^23 + a^2*q^25 + (a^4 - a^3 + 1)*q^28 + 
        a^2*q^29 + a^5*q^32 + (-a^5 + a^2 - a)*q^36 + (a^4 + a^2)*q^37 + O(q^38)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
203
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^7 - q^9 + q^16 - 2*q^23 + q^25 - q^28 - q^29 - q^36 + O(q^38)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
204
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
204
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
204
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
204
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
204
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
204
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
204
);
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:=
62
;
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 + O(q^62),
    q^3 + a*q^6 - q^12 + (-a - 1)*q^15 - a*q^24 + a*q^27 + (-a + 1)*q^30 + q^48 
        - q^51 - q^54 + (a + 1)*q^60 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
204
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
204
);
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:=
62
;
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 + O(q^62),
    q^3 - q^6 + q^12 - q^24 - q^27 - 2*q^39 + q^48 + q^51 + q^54 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
204
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 8*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^13 - q^15 - q^19 - q^33 - q^43 + q^49 + q^51 + q^55 + O(q^62),
    q^3 - q^5 - q^11 + q^17 - q^23 + q^27 + 2*q^29 - q^39 - q^41 - q^45 - q^57 +
        O(q^62)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
205
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
206
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
102
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
206
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
206
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
206
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
51*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^13 - q^14 - q^16 - q^19 - q^23 + q^25 + q^26 + q^32 - q^34 + 
        q^38 - q^41 + q^46 + O(q^50),
    q^2 - q^14 - q^16 + q^18 - q^28 - q^34 + O(q^50),
    q^4 - q^8 - q^14 + q^26 - q^34 + q^36 + q^38 + q^46 + O(q^50),
    q^7 + q^8 - q^13 - q^16 + q^17 - q^19 - q^23 - q^28 + q^29 - q^41 - q^49 + 
        O(q^50)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
207
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
207
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
207
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
207
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
207
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
207
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
207
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^2 - q^8 - q^13 - q^16 - q^23 + q^25 - q^26 + q^29 - q^31 + q^41 + 
        O(q^42)
]
;
Bo:=
[
    q - q^2 + q^8 - q^13 - q^16 + q^23 + q^25 + q^26 - q^29 - q^31 - q^41 + 
        O(q^42),
    q^3 - q^6 + q^24 - q^27 - q^39 + O(q^42),
    q^9 - q^18 - q^27 + O(q^42)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
207
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 - a*q^6 - q^8 + q^12 - a*q^16 + (a - 1)*q^18 + (a - 1)*q^23 
        + q^24 - a*q^25 + 2*q^26 - a*q^27 + (-a + 1)*q^32 + (a - 1)*q^36 + (a - 
        1)*q^39 + O(q^42),
    q^2 + (a - 1)*q^4 - a*q^6 + (a - 1)*q^8 + q^9 - a*q^12 - a*q^13 - q^16 + 
        q^24 + q^26 + (a - 1)*q^29 + q^31 + (-a + 1)*q^32 + (a - 1)*q^36 + (a - 
        1)*q^39 + (a - 1)*q^41 + O(q^42),
    q^3 + (-a - 1)*q^4 + (-a + 1)*q^6 + a*q^9 - a*q^18 + (a - 1)*q^24 + (2*a - 
        1)*q^26 + (a - 2)*q^29 + (a + 1)*q^31 + (a + 1)*q^32 - q^39 + (-a - 
        1)*q^41 + O(q^42)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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(
12
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^46)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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(
12
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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(
4
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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(
4
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
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 + O(q^46),
    q^2 - q^10 + (a - 1)*q^18 - a*q^26 + (-a + 1)*q^34 + O(q^46),
    q^4 - a*q^8 + (a - 1)*q^16 - q^20 + q^32 + (a - 1)*q^36 + a*q^40 + O(q^46)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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(
12
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^13 - 2*q^17 + q^25 - 2*q^29 + O(q^46)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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(
4
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
208
);
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:=Rationals();
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 - q^17 + q^27 + q^35 - q^43 + O(q^46),
    q^2 - q^6 + q^8 - q^20 - q^24 - q^28 + q^32 - q^34 + O(q^46),
    q^4 - q^10 - q^12 - q^14 + q^16 + q^26 + q^30 - q^40 + q^42 + O(q^46),
    q^5 + q^7 - q^13 - q^15 - q^21 - 2*q^31 + q^37 + q^39 + O(q^46)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^38),
    q^2 - a*q^6 + (a - 1)*q^8 - a*q^10 + (a - 1)*q^11 + a*q^13 - q^17 + (-a + 
        1)*q^19 + q^24 - a*q^29 + (a - 1)*q^30 + q^33 + O(q^38)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
209
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^38)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
210
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
210
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
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(
210
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
210
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
210
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
210
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
210
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
210
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
210
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
210
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
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(
210
);
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(
4
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
210
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
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(
211
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
210
);
qprec:=
35
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
211
);
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:=
35
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
211
);
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:=
35
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
211
);
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:=
35
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
211
);
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:=
35
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
211
);
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:=
35
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
211
);
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:=
35
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
211
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
105*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
35
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^5 + q^9 - q^11 - q^13 + q^16 - q^19 - q^20 + O(q^35)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
212
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
212
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
212
);
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(
26
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
212
);
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(
26
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + a^2*q^4 + (a^10 + a^6)*q^5 - a^3*q^8 + a^8*q^9 + (-a^11 - 
        a^7)*q^10 + (-a^5 + a^4)*q^13 + a^4*q^16 + (-a^11 - a^9)*q^17 - a^9*q^18
        + (a^11 - a^10 + a^9 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^20 +
        (a^11 - a^10 + a^9 - a^8 - a^6 + a^5 - a^4 - a^2 + a - 1)*q^25 + (a^6 - 
        a^5)*q^26 + (a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 + a -
        1)*q^29 - a^5*q^32 + (a^11 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - 
        a^2 + a - 1)*q^34 + a^10*q^36 + (-a^7 - a)*q^37 + (-a^9 + 1)*q^40 + 
        (-a^9 - a^3)*q^41 + (-a^5 - a)*q^45 + a^2*q^49 + O(q^50)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
212
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
212
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 26*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^6 - q^13 + q^16 - q^17 - q^24 + q^25 - q^29 - q^37 - q^38 - q^46
        + q^49 + O(q^50),
    q^2 - q^3 + q^8 - q^12 - q^19 - q^23 - q^26 + q^27 + 2*q^31 + q^32 - q^34 + 
        q^39 - q^48 + O(q^50)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
213
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
213
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
213
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
213
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
213
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
213
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
213
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
213
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
35*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 - q^12 - q^15 + q^20 + q^24 + q^25 + q^30 - q^32 + q^38 - q^40 - 
        q^43 + O(q^46),
    q^2 - q^16 - q^18 + q^19 - q^20 - q^25 + q^27 - q^29 + q^37 + q^40 + 
        O(q^46),
    q^3 - q^15 - q^18 + q^27 - q^36 - q^45 + O(q^46),
    q^4 + q^5 - q^8 - q^10 - q^25 + q^27 - q^29 - q^36 + q^38 + q^43 - q^45 + 
        O(q^46),
    q^6 - q^12 - q^15 - q^18 + q^24 + q^27 + q^30 + O(q^46),
    q^9 - q^12 - q^15 + q^24 + q^30 - q^45 + O(q^46)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
214
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
106
);
qprec:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
214
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
53*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
52
;
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 + 
        O(q^52),
    q^2 - q^6 + q^8 - q^22 - q^24 - q^26 + q^32 - q^38 - q^46 + q^50 + O(q^52)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
215
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^10 + q^11 - 2*q^14 - q^15 - q^16 + q^25 - q^31 - q^35 - q^36 - q^41 + 
        O(q^42),
    q^2 - q^7 - q^12 + q^27 + q^37 + O(q^42),
    q^3 - q^7 - q^8 + q^20 + q^22 + q^27 - q^30 - q^33 + O(q^42),
    q^4 - q^6 - q^10 - q^11 + q^14 + q^15 + q^16 - q^24 + q^36 - q^40 + q^41 + 
        O(q^42),
    q^5 - q^7 - q^8 + q^12 - q^18 + q^20 + 2*q^22 - q^28 - q^30 - q^32 - q^33 + 
        O(q^42),
    q^9 - q^10 - q^11 + q^14 + q^16 - q^21 - q^24 + q^31 + q^35 + O(q^42)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
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(
18
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + a^4*q^3 + a^2*q^4 - a^5*q^6 - a^3*q^8 + (a^5 - a^2)*q^9 + (a^3 +
        a^2 - 1)*q^11 + (a^3 - 1)*q^12 + a^4*q^16 + (-a^5 - a^4 + a)*q^17 + q^18
        + (a^5 - a^4 - a^2 + a)*q^19 + (-a^4 - a^3 + a)*q^22 + (-a^4 + a)*q^24 -
        a*q^25 - a^3*q^27 - a^5*q^32 + (a^3 - a - 1)*q^33 + (a^5 + a^3 - a^2 - 
        1)*q^34 - a*q^36 + (a^5 - a^2 + 1)*q^38 + (a^4 - a^3)*q^41 + (-a^5 - 
        a^3)*q^43 + (a^5 + a^4 - a^2)*q^44 + (a^5 - a^2)*q^48 - a^5*q^49 + 
        O(q^50)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
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(
6
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
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(
6
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 + (a - 1)*q^4 - q^8 - a*q^11 - a*q^16 + q^17 - q^19 + (-a + 
        1)*q^22 - a*q^25 + (-a + 1)*q^32 + a*q^34 - a*q^38 + (a - 1)*q^41 + 
        a*q^43 + q^44 + (a - 1)*q^49 + O(q^50)
]
;
Bo:=
[
    q - a*q^2 + (a - 1)*q^4 + q^8 + a*q^11 - a*q^16 - q^17 - q^19 + (-a + 
        1)*q^22 - a*q^25 + (a - 1)*q^32 + a*q^34 + a*q^38 + (-a + 1)*q^41 + 
        a*q^43 - q^44 + (a - 1)*q^49 + O(q^50),
    q^3 - a*q^6 - a*q^9 + (a - 1)*q^12 + (a - 1)*q^18 + q^24 + (a - 1)*q^27 + 
        a*q^33 + q^36 - a*q^48 + O(q^50)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 - q^13 - q^19 + q^25 + 2*q^31 - q^37 + 2*q^43 + O(q^50),
    q^2 - q^14 - q^26 - q^38 + O(q^50)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
216
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^7 - q^10 + q^16 - q^22 - q^28 - q^31 - q^40 + O(q^50),
    q^2 - q^5 + q^8 - q^11 - q^14 - q^20 + 2*q^29 + q^32 + q^35 - q^44 + O(q^50)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 - q^5 + q^8 + q^9 + q^10 - q^16 - q^18 - q^19 + q^31 + q^38 + 
        O(q^40),
    q^7 - q^14 - q^35 + O(q^40)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
217
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^5 + 1/3*(-a - 1)*q^7 - q^8 + (a - 1)*q^9 + a*q^10 + 1/3*(-2*a
        + 1)*q^14 + (a - 1)*q^16 + (a - 1)*q^19 + 2*q^20 - 2*a*q^25 - a*q^28 - 
        a*q^31 + 1/3*(4*a - 5)*q^35 + O(q^40),
    q^2 + 1/3*(-a + 2)*q^7 - a*q^8 + (a - 1)*q^10 + 1/3*(a + 1)*q^14 - q^16 + (a
        - 1)*q^18 - q^19 + a*q^20 + (-a + 1)*q^25 - a*q^28 + 1/3*(a - 2)*q^35 + 
        (-a + 1)*q^38 + O(q^40),
    q^4 - a*q^5 + 1/3*(a - 2)*q^7 + 1/3*(-a + 2)*q^14 + a*q^19 - q^25 - q^32 + 
        1/3*(2*a - 1)*q^35 + (a - 1)*q^36 - q^38 + O(q^40)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
218
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
108
);
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
218
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
218
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
218
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
72
);
qprec:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^47)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^47)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^47)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^6 - q^9 - q^10 + (-a + 1)*q^13 - a*q^15 + (-a + 1)*q^16 + (a -
        1)*q^19 + q^22 + q^24 + (a - 1)*q^31 + a*q^33 - a*q^37 + a*q^40 + 2*q^43
        - q^46 + O(q^47),
    q^2 + (a - 1)*q^4 + (a - 1)*q^5 - q^6 + a*q^7 - a*q^8 - 2*a*q^9 - a*q^10 + 
        (-a + 1)*q^11 + (a - 1)*q^12 + 3*q^13 + (-a + 1)*q^15 + 2*q^16 - q^18 - 
        2*q^19 + a*q^21 + a*q^22 + (a - 1)*q^23 + a*q^24 + q^25 + (-a + 1)*q^26 
        - 2*a*q^27 + (-a + 1)*q^28 - q^29 - a*q^30 - 2*q^31 + (a - 1)*q^33 + (a 
        - 1)*q^36 + (a - 1)*q^37 + (a - 1)*q^38 + 3*q^39 + (a - 1)*q^40 + (a - 
        1)*q^41 + 3*a*q^43 + (-a + 1)*q^45 - a*q^46 + O(q^47),
    q^3 - a*q^4 + (-a + 1)*q^6 - q^7 + 2*q^9 + q^10 - a*q^12 + (3*a - 3)*q^13 + 
        a*q^15 + (2*a - 2)*q^16 + (-2*a + 2)*q^19 - q^21 - q^22 - q^24 + (a - 
        1)*q^25 + q^27 + a*q^28 + (-2*a + 2)*q^31 - a*q^33 - a*q^36 - a*q^37 + 
        (2*a - 2)*q^39 - a*q^40 - 3*q^43 + q^46 + O(q^47)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
219
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^3 + q^4 + q^9 - q^12 + q^16 - 2*q^19 - q^25 - q^27 + q^36 - 2*q^37 + 
        O(q^47)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
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(
20
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
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(
10
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
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 + O(q^62),
    q^5 - q^15 - q^25 + q^55 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
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(
4
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
220
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + 1/2*q^5 - 2*q^9 - q^11 + 3/2*q^15 - 1/2*q^25 + q^31 - q^45 - q^49 - 
        1/2*q^55 - q^59 + O(q^62),
    q^3 - 1/2*q^5 + 1/2*q^15 - q^23 - 1/2*q^25 - q^27 - q^33 + q^37 + q^45 + 
        1/2*q^55 + O(q^62)
]
;
Bo:=
[
    q - q^5 + q^9 - q^11 + q^25 - 2*q^31 - q^45 - q^49 + q^55 + 2*q^59 + 
        O(q^62),
    q^2 - q^8 - q^10 + q^18 - q^22 + q^32 + q^40 + q^50 + O(q^62),
    q^4 - q^16 - q^20 + q^36 - q^44 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
221
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
222
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
222
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
222
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
222
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
222
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
222
);
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:=
70
;
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 + O(q^70),
    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 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
222
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
222
);
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:=
70
;
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 + O(q^70),
    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 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
222
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 18*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 + q^9 - q^10 - q^12 - q^21 + q^28 + q^30 + q^34 - q^46 + q^48 + q^49
        + q^58 - q^63 - q^64 - q^67 + O(q^70),
    q^2 - q^14 + q^18 - q^20 - q^24 - q^42 + q^56 + q^60 + q^68 + O(q^70),
    q^3 - q^7 - q^12 + q^16 - q^21 - q^25 + q^27 + q^28 + q^37 - q^40 + 2*q^49 -
        q^63 - q^64 - q^67 + O(q^70),
    q^4 - q^10 - q^12 + q^30 + q^34 + q^36 - q^40 - q^46 + q^58 - q^64 + 
        O(q^70),
    q^5 + q^8 - q^15 - q^17 - q^20 + q^23 - q^24 - q^29 + q^45 + q^51 - q^59 + 
        q^60 + q^68 - q^69 + O(q^70),
    q^6 - q^8 - q^14 + q^20 + q^32 - q^42 - q^50 + q^54 + q^56 - q^60 - q^68 + 
        O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
223
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
222
);
qprec:=
37
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
223
);
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:=
37
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
223
);
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:=
37
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
223
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
111*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
37
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^14 - q^17 - q^19 + q^25 - q^28 - q^32 + O(q^37),
    q^2 - q^7 - q^14 - q^16 + q^18 + q^29 + q^31 + O(q^37),
    q^4 - q^7 - q^8 + q^17 + q^19 - q^34 + q^36 + O(q^37)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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(
6
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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:=
50
;
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 + 
        O(q^50),
    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 + O(q^50)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 + a^2*q^4 - a*q^7 + a^3*q^8 + a^3*q^9 + (-a^3 - a^2)*q^11 - 
        a^2*q^14 - q^16 - q^18 + (-a^3 + 1)*q^22 + (a^2 - 1)*q^23 + a*q^25 - 
        a^3*q^28 + (-a^2 - a)*q^29 - a*q^32 - a*q^36 + (-a^3 + a^2)*q^37 + (a - 
        1)*q^43 + (a + 1)*q^44 + (a^3 - a)*q^46 + a^2*q^49 + O(q^50)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
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 + O(q^50),
    q^2 + a*q^4 - q^8 + a*q^14 - a*q^16 - a*q^18 + (-a - 1)*q^22 - q^28 + q^32 +
        q^36 + (-a + 1)*q^44 + O(q^50)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
224
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^7 - q^9 - 2*q^23 - q^25 + q^49 + O(q^50)
]
;
Bo:=
[
    q - q^7 - q^9 + 2*q^23 - q^25 + q^49 + O(q^50),
    q^2 - q^14 - q^18 + 2*q^46 + O(q^50),
    q^4 - q^8 + q^16 - q^28 - q^32 - q^36 + O(q^50)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 - q^16 + 2*a*q^19 - 2*q^31 + O(q^38)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
225
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
226
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
112
);
qprec:=
55
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
226
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
55
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
227
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
226
);
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
227
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
113*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^7 - q^11 + q^16 - q^21 + q^25 - q^27 - q^28 - q^33 + O(q^38),
    q^3 - q^7 - q^9 - q^11 + q^12 + q^19 + q^23 - q^28 + q^29 - q^36 + O(q^38)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
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:=
70
;
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 + O(q^70),
    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 + 
        O(q^70),
    q^4 - a*q^12 + (a - 1)*q^16 - q^28 + (a - 1)*q^36 + q^48 + (-a + 1)*q^52 - 
        a*q^64 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
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 + O(q^70),
    q^3 - q^15 - q^21 + q^27 - q^33 - q^51 + q^57 + 2*q^69 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
228
);
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:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
229
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
228
);
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
229
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
229
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
229
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^3 - a*q^4 + a*q^5 + (a - 1)*q^7 - a*q^11 - a*q^12 + (-a - 1)*q^13 + 
        a*q^15 - q^16 + q^17 - q^19 + q^20 + (a - 1)*q^21 + (a + 1)*q^23 - q^27 
        + (a + 1)*q^28 - a*q^33 + (-a - 1)*q^35 + O(q^38),
    q^2 + (a - 1)*q^3 + (a + 1)*q^4 - q^6 - a*q^7 + a*q^10 + q^13 + (-a - 
        1)*q^15 + (-a + 1)*q^16 + (a - 1)*q^17 + (-a + 1)*q^19 + (a - 1)*q^20 - 
        a*q^21 - a*q^22 - 2*q^23 + (-a + 1)*q^27 - q^28 - a*q^30 - q^31 + q^32 +
        (a + 1)*q^33 - q^34 + q^35 + O(q^38)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
230
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
230
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
230
);
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(
22
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
230
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
230
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
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 + O(q^66),
    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 + O(q^66),
    q^5 - q^15 - q^20 + q^40 + q^60 - q^65 + O(q^66),
    q^10 - q^20 - q^30 + q^60 + O(q^66)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
230
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^2 + a - 1)*q^2 + (-a^3 + a^2 - a)*q^4 + a^2*q^7 + a^3*q^8 - a*q^9 + 
        (a^3 - a^2 + a - 1)*q^11 + (-a + 1)*q^14 + (a^3 - a^2 + a)*q^18 + (-a^3 
        + a^2)*q^22 + (-a^3 + a^2)*q^23 - a^3*q^25 + (-a^2 + a)*q^28 + (-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^3 - a^2 + a - 
        1)*q^49 + (a^2 - a)*q^50 + (a^2 + 1)*q^53 - q^56 + O(q^58),
    q^3 + (-a^2 + a - 1)*q^6 + (-a^3 + a^2 - a)*q^12 + a^2*q^21 + a^3*q^24 - 
        a*q^27 + (a^3 - a^2 + a - 1)*q^33 + (-a + 1)*q^42 + (a^3 - a^2 + a)*q^54
        + O(q^58)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
231
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^15 - q^16 - q^22 - q^37 - q^42 + q^49 + O(q^58),
    q^2 - q^8 - q^11 + q^18 - q^21 + q^29 - q^30 + q^35 + q^39 + q^57 + O(q^58),
    q^3 - q^5 - q^14 + q^26 + q^27 + q^38 - q^45 - q^47 - q^48 + q^56 + O(q^58),
    q^6 - q^7 - q^10 + q^13 + q^19 - q^24 - q^33 + q^40 + q^54 + q^55 + O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
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(
14
);
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
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:=
54
;
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 
        + O(q^54),
    q^2 - a*q^4 + a^2*q^8 + (-a^5 + a^4)*q^10 - a^3*q^16 - a^3*q^18 + (-a^4 + 
        a^3 - a^2 + a - 1)*q^20 + (a^5 - a^4 + a^3 + a - 1)*q^26 + a^4*q^32 + 
        (a^5 - a^4 + a^3 - a^2 - 1)*q^34 + a^4*q^36 + (a^5 - a^4 + a^3 - a^2 + 
        a)*q^40 + (-a^3 + a^2 - a)*q^50 + (-a^3 + 1)*q^52 + O(q^54)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
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(
14
);
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 - q^13 + q^29 + q^33 + q^49 - q^53 + O(q^54),
    q^2 + q^8 - q^10 - q^12 - q^26 + q^32 - q^40 - q^44 - q^48 + O(q^54),
    q^3 + q^11 - q^15 - 2*q^19 - q^27 + q^31 - q^39 + q^43 + q^47 + O(q^54),
    q^4 - q^6 + q^16 - q^20 - q^22 - q^24 + q^30 + 2*q^38 - q^52 + O(q^54)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
232
);
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:=Rationals();
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
233
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
232
);
qprec:=
39
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
233
);
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:=
39
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
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(
234
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
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(
12
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
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(
6
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
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(
6
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
70
;
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 + O(q^70),
    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 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
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(
6
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
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(
6
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
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(
6
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
234
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
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 + 
        O(q^70),
    q^2 - q^8 - q^26 + q^32 - q^50 + O(q^70),
    q^3 - q^9 - q^12 + q^27 + q^36 - q^39 + q^48 + O(q^70),
    q^6 - q^18 - q^24 + q^54 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
235
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
235
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
235
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
235
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
235
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
46
;
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 + O(q^46),
    q^2 - q^3 - q^4 + q^7 + q^9 - q^14 - q^17 + q^24 + q^28 - q^37 - q^42 + 
        O(q^46),
    q^5 - q^15 - q^30 - q^40 + q^45 + O(q^46),
    q^10 - q^15 - q^20 + q^35 + q^45 + O(q^46)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
235
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
236
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
236
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
236
);
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(
58
);
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
236
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
29*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^15 - q^17 - q^21 + q^25 - q^27 - q^35 - q^45 + q^49 + O(q^56),
    q^3 - q^7 - q^9 + q^21 + q^25 + q^27 - q^29 - q^35 + q^41 - q^45 - q^51 + 
        q^53 + O(q^56),
    q^5 - q^7 - q^9 + q^15 + q^19 - q^29 - q^35 + q^49 + O(q^56)
]
;
Bo:=
[
    q - q^3 - q^5 - q^7 + q^15 + 2*q^17 - q^19 + q^21 + q^27 - q^29 + q^35 - 
        q^41 - 2*q^51 - q^53 + O(q^56),
    q^2 - q^6 + q^8 - q^10 - q^14 - q^24 + q^30 + q^32 + 2*q^34 - q^38 - q^40 + 
        q^42 + q^54 + O(q^56),
    q^4 - q^12 + q^16 - q^20 - q^28 - q^48 + O(q^56)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
237
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
237
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
237
);
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:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
237
);
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:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
237
);
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:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^51)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
237
);
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:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
237
);
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:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
237
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
39*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
51
;
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 + O(q^51),
    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 + O(q^51),
    q^3 - q^15 - q^24 + q^27 - q^30 + O(q^51),
    q^6 - q^12 - q^15 + q^33 + q^39 + O(q^51)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
238
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
238
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
238
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
238
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
238
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
238
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
238
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
238
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
238
);
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(
6
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
238
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 8*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^15 - q^16 - q^18 - q^21 + q^32 + q^42 - q^43 + q^49 + q^50 - 
        q^51 + O(q^66),
    q^2 - q^16 - q^30 - q^36 + q^50 + q^64 + O(q^66),
    q^3 - q^7 - q^12 - q^17 + 2*q^24 + q^27 + q^28 - q^40 + q^41 - q^45 - 2*q^48
        - q^56 + q^61 - q^63 + O(q^66),
    q^4 + q^9 - q^16 - q^18 - q^21 - q^25 + q^35 + q^42 - q^43 + q^50 - q^51 + 
        q^53 - q^60 + O(q^66),
    q^5 - q^7 - q^17 - q^20 + q^24 + q^27 + q^28 + q^31 - q^40 - q^45 - q^48 + 
        O(q^66),
    q^6 - 2*q^12 - q^14 + q^20 + 2*q^24 + q^28 - q^34 - q^40 - q^48 + q^54 - 
        q^56 + O(q^66),
    q^8 + q^9 - q^16 - q^21 - q^25 + q^35 - q^36 - q^43 - q^51 + q^53 + O(q^66),
    q^10 - q^12 - q^14 + q^20 + q^24 - q^34 - q^40 + q^54 + q^62 + O(q^66)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
239
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
238
);
qprec:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
239
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
239
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
239
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
119*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^15 - q^18 - q^20 + q^25 - q^29 - q^33 + O(q^40),
    q^2 - q^9 - q^11 - q^12 + q^15 + q^17 + q^18 - q^22 - q^24 - q^25 - q^27 + 
        q^31 + q^32 + q^33 + q^36 + O(q^40),
    q^3 - q^8 - q^9 - q^11 + q^15 + q^17 + q^20 - q^25 + q^34 + O(q^40),
    q^4 - q^8 - q^9 - q^11 - q^12 + 2*q^15 + q^16 + q^17 + q^18 + q^20 - q^22 - 
        q^24 - q^25 - q^27 + q^29 - q^30 + q^33 + q^36 + O(q^40),
    q^5 - q^8 - q^9 - q^11 + q^15 + q^16 + q^17 + q^18 + q^20 - q^22 - q^24 - 
        q^25 - q^27 + q^34 + O(q^40),
    q^6 - q^8 - q^9 + q^15 + q^17 - q^27 - q^30 + O(q^40),
    q^10 - q^11 - q^12 + q^15 + q^17 - q^22 - q^25 + q^32 + q^36 + O(q^40)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
240
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
240
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
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(
240
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
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(
240
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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(
4
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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(
4
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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(
4
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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:=
74
;
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 + O(q^74),
    q^3 - q^15 - q^27 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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(
4
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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(
4
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + a*q^6 - a*q^9 + q^10 - q^15 - q^16 + (a - 1)*q^19 + q^24 + 
        a*q^25 + (a - 1)*q^34 - q^36 - a*q^40 + (-a - 1)*q^46 - q^49 + (-a + 
        1)*q^51 + q^54 + a*q^60 + (-a + 1)*q^61 + a*q^64 + (a + 1)*q^69 + 
        O(q^74),
    q^2 - q^3 + a*q^5 - a*q^8 + a*q^12 + (-a - 1)*q^17 - a*q^18 + q^20 + (-a + 
        1)*q^23 + a*q^27 - q^30 - q^32 + (a - 1)*q^38 + q^45 + (a + 1)*q^47 + 
        q^48 + a*q^50 + (-a + 1)*q^57 + (a - 1)*q^68 - q^72 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
240
);
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:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 + q^15 - q^25 - 2*q^31 + q^49 + O(q^74),
    q^2 - q^8 - q^12 - q^18 + q^20 + q^30 + q^32 + q^48 - q^50 - 2*q^62 + q^72 +
        O(q^74),
    q^3 - q^5 - q^27 + q^45 + 2*q^53 + O(q^74),
    q^4 + q^6 - q^10 - q^16 - q^24 - q^36 + q^40 - q^54 + q^60 + q^64 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
241
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
240
);
qprec:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
241
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
241
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
241
);
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:=
40
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
242
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
110
);
qprec:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
242
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
242
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
242
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
55*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
243
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
162
);
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
243
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
243
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
243
);
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:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^38)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
243
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
81*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
38
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^7 - q^13 + q^16 - q^19 + q^25 - q^28 - q^31 - q^37 + O(q^38)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + a^2*q^4 + (-a^7 - a^6 - a^5 + a^3 + a^2 - 1)*q^5 - a^3*q^8 + 
        (a^7 - a^2)*q^9 + (a^6 + a^5 - 1)*q^10 + (-a^5 - a^4 + a + 1)*q^13 + 
        a^4*q^16 + (-a^7 - a^6 + a^5 + a^4 + a^3 - 1)*q^17 + (a^7 - a^5 - a^4 + 
        a + 1)*q^18 + (-a^7 - a^6 + a)*q^20 + (a^7 + a^6 + a^5 - a^4 - 2*a^3 - 
        a^2)*q^25 + (a^6 + a^5 - a^2 - a)*q^26 + (a^6 + a^4)*q^29 - a^5*q^32 + 
        (-a^6 + a^3 - 1)*q^34 + (a^7 + a^6 - a^4 - a^3 - a^2 + 1)*q^36 + (a^7 + 
        a^6 - a^3 - a^2 + 1)*q^37 + (a^5 + a^4 + a^3 - a^2 - a - 1)*q^40 + (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^4 + a + 1)*q^50 + (-a^7 - a^6 + a^3 + a^2)*q^52 + (-a^6 + a^5 
        + a - 1)*q^53 + O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
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(
10
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
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(
10
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + a^2*q^4 + (a^3 - a^2 + a)*q^5 - a^3*q^8 + a^2*q^9 + (-a + 
        1)*q^10 + (-a^3 + a^2)*q^13 + (a^3 - a^2 + a - 1)*q^16 + (-a^3 - a)*q^17
        - a^3*q^18 + (a^2 - a)*q^20 + (-a^2 + a)*q^25 + (-a^2 + a - 1)*q^26 + 
        (a^3 - a^2 - 1)*q^29 + q^32 + (a^3 + a - 1)*q^34 + (a^3 - a^2 + a - 
        1)*q^36 + (2*a^3 - 2*a^2 + 2*a - 2)*q^37 + (-a^3 + a^2)*q^40 + (a^2 - 
        a)*q^41 + (a^2 - a)*q^45 - a^3*q^49 + (a^3 - a^2)*q^50 + (a^3 - a^2 + 
        a)*q^52 + (-a + 1)*q^53 + O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + (a - 1)*q^4 + a*q^5 + q^8 + q^9 + (-a + 1)*q^10 - 2*a*q^13 - 
        a*q^16 + (2*a - 2)*q^17 - a*q^18 - q^20 + (2*a - 2)*q^26 + (-a + 1)*q^29
        + (a - 1)*q^32 + 2*q^34 + (a - 1)*q^36 - q^37 + a*q^40 - q^41 + a*q^45 +
        (a - 1)*q^49 + 2*q^52 - q^53 + O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
244
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 30*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^5 + q^9 - q^13 - q^14 + q^16 - q^20 - q^22 + q^36 - q^41 - q^45 
        - q^46 - q^52 - q^56 + O(q^58),
    q^2 - q^7 + q^8 - q^10 - q^11 + q^18 - q^23 - q^26 - q^28 + 2*q^31 + q^32 + 
        q^35 - q^40 + 2*q^43 - q^44 + q^55 + O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
245
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
246
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
246
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
246
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
246
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
246
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
246
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
246
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
246
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 20*H.2
;
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(
247
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
247
);
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:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^16 - q^17 - q^23 + q^25 - q^26 - q^38 - q^43 + O(q^44),
    q^2 - q^8 - q^13 + q^18 - q^19 + q^31 - q^34 + q^37 + q^41 + O(q^44)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
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(
10
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
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(
6
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
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:=
58
;
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 + O(q^58),
    q^2 - q^8 + (a - 1)*q^10 - a*q^12 + (-a + 1)*q^26 + a*q^28 + q^32 - a*q^34 +
        (-a + 1)*q^40 + (a - 1)*q^42 + (a - 1)*q^44 + a*q^48 + O(q^58),
    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 + O(q^58),
    q^4 + a*q^6 - a*q^14 - q^16 + (a - 1)*q^20 + (-a + 1)*q^22 - a*q^24 - q^30 +
        a*q^38 + (-a + 1)*q^52 - q^54 + a*q^56 + O(q^58)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 - q^7 + q^9 - q^19 + q^31 + q^35 - q^41 - q^45 + 2*q^47 + O(q^58),
    q^2 - q^10 - q^14 + q^18 - q^38 + O(q^58),
    q^4 - q^16 - q^20 - q^28 + q^32 + q^36 + O(q^58),
    q^8 - q^16 - q^40 - q^56 + O(q^58)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
248
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 15*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^8 - q^9 + q^10 - q^14 - q^20 - q^25 - q^28 + q^31 - q^38 - 2*q^47 + 
        q^49 + q^50 + O(q^58),
    q^2 - q^7 + q^8 - q^9 - q^14 - q^28 + q^31 + q^32 + q^33 - q^36 + q^39 - 
        q^41 - q^47 + 2*q^49 + q^50 - q^56 + O(q^58),
    q^3 - q^6 - q^11 + q^12 - q^13 + q^22 - q^24 + q^26 + q^29 + q^37 - q^43 - 
        q^44 + q^48 - q^52 - q^53 + O(q^58),
    q^4 - q^7 - q^8 + q^9 - q^10 + q^16 - q^18 + q^20 + 2*q^25 - q^31 - q^33 + 
        q^38 - q^39 - q^41 + q^47 - q^50 - q^56 + O(q^58),
    q^5 + q^8 - q^9 - q^14 - q^16 + q^18 - q^19 - q^20 - q^25 + q^31 + q^32 + 
        q^33 + q^35 - q^36 + q^39 + q^40 - q^45 - q^47 + q^49 + 2*q^50 + O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
249
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
249
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
82
);
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
249
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
249
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
41*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
54
;
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 + O(q^54),
    q^3 - q^9 + q^12 - q^21 - q^33 - q^36 + q^48 - q^51 + O(q^54)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
250
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
100
);
qprec:=
57
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
250
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
57
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
250
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
25*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
57
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
251
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
250
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
251
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
251
);
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:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
251
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
125*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^7 - q^15 + q^16 - q^17 + q^25 - q^28 - q^35 - q^39 - q^41 + 
        O(q^42),
    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 + O(q^42),
    q^5 - q^7 - q^9 + q^13 - q^17 + q^20 + q^21 + q^27 - q^28 - q^35 - q^36 - 
        q^41 + O(q^42)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
252
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
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(
252
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
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 + O(q^74),
    q^3 - a*q^9 + (a - 1)*q^21 + (a - 1)*q^27 - q^39 + (-a + 1)*q^57 + q^63 + 
        O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 + q^25 - 2*q^37 - 2*q^43 + q^49 + 2*q^67 + O(q^74),
    q^2 - q^8 - q^14 + q^32 + q^50 + q^56 + O(q^74),
    q^4 - q^16 - q^28 + q^64 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
252
);
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:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^16 - q^22 - q^25 + q^28 + q^46 - q^49 + q^58 + O(q^74),
    q^2 - q^11 + q^23 - q^29 - q^32 - q^44 - q^50 + q^53 + q^56 + q^71 + 
        O(q^74),
    q^4 - q^7 - q^22 + 2*q^43 + q^46 - q^58 - q^64 + O(q^74),
    q^8 + q^11 - q^14 - q^23 - q^29 - q^44 + q^53 - q^71 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
253
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
253
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
253
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
253
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
253
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
253
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 
        + O(q^46)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
253
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
46
;
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 + O(q^46),
    q^11 - q^22 - q^33 + O(q^46)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
253
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
254
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
126
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
254
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
254
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
254
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
254
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
254
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
63*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^16 - q^17 - q^19 - q^22 + q^25 - q^26 - q^31 + q^32 + q^34 - 
        q^37 + q^38 + q^49 - q^61 + O(q^62),
    q^2 - q^16 + q^18 - q^22 - q^26 - q^44 + q^50 - q^52 + O(q^62),
    q^4 + q^11 + q^13 - q^16 - q^17 - q^19 - q^22 - q^26 - q^31 + q^34 + q^36 - 
        q^37 + q^38 + q^41 - q^44 + q^47 - q^52 - q^61 + O(q^62),
    q^8 + q^11 + q^13 - q^16 - q^17 - q^19 - q^31 - q^37 + q^41 - q^44 + q^47 - 
        q^52 - q^61 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^3 - a^2 - a)*q^4 + (a^3 - 1)*q^6 + a*q^9 + (a^2 + a)*q^10 - a^3*q^15
        + (a^3 - a - 1)*q^16 + (a^2 - 1)*q^19 + (a^3 + a^2 + a + 1)*q^24 - 
        a*q^25 + (a^3 - a^2)*q^31 + (-a^3 + 1)*q^34 + (-a^3 - a^2 + 1)*q^36 + 
        (-a^3 - a^2 + a + 1)*q^40 + a^3*q^49 - a*q^51 + (-a - 1)*q^54 + (-a^2 - 
        a - 1)*q^60 + (-a^3 - 1)*q^61 + a^2*q^64 + O(q^66),
    q^2 + 1/2*(a^3 - a^2 - a + 1)*q^3 + 1/2*(a^3 - a^2 + a - 1)*q^5 + (-a^3 - 
        a)*q^8 + 1/2*(a^3 + a^2 - a - 1)*q^12 + 1/2*(-a^3 + a^2 + a - 1)*q^17 + 
        a*q^18 + 1/2*(a^3 + a^2 + a + 1)*q^20 + 1/2*(-a^3 - a^2 + a - 1)*q^27 - 
        a^3*q^30 - q^32 + (a^2 - 1)*q^38 + 1/2*(-a^3 + a^2 - a - 1)*q^45 + (a^3 
        - a^2 + 1)*q^47 + 1/2*(a^3 + a^2 + a + 1)*q^48 - a*q^50 - q^53 + (-a^3 +
        a^2)*q^57 + (a^3 - a^2)*q^62 + O(q^66)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 + (-a + 1)*q^6 + a*q^9 + (a - 1)*q^10 - a*q^15 - q^16 + a*q^25 + (-a
        - 1)*q^31 + (-a + 1)*q^34 - a*q^36 + (2*a + 2)*q^46 - a*q^49 + a*q^51 + 
        (a + 1)*q^54 + a*q^60 + (-a + 1)*q^61 + q^64 + O(q^66),
    q^2 + 1/2*(a - 1)*q^3 + 1/2*(-a + 1)*q^5 + 1/2*(-a + 1)*q^12 + 1/2*(a - 
        1)*q^17 + a*q^18 + 1/2*(a - 1)*q^20 + (-a - 1)*q^23 + 1/2*(-a - 1)*q^27 
        - a*q^30 - q^32 + 1/2*(a + 1)*q^45 + a*q^47 + 1/2*(-a + 1)*q^48 + a*q^50
        + q^53 + (-a - 1)*q^62 + O(q^66)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
255
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^16 - q^19 - q^21 + q^25 - q^30 - q^34 - q^55 + q^64 + O(q^66),
    q^2 - q^8 - q^15 - q^17 + q^18 + q^33 + q^35 - q^38 - q^42 + q^47 + q^50 + 
        q^53 + O(q^66),
    q^3 - q^7 - q^10 + q^22 + q^27 - q^37 + q^40 - q^48 - q^57 + q^58 - q^63 + 
        O(q^66),
    q^4 + 2*q^9 + q^15 - 2*q^16 - 3*q^19 - q^21 + 2*q^25 - q^30 - q^34 - q^36 + 
        q^49 + q^51 - q^55 - q^60 + 2*q^64 + O(q^66),
    q^5 + q^7 + q^10 - q^12 + q^17 - q^20 - q^22 - 2*q^23 - 2*q^27 + q^37 - q^40
        - q^45 + 2*q^48 + 3*q^57 - q^58 + q^63 + O(q^66),
    q^6 + q^7 + q^10 + q^11 - q^12 - q^14 + q^17 - q^20 - q^22 - 2*q^23 - q^24 -
        2*q^27 + q^29 + q^37 - q^40 + q^41 - 2*q^45 + 2*q^48 - q^51 + q^54 + 
        q^56 + 3*q^57 - q^58 + q^63 + O(q^66)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
256
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - 2*q^17 - q^25 - 2*q^41 + O(q^42)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
256
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
64
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
256
);
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(
32
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
256
);
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(
16
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
256
);
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(
8
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
256
);
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(
4
);
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
256
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 32*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
42
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 - 2*q^17 + q^25 + 2*q^41 + O(q^42),
    q^2 - q^18 - 2*q^34 + O(q^42)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
257
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
256
);
qprec:=
43
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
258
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
258
);
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(
258
);
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(
258
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
258
);
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(
14
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 - a^5*q^4 + (a^4 - a^3)*q^7 + a^2*q^9 + (a^5 - a^4 + a^3 - a^2 + a
        - 1)*q^12 + (a^5 - a^4 + a^3 + a - 1)*q^13 - a^3*q^16 + (a^5 + a^3 - a^2
        + a - 1)*q^19 + (-a^5 + a^4)*q^21 - a*q^25 - a^3*q^27 + (a^2 - a)*q^28 +
        (-a^5 + 1)*q^31 + q^36 + (-a^5 + a^2)*q^37 + (-a^3 + 1)*q^39 - a*q^43 + 
        a^4*q^48 + (a^5 - a^4 + a^3 - a^2)*q^49 + (a^4 + 1)*q^52 + (-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*q^64 + (a^2 - a)*q^67 + (-a^5 - a^3)*q^73 + a^2*q^75 + (a^4 
        + a^2)*q^76 + (a^4 - a^3)*q^79 + a^4*q^81 + O(q^82),
    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 +
        O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
258
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
258
);
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(
258
);
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:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^4 + a^3 + a)*q^2 + (-a^5 + a^3 + a - 1)*q^4 + (a^4 - a)*q^7 + (-a^5 
        + a^4 - a^3 + a^2 - 1)*q^8 + (a^5 - a^2)*q^9 + (-a^5 - a^4 + a^2)*q^11 +
        (a^5 - a)*q^14 + (a^4 - 2*a^3 + a^2 - 2*a + 1)*q^16 + (a^3 - a^2 - 
        1)*q^18 + (-a^4 - a^3 + a + 1)*q^22 + (a^4 - a^2)*q^23 + a^5*q^25 + (a^5
        - a^4 + a^3 - a^2)*q^28 + (a^2 + a)*q^29 + (2*a^5 - a^4 - a^3 - a^2 - a 
        + 2)*q^32 + (-a^5 + a^4 - 1)*q^36 - q^37 + (-2*a^3 + 1)*q^43 + (-a^4 + 
        a)*q^44 + (-a^5 + a^4 + a^2 - a - 1)*q^46 + O(q^48)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^5 + a^3 - 1)*q^2 + (-a^3 + a^2 - a)*q^4 - a^5*q^7 + (a^5 - a^4 + a^3
        - a^2 + a)*q^8 + (-a^4 + a)*q^9 + (a^5 - a^4 - a^2 + a)*q^11 + (a^2 - 
        a)*q^14 + (-a^5 + a^4 + a^2 - 1)*q^16 + (a^4 - a^3)*q^18 + (-a^5 + 2*a^4
        - a^3)*q^22 + (a^5 + a^4 - a^2)*q^23 - a*q^25 + (a^5 - a^4 + a^3 - a^2 +
        a - 1)*q^28 + (a^4 + a^2)*q^29 + (a^5 - a^4 - a^3 + 1)*q^32 + (a^5 - a^2
        - a + 1)*q^36 + q^37 - q^43 + (a^5 - 2*a + 2)*q^44 + (-a^5 + a^4 - a + 
        1)*q^46 + O(q^48)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a - 1)*q^2 + 2*a*q^4 + a*q^7 + (-2*a + 1)*q^8 + (a - 1)*q^9 + q^11 + 
        (-2*a + 1)*q^14 + (a - 1)*q^16 + (-a + 2)*q^18 + (-a - 1)*q^22 + (-2*a +
        1)*q^23 + (-a + 1)*q^25 + (2*a - 2)*q^28 + (2*a - 1)*q^29 - 2*q^36 - 
        q^37 + 2*a*q^44 + (3*a - 3)*q^46 + O(q^48)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 + (a - 1)*q^7 + q^8 - a*q^9 - q^11 - q^14 + a*q^16 + (-a + 1)*q^18
        - a*q^22 - q^23 - a*q^25 - q^29 + q^37 + 2*q^43 - a*q^46 + O(q^48)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
259
);
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:=
48
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^7 + q^9 - 2*q^11 + q^16 - q^25 - q^28 + q^36 - q^37 - 2*q^44 + 
        O(q^48)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
260
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^2 + (a^2 - 1)*q^4 + (a^3 - a)*q^5 - q^8 + a*q^9 - a*q^10 + (-a^3 +
        a)*q^13 - a^2*q^16 + (-a^3 - a^2)*q^17 + a^3*q^18 - a^3*q^20 + (-a^2 + 
        1)*q^25 + a*q^26 + (a^3 - a)*q^29 + (-a^2 + 1)*q^32 + (-a^3 - a^2 + a + 
        1)*q^34 + (a^3 - a)*q^36 + (a^2 - 2)*q^37 + (-a^3 + a)*q^40 + (a^3 - a^2
        + 1)*q^41 - q^45 + a^2*q^49 + q^50 + a^3*q^52 + (a^2 - a)*q^53 - a*q^58 
        + (-2*a^3 + a)*q^61 + q^64 + (a^2 - 1)*q^65 + (a + 1)*q^68 - a*q^72 - 
        q^73 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^3 + a)*q^2 + (-a^2 + 1)*q^4 + (a^2 - 1)*q^5 - a^3*q^8 - a*q^9 + 
        a^3*q^10 + a^2*q^13 - a^2*q^16 + (a^3 - a - 1)*q^17 - q^18 + a^2*q^20 - 
        a^2*q^25 + a*q^26 + (-a^3 + a)*q^29 - a*q^32 + (a^3 + a^2 - a - 1)*q^34 
        + (a^3 - a)*q^36 + (a^3 + a)*q^37 + a*q^40 + (a^3 - a^2 + 1)*q^41 + 
        (-a^3 + a)*q^45 - a^2*q^49 - a*q^50 + q^52 + (a^3 - a^2 - a + 1)*q^53 + 
        (-a^2 + 1)*q^58 + (-2*a^3 + a)*q^61 - q^64 - q^65 + (a^3 + a^2 - 1)*q^68
        + (a^2 - 1)*q^72 - a^3*q^73 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + 1/2*(-2*a + 1)*q^5 + a*q^9 + 1/2*(a - 1)*q^10 + (a - 1)*q^16 + 
        1/2*(a - 2)*q^20 - 1/2*q^25 + a*q^26 + (a - 1)*q^29 + (-2*a + 1)*q^34 + 
        (-a + 1)*q^36 + 1/2*q^40 + (-a - 1)*q^41 + 1/2*(-a + 2)*q^45 + (a - 
        1)*q^49 + 1/2*(a + 1)*q^50 - a*q^61 + q^64 + 1/2*(-a + 1)*q^65 + 
        O(q^74),
    q^2 - 1/2*a*q^5 - a*q^8 + 1/2*(-2*a + 1)*q^10 - q^13 + (a + 1)*q^17 + a*q^18
        + 1/2*(a - 1)*q^20 + 1/2*(a - 2)*q^25 + (a - 1)*q^32 - q^37 + 1/2*(a - 
        2)*q^40 + 1/2*(-a + 1)*q^45 - 1/2*q^50 + a*q^52 + (-a + 2)*q^53 + (a - 
        1)*q^58 + 1/2*(2*a - 1)*q^65 + (-2*a + 1)*q^68 + (-a + 1)*q^72 + a*q^73 
        + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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(
4
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 - q^4 + q^5 + a*q^8 - a*q^9 - a*q^10 - q^13 + q^16 + (a - 1)*q^17 
        - q^18 - q^20 + q^25 + a*q^26 + 2*a*q^29 - a*q^32 + (a + 1)*q^34 + 
        a*q^36 + a*q^40 + (-a - 1)*q^41 - a*q^45 + q^49 - a*q^50 + q^52 + (a - 
        1)*q^53 + 2*q^58 - q^64 - q^65 + (-a + 1)*q^68 + q^72 - 2*a*q^73 + 
        O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^2 + q^4 + a*q^5 - q^8 + a*q^9 - a*q^10 - a*q^13 + q^16 + (a + 1)*q^17 
        - a*q^18 + a*q^20 - q^25 + a*q^26 - 2*a*q^29 - q^32 + (-a - 1)*q^34 + 
        a*q^36 - a*q^40 + (-a - 1)*q^41 - q^45 - q^49 + q^50 - a*q^52 + (-a - 
        1)*q^53 + 2*a*q^58 + q^64 + q^65 + (a + 1)*q^68 - a*q^72 + 2*q^73 + 
        O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 + (a - 1)*q^4 + q^8 + (a - 1)*q^9 - a*q^13 - a*q^16 + (-a + 
        1)*q^17 + q^18 - q^25 + (a - 1)*q^26 + a*q^29 + (a - 1)*q^32 - q^34 - 
        a*q^36 + a*q^37 + a*q^41 - a*q^49 + a*q^50 + q^52 - q^53 + (-a + 1)*q^58
        + (-a + 1)*q^61 + q^64 + a*q^68 + (a - 1)*q^72 - q^73 + O(q^74),
    q^5 - a*q^10 + (a - 1)*q^20 - q^25 + q^40 + (a - 1)*q^45 + a*q^50 - a*q^65 +
        O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
260
);
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:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^9 - q^10 + q^16 + q^25 - q^26 - 2*q^29 - q^36 - q^40 + q^49 - 
        2*q^61 + q^64 + q^65 + O(q^74),
    q^2 - q^5 + q^8 - q^13 - q^18 - q^20 + q^32 + 2*q^37 + q^45 + q^50 - q^52 - 
        2*q^58 - q^72 + 2*q^73 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^54),
    q^2 + (a + 1)*q^5 - a*q^8 - q^11 - q^14 + q^17 + (a - 1)*q^23 - a*q^26 - 
        q^29 + (-a - 1)*q^35 + a*q^47 - q^50 + O(q^54)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
261
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 - q^13 - q^16 + q^22 + q^25 + q^34 + O(q^54),
    q^2 - q^8 + q^11 - q^14 + q^17 - q^26 - q^29 - 2*q^41 + q^47 + q^50 + 
        O(q^54),
    q^3 - q^18 - q^21 + q^27 - q^39 - q^48 + O(q^54),
    q^6 - q^9 - q^24 + q^33 - q^42 + q^51 + O(q^54)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
262
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
130
);
qprec:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
262
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
26
);
qprec:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
262
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
262
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
65*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^5 - q^7 - q^15 + q^16 - q^20 - q^21 + q^25 - q^27 - q^28 + q^33 
        + 2*q^35 + q^39 - q^43 + q^45 + q^49 + 2*q^53 - q^55 - q^59 - q^60 - 
        q^61 + q^63 + O(q^64),
    q^2 + q^8 - q^10 - q^14 - q^30 + q^32 - q^40 - q^42 + q^50 - q^54 - q^56 + 
        O(q^64),
    q^3 - q^5 - q^7 - q^9 + q^11 + q^12 + q^13 - q^20 + q^25 - q^28 - q^33 + 
        q^35 - q^36 - q^39 + q^41 - q^43 + q^44 + q^48 + q^49 + q^52 - q^59 - 
        q^61 + O(q^64),
    q^6 - q^10 - q^14 - q^18 + q^22 + q^24 + q^26 - q^40 + q^50 - q^56 + O(q^64)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
263
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
262
);
qprec:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
263
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
131*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
44
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^17 - q^18 - q^24 + q^25 - q^27 - q^39 + O(q^44),
    q^2 - q^9 - q^12 + q^18 - q^22 - q^31 + q^33 + q^39 + q^43 + O(q^44),
    q^3 - q^8 - q^9 + q^24 + q^26 + q^27 - q^31 - q^34 + O(q^44),
    q^4 - q^8 - q^9 - q^12 + q^16 + q^17 + q^18 - q^22 + q^24 + q^27 - q^31 - 
        q^32 - q^34 + q^39 + O(q^44),
    q^6 - q^8 - q^9 + q^13 - q^22 + q^23 + q^24 + q^26 - q^31 - q^32 - q^34 - 
        q^36 + O(q^44),
    q^11 - q^12 - q^13 + q^16 + q^18 - q^23 - q^26 + q^33 + q^37 + O(q^44)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
264
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
264
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
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(
264
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
264
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
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(
264
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
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(
264
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
264
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
264
);
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(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + 1/2*(-a^2 + a)*q^3 - a*q^4 + 1/2*(a^3 - a^2 + a - 2)*q^6 + 1/2*(a^3 + a 
        - 1)*q^9 + 1/2*(a^3 - a^2)*q^12 + a^2*q^16 + 1/2*(a^2 - 1)*q^18 + (-a^3 
        - 1)*q^19 - a^2*q^22 + 1/2*(a + 1)*q^24 + (-a^3 + a^2 - a + 1)*q^25 + 
        1/2*(a^3 + a)*q^27 + 1/2*(-a - 1)*q^33 + (-a^3 + a^2 + 1)*q^34 + 
        1/2*(-a^3 + 1)*q^36 + (a^3 + a^2)*q^43 + 1/2*(a^2 - a + 1)*q^48 - 
        a^2*q^49 + 1/2*(-2*a^3 - a + 2)*q^51 + 1/2*(-a^3 + a^2 - 2*a + 1)*q^54 +
        1/2*(-a^3 + 2*a^2 - 2*a)*q^57 - a^3*q^64 + 1/2*(-a^2 + a - 1)*q^66 + 
        (a^3 - a^2 - 1)*q^67 + 1/2*(-a^3 + a)*q^72 + (2*a^3 - a^2 + a - 1)*q^73 
        + 1/2*(-a + 1)*q^75 + (a^3 - a^2 + 2*a - 1)*q^76 + 1/2*(-a^2 + a - 
        1)*q^81 + O(q^82),
    q^2 + 1/2*(-2*a^3 + a^2 - a + 1)*q^3 + 1/2*(-a^2 + a)*q^6 - a*q^8 + 
        1/2*(-a^3 + a^2 - 2*a + 1)*q^9 + a*q^11 + 1/2*(a^3 - a^2 + a - 2)*q^12 +
        (a^3 - 1)*q^17 + 1/2*(a^3 + a - 1)*q^18 + 1/2*(a^3 - a^2)*q^24 + 
        1/2*(a^3 + 1)*q^27 + a^2*q^32 + 1/2*(-a^3 + a^2)*q^33 + 1/2*(a^2 - 
        1)*q^36 + (-a^3 - 1)*q^38 + (-a^2 + a - 1)*q^41 - a^2*q^44 + 1/2*(a + 
        1)*q^48 + (-a^3 + a^2 - a + 1)*q^50 + 1/2*a^3*q^51 + 1/2*(a^3 + a)*q^54 
        + 1/2*(2*a^3 - 2*a^2 - 1)*q^57 + (a^3 - 2*a^2 + a - 1)*q^59 + 1/2*(-a - 
        1)*q^66 + (-a^3 + a^2 + 1)*q^68 + 1/2*(-a^3 + 1)*q^72 + 1/2*(-a^3 - 
        a^2)*q^75 + 1/2*(a + 1)*q^81 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
264
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
264
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 + a^2*q^4 - a^3*q^8 + a*q^9 - a^3*q^11 + (a^3 - a^2 + a - 1)*q^16 
        + (a^2 - a)*q^17 - a^2*q^18 + (-a + 1)*q^19 + (a^3 - a^2 + a - 1)*q^22 -
        a^3*q^25 + (a^3 - 1)*q^27 + q^32 + (-a^3 + a^2)*q^34 + a^3*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^2 
        + a - 1)*q^49 + (a^3 - a^2 + a - 1)*q^50 + (-a^3 + a^2 + 1)*q^54 + (a^3 
        - a^2 + a)*q^59 - a*q^64 + (-a^3 + a^2)*q^67 + (-a^2 + a - 1)*q^68 + 
        (-a^3 + a^2 - a + 1)*q^72 + (-a^3 - a)*q^73 + (-a^3 + a^2)*q^76 + (-a^3 
        - a)*q^81 + O(q^82),
    q^3 - a*q^6 + (a^3 + a - 1)*q^9 + a^2*q^12 + (-a^3 + 1)*q^18 - a^3*q^24 + 
        (-a^2 - 1)*q^27 - a^3*q^33 + (a^3 - a^2 - 1)*q^36 + (a^3 - a^2 + a - 
        1)*q^48 + (a^2 - a)*q^51 + (a^3 + a)*q^54 + (-a + 1)*q^57 + (a^3 - a^2 +
        a - 1)*q^66 + (a^2 + 1)*q^72 - a^3*q^75 + (-a^3 + a^2 - a + 1)*q^81 + 
        O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
264
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
264
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 + (a^3 - a^2 + a - 1)*q^6 + (-a^3 - a)*q^7 - a*q^9 + (-a^3 + 
        a^2)*q^10 + (a^3 - a^2 + a)*q^15 + (a^3 - a^2 + a - 1)*q^16 - a*q^22 - 
        a*q^24 + (a - 1)*q^25 + (-a^3 + 1)*q^28 + (a^2 + 1)*q^31 - a^3*q^33 - 
        a^3*q^36 + (a^3 - a^2 + a)*q^40 + (a^2 + 1)*q^42 + (a^3 - 1)*q^49 + q^54
        + (a^2 - a)*q^55 + (-a + 1)*q^58 + (a^2 - a)*q^60 + (a^3 + a - 1)*q^63 -
        a*q^64 - a^2*q^70 + (a^3 - a^2 + a)*q^73 + (-a^2 + a - 1)*q^79 + 
        a^2*q^81 + O(q^82),
    q^2 + a^2*q^3 + (-a + 1)*q^5 + a^2*q^8 + (a^3 - a^2 + a - 1)*q^11 + (a^3 - 
        a^2 + a - 1)*q^12 + (-a^3 - a)*q^14 - a*q^18 + (-a^3 + a^2)*q^20 + (-a^3
        + 1)*q^21 - a^3*q^27 + (-a^2 + a - 1)*q^29 + (a^3 - a^2 + a)*q^30 + (a^3
        - a^2 + a - 1)*q^32 - q^35 - a*q^44 + (a^2 - a)*q^45 - a*q^48 + (a - 
        1)*q^50 + (a^3 - a^2 - 1)*q^53 + (-a^3 + 1)*q^56 + (a^2 + 1)*q^59 + (a^2
        + 1)*q^62 - a^3*q^66 - a^3*q^72 + (a^3 - a^2)*q^75 + (a^2 + 1)*q^77 + 
        (a^3 - a^2 + a)*q^80 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
264
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 - q^9 + q^11 - q^23 + q^27 - q^31 - q^37 + q^45 + 2*q^47 + q^49 + 
        2*q^53 - q^55 - q^59 - q^67 - q^71 + O(q^82),
    q^2 - q^10 - q^18 + q^22 - q^46 + q^54 - q^62 - q^74 + O(q^82),
    q^3 - q^9 - q^15 + q^33 + q^45 - q^69 + q^81 + O(q^82),
    q^6 - q^18 - q^30 + q^66 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
264
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
264
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
264
);
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:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^3 + q^4 + q^9 - q^12 + q^16 - q^22 - q^25 - q^27 - 2*q^34 + q^36 - 
        q^48 - q^49 + q^64 + q^66 + 2*q^67 + q^75 + q^81 + O(q^82),
    q^2 - q^6 + q^8 - q^11 - 2*q^17 + q^18 - q^24 + q^32 + q^33 + 2*q^41 - q^44 
        - q^50 + 2*q^51 - q^54 - 2*q^68 + q^72 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
265
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
265
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
265
);
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:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
265
);
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:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
265
);
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:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
265
);
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:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
265
);
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:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
265
);
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:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*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(
266
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a + 1)*q^4 - q^8 + (a - 1)*q^15 + a*q^21 + (a - 1)*q^23 + (-a + 
        1)*q^29 + (a - 1)*q^32 - a*q^35 - q^39 - a*q^43 - q^49 + (-a + 1)*q^51 +
        (-a + 1)*q^53 - a*q^57 + a*q^60 + q^64 + q^65 + (a - 1)*q^67 + a*q^71 + 
        O(q^74),
    q^2 - a*q^4 - q^16 + (a - 1)*q^30 + a*q^32 + a*q^42 + (a - 1)*q^46 + (-a + 
        1)*q^58 + q^60 - a*q^70 + O(q^74),
    q^3 - q^5 + (a - 1)*q^7 + (-a + 1)*q^12 - a*q^13 + q^17 + (-a + 1)*q^19 + (a
        - 1)*q^20 - q^24 + (a - 1)*q^27 + a*q^28 + q^40 + q^41 - a*q^47 - q^52 +
        (-a + 1)*q^56 - q^59 + a*q^61 + (-a + 1)*q^68 + (a - 1)*q^69 - q^73 + 
        O(q^74),
    q^6 - q^10 - a*q^12 + (a - 1)*q^14 + a*q^20 - a*q^26 + q^28 + q^34 + (-a + 
        1)*q^38 - q^48 + (a - 1)*q^52 + (a - 1)*q^54 - a*q^68 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
266
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
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(
266
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + (-a + 1)*q^5 + (a - 1)*q^7 + (a - 1)*q^9 + a*q^11 + (a - 1)*q^16
        - 2*a*q^17 + (a - 1)*q^19 - q^20 + (-a + 1)*q^23 + q^28 + a*q^35 + q^36 
        - q^43 + (-a + 1)*q^44 + a*q^45 + (-a + 1)*q^47 - a*q^49 + q^55 + (-a + 
        1)*q^61 - a*q^63 + q^64 + (2*a - 2)*q^68 + a*q^73 + O(q^74),
    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 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
267
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
267
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
88
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
267
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
267
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
267
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
267
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
267
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
267
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
268
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
268
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
268
);
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:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
268
);
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:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
268
);
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:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
268
);
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:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
268
);
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:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
268
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
33*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^17 - q^19 - q^23 + q^25 - q^29 - q^37 - q^47 + q^49 - q^59 + 
        O(q^64)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
269
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
268
);
qprec:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
269
);
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:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
270
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
270
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
270
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*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(
270
);
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(
270
);
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(
270
);
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(
12
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
270
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
270
);
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(
6
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
270
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*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^20 - q^32 - q^38 + q^50 - q^62 + q^68 + q^80 + O(q^86),
    q^4 - q^10 - q^16 + q^34 + q^46 - q^76 + O(q^86),
    q^5 + q^8 - q^17 - q^20 - q^23 - q^32 + 2*q^47 - q^53 + q^68 - q^83 + 
        O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
271
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
270
);
qprec:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
271
);
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:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
271
);
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:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
271
);
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:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
271
);
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:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
271
);
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:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
271
);
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:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
271
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
135*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^17 - q^20 - q^22 + q^25 - q^31 - q^35 + O(q^45),
    q^2 - q^10 - q^11 + q^18 - q^25 - q^28 + q^35 + q^37 + O(q^45),
    q^4 - q^8 - q^10 - q^11 + q^16 + q^17 + q^20 + q^22 - q^25 - q^28 + q^31 - 
        q^32 - q^34 + q^35 + q^36 - q^40 - q^44 + O(q^45),
    q^5 - q^8 - q^10 - q^11 + q^14 + q^16 + q^20 + q^22 - q^25 - q^32 - q^34 - 
        q^44 + O(q^45),
    q^7 - q^8 - q^11 + q^14 + q^20 - q^25 - q^34 + q^41 + O(q^45)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^62)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
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 + O(q^62),
    q^2 + a^3*q^4 + (-a^3 + a^2)*q^6 - a^2*q^8 + (a^2 - a)*q^12 + a*q^16 + (-a^2
        + a - 1)*q^18 + (a^3 - 1)*q^22 + (-a + 1)*q^24 - q^32 - a^3*q^34 + (-a^3
        + a - 1)*q^36 + (-a^3 - a^2)*q^44 + (a^3 + 1)*q^48 - a*q^50 + (a^3 - a^2
        - a + 1)*q^54 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
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 + O(q^62),
    q^2 + (-a - 1)*q^10 + a*q^18 - q^34 + a*q^50 + (a + 1)*q^58 + O(q^62),
    q^4 + a*q^8 - q^16 + (-a - 1)*q^20 - a*q^32 + a*q^36 + (-a + 1)*q^40 + 
        O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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(
4
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
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 + 
        O(q^62),
    q^2 - a*q^4 + (-a - 1)*q^6 - q^8 + (a - 1)*q^12 + a*q^16 + a*q^18 + (-a + 
        1)*q^22 + (a + 1)*q^24 + q^32 - a*q^34 + q^36 + 2*a*q^38 + (-a - 1)*q^44
        + (-a + 1)*q^48 + a*q^50 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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(
4
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^17 - 2*q^21 + q^25 - 2*q^33 + q^49 - 2*q^53 + O(q^62),
    q^3 - q^7 - q^11 + q^23 + q^31 - q^51 + O(q^62)
]
;
Bo:=
[
    q - q^9 - 2*q^13 + q^17 + q^25 - q^49 + 2*q^53 + O(q^62),
    q^2 - q^18 - 2*q^26 + q^34 + q^50 + O(q^62),
    q^4 - q^8 + q^16 - q^32 - q^36 - 2*q^52 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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(
4
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
272
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^17 - 2*q^19 - q^25 + 2*q^43 - q^49 + 2*q^59 + O(q^62),
    q^2 - q^4 + q^8 - q^16 + q^18 + q^32 - q^34 - q^36 - 2*q^38 - q^50 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^68)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^68)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^68)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^68)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^68),
    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 + O(q^68)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^6 - a*q^7 + a*q^9 + (-a + 1)*q^10 - q^13 - a*q^15 - q^16 + (a 
        - 1)*q^24 + a*q^31 + q^34 + q^37 + (-a + 1)*q^40 + q^42 + (a - 1)*q^43 +
        q^46 + (a - 1)*q^49 + (-a + 1)*q^51 - q^54 - a*q^58 + (-a + 1)*q^63 - 
        q^64 + O(q^68),
    q^2 + q^4 + (a - 1)*q^5 + (-a + 1)*q^6 + (2*a - 1)*q^7 + q^8 - 2*a*q^9 + (a 
        - 1)*q^10 + (a - 1)*q^12 + (-a + 1)*q^13 - a*q^14 + a*q^15 + 2*q^16 - 
        q^17 + a*q^18 + a*q^19 + (-a - 1)*q^21 - q^23 + (-a + 1)*q^24 - a*q^25 -
        q^26 + 2*q^27 + (a - 1)*q^28 + a*q^29 - a*q^30 - 3*a*q^31 - q^34 + q^35 
        - a*q^36 - 2*q^37 + a*q^39 + (a - 1)*q^40 - a*q^41 - q^42 + (-2*a + 
        2)*q^43 - q^45 - q^46 + (a - 1)*q^47 + (2*a - 2)*q^48 + (-2*a + 1)*q^49 
        + (a - 1)*q^51 - a*q^52 - a*q^53 + q^54 - a*q^56 - q^57 + a*q^58 + q^59 
        + a*q^61 + a*q^62 + a*q^63 + 2*q^64 + (-a + 1)*q^65 + (2*a - 2)*q^67 + 
        O(q^68),
    q^3 - a*q^4 - q^6 + (-a + 2)*q^7 + (2*a - 2)*q^9 + q^10 + q^12 - q^13 + (-a 
        + 1)*q^15 - 2*a*q^16 + (-a + 1)*q^19 + (a - 1)*q^21 - q^24 + (a - 
        1)*q^25 - a*q^27 + q^28 + (3*a - 3)*q^31 + a*q^34 + (a - 1)*q^36 + 
        2*a*q^37 - a*q^39 + q^40 + a*q^42 - 2*q^43 + a*q^46 + q^48 + (a - 
        2)*q^49 + q^51 + (a - 1)*q^52 - a*q^54 + a*q^57 + (-a + 1)*q^58 + (-a + 
        1)*q^61 + (-a + 1)*q^63 - 2*a*q^64 + 2*q^67 + O(q^68)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^6 + q^7 - q^9 - q^10 - q^13 - a*q^15 + (-a + 1)*q^16 + q^24 + 
        (-a + 1)*q^31 + q^34 + (a - 1)*q^37 + a*q^40 + (a - 1)*q^42 + (a - 
        1)*q^43 - a*q^46 + q^49 + a*q^51 + (-a + 1)*q^54 + q^58 - q^63 - q^64 + 
        O(q^68),
    q^2 + (a - 1)*q^4 + (a - 1)*q^5 - q^6 + (a + 1)*q^7 - a*q^8 - 2*a*q^9 - 
        a*q^10 + (a - 1)*q^12 - q^13 + q^14 + (-a + 1)*q^15 + 2*q^16 + (-a + 
        1)*q^17 - q^18 + a*q^19 + (a + 1)*q^21 - q^23 + a*q^24 + q^25 - q^26 - 
        2*a*q^27 - a*q^28 + (-a + 1)*q^29 - a*q^30 + 3*q^31 + a*q^34 + (a - 
        1)*q^35 + (a - 1)*q^36 - 2*q^37 - q^39 + (a - 1)*q^40 + (a - 1)*q^41 - 
        q^42 - 2*q^43 + (-a + 1)*q^45 + (-a + 1)*q^46 + (a - 1)*q^47 + 2*q^48 + 
        (2*a - 1)*q^49 + (a - 1)*q^51 + q^52 + q^53 + q^54 - a*q^56 + a*q^57 + 
        a*q^58 + (a - 1)*q^59 + a*q^61 + (-a + 1)*q^62 + (-a + 1)*q^63 - 
        2*a*q^64 + (-a + 1)*q^65 - 2*a*q^67 + O(q^68),
    q^3 - a*q^4 + (-a + 1)*q^6 + (a - 2)*q^7 + 2*q^9 + q^10 - a*q^12 + (-a + 
        1)*q^13 + a*q^15 + (2*a - 2)*q^16 - q^19 + (a - 1)*q^21 - q^24 + (a - 
        1)*q^25 + q^27 + q^28 + (3*a - 3)*q^31 - q^34 - a*q^36 + (-2*a + 2)*q^37
        - a*q^39 - a*q^40 + (-a + 1)*q^42 + (-2*a + 2)*q^43 + a*q^46 + (a - 
        1)*q^48 + (-a - 1)*q^49 - a*q^51 + (a - 1)*q^52 + (a - 1)*q^54 - q^57 - 
        q^58 - q^61 + a*q^63 + 2*q^64 + 2*q^67 + O(q^68)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
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 + O(q^68),
    q^7 - q^21 - q^28 + q^63 + O(q^68)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
273
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
274
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
136
);
qprec:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
274
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^9 - q^11 + q^16 - 2*q^31 - q^36 - q^44 + q^49 + O(q^50)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 +
        O(q^50)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^50)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
275
);
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:=
50
;
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 + O(q^50),
    q^5 - q^20 - q^25 + q^45 + O(q^50)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
276
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
276
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
276
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
276
);
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(
22
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
276
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
276
);
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(
22
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
276
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
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 + O(q^86),
    q^2 - q^8 + q^16 - q^18 - q^26 + q^46 + q^50 + q^54 - q^58 - q^62 - q^64 + 
        q^72 - q^82 + O(q^86),
    q^3 - q^9 - q^39 + q^69 + q^75 + q^81 + O(q^86),
    q^4 - q^8 + q^32 - q^36 - q^52 - q^64 + q^72 + O(q^86),
    q^6 - q^18 - q^24 + q^48 + q^72 - q^78 + O(q^86),
    q^12 - q^24 - q^36 + q^72 + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
276
);
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:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^13 + q^16 - q^24 - q^25 + q^26 + q^29 + q^31 - q^32 + q^36 - q^39 - 
        q^41 - q^46 - q^47 + q^48 - q^49 - 2*q^52 - q^54 - q^58 - q^62 + q^64 + 
        q^69 + q^71 - q^72 + q^73 + 2*q^78 + q^81 + q^82 + O(q^86),
    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 + O(q^86),
    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 + 2*q^54 - q^69 + q^72 - 2*q^73 - q^75 - 2*q^78 - q^81 + O(q^86),
    q^4 + q^9 + q^12 - 3*q^13 + 2*q^16 - q^18 - 2*q^24 + q^26 + q^29 + q^31 - 
        q^32 + q^36 - q^39 - q^41 - 2*q^46 - q^47 - 2*q^52 - 2*q^54 + q^58 - 
        q^62 + 2*q^69 + q^71 - q^72 + 3*q^73 + 3*q^78 + 2*q^81 - q^82 + O(q^86),
    q^6 + 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^39 - 2*q^41 - 2*q^46 - 2*q^47 + q^48 - 2*q^52 - 
        2*q^54 - 2*q^62 + 2*q^69 + 2*q^71 - 2*q^72 + 2*q^73 + 3*q^78 + 2*q^81 + 
        O(q^86),
    q^8 - q^12 + q^13 - q^16 + q^18 - q^23 + q^24 - 2*q^26 - q^27 - q^29 - q^31 
        + q^32 - q^36 + 2*q^39 + q^41 + q^46 + q^47 - q^48 + q^52 + q^54 + 
        2*q^59 - q^69 - q^71 + q^72 - q^73 - q^78 - q^81 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
277
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
276
);
qprec:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
277
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
277
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
277
);
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:=
46
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
278
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
138
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
278
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
278
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
278
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
69*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
68
;
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 + O(q^68),
    q^2 + q^8 - q^10 - q^14 + q^18 - q^22 - q^26 + q^32 - q^40 - q^56 - q^58 - 
        q^62 + O(q^68)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + 
        O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
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 + O(q^58),
    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 + O(q^58)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^7 - q^10 + q^16 - q^19 - 2*q^28 - q^31 - q^40 + 2*q^49 + O(q^58),
    q^2 - q^7 + q^10 - q^14 - q^16 - q^20 + q^28 + q^31 + q^41 - q^47 - q^49 + 
        q^50 + O(q^58),
    q^4 - q^7 - q^10 + q^19 + q^25 - q^40 - q^49 + O(q^58),
    q^5 - q^7 - q^8 + q^10 - q^16 + q^20 + q^28 + q^31 - q^35 - q^38 - q^47 - 
        q^49 - q^50 + q^56 + O(q^58)
]
;
Bo:=
[
    q - q^2 - q^5 - q^7 + q^8 + q^10 + q^14 - q^16 - q^19 + q^31 + q^35 + q^38 -
        q^40 - q^41 + 2*q^47 - q^56 + O(q^58),
    q^3 - q^6 - q^15 - q^21 + q^24 + q^27 + q^30 + q^42 - q^48 - q^54 - q^57 + 
        O(q^58),
    q^9 - q^18 - q^45 + O(q^58)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
279
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
280
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
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(
280
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
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(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
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 + O(q^82),
    q^2 - a*q^8 + (a - 1)*q^10 - q^12 + q^28 + (a - 1)*q^32 + q^40 + (-a + 
        1)*q^42 + a*q^48 - a*q^50 - q^58 + (-a + 1)*q^60 + O(q^82),
    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 + O(q^82),
    q^4 + (-a + 1)*q^6 + (a - 1)*q^14 - a*q^16 + (a - 1)*q^20 - q^24 + a*q^30 - 
        q^46 - a*q^54 + q^56 + (a - 1)*q^64 - a*q^70 + q^80 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (a - 1)*q^9 - a*q^10 + a*q^11 + (a - 1)*q^14 + (a - 1)*q^16 + 
        (-a + 1)*q^19 - a*q^25 + (-a + 1)*q^26 + (a - 1)*q^35 + q^36 + (a - 
        1)*q^40 - q^41 + (-a + 1)*q^44 + a*q^46 + q^49 + q^56 - 2*a*q^59 + q^64 
        + (-a + 1)*q^65 + a*q^74 - q^76 - a*q^81 + O(q^82),
    q^2 + q^5 - a*q^7 - a*q^8 + a*q^13 + (a - 1)*q^18 - a*q^20 + a*q^22 - q^23 +
        (a - 1)*q^28 + (a - 1)*q^32 - q^37 + (-a + 1)*q^38 + (a - 1)*q^45 - q^47
        - a*q^50 + (-a + 1)*q^52 + (-a + 1)*q^53 + a*q^55 + q^63 + (a - 1)*q^70 
        + q^72 + (-a + 1)*q^77 + (a - 1)*q^80 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.4
;
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(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 + q^4 - q^7 - q^8 - q^9 + q^14 + q^16 + q^18 + 2*q^23 - q^25 - q^28 
        - q^32 - q^36 - 2*q^46 + q^49 + q^50 + q^56 + q^63 + q^64 - 2*q^71 + 
        q^72 - 2*q^79 + q^81 + O(q^82),
    q^5 - q^10 + q^20 - q^35 - q^40 - q^45 + q^70 + q^80 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=
82
;
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 + O(q^82),
    q^2 - q^22 - q^30 - q^42 + q^50 - q^58 + q^70 + q^78 + O(q^82),
    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 + O(q^82),
    q^6 - q^10 - q^14 + q^26 + q^34 - q^54 - q^66 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
280
);
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:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 - q^9 + q^14 - q^15 + q^16 - q^30 + q^36 + 2*q^39 - q^49 - q^50 - 
        q^56 + q^60 - q^64 + q^65 - q^81 + O(q^82),
    q^2 - q^7 - q^8 + q^15 - q^18 + q^25 + q^28 - q^30 + q^32 - 2*q^57 - q^60 + 
        q^63 - q^65 + q^72 + 2*q^78 + O(q^82),
    q^3 + q^6 + q^10 - q^12 - q^13 + q^19 - q^21 - q^24 - q^26 - q^35 - q^38 - 
        q^40 + q^42 + q^48 + q^52 - q^59 + q^61 + q^75 - q^76 + O(q^82),
    q^5 - 2*q^6 - q^10 - 2*q^19 - q^20 + 2*q^21 + 2*q^24 + 2*q^26 + q^35 + q^40 
        - q^45 + 2*q^59 - 2*q^61 + q^70 - 2*q^75 + 2*q^76 + q^80 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
281
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
280
);
qprec:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
281
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
281
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
281
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
282
);
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(
282
);
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(
282
);
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(
46
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
282
);
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:=
[]
;
Bo:=
[
    q - q^8 + q^14 - q^17 - q^21 + q^24 + q^25 - q^28 + q^32 - q^34 - q^36 - 
        q^37 + q^47 - q^48 + q^51 + q^54 + q^68 - q^71 + q^72 - q^74 - q^79 - 
        q^81 + 2*q^83 + q^84 + O(q^90),
    q^2 - q^16 - q^18 + q^28 - q^34 + q^50 + q^54 - q^56 + q^64 - q^68 - q^74 + 
        O(q^90),
    q^3 - q^18 - q^21 + q^42 - q^48 + q^54 - q^63 + q^72 + q^75 - q^81 + 
        O(q^90),
    q^4 - q^8 + q^14 - q^28 - q^34 - q^36 + q^54 + q^56 + q^72 - q^74 + O(q^90),
    q^6 - q^18 - q^36 - q^48 + q^54 + q^72 + q^84 + O(q^90),
    q^7 - q^8 + q^16 - q^17 + q^27 - q^28 - q^37 - q^49 + q^53 + q^56 + q^59 + 
        q^61 - q^63 + q^68 - q^71 + q^72 - q^79 - q^81 + q^89 + O(q^90),
    q^9 - q^21 + q^24 - q^27 - q^36 - q^48 + q^51 + q^84 + O(q^90),
    q^12 - q^18 - q^24 + q^42 + q^54 - q^84 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
283
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
282
);
qprec:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
283
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
283
);
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:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
283
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
141*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
47
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^6 - q^7 + q^10 - q^15 - q^23 - q^29 + q^36 - q^38 - q^42 - q^44 + 
        O(q^47),
    q^2 - q^3 - q^5 + q^12 - q^14 - q^18 + q^19 + q^20 + q^21 + q^22 + q^26 - 
        2*q^30 + q^31 - q^32 - q^33 + q^35 - q^39 + q^43 + q^45 - q^46 + 
        O(q^47),
    q^4 - q^6 + q^9 - q^10 - q^11 - q^13 + q^15 + q^16 + q^25 - q^28 + q^38 - 
        q^41 + q^42 + O(q^47)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
284
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
284
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
284
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
284
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
284
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
284
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
284
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
284
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
35*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^15 - q^19 + q^25 - q^37 - q^45 + q^49 + O(q^68),
    q^2 - q^20 - q^24 - q^30 + q^36 - q^38 + q^40 + q^50 + O(q^68),
    q^3 - q^9 - q^15 - q^19 + q^25 + q^27 + q^29 - q^37 + q^57 + O(q^68),
    q^4 - q^20 - q^24 + q^36 - q^48 - q^60 + O(q^68),
    q^5 - q^9 - q^19 + q^27 - q^37 + q^43 + q^57 + O(q^68),
    q^6 + q^16 - q^18 - q^24 - q^30 - q^38 - q^48 + q^50 + q^54 + q^58 + 
        O(q^68),
    q^8 - q^16 - q^20 - q^24 + q^32 + q^36 + q^40 - q^64 + O(q^68),
    q^10 + q^16 - q^18 - q^32 - q^38 - q^40 - q^48 + q^54 + q^64 + O(q^68),
    q^12 - q^16 - q^20 + q^32 + q^40 - q^60 + O(q^68)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
285
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^4 + a^3 + a^2 + a - 1)*q^4 + (-a^4 - a^3 + a)*q^6 + (a^5 - a^2)*q^9 
        + (a^3 - a - 1)*q^10 + a^2*q^15 + (a^4 - a^3 - a^2 + 1)*q^16 + a^4*q^19 
        + (-a^5 + a^4 - a + 1)*q^24 - a^5*q^25 + (a^2 - a)*q^31 + (-a^3 - a^2 - 
        a)*q^34 + (-a^5 + a^3 - a - 1)*q^36 + (a^5 - a^3 - a^2 + a)*q^40 + (a^5 
        + a)*q^46 - a^3*q^49 + (a^4 + a^3 - 1)*q^51 + (a^3 + a^2 - 1)*q^54 + 
        (a^5 + a^4 - a^2 + 1)*q^60 - a^2*q^61 + (-a^5 - a^4 + a^2)*q^64 + (-a^3 
        + 1)*q^69 + O(q^74),
    q^2 + (-a^5 + a^4 - a^3 + a^2 - a)*q^3 + (a^3 - a^2 + a - 1)*q^5 + (-a^4 + 
        a^3 + a - 1)*q^8 + (a^5 - a^4 - a^3 + 1)*q^12 + (2*a^5 - a^4 - a^2 - a +
        1)*q^17 + (a^5 - a^2)*q^18 + (-a^5 + a^4 + a^2 - a - 1)*q^20 + (-a^5 + 
        a^3 + a - 1)*q^23 + (a^4 - a^3 + a^2 - a + 1)*q^27 + a^2*q^30 + (-a^5 + 
        a^4 - a^3)*q^32 + a^4*q^38 + (-a^5 + a - 1)*q^45 + (-a^4 + a)*q^47 + 
        (a^3 - a^2)*q^48 - a^5*q^50 + (a^5 - a^3 + a^2 - a + 2)*q^53 + (-a^4 + 
        a^3 - a^2 + a)*q^57 + (a^2 - a)*q^62 + (-a^4 + a^3 - 2*a^2 + a - 1)*q^68
        + (-a^5 + a^3 - 1)*q^72 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
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 + O(q^74),
    q^5 - a*q^15 + (a - 1)*q^20 - q^35 + (a - 1)*q^45 + q^60 + (-a + 1)*q^65 + 
        O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + 
        O(q^74),
    q^2 - q^3 - q^5 + (-a + 1)*q^8 + q^17 + (a - 1)*q^18 + 2*a*q^23 + (-a + 
        1)*q^27 + (a - 1)*q^30 - a*q^38 + (-a + 1)*q^45 - a*q^47 - a*q^48 + (a -
        1)*q^50 - a*q^53 + a*q^57 - q^62 + a*q^72 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
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(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
285
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 - q^11 - q^20 + q^25 + q^26 + q^44 + q^49 + q^54 - q^55 - q^61 - 
        q^64 + O(q^74),
    q^2 - q^10 + q^13 - q^18 + q^27 - q^32 - q^37 - q^38 + q^50 + q^52 - q^53 - 
        q^65 + q^67 + O(q^74),
    q^3 - q^18 - q^33 - q^60 + O(q^74),
    q^4 - q^5 + q^11 - q^16 - q^19 + q^26 - q^36 - q^44 + q^45 + q^54 + q^55 + 
        q^61 + O(q^74),
    q^6 - q^9 - q^30 - q^36 + q^39 + q^45 + q^54 + O(q^74),
    q^12 - q^15 - q^18 + q^27 + q^33 - q^48 - q^57 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
286
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
286
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*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(
286
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
286
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
286
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
286
);
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(
6
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
286
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
286
);
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(
20
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
286
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
286
);
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(
6
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
286
);
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(
10
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
286
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - 2*q^14 - q^16 + q^22 - q^23 + q^25 + q^26 - q^27 + q^38 - q^42 + q^49 + 
        2*q^56 + q^64 + q^66 - q^69 - q^77 + O(q^78),
    q^2 - q^24 - q^28 - q^46 + q^50 - q^54 + q^72 + q^76 + O(q^78),
    q^3 - q^9 - q^14 + q^22 - q^23 + q^26 - q^42 - q^48 + q^49 + q^53 + q^56 + 
        q^64 + q^75 - q^77 + O(q^78),
    q^4 - 2*q^14 - q^16 + q^22 + q^26 + q^38 - q^42 - q^48 + q^56 + q^64 + q^66 
        + O(q^78),
    q^6 + q^11 + q^13 - q^18 - q^19 - q^21 - q^24 + q^32 - q^33 - q^39 - q^46 + 
        2*q^57 + q^63 + q^72 - q^73 + O(q^78),
    q^7 - q^11 - q^13 + q^21 + q^24 - q^28 - q^32 + q^41 + q^44 + q^52 - q^57 - 
        q^63 - q^72 + O(q^78),
    q^8 + q^11 + q^13 - q^19 - q^21 - 2*q^24 + q^32 - q^33 - q^39 - q^44 - q^52 
        + 2*q^57 + q^63 + 2*q^72 - q^73 + q^76 + O(q^78),
    q^12 - q^14 - q^16 + q^22 + q^26 - q^36 - q^42 + q^56 + q^64 + O(q^78)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
287
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^18 - q^21 - q^23 + q^25 - q^32 - q^36 + q^49 - q^51 + O(q^54),
    q^2 - q^9 - q^16 + q^37 - q^43 + q^50 + q^51 + O(q^54),
    q^3 - q^7 - q^13 - q^14 + q^17 + q^19 - q^26 + 2*q^34 + 2*q^38 - q^41 - q^47
        - q^52 + O(q^54),
    q^4 - q^8 - q^9 + q^21 + q^23 + q^36 - q^39 - q^42 - q^43 - q^46 + q^51 + 
        O(q^54),
    q^6 - q^7 - q^13 - q^14 + 2*q^17 + 2*q^19 - 2*q^26 - q^27 - q^28 + 2*q^34 + 
        2*q^38 - q^41 - q^47 - q^48 + O(q^54),
    q^12 - q^13 - q^14 + q^17 + q^19 - q^24 - q^27 + q^34 + q^38 - q^47 - q^52 +
        O(q^54)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - 2*q^13 - q^25 + 2*q^37 + q^49 + 2*q^61 + O(q^66),
    q^2 - 2*q^26 - q^50 + O(q^66)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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(
6
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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:=
66
;
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 + O(q^66),
    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 + 
        O(q^66)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^3 + (a - 1)*q^9 - a*q^11 - q^17 + q^19 - a*q^25 - q^27 + (-a + 
        1)*q^33 + (-a + 1)*q^41 - a*q^43 + (a - 1)*q^49 - a*q^51 + a*q^57 + (a -
        1)*q^59 + O(q^66)
]
;
Bo:=
[
    q - a*q^3 + (a - 1)*q^9 + a*q^11 - q^17 - q^19 - a*q^25 + q^27 + (-a + 
        1)*q^33 + (-a + 1)*q^41 + a*q^43 + (a - 1)*q^49 + a*q^51 + a*q^57 + (-a 
        + 1)*q^59 + O(q^66),
    q^2 - a*q^6 + (a - 1)*q^18 + a*q^22 - q^34 - q^38 - a*q^50 + q^54 + O(q^66),
    q^4 - a*q^8 - a*q^12 + (a - 1)*q^16 + (a - 1)*q^24 + q^32 + (a - 1)*q^36 + 
        a*q^44 + q^48 - a*q^64 + O(q^66)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^25 - 2*q^37 - q^49 + 2*q^61 + O(q^66),
    q^5 - q^17 - q^29 + q^41 - q^53 + O(q^66)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
288
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + 3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
289
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
272
);
qprec:=
35
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
289
);
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:=
35
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
290
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
84
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
290
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
84
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
290
);
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(
28
);
qprec:=
84
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
290
);
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(
28
);
qprec:=
84
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
290
);
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:=
84
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
290
);
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:=
84
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
290
);
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(
4
);
qprec:=
84
;
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 + O(q^84),
    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 + O(q^84)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
290
);
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(
4
);
qprec:=
84
;
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 + 
        O(q^84),
    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 + 
        O(q^84)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
96
);
qprec:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
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:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
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:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
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:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
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:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^63)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
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:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
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:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^63)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
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:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
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:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^63)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
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:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
291
);
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:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^63)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
72
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^4*q^2 + (a^5 - a^2)*q^4 + (-a^5 + 2*a^2)*q^5 + a^3*q^8 + (a^3 - 1)*q^9
        + (-2*a^3 + 1)*q^10 + (-a^5 - 1)*q^13 + (-a^4 + a)*q^16 + (-a^2 - 
        a)*q^17 + a*q^18 + (a^4 - 2*a)*q^20 + 2*a*q^25 + (a^4 - 1)*q^26 + (a^5 -
        a^3)*q^29 - a^2*q^32 + (a^5 + a^3 - 1)*q^34 - a^5*q^36 + (a^4 + a^3 - 
        a)*q^37 + (a^5 + a^2)*q^40 + (a^4 - a^3 - a + 1)*q^41 + (2*a^5 - 
        a^2)*q^45 + (-a^3 + 1)*q^49 - 2*a^5*q^50 + (-a^5 + a^4 + a^2)*q^52 + 
        (a^4 - a + 1)*q^58 + (a^3 + a)*q^61 + (a^3 - 1)*q^64 + (a^5 - 2*a^4 - 
        2*a^2 + a)*q^65 + (a + 1)*q^68 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^5 - a^2)*q^2 + (-a^4 + a)*q^4 + a*q^5 + (a^3 - 1)*q^8 - a^3*q^9 - 
        q^10 + (-a + 1)*q^13 - a^5*q^16 + (a^4 + a^2)*q^17 + a^2*q^18 + (-a^5 + 
        a^2)*q^20 + (a^5 - a^2 + 1)*q^26 + (a^3 - a - 1)*q^29 + a^4*q^32 + (-a^3
        - a)*q^34 - a*q^36 + (-a^5 + a^3 - 1)*q^37 + (a^4 - a)*q^40 + (-a^5 - 
        a^3)*q^41 - a^4*q^45 - a^3*q^49 + (a^5 - a^4 - a^2 + a)*q^52 + (2*a^5 - 
        2*a^2)*q^53 + (-a^5 + 1)*q^58 + (a^3 + a^2 - 1)*q^61 - a^3*q^64 + (-a^2 
        + a)*q^65 + (a^2 + 1)*q^68 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 + (a - 1)*q^4 - q^8 + q^9 + (a - 2)*q^13 - a*q^16 + (-2*a + 
        1)*q^17 + a*q^18 - a*q^25 + (-a - 1)*q^26 + (-a + 2)*q^29 + (-a + 
        1)*q^32 + (-a + 2)*q^34 + (a - 1)*q^36 + (a - 1)*q^37 + (a - 1)*q^41 - 
        q^49 + (-a + 1)*q^50 + (-2*a + 1)*q^52 + (a + 1)*q^58 + (a - 1)*q^61 + 
        q^64 + (a + 1)*q^68 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^2 - a*q^4 - 2*a*q^5 + q^8 + q^9 + 2*q^10 + (-a + 1)*q^13 + (a 
        - 1)*q^16 - q^17 + (a - 1)*q^18 + (2*a - 2)*q^20 + (3*a - 3)*q^25 + 
        a*q^26 + (-a + 1)*q^29 - a*q^32 + (-a + 1)*q^34 - a*q^36 + a*q^37 - 
        2*a*q^40 + a*q^41 - 2*a*q^45 + q^49 - 3*a*q^50 - q^52 + (2*a - 2)*q^53 +
        a*q^58 + a*q^61 + q^64 - 2*q^65 + a*q^68 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
292
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^2 + q^4 - q^8 + q^9 + q^16 - q^18 + q^25 - q^32 + q^36 - 2*q^37 - 
        2*q^41 - q^49 - q^50 - 2*q^61 + q^64 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
293
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
292
);
qprec:=
49
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
293
);
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:=
49
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
294
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
294
);
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(
294
);
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(
294
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
294
);
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(
14
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 - a^3*q^4 - a^5*q^7 + a^2*q^9 + a^4*q^12 + (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^5 - a^4 + a^3 - a^2 + a - 1)*q^21 + a^2*q^25 - a^3*q^27 - a*q^28 + 
        (a^4 - a^3)*q^31 - a^5*q^36 + (-a + 1)*q^37 + (-a^5 + 1)*q^39 + (a^4 - 
        a)*q^43 + q^48 - a^3*q^49 + (a^2 + 1)*q^52 + (a^5 - a^4 - a^2 + a - 
        1)*q^57 + (-a + 1)*q^61 + q^63 + 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^3*q^75 + (-a^5 - a)*q^76 +
        (a^4 - a^3)*q^79 + a^4*q^81 + O(q^82),
    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 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
294
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
294
);
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(
294
);
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:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
295
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
295
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
58
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
295
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
295
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
295
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
29*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
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 + O(q^58),
    q^5 - q^15 + q^20 - q^25 - q^35 + O(q^58)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
295
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^19 - q^20 + q^25 - q^26 - q^29 - q^41 - q^46 + q^49 + O(q^58),
    q^2 - q^10 - q^13 + q^18 - q^23 - q^32 + q^37 + q^43 + q^47 + q^50 - q^52 + 
        O(q^58),
    q^3 + q^7 + q^9 - q^12 - q^15 - q^19 + q^21 + q^25 - q^27 - q^28 - q^29 - 
        q^35 - q^36 - q^41 + q^45 + q^48 + q^49 - q^53 + q^57 + O(q^58),
    q^4 + 2*q^9 - q^15 - q^16 - q^19 - q^20 + 2*q^21 + q^25 - q^26 - q^29 - q^35
        - q^36 - q^41 - q^45 - q^46 + 2*q^49 + O(q^58),
    q^5 + 2*q^9 - q^15 - 2*q^19 - q^20 + 2*q^21 + q^25 - 2*q^29 - q^35 - 2*q^36 
        - 2*q^41 + 2*q^49 + O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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(
18
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
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 + O(q^70),
    q^2 - a*q^4 + a^2*q^8 + (a^4 + a^3 - 1)*q^10 - a^3*q^16 + (-a^4 + a)*q^18 + 
        (-a^5 - a^4 + a)*q^20 - a^2*q^26 + a^4*q^32 + (-a^3 + a^2)*q^34 + (a^5 -
        a^2)*q^36 + (a^5 + a^3 - a^2 - 1)*q^40 + (a^5 - a^3 - a^2 - a)*q^50 + 
        a^3*q^52 + (-a^5 - a)*q^58 - a^5*q^64 + (a^4 - a^3)*q^68 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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(
6
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^3 + (a - 1)*q^5 - q^7 + a*q^11 + (-a + 1)*q^13 + (-a - 1)*q^15 - 
        a*q^21 + (-a + 1)*q^23 - a*q^25 + a*q^27 + (a + 1)*q^29 - q^33 + (-a + 
        1)*q^35 - q^37 + (a + 1)*q^39 - a*q^41 + (-a + 1)*q^43 - q^47 - q^53 + 
        (-a - 1)*q^55 + 2*a*q^65 - 2*a*q^67 + (a + 1)*q^69 + O(q^70)
]
;
Bo:=
[
    q - a*q^3 - q^7 + a*q^11 + (a - 1)*q^17 + (-a + 1)*q^19 + a*q^21 + (a - 
        1)*q^23 + a*q^25 - a*q^27 + (-a - 1)*q^29 + q^33 - a*q^37 - a*q^41 + 
        q^47 + (a + 1)*q^51 + q^53 + (-a - 1)*q^57 + (a + 1)*q^69 + O(q^70),
    q^2 - a*q^6 - q^14 + a*q^22 + (a - 1)*q^34 + (-a + 1)*q^38 + a*q^42 + (a - 
        1)*q^46 + a*q^50 - a*q^54 + (-a - 1)*q^58 + q^66 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
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 + 
        O(q^70),
    q^2 - a*q^4 + (a - 1)*q^8 + (-a + 1)*q^10 + q^16 - a*q^18 - q^20 + (2*a - 
        2)*q^26 - a*q^32 + a*q^34 + (a - 1)*q^36 + a*q^40 + 2*q^52 - q^58 + (a -
        1)*q^64 + (-a + 1)*q^68 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
296
);
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:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^10 - q^11 + q^16 + q^25 - q^27 - q^30 - q^33 - q^40 - q^44 + 
        q^49 - q^62 + q^64 - q^65 - q^67 + O(q^70),
    q^2 - q^6 + q^8 - q^13 - q^15 + q^18 - q^23 - q^24 - q^29 + q^32 + q^37 + 
        2*q^39 + q^45 - q^52 - q^54 + q^55 - q^60 - q^66 + 2*q^69 + O(q^70),
    q^3 - q^9 - q^10 - q^11 + q^12 + q^25 + q^26 - q^36 - q^40 + q^41 - q^44 + 
        q^46 + q^48 + q^58 - q^62 - q^67 + O(q^70),
    q^5 - q^6 - q^13 + q^18 + q^20 + q^22 - q^23 - q^24 - q^29 + q^31 + q^39 - 
        q^50 - q^52 - q^55 + q^61 + q^69 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 
        + O(q^62)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
297
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 + (a - 1)*q^5 + a*q^11 - a*q^16 - a*q^20 + (-2*a + 2)*q^23 +
        (-a + 1)*q^31 - q^37 - q^44 - a*q^47 + (a - 1)*q^49 + q^53 - q^55 + (a -
        1)*q^59 + O(q^62)
]
;
Bo:=
[
    q + (a - 1)*q^4 + (-a + 1)*q^5 - a*q^11 - a*q^16 + a*q^20 + (2*a - 2)*q^23 +
        (-a + 1)*q^31 - q^37 + q^44 + a*q^47 + (a - 1)*q^49 - q^53 - q^55 + (-a 
        + 1)*q^59 + O(q^62),
    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 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
298
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
148
);
qprec:=
73
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
298
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
37*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
73
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 - q^3 + q^6 + q^8 - q^16 + q^23 - q^24 + q^25 + q^27 - q^29 - q^31 -
        q^41 - q^46 - q^47 + q^48 + q^49 - q^50 + O(q^54),
    q^13 - q^26 - q^39 + O(q^54)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 + (a - 2)*q^6 + (-2*a + 1)*q^8 - a*q^9 + q^12 + (a - 1)*q^16 + (a 
        - 1)*q^23 + (-a - 1)*q^24 - q^25 + (a - 1)*q^26 + q^27 + (-a + 2)*q^32 +
        (-2*a + 2)*q^36 - q^39 + 3*a*q^48 + (-a + 1)*q^49 + q^52 + O(q^54),
    q^2 + (-a - 1)*q^4 + (-2*a + 2)*q^6 + a*q^8 + (a + 1)*q^9 + (a - 2)*q^12 + 
        (a - 1)*q^13 + (-2*a + 1)*q^16 + 2*q^24 - a*q^26 + (2*a - 1)*q^29 - 
        2*a*q^31 + (3*a - 3)*q^32 + (2*a - 1)*q^36 + q^39 + q^41 + (a - 1)*q^46 
        - a*q^47 + (-2*a - 2)*q^48 - q^50 + (a - 1)*q^52 + O(q^54),
    q^3 + (-a + 1)*q^4 + (a + 1)*q^6 + (2*a - 2)*q^9 - a*q^13 + (a - 2)*q^18 + 
        (-a + 1)*q^26 - a*q^27 - 2*q^29 + (-a + 2)*q^31 + (-a - 1)*q^32 - q^36 +
        a*q^39 + (2*a - 1)*q^41 + (-2*a + 2)*q^48 + O(q^54)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 + (-a + 1)*q^6 - q^8 + (a - 1)*q^9 - q^12 - a*q^16 + 2*q^18 
        - a*q^23 + a*q^24 + q^25 - a*q^26 - q^27 + (-a + 1)*q^32 + q^39 + (a - 
        1)*q^48 - a*q^49 + q^52 + O(q^54),
    q^2 + a*q^4 + (a - 1)*q^8 - a*q^9 + (-a + 1)*q^12 + 1/3*(a - 2)*q^13 - q^16 
        + 1/3*(-a - 1)*q^26 + q^29 - a*q^32 + q^36 + 1/3*(2*a - 1)*q^39 - q^41 -
        a*q^46 + (a - 1)*q^47 + q^50 - a*q^52 + O(q^54),
    q^3 + a*q^4 - a*q^6 + 1/3*(-a - 1)*q^13 + (-a + 1)*q^18 + 1/3*(a - 2)*q^26 +
        (a - 1)*q^27 + (a - 1)*q^31 - a*q^32 - q^36 + 1/3*(a + 1)*q^39 - q^41 + 
        O(q^54)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
299
);
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:=
54
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^12 - 1/2*q^13 + q^16 + 1/2*q^26 - q^27 - q^35 - 1/2*q^39 + O(q^54),
    q^2 + q^6 - q^8 - 1/2*q^13 - q^24 - 1/2*q^26 - q^31 - 1/2*q^39 + q^41 + q^46
        + q^47 - q^50 + q^52 + O(q^54),
    q^3 - 2*q^9 + q^12 - q^13 - q^23 + q^25 + 2*q^27 + q^29 - q^35 - 2*q^36 + 
        q^39 + q^48 + q^49 - q^52 + O(q^54),
    q^4 - q^9 + q^12 - 1/2*q^13 - q^23 + q^25 - 1/2*q^26 + q^27 - q^35 - q^36 + 
        1/2*q^39 + q^49 - q^52 + O(q^54),
    q^5 - q^7 - q^11 + q^19 + q^20 - q^28 + q^37 - q^44 - q^45 + O(q^54)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
300
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
300
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^19 - q^21 - q^31 - q^39 - q^61 + 2*q^79 + q^81 + O(q^86),
    q^3 - q^7 - q^13 + q^27 + 2*q^37 - q^43 - q^57 - q^63 - q^67 + 2*q^73 + 
        O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
300
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
300
);
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(
20
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
300
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
300
);
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(
10
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
300
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 + a^2*q^4 - a^3*q^5 - a^3*q^8 + (a^3 - a^2 + a - 1)*q^9 + (a^3 - 
        a^2 + a - 1)*q^10 + (a^2 - a)*q^13 + (a^3 - a^2 + a - 1)*q^16 + (a^3 + a
        - 1)*q^17 + q^18 + q^20 - a*q^25 + (-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*q^40 + (a^2 - 
        a)*q^41 + a^2*q^45 + q^49 + a^2*q^50 + (-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 + a)*q^65 + (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^2*q^80 - a^3*q^81 + (-a^3 + a^2)*q^82 + (a^2 + 
        1)*q^85 + O(q^86),
    q^3 - a*q^6 + a^2*q^12 - a^3*q^15 - a^3*q^24 + (a^3 - a^2 + a - 1)*q^27 + 
        (a^3 - a^2 + a - 1)*q^30 + (a^2 - a)*q^39 + (a^3 - a^2 + a - 1)*q^48 + 
        (a^3 + a - 1)*q^51 + q^54 + q^60 - a*q^75 + (-a^3 + a^2)*q^78 + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
300
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
300
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
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(
300
);
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(
4
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 - q^6 - a*q^9 - q^16 - a*q^24 + q^36 + 2*q^46 + a*q^49 + a*q^54 - 
        2*q^61 - a*q^64 + 2*a*q^69 - q^81 + O(q^86),
    q^2 + a*q^3 + a*q^8 - q^12 - a*q^18 - 2*a*q^23 + q^27 - q^32 - 2*q^47 - 
        a*q^48 + q^72 + 2*a*q^83 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
300
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.3
;
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(
300
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^9 + q^19 - q^21 - q^31 + q^39 - q^61 - 2*q^79 + q^81 + O(q^86),
    q^3 + q^7 - q^13 - q^27 - 2*q^37 - q^43 + q^57 - q^63 + q^67 + 2*q^73 + 
        O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^10 + a^9 + a^3 - a^2)*q^2 + (-3*a^11 - a^10 + a^9 + 2*a^8 + a^7 - 
        2*a^6 - a^5 + a^4 + 2*a^3 + a^2 - a - 2)*q^4 + (a^7 - 1)*q^7 + (-a^9 + 
        a^8 - a^7 + a^6)*q^8 + a^2*q^9 + (-a^8 - a^3 + a)*q^11 + (a^10 - 
        a^9)*q^14 + (-a^5 + a^4 - a^3 + a^2 - a)*q^16 + (2*a^11 - a^9 - a^8 + 
        a^6 + a^5 - 2*a^4 - a^3 + a + 1)*q^18 + (a^11 + 2*a^10 - a^9 - 2*a^8 - 
        a^7 + a^6 + 2*a^5 - a^4 - 2*a^3 - a^2 + a + 2)*q^22 + (a^10 + a^9 - a^7 
        - a^6 + a^5 + a^4 - a^2 - a)*q^23 + a^8*q^25 + (a^6 - a^5 + a^4)*q^28 + 
        (a^11 - a^4 - a)*q^29 + (3*a^11 - a^9 - 2*a^8 - a^7 + a^6 + 2*a^5 - 
        2*a^4 - a^3 - a^2 + 3)*q^32 + (-a^11 - a^10 + 2*a^7 - a^6 - a^5 + a^3 + 
        a^2 + a - 2)*q^36 + (a^10 + a^4)*q^37 - a^5*q^43 + (a^9 - a^8 + a^6 - 
        a^5 - a^2 + a - 1)*q^44 + (a^9 - a^7 - a^2 + a)*q^46 - a^7*q^49 + (a^4 -
        a^3)*q^50 + (-a^11 - a^10 + a^8 - a^6 - a^5 + a^3 + a^2 - 1)*q^53 + 
        O(q^56)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^3 + a^2)*q^2 + (a^3 - a^2 + a - 1)*q^4 + q^7 + (a^5 - a^4 + a^3)*q^8
        + a^2*q^9 + (-a^3 - a)*q^11 + (-a^3 + a^2)*q^14 + (-a^5 + a^4 - a^3 + 
        a^2 - a)*q^16 + (-a^5 + a^4)*q^18 + (-a^2 + a - 1)*q^22 + (-a^4 + a^3 - 
        a^2 + a - 1)*q^23 - a*q^25 + (a^3 - a^2 + a - 1)*q^28 + (a^4 - a)*q^29 -
        a^2*q^32 + (a^5 - a^4 + a^3 - a^2)*q^36 + (a^4 - a^3)*q^37 - a^5*q^43 + 
        (-a^4 + a^3 + 1)*q^44 + (a^2 - 2*a + 1)*q^46 + q^49 + (a^4 - a^3)*q^50 +
        (a^5 - a^4 + a^3 - a^2 + a)*q^53 + O(q^56)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^2 + (a - 1)*q^7 + q^8 + (a - 1)*q^9 + 2*q^11 + (-a + 1)*q^14 - q^16 + 
        (-a + 1)*q^18 - 2*q^22 + a*q^23 + (a - 1)*q^25 + (-a + 1)*q^29 - 
        2*a*q^37 + (a - 1)*q^43 - a*q^46 - a*q^49 + (-a + 1)*q^50 - 2*a*q^53 + 
        O(q^56)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
301
);
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:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^6 + a*q^10 - a*q^11 + (a - 1)*q^14 - q^15 + (-a + 1)*q^16 + a*q^17 - 
        a*q^21 + (-a + 1)*q^23 + a*q^24 - a*q^31 + (a - 1)*q^35 - a*q^38 + (-a +
        1)*q^40 + q^43 + (a - 1)*q^47 - q^49 + a*q^53 + (-a + 1)*q^54 + O(q^56),
    q^2 + (a - 1)*q^3 + q^5 + a*q^7 - a*q^8 - q^19 - a*q^22 - a*q^27 - q^30 + 
        q^33 + a*q^34 - q^37 - a*q^42 + (-a + 1)*q^46 + a*q^48 - q^51 - a*q^55 +
        O(q^56)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
302
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
150
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
302
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
50
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
302
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
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(
302
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*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(
302
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
25*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
302
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
75*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^19 - q^20 - q^22 - q^29 - q^34 + q^38 + q^44 - q^47 + q^49 + 
        q^50 - q^55 + q^58 - q^64 + q^68 + O(q^74),
    q^2 + q^18 - q^20 - q^22 - q^34 - q^40 + q^50 - q^64 + O(q^74),
    q^4 + q^11 + q^17 - q^19 - q^20 - q^22 - q^25 - q^29 - q^34 + q^36 + q^37 + 
        q^38 - q^40 - q^47 + q^50 + q^58 - q^64 + O(q^74),
    q^5 - q^11 + q^16 - q^17 - q^20 + q^31 - q^32 - q^37 + q^43 + q^44 + q^45 - 
        q^55 + q^59 + q^68 + O(q^74),
    q^8 + q^11 - q^16 + q^17 - q^19 - q^25 - q^29 + q^32 + q^37 - q^40 - q^44 - 
        q^47 - q^64 - q^68 + q^72 + O(q^74),
    q^10 + q^11 + q^17 - q^19 - q^22 - q^25 - q^29 + q^32 - q^34 + q^37 - q^40 -
        q^47 + q^62 - q^64 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
303
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
303
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
100
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
303
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
303
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
303
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
303
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
303
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
303
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
303
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^19 - q^22 - q^24 + q^25 - q^33 - q^37 + q^49 - q^52 - q^58 + 
        O(q^66),
    q^2 - q^11 - q^12 + q^18 - q^26 - q^29 + q^39 + q^41 + q^50 + q^53 - q^57 + 
        q^59 - q^62 + O(q^66),
    q^3 - q^8 - q^11 + q^26 + q^27 - q^29 + q^32 - q^38 + q^44 - q^57 + q^62 + 
        O(q^66),
    q^4 - q^6 - q^13 + q^19 - q^31 + q^33 + q^36 + q^37 - q^43 - q^52 - q^54 - 
        q^64 + O(q^66)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^5 - a^3)*q^3 + (a^5 + a^3 - a^2 - a - 1)*q^9 + (a^5 - a^4 - a^2 + 
        a)*q^11 + a*q^17 + a^2*q^19 - a^5*q^25 + (a^4 + a^3 + a^2)*q^27 + (a^4 -
        a^3 + a^2 - a)*q^33 + (a^3 + a^2 - 1)*q^41 + (a^4 - a)*q^43 - a^3*q^49 +
        (-a^4 - a^3 + 1)*q^51 + (-a^5 - a^4 + a)*q^57 + (-a^5 + a^3 - 1)*q^59 + 
        (a^3 - a - 1)*q^67 + O(q^70),
    q^2 - a*q^4 + (-a^5 - a^3)*q^6 + a^2*q^8 + (a^4 + a^3 - 1)*q^12 - a^3*q^16 +
        (a^5 + a^3 - a^2 - a - 1)*q^18 + (a^5 - a^4 - a^2 + a)*q^22 + (-a^5 - 
        a^4 + a)*q^24 + a^4*q^32 + a*q^34 + (-a^4 + a^2 + a + 1)*q^36 + a^2*q^38
        + (a^5 - a^2 + 1)*q^44 + (a^5 + a^3 - a^2 - 1)*q^48 - a^5*q^50 + (a^4 + 
        a^3 + a^2)*q^54 - a^5*q^64 + (a^4 - a^3 + a^2 - a)*q^66 - a^2*q^68 + 
        O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^3 - q^11 - 2*a*q^17 + (a - 1)*q^19 + (a - 1)*q^25 + q^27 - a*q^33 + 
        a*q^41 - 2*a*q^43 + q^49 + (-2*a + 2)*q^51 - q^57 + a*q^59 + (-a + 
        1)*q^67 + O(q^70),
    q^2 - a*q^4 + a*q^6 + (a - 1)*q^8 + (-a + 1)*q^12 + q^16 - q^22 - q^24 - 
        a*q^32 - 2*a*q^34 + (a - 1)*q^38 + a*q^44 + a*q^48 + (a - 1)*q^50 + q^54
        + (a - 1)*q^64 - a*q^66 + (2*a - 2)*q^68 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^70)
]
;
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 + O(q^70),
    q^2 - q^10 - q^14 + q^18 - q^22 - q^34 + q^38 + 2*q^46 + O(q^70),
    q^4 - q^20 - q^28 + q^36 - q^44 - q^68 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
304
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 - q^17 - q^23 + q^25 + q^39 + 2*q^47 - q^57 + O(q^70),
    q^2 + q^8 - q^12 - q^14 + q^32 - q^34 - q^46 - q^48 + q^50 - q^52 - q^56 + 
        O(q^70),
    q^3 + q^13 - q^19 - q^21 - q^27 + q^29 - 2*q^37 - q^51 + q^53 + q^59 + q^67 
        - q^69 + O(q^70),
    q^4 - q^6 + q^16 - q^24 - q^26 - q^28 + q^38 + q^42 + q^54 - q^58 + q^64 - 
        q^68 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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(
20
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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(
20
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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(
20
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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(
4
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
305
);
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(
4
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
306
);
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(
306
);
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(
306
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
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(
306
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
306
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
306
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
306
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
306
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
306
);
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(
6
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
306
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1 + 8*H.2
;
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(
307
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
306
);
qprec:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
307
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
102
);
qprec:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
307
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
34
);
qprec:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
307
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
17*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
307
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
51*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
307
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
153*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
51
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^7 + q^9 - q^11 + q^16 - q^17 - q^19 + q^25 - q^28 + q^36 - q^37 
        - q^41 - q^44 + O(q^51)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
308
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
308
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*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(
308
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
308
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (2*a^3 - 2*a^2 + a)*q^7 + (-a^3 - 1)*q^8 + a^3*q^9 + (a^2 - 2*a 
        + 2)*q^11 + (2*a^2 - 2*a)*q^14 + (a^3 - 2*a^2 + a)*q^16 + (-2*a^3 + 
        2*a^2)*q^22 + (-3*a^3 + 3*a^2 - 1)*q^23 + (a^3 - a^2 + a - 1)*q^25 + 
        (-a^2 + 2*a - 2)*q^28 + (-2*a^3 + a^2 - a + 1)*q^29 + (2*a^2 - 2*a + 
        1)*q^32 + (-a^3 + a^2 - a + 1)*q^36 + (-a^2 - 1)*q^37 + (a^3 - 3*a^2 + 
        4*a - 2)*q^43 + (a^3 - 2*a^2 + 2*a)*q^44 + (2*a^3 - 4*a^2 + 4*a)*q^46 + 
        a^2*q^49 + (a - 1)*q^53 + (a^3 - a^2 + 1)*q^56 + (a^3 - a^2 - a + 
        1)*q^63 + (2*a - 2)*q^64 + (-a^3 + a^2 - 2)*q^67 + (a^3 - 3*a^2 + 
        a)*q^71 + (-a^3 + a)*q^72 - a^3*q^77 + (-2*a^3 + 4*a^2 - 3*a + 1)*q^79 -
        a*q^81 + O(q^86),
    q^2 + (-a^3 + 2*a^2 - a + 1)*q^4 + (-2*a + 2)*q^7 + (-a^2 + 2*a - 1)*q^8 + 
        (2*a^2 - 2*a)*q^11 + (-2*a^3 + 2*a^2 - a)*q^14 + (a^3 - a^2 - a + 
        1)*q^16 + a^3*q^18 + (-a^2 + 2*a - 2)*q^22 + (-2*a^2 + 4*a - 4)*q^23 + 
        (a^3 - 2*a^2 + 2*a - 1)*q^28 + (-2*a^3 + 2*a^2 - 2*a)*q^32 + (a^2 - 
        1)*q^36 + (2*a^3 - 4*a^2 + 2*a)*q^43 + (a^3 - a^2 + 1)*q^44 + (3*a^3 - 
        3*a^2 + 1)*q^46 + (a^3 - a^2 + a - 1)*q^50 + (a^3 - a)*q^56 + (-2*a^3 + 
        a^2 - a + 1)*q^58 + (2*a^2 - 2*a + 2)*q^63 + (-2*a^2 + 2*a - 1)*q^64 + 
        (-2*a^3 + 2*a)*q^67 + (2*a^3 + 2)*q^71 + (a^3 - 2*a^2 + 2*a - 1)*q^72 + 
        (-a^2 - 1)*q^74 + (-2*a^3 + 2*a^2 - 2)*q^79 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a^2*q^7 - a*q^9 + (a^3 - a^2 + a - 1)*q^11 + (-a^3 + a^2)*q^23 - 
        a^3*q^25 + (-a^3 - a)*q^29 + (a^3 - a^2 + a)*q^37 + (a^3 - a^2 - 1)*q^43
        + (a^3 - a^2 + a - 1)*q^49 + (a^2 + 1)*q^53 - a^3*q^63 + (a^3 - a^2 - 
        1)*q^67 + (-a^3 + 1)*q^71 - a*q^77 + (a^2 + 1)*q^79 + a^2*q^81 + 
        O(q^86),
    q^2 - a^2*q^8 + a^2*q^14 + (a - 1)*q^16 - a*q^18 + (a^3 - a^2 + a - 1)*q^22 
        + (a^2 - a)*q^32 + (-a^3 + a^2)*q^46 - a^3*q^50 + (-a^3 + a^2 - a + 
        1)*q^56 + (-a^3 - a)*q^58 + q^64 + a^3*q^72 + (a^3 - a^2 + a)*q^74 + 
        O(q^86),
    q^4 + (-a^2 + a - 1)*q^8 + (-a^3 + a^2 - a)*q^16 + a^2*q^28 + a^3*q^32 - 
        a*q^36 + (a^3 - a^2 + a - 1)*q^44 + (-a + 1)*q^56 + (a^3 - a^2 + a)*q^72
        + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
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 + O(q^86),
    q^7 - q^21 - q^35 + q^77 + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
308
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^9 - q^14 + q^16 - q^22 + q^25 - q^36 - 2*q^37 + q^49 - 2*q^53 - 
        q^56 + q^64 + q^77 + q^81 + O(q^86),
    q^2 - q^7 + q^8 - q^11 - q^18 - q^28 + q^32 + 2*q^43 - q^44 + q^50 + q^63 - 
        q^72 - 2*q^74 + 2*q^79 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
309
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
309
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
102
);
qprec:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
309
);
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:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
309
);
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:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
309
);
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:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^5*q^3 - a^3*q^4 + (a^15 - a^14 + a^13 - a^12 + a^11 - a^10 - a^8 + a^7
        - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^7 + a^10*q^9 + a^8*q^12 + (-a^7
        - a)*q^13 + a^6*q^16 + (-a^13 - a^11)*q^19 + (a^14 + a^4)*q^21 + 
        a^2*q^25 - a^15*q^27 + (a^12 + a^2)*q^28 + (-a^15 + a^14)*q^31 - 
        a^13*q^36 + (a^12 + a^4)*q^37 + (a^12 + a^6)*q^39 + (-a^11 - a^7)*q^43 -
        a^11*q^48 + (-a^15 + a^8 - a)*q^49 + (a^10 + a^4)*q^52 + (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 - 1)*q^57 + (-a^13 + a^8)*q^61 + (-a^9 + a^2)*q^63 - a^9*q^64 + 
        O(q^67)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
309
);
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:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
309
);
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:=
67
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^3 + a*q^7 + q^9 + q^10 + (-a + 1)*q^16 + (a - 1)*q^19 - a*q^21 - q^22 
        - q^27 - q^30 - q^34 - a*q^40 + (a - 1)*q^43 + (-2*a + 2)*q^46 + (a - 
        1)*q^48 + (a - 1)*q^55 + (-a + 1)*q^57 - a*q^58 + a*q^63 - q^64 + q^66 +
        O(q^67),
    q^2 + (-a + 1)*q^5 - q^6 - a*q^8 + (a - 1)*q^11 + a*q^14 + (a - 1)*q^15 + (a
        - 1)*q^17 + q^18 - 2*a*q^23 + a*q^24 - q^29 + (-a + 1)*q^33 + q^35 + (a 
        - 1)*q^38 + q^41 - a*q^42 + (-a + 1)*q^45 + (a - 1)*q^47 + (-a + 1)*q^51
        + (a - 1)*q^53 - q^54 + (-a + 1)*q^56 + q^59 + O(q^67)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
309
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
51*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
67
;
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 + 
        O(q^67),
    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 + O(q^67),
    q^3 - q^21 - q^24 + q^27 - q^42 - q^51 + O(q^67),
    q^6 - q^12 - q^21 + q^39 - q^51 + q^54 + q^57 + O(q^67)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
310
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
310
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
310
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
310
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
310
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
310
);
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(
10
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
310
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
310
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
310
);
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(
20
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
310
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
310
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^4 - q^7 + q^8 + q^9 - q^19 - q^25 + q^28 + q^31 - q^32 - q^36 - q^41 +
        2*q^47 - q^56 - q^59 - q^63 + q^64 + 2*q^67 - q^71 + q^72 + q^76 + q^81 
        + O(q^90),
    q^2 - q^4 - q^14 + q^16 + q^18 + q^28 - q^32 - q^36 - q^38 - q^50 + q^62 + 
        q^76 - q^82 + O(q^90),
    q^5 - q^20 - q^25 - q^35 + q^40 + q^45 + O(q^90),
    q^10 - q^20 - q^50 - q^70 + q^80 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
310
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 - 1/2*q^10 + q^14 - 1/2*q^20 - q^31 + q^35 - q^49 - 1/2*q^50 + q^64 
        + 1/2*q^70 - q^76 - 1/2*q^80 + q^81 + O(q^90),
    q^2 - 1/2*q^10 - q^18 - 1/2*q^20 + q^28 + q^32 - q^38 - q^40 + 1/2*q^50 - 
        q^62 + 1/2*q^70 + 1/2*q^80 + q^82 + O(q^90),
    q^4 + 1/2*q^10 - q^14 - q^16 + 1/2*q^20 - q^36 - q^40 + 1/2*q^50 + 2*q^56 - 
        1/2*q^70 + q^76 - 1/2*q^80 + O(q^90),
    q^5 - 2*q^16 + 2*q^19 + q^20 - q^25 + q^35 - q^40 - 2*q^41 - q^45 - 2*q^49 +
        2*q^56 - 2*q^59 + 2*q^71 + 2*q^76 + O(q^90),
    q^7 - 1/2*q^10 - q^16 + q^19 + 1/2*q^20 - q^25 + q^32 + q^35 - q^38 - q^40 -
        q^41 - q^49 + 1/2*q^50 + q^56 - q^59 - q^63 - 1/2*q^70 + q^71 + q^76 + 
        1/2*q^80 + q^82 + O(q^90),
    q^8 - 1/2*q^10 + 1/2*q^20 - q^28 - q^38 + 1/2*q^50 - 1/2*q^70 - q^72 - 
        1/2*q^80 + q^82 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
311
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
310
);
qprec:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
311
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
62
);
qprec:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
311
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
31*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
311
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
155*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^20 - q^21 + q^25 - q^27 - q^30 - q^42 - q^47 + q^49 + O(q^52),
    q^2 - q^10 - q^15 + q^18 - q^21 - q^36 + q^39 + q^45 - q^48 + q^49 + q^50 + 
        O(q^52),
    q^3 - q^9 - q^10 + q^27 + q^28 + q^30 - q^32 - q^35 + q^50 + O(q^52),
    q^4 - q^9 - q^10 - q^12 + q^16 + q^20 + q^21 - q^26 + q^27 + q^30 - q^32 - 
        q^35 - q^40 + q^42 + q^47 - q^48 + O(q^52),
    q^5 - q^9 - q^10 - q^12 + q^16 + q^18 + q^20 + q^24 - q^26 + q^30 - q^32 - 
        q^35 - q^36 - q^40 + q^42 + q^45 - q^48 + O(q^52),
    q^6 - q^9 - q^10 - q^12 + q^14 + q^15 + q^24 + q^25 - q^26 + q^28 - q^32 - 
        q^35 - q^36 - q^40 + O(q^52),
    q^7 - q^9 - q^10 + q^14 + q^24 - q^26 + q^28 + q^30 - q^32 - q^35 - q^36 - 
        q^40 + q^45 + q^50 + O(q^52),
    q^8 - q^9 - q^12 + q^15 + q^21 - q^26 - q^35 + q^42 + O(q^52),
    q^13 - q^14 - q^15 + q^18 + q^20 - q^25 - q^28 + q^35 + q^39 - q^48 + 
        O(q^52)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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(
312
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 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(
312
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
312
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
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(
312
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
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(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a + 1)*q^3 + (a - 2)*q^7 - a*q^9 + a*q^13 + (2*a - 1)*q^21 - q^25 - 
        q^27 + (-2*a + 1)*q^31 + q^39 + a*q^43 + (-2*a + 2)*q^49 - a*q^61 + (a +
        1)*q^63 + (a + 1)*q^67 + (-2*a + 1)*q^73 + (a - 1)*q^75 + q^79 + (a - 
        1)*q^81 + (-a - 1)*q^91 + (-a - 1)*q^93 + (a - 2)*q^97 + O(q^98),
    q^2 + (-a + 1)*q^6 + (a - 2)*q^14 - a*q^18 + a*q^26 + (2*a - 1)*q^42 - q^50 
        - q^54 + (-2*a + 1)*q^62 + q^78 + a*q^86 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
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 - a*q^4 + (a - 1)*q^8 - q^10 + q^16 + (a - 1)*q^18 + a*q^20 - a*q^26 - 
        a*q^32 + (-a + 1)*q^34 + q^36 + (-a + 1)*q^40 + (a - 1)*q^52 + a*q^58 + 
        (a - 1)*q^64 - q^68 - a*q^72 + a*q^74 - q^80 + a*q^82 + (-a + 1)*q^90 + 
        O(q^98),
    q^3 - q^15 + (a - 1)*q^27 - a*q^39 + (-a + 1)*q^51 + a*q^87 + O(q^98),
    q^6 - a*q^12 + (a - 1)*q^24 - q^30 + q^48 + (a - 1)*q^54 + a*q^60 - a*q^78 -
        a*q^96 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 + (-a + 1)*q^7 + (a - 1)*q^9 + (a - 1)*q^13 + (2*a - 2)*q^19 - 
        q^21 + q^25 + q^27 - q^31 - 2*a*q^37 + q^39 + (-a + 1)*q^43 + 2*q^57 + 
        (-a + 1)*q^61 + a*q^63 + a*q^67 - q^73 - a*q^75 - q^79 - a*q^81 + a*q^91
        + a*q^93 + (-a + 1)*q^97 + O(q^98),
    q^2 - a*q^6 + (-a + 1)*q^14 + (a - 1)*q^18 + (a - 1)*q^26 + (2*a - 2)*q^38 -
        q^42 + q^50 + q^54 - q^62 - 2*a*q^74 + q^78 + (-a + 1)*q^86 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^9 - q^10 - q^14 + q^16 - q^17 + q^26 + q^27 + q^35 - q^36 - q^40
        - q^43 - q^56 + 2*q^62 + q^64 - q^65 - q^68 - q^74 + q^90 - q^91 - q^94 
        + O(q^98),
    q^2 - q^5 - q^7 + q^8 + q^13 - q^18 - q^20 - q^28 + 2*q^31 + q^32 - q^34 - 
        q^37 + q^45 - q^47 + q^52 + q^54 + q^63 + q^70 - q^71 - q^72 - q^80 + 
        q^85 - q^86 + O(q^98),
    q^3 - q^9 + q^12 - q^30 - q^36 - q^42 + q^48 - q^51 + q^78 + q^81 + q^90 + 
        O(q^98),
    q^6 - q^15 - q^18 - q^21 + q^24 + q^39 + q^45 - q^60 + q^63 - q^72 - q^84 + 
        2*q^93 + q^96 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3 + 6*H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 + q^9 - q^13 - q^25 - q^27 + q^39 + 2*q^43 + q^49 - 2*q^61 + q^75 - 
        2*q^79 + q^81 + O(q^98),
    q^2 - q^6 + q^18 - q^26 - q^50 - q^54 + q^78 + 2*q^86 + O(q^98),
    q^4 - q^12 - q^16 + q^36 + q^48 - q^52 + q^64 + O(q^98),
    q^8 - q^24 - q^32 + q^72 + q^96 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
312
);
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:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^9 - q^10 + q^12 - q^16 + q^22 - q^25 + q^30 - q^39 - q^40 + q^49 + 
        q^52 + 2*q^55 - q^66 + q^81 - q^82 + q^88 + q^90 - q^94 + O(q^98),
    q^2 + q^6 - q^8 + 2*q^15 - q^18 - 2*q^20 + q^24 + q^26 - q^32 - 2*q^33 - 
        2*q^41 + 2*q^44 - 2*q^47 - q^50 - q^54 + 2*q^65 + 2*q^71 + q^72 - q^78 +
        2*q^89 - q^96 + O(q^98),
    q^3 - q^4 - q^10 + q^13 + q^22 - q^27 - q^30 + q^36 + q^40 - q^48 - 2*q^61 +
        q^64 + q^66 - q^75 + q^82 - q^88 + q^90 + q^94 + O(q^98),
    q^5 - q^6 + q^8 - q^11 - q^15 + q^20 - q^26 + q^33 + q^41 - q^44 - q^45 + 
        q^47 + q^54 + q^59 + q^60 - q^65 - q^71 - q^72 - q^80 - q^83 - q^89 + 
        q^96 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
313
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
312
);
qprec:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
313
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
104
);
qprec:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
313
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
24
);
qprec:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
313
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
39*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
8
);
qprec:=
52
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
314
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
156
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
314
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
314
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
77
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
314
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
39*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(
315
);
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(
315
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
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(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
315
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
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 + O(q^82),
    q^5 - q^20 - q^35 + q^80 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
315
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.2 + 3*H.3
;
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(
315
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 + q^9 + a*q^11 + (a - 1)*q^15 - a*q^16 - a*q^21 - a*q^25 - 
        2*a*q^29 + q^35 + (a - 1)*q^36 + (-a + 1)*q^39 - q^44 + (a - 1)*q^49 - 
        q^51 - a*q^60 + q^64 + a*q^65 - q^71 + a*q^79 + q^81 + O(q^82),
    q^3 + (a - 1)*q^5 - a*q^7 + (a - 1)*q^12 + (-a + 1)*q^13 - q^17 - a*q^20 + 
        q^27 + q^28 + a*q^33 + (a - 1)*q^45 + a*q^47 - a*q^48 + a*q^52 - q^55 - 
        a*q^63 + (-a + 1)*q^68 - q^73 - a*q^75 + (-a + 1)*q^77 + q^80 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
316
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
316
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
316
);
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:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
316
);
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:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
316
);
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:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
316
);
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:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
316
);
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:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
316
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
39*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
76
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^11 - q^13 - q^31 + q^49 - q^55 - q^65 + O(q^76),
    q^2 + q^18 - q^20 - q^22 - q^26 - q^32 + q^44 + q^52 - q^62 + q^64 + 
        O(q^76),
    q^4 - q^20 - q^32 + q^36 - q^40 + O(q^76),
    q^5 - q^11 - q^13 + q^19 + q^23 - q^25 - q^31 + q^45 + q^67 + q^73 + 
        O(q^76),
    q^8 - q^16 - q^20 + q^44 + q^52 + q^72 + O(q^76),
    q^10 + q^16 - q^22 - q^26 - q^32 + q^38 - q^40 + q^46 - q^50 - q^62 + 
        O(q^76)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
317
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
316
);
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
317
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
79*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
318
);
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(
318
);
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(
318
);
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(
26
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
318
);
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(
26
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
318
);
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(
318
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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^9 - q^10 - q^13 - q^15 - q^24 + q^25 - q^28 + q^40 + q^42 - q^43 + 
        q^46 + q^52 + q^60 - q^78 + q^81 + q^82 - q^90 - q^91 + q^96 - q^97 - 
        q^100 + O(q^102),
    q^2 + q^18 - q^20 - q^26 - q^30 - q^48 + q^50 - q^56 + q^80 + q^84 - q^86 + 
        q^92 + O(q^102),
    q^3 + q^14 - q^21 - q^23 - q^26 + q^27 - q^30 + q^32 - q^35 - q^41 - q^48 + 
        q^50 + q^53 - q^56 + q^65 + q^74 - q^86 - q^98 + 2*q^101 + O(q^102),
    q^4 - q^10 - q^24 - q^28 + q^36 + q^42 + q^46 - q^78 + q^82 - q^90 + 
        O(q^102),
    q^5 + q^12 + q^14 - q^20 - q^21 - q^23 - q^26 - q^30 + q^39 - q^41 + q^45 - 
        q^48 + q^50 - q^65 + q^71 + q^74 - q^75 + q^80 + q^83 - q^86 - q^98 + 
        O(q^102),
    q^6 - q^10 - q^16 + q^28 + q^40 - q^52 + q^54 - q^60 + q^64 - q^70 - q^78 - 
        q^90 + q^100 + O(q^102),
    q^7 - q^13 - q^15 + q^16 - q^24 + q^25 - q^28 + q^37 - q^43 - q^49 + q^52 + 
        q^60 + q^63 + q^69 - q^97 - q^100 + O(q^102),
    q^8 - q^12 - q^14 + q^26 + q^30 - q^50 - q^56 + q^72 - q^74 - q^80 + q^84 + 
        q^86 + q^92 + q^98 + O(q^102)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
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(
140
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
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(
14
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
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(
70
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
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(
14
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
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(
20
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
319
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 14*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^20 - q^23 - q^34 - q^38 + q^49 - q^53 + O(q^58),
    q^2 - q^10 - q^17 + q^18 - q^19 - q^40 + q^41 + q^43 - q^44 + q^50 + q^55 + 
        O(q^58),
    q^4 - q^5 - q^20 - q^22 + q^23 + q^25 + q^36 - q^45 + q^53 + O(q^58),
    q^8 - q^10 - q^11 + q^17 + q^19 - q^29 - q^32 + q^46 + q^50 + O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
320
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^74)
]
;
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 + O(q^74),
    q^2 - a*q^10 + a*q^18 + (a - 1)*q^26 + (-a - 1)*q^34 - q^50 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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(
8
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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(
4
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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(
8
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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(
4
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
12*H.2 + H.3
;
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(
320
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^5 - q^9 + q^25 - 2*q^29 - 2*q^41 - q^45 - q^49 + 2*q^61 + O(q^74)
]
;
Bo:=
[
    q - q^5 - q^9 + q^25 + 2*q^29 - 2*q^41 + q^45 - q^49 - 2*q^61 + O(q^74),
    q^2 - q^10 - q^18 + q^50 + 2*q^58 + O(q^74),
    q^4 - q^20 - q^36 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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(
16
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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(
4
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
320
);
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:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
321
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
321
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
106
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
321
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
321
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
53*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^9 - q^11 - q^13 + q^16 - q^19 - q^23 + q^25 + q^27 + 2*q^29 - 
        q^36 - q^37 - q^41 - q^44 + 2*q^47 + q^49 - q^52 - q^53 - q^61 + q^64 + 
        O(q^70),
    q^3 - q^9 + q^12 - q^33 - q^36 - q^39 + q^48 - q^57 - q^69 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
322
);
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(
322
);
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(
322
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
322
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
322
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
322
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a^4*q^4 + a^8*q^7 + (-a^9 + a^8 - a^7 + a^6 - a^5 + 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^8 + a^5 - 1)*q^16 - a*q^23 + a^2*q^25 + a*q^28 + 
        (-a^9 - a^5)*q^29 + (a^9 - a^6 + a^3 - 1)*q^32 + a^3*q^36 + (-a^7 + 
        a^2)*q^37 + (a^6 + a^4)*q^43 + (-a^8 + a^7)*q^44 - a^5*q^49 + (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^4 - a^3 + a^2 - a + 1)*q^56 - a^7*q^63 + (a^9 + a^7 - a^6 - a^4 + 
        a)*q^64 + (-a^9 + a^6)*q^67 + (a^8 - a^7)*q^71 + (a^9 + a)*q^72 + (-a + 
        1)*q^77 + (-a^5 - a)*q^79 - a^9*q^81 + (-a^6 + a^5 + a^3 - a^2)*q^88 + 
        O(q^90),
    q^2 + (-a^9 + a^6)*q^4 + (-a^7 + a^4 - a)*q^8 + a^8*q^14 + (a^9 - a^8 - a^6 
        - a^4 + a^3 + a - 1)*q^16 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - 
        a^2 + a - 1)*q^18 + (a^4 - a^3)*q^22 + (a^6 - a^3)*q^28 + (a^8 - a^5 - 
        a^3 + a^2 + 1)*q^32 + (a^8 - a^5)*q^36 + (-a^8 + a^7 - a^6 + a^5 - a^4 +
        a^3 - 1)*q^44 - a*q^46 + a^2*q^50 + (-a^9 + a^4 - a)*q^56 + (-a^9 - 
        a^5)*q^58 + (-a^9 + a^8 + a^6 - a^3 - a + 1)*q^64 + (a^6 - a^3 + 1)*q^72
        + (-a^7 + a^2)*q^74 + (a^6 + a^4)*q^86 + (a^9 - a^6 + a^3 - a^2 + 
        a)*q^88 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
322
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
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 + O(q^90),
    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 + O(q^90),
    q^7 - q^21 - q^28 + q^56 + q^84 + O(q^90),
    q^14 - q^28 - q^42 + q^84 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
322
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
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(
144
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
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:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
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(
48
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
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(
8
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^2*q^4 + (a - 1)*q^5 + (-a^2 - a)*q^7 + a*q^9 + (-a^3 + 1)*q^11 - q^16 
        + a^3*q^17 + a^3*q^19 + (-a^3 + a^2)*q^20 + (a^2 - a)*q^23 + (a^2 - a + 
        1)*q^25 + (a^3 - 1)*q^28 + (-a^3 + a)*q^35 - a^3*q^36 + (-a^2 - a)*q^44 
        + (a^2 - a)*q^45 + (a^3 + a)*q^47 + (a^3 + a^2 - 1)*q^49 + (a^3 + 
        a)*q^55 + O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
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(
4
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 + (a + 1)*q^5 + (a - 1)*q^7 + a*q^9 + (-a + 1)*q^11 + q^16 - a*q^17 
        - a*q^19 + (-a - 1)*q^20 + (a - 1)*q^23 + a*q^25 + (-a + 1)*q^28 - 
        2*q^35 - a*q^36 - 2*a*q^43 + (a - 1)*q^44 + (a - 1)*q^45 - a*q^49 + 
        2*q^55 + O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
323
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + 9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^9 + q^16 - q^17 - q^19 + q^25 - q^36 - 2*q^43 - 2*q^47 + q^49 + 
        O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
324
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^10 - q^13 + q^16 - q^34 - q^37 - q^40 + q^49 - q^52 - q^58 - 
        q^61 + q^64 - q^73 + O(q^74),
    q^2 - q^5 + q^8 - q^17 - q^20 - q^26 - q^29 + q^32 + 2*q^41 + 2*q^53 + q^65 
        - q^68 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
324
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
324
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
324
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
324
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
324
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*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^7 + a*q^13 - q^19 + (a - 1)*q^25 - 2*a*q^31 - q^37 + (2*a - 
        2)*q^43 + (-a + 1)*q^61 + a*q^67 - q^73 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
324
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 - q^10 + (-a + 1)*q^13 - a*q^16 + a*q^34 - q^37 + (-a + 
        1)*q^40 + (a - 1)*q^49 + a*q^52 + (-a + 1)*q^58 + a*q^61 + q^64 - q^73 +
        O(q^74),
    q^2 + a*q^5 + (a - 1)*q^8 + (-a + 1)*q^17 - q^20 + (-a + 1)*q^26 - q^29 - 
        a*q^32 - 2*a*q^41 + (2*a - 2)*q^53 + q^65 + a*q^68 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
324
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
74
;
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 +
        O(q^74),
    q^3 - q^21 - q^39 - q^57 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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(
12
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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(
12
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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(
20
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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(
4
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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(
12
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^2 - 1)*q^6 - a^2*q^11 - a^3*q^14 - a^2*q^16 + a*q^19 - q^21 + (a^3 - 
        a)*q^24 + a^2*q^26 + (a^3 - a)*q^29 + a^3*q^34 + (-a^3 + a)*q^39 + 
        a^2*q^41 + (-a^2 + 1)*q^46 + q^51 + (-a^3 + a)*q^54 + (-a^2 + 1)*q^56 - 
        a*q^59 + O(q^60),
    q^2 - a^3*q^3 + a^2*q^7 + a*q^8 - a*q^13 - a^2*q^17 - a^2*q^22 + a^3*q^23 + 
        (a^2 - 1)*q^27 + (a^3 - a)*q^33 - q^37 + a*q^38 - q^42 + (-a^3 + a)*q^43
        + (a^3 - a)*q^48 + (-a^2 + 1)*q^57 + (a^3 - a)*q^58 + O(q^60)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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(
20
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
325
);
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(
4
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
326
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
162
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
326
);
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:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
326
);
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:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
326
);
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:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
326
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
81*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(
327
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
327
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
108
);
qprec:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
327
);
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:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
327
);
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:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
327
);
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:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
327
);
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:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^5 + a^2)*q^3 + a^3*q^4 + (-a^3 - a)*q^7 + (-a^4 + a)*q^9 + a^2*q^12 
        + (2*a^5 - a^2)*q^13 + (a^3 - 1)*q^16 + (-a^5 + a^4 - a)*q^19 + (-a^2 - 
        1)*q^21 + a^4*q^25 + (-a^3 + 1)*q^27 + (-a^4 - a^3 + 1)*q^28 + (-a^4 + 
        a)*q^31 + a*q^36 + (-a^5 - 1)*q^37 + (2*a^4 - a)*q^39 + (-a^2 + a)*q^43 
        + a^5*q^48 + (a^4 + a^3 + a^2 - 1)*q^49 + (a^5 - 2*a^2)*q^52 + (-a^4 + 
        a^3 - 1)*q^57 + (-a^4 - a^3 + a)*q^61 + (a^5 - a^2 - a)*q^63 - q^64 + 
        O(q^71)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
327
);
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:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
327
);
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:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^4 + a)*q^3 + (a^3 - 1)*q^4 + (a^3 + a^2 - 1)*q^7 - a^5*q^9 + 
        a^4*q^12 - a^4*q^13 - a^3*q^16 + (-a^5 - a)*q^19 + (a^4 + 1)*q^21 + (a^5
        - a^2)*q^25 - a^3*q^27 + (a^5 - a^3 - a^2)*q^28 + a^5*q^31 + a^2*q^36 + 
        (-a + 1)*q^37 - a^2*q^39 + (a^4 + a^2)*q^43 - a*q^48 + (a^5 + a^4 - a^3 
        - a^2)*q^49 + a*q^52 + (a^5 - a^3 - a^2)*q^57 + (-a^5 + a^3 - 1)*q^61 + 
        (-a^4 + a^2 + a)*q^63 + q^64 - 2*a^5*q^67 + O(q^71)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
327
);
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:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^3 - q^4 + (-a + 1)*q^7 - a*q^9 + (a - 1)*q^12 + q^16 + (2*a -
        1)*q^19 - a*q^21 - a*q^25 - q^27 + (a - 1)*q^28 + 2*a*q^31 + a*q^36 + (a
        - 2)*q^37 + q^43 + (-a + 1)*q^48 + (a + 1)*q^57 + (-a + 1)*q^61 - q^63 -
        q^64 + O(q^71)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
327
);
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:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
327
);
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:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + q^4 + a*q^7 + (a - 1)*q^9 - a*q^12 - 2*a*q^13 + q^16 - q^19 + 
        (-a + 1)*q^21 + (a - 1)*q^25 + q^27 + a*q^28 + (2*a - 2)*q^31 + (a - 
        1)*q^36 + (-a + 1)*q^37 + (2*a - 2)*q^39 - q^43 - a*q^48 - 2*a*q^52 + 
        a*q^57 + a*q^61 - q^63 + q^64 + (2*a - 2)*q^67 + O(q^71)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
327
);
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:=
71
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^21 - q^22 + q^25 - q^28 - q^31 - q^43 - q^48 + q^49 - q^66 + 
        O(q^71),
    q^2 - q^11 - q^14 + q^18 - q^24 - q^33 + q^41 + q^47 + q^50 + q^51 - q^53 - 
        q^68 + q^69 + O(q^71),
    q^3 - q^7 - q^16 - q^22 + q^27 + q^28 + q^34 + q^46 - q^49 - q^61 - q^63 + 
        q^64 - q^66 + O(q^71),
    q^4 - q^7 - q^12 + q^21 + q^31 - q^34 + q^36 + q^43 - q^46 - q^49 - q^61 - 
        q^63 + O(q^71),
    q^6 - q^8 - q^11 + q^17 + q^23 - q^33 - q^42 - q^53 + q^54 + q^56 + q^59 - 
        q^62 + q^68 + O(q^71)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
328
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
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(
328
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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(
20
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^3*q^2 + (a^7 + a^6 - a^4 + a^2 - 1)*q^3 + a^6*q^4 + (-a - 1)*q^6 + 
        (a^7 - a^5 + a^3 - a)*q^8 + (-a^6 - a^5 - a^4)*q^9 + (-a^6 + a^5 + a^4 -
        a^2 + 1)*q^11 + (-a^4 - a^3)*q^12 - a^2*q^16 + (a^7 - a^5 + a^4 + a^3 - 
        a)*q^17 + (-2*a^7 - a^6 + a^5 + a^4 - a^3 - a^2 + a + 1)*q^18 + (-a^7 + 
        a^5 - a^3 + a - 1)*q^19 + (a^6 - a^4 + a^2 + a - 1)*q^22 + (-a^7 - 
        a^6)*q^24 + a^2*q^25 + (a^4 + a^3 + a^2 + a)*q^27 - a^5*q^32 + (a^6 + 
        a^5 - a^3 - a^2)*q^33 + (a^7 - a^2)*q^34 + (a^2 + a + 1)*q^36 + (-a^3 + 
        a^2)*q^38 + a*q^41 + (-a^5 - a)*q^43 + (a^4 - a)*q^44 + (-a^7 + a^5 - 
        a^3 + a + 1)*q^48 + (-a^7 + a^5 - a^3 + a)*q^49 + a^5*q^50 + (-a^7 - a^6
        - a^2 - a)*q^51 + (a^7 + a^6 + a^5 + a^4)*q^54 + (a^4 - a^2 + 1)*q^57 + 
        (-a^6 + a^4 - a^2 + 1)*q^64 + (a^7 - 2*a^5 - a^4 + a^3 + a^2 - a - 
        1)*q^66 + (-a^7 + 1)*q^67 + (-a^5 - 1)*q^68 + (a^5 + a^4 + a^3)*q^72 + 
        (-a^7 - a^3)*q^73 + (a^7 - a^5 + a^3 - a - 1)*q^75 + (-a^6 + a^5)*q^76 +
        O(q^78)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a^2 - a + 1)*q^5 - q^9 + (a^3 - 2*a^2 + a - 1)*q^13 + (a^2 + a)*q^17 + 
        (-a^3 + a^2 - a)*q^25 + (-a^2 - 1)*q^37 - a^3*q^41 + (-a^2 + a - 1)*q^45
        + (-a^3 + a^2 - a + 1)*q^49 + (2*a^3 - a^2 + a - 1)*q^53 + (-a^3 - 
        a)*q^61 + (a^3 - a^2 - a + 1)*q^65 + (-a^3 + a^2 + 1)*q^73 + O(q^78),
    q^2 - a^3*q^4 - a*q^8 + (a^2 - a + 1)*q^10 + (a^3 - a^2 + a - 1)*q^16 - q^18
        + (-a^2 + a)*q^20 + (a^3 - 2*a^2 + a - 1)*q^26 + a^2*q^32 + (a^2 + 
        a)*q^34 + a^3*q^36 + (-a^3 + a^2 - a)*q^40 + (-a^3 + a^2 - a)*q^50 + 
        (a^2 - 1)*q^52 + q^64 + (-a^3 + a^2 - a + 2)*q^68 + a*q^72 + (-a^2 - 
        1)*q^74 + O(q^78)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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(
10
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^3*q^2 + (-a^3 - a^2)*q^3 - a*q^4 + (a + 1)*q^6 + (-a^3 + a^2 - a + 
        1)*q^8 + (a^3 - a^2 - 2)*q^9 + (-a^3 - 1)*q^11 + (2*a^3 - a^2 + a - 
        1)*q^12 + a^2*q^16 + (-2*a^3 - a + 1)*q^18 + (-a^3 + a^2 - a + 2)*q^19 +
        (-a^3 + a)*q^22 + (-a^2 - a)*q^24 + a^2*q^25 + (2*a^3 + 2*a - 1)*q^27 - 
        q^32 + (a^3 + a^2 - a - 1)*q^33 + (a^2 + a + 1)*q^36 + (a^3 + a^2)*q^38 
        + a*q^41 + (a - 1)*q^43 + (a^3 - a^2 + 2*a - 1)*q^44 + (-a^3 + a^2 - a +
        2)*q^48 + (-a^3 + a^2 - a + 1)*q^49 - q^50 + (a^3 - 2*a^2 - 2)*q^54 + 
        (-a^3 - 2*a^2 - a)*q^57 + 2*a^3*q^59 - a^3*q^64 + (-2*a^3 + a^2 - 
        2*a)*q^66 + (-a^2 + 1)*q^67 + (2*a^3 - a^2 + a - 2)*q^72 + (a^3 - 
        a^2)*q^73 + (-a^3 + a^2 - a + 2)*q^75 + (-a - 1)*q^76 + O(q^78)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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(
8
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 + a^2*q^4 + (a^2 - a)*q^7 + a^3*q^8 - a^3*q^9 + (a^3 - a^2)*q^14 -
        q^16 + (a^3 - a^2)*q^17 + q^18 + (-a^3 - a)*q^23 - a^2*q^25 + (-a^3 - 
        1)*q^28 + (a^3 + a)*q^31 - a*q^32 + (-a^3 - 1)*q^34 + a*q^36 + a*q^41 + 
        (-a^2 + 1)*q^46 + (-a - 1)*q^47 + (-a^3 + a^2 - 1)*q^49 - a^3*q^50 + (-a
        + 1)*q^56 + (a^2 - 1)*q^62 + (a - 1)*q^63 - a^2*q^64 + (-a + 1)*q^68 + 
        (-a^2 + a)*q^71 + a^2*q^72 + (a^2 + 1)*q^73 + O(q^78)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^3 - a)*q^5 + q^9 + (-a^2 + a - 1)*q^13 + (a^3 + a - 1)*q^17 + (a^3 -
        1)*q^25 + 2*a^2*q^29 + (a^3 - a^2 + a)*q^37 - a*q^41 + (-a^3 - a)*q^45 -
        a^3*q^49 + (-a^3 - a)*q^53 + (a^2 - a)*q^61 + a^3*q^65 + (-a^3 + 
        a^2)*q^73 + O(q^78),
    q^2 - a*q^4 + a^2*q^8 + (-a^3 - a)*q^10 - a^3*q^16 + q^18 + (a^3 + a - 
        1)*q^20 + (-a^2 + a - 1)*q^26 + (a^3 - a^2 + a - 1)*q^32 + (a^3 + a - 
        1)*q^34 - a*q^36 + (-a^3 + 1)*q^40 + (a^3 - 1)*q^50 + (a^3 - a^2 + 
        a)*q^52 + 2*a^2*q^58 + q^64 + (-a^3 + 1)*q^68 + a^2*q^72 + (a^3 - a^2 + 
        a)*q^74 + O(q^78)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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(
10
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + (a^3 - a^2 - 1)*q^3 + a^2*q^4 + (a^2 + 1)*q^6 - a^3*q^8 + (-a^3 
        + a^2 + 1)*q^9 + (-a + 1)*q^11 + (-a^3 - a)*q^12 + (a^3 - a^2 + a - 
        1)*q^16 - 2*a^3*q^17 + (-a^2 - 1)*q^18 + (-a^3 + 1)*q^19 + (a^2 - 
        a)*q^22 + (a^3 + a - 1)*q^24 + (a^3 - a^2 + a - 1)*q^25 - q^27 + q^32 + 
        a^3*q^33 + (2*a^3 - 2*a^2 + 2*a - 2)*q^34 + (a^3 + a)*q^36 + (a^3 - a^2 
        - 1)*q^38 + a^2*q^41 + (a^2 + 1)*q^43 + (-a^3 + a^2)*q^44 + (-a^3 + 
        1)*q^48 - a^3*q^49 + q^50 + (2*a^3 + 2*a - 2)*q^51 + a*q^54 + (2*a^3 - 
        a^2 + a - 2)*q^57 - 2*a*q^59 - a*q^64 + (-a^3 + a^2 - a + 1)*q^66 + (a^3
        - a^2 + a)*q^67 + 2*q^68 + (-a^3 - a + 1)*q^72 + (a^3 - a^2 - 1)*q^73 + 
        (-a^3 + 1)*q^75 + (a^2 + 1)*q^76 + O(q^78)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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(
4
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + (-a + 1)*q^3 - q^4 + (-a - 1)*q^6 + a*q^8 - a*q^9 + (a - 1)*q^11
        + (a - 1)*q^12 + q^16 + (a + 1)*q^17 - q^18 + (-a - 1)*q^19 + (a + 
        1)*q^22 + (a + 1)*q^24 - q^25 - a*q^32 + 2*a*q^33 + (-a + 1)*q^34 + 
        a*q^36 + (a - 1)*q^38 + a*q^41 - 2*a*q^43 + (-a + 1)*q^44 + (-a + 
        1)*q^48 - a*q^49 + a*q^50 + 2*q^51 - 2*q^57 - q^64 + 2*q^66 + (a + 
        1)*q^67 + (-a - 1)*q^68 + q^72 + 2*a*q^73 + (a - 1)*q^75 + (a + 1)*q^76 
        + O(q^78)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - 2*q^21 - q^25 - 2*q^33 + q^41 + q^49 + 2*q^57 - 2*q^61 + 2*q^77 + 
        O(q^78),
    q^2 + q^8 - q^10 - q^20 + q^32 - q^36 - q^40 - q^42 + q^50 - q^66 - q^74 + 
        O(q^78),
    q^3 - q^7 - q^11 + q^19 + q^47 - q^63 - q^67 + q^71 - q^75 + O(q^78),
    q^4 - q^10 + q^16 - q^18 - q^20 - q^40 + q^42 + 2*q^50 + q^64 + q^66 - q^72 
        - q^74 + O(q^78),
    q^5 + q^9 - q^21 - 2*q^25 - q^33 + q^37 - q^45 + q^49 + q^57 - 2*q^61 + q^73
        + q^77 + O(q^78),
    q^6 - q^12 - q^14 - q^22 + q^24 + q^28 + q^38 + q^44 - q^48 - q^56 - q^76 + 
        O(q^78)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
328
);
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:=Rationals();
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^2 + q^4 - q^8 + q^9 + q^16 - q^18 + q^25 - q^32 + q^36 - q^41 - 2*q^43
        - q^49 - q^50 - 2*q^59 + q^64 - q^72 - 2*q^73 + O(q^78)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
329
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
329
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
329
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
46
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
329
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
329
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
329
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
329
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^3 - q^6 - q^8 + q^9 + q^12 - q^17 + q^18 + q^24 + q^25 - q^27 + q^32 -
        q^34 - q^36 - q^37 + q^47 - q^49 + 2*q^51 + O(q^62),
    q^2 - q^3 - q^4 + q^9 - q^17 + q^24 - q^37 + q^50 + q^51 + q^53 - q^54 + 
        q^59 + q^61 + O(q^62),
    q^7 - q^21 - q^42 - q^56 + O(q^62),
    q^14 - q^21 - q^28 + q^49 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
329
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + 1/3*(2*a - 1)*q^7 + (-a + 1)*q^12 + 1/3*(2*a - 1)*q^14 + (a - 1)*q^16 - 
        a*q^17 + 1/3*(-a + 2)*q^21 - a*q^24 - a*q^25 - q^27 + 1/3*(a - 2)*q^28 +
        a*q^32 + q^36 + (a - 1)*q^37 + 1/3*(a - 2)*q^42 + (a - 1)*q^47 + 1/3*(-a
        - 1)*q^49 - a*q^53 + 1/3*(a + 1)*q^56 + O(q^62),
    q^2 + 1/3*(-2*a + 1)*q^7 - a*q^8 - q^9 + q^12 + (a - 1)*q^18 + 1/3*(-a - 
        1)*q^21 + (-a + 1)*q^24 + a*q^27 + (a - 1)*q^28 + (a - 1)*q^32 + a*q^34 
        + a*q^36 + 1/3*(-a - 1)*q^42 - 2*a*q^48 - a*q^50 + 1/3*(-a + 2)*q^56 + 
        (a - 1)*q^59 + q^61 + O(q^62),
    q^3 + (a - 1)*q^8 - a*q^12 + 1/3*(-a + 2)*q^14 - q^17 - q^18 + 1/3*(-2*a + 
        1)*q^21 + (a - 1)*q^27 + 1/3*(a + 1)*q^28 + q^32 + (-a + 1)*q^34 + (-a +
        1)*q^36 + a*q^37 + (a - 1)*q^42 + 1/3*(-a - 1)*q^49 + a*q^54 + O(q^62),
    q^4 + 1/3*(a + 1)*q^7 - a*q^9 + 1/3*(-2*a + 1)*q^14 - q^17 - q^18 + 
        1/3*(-2*a + 1)*q^21 + q^24 + (a - 1)*q^27 + 1/3*(2*a - 1)*q^28 + a*q^37 
        + 1/3*(-a - 1)*q^42 + (-a + 1)*q^48 + 1/3*(a - 2)*q^49 + a*q^51 - q^53 +
        a*q^54 + 1/3*(2*a - 1)*q^56 + O(q^62),
    q^6 + 1/3*(2*a - 1)*q^7 + (-a + 1)*q^9 + (a - 1)*q^16 + 1/3*(-2*a + 1)*q^21 
        - q^27 - q^34 + 1/3*(-2*a + 1)*q^42 + (a - 1)*q^51 - a*q^53 + (a - 
        1)*q^54 + 1/3*(a + 1)*q^56 + O(q^62)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
330
);
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(
330
);
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(
330
);
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:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
330
);
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(
330
);
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(
20
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
330
);
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(
330
);
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:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
330
);
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(
330
);
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(
10
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
330
);
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(
330
);
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(
4
);
qprec:=
130
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + q^5 + a*q^9 - q^11 + (a - 1)*q^15 - q^16 - a*q^20 + (a - 1)*q^23
        - q^25 + (-a - 1)*q^27 + (-a + 1)*q^33 + q^36 + (a + 1)*q^37 + a*q^44 - 
        a*q^45 + (a + 1)*q^47 + a*q^49 + (-a + 1)*q^53 + q^55 - 2*a*q^59 + (a + 
        1)*q^60 + a*q^64 + (-a - 1)*q^67 - 2*a*q^69 - q^80 + q^81 + (a + 1)*q^92
        + (-a - 1)*q^97 + a*q^99 + a*q^100 + (a - 1)*q^103 + (a - 1)*q^108 + (a 
        - 1)*q^113 + (-a + 1)*q^115 - q^121 - q^125 + O(q^130),
    q^2 - a*q^8 + q^10 + a*q^18 - q^22 + (a - 1)*q^30 - q^32 - a*q^40 + (a - 
        1)*q^46 - q^50 + (-a - 1)*q^54 + (-a + 1)*q^66 + q^72 + (a + 1)*q^74 + 
        a*q^88 - a*q^90 + (a + 1)*q^94 + a*q^98 + (-a + 1)*q^106 + q^110 - 
        2*a*q^118 + (a + 1)*q^120 + a*q^128 + O(q^130),
    q^3 + (a + 1)*q^5 + (a - 1)*q^9 + (-a - 1)*q^11 - a*q^12 - q^15 + (-a + 
        1)*q^20 - 2*q^23 - a*q^27 + q^33 + (a + 1)*q^36 + (a - 1)*q^44 + 
        2*a*q^47 - q^48 + 2*q^53 + (-2*a + 2)*q^59 + a*q^60 + (-a + 1)*q^69 - 
        q^75 + (-a - 1)*q^80 + 2*a*q^92 - q^108 + (a + 1)*q^111 - 2*q^113 + (-a 
        - 1)*q^125 + O(q^130),
    q^6 + (a + 1)*q^10 + (a - 1)*q^18 + (-a - 1)*q^22 - a*q^24 - q^30 + (-a + 
        1)*q^40 - 2*q^46 - a*q^54 + q^66 + (a + 1)*q^72 + (a - 1)*q^88 + 
        2*a*q^94 - q^96 + 2*q^106 + (-2*a + 2)*q^118 + a*q^120 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
330
);
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:=
[]
;
Bo:=
[
    q - q^4 - q^5 + q^9 - q^11 + q^16 + q^20 + q^25 - 2*q^31 - q^36 + q^44 - 
        q^45 - q^49 + q^55 + 2*q^59 - q^64 + 2*q^71 - q^80 + q^81 - 2*q^89 - 
        q^99 - q^100 + q^121 + 2*q^124 - q^125 + O(q^130),
    q^2 - q^8 - q^10 + q^18 - q^22 + q^32 + q^40 + q^50 - 2*q^62 - q^72 + q^88 -
        q^90 - q^98 + q^110 + 2*q^118 - q^128 + 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^6 - q^24 - q^30 + q^54 - q^66 + q^96 + q^120 + O(q^130)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
331
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
330
);
qprec:=
55
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
331
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
110
);
qprec:=
55
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
331
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
55
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
331
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
55
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
331
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
55
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
331
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
33*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
55
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
331
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
55*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
55
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
331
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
165*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
55
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^5 - q^6 + q^14 + q^21 - q^22 + q^30 - q^33 + q^36 - q^43 - q^53 + 
        O(q^55),
    q^2 + q^3 - q^7 - q^10 + q^11 - q^12 - q^15 - q^18 + q^28 - q^29 - q^32 + 
        q^34 + q^35 + q^37 + q^38 - q^41 + 2*q^42 - q^44 - q^48 + q^51 + 
        O(q^55),
    q^4 + q^6 + q^9 - q^14 + q^16 - q^17 - q^19 - q^20 - q^21 + q^22 - q^30 - 
        q^31 + q^33 - q^45 + q^49 + O(q^55)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
332
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
332
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
82
);
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
332
);
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:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
332
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
41*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
80
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^21 - q^23 + q^25 - q^27 - q^33 - q^41 + q^49 - q^51 - q^63 - 
        q^77 + O(q^80),
    q^3 - q^9 - q^11 + q^27 + q^29 - q^31 + q^33 - q^37 + q^49 + q^61 - q^63 - 
        q^69 + q^75 - q^77 + O(q^80),
    q^7 - q^9 - q^11 + q^17 + q^21 - q^31 - q^37 + q^51 + q^59 - q^77 + O(q^80)
]
;
Bo:=
[
    q - q^3 - q^7 - q^11 - q^17 + q^21 + 2*q^23 + q^25 + q^27 - q^29 - q^31 + 
        q^33 - q^37 + 2*q^41 + q^51 - q^59 - q^61 - 2*q^69 - q^75 + q^77 + 
        O(q^80),
    q^2 - q^6 + q^8 - q^14 - q^22 - q^24 + q^32 - q^34 + q^42 + 2*q^46 + q^50 + 
        q^54 - q^56 - q^58 - q^62 + q^66 - q^74 + O(q^80),
    q^4 - q^12 + q^16 - q^28 - q^44 - q^48 + q^64 - q^68 + O(q^80)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (-2*a^3 + a)*q^7 + (a^3 - a^2)*q^13 + a^2*q^16 + (-a^2 + a + 
        1)*q^19 + (a^3 - a)*q^25 + (a^2 - 2)*q^28 + (a^3 + a^2 - a - 1)*q^31 - 
        q^37 + (a^2 + a)*q^43 - 2*a^2*q^49 + (a^3 - a^2 + 1)*q^52 + (a^2 + a - 
        1)*q^61 - a^3*q^64 + a*q^67 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^4 - a*q^7 + (a - 2)*q^13 + (a - 1)*q^16 + (-a + 1)*q^25 + (-a + 
        1)*q^28 + (-2*a + 1)*q^31 + q^37 + (2*a - 1)*q^43 + (-a - 1)*q^52 - q^64
        - a*q^67 + O(q^70),
    q^3 - a*q^9 + a*q^12 - a*q^21 + (a - 1)*q^27 + (-a + 1)*q^36 + (a - 2)*q^39 
        + (a - 1)*q^48 + (a - 1)*q^63 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (-a + 1)*q^13 - q^16 + (a - 1)*q^19 + a*q^25 + (a + 1)*q^31 - 
        q^37 + (a - 1)*q^43 - q^49 + (-a - 1)*q^52 + (a + 1)*q^61 + a*q^64 - 
        2*a*q^67 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^4 + (-a + 1)*q^7 - 2*q^10 + (a - 1)*q^13 + a*q^16 + 2*a*q^22 
        + a*q^25 - a*q^28 - q^31 - q^37 - q^43 - 2*a*q^46 + a*q^52 + (-2*a + 
        2)*q^55 + (-2*a + 2)*q^61 + q^64 + (-a + 1)*q^67 + O(q^70),
    q^2 - a*q^5 + (a - 1)*q^11 + (-a + 1)*q^14 - q^20 + (-a + 1)*q^23 + (a - 
        1)*q^26 + a*q^32 - q^35 + a*q^44 + a*q^50 + q^53 - q^59 - q^62 + q^65 + 
        O(q^70)
]
;
Bo:=
[
    q + (a - 1)*q^4 + (-a + 1)*q^7 + (-a + 1)*q^13 - a*q^16 + (2*a - 2)*q^19 - 
        a*q^25 + a*q^28 - q^31 + q^37 - q^43 + a*q^52 + (2*a - 2)*q^61 + q^64 + 
        (-a + 1)*q^67 + O(q^70),
    q^3 + (a - 1)*q^9 + (a - 1)*q^12 + (-a + 1)*q^21 - a*q^27 - a*q^36 + (-a + 
        1)*q^39 - a*q^48 + (2*a - 2)*q^57 + a*q^63 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
333
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 - q^10 + q^28 + q^34 - q^46 + q^49 + q^58 - q^64 - q^67 + O(q^70),
    q^2 - q^5 + q^17 - q^20 - q^23 + q^29 - q^32 + q^50 + q^59 + q^68 + O(q^70),
    q^3 - q^21 + q^27 - q^30 - q^36 - q^63 + O(q^70),
    q^4 + q^7 - q^10 - q^16 + q^25 - q^28 + q^34 - q^37 - q^46 - 2*q^49 + q^58 +
        q^67 + O(q^70),
    q^6 - q^15 - q^18 + q^45 + q^51 + q^54 - q^60 - q^69 + O(q^70),
    q^9 - q^12 - q^21 + q^30 + q^48 - q^63 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
334
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
166
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
334
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
83*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^12 - q^16 - q^18 - q^19 + q^24 + q^25 + q^32 + q^36 - q^38 + q^42 - 
        q^47 + q^49 + q^54 - q^56 + q^62 - q^63 - q^64 + q^76 - q^77 + O(q^82),
    q^2 + q^18 - q^22 - q^24 - q^36 - q^42 + q^50 - q^66 - q^76 + O(q^82),
    q^3 + q^16 + q^18 - q^21 - q^22 - q^24 - q^31 - q^36 + q^38 - q^42 + q^44 - 
        q^49 + q^61 - q^66 + q^75 - q^76 + q^77 + O(q^82),
    q^4 - q^12 - q^18 + q^36 - q^38 + q^42 + q^54 - q^56 + q^62 + O(q^82),
    q^6 - q^12 - q^16 - q^18 + q^24 + q^28 + q^32 + q^36 - q^38 - q^44 + q^54 - 
        q^64 - q^72 + q^76 + O(q^82),
    q^7 + q^12 + q^16 + q^18 - q^21 - q^22 - 2*q^24 - q^27 - q^28 + q^29 - q^31 
        + q^33 - q^36 + q^38 - q^42 + q^44 - q^49 - q^57 + q^63 + q^64 - q^66 + 
        q^72 - q^76 + q^81 + O(q^82),
    q^8 - q^12 - q^16 - q^18 + q^22 + q^24 + q^32 + q^36 - q^38 + q^42 - q^44 - 
        q^48 - q^56 - q^64 + q^66 + q^76 + O(q^82),
    q^9 + q^12 + q^16 + q^18 + q^19 - q^21 - q^22 - 2*q^24 - q^27 - q^31 - q^32 
        - 2*q^36 + q^38 - q^42 + q^44 + q^47 + q^48 - q^49 + q^56 - q^57 + q^63 
        + q^64 - q^66 + q^72 - 2*q^76 + q^77 + q^81 + O(q^82),
    q^11 + q^12 + q^18 - q^22 - q^24 - q^27 - q^31 + q^33 - q^36 + q^38 - q^42 -
        q^49 + q^56 - q^57 + q^63 - q^66 - q^76 + O(q^82),
    q^14 - q^16 - q^18 + q^24 + q^28 - q^38 - q^44 + q^58 + q^66 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
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(
22
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
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(
44
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
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(
12
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
33*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
335
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 33*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^21 - q^24 + q^25 - q^26 - q^35 - q^39 + q^49 - q^54 - q^60 + 
        O(q^66),
    q^2 - q^12 - q^13 + q^18 - q^27 - q^30 + q^43 + q^45 + q^50 + q^57 - q^58 + 
        O(q^66),
    q^3 - q^8 - q^13 + q^28 + q^38 - q^63 + O(q^66),
    q^4 - q^9 - q^10 - q^15 + q^19 + 2*q^21 - q^29 + q^35 - q^49 - 2*q^56 - q^59
        + q^60 + q^64 + q^65 + O(q^66),
    q^5 - q^8 - q^12 - q^13 + 2*q^18 + q^20 - q^27 + 2*q^28 - q^30 - q^32 - q^42
        + q^45 + q^48 - q^52 - q^58 - q^63 + O(q^66),
    q^6 - q^9 - q^10 + q^19 + q^21 - q^36 - q^39 + q^54 - q^56 - q^59 + q^60 + 
        q^64 + q^65 + O(q^66),
    q^7 - q^8 - q^13 + q^18 + q^20 - q^27 + q^28 - q^30 - q^32 + q^38 - q^52 + 
        q^53 + q^57 - q^58 + O(q^66),
    q^14 - q^15 - q^16 + q^19 + q^21 - q^26 - q^29 + q^36 + q^40 - q^49 - q^54 +
        q^65 + O(q^66)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
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(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^9 + (2*a - 1)*q^13 - q^21 + (-a + 1)*q^25 - a*q^37 + (a - 1)*q^49 + 
        q^57 + (-a - 1)*q^73 + (a - 1)*q^81 + a*q^93 + O(q^106),
    q^3 + (-a + 1)*q^7 + (a - 1)*q^19 - a*q^27 - q^31 + (2*a - 1)*q^39 + (a - 
        2)*q^43 - q^63 + (-2*a + 1)*q^67 + (-a + 1)*q^75 + (a + 1)*q^79 + (a + 
        1)*q^91 + (-a + 1)*q^103 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + 
        O(q^106)
]
;
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 + 
        O(q^106),
    q^2 - a*q^6 + (a - 1)*q^14 + (a - 1)*q^18 - q^26 + (-a + 1)*q^38 + q^42 - 
        a*q^50 + q^54 + a*q^62 + (-a + 1)*q^74 + a*q^78 - q^86 - a*q^98 + 
        O(q^106),
    q^4 - a*q^12 + (a - 1)*q^28 + (a - 1)*q^36 - q^52 + (-a + 1)*q^76 + q^84 - 
        a*q^100 + O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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(
6
);
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^7 + (a - 1)*q^9 - q^15 + a*q^31 + (-a + 1)*q^33 + (a - 1)*q^49 + 
        q^55 + q^63 - 2*a*q^73 + (-a + 1)*q^79 - a*q^81 + a*q^87 - q^97 + (2*a -
        2)*q^103 + a*q^105 + O(q^106),
    q^2 - a*q^8 + q^12 - a*q^14 + (a - 1)*q^18 + a*q^20 - q^30 + (a - 1)*q^32 - 
        q^44 - a*q^48 + (a - 1)*q^56 + a*q^62 + (-a + 1)*q^66 + q^72 + (-a + 
        1)*q^80 - a*q^84 + (a - 1)*q^98 + O(q^106),
    q^3 + a*q^5 - q^11 - a*q^21 + (a - 1)*q^27 + (-a + 1)*q^29 + (-a + 1)*q^35 -
        q^45 - q^53 - q^59 + a*q^77 + (-a + 1)*q^83 + a*q^93 + (-a + 1)*q^99 + 
        2*q^101 + O(q^106),
    q^4 + (a - 1)*q^6 - q^10 - a*q^16 + (-a + 1)*q^22 + q^24 - a*q^28 + (a - 
        1)*q^36 + a*q^40 + q^42 - a*q^54 + a*q^58 - q^60 + (a - 1)*q^64 + a*q^70
        - q^88 + (-a + 1)*q^90 - a*q^96 + O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.4
;
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(
336
);
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:=
106
;
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 + O(q^106),
    q^3 + a*q^6 - q^12 + a*q^21 - a*q^24 - a*q^27 + (-a - 1)*q^33 - q^42 + q^48 
        + q^54 + (-a + 1)*q^66 + a*q^75 - a*q^84 + (a - 1)*q^87 + a*q^96 + 
        O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
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 + 
        O(q^106),
    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 + O(q^106),
    q^3 - q^21 - q^27 + 2*q^69 - q^75 + O(q^106),
    q^6 - q^12 + q^24 - q^42 - q^48 - q^54 + q^84 + q^96 + O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^21 - q^25 - 2*q^37 + q^49 - 2*q^57 + q^81 + 2*q^93 + O(q^106),
    q^3 - q^7 - 2*q^19 + q^27 + 2*q^31 - q^63 - q^75 + 2*q^103 + O(q^106)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
336
);
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:=Rationals();
qprec:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
337
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
336
);
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
337
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
112
);
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
337
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
48
);
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
337
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
56
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
338
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
156
);
qprec:=
65
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
338
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
65
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
338
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
13*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
65
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
338
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
39*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
65
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
339
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
339
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
112
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
339
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
339
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
339
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
339
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
339
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
339
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
339
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
339
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^7 + q^9 - q^13 - q^15 + q^16 - q^28 - q^31 + q^36 - q^51 - q^52 
        - q^60 - q^61 - q^63 + q^64 - q^69 + O(q^74),
    q^3 - q^5 + q^12 - q^17 - q^20 - q^21 - q^23 + q^27 + 2*q^29 + q^35 - q^39 -
        q^45 + 2*q^47 + q^48 - q^59 + q^65 - q^68 - q^71 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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(
340
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 + a^2*q^4 + a^7*q^5 + a^3*q^8 - a^5*q^9 - q^10 + (a^5 - a^3)*q^13 
        + a^4*q^16 - a^2*q^17 - a^6*q^18 - a*q^20 - a^6*q^25 + (a^6 - a^4)*q^26 
        + (-a^4 - a)*q^29 + a^5*q^32 - a^3*q^34 - a^7*q^36 + (-a^7 + a^6)*q^37 -
        a^2*q^40 + (a^3 - 1)*q^41 + a^4*q^45 - a^7*q^49 - a^7*q^50 + (a^7 - 
        a^5)*q^52 + (a^6 + a^4)*q^53 + (-a^5 - a^2)*q^58 + (a^2 + a)*q^61 + 
        a^6*q^64 + (-a^4 + a^2)*q^65 - a^4*q^68 + q^72 + (-a - 1)*q^73 + (a^7 + 
        1)*q^74 - a^3*q^80 - a^2*q^81 + (a^4 - a)*q^82 + a*q^85 + (a^3 + a)*q^89
        + a^5*q^90 + (-a^6 + a^3)*q^97 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^5*q^2 - a^2*q^4 - a^6*q^5 + a^7*q^8 + a^5*q^9 - a^3*q^10 + (-a^7 - 
        a)*q^13 + a^4*q^16 + a^6*q^17 + a^2*q^18 - q^20 - a^4*q^25 + (a^6 - 
        a^4)*q^26 + (a^4 + a)*q^29 + a*q^32 + a^3*q^34 - a^7*q^36 + (-a^3 + 
        a^2)*q^37 + a^5*q^40 + (a^3 - 1)*q^41 + a^3*q^45 + a^7*q^49 - a*q^50 + 
        (a^3 - a)*q^52 + (-a^2 - 1)*q^53 + (-a^6 + a)*q^58 + (a^2 + a)*q^61 - 
        a^6*q^64 + (a^7 - a^5)*q^65 + q^68 - a^4*q^72 + (-a^5 - a^4)*q^73 + 
        (-a^7 - 1)*q^74 + a^2*q^80 - a^2*q^81 + (a^5 + 1)*q^82 + a^4*q^85 + 
        (-a^3 - a)*q^89 + q^90 + (-a^7 - a^2)*q^97 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 + 1/2*(-a^3 - a^2)*q^5 - a*q^9 + 1/2*(a^3 + 1)*q^10 - q^16 + 
        1/2*(a + 1)*q^20 + 1/2*(-a^2 - 1)*q^25 + (-a^2 - 1)*q^26 + (a - 1)*q^29 
        + a^3*q^34 - a^3*q^36 + 1/2*(a^2 - a)*q^40 + (a^3 + 1)*q^41 + 1/2*(a^3 -
        1)*q^45 - a^3*q^49 + 1/2*(-a^3 + a)*q^50 + (a^2 + a)*q^61 - a^2*q^64 + 
        1/2*(-a^3 + a^2 - a - 1)*q^65 + (-a^3 + 1)*q^74 + 1/2*(a^3 + a^2)*q^80 +
        a^2*q^81 + 1/2*(a - 1)*q^85 + (a^3 + a)*q^89 + 1/2*(-a + 1)*q^90 + 
        O(q^98),
    q^2 + 1/2*(-a^2 + a)*q^5 + a^2*q^8 + 1/2*(-a^3 - a^2)*q^10 + (a^2 - 1)*q^13 
        + a*q^17 - a*q^18 + 1/2*(a^3 + 1)*q^20 + 1/2*(-a^3 - a)*q^25 - q^32 + 
        (-a^2 - a)*q^37 + 1/2*(a + 1)*q^40 + 1/2*(a^3 - a^2)*q^45 + 1/2*(-a^2 - 
        1)*q^50 + (-a^2 - 1)*q^52 + (a^3 - a)*q^53 + (a - 1)*q^58 + 1/2*(a^3 + 
        a^2 + a + 1)*q^65 + a^3*q^68 - a^3*q^72 + (-a^3 + 1)*q^73 + 1/2*(a^2 - 
        a)*q^80 + (a^3 + 1)*q^82 + 1/2*(-a^3 + 1)*q^85 + 1/2*(a^3 - 1)*q^90 + 
        (a^2 - a)*q^97 + O(q^98)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + a*q^2 - q^4 - a*q^8 + a*q^9 + q^16 - q^17 - q^18 - a*q^25 + (a + 1)*q^29
        + a*q^32 - a*q^34 - a*q^36 + (-a - 1)*q^37 + (-a + 1)*q^41 - 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 - q^81 + (a + 1)*q^82 + (-a - 1)*q^97 + O(q^98),
    q^5 + a*q^10 - q^20 + (-a - 1)*q^25 - a*q^40 + a*q^45 + (-a + 1)*q^50 + q^80
        - q^85 - q^90 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
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 + O(q^98),
    q^5 - q^10 + q^20 - q^40 - q^45 - 2*q^65 + q^80 + q^85 + q^90 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
340
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
30
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^7 - a^5 + a + 1)*q^3 - a^3*q^4 + (-a^7 - a^6 + a^3 + a^2 - a - 1)*q^5
        + (-a^7 - a^6 + a^5 + a^4 + a^3 + a^2 - 1)*q^9 + (-a^7 + a^5 + a^4 + a^3
        - a - 1)*q^11 + (-a^7 - a)*q^12 + (a^7 + a^6 - 2*a^5 - 2*a^4 - a^3 - a^2
        + a + 2)*q^15 + a^6*q^16 + (a^7 + a^4 - a^2)*q^20 + (a^7 + a^6 + a^5 - 
        a^4 - a^3 - a^2)*q^23 + (a^5 - a^3 + a^2 - 1)*q^25 + a^3*q^27 + (a^5 - 
        1)*q^31 + (a^7 + a^6 - a^2)*q^33 + (a^7 - a^5 - a^4 - a^3 - a^2 + a + 
        1)*q^36 + (-a^5 + 1)*q^37 + (-a^6 + a)*q^44 + (-2*a^6 - a^5 + a^2 + a - 
        1)*q^45 + (-a^7 - a^5)*q^47 + (a^5 + a^4 - 1)*q^48 + (-a^6 + a)*q^49 + 
        (a^7 + a^6 - a^5 - a^4 + a + 1)*q^53 + (-a^7 - a^6 + a^3 + 2*a^2 - 
        1)*q^55 + (a^7 + a^6 - a^4 - 2*a^3 - a^2 + 1)*q^59 + (-a^7 + 2*a^5 + a^4
        + a^3 + a^2 - 2*a - 2)*q^60 + O(q^62)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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(
10
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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(
10
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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(
30
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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(
10
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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(
10
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^2 + a - 1)*q^3 - a^3*q^4 + (a^3 - a^2 - 1)*q^5 + (-a^3 + a^2 - 
        a)*q^9 - a^3*q^11 + (a^2 - a)*q^12 + a*q^15 - a*q^16 + (a^3 + a - 
        1)*q^20 + (a^3 - a^2 + a)*q^23 + (-a^3 + a^2 + 1)*q^25 + a^3*q^27 + q^31
        + (a^2 - a)*q^33 + (a^3 - a^2)*q^36 + 2*q^37 - a*q^44 + a^2*q^45 + (a^2 
        + 1)*q^47 + (a^3 - a^2 + a)*q^48 - a*q^49 + (-a^3 - a)*q^53 + (a^3 + a -
        1)*q^55 + (-a^2 + a - 1)*q^59 + (-a^3 + a^2 - a + 1)*q^60 + O(q^62)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - 2*a*q^3 + q^4 + (-a + 1)*q^5 + (3*a - 3)*q^9 + (a - 1)*q^11 - 2*a*q^12 -
        2*q^15 + q^16 + (-a + 1)*q^20 - q^23 + 4*q^27 - a*q^31 + 2*q^33 + (3*a -
        3)*q^36 + a*q^37 + (a - 1)*q^44 + 3*a*q^45 - q^47 - 2*a*q^48 + (a - 
        1)*q^49 + (-a + 1)*q^53 + a*q^55 + a*q^59 - 2*q^60 + O(q^62)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
62
;
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 + O(q^62),
    q^11 - q^22 - q^55 + O(q^62)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
341
);
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(
10
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
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(
342
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*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(
342
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
342
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
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:=
106
;
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^106),
    q^2 - a*q^8 + q^14 + (a - 2)*q^26 + (a - 1)*q^32 - q^38 + a*q^50 - a*q^56 + 
        (-2*a + 1)*q^62 + (2*a - 1)*q^74 + (-a + 1)*q^86 + (a + 1)*q^104 + 
        O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
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:=
106
;
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 + O(q^106),
    q^2 + (a - 1)*q^8 - q^14 + (-a + 1)*q^26 - a*q^32 + q^38 + (a - 1)*q^50 + 
        (-a + 1)*q^56 - q^62 - q^74 + a*q^86 + a*q^104 + O(q^106),
    q^3 - a*q^9 + (a - 1)*q^12 - q^21 + (a - 1)*q^27 + q^36 + (-a + 1)*q^39 - 
        a*q^48 + q^57 + a*q^63 + (a - 1)*q^75 + q^81 + (-a + 1)*q^84 - q^93 + 
        O(q^106),
    q^6 - a*q^18 + (a - 1)*q^24 - q^42 + (a - 1)*q^54 + q^72 + (-a + 1)*q^78 - 
        a*q^96 + O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
106
;
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^106),
    q^2 + q^8 - 2*q^14 + q^32 - q^38 - q^50 - 2*q^56 + 2*q^86 + 3*q^98 + 
        O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
342
);
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:=
106
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^5 - a*q^6 - a*q^7 - q^9 + a*q^11 + a*q^16 + (-a + 1)*q^23 + 
        q^24 - q^26 + q^30 + q^35 - a*q^38 + (a - 1)*q^39 + (a - 1)*q^42 - 
        a*q^43 + (-a + 1)*q^45 - a*q^47 + a*q^54 - q^55 - q^57 + (a - 1)*q^58 + 
        a*q^61 + q^62 + a*q^63 - q^64 + (-a + 1)*q^66 + (-a + 1)*q^77 - q^80 + 
        q^81 - q^82 + a*q^83 + a*q^87 + (-a + 1)*q^93 - a*q^99 - a*q^101 + (-a +
        1)*q^104 + O(q^106),
    q^2 + (a - 1)*q^10 - a*q^12 - a*q^14 - q^18 + a*q^22 + a*q^32 + (-a + 
        1)*q^46 + q^48 - q^52 + q^60 + q^70 - a*q^76 + (a - 1)*q^78 + (a - 
        1)*q^84 - a*q^86 + (-a + 1)*q^90 - a*q^94 + O(q^106),
    q^3 - q^8 + (a - 1)*q^12 + (-a + 1)*q^13 + (a - 1)*q^15 + q^19 - a*q^21 - 
        q^27 - a*q^29 + (a - 1)*q^31 + (-a + 1)*q^32 + a*q^33 + (-a + 1)*q^40 + 
        (-a + 1)*q^41 + a*q^52 + a*q^56 + (a - 1)*q^59 - a*q^60 + a*q^65 + (a - 
        1)*q^67 + (-a + 1)*q^69 + q^72 + (a - 1)*q^76 - a*q^79 + q^84 - a*q^88 -
        q^91 + (a - 1)*q^95 + a*q^97 + (-a + 1)*q^103 + q^105 + O(q^106),
    q^4 + (-a + 1)*q^6 + (a - 1)*q^16 + (a - 1)*q^20 - a*q^26 - a*q^28 + a*q^30 
        - q^36 + (-a + 1)*q^38 - q^42 + a*q^44 + (a - 1)*q^54 - q^58 + a*q^62 + 
        q^66 - a*q^80 - a*q^82 + (-a + 1)*q^92 + q^96 + O(q^106)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
343
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
294
);
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
343
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
98
);
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
343
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
343
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
343
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
49*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^9 - q^22 + a*q^23 + (a - 1)*q^25 - q^29 + (-a + 1)*q^32 + a*q^44 + 
        O(q^53),
    q^2 + a*q^11 - q^16 - a*q^18 + (-a + 1)*q^22 - q^37 + (a - 1)*q^43 + (a - 
        1)*q^50 + O(q^53),
    q^4 + a*q^8 - q^11 + (a - 1)*q^23 - a*q^29 - a*q^36 + (-a + 1)*q^37 - q^46 +
        O(q^53)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
343
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
147*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
53
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^22 - q^23 + q^25 - q^29 - q^32 - q^44 + O(q^53),
    q^2 - q^11 - q^16 + q^18 - q^22 - q^37 + q^43 + q^50 + O(q^53),
    q^4 - q^8 - q^11 + q^23 + q^29 + q^36 - q^37 - q^46 + O(q^53)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
344
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
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(
344
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
344
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
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(
344
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
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(
42
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^6*q^2 + (-a^11 + a^8 + a^7 - a^6 - a^5 + a^3 + a^2 - 1)*q^3 + (-a^11 +
        a^9 + a^8 - a^6 + a^4 + a^3 - a - 1)*q^4 + (a^11 - a^8 + a^6 + a^5 - a^4
        - a^3 - a^2 + a + 1)*q^6 + (a^11 - a^4)*q^8 + (a^11 + a^10 - a^8 - a^7 -
        a^3 + 1)*q^9 + (-a^10 + a^3 - a)*q^11 + (a^4 - a)*q^12 - a^3*q^16 + 
        (a^11 - a^9 - 2*a^8 + a^6 + a^5 - a^4 - a^3 + 2*a + 1)*q^17 + (-a^11 + 
        a^8 - a^5)*q^18 + (a^7 - a^3 - 1)*q^19 + (-a^7 + a^2)*q^22 + (a^10 - 
        a^7)*q^24 + a^8*q^25 + (-a^6 + a^3 - 1)*q^27 - a^9*q^32 + (-a^11 - a^9 +
        a^7 + a^6 - 1)*q^33 + (a^4 + 1)*q^34 + (-a^11 - a^10 + a^7 + a^3 - 
        1)*q^36 + (a^11 + a^10 - a^9 - a^8 - a^7 + a^5 - a^3 - a^2 + 1)*q^38 + 
        (-a^10 + a^9 + a^3 - a^2)*q^41 + (a^11 + a^10 - a^8 - a^7 + a^5 - a^3 - 
        a^2 + 1)*q^43 + (-a^11 - a^10 + 2*a^8 + a^7 - a^6 - a^5 + a^3 + a^2 - 
        1)*q^44 + (-a^11 - a^10 + a^9 + a^8 + a^7 - a^6 - a^5 + a^3 - 1)*q^48 - 
        a^7*q^49 + (a^7 - 1)*q^50 + (-a^11 + a^8 - a^7 + a^4)*q^51 + (a^11 - a^8
        - a^4 - a^3 + a + 1)*q^54 + (-a^11 - a^10 + a^9 + a^8 + a^7 - a^5 - 
        1)*q^57 + (a^4 + a^2)*q^59 + (-a^8 + a)*q^64 + (a^9 - a^8 - a^7 - a^6 + 
        a^5 + a^4 + a^3 - a^2)*q^66 + (-a^11 + a^9 + a^8 - a^6 - a^5 + a^4 + a^3
        - a - 1)*q^67 + (a^10 + a^6)*q^68 + (a^11 - a^8 - a^7 + a^5 + 1)*q^72 + 
        a^11*q^73 + (a^11 - a^4 + 1)*q^75 + (-a^8 - a^5 + a)*q^76 + (a^11 + a^10
        - a^9 - a^8 - a^7 + a^6 + a^5 - a^3 + 1)*q^81 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
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(
14
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
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(
14
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^2 + (a^5 - a^4 - a^2 + a - 1)*q^3 - 
        a^5*q^4 + (-a^5 + a^2)*q^6 + a^4*q^8 + (-a^4 + a^3 + a - 1)*q^9 + (-a^3 
        - a)*q^11 + (a^4 - a)*q^12 - a^3*q^16 + (-a^5 - a)*q^17 + (-a^5 + a^4 - 
        a)*q^18 + (-a^3 + 1)*q^19 + (a^2 + 1)*q^22 + (-a^3 + 1)*q^24 - a*q^25 + 
        (-a^5 + a^4 + a^2 - a)*q^27 + a^2*q^32 + (a^5 + a^3 + a)*q^33 + (a^4 + 
        1)*q^34 + (a^4 - a^3 + 1)*q^36 + (a^5 - a^4 + a^3 + a - 1)*q^38 + (-a^3 
        + a^2)*q^41 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^43 + (a^5 - a^4 + a^3 - 
        a^2 - 1)*q^44 + (a^5 - a^4 + a^3 + a - 1)*q^48 + q^49 + q^50 + (2*a^4 - 
        a + 1)*q^51 + (a^4 - a^3 - a + 1)*q^54 + (2*a^5 - 2*a^4 + a^3 - a^2 + 
        2*a - 2)*q^57 + (a^4 + a^2)*q^59 - a*q^64 + (-a^4 - a^2 - 1)*q^66 - 
        2*a^5*q^67 + (a^5 - a^4 - a^2 + a - 1)*q^68 + (a^5 - a^4 + a - 1)*q^72 +
        2*a^4*q^73 + (a^4 + 1)*q^75 + (-a^5 - a)*q^76 + (-a^5 + a^4 - a^3 - a + 
        1)*q^81 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - 1/3*q^4 - 1/3*a*q^5 - a*q^6 + 1/3*(a - 1)*q^7 + 2/3*q^8 + (a - 1)*q^9 - 
        2/3*a*q^10 - 1/3*q^11 - 4/3*a*q^12 + 1/3*(-a + 1)*q^13 + 1/3*(2*a - 
        2)*q^14 + 1/3*(-a + 1)*q^15 + q^16 + 1/3*(a - 1)*q^17 + (a - 1)*q^18 - 
        1/3*a*q^19 + 1/3*a*q^20 - 1/3*q^21 - 1/3*q^22 + 1/3*a*q^23 - 1/3*a*q^24 
        + 1/3*(a - 1)*q^25 + 1/3*(-2*a + 2)*q^26 + 2*q^27 + 1/3*(-a + 1)*q^28 + 
        1/3*(a - 1)*q^29 + 1/3*(-2*a + 2)*q^30 + 1/3*a*q^31 + 2/3*a*q^33 + 
        1/3*(-2*a + 2)*q^34 - 2/3*q^35 + (a - 1)*q^36 + 1/3*a*q^37 + 2/3*a*q^38 
        + 1/3*q^39 + 2/3*a*q^40 - 5/3*q^41 - 2/3*q^42 + 1/3*(a + 1)*q^43 - 
        1/3*q^44 + 2/3*a*q^46 - 1/3*a*q^49 + 1/3*(a - 1)*q^50 - 4/3*q^51 + 
        1/3*(a - 1)*q^52 - 1/3*a*q^53 + q^54 + 1/3*(-2*a + 2)*q^56 + 1/3*(-4*a +
        4)*q^57 + 1/3*(2*a - 2)*q^58 - 1/3*q^59 + 1/3*(a - 1)*q^60 + 1/3*(-a + 
        1)*q^61 + 2/3*a*q^62 - 1/3*q^64 + 2/3*q^65 + 2/3*a*q^66 + a*q^67 + (-a +
        1)*q^68 + 1/3*(a - 1)*q^69 + 1/3*q^70 + 1/3*(-a + 1)*q^71 + (a - 1)*q^72
        + (-a + 1)*q^73 + 2/3*a*q^74 + 2/3*q^75 + a*q^76 + 2/3*q^78 + 1/3*(-a + 
        1)*q^79 - 1/3*a*q^80 - a*q^81 + O(q^82),
    q^2 + a*q^5 + a*q^6 + (-a + 1)*q^7 - q^8 + (a - 1)*q^13 + (a - 1)*q^15 - 
        a*q^20 + q^21 - a*q^23 - a*q^24 + (a - 1)*q^28 + (-a + 1)*q^29 - a*q^31 
        + q^32 + (a - 1)*q^34 - a*q^37 - a*q^38 - q^39 + (-a + 1)*q^52 + a*q^53 
        + q^54 + (-a + 1)*q^60 + (a - 1)*q^61 + (-a + 1)*q^69 - q^70 + (a - 
        1)*q^71 + (a - 1)*q^79 + a*q^80 + O(q^82),
    q^3 + 1/3*(2*a - 2)*q^4 + 1/3*q^5 + q^6 - 1/3*a*q^7 + 1/3*(2*a - 2)*q^8 - 
        a*q^9 - 1/3*q^10 + 1/3*(-a + 1)*q^11 + 1/3*q^12 + 1/3*a*q^13 + 
        1/3*a*q^14 + 1/3*a*q^15 + 2/3*a*q^17 - a*q^18 - 2/3*q^19 - 1/3*q^20 + 
        1/3*(-a + 1)*q^21 + 1/3*(-a + 1)*q^22 - 1/3*q^23 + 1/3*q^24 - 1/3*a*q^25
        - 1/3*a*q^26 + (a - 1)*q^27 + 1/3*a*q^28 - 1/3*a*q^29 - 1/3*a*q^30 - 
        1/3*q^31 - 2/3*q^33 + 2/3*a*q^34 + 1/3*(a - 1)*q^35 - a*q^36 - 1/3*q^37 
        - 2/3*q^38 + 1/3*(a - 1)*q^39 + 1/3*q^40 + 1/3*(a - 1)*q^41 + 1/3*(a - 
        1)*q^42 + 1/3*(-2*a + 1)*q^43 + 1/3*(-a + 1)*q^44 + 1/3*q^46 + q^48 + 
        1/3*q^49 - 1/3*a*q^50 + 1/3*(-a + 1)*q^51 - 1/3*a*q^52 + 1/3*q^53 + (a -
        1)*q^54 - 1/3*a*q^56 + 1/3*a*q^57 + 1/3*a*q^58 + 1/3*(-a + 1)*q^59 - 
        1/3*a*q^60 + 1/3*a*q^61 + 1/3*q^62 + 1/3*(2*a - 2)*q^64 + 1/3*(-a + 
        1)*q^65 - 2/3*q^66 - 1/3*a*q^69 + 1/3*(a - 1)*q^70 + 1/3*a*q^71 - a*q^72
        + 1/3*q^74 + 1/3*(2*a - 2)*q^75 + 1/3*(-a + 1)*q^78 + 1/3*a*q^79 + 
        1/3*q^80 + 2*q^81 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^9 - q^11 + q^13 - 2*q^15 - q^17 + 2*q^21 + q^23 - q^25 + q^31 + 2*q^35
        + q^41 - q^43 - q^49 - q^53 - q^67 - q^81 + O(q^82),
    q^3 + q^5 - q^7 - q^29 - q^33 + q^39 - q^45 - q^51 - q^55 - q^61 + q^63 + 
        q^65 + q^69 + q^73 - q^75 + q^77 + O(q^82)
]
;
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 + O(q^82),
    q^2 + q^18 - q^22 - q^26 - q^34 - q^46 + q^50 - q^62 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
344
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 21*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^10 - q^15 + q^16 - q^23 + q^25 - q^38 - q^40 - q^41 + q^49 - 
        q^54 - q^57 - q^60 + q^64 - q^79 + O(q^82),
    q^2 - q^5 + q^8 - q^19 - q^20 - q^27 - q^30 + q^32 + q^43 + q^45 - q^46 + 
        q^50 + q^51 + 2*q^61 - q^69 + q^75 - q^76 - q^80 + O(q^82),
    q^3 - q^5 + q^12 - q^18 - q^19 - q^20 + q^29 + q^34 + q^37 - q^46 + q^48 + 
        q^50 - q^51 + q^62 - q^72 - q^76 - q^80 + O(q^82),
    q^6 - q^9 - q^10 + q^17 - q^23 + q^24 + q^25 + q^31 - q^36 - q^38 - q^40 - 
        q^41 + q^47 + q^58 + q^68 + q^74 - q^79 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
345
);
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(
345
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
345
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
345
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
345
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
345
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
345
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
345
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
345
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^5 + a^4 - a^3)*q^4 + (a^2 - a)*q^6 + (a^9 - a^8 + a^7 - a^6 + a^5 - 
        a^4 + a^3 - a^2 + a - 1)*q^9 + (-a^9 + a^8)*q^10 + a^6*q^15 + (a^5 - a^4
        + a^3 - a^2 + a - 1)*q^16 + (-a^7 - a)*q^19 + (-a^7 + a^6 - a^5 + 
        a^4)*q^24 + a^2*q^25 + (-a^9 - a^3)*q^31 + (a^9 - a^6 + a^5 - a^4 + a^3 
        - a^2 + a)*q^34 + (a^4 - a^3 + a^2)*q^36 + (-a^3 + a^2 - a + 1)*q^40 + 
        (a^6 - a^5)*q^46 - a^5*q^49 + (a^8 - a^5)*q^51 + (-a + 1)*q^54 + (-a^8 +
        a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a)*q^60 + (a^8 + a^4)*q^61 + (-a^8 +
        a^7 - a^6 + a^5)*q^64 - a^3*q^69 + (a^9 - a^8 + a^7 + a^3 - a^2)*q^76 + 
        (a^4 + a^2)*q^79 - a^9*q^81 + (a^4 - a)*q^85 + O(q^90),
    q^2 + (-a^9 + a^8 + a^6 + a^4 + a^2 + 1)*q^3 + (-a^9 - a^7 - a^5 + a^4 + a^2
        + 1)*q^5 + (-a^5 - a^3)*q^8 + (-a^9 - a^7 - a^5 - a^3 + a^2 - a + 
        1)*q^12 + (a^6 + a^5 + a^4)*q^17 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + 
        a^3 - a^2 + a - 1)*q^18 + (-a^6 - a^4 - a^2 - 1)*q^20 + (a^9 + a^7 + a^5
        + a^3 - 1)*q^23 + (a^9 - a^6 - a^4 - a^2 - 1)*q^27 + a^6*q^30 + (a^9 + 
        a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^32 + (-a^7 - a)*q^38 + (a^9 + a^7
        + a^5 - a^2 - 1)*q^45 + (2*a^9 + 2*a^7 + a^5 - a^4 + a^3 - a^2 - 2)*q^47
        + (a^9 - a^2 - 1)*q^48 + a^2*q^50 + (-a^9 - a^8 - a^7 - a^6 - a^5 - a^4 
        - a^3)*q^53 + (-a^9 - a^8 - a^7 - a^6 - a^5)*q^57 + (-a^9 - a^3)*q^62 + 
        (-a^9 - a^7 + 1)*q^68 + (a^4 + a^2)*q^72 + (a^9 + a^7 + a^5 + a^3 + 
        a)*q^75 + (a^9 + a^7 + a^5)*q^80 + a^8*q^83 + O(q^90)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
345
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
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 + O(q^90),
    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 + O(q^90),
    q^5 - q^10 + q^40 - q^45 - q^65 - q^80 + O(q^90),
    q^15 - q^30 - q^45 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
345
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
345
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
346
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
172
);
qprec:=
85
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
346
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
43*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(
347
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
346
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
347
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
173*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^11 - q^13 + q^16 + q^25 - q^27 - q^33 - q^39 - q^44 + q^49 - 
        q^52 + O(q^58),
    q^3 - q^9 - q^11 + q^12 - q^13 + q^29 + q^31 - q^36 + q^43 - q^44 + q^48 - 
        q^52 + q^53 + O(q^58)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
348
);
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(
348
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
348
);
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(
348
);
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:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
348
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
348
);
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(
14
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
348
);
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*q^2 + a^2*q^4 + (-a^5 + a^4)*q^5 - a^3*q^8 - a^3*q^9 + (-a^4 + a^3 - 
        a^2 + a - 1)*q^10 + (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^5 - a^4 + a^3 - a^2 + a)*q^20 
        + (-a^3 + a^2 - a)*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 + 1)*q^40 + (-a^5 + a^2)*q^41
        + (-a + 1)*q^45 - a^3*q^49 + (a^4 - a^3 + a^2)*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^5 - a^2 + a)*q^65 + (-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^2 - a)*q^80 + (a^5 - a^4 + a^3 - a^2 + a - 
        1)*q^81 + (a^5 - a^4 - a^2 + a - 1)*q^82 + (-a^2 + a - 1)*q^85 + (-a^5 +
        a^4)*q^89 + (a^2 - a)*q^90 + (a^4 + 1)*q^97 + a^4*q^98 + (-a^5 + a^4 - 
        a^3)*q^100 + (-a^3 + a^2)*q^101 + (-a^5 + a^2)*q^104 + (-a^3 - a)*q^106 
        + (-a^3 + 1)*q^109 + O(q^110),
    q^3 - a*q^6 + a^2*q^12 + (-a^5 + a^4)*q^15 - a^3*q^24 - a^3*q^27 + (-a^4 + 
        a^3 - a^2 + a - 1)*q^30 + (a^5 - a^4 + a^3 + a - 1)*q^39 + a^4*q^48 + 
        (a^5 - a^4 + a^3 - a^2 - 1)*q^51 + a^4*q^54 + (a^5 - a^4 + a^3 - a^2 + 
        a)*q^60 + (-a^3 + a^2 - a)*q^75 + (-a^3 + 1)*q^78 + a^4*q^87 - a^5*q^96 
        + (a^2 + 1)*q^102 - a^5*q^108 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
348
);
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(
14
);
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
348
);
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(
348
);
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:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
348
);
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:=
[]
;
Bo:=
[
    q + q^4 - q^5 - q^9 - q^13 + q^16 - q^20 - q^22 + q^29 - q^36 + 2*q^38 + 
        q^45 + q^49 - q^52 - q^53 + q^54 - q^62 + q^64 + q^65 - q^80 - q^86 - 
        q^88 - q^94 - q^109 + O(q^110),
    q^2 + q^8 - q^10 - q^11 - q^18 + 2*q^19 - q^26 + q^27 - q^31 + q^32 - q^40 -
        q^43 - q^44 - q^47 + q^55 + q^58 - q^72 + 2*q^76 - q^79 + q^90 - 2*q^95 
        + q^98 + q^99 - q^104 - q^106 + q^108 + O(q^110),
    q^3 + q^12 - q^15 - q^18 - q^39 + q^48 - q^60 - q^66 - q^72 + q^87 + q^90 + 
        q^99 + O(q^110),
    q^6 - q^9 + q^24 - q^30 - q^33 - q^36 + q^45 + 2*q^57 - q^78 + q^81 - q^93 +
        q^96 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
348
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 14*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 + q^9 - q^13 + q^25 - q^33 - q^51 - q^63 - q^67 + q^81 + q^87 + q^91
        + 2*q^103 - q^109 + O(q^110),
    q^2 - q^12 - q^14 + q^18 - q^26 - q^32 + q^44 + q^48 + q^50 - q^66 + q^68 + 
        q^84 - q^102 - q^108 + O(q^110),
    q^3 - q^11 - q^17 - q^21 + q^27 + q^29 - q^39 + 2*q^41 - q^47 + q^75 + q^77 
        - q^89 - q^99 - q^101 + O(q^110),
    q^4 - q^24 - q^28 + q^36 - q^52 - q^64 + q^88 + q^96 + q^100 + O(q^110),
    q^6 + q^16 - q^22 - q^24 - q^34 - q^42 + q^54 + q^58 - q^64 - q^78 + 2*q^82 
        + q^88 - q^94 + O(q^110),
    q^8 - q^12 - q^32 + q^44 - q^56 + q^68 + q^72 + q^84 - q^104 - q^108 + 
        O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
349
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
348
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
349
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
116
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
349
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
29*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
349
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
87*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
58
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
350
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
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(
350
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
350
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
350
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
350
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
350
);
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(
6
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
350
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
350
);
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(
12
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
350
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
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 + O(q^98),
    q^2 + q^18 - q^22 - q^28 - q^32 - q^58 + q^92 + O(q^98),
    q^4 - q^14 - q^16 + q^36 - q^44 + q^46 + q^74 + q^86 + O(q^98),
    q^7 + q^8 - q^23 - q^28 - q^32 - q^37 - q^43 + 2*q^53 + q^63 - q^67 + q^72 -
        q^77 - q^88 + q^92 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
350
);
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(
10
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
350
);
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(
10
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
350
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
10*H.1 + 3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
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 + O(q^98),
    q^2 - q^18 - q^22 + q^28 - q^32 + q^58 + q^92 + O(q^98),
    q^4 - q^14 + q^16 - q^36 - q^44 - q^46 + q^74 - q^86 + O(q^98),
    q^7 - q^8 + q^23 + q^28 - q^32 - q^37 + q^43 - 2*q^53 - q^63 - q^67 + q^72 -
        q^77 + q^88 + q^92 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*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(
351
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (-a^2 + a + 1)*q^7 - a^3*q^13 + a^2*q^16 + (-a^3 + a - 1)*q^19 +
        a^3*q^25 + (a^3 - a^2 - a)*q^28 + (a^3 + a^2 - a - 1)*q^31 + (a^3 + a^2 
        - 1)*q^37 + (-a^2 - 1)*q^43 + (-a^3 + a)*q^49 + (a^2 - 1)*q^52 + (-2*a^3
        + a)*q^61 - a^3*q^64 + (a^3 - a^2 + 1)*q^67 + (a^2 + a)*q^73 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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(
12
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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(
12
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 - q^13 + (a - 1)*q^16 + (-a + 2)*q^19 - q^25 + (-2*a + 1)*q^31 + 
        (-a - 1)*q^37 + a*q^43 + (a - 1)*q^49 - a*q^52 - a*q^61 - q^64 + (-a - 
        1)*q^67 + (2*a - 1)*q^73 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
74
;
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 + O(q^74),
    q^3 - a*q^12 + (a - 1)*q^21 + a*q^39 - q^48 + (-a - 1)*q^57 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 + (2*a - 2)*q^7 + q^13 - a*q^16 + (-a + 1)*q^19 + q^25 - 
        2*a*q^28 - q^31 + a*q^37 + (-a + 1)*q^43 - 3*a*q^49 + (a - 1)*q^52 + (-a
        + 1)*q^61 + q^64 + a*q^67 - q^73 + O(q^74)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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(
6
);
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
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:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
351
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1 + 6*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
74
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^10 + q^13 - q^16 - 2*q^22 - q^40 - q^43 + q^49 - 2*q^55 - q^61 + q^64 
        + O(q^74),
    q^2 - q^11 - q^20 - q^41 + q^47 + q^50 + q^59 + q^65 + O(q^74),
    q^4 - 2*q^10 - q^13 + q^16 + q^22 + q^25 - q^40 - q^52 + q^55 + q^61 - q^64 
        + O(q^74),
    q^5 - q^8 - q^11 + q^20 + q^26 - q^41 - q^50 + q^71 + O(q^74)
]
;
Bo:=
[
    q - q^4 - q^13 + q^16 - q^25 + 2*q^43 + q^49 + q^52 - 2*q^61 - q^64 + 
        O(q^74),
    q^3 - q^12 - q^39 + q^48 + O(q^74),
    q^9 - q^27 - q^36 + O(q^74)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
352
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
352
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
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(
352
);
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(
20
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
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(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
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(
40
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
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(
20
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
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(
10
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^3 - a + 1)*q^3 + (-a^2 - 1)*q^9 + a^3*q^11 + (a^2 - a)*q^17 + (a - 
        1)*q^19 - a^3*q^25 + (a^3 - a^2 + a - 1)*q^27 + (a^2 + 1)*q^33 + (a^3 + 
        a - 1)*q^41 + (-a^3 + a^2 + 1)*q^43 + (a^3 - a^2 + a - 1)*q^49 + 
        a^2*q^51 + a*q^57 + (-a^3 + a^2 - a)*q^59 + (a^3 - a^2)*q^67 + (-a^3 - 
        a)*q^73 + (-a^2 - 1)*q^75 + O(q^82)
]
;
Bo:=
[
    q + (a^3 + a - 1)*q^3 + (-a^2 - 1)*q^9 - a^3*q^11 + (a^2 - a)*q^17 + (-a + 
        1)*q^19 - a^3*q^25 + (-a^3 + a^2 - a + 1)*q^27 + (a^2 + 1)*q^33 + (a^3 +
        a - 1)*q^41 + (a^3 - a^2 - 1)*q^43 + (a^3 - a^2 + a - 1)*q^49 - a^2*q^51
        + a*q^57 + (a^3 - a^2 + a)*q^59 + (-a^3 + a^2)*q^67 + (-a^3 - a)*q^73 + 
        (a^2 + 1)*q^75 + O(q^82),
    q^2 + (a^3 + a - 1)*q^6 + (-a^2 - 1)*q^18 - a^3*q^22 + (a^2 - a)*q^34 + (-a 
        + 1)*q^38 - a^3*q^50 + (-a^3 + a^2 - a + 1)*q^54 + (a^2 + 1)*q^66 + 
        O(q^82),
    q^4 - a*q^8 + (a^3 + a - 1)*q^12 + a^2*q^16 + (-a^3 + 1)*q^24 - a^3*q^32 + 
        (-a^2 - 1)*q^36 - a^3*q^44 + (a^3 - a^2 - 1)*q^48 + (a^3 - a^2 + a - 
        1)*q^64 + (a^2 - a)*q^68 + (a^3 + a)*q^72 + (-a + 1)*q^76 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^5 - q^33 - q^37 + q^49 + 2*q^53 + q^69 - q^81 + O(q^82),
    q^2 - q^10 - q^66 - q^74 + O(q^82),
    q^3 - q^11 - q^15 + q^23 - q^27 + q^31 - 2*q^47 + q^55 + q^59 + q^67 + q^71 
        + O(q^82),
    q^4 - q^12 - q^20 + q^44 + q^60 + O(q^82),
    q^6 - q^22 - q^30 + q^46 - q^54 + q^62 + O(q^82),
    q^8 - q^24 - q^40 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
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(
8
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
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(
4
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
352
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
4*H.2 + 5*H.3
;
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(
353
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
352
);
qprec:=
59
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
353
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
32
);
qprec:=
59
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
354
);
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(
354
);
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(
354
);
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(
58
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
354
);
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:=
[]
;
Bo:=
[
    q + q^4 - q^5 - q^7 - q^9 + q^16 + 2*q^17 - q^19 - q^20 + q^27 - q^28 - q^29
        + q^35 - q^36 - q^41 + q^45 - q^53 + q^59 + q^63 + q^64 + 2*q^68 + 
        2*q^71 - q^76 - q^79 - q^80 - 2*q^85 + q^95 - q^107 + q^108 - q^112 + 
        O(q^114),
    q^2 + q^8 - q^10 - q^14 - q^18 + q^32 + 2*q^34 - q^38 - q^40 + q^54 - q^56 -
        q^58 + q^70 - q^72 - q^82 + q^90 - q^106 + O(q^114),
    q^3 - q^9 + q^12 - q^15 - q^21 - q^36 + q^45 + q^48 + 2*q^51 - q^57 - q^60 +
        q^63 + q^81 - q^84 - q^87 + q^105 + O(q^114),
    q^6 - q^18 + q^24 - q^30 - q^42 - q^72 + q^90 + q^96 + 2*q^102 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
355
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
355
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
70
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
355
);
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(
70
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
355
);
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(
140
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
355
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
355
);
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(
14
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
355
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
355
);
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(
10
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
355
);
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(
28
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
355
);
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(
20
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
355
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
35*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^6 + q^9 - q^12 + q^18 + q^24 - q^25 - q^27 - q^32 + q^38 - q^43 + q^48
        + q^49 - q^54 - q^57 - q^58 + O(q^70),
    q^2 - q^4 - q^6 + q^8 + q^9 - q^16 + q^19 - q^27 + q^36 + q^37 - q^38 - q^43
        + q^48 - q^50 - q^57 - q^58 + O(q^70),
    q^3 - q^4 + q^8 - q^18 + q^29 - q^38 - q^43 + q^54 + O(q^70),
    q^5 - q^25 - q^30 + q^45 - q^60 + O(q^70),
    q^10 - q^20 - q^25 - q^30 + q^40 + q^45 + q^50 + O(q^70),
    q^15 - q^20 - q^25 + q^40 + q^50 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
355
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 35*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^12 - 1/2*q^15 + q^16 + q^18 - q^19 - 3/2*q^20 + q^24 + 1/2*q^25 - q^27
        - q^29 - q^32 + q^36 - q^38 + 1/2*q^40 - q^43 - q^45 - q^48 - q^49 - 
        1/2*q^50 + q^57 + q^58 + O(q^70),
    q^2 - q^8 + 1/2*q^10 - q^12 + 1/2*q^15 - q^18 + 1/2*q^30 + q^32 - q^37 - 
        q^40 + 1/2*q^45 + 2*q^48 - q^60 + O(q^70),
    q^3 - q^8 + 1/2*q^10 - q^12 + 1/2*q^20 - 1/2*q^25 - q^27 + 1/2*q^30 + q^32 -
        1/2*q^40 - 1/2*q^45 + q^48 + 1/2*q^50 + q^57 - q^58 - q^60 + O(q^70),
    q^4 + 1/2*q^10 + q^12 - q^15 + q^18 - 1/2*q^20 + 1/2*q^25 - q^27 - q^29 + 
        1/2*q^30 - q^32 - q^38 + 1/2*q^40 - q^43 - 1/2*q^45 - q^48 - 1/2*q^50 - 
        q^54 + q^57 + q^58 + q^60 + O(q^70),
    q^5 + 2*q^12 - q^15 + 2*q^18 - q^20 - 2*q^27 + q^30 - 2*q^32 - 2*q^38 + q^40
        - 2*q^43 - q^45 - 2*q^48 - q^50 + 2*q^57 + 2*q^58 + q^60 + O(q^70),
    q^6 - 1/2*q^10 - q^16 + 1/2*q^20 - q^24 - 1/2*q^25 + q^29 + 1/2*q^30 - q^36 
        + 1/2*q^40 + 1/2*q^45 - 1/2*q^50 + q^64 + O(q^70),
    q^9 - 1/2*q^10 + 1/2*q^15 - q^19 - q^24 + 1/2*q^30 - 1/2*q^45 + q^54 + q^64 
        + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
356
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
356
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
88
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
356
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
356
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^8*q^2 - a^5*q^4 + (-a^3 - a)*q^5 - a^2*q^8 + a*q^9 + (a^9 - 1)*q^10 + 
        (-a^7 + a^5)*q^13 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a -
        1)*q^16 + (-a^9 + a^8 + a^6 - a^5 + a^4 - a^3 + a^2 - a + 1)*q^17 - 
        a^9*q^18 + (a^8 + a^6)*q^20 + (a^6 + a^4 + a^2)*q^25 + (-a^4 + a^2)*q^26
        + (-a^9 - a^6)*q^29 + a^7*q^32 + (-a^7 + a^4)*q^34 - a^6*q^36 + (a^8 + 
        a^3)*q^37 + (a^5 + a^3)*q^40 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 
        - a^2 + a - 2)*q^41 + (-a^4 - a^2)*q^45 - a^4*q^49 + (-a^9 + a^8 - a^7 +
        a^6 - a^5 + a^4 + a^2 + 1)*q^50 + (-a^9 + a^8 - a^7 + a^6 - a^5 + a^4 - 
        a^3 + a^2 - 2*a + 1)*q^52 + (a^9 + a^3)*q^53 + (-a^6 - a^3)*q^58 + (a^9 
        - a^5)*q^61 + a^4*q^64 + (a^9 - a^8 + a^7 - 2*a^6 + a^5 - a^4 + a^3 - 
        a^2 + a - 1)*q^65 + (-a^4 + a)*q^68 - a^3*q^72 + (-a^5 + a^4)*q^73 + 
        (a^5 + 1)*q^74 + (a^2 + 1)*q^80 + a^2*q^81 + (a^8 + a^7)*q^82 + (-a^9 - 
        a^7 + a^6 - a^5 + a^4 - a^3 - a)*q^85 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
356
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^5*q^2 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^4 + 
        (a^6 + a^2)*q^5 + a^4*q^8 + a^2*q^9 + (-a^7 + 1)*q^10 + (a^9 - a^8 + a^7
        - a^6 + a^5 - a^4 - a^2 + a - 1)*q^13 - a^9*q^16 + (-a^9 - a^3)*q^17 - 
        a^7*q^18 + (-a^5 - a)*q^20 + (a^8 + a^4 - a)*q^25 + (a^8 + a^4)*q^26 + 
        (-a^7 - a)*q^29 - a^3*q^32 + (a^8 - a^3)*q^34 - a*q^36 + (a^6 - 
        a^5)*q^37 + (a^9 - a^8 + a^7 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^40 + 
        (-a^9 + 1)*q^41 + (a^8 + a^4)*q^45 + a^8*q^49 + (-a^9 + a^6 + a^2)*q^50 
        + (-a^9 + a^2)*q^52 + (-a^7 + a^6)*q^53 + (a^6 - a)*q^58 + (a^9 - a^8 - 
        a^6 + a^5 - a^4 + a^3 - a^2 + a - 1)*q^61 + a^8*q^64 + (-a^9 - 2*a^5 - 
        a)*q^65 + (a^8 + a^2)*q^68 + a^6*q^72 + (a^9 + a^7 - a^6 + a^5 - a^4 + 
        a^3 - a^2 + a - 1)*q^73 + (a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - a^2
        + a)*q^74 + (a^4 + 1)*q^80 + a^4*q^81 + (-a^5 - a^3)*q^82 + (-a^9 - a^5 
        + a^4 + 1)*q^85 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
356
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
356
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
356
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^10 + q^16 - q^17 - q^21 + q^25 - q^40 - q^42 - q^45 + q^49 - 
        q^50 - q^53 + q^64 - q^68 - q^84 - q^85 + O(q^86),
    q^2 + q^8 - q^9 - q^10 - q^17 + q^18 - q^21 + q^32 - q^36 - q^40 - q^42 + 
        q^45 + 2*q^49 - q^53 + 2*q^57 - q^68 + 2*q^69 + q^72 - q^81 - q^84 + 
        q^85 + O(q^86),
    q^3 - q^7 + q^12 - q^14 - q^15 - q^28 + q^31 + q^35 + q^38 + q^46 + q^48 - 
        q^54 - q^56 - q^59 - q^60 + q^70 - q^83 + O(q^86),
    q^5 - q^9 - q^10 - q^17 + q^18 + q^20 + q^25 + q^34 - q^36 - q^40 - q^50 - 
        q^53 + q^57 - q^68 + q^69 + q^72 + q^73 + q^80 - q^85 + O(q^86),
    q^6 - q^7 - q^14 + q^19 + q^23 + q^24 - q^27 - q^28 - q^30 + q^35 + q^43 - 
        q^51 - q^56 - q^59 + q^62 + q^70 + q^76 - q^83 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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(
357
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
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(
357
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
357
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^8 - 2*q^18 - q^21 + q^25 + q^30 + q^32 - q^35 + 2*q^36 + q^42 + q^49 +
        q^50 - q^51 - q^53 - q^60 - q^67 - q^70 + q^81 - q^84 - q^85 + q^86 + 
        O(q^90),
    q^2 - q^4 - q^18 + q^25 - q^35 + q^36 + q^43 - q^53 + q^64 - q^67 + q^81 - 
        q^85 - q^86 + O(q^90),
    q^3 - q^24 - q^45 - q^54 + q^75 + O(q^90),
    q^5 - q^14 + q^27 + q^28 + q^31 - q^34 - q^40 - q^41 - q^45 - q^54 - q^61 + 
        q^68 - q^73 + q^82 + O(q^90),
    q^6 - q^12 - q^27 + q^54 + q^63 + q^75 + O(q^90),
    q^7 - q^10 - q^14 + q^17 + q^20 + q^27 + q^28 - q^34 - q^41 - 2*q^54 - q^56 
        - q^61 - q^62 - q^63 + q^68 - q^73 + 2*q^82 + O(q^90),
    q^9 - 2*q^18 - q^21 + q^30 + 2*q^36 + q^42 - q^51 - q^60 - q^72 + q^81 - 
        q^84 + O(q^90),
    q^15 - q^18 - q^21 + q^30 + q^36 - q^51 - q^60 + q^81 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
358
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
178
);
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
358
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
89*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
88
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^5 - q^13 - q^15 + q^16 - q^20 + q^25 - q^27 - q^31 - q^39 - q^43
        + q^45 + 2*q^47 + q^49 + q^51 - q^52 + q^57 - q^60 + q^64 + 2*q^65 + 
        q^75 - q^80 - q^83 - q^85 + q^87 + O(q^88),
    q^2 + q^8 - q^10 - q^26 - q^30 + q^32 - q^40 + q^50 - q^54 - q^62 - q^78 - 
        q^86 + O(q^88),
    q^3 - q^5 - q^9 + q^12 - q^13 + q^17 + q^19 - q^20 + q^25 + q^29 - q^31 - 
        q^36 - q^43 + q^48 - q^51 - q^52 - q^57 + q^59 + q^61 + q^65 + q^67 + 
        q^68 + q^76 - q^80 - q^83 - q^87 + O(q^88),
    q^6 - q^10 - q^18 + q^24 - q^26 + q^34 + q^38 - q^40 + q^50 + q^58 - q^62 - 
        q^72 - q^86 + O(q^88)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
359
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
358
);
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
359
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
179*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
60
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^11 + q^12 - q^18 - q^20 - q^23 - q^24 + q^25 - q^45 - q^47 + q^49 - 
        q^50 - q^51 + O(q^60),
    q^2 - q^12 - q^16 - q^17 + q^18 + q^20 + q^22 - q^25 - q^27 - q^30 - q^34 + 
        q^37 + q^41 + q^45 + q^51 - q^54 + O(q^60),
    q^3 - q^10 - q^11 + q^27 + q^32 - q^33 + q^34 - q^36 + q^54 + O(q^60),
    q^4 - q^10 - q^11 - q^12 + q^16 + q^23 + q^24 - q^40 - q^44 + q^45 - q^48 + 
        q^50 + O(q^60),
    q^5 - q^10 - q^11 - q^12 + q^18 + q^20 + q^22 + q^24 - q^30 - q^33 - q^44 + 
        q^45 - q^48 + O(q^60),
    q^6 - q^10 - q^11 - q^12 + q^16 + q^17 + q^24 + q^27 - q^33 - q^36 - q^40 - 
        q^44 - q^48 + q^50 + q^54 + q^55 + O(q^60),
    q^8 - q^10 - q^11 + q^16 + q^17 - q^20 - q^22 + q^25 + q^27 + q^32 - q^33 + 
        q^34 - q^36 - q^37 - q^40 - q^41 - q^44 + q^46 + q^50 + q^54 + q^55 + 
        O(q^60),
    q^9 - q^11 - q^12 + q^18 + q^20 - q^30 - q^33 + q^47 + q^51 + O(q^60),
    q^15 - q^16 - q^17 + q^20 + q^22 - q^27 - q^30 + q^37 + q^41 - q^50 - q^55 +
        O(q^60)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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(
360
);
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(
360
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=
114
;
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 + O(q^114),
    q^5 - a*q^10 - a*q^15 + (a - 1)*q^20 + (a - 1)*q^30 + q^40 + (a - 1)*q^45 + 
        a*q^55 + q^60 - a*q^80 - q^85 + q^90 - q^95 + (-a + 1)*q^110 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3
;
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(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.4
;
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(
360
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.4
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (-a - 1)*q^7 + q^10 - q^16 + (a + 1)*q^22 + a*q^25 + (a - 
        1)*q^28 - a*q^40 + a*q^49 + (a - 1)*q^55 + (a - 1)*q^58 + a*q^64 + (-a -
        1)*q^70 + (-a + 1)*q^73 + (-a + 1)*q^88 + (-a - 1)*q^97 + q^100 + (-a + 
        1)*q^103 + (a + 1)*q^112 + O(q^114),
    q^2 + a*q^5 - a*q^8 + (a - 1)*q^11 + (-a - 1)*q^14 + q^20 + (-a - 1)*q^29 - 
        q^32 + (-a + 1)*q^35 + (a + 1)*q^44 + a*q^50 + (a - 1)*q^56 + (a + 
        1)*q^59 + 2*q^77 - a*q^80 - 2*a*q^83 + a*q^98 + (-a + 1)*q^101 - 2*q^107
        + (a - 1)*q^110 + O(q^114)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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(
4
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^13 - a*q^25 + (-a - 1)*q^37 + a*q^49 + (-a + 1)*q^73 + (a + 
        1)*q^97 + O(q^114),
    q^2 - a*q^8 + a*q^20 + (a - 1)*q^26 - q^32 - a*q^50 + (-a - 1)*q^74 + q^80 +
        a*q^98 + (a + 1)*q^104 + O(q^114),
    q^4 - q^10 - a*q^16 + a*q^40 + (a - 1)*q^52 + (a + 1)*q^58 - q^64 + (-a + 
        1)*q^82 - a*q^100 + O(q^114),
    q^5 + (-a - 1)*q^29 + (a - 1)*q^41 + (a - 1)*q^65 + (a + 1)*q^89 + (-a + 
        1)*q^101 - 2*a*q^113 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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(
4
);
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^25 - q^49 - 2*q^61 + 2*q^85 + 2*q^109 + O(q^114),
    q^2 - q^8 - q^20 + q^32 - q^50 + 2*q^68 + q^80 - q^98 + O(q^114),
    q^4 + q^10 - q^16 - 2*q^34 - q^40 + q^64 - q^100 + 2*q^106 + O(q^114),
    q^5 - 2*q^17 + 2*q^53 - 2*q^113 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^10 + q^16 - 2*q^19 + q^25 - q^40 - 2*q^46 - q^49 + q^64 - 2*q^76
        + 2*q^94 + q^100 + 2*q^106 + O(q^114),
    q^2 - q^5 + q^8 - q^20 - 2*q^23 + q^32 - 2*q^38 + 2*q^47 + q^50 + 2*q^53 - 
        q^80 - 2*q^92 + 2*q^95 - q^98 + O(q^114)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^5 - a*q^9 - q^21 - a*q^25 + a*q^29 + (-a + 1)*q^41 + q^45 + 
        a*q^61 + a*q^69 + (a - 1)*q^81 - q^89 - 2*a*q^101 + (-a + 1)*q^105 - 
        q^109 + O(q^114),
    q^2 + (a - 1)*q^8 + (a - 1)*q^10 + q^12 - a*q^18 + (-a + 1)*q^28 - a*q^32 - 
        a*q^40 - q^42 + (a - 1)*q^48 - a*q^50 + a*q^58 + (a - 1)*q^60 + q^72 + 
        (-a + 1)*q^82 + q^90 - q^92 - a*q^108 + a*q^112 + O(q^114),
    q^3 + (-a + 1)*q^7 + (a - 1)*q^15 - q^23 - a*q^27 + a*q^35 + (2*a - 2)*q^43 
        + (-a + 1)*q^47 - q^63 - q^67 - a*q^75 + (-a + 1)*q^83 + a*q^87 + 
        2*q^103 + a*q^107 + O(q^114),
    q^4 - a*q^6 - q^14 + (a - 1)*q^16 + (a - 1)*q^20 + q^24 + q^30 - a*q^36 + 
        a*q^46 + (a - 1)*q^54 + (-a + 1)*q^56 - a*q^64 + (-a + 1)*q^70 - a*q^80 
        - q^84 + 2*q^86 - q^94 + (a - 1)*q^96 - a*q^100 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
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:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
360
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.3 + 2*H.4
;
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(
360
);
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:=Rationals();
qprec:=
114
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^4 + q^10 + q^16 - q^25 - 2*q^31 - q^40 + q^49 - q^64 + 2*q^79 + q^100 
        - 2*q^106 + O(q^114),
    q^2 - q^5 - q^8 + q^20 + q^32 - q^50 + 2*q^53 - 2*q^62 - q^80 - 2*q^83 + 
        q^98 + 2*q^107 + O(q^114),
    q^3 - q^12 - q^18 - q^27 + q^30 + q^45 + q^48 + q^72 - q^75 - 2*q^93 + q^108
        + O(q^114),
    q^6 + q^9 - q^15 - q^24 - q^36 - q^54 + q^60 - q^81 + q^90 + q^96 + O(q^114)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
361
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
342
);
qprec:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
361
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
114
);
qprec:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
361
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
38
);
qprec:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
361
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
19*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
361
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
57*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
361
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
171*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
45
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
362
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
180
);
qprec:=
89
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
362
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
60
);
qprec:=
89
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
362
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
89
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
362
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
89
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
362
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
15*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
89
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
362
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
45*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
89
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
363
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^3 + q^4 + q^9 - q^12 + q^16 + q^25 - q^27 - 2*q^31 + q^36 - 2*q^37 - 
        q^48 - q^49 + q^64 + O(q^66)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
363
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
110
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
363
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
363
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
363
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
363
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
363
);
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:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^3*q^3 + a^2*q^4 - a*q^9 - q^12 + (a^3 - a^2 + a - 1)*q^16 - a^3*q^25 +
        (-a^3 + a^2 - a + 1)*q^27 + 2*a*q^31 - a^3*q^36 - 2*a^2*q^37 - a^2*q^48 
        + (-a^3 + a^2 - a + 1)*q^49 - a*q^64 + O(q^66)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
363
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
55*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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(
364
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*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(
364
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
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 + O(q^102),
    q^7 - a*q^14 + (a - 1)*q^28 - q^35 + q^56 + (a - 1)*q^63 + a*q^70 - a*q^91 +
        O(q^102)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + (a - 1)*q^9 + q^13 - a*q^14 + (a - 1)*q^16 + a*q^17 - q^22 - 
        a*q^25 - q^29 + q^36 + a*q^38 - a*q^49 - a*q^52 + a*q^53 + (a - 1)*q^56 
        + (-a + 1)*q^61 + 2*q^62 + q^64 + (-a + 1)*q^68 - q^77 - a*q^81 + a*q^88
        + a*q^94 + (a - 1)*q^100 - 2*a*q^101 + O(q^102),
    q^2 + q^7 - a*q^8 + (-a + 1)*q^11 + (a - 1)*q^18 - q^19 + q^26 - a*q^28 + 
        (2*a - 2)*q^31 + (a - 1)*q^32 + a*q^34 - q^44 - q^47 - a*q^50 - q^58 + 
        (-a + 1)*q^59 + (a - 1)*q^63 + (-a + 1)*q^67 + a*q^71 + q^72 + a*q^76 - 
        2*a*q^83 + q^91 - a*q^98 + a*q^99 + O(q^102)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
364
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^23 - q^29 - q^35 - q^43 + q^49 - q^53 - q^65 - q^79 + q^81 + 
        q^91 + q^95 + O(q^102),
    q^5 - q^7 - q^13 + q^19 + q^31 - 2*q^41 + q^45 + q^47 - 2*q^59 - q^63 + q^73
        + q^83 + q^89 + q^97 + O(q^102)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
365
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
72
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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(
36
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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(
8
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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(
12
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
365
);
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(
4
);
qprec:=
72
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
366
);
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(
366
);
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(
366
);
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(
366
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
366
);
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(
366
);
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(
366
);
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(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a^3*q^3 + a*q^4 + (a^3 - a^2 + a - 2)*q^7 - a*q^9 + (-a^3 + a^2 - a + 
        1)*q^12 + (a^3 - a^2)*q^13 + a^2*q^16 + (-a^3 - a + 1)*q^19 + (a^3 + 
        a^2)*q^21 + a^2*q^25 + (a^3 - a^2 + a - 1)*q^27 + (-a - 1)*q^28 + (a^3 -
        a)*q^31 - a^2*q^36 + (-a^3 + a)*q^37 + (a - 1)*q^39 + q^48 + (-2*a^3 + 
        a^2 - a + 2)*q^49 + (-a^2 + a - 1)*q^52 + (-a^2 - 1)*q^57 + q^61 + (a + 
        1)*q^63 + a^3*q^64 + (a^2 - a)*q^73 + q^75 + (-a^3 + 1)*q^76 + (-a^3 - 
        1)*q^79 + a^2*q^81 + (2*a^3 - a^2 + a - 1)*q^84 + (-a^3 + a)*q^91 + (a^3
        - a^2 + 2*a - 1)*q^93 + (-a^3 + a^2 - a)*q^97 + a^3*q^100 + (-a^3 - a + 
        1)*q^103 - q^108 + (a^3 - a^2 - 1)*q^109 + (-a^3 + a^2 - 2*a + 1)*q^111 
        + (-a^2 - a)*q^112 + (a^2 - a + 1)*q^117 + O(q^118),
    q^2 - a^3*q^6 + a*q^8 + (a^3 - a^2 + a - 2)*q^14 - a*q^18 + (-a^3 + a^2 - a 
        + 1)*q^24 + (a^3 - a^2)*q^26 + a^2*q^32 + (-a^3 - a + 1)*q^38 + (a^3 + 
        a^2)*q^42 + a^2*q^50 + (a^3 - a^2 + a - 1)*q^54 + (-a - 1)*q^56 + (a^3 -
        a)*q^62 - a^2*q^72 + (-a^3 + a)*q^74 + (a - 1)*q^78 + q^96 + (-2*a^3 + 
        a^2 - a + 2)*q^98 + (-a^2 + a - 1)*q^104 + (-a^2 - 1)*q^114 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
366
);
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(
366
);
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(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 + a^2*q^4 + (-a^3 + 1)*q^7 + a^2*q^9 - a^3*q^12 + (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 - 
        1)*q^21 + (a^3 - a^2 + a - 1)*q^25 - a^3*q^27 + (a^2 + 1)*q^28 + (a^2 - 
        a)*q^31 + (a^3 - a^2 + a - 1)*q^36 + (a^2 - a)*q^37 + (a^2 + 1)*q^39 - 
        2*a^3*q^43 + q^48 + (-a^3 - a + 1)*q^49 + (-a^3 - a)*q^52 + (a^3 - a^2 +
        a)*q^57 + q^61 + (a^2 + 1)*q^63 - a*q^64 + 2*a^2*q^67 + (a^3 + a - 
        1)*q^73 + q^75 + (-a + 1)*q^76 + (-a + 1)*q^79 + (a^3 - a^2 + a - 
        1)*q^81 + (-a^3 - a)*q^84 + (2*a^3 - a^2 + a - 2)*q^91 + (-a^3 + 
        a^2)*q^93 + (-a^3 + 1)*q^97 - a*q^100 + (-a^2 + a - 1)*q^103 + q^108 + 
        (-a^3 + a^2)*q^109 + (-a^3 + a^2)*q^111 + (a^3 + a - 1)*q^112 + (-a^3 - 
        a)*q^117 + O(q^118),
    q^2 - a*q^6 + a^2*q^8 + (-a^3 + 1)*q^14 + a^2*q^18 - a^3*q^24 + (a^3 - a^2 -
        1)*q^26 + (a^3 - a^2 + a - 1)*q^32 + (-a^2 + a - 1)*q^38 + (a^3 - a^2 - 
        1)*q^42 + (a^3 - a^2 + a - 1)*q^50 - a^3*q^54 + (a^2 + 1)*q^56 + (a^2 - 
        a)*q^62 + (a^3 - a^2 + a - 1)*q^72 + (a^2 - a)*q^74 + (a^2 + 1)*q^78 - 
        2*a^3*q^86 + q^96 + (-a^3 - a + 1)*q^98 + (-a^3 - a)*q^104 + (a^3 - a^2 
        + a)*q^114 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
366
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
366
);
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(
366
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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^9 - q^12 - q^13 - q^19 - q^22 + q^25 - q^34 - q^39 + q^46 + q^48 + 
        q^49 + q^52 - q^57 + q^58 - q^64 + q^66 + q^76 + q^81 - q^97 + q^102 - 
        q^103 - q^106 - q^108 - q^117 + O(q^118),
    q^2 + q^18 - q^24 - q^26 - q^38 - q^44 + q^50 - q^68 - q^78 + q^92 + q^96 + 
        q^98 + q^104 - q^114 + q^116 + O(q^118),
    q^3 - q^12 - q^13 + q^16 - q^19 + q^27 - q^39 + q^52 - q^57 + q^61 - q^64 + 
        2*q^73 + q^75 + q^76 - q^88 - q^97 - q^103 - q^108 + 2*q^109 - q^117 + 
        O(q^118),
    q^4 - q^12 - q^22 - q^34 + q^36 + q^46 + q^58 - q^64 + q^66 - q^88 + q^100 +
        q^102 - q^106 - q^108 + O(q^118),
    q^6 + q^11 + q^17 - q^23 - q^24 - q^26 - q^29 + q^32 - q^33 - q^38 - q^51 + 
        q^53 + q^54 - q^59 + q^69 + q^71 - q^78 + q^87 - q^89 + q^99 - q^101 + 
        q^104 - q^114 + O(q^118),
    q^8 + q^11 + q^17 - q^23 - q^24 - q^29 - q^33 - q^44 - q^51 + q^53 - q^59 - 
        q^68 + q^69 + q^71 + q^72 + q^87 - q^89 + q^92 + q^99 - q^101 + q^116 + 
        O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
367
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
366
);
qprec:=
61
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
367
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
122
);
qprec:=
61
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
367
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
61*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
61
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
367
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
183*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
61
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^23 + q^25 - q^26 - q^28 - q^37 - q^41 + q^49 - q^56 + O(q^61),
    q^2 - q^13 - q^14 + q^18 - q^28 - q^31 + q^47 + q^49 + q^50 - q^59 + 
        O(q^61),
    q^4 - q^8 - q^13 - q^14 + q^16 + q^23 + q^26 - q^31 - q^32 + q^36 + q^37 + 
        q^41 - q^46 - q^52 - q^59 + O(q^61),
    q^7 - q^8 - q^13 + q^16 + q^26 - q^31 - q^46 + q^53 - q^59 + O(q^61)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
368
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
368
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
368
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
368
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
22
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
368
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
44
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
368
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
368
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
368
);
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(
44
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
368
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
368
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    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 + O(q^86)
]
;
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 + O(q^86),
    q^2 - q^6 - q^26 + q^46 + q^50 + q^54 - q^58 - q^62 + q^78 - q^82 + O(q^86),
    q^4 - q^12 - q^52 + O(q^86),
    q^8 - q^24 - q^32 + q^64 + O(q^86),
    q^16 - q^32 - q^48 + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
368
);
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(
4
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^6 + a*q^8 - a*q^9 - q^12 - a*q^18 - a*q^23 + a*q^25 + a*q^26 + (a + 
        1)*q^27 + q^36 - a*q^48 - q^49 - a*q^52 + a*q^54 + q^58 + (-a - 1)*q^59 
        + q^62 - q^64 + q^72 + q^78 - q^81 - q^82 + O(q^86),
    q^2 - q^4 - a*q^6 + (-a + 1)*q^9 - q^12 - 2*q^13 + a*q^16 + q^26 + (a + 
        1)*q^31 - a*q^32 + (a - 1)*q^39 + (-a + 1)*q^41 - a*q^46 + (a + 1)*q^47 
        + q^48 + a*q^50 + a*q^52 + a*q^54 + a*q^58 - q^62 + (-a + 1)*q^71 + (a +
        1)*q^72 + (a - 1)*q^73 + q^78 - q^82 + O(q^86),
    q^3 - a*q^4 + q^6 + a*q^9 - a*q^13 - q^18 + a*q^24 + a*q^26 - a*q^27 - q^29 
        - q^31 + q^32 - q^36 - q^39 + q^41 + a*q^47 + a*q^48 - a*q^54 - q^58 - 
        a*q^62 - a*q^69 + a*q^71 - q^72 - q^73 + a*q^75 + a*q^78 + (a + 1)*q^81 
        - a*q^82 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
368
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^23 - q^25 - q^31 + q^39 - q^41 + q^47 + q^49 + q^71 - q^73 + q^81 + 
        O(q^86),
    q^2 + q^12 - q^16 - q^18 + q^24 - q^36 - q^46 - q^50 - q^52 + q^72 + 2*q^78 
        + O(q^86),
    q^3 - q^13 - q^27 + q^29 - q^69 - q^75 + O(q^86),
    q^4 - q^8 + q^12 - 2*q^18 + q^24 - q^32 - q^52 + 2*q^62 + q^64 + 2*q^78 + 
        2*q^82 + O(q^86),
    q^6 - q^8 + q^12 - q^18 - q^26 + q^36 - q^48 - q^52 - q^54 + q^58 + q^62 + 
        q^64 + q^72 + q^78 + q^82 + O(q^86),
    q^9 - q^31 - q^39 - q^41 + q^47 + q^71 - q^73 + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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(
369
);
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(
369
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
40
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
369
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
370
);
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(
370
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
370
);
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:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
370
);
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:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
370
);
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:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
370
);
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:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
370
);
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:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
370
);
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:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
370
);
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:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
370
);
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(
4
);
qprec:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
370
);
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:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
370
);
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:=
108
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
52
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^11 - a^10 + a^9 - a^8 + a^7 - a^6 + a^5 - a^4 + a^3 - 2*a^2 + a - 
        1)*q^2 + (-a^11 + a^4 + a)*q^4 - a^7*q^7 + (a^10 - a^6 - a^3 - 1)*q^8 - 
        a^4*q^9 + (-a^11 + a^10 - a^9 + a^8 + a^6 - a^5 + a^4 - a^3 + a^2 - a + 
        1)*q^11 + (a^9 + a^6)*q^14 + (-a^11 + a^10 - 2*a^9 + 2*a^8 - a^7 + a^6 +
        a^4 - a^3 + 2*a^2 - a + 1)*q^16 + (a^6 + a^3)*q^18 + (a^11 - a^9 - a^6 -
        a)*q^22 + (-a^10 - a^3)*q^23 - a^8*q^25 + (-a^11 - a^8 - a^5)*q^28 + 
        (-a^5 + a^2)*q^29 + (a^11 - a^10 + a^8 - a^7 - a^4 - a)*q^32 + (-a^8 - 
        a^5 - a^2)*q^36 + (a^3 + a)*q^37 + (a^9 - 1)*q^43 + (a^11 - a^10 + a^8 +
        a^5 + a^3 + 1)*q^44 + (a^11 - a^10 + 2*a^9 - a^8 + a^7 - a^6 + 2*a^5 - 
        a^4 + a^3 + a - 1)*q^46 - a*q^49 + (a^10 + a^7)*q^50 - a^9*q^53 + (a^10 
        + a^7 + a^4 - 1)*q^56 + (a^7 - a)*q^58 + a^11*q^63 + (a^11 - 2*a^10 + 
        2*a^9 - a^8 + a^5 - a^4 + 2*a^3 - a^2 + a)*q^64 + (a^10 + a^5)*q^67 + 
        O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^11 + a^4)*q^2 + (-a^9 + a^8 + a^2)*q^4 - a*q^7 + (a^11 - a^10 + a^9 
        - a^8 + a^5 - a^4 + a^3 - a^2 + a)*q^8 + a^8*q^9 + (-a^11 - a)*q^11 + 
        (a^11 - a^10 + a^9 - a^8 + a^7 - a^6 - a^4 + a^3 - a^2 + a - 1)*q^14 + 
        (-a^11 + a^10 - a^5 + a^4 - a^3)*q^16 + (a^11 - a^10 + a^9 - a^8 + a^7 +
        a^5 - a^4 + a^3 - a^2 + a - 1)*q^18 + (a^11 - a^10 - a^8 + a^7 - a^6 - 
        a^4 + a^3 + a - 1)*q^22 + (-a^7 + a^6)*q^23 - a^3*q^25 + (a^10 - a^9 - 
        a^3)*q^28 + (a^10 + a^4)*q^29 + (-a^9 + a^8 - a^7 - a^3 + a^2 - a)*q^32 
        + (a^10 + a^4 - a^3)*q^36 + (a^6 + a^2)*q^37 + (-a^5 + 1)*q^43 + (a^10 -
        a^9 - a^7 + a^6 - a^3 + 1)*q^44 + (-a^11 + a^10 - a^5 + a^4)*q^46 + 
        a^2*q^49 + (-a^7 - a)*q^50 - a^5*q^53 + (a^8 - a^7 - a + 1)*q^56 + 
        (2*a^8 + a^2 - a)*q^58 - a^9*q^63 + (-a^10 + a^9 - a^8 - a^4 + a^3 - 
        a^2)*q^64 + (a^10 - a^7)*q^67 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^3 - a)*q^4 + (-a^2 - a + 1)*q^5 + (-a^3 + a)*q^7 + a*q^9 + (-a^3 + 
        a)*q^11 - q^13 + (-a^2 + 1)*q^16 + (-a^3 + a)*q^17 + (a^2 - a - 1)*q^19 
        + (a^3 + 1)*q^20 + (a^3 - a)*q^25 + (a^2 - 1)*q^28 + a^3*q^29 + (a^3 + 
        a^2 - a)*q^31 + (-a^3 - 1)*q^35 - q^36 - a*q^37 + a^3*q^43 + (a^2 - 
        1)*q^44 + (-a^3 - a^2 + a)*q^45 + (a^2 - 1)*q^47 + (-a^2 + 1)*q^49 + 
        (-a^3 + a)*q^52 - a^2*q^53 + (-a^3 - 1)*q^55 + (-a^3 + a)*q^59 + q^63 + 
        a^3*q^64 + (a^2 + a - 1)*q^65 + (a^2 - 1)*q^68 + O(q^70),
    q^2 + (a^2 - 1)*q^3 + (a^2 - a - 1)*q^4 + (-a^3 - a^2 + a)*q^6 + (-a^2 + a +
        1)*q^7 + (a^3 + 1)*q^9 + (-a^2 - a + 1)*q^10 + a^3*q^12 + (a^3 - a)*q^14
        + (-a^3 + a^2 + a)*q^15 + (-a^3 + 1)*q^16 + (-a^2 + a + 1)*q^17 - a*q^18
        - q^19 + 2*a^2*q^20 - a^3*q^21 + (-a^3 + a)*q^22 - q^26 + (a^3 + a^2 - 
        a)*q^29 - 2*q^30 + (2*a^2 - 2)*q^31 + (a^2 - 1)*q^32 + a^3*q^33 + (a^3 -
        a)*q^34 - 2*a^2*q^35 + (-a^3 - 1)*q^37 + (-a^2 + 1)*q^39 + (a^2 + a - 
        1)*q^42 + (a^3 - 1)*q^44 + (-2*a^2 + 2)*q^45 + (a^3 - 1)*q^47 - a^2*q^48
        + (a^3 - a)*q^50 - a^3*q^51 + (-a^2 + a + 1)*q^52 + (-a^2 + 1)*q^53 - 
        a^3*q^58 + (-a^2 + a + 1)*q^60 - a^3*q^61 + (-a^3 - a^2 + a)*q^62 + 
        (-a^2 - a + 1)*q^66 - a*q^67 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^4 + (a - 1)*q^7 + a*q^9 + (a - 1)*q^11 + (-2*a + 1)*q^13 - 
        a*q^16 + (a + 1)*q^17 + (-a + 1)*q^25 - a*q^28 - q^29 - q^36 - a*q^37 + 
        q^43 - a*q^44 + (-a + 2)*q^47 - a*q^49 + (a + 1)*q^52 + (a - 1)*q^53 + 
        (-a - 1)*q^59 - q^63 + q^64 + (a - 2)*q^68 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
371
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^11 - q^15 + q^16 - q^37 - q^43 - q^44 + q^49 - q^57 - q^60 - 
        q^63 + q^64 + O(q^70),
    q^3 - q^5 + q^12 - q^19 - q^20 - q^21 + q^31 + q^35 + q^41 - q^45 + q^48 + 
        q^61 + O(q^70),
    q^7 - q^9 - q^11 + q^15 - q^25 + q^28 + 2*q^29 - q^36 - q^37 - q^43 - q^44 +
        q^53 + q^57 + q^60 + O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
372
);
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(
372
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
372
);
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(
372
);
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:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
372
);
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(
372
);
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:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + (-a^7 + a^4)*q^7 + a^2*q^9 + (-a^6 - a^5 - a^4 + a^3 + a^2 + 
        a)*q^13 + (a^7 - a^6 - a^2 + a)*q^19 + (-a^7 + a^4 + a^3 - a - 1)*q^21 +
        (a^5 - 1)*q^25 - a^3*q^27 + a^6*q^31 + (a^7 + 2*a^6 - a^4 - a^3 - a^2 + 
        1)*q^37 + (a^7 + a^6 + a^5 - a^4 - a^3 - a^2)*q^39 + (-a^5 - a^3)*q^43 +
        (a^5 - a^2)*q^49 + (2*a^7 - a^5 - a^4 - a^2 + a + 1)*q^57 + (a^7 - a^3 -
        a^2)*q^61 + (-a^7 + a^3 + a^2 - 1)*q^63 + (-a^7 + a^5 + a^4 + a^3 + a^2 
        - a - 1)*q^67 + (-2*a^7 - a^6 + a^3 + a^2 - 1)*q^73 + (-a^6 + a)*q^75 + 
        (a^5 + a^4 - 1)*q^79 + a^4*q^81 + (a^7 - 2*a^5 - a^4 + a^2 + 1)*q^91 - 
        a^7*q^93 + (-a^5 - a)*q^97 + (a^7 - a^5 - a^4 + a + 2)*q^103 + (a^5 + 
        a^2 - 1)*q^109 + (-a^7 + 1)*q^111 + (-a^6 + a + 1)*q^117 + O(q^118)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
372
);
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(
372
);
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(
10
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
372
);
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(
372
);
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:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
372
);
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(
372
);
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:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 + (a^3 + a - 1)*q^7 + a^2*q^9 + (-a^2 + a - 1)*q^13 + (a^2 - 
        a)*q^19 + (-a^3 + 1)*q^21 + q^25 - a^3*q^27 - a*q^31 + (a^3 - a^2 - 
        1)*q^37 + (a^3 - a^2 + a)*q^39 + (-a^3 + 1)*q^43 + (-a^2 - 1)*q^49 + 
        (-a^3 + a^2)*q^57 + (-a^3 + a^2)*q^61 + (a^3 - a^2 - 1)*q^63 + (-a^3 + 
        a^2)*q^67 + (a^3 + a - 1)*q^73 - a*q^75 + (a^3 - a^2 + a)*q^79 + (a^3 - 
        a^2 + a - 1)*q^81 + (-a^3 + a^2 - a + 1)*q^91 + a^2*q^93 + (-a + 1)*q^97
        + (-a^3 + 1)*q^103 + (a^2 + 1)*q^109 + (a^2 + 1)*q^111 + (-a + 1)*q^117 
        + O(q^118),
    q^2 - a*q^6 - a^3*q^8 + (a^3 + a - 1)*q^14 + a^2*q^18 + (a^3 - a^2 + a - 
        1)*q^24 + (-a^2 + a - 1)*q^26 - a*q^32 + (a^2 - a)*q^38 + (-a^3 + 
        1)*q^42 + q^50 - a^3*q^54 + (a^2 + 1)*q^56 - a*q^62 + q^72 + (a^3 - a^2 
        - 1)*q^74 + (a^3 - a^2 + a)*q^78 + (-a^3 + 1)*q^86 + a^2*q^96 + (-a^2 - 
        1)*q^98 + (a^2 - a)*q^104 + (-a^3 + a^2)*q^114 + O(q^118),
    q^4 - a*q^12 - a^3*q^16 + (a^3 + a - 1)*q^28 + a^2*q^36 + (a^3 - a^2 + a - 
        1)*q^48 + (-a^2 + a - 1)*q^52 - a*q^64 + (a^2 - a)*q^76 + (-a^3 + 
        1)*q^84 + q^100 - a^3*q^108 + (a^2 + 1)*q^112 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
372
);
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 - q^4 + (a - 1)*q^5 + (a - 1)*q^9 + (-a + 1)*q^13 + a*q^14 + q^16 - a*q^17
        + (-a + 1)*q^20 + (a - 1)*q^22 + (-a + 1)*q^36 - a*q^37 - a*q^38 + (a - 
        1)*q^41 - a*q^45 + (a - 1)*q^52 + (-a + 1)*q^53 + q^54 - a*q^56 + q^62 -
        q^64 + a*q^65 + a*q^68 - q^70 + (a - 1)*q^73 + q^77 + (a - 1)*q^80 + 
        q^85 - a*q^86 + (-a + 1)*q^88 - a*q^110 + (-a + 1)*q^113 + a*q^117 + 
        O(q^118),
    q^2 - a*q^7 - q^8 + (a - 1)*q^10 + (-a + 1)*q^11 + (a - 1)*q^18 + a*q^19 + 
        (-a + 1)*q^26 - q^27 + a*q^28 - q^31 + q^32 - a*q^34 + q^35 + (-a + 
        1)*q^40 + a*q^43 + (a - 1)*q^44 + a*q^55 - a*q^59 + q^63 + (-a + 1)*q^67
        + (a - 1)*q^71 + (-a + 1)*q^72 - a*q^74 - a*q^76 - a*q^79 + (a - 1)*q^82
        + (a - 1)*q^83 - a*q^90 - q^91 - q^95 + a*q^99 + (-a + 1)*q^103 + (a - 
        1)*q^104 + (-a + 1)*q^106 + a*q^107 + q^108 - a*q^112 + O(q^118),
    q^3 - q^12 + (a - 1)*q^15 - a*q^18 + (-a + 1)*q^39 + a*q^42 + q^48 - a*q^51 
        + (-a + 1)*q^60 + (a - 1)*q^63 + (a - 1)*q^66 + a*q^72 + q^90 - q^99 - 
        a*q^111 - a*q^114 + O(q^118),
    q^6 + a*q^9 - a*q^21 - q^24 + (a - 1)*q^30 + (-a + 1)*q^33 - a*q^36 - q^45 +
        a*q^57 + (-a + 1)*q^78 - q^81 + a*q^84 - q^93 + q^96 - a*q^102 + q^105 +
        q^117 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
372
);
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(
6
);
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 - 2*a*q^7 + (a - 1)*q^9 + (-a + 1)*q^13 + a*q^19 + (2*a - 2)*q^21 
        - a*q^25 + q^27 + q^31 + a*q^37 - q^39 + a*q^43 + (3*a - 3)*q^49 + (-a +
        1)*q^57 + 2*q^61 + 2*q^63 + (2*a - 2)*q^67 + (-a + 1)*q^73 + (a - 
        1)*q^75 - 2*a*q^79 - a*q^81 - 2*q^91 - a*q^93 - q^97 + (-a + 1)*q^103 - 
        q^109 + (-a + 1)*q^111 + a*q^117 + O(q^118)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
372
);
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:=
[]
;
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^8 - q^10 - q^14 + q^16 + q^18 - q^38 + q^40 + q^56 + q^62 - q^64 + 
        q^70 - q^72 - q^80 - q^82 - q^90 + 2*q^94 - q^112 + O(q^118),
    q^3 - q^15 - q^21 + q^27 - q^57 + q^93 + q^105 + O(q^118),
    q^4 - q^8 - q^20 - q^28 + q^32 + q^36 + q^40 + q^56 - q^64 - q^72 - q^76 + 
        O(q^118),
    q^6 - q^24 - q^30 - q^42 + q^48 + q^54 - q^114 + O(q^118),
    q^12 - q^24 - q^60 - q^84 + q^96 + q^108 + O(q^118)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
372
);
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:=Rationals();
qprec:=
118
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
373
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
372
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
373
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
124
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
373
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
31*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
373
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
93*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
62
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
374
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
374
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*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(
374
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
374
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
374
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
374
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
374
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
374
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
374
);
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:=
102
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
374
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1 + 8*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(
375
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^9 + q^24 - q^31 + q^34 - q^46 - q^49 - q^51 + q^69 - q^76 + q^81 + 
        O(q^82),
    q^2 - q^12 - q^17 - q^18 + q^23 + q^38 + q^47 - q^53 + q^57 + O(q^82),
    q^3 - q^8 + q^17 - q^23 - q^27 - q^32 + q^38 + q^62 + q^68 + q^72 + O(q^82),
    q^4 + q^6 - q^19 - q^31 - q^36 - q^51 - q^54 + q^61 - q^64 + q^69 + q^76 - 
        q^79 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
375
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
100
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
375
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
375
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
375
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
375
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
375
);
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(
375
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
375
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^24 - q^31 - q^34 - q^46 + q^49 - q^51 - q^69 - q^76 + q^81 + 
        O(q^82),
    q^2 - q^12 - q^17 + q^18 - q^23 - q^38 + q^47 + q^53 + q^57 + O(q^82),
    q^3 - q^8 - q^17 - q^23 + q^27 + q^32 + q^38 - q^62 + q^68 - q^72 + O(q^82),
    q^4 - q^6 - q^19 + q^31 + q^36 + q^51 - q^54 - q^61 - q^64 + q^69 - q^76 - 
        q^79 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
376
);
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(
376
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
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(
376
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
376
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
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(
376
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
376
);
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(
46
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
376
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
23*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^7 - q^21 + q^25 - q^27 + q^47 + q^49 + q^51 - q^53 - q^59 - q^61 + 
        q^63 + 2*q^83 - q^89 + O(q^90),
    q^2 - q^14 - q^42 + q^50 - q^54 + O(q^90),
    q^3 - q^7 - q^9 + q^17 + q^37 + q^49 - q^51 - q^53 - q^59 - q^61 + q^71 + 
        q^75 + q^79 - q^89 + O(q^90),
    q^4 - q^24 - q^28 + q^56 - q^64 + q^72 - q^84 + O(q^90),
    q^6 - q^14 - q^18 + q^34 + q^74 + O(q^90),
    q^8 - q^24 - q^48 - q^64 + q^72 + O(q^90),
    q^12 - q^28 + q^32 - q^36 - q^48 - q^64 + q^68 + O(q^90),
    q^16 - q^24 - q^32 + q^56 + q^72 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
376
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 23*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^9 - q^12 - q^14 + q^18 + q^24 - q^25 + q^32 + q^42 + q^47 + q^49 - 
        q^54 - 2*q^63 - q^68 + q^81 - q^84 + O(q^90),
    q^2 - q^7 + q^9 - q^18 - q^21 - q^24 + q^27 - q^28 + q^36 + q^48 - q^50 + 
        q^51 + q^53 - q^59 - q^61 + q^63 + q^64 - q^81 + q^84 - q^89 + O(q^90),
    q^3 + q^7 - 2*q^9 - q^12 - q^14 - q^16 + 2*q^18 + q^21 + q^24 - q^25 - q^27 
        + q^28 + q^32 + q^34 - 2*q^36 - q^37 + q^47 - q^48 + q^49 + q^50 + q^55 
        - 2*q^63 - q^64 + q^65 + q^72 - q^75 + q^79 + q^81 - q^84 + q^89 + 
        O(q^90),
    q^4 - q^7 + 2*q^9 + q^12 + q^16 - q^17 - q^18 - q^24 + q^25 - q^28 - q^32 - 
        q^34 + q^36 - q^42 - q^47 - q^50 + q^54 - q^55 - q^56 + q^63 + q^64 - 
        q^65 - q^71 + q^84 - q^89 + O(q^90),
    q^5 - q^10 - q^11 - q^13 + q^19 + q^20 + q^22 + q^26 - q^29 - q^38 - q^40 + 
        q^43 - q^44 + q^45 - q^52 + q^58 - q^67 + q^76 + q^80 - q^86 + q^88 + 
        O(q^90),
    q^6 + q^7 - q^9 - q^12 - q^16 - q^21 + q^27 + q^34 + q^42 + q^51 + q^53 - 
        q^54 + q^56 - q^59 - q^61 - q^63 + q^68 - q^72 - q^74 + q^81 - q^84 + 
        q^89 + O(q^90),
    q^8 - q^9 - q^14 - q^17 + 2*q^18 + q^21 + q^24 - q^25 - q^27 + q^32 - q^34 -
        q^36 + q^47 - q^48 + 2*q^49 + q^50 - q^51 - q^53 + q^55 - q^56 + q^59 + 
        q^61 - 2*q^63 - q^64 + q^65 - q^68 - q^71 + q^72 + 2*q^79 + q^81 - q^84 
        + O(q^90)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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(
84
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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(
28
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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(
28
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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(
84
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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(
12
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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(
4
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
377
);
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(
4
);
qprec:=
68
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
378
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*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(
378
);
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^2 + (-a + 1)*q^8 - q^14 + (2*a - 1)*q^26 - a*q^32 + (a - 1)*q^50 + (a - 
        1)*q^56 + (-a - 1)*q^62 - a*q^74 + q^86 + q^98 + (a + 1)*q^104 + 
        O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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:=
[]
;
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^2 - a*q^8 + q^14 - q^26 + (a - 1)*q^32 + (2*a - 2)*q^38 - a*q^50 - a*q^56 
        + a*q^62 + (-a + 1)*q^74 - q^86 + q^98 + a*q^104 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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(
6
);
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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:=
[
    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^2 - q^8 - q^14 + q^32 + q^50 + q^56 - 2*q^74 - 2*q^86 + q^98 + O(q^122),
    q^3 - q^12 - q^21 + q^48 + q^75 + q^84 - 2*q^111 + O(q^122),
    q^6 - q^24 - q^42 + q^96 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
378
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
379
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
378
);
qprec:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
379
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
126
);
qprec:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
379
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
54
);
qprec:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
379
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
42
);
qprec:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
379
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
379
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
27*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
14
);
qprec:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
379
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
63*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
6
);
qprec:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
379
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
189*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
63
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^5 + q^9 + q^16 - q^19 - q^20 - q^23 + q^36 - q^37 - q^41 - q^45 
        + q^49 - q^61 + O(q^63)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
380
);
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(
380
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
380
);
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(
380
);
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(
380
);
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:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
380
);
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(
380
);
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(
380
);
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:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
380
);
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:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
380
);
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(
380
);
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:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
380
);
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:=
[
    q + (a - 1)*q^5 + a*q^9 + q^11 - a*q^19 - a*q^25 + (a - 2)*q^29 + (-2*a + 
        1)*q^31 - q^45 + q^49 + (a - 1)*q^55 + (-a - 1)*q^59 - a*q^61 + (a + 
        1)*q^71 + (-a - 1)*q^79 + (a - 1)*q^81 + (-a + 2)*q^89 + q^95 + a*q^99 -
        a*q^101 + (a + 1)*q^109 + O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
380
);
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(
380
);
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:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^3 - a^2 - a)*q^3 + a^2*q^5 + a*q^9 + q^11 + (a^2 + a - 1)*q^13 + 
        (-a^2 - a + 1)*q^15 + (-a^3 - a^2 + a)*q^17 + a*q^19 + (a^2 - 1)*q^25 - 
        a*q^29 - q^31 + (a^3 - a^2 - a)*q^33 - 2*a^3*q^39 + a^3*q^45 + (a^2 - a 
        - 1)*q^47 - a^3*q^49 + (2*a^2 - 2)*q^51 + (-a^2 - a + 1)*q^53 + a^2*q^55
        + (-a^3 - 1)*q^57 + (a^3 - a)*q^59 + (a^2 - 1)*q^61 + (a^3 - 1)*q^65 + 
        (-a^2 + a + 1)*q^67 - a^2*q^71 + (-a^3 + 1)*q^75 + (-a^3 + a)*q^79 - 
        a^2*q^81 + (-a^2 + a + 1)*q^85 + (a^3 + 1)*q^87 + a*q^89 + (-a^3 + a^2 +
        a)*q^93 + a^3*q^95 + a*q^99 + (-a^2 + 1)*q^101 + (a^3 - a)*q^109 + 
        O(q^110)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
380
);
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:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
380
);
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:=
[]
;
Bo:=
[
    q - q^7 + q^9 - q^11 - q^17 + q^19 + 2*q^23 - q^25 - q^43 - q^47 - q^61 - 
        q^63 - q^73 + q^77 + q^81 + 2*q^83 - q^99 + 2*q^101 + O(q^110),
    q^5 - q^25 - q^35 + q^45 - q^55 - q^85 + q^95 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
380
);
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:=
110
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
380
);
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:=
[
    q + q^7 - q^9 + q^11 - q^17 + q^19 - q^25 - 2*q^35 + q^43 - q^47 - 2*q^49 + 
        q^61 - q^63 - q^73 + q^77 + q^81 + 2*q^85 - q^99 - 2*q^101 + O(q^110),
    q^5 + 2*q^7 - 2*q^17 - q^25 - q^35 + 2*q^43 - q^45 - 2*q^47 + q^55 - 2*q^63 
        - 2*q^73 + 2*q^77 + q^85 + q^95 + O(q^110)
]
;
Bo:=
[
    q - q^11 + q^25 - q^39 - q^45 + q^49 - q^55 - q^61 + q^95 + q^99 - q^101 + 
        O(q^110),
    q^2 - q^12 - q^22 - q^40 + q^50 + q^52 + q^60 + q^72 - q^78 + q^88 - q^90 + 
        q^98 + O(q^110),
    q^3 - q^13 - q^15 + q^37 + q^53 - q^57 + q^65 - q^67 + q^75 + q^97 - q^103 -
        q^107 + O(q^110),
    q^4 - q^24 - q^44 - q^80 + q^100 + q^104 + O(q^110),
    q^5 - q^9 - q^11 + q^19 + q^39 - q^55 - q^61 + q^81 + q^99 - q^101 + 
        O(q^110),
    q^6 + q^20 - q^26 - q^30 - q^36 - q^44 + q^64 + q^74 + q^76 - q^80 - q^96 + 
        q^106 + O(q^110),
    q^8 - q^12 - q^40 - q^48 + q^52 + q^60 + q^72 + O(q^110),
    q^10 - q^18 - q^22 + q^32 + q^38 - q^40 - q^48 + q^72 + q^78 + q^88 + 
        O(q^110),
    q^16 - q^20 - q^24 + q^36 + q^44 - q^64 - q^76 + q^104 + O(q^110)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
126
);
qprec:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
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:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
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:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
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:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + (a^11 - a^4)*q^4 + (-a^11 - a^10 + a^8 - a^6 - a^5 + a^3 + a^2 -
        1)*q^7 + a^2*q^9 + (a^11 - a^9 - a^8 + a^6 + a^5 - a^4 - a^3 + a + 
        1)*q^12 + (-a^11 - a^9)*q^13 + (-a^8 + a)*q^16 + (a^9 - a^5 - a^2)*q^19 
        + (a^8 + a^7 - 1)*q^21 + a^6*q^25 - a^3*q^27 + (a^10 + a^4)*q^28 + 
        (-a^11 - a^10 + a^9 + a^8 - a^6 + a^4 + 2*a^3 - a - 1)*q^31 + (a^11 + 
        a^10 - a^8 - a^7 + a^5 - a^3 - a^2 + 1)*q^36 + (a^4 - a^3)*q^37 + (-a^11
        + a^10 + a^9 + a^8 - a^6 + a^4 + a^3 - a - 1)*q^39 + (a^11 - a^8 - a^7 +
        a^5 - a^2 + 1)*q^43 + (a^9 - a^2)*q^48 + (a^11 + a^10 - a^8 - a^3 - 
        a^2)*q^49 + (a^8 + a^6)*q^52 + (-a^10 + a^6 + a^3)*q^57 + (-a^9 - a^8 + 
        a^6 + a^5 - a^4 - a^3 + a + 1)*q^61 + (-a^9 - a^8 + a)*q^63 + (-a^11 + 
        a^9 + a^8 - a^6 + a^4 + a^3 - a - 1)*q^64 + a*q^67 + (a^10 + a^7 - 
        1)*q^73 - a^7*q^75 + (-a^11 - a^10 + a^8 + a^7 - a^6 - a^5 + a^3 + 2*a^2
        - 1)*q^76 + (-a^9 + a^2)*q^79 + a^4*q^81 + O(q^83)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
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:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
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:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
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:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
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:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + a^4*q^4 + (a^5 - a^4 + a^3 - a^2 + a)*q^7 + a^2*q^9 - a^5*q^12 +
        (a^4 + a^2)*q^13 - a*q^16 + (-a^5 + a^2)*q^19 + (-a + 1)*q^21 + (a^5 - 
        a^4 + a^3 - a^2 + a - 1)*q^25 - a^3*q^27 + (a^4 - a^3)*q^28 + (-a^5 - 
        a^3)*q^31 + (a^5 - a^4 + a^3 - a^2 + a - 1)*q^36 + (a^4 - a^3)*q^37 + 
        (-a^5 - a^3)*q^39 + (a^5 - a^4 - a^2 + a - 1)*q^43 + a^2*q^48 + (-a^4 + 
        a^3 - a^2 + a)*q^49 + (a^5 - a^4 + a^3 - a^2 - 1)*q^52 + (a^5 - a^4 - 
        a^2 + a - 1)*q^57 + (-a^5 + a^4)*q^61 + (a^2 - a)*q^63 - a^5*q^64 - 
        2*a*q^67 + (-a^3 + 1)*q^73 + q^75 + (a^5 - a^4 + a^3 + a - 1)*q^76 + 
        2*a^2*q^79 + a^4*q^81 + O(q^83)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
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:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
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:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + q^4 - 2*a*q^7 + (a - 1)*q^9 - a*q^12 + a*q^13 + q^16 - q^19 + 
        (2*a - 2)*q^21 + q^25 + q^27 - 2*a*q^28 + a*q^31 + (a - 1)*q^36 + (-a + 
        1)*q^37 + (-a + 1)*q^39 + (2*a - 2)*q^43 - a*q^48 + (3*a - 3)*q^49 + 
        a*q^52 + a*q^57 - q^61 + 2*q^63 + q^64 + a*q^67 - q^73 - a*q^75 - q^76 +
        a*q^79 - a*q^81 + O(q^83)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
381
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
63*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
83
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^8 + q^9 - q^11 - q^13 - q^22 + q^25 - q^26 + q^32 + q^34 + q^38 - q^41
        + q^44 - q^47 + q^49 + q^52 + q^62 - q^68 - q^72 - q^73 + q^74 - q^76 - 
        q^79 + q^81 - q^82 + O(q^83),
    q^2 - q^4 - q^11 - q^13 + q^17 + q^18 + q^19 + q^31 - q^34 - q^36 + q^37 - 
        q^38 - q^41 - q^47 + q^50 + q^61 - q^62 + q^64 + q^68 + q^71 - q^73 - 
        q^74 + q^76 - q^79 + O(q^83),
    q^3 - q^24 + q^27 - q^33 - q^39 - q^66 + q^75 - q^78 + O(q^83),
    q^6 - q^12 - q^33 - q^39 + q^51 + q^54 + q^57 + O(q^83)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
382
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
190
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
382
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
38
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
382
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
19*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(
382
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
95*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^15 + q^17 - q^18 - q^20 - q^23 + q^26 - q^27 - q^34 + q^36 - q^39 - 
        q^43 - q^46 + q^49 + q^50 + q^51 - q^52 + q^54 - q^64 + q^68 - q^69 - 
        q^75 + q^78 - q^79 + q^80 - q^85 - q^86 + q^92 + O(q^94),
    q^2 + q^18 - q^24 - q^30 - q^34 + q^50 - q^52 - q^60 - q^90 + O(q^94),
    q^3 + q^18 + q^20 - q^24 - q^25 - q^30 - q^34 - q^39 + q^40 - q^45 + q^46 - 
        q^52 - q^60 + q^65 + q^75 - q^79 + q^85 + q^86 - q^90 + O(q^94),
    q^4 + q^15 + q^17 - q^24 - q^25 - q^27 - q^30 - q^34 + q^36 - q^39 + q^50 + 
        q^51 - q^52 + q^54 - q^60 - q^69 + q^78 - q^79 + O(q^94),
    q^5 - q^15 - q^17 + q^18 - q^26 - q^30 + q^39 + q^46 + q^64 + q^67 - q^72 - 
        q^80 + q^86 + O(q^94),
    q^6 + q^15 + q^17 - q^18 - q^20 - q^25 + q^26 - q^27 + q^32 - q^34 + q^36 - 
        q^39 - q^46 - q^48 + q^51 + q^54 - q^64 - q^69 - q^79 + q^80 - q^86 - 
        q^90 + q^92 + O(q^94),
    q^8 + q^15 + q^17 - q^18 - q^20 - q^25 + q^26 - q^27 + q^30 + q^32 - q^39 - 
        q^40 - q^46 - q^48 + q^51 - q^64 - q^69 + q^72 - q^79 - q^86 + O(q^94),
    q^9 - q^15 - q^17 + q^18 + q^20 + q^23 - q^24 - q^26 - q^30 - q^36 + q^43 - 
        q^45 + q^46 + q^48 - q^51 + q^64 + q^75 - q^80 + q^81 + q^85 + q^86 - 
        q^92 + O(q^94),
    q^10 + q^15 + q^17 - q^18 - q^25 + q^26 - q^27 - q^34 + q^36 - q^39 - q^46 +
        q^51 - q^52 - q^60 - q^64 - q^69 + q^72 + q^78 - q^79 + q^80 - q^86 + 
        q^92 + O(q^94),
    q^12 + q^15 + q^17 - q^24 - q^25 + q^26 - q^27 - q^34 - q^39 + q^51 - q^52 -
        q^60 - q^69 + q^72 - q^79 + q^80 - q^90 + O(q^94),
    q^13 - q^17 + q^18 + q^20 - q^24 - q^26 - q^30 - q^32 + q^40 - q^45 + q^46 +
        q^48 - q^51 - q^52 + q^59 - q^60 + q^64 + q^65 + q^75 + q^81 + q^86 + 
        O(q^94),
    q^16 - q^18 - q^20 + q^26 + q^30 - q^40 - q^46 + q^60 + q^68 - q^86 + 
        O(q^94)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
383
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
382
);
qprec:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
383
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
191*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
64
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^24 + q^25 - q^27 - q^29 - q^38 - q^42 + q^49 - q^57 - q^63 + 
        O(q^64),
    q^2 - q^12 + q^18 - q^19 - q^21 - q^42 - q^46 + q^49 + q^50 + q^51 + q^63 + 
        O(q^64),
    q^3 - q^9 - q^14 + q^27 - q^28 + q^32 + q^42 - q^43 + q^46 + O(q^64),
    q^4 - q^9 - q^12 - q^14 + q^17 + q^18 - q^21 - q^23 + q^24 + q^27 + q^29 + 
        q^31 - q^34 - q^43 - q^48 + q^51 + q^57 - q^62 + q^63 + O(q^64),
    q^6 - q^9 - q^12 - q^14 + q^17 + q^18 + q^24 + q^31 - q^34 - q^36 - q^43 - 
        q^48 + q^51 + q^54 - q^62 + O(q^64),
    q^7 - q^9 - q^12 + q^18 + q^24 - q^34 - q^43 + q^57 - q^62 + q^63 + O(q^64),
    q^8 - q^9 - q^14 + q^19 + q^21 - q^28 + q^32 - q^34 - q^36 + q^42 - q^43 + 
        q^46 + q^54 - q^56 + q^58 - q^62 + O(q^64),
    q^16 - q^17 - q^18 + q^21 + q^23 - q^28 - q^31 + q^38 + q^42 - q^51 - q^56 +
        O(q^64)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
384
);
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(
384
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 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(
384
);
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(
16
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
384
);
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(
8
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
384
);
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(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
384
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 16*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
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^3 - q^27 - 2*q^51 + q^75 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
384
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
384
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
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(
384
);
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:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
384
);
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(
8
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
384
);
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(
4
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
384
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
16*H.2 + H.3
;
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 - q^49 - 2*q^73 + q^81 + 2*q^97 + O(q^98),
    q^3 - 2*q^11 + q^27 + 2*q^59 - q^75 - 2*q^83 + O(q^98)
]
;
Bo:=
[
    q - q^9 - q^25 - q^49 + 2*q^57 + 2*q^73 + q^81 - 2*q^97 + O(q^98),
    q^2 - q^18 - q^50 + O(q^98),
    q^3 - 2*q^19 - q^27 + 2*q^43 + 2*q^67 - q^75 + O(q^98),
    q^6 - 2*q^38 - q^54 + 2*q^86 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
385
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2
;
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(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
10
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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(
10
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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(
20
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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(
30
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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(
60
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (-a^2 + a - 1)*q^2 + (-a^3 + a^2 - a)*q^4 + a^2*q^7 + a^3*q^8 - a*q^9 + 
        (a^3 - a^2 + a - 1)*q^11 + (-a + 1)*q^14 + (a^3 - a^2 + a)*q^18 + (-a^3 
        + a^2)*q^22 + (-a^3 + a^2)*q^23 - a^3*q^25 + (-a^2 + a)*q^28 + (-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^3 - a^2 + a - 
        1)*q^49 + (a^2 - a)*q^50 + (a^2 + 1)*q^53 - q^56 + a^3*q^58 - a^3*q^63 +
        (-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*q^77 + (a^2 + 1)*q^79 + 
        a^2*q^81 + a*q^86 - a^2*q^88 + O(q^90),
    q^5 + (-a^2 + a - 1)*q^10 + (-a^3 + a^2 - a)*q^20 + a^2*q^35 + a^3*q^40 - 
        a*q^45 + (a^3 - a^2 + a - 1)*q^55 + (-a + 1)*q^70 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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(
10
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^2*q^4 + (a^2 - a + 1)*q^9 - a*q^11 + (a^3 - a^2 + a)*q^15 + (a^3 - a^2
        + a - 1)*q^16 + (-a^3 + a^2)*q^21 - a^3*q^25 + (-a^3 - a)*q^29 - a*q^35 
        + (a - 1)*q^36 + (a^3 - 2*a^2 + 2*a - 1)*q^39 - a^3*q^44 + (a^3 - a^2 + 
        a - 1)*q^49 - a^2*q^51 + (a^2 - a)*q^60 - a*q^64 + (-a^3 + a^2)*q^65 + 
        (a^2 - a)*q^71 + (-a^2 + a - 1)*q^79 + (a^3 - a^2 + a)*q^84 + (a^3 + a -
        1)*q^85 + O(q^90),
    q^3 + (-a^2 - 1)*q^5 + (a^3 - 1)*q^7 + a^2*q^12 - a^3*q^13 + (a^2 + a + 
        1)*q^17 + (-a^3 - a + 1)*q^20 + (a^2 + 1)*q^27 + (-a^2 - 1)*q^28 - 
        a*q^33 - a^2*q^45 + (a^3 - a^2 - 2)*q^47 + (a^3 - a^2 + a - 1)*q^48 + 
        q^52 + (a^3 + a)*q^55 - q^63 + (2*a^3 + a - 1)*q^68 + (-2*a^3 + a^2 - a 
        + 2)*q^73 - a^3*q^75 + (-a^3 + a^2 + 1)*q^77 + (-a^3 + a^2 + 1)*q^80 - 
        a*q^83 + (-a^3 - a)*q^87 + O(q^90)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
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(
385
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^4 - q^5 + q^9 - q^11 + q^16 + q^20 + q^25 - 2*q^31 - q^36 + q^44 - 
        q^45 - q^49 + q^55 + 2*q^59 - q^64 + 2*q^71 - q^80 + q^81 - 2*q^89 + 
        O(q^90),
    q^7 - q^28 - q^35 + q^63 - q^77 + O(q^90)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a - 1)*q^5 + (a - 1)*q^9 - a*q^11 + (-a + 1)*q^14 + (-a + 1)*q^16 - 
        a*q^25 + (a - 1)*q^26 + a*q^31 - 2*q^34 - a*q^45 + q^49 + q^55 + q^56 + 
        a*q^59 + q^64 + a*q^70 - q^71 + a*q^80 - a*q^81 + (a - 1)*q^86 + (-a + 
        1)*q^89 + O(q^90),
    q^2 + (-a + 1)*q^8 + q^10 - a*q^13 - a*q^17 + (a - 1)*q^18 + (a - 1)*q^22 + 
        a*q^28 + (a - 1)*q^35 - q^40 + (a - 1)*q^43 - a*q^50 + (a - 2)*q^52 + 
        (-a + 1)*q^62 - a*q^65 + a*q^72 + q^73 - a*q^77 + (a - 1)*q^83 + q^85 + 
        (-a + 1)*q^88 + O(q^90),
    q^4 + a*q^5 - q^11 - q^14 - a*q^16 + (-a + 1)*q^20 - a*q^26 + q^31 + (a - 
        1)*q^34 + (a - 1)*q^36 + a*q^44 - q^45 + (-a + 1)*q^49 + q^56 + (-a + 
        1)*q^64 + a*q^70 + 2*a*q^86 - a*q^89 + O(q^90),
    q^7 + (a + 1)*q^8 + (2*a - 1)*q^10 + (-2*a + 1)*q^17 + (-a - 1)*q^22 - q^28 
        - q^35 + (-a - 1)*q^43 + (-2*a + 1)*q^52 + (a + 1)*q^62 + (a - 1)*q^63 +
        (-a + 2)*q^65 + (a - 2)*q^72 + (2*a - 1)*q^73 + (-a + 1)*q^77 + (-a - 
        1)*q^83 + (a + 1)*q^85 + O(q^90)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
385
);
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<a>:=CyclotomicField(
4
);
qprec:=
90
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
386
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
192
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
386
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
64
);
qprec:=
95
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
387
);
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(
387
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
387
);
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(
387
);
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(
387
);
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(
387
);
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(
387
);
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(
387
);
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(
387
);
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 - a^4 + a^3 - a^2 + a - 1)*q^4 + (a^5 + a^2)*q^7 + (a^3 + a)*q^13 -
        a^5*q^16 + (-a^3 - a^2)*q^19 + a^4*q^25 + (-a^4 - a)*q^28 + (-a^5 + a^4 
        - a^3 + a^2 - a)*q^31 + (-a^5 + a^4 - a^3 + a^2 - 2*a + 1)*q^37 - 
        a^4*q^43 + (a^4 - a^3 - 1)*q^49 + (-a^2 - 1)*q^52 + (-a^5 + a^3)*q^61 + 
        a^4*q^64 + (-a^4 + a)*q^67 + (-2*a^5 + a^4 - a^3 + a^2 - a + 1)*q^73 + 
        (a^2 + a)*q^76 + (a^5 - a^2)*q^79 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
387
);
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(
387
);
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(
387
);
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^5*q^4 + (a^4 - a^3)*q^7 + (a^5 - a^4 + a^3 + a - 1)*q^13 - a^3*q^16 + 
        (a^5 + a^3 - a^2 + a - 1)*q^19 - a*q^25 + (a^2 - a)*q^28 + (-a^5 + 
        1)*q^31 + (-a^5 + a^2)*q^37 - a*q^43 + (a^5 - a^4 + a^3 - a^2)*q^49 + 
        (a^4 + 1)*q^52 + (a^5 - a^4 - a^2 + a - 1)*q^61 - a*q^64 + (a^2 - 
        a)*q^67 + (-a^5 - a^3)*q^73 + (a^4 + a^2)*q^76 + (a^4 - a^3)*q^79 + 
        O(q^82),
    q^3 - a*q^9 - a^5*q^12 + (a^4 - a^3)*q^21 + a^2*q^27 + (a^5 - a^4 + a^3 - 
        a^2 + a - 1)*q^36 + (a^5 - a^4 + a^3 + a - 1)*q^39 - a^3*q^48 + (a^5 + 
        a^3 - a^2 + a - 1)*q^57 + (-a^5 + a^4)*q^63 - a*q^75 - a^3*q^81 + 
        O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
387
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
387
);
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(
387
);
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(
387
);
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(
387
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
387
);
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(
387
);
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:=
[
    q + q^4 - 2*q^13 + q^16 + q^25 - 2*q^31 - q^43 + q^49 - 2*q^52 + q^64 - 
        2*q^67 - 2*q^79 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
387
);
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(
388
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
388
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
96
);
qprec:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
388
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
388
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
388
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a^5*q^2 + (a^6 - a^2)*q^4 + (-a^5 + a^4 + a)*q^5 - a^3*q^8 + (-a^6 + 
        a^2)*q^9 + (a^5 + a^2 - a)*q^10 + (-a - 1)*q^13 + (-a^4 + 1)*q^16 + (a^7
        + a^6 - a^3)*q^17 + a^3*q^18 + (a^7 - a^2)*q^20 + (-a^6 + a^4 + a - 
        1)*q^25 + (-a^6 - a^5)*q^26 + (-a^7 + a^3 - a^2)*q^29 + a*q^32 + (a^7 - 
        a^4 - a^3)*q^34 + (a^4 - 1)*q^36 + (-a^4 + a^3)*q^37 + (-a^7 - 1)*q^40 +
        (-a^5 - a^4 + 1)*q^41 + (-a^7 + a^2)*q^45 + a^7*q^49 + (-a^7 + a^6 + a^3
        - a)*q^50 + (-a^7 - a^6 + a^3 + a^2)*q^52 + (-a^7 - a^3)*q^53 + (-a^7 + 
        a^4)*q^58 + (a^7 + a^5 - a)*q^61 + a^6*q^64 + (a^6 - a^4 - a^2 - a)*q^65
        + (-a^5 - a^4 + a)*q^68 - a*q^72 + (-a^7 + a^5 + a^3)*q^73 + (-a^5 + a^4
        + a - 1)*q^74 + (-a^5 + 1)*q^80 + (-a^4 + 1)*q^81 + (-a^6 + a^2 + 
        a)*q^82 + (a^6 + a^4 - a^2 - 1)*q^85 + (a^5 + a)*q^89 + (a^7 + 1)*q^90 +
        O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
388
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
388
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (a^3 - a)*q^2 + (-a^2 + 1)*q^4 + (-a^3 + a^2 - 1)*q^5 + a^3*q^8 + (-a^2 
        + 1)*q^9 + (-a^3 + a^2)*q^10 + (a + 1)*q^13 - a^2*q^16 + (-a^3 + a - 
        1)*q^17 + a^3*q^18 + (a^2 - a)*q^20 + (-a^2 + a - 1)*q^25 + (a^3 - a - 
        1)*q^26 + (-a^3 + a^2 + a)*q^29 + a*q^32 + (-a^3 + a^2 + a - 1)*q^34 - 
        a^2*q^36 + (a^3 + a^2 - 1)*q^37 + (-a + 1)*q^40 + (a^3 - a^2 - a)*q^41 +
        (a^2 - a)*q^45 - a*q^49 + (-a^3 + 2*a - 1)*q^50 + (-a^3 - a^2 + a + 
        1)*q^52 + (a^3 - a)*q^53 + (a^2 - a - 1)*q^58 + (-a^3 - a)*q^61 - q^64 -
        a*q^65 + (-a^3 + a^2 - 1)*q^68 + a*q^72 + (-a^3 - a^2)*q^74 + (a^3 - a +
        1)*q^80 - a^2*q^81 + (-a^2 + a + 1)*q^82 + (2*a^3 - 2*a^2 + 1)*q^85 + 
        a^3*q^89 + (-a + 1)*q^90 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
388
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + a^2*q^4 + (-a - 1)*q^5 - a^3*q^8 - a^2*q^9 + (a^2 + a)*q^10 + 
        (-a - 1)*q^13 - q^16 + (a^3 - a^2)*q^17 + a^3*q^18 + (-a^3 - a^2)*q^20 +
        (a^2 + a + 1)*q^25 + (a^2 + a)*q^26 + (-a^3 - a^2)*q^29 + a*q^32 + (a^3 
        + 1)*q^34 + q^36 + (a^3 + 1)*q^37 + (a^3 - 1)*q^40 + (a - 1)*q^41 + (a^3
        + a^2)*q^45 - a^3*q^49 + (-a^3 - a^2 - a)*q^50 + (-a^3 - a^2)*q^52 + 
        (a^3 - 1)*q^58 + (-a^3 + a)*q^61 - a^2*q^64 + (a^2 + 2*a + 1)*q^65 + (-a
        + 1)*q^68 - a*q^72 + (-a^3 - a)*q^73 + (-a + 1)*q^74 + (a + 1)*q^80 - 
        q^81 + (-a^2 + a)*q^82 + (a^2 + 1)*q^85 + (-a^3 + 1)*q^90 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
388
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^2 - a*q^4 + (-a - 1)*q^5 - q^8 - a*q^9 + (a - 2)*q^10 + (a + 
        1)*q^13 + (a - 1)*q^16 + (-a + 2)*q^17 - q^18 + (2*a - 1)*q^20 + 
        2*a*q^25 + (-a + 2)*q^26 + a*q^32 + (-2*a + 1)*q^34 + (a - 1)*q^36 + (-a
        - 1)*q^37 + (a + 1)*q^40 + (2*a - 1)*q^45 + a*q^49 + 2*q^50 + (-2*a + 
        1)*q^52 + (a - 1)*q^53 + (a - 1)*q^61 + q^64 - 3*a*q^65 + (-a - 1)*q^68 
        + a*q^72 + (-2*a + 2)*q^73 + (a - 2)*q^74 + (-a + 2)*q^80 + (a - 1)*q^81
        - 3*q^85 + q^89 + (a + 1)*q^90 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
388
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 - q^4 + (a + 1)*q^5 - a*q^8 - q^9 + (a - 1)*q^10 + (a + 1)*q^13 + 
        q^16 + (-a - 1)*q^17 - a*q^18 + (-a - 1)*q^20 + a*q^25 + (a - 1)*q^26 + 
        (-a - 1)*q^29 + a*q^32 + (-a + 1)*q^34 + 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^52 -
        2*a*q^53 + (-a + 1)*q^58 - q^64 + 2*a*q^65 + (a + 1)*q^68 + a*q^72 + (a 
        + 1)*q^74 + (a + 1)*q^80 + q^81 + (a - 1)*q^82 - 2*a*q^85 + 2*a*q^89 + 
        (-a + 1)*q^90 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
388
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^2 + (a - 1)*q^4 + a*q^5 + q^8 + (a - 1)*q^9 + (-a + 1)*q^10 + a*q^13
        - a*q^16 + (-a + 1)*q^17 + q^18 - q^20 + (-a + 1)*q^26 - 2*a*q^29 + (a -
        1)*q^32 - q^34 - a*q^36 + a*q^37 + a*q^40 - 2*a*q^41 - q^45 + (a - 
        1)*q^49 - q^52 + a*q^53 + (2*a - 2)*q^58 + a*q^61 + q^64 + (a - 1)*q^65 
        + a*q^68 + (a - 1)*q^72 - 2*a*q^73 + (-a + 1)*q^74 + (-a + 1)*q^80 - 
        a*q^81 + (2*a - 2)*q^82 + q^85 - q^89 + a*q^90 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
388
);
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:=
94
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^2 + q^4 - q^8 + q^9 + q^16 - q^18 + q^25 - q^32 + q^36 - q^49 - q^50 -
        2*q^53 - 2*q^61 + q^64 - q^72 - 2*q^73 + q^81 - 2*q^89 + O(q^94)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
389
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
388
);
qprec:=
65
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
389
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
97*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
65
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
390
);
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(
390
);
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(
390
);
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:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
390
);
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(
390
);
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(
390
);
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(
390
);
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(
390
);
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(
390
);
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(
390
);
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(
390
);
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:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
390
);
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(
4
);
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
390
);
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(
390
);
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:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
390
);
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(
390
);
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(
390
);
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(
390
);
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:=
154
;
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 + O(q^154),
    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 + O(q^154),
    q^5 - q^15 - q^20 + q^45 + q^60 - q^65 + q^80 - q^125 - q^135 + O(q^154),
    q^10 - q^30 - q^40 + q^90 + q^120 - q^130 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
390
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
390
);
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:=Rationals();
qprec:=
154
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 - q^12 - q^16 + q^22 + q^30 + q^39 + q^40 - q^49 + q^52 - q^55 - 
        q^66 - q^75 + q^81 - q^82 - q^88 + q^94 - q^100 + q^108 + q^118 + q^121 
        - q^130 + 2*q^139 - q^142 + q^144 + O(q^154),
    q^2 - q^11 - q^15 - q^18 + q^20 + q^24 - q^32 + q^33 + q^41 - q^44 - q^47 - 
        q^59 + q^65 + q^71 + q^78 + q^83 + q^89 - q^98 + q^99 - q^104 - q^110 - 
        q^123 - q^125 - q^132 + q^135 + q^137 - q^141 - q^143 - q^149 - q^150 + 
        O(q^154),
    q^3 + q^12 - q^13 + q^25 - q^27 - q^40 - q^48 - q^52 - q^55 + 2*q^88 + q^100
        - q^108 + q^117 + q^120 + 2*q^127 - q^147 + O(q^154),
    q^4 + q^12 - q^22 - q^30 - q^36 - q^52 - q^64 + q^66 + q^82 + q^88 - q^94 + 
        q^100 - q^108 - q^118 + q^120 + q^130 + q^142 + O(q^154),
    q^5 - 2*q^11 - q^15 + q^20 + 2*q^24 + 2*q^41 - 2*q^44 - q^45 - 2*q^59 - q^60
        + q^65 + 2*q^71 - q^80 + 2*q^89 + 2*q^99 - 2*q^104 - q^125 + q^135 - 
        2*q^141 - 2*q^149 + O(q^154),
    q^6 - q^20 - q^24 - q^26 + 2*q^44 + q^50 - q^54 + q^60 - q^96 + q^104 - 
        q^110 + O(q^154),
    q^8 - q^11 - q^15 + q^24 + q^33 + q^41 - q^44 - q^47 - q^59 - q^60 + q^65 + 
        q^71 - q^72 + q^83 + q^89 + q^99 - q^104 - q^123 - q^125 - q^128 + q^132
        + q^135 + q^137 - q^141 - q^143 - q^149 + O(q^154),
    q^10 + 2*q^12 - 2*q^22 - q^30 - q^40 - 2*q^52 + 2*q^82 + 2*q^88 - q^90 + 
        2*q^100 - 2*q^108 - 2*q^118 + q^120 + q^130 + 2*q^142 + O(q^154)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
391
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
16
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
391
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
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(
391
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
391
);
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(
44
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
391
);
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(
22
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
391
);
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(
176
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
391
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.2
;
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^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 + O(q^70),
    q^17 - q^34 - q^51 + O(q^70)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
391
);
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:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
391
);
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(
4
);
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
391
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
8*H.1 + 11*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
70
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^26 - q^32 - q^35 - q^47 + q^49 - q^52 + O(q^70),
    q^2 - q^13 - q^16 + q^18 - q^26 - q^35 + q^49 + q^50 + q^59 + O(q^70),
    q^4 - q^8 - q^13 + q^25 + q^36 + q^47 - q^50 - q^55 + O(q^70),
    q^5 - 2*q^11 - 2*q^14 + q^17 + 2*q^20 + q^22 + q^23 - q^28 + q^34 - 2*q^37 -
        2*q^40 + q^45 + q^46 + q^56 - 2*q^65 - q^68 + O(q^70),
    q^7 - 2*q^11 - q^14 + q^17 + q^20 + q^22 + q^23 - q^28 - 2*q^37 - q^40 + 
        q^44 + q^56 + q^61 + q^63 - q^65 - q^68 + O(q^70),
    q^10 - q^11 - q^14 + q^17 + q^23 - q^28 - q^37 + q^44 + q^56 - q^65 + 
        O(q^70)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^25 - 2*q^29 - 2*q^37 + 2*q^53 + q^81 + O(q^82),
    q^2 - q^4 + q^8 - q^16 + q^18 + q^32 - q^36 - q^50 - 2*q^58 - q^64 + q^72 - 
        2*q^74 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^4 - q^11 + q^16 - q^18 - q^22 + q^25 - q^43 - q^44 - q^51 - q^57 + 
        q^64 - q^72 + O(q^82),
    q^2 + q^8 - q^9 - q^11 - q^22 + q^32 - q^36 - q^43 - q^44 + q^50 + q^51 + 
        q^57 + 2*q^67 + q^81 + O(q^82),
    q^3 - q^6 + q^12 - q^17 - q^19 - q^24 + q^34 + q^38 + q^41 + q^48 - q^59 - 
        q^68 + q^73 + q^75 - q^76 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
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(
392
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
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(
392
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
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(
42
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
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(
14
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
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(
14
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^2 + (a - 1)*q^4 - q^8 + a*q^9 - a*q^16 + (a - 1)*q^18 - 2*a*q^23 + 
        (-a + 1)*q^25 + (-a + 1)*q^32 - q^36 + (-2*a + 2)*q^46 + q^50 + q^64 - 
        2*q^71 - a*q^72 + 2*a*q^79 + (a - 1)*q^81 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
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:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + (a - 1)*q^9 + a*q^25 - 2*q^29 + (-2*a + 2)*q^37 - 2*a*q^53 - a*q^81 + 
        O(q^82),
    q^2 + (-a + 1)*q^4 - a*q^8 - q^16 + (a - 1)*q^18 + (a - 1)*q^32 + a*q^36 + 
        a*q^50 - 2*q^58 + a*q^64 + q^72 + (-2*a + 2)*q^74 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
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(
6
);
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^4 + a*q^11 + (a - 1)*q^16 + a*q^18 - q^22 - a*q^25 - q^43 + (-a + 
        1)*q^44 + (-a + 1)*q^51 - q^57 + q^64 + (-a + 1)*q^72 + O(q^82),
    q^2 - a*q^8 - q^9 + (-a + 1)*q^11 + a*q^22 + (a - 1)*q^32 + a*q^36 + a*q^43 
        - q^44 - a*q^50 + q^51 - a*q^57 + (2*a - 2)*q^67 + (a - 1)*q^81 + 
        O(q^82),
    q^3 + (-a + 1)*q^6 - a*q^12 - q^17 + a*q^19 - q^24 + (a - 1)*q^34 + q^38 + 
        (a - 1)*q^41 + (a - 1)*q^48 - q^59 + a*q^68 + q^73 - a*q^75 + (-a + 
        1)*q^76 + O(q^82)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
392
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
21*H.3
;
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(
392
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + 21*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
82
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^2 + q^4 - q^8 - q^9 + q^16 + q^18 + 2*q^23 - q^25 - q^32 - q^36 - 
        2*q^46 + q^50 + q^64 - 2*q^71 + q^72 - 2*q^79 + q^81 + O(q^82),
    q^7 - q^14 + q^28 - q^49 - q^56 - q^63 + O(q^82)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
393
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
393
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
130
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
393
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
393
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
393
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
393
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
393
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
393
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
65*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^4 - q^11 - q^13 - q^15 + q^16 - q^21 + q^33 + q^35 + q^39 - q^41 - 
        q^44 - q^52 + 2*q^53 - q^55 - q^60 + q^64 - q^65 + q^75 - q^77 - q^81 - 
        q^84 + O(q^86),
    q^3 + q^12 - q^15 - q^21 - q^45 + q^48 - q^60 - q^63 + q^75 - q^81 - q^84 + 
        O(q^86),
    q^5 + q^7 - q^11 - q^13 + q^20 - q^25 + q^27 + q^28 - q^35 - q^41 + q^43 - 
        q^44 - q^45 - q^49 - q^52 + q^59 + q^61 - q^63 + q^80 - q^81 + O(q^86),
    q^9 - q^15 - q^21 - q^27 + q^33 + q^36 + q^39 - q^60 + q^75 - q^84 + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
394
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
196
);
qprec:=
97
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
394
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
7*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
28
);
qprec:=
97
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
394
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
49*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
97
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
78
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
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(
156
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
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(
26
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
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(
52
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
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:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
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(
12
);
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
39*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^8 + q^9 - q^19 + q^22 - q^23 - q^25 + q^26 + q^32 - q^38 - q^44 - q^46
        + q^49 - q^52 + q^62 - q^67 - q^72 - q^73 + q^76 + O(q^78),
    q^2 - q^4 + q^11 + q^13 + q^18 - q^19 - q^22 - q^23 - q^26 + q^31 - q^36 + 
        q^44 - q^50 + q^52 - q^62 + q^64 - q^67 - q^73 + O(q^78),
    q^5 - q^25 - q^40 + q^45 - q^50 + O(q^78),
    q^10 - q^20 - q^25 + q^55 + q^65 + O(q^78)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
395
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
2*H.1 + 39*H.2
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
78
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - 1/2*q^9 - 1/2*q^11 + q^16 - 1/2*q^19 + 1/2*q^20 - 1/2*q^21 + 1/2*q^25 - 
        q^26 + 1/2*q^36 + 1/2*q^40 - 1/2*q^44 - 1/2*q^45 - 1/2*q^49 + 1/2*q^50 -
        1/2*q^51 - 1/2*q^55 - 3/2*q^76 + O(q^78),
    q^2 - 1/2*q^9 - 1/2*q^11 + q^13 - q^18 - 1/2*q^19 + 1/2*q^20 + 1/2*q^21 + 
        q^22 - q^23 - 1/2*q^25 + q^31 - 1/2*q^36 + 1/2*q^40 - 1/2*q^44 + 
        1/2*q^45 - 1/2*q^49 - 1/2*q^50 + 1/2*q^51 - q^52 - 3/2*q^55 - q^62 - 
        q^67 + q^73 - 1/2*q^76 + O(q^78),
    q^3 - q^7 + q^12 - q^15 - q^17 - q^28 + q^35 + q^37 + q^43 + q^47 + q^48 - 
        q^53 - q^60 - q^63 - q^68 + q^75 + O(q^78),
    q^4 + 1/2*q^9 - 1/2*q^11 - 1/2*q^19 - 1/2*q^20 - 1/2*q^21 + 1/2*q^25 + q^26 
        - 1/2*q^36 - 1/2*q^40 - 1/2*q^44 - 1/2*q^45 + 1/2*q^49 - 1/2*q^50 - 
        1/2*q^51 - 1/2*q^55 + q^64 + 1/2*q^76 + O(q^78),
    q^5 - q^9 - q^11 - q^19 + q^20 + q^21 + 2*q^31 - q^36 - q^44 - q^49 + q^51 -
        q^55 - q^76 + O(q^78),
    q^8 - 1/2*q^9 - 3/2*q^11 + q^16 - 1/2*q^19 + 3/2*q^20 + 1/2*q^21 + q^22 - 
        q^23 + 1/2*q^25 + 2*q^31 - q^32 - 1/2*q^36 - q^38 - 1/2*q^40 - 1/2*q^44 
        + 1/2*q^45 - q^46 - 1/2*q^49 - 1/2*q^50 + 1/2*q^51 + q^52 - 3/2*q^55 - 
        q^62 - q^67 - q^72 + q^73 - 3/2*q^76 + O(q^78),
    q^10 + 2*q^11 - 2*q^16 - q^20 - q^25 - 2*q^31 + 2*q^46 + q^55 + q^65 + 
        2*q^76 + O(q^78)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
396
);
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(
396
);
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(
396
);
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(
396
);
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(
396
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
396
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
396
);
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(
396
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
396
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
396
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
396
);
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:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
396
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
396
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^5 - q^11 + q^23 - q^31 - q^37 - 2*q^47 + q^49 - 2*q^53 - q^55 + q^59 -
        q^67 + q^71 + q^89 - q^97 + 2*q^103 + q^113 + q^115 + q^121 + O(q^122)
]
;
Bo:=
[
    q - q^5 + q^11 - q^23 - q^31 - q^37 + 2*q^47 + q^49 + 2*q^53 - q^55 - q^59 -
        q^67 - q^71 - q^89 - q^97 + 2*q^103 - q^113 + q^115 + q^121 + O(q^122),
    q^3 - q^15 - q^27 + q^33 - q^69 + q^81 - q^93 - q^111 + O(q^122),
    q^9 - q^27 - q^45 + q^99 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
396
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
396
);
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:=
[
    q - q^5 + a*q^9 - a*q^11 + (a - 2)*q^15 + (-a + 1)*q^23 + (-2*a + 1)*q^25 + 
        q^27 + a*q^31 + (-a + 1)*q^37 + (a - 1)*q^45 + a*q^47 + (a - 1)*q^49 - 
        q^53 + a*q^55 + a*q^59 - q^67 + (-a + 1)*q^71 + (-2*a + 1)*q^75 - q^89 +
        (-a + 2)*q^93 - q^97 + (-a + 1)*q^99 + (-a + 1)*q^103 + (-a - 1)*q^111 +
        a*q^113 + (a - 1)*q^115 + (a - 1)*q^121 + O(q^122),
    q^3 + (2*a - 1)*q^5 + (-a + 1)*q^9 + a*q^15 + (-a - 1)*q^25 + (-2*a + 
        1)*q^31 - a*q^33 + (a - 2)*q^37 + (a - 1)*q^45 + (-a + 2)*q^55 + (-2*a +
        1)*q^59 + (2*a - 1)*q^67 + (-a + 1)*q^69 + (a - 2)*q^71 + (-a - 1)*q^75 
        + q^81 - q^93 + (a + 1)*q^97 - q^99 + a*q^111 + (-2*a + 1)*q^113 + (a + 
        1)*q^115 + O(q^122)
]
;
Bo:=
[
    q + (a - 1)*q^3 + (-a + 1)*q^5 - a*q^9 - a*q^11 + a*q^15 + (2*a - 2)*q^23 + 
        q^27 + (-a + 1)*q^31 + q^33 - q^37 - q^45 + a*q^47 + (a - 1)*q^49 - q^53
        - q^55 + (-a + 1)*q^59 + (-a + 1)*q^67 - 2*a*q^69 - q^71 + (a - 1)*q^81 
        + 2*q^89 + a*q^93 + a*q^97 + (a - 1)*q^99 + (-a + 1)*q^103 + (-a + 
        1)*q^111 + (-a + 1)*q^113 + 2*a*q^115 + (a - 1)*q^121 + O(q^122),
    q^2 + (a - 1)*q^6 + (a - 1)*q^8 + (-a + 1)*q^10 - a*q^18 - a*q^22 - a*q^24 +
        a*q^30 - a*q^32 + a*q^40 + (2*a - 2)*q^46 + q^54 + (-a + 1)*q^62 + q^66 
        + q^72 - q^74 + q^88 - q^90 + a*q^94 + q^96 + (a - 1)*q^98 - q^106 - 
        q^110 + (-a + 1)*q^118 - q^120 + O(q^122),
    q^4 + (a - 1)*q^12 + (a - 1)*q^16 + (-a + 1)*q^20 - a*q^36 - a*q^44 - a*q^48
        + a*q^60 - a*q^64 + a*q^80 + (2*a - 2)*q^92 + q^108 + O(q^122)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
396
);
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:=
122
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - q^4 + q^16 - q^22 - q^25 + q^49 - q^64 + 2*q^70 + q^88 - 2*q^97 + q^100 
        - q^121 + O(q^122),
    q^2 - q^8 + q^11 + q^32 - 2*q^35 - q^44 - q^50 + 2*q^95 + q^98 + O(q^122),
    q^5 - q^14 - q^20 + q^38 - q^53 + q^56 - q^77 + q^80 + q^86 + q^89 - q^110 -
        q^113 + O(q^122),
    q^7 + q^10 - q^19 - q^28 - q^40 - q^43 + q^55 + q^76 - q^79 - q^106 + q^112 
        + O(q^122)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
397
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
396
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
397
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
132
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
397
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
44
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
397
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
36
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
397
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
33*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
12
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
397
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
99*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
4
);
qprec:=
66
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
398
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
198
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
398
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
66
);
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
398
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.1
;
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(
398
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
11*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(
398
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
33*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(
398
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
99*H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
98
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q + q^9 - q^26 - q^28 - q^31 - q^35 - q^40 - q^46 + q^49 + q^50 + q^52 - 
        q^53 + q^56 - q^61 + q^62 + q^81 - q^91 + q^92 + O(q^98),
    q^2 + q^18 - q^26 - q^28 - q^40 - q^46 + q^50 - q^70 - q^80 + O(q^98),
    q^4 - q^14 - q^20 + q^36 - q^40 + q^50 - q^58 + q^62 + q^70 + O(q^98),
    q^5 + q^14 + q^16 - q^25 - q^26 - q^28 - q^31 - q^35 - q^40 + q^43 + q^45 - 
        q^46 + q^47 + q^52 - q^53 + q^58 - q^61 - q^70 + q^79 - q^80 + q^92 + 
        O(q^98),
    q^7 + q^14 + q^16 + q^20 - q^25 - q^26 - 2*q^28 + q^29 - q^31 - q^32 - q^35 
        - q^40 - q^46 + q^49 + q^52 - q^53 + q^56 + q^58 - q^61 + q^63 + q^64 + 
        q^65 - q^70 - q^80 - q^91 + q^92 + O(q^98),
    q^8 - q^14 - q^16 - q^20 + q^26 + q^28 + q^32 + q^46 - q^52 - q^56 - q^58 - 
        q^64 + q^70 + q^72 - q^92 + O(q^98),
    q^10 - q^14 - q^16 + q^28 + q^32 - q^52 - q^58 + q^86 + q^90 - q^92 + q^94 +
        O(q^98),
    q^13 + q^14 + q^20 + q^23 - q^25 - q^26 - q^28 - q^31 - q^46 - q^53 + q^58 -
        q^61 + q^65 - q^70 - q^80 + q^89 - q^91 + O(q^98)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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(
399
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
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(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*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(
399
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
18
);
qprec:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^5 + a^2)*q^3 + (a^4 - a)*q^4 + a^4*q^7 + (-a^4 + a)*q^9 + (a^3 - 
        1)*q^12 + (-a^3 + a^2)*q^13 - a^5*q^16 - q^19 + a^3*q^21 - a^4*q^25 + 
        (-a^3 + 1)*q^27 - a^2*q^28 + (a^5 - a^2 - a)*q^31 + a^5*q^36 + (a^5 - 
        a)*q^37 + (-a^2 + a)*q^39 + (-a^3 + a + 1)*q^43 - a^4*q^48 + (a^5 - 
        a^2)*q^49 + (a - 1)*q^52 + (a^5 - a^2)*q^57 + (-a^5 + a^3)*q^61 + 
        a^2*q^63 + a^3*q^64 + (a^5 + a^3 - 1)*q^67 + (-a^4 - a^3)*q^73 - 
        a^3*q^75 + (-a^4 + a)*q^76 + (a^4 - a^3 + 1)*q^79 - a^5*q^81 - a*q^84 + 
        (-a^4 + a^3 + a - 1)*q^91 + (a^4 - a - 1)*q^93 - a^5*q^97 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a^5*q^3 - a^4*q^4 + a^2*q^7 - a*q^9 - q^12 + (a^3 - a^2)*q^13 + (a^5 - 
        a^2)*q^16 - a^3*q^19 + (-a^4 + a)*q^21 + a*q^25 + (a^3 - 1)*q^27 + (-a^3
        + 1)*q^28 + (a^5 + a^4 - a)*q^31 + a^5*q^36 + (-a^5 + a^4 + a^2)*q^37 + 
        (-a^5 + a^4 + a^2 - a)*q^39 + (-a^3 + a + 1)*q^43 + a^4*q^48 + a^4*q^49 
        + (-a^4 + a^3 + a - 1)*q^52 + (a^5 - a^2)*q^57 + (-a^5 + a^3 + a^2 - 
        1)*q^61 - a^3*q^63 + a^3*q^64 + (-a^3 - a^2)*q^67 + (-a - 1)*q^73 + 
        (-a^3 + 1)*q^75 + (a^4 - a)*q^76 + (-a^4 + a - 1)*q^79 + a^2*q^81 - 
        a^2*q^84 + (a^5 - a^4)*q^91 + (a^3 + a)*q^93 + a^5*q^97 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^4 + a)*q^3 - a^5*q^4 + (a^5 - a^2)*q^7 - a^5*q^9 - a^3*q^12 + (a^4 +
        a^3 - 1)*q^13 - a*q^16 + q^19 + (a^3 - 1)*q^21 + (a^5 - a^2)*q^25 - 
        a^3*q^27 + a^4*q^28 + (-a^4 + a^2 + a)*q^31 - a*q^36 + (a^2 - a)*q^37 + 
        (a^4 + a^2)*q^39 + (-a^3 + a^2)*q^43 + (a^5 - a^2)*q^48 + (-a^4 + 
        a)*q^49 + (a^2 + 1)*q^52 + (-a^4 + a)*q^57 + (a^3 - a - 1)*q^61 + 
        a^4*q^63 + (a^3 - 1)*q^64 + (-a^3 - a)*q^67 + (a^5 + a^3 - a^2 - 1)*q^73
        + (a^3 - 1)*q^75 - a^5*q^76 + (a^5 - a^3 - a^2)*q^79 - a*q^81 + a^2*q^84
        + (-a^5 - a^3)*q^91 + (-a^5 + 1)*q^93 + a*q^97 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q - a*q^3 + (a^5 - a^2)*q^4 + a^4*q^7 + a^2*q^9 + q^12 + (a^4 + a^3 - 
        1)*q^13 + (-a^4 + a)*q^16 + (a^3 - 1)*q^19 - a^5*q^21 + a^2*q^25 - 
        a^3*q^27 - a^3*q^28 + (-a^5 - a)*q^31 - a*q^36 + (a^5 - a^4 - a^2 + 
        a)*q^37 + (-a^5 - a^4 + a)*q^39 + (-a^3 + a^2)*q^43 + (a^5 - a^2)*q^48 +
        (a^5 - a^2)*q^49 + (-a^5 - a^3)*q^52 + (-a^4 + a)*q^57 + (-a^4 - a^3 + 
        a)*q^61 + (a^3 - 1)*q^63 + (a^3 - 1)*q^64 + (a^4 + a^3 - 1)*q^67 + (a^2 
        + 1)*q^73 - a^3*q^75 - a^5*q^76 + (-a^5 + 1)*q^79 + a^4*q^81 + a^4*q^84 
        + (a^5 - a^2 - a)*q^91 + (a^3 + a^2 - 1)*q^93 + a*q^97 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + a*q^4 - 1/2*q^7 - a*q^9 + (a - 1)*q^16 + 1/2*(-a - 1)*q^21 + a*q^25 - 
        1/2*a*q^28 + (-a + 1)*q^36 + (-2*a + 1)*q^37 + q^39 + (a - 1)*q^43 - 
        1/2*q^49 + (a - 1)*q^57 + 1/2*a*q^63 - q^64 + (-a + 2)*q^67 + (-a - 
        1)*q^79 + (a - 1)*q^81 + 1/2*(-2*a + 1)*q^84 + 1/2*(-a + 2)*q^91 + (a - 
        1)*q^93 + O(q^100),
    q^3 + 1/2*(-a + 2)*q^7 + a*q^12 + (a - 1)*q^13 - a*q^19 - 1/2*q^21 - a*q^27 
        + 1/2*(a + 1)*q^28 - a*q^31 + (a - 1)*q^48 + 1/2*(a - 2)*q^49 - q^52 + 
        (-a - 1)*q^61 + 1/2*(-a - 1)*q^63 + (2*a - 1)*q^73 + a*q^75 + (-a + 
        1)*q^76 - 1/2*a*q^84 + 1/2*(-a + 1)*q^91 + 2*q^97 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^3 + (a - 1)*q^4 + (a - 1)*q^9 + q^12 + (-a + 1)*q^13 - a*q^16 + q^19
        + (a - 1)*q^25 + q^27 - q^31 - a*q^36 - q^37 - q^39 + a*q^43 + (a - 
        1)*q^48 - q^49 + a*q^52 - a*q^57 + (-a + 1)*q^61 + q^64 + (-a + 1)*q^67 
        + a*q^73 + q^75 + (a - 1)*q^76 + a*q^79 - a*q^81 + a*q^93 - 2*a*q^97 + 
        O(q^100),
    q^7 - a*q^21 + (a - 1)*q^28 - q^49 + (a - 1)*q^63 + q^84 + (-a + 1)*q^91 + 
        O(q^100)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^6 - q^7 + a*q^9 - q^10 + (a - 1)*q^13 + (-a + 1)*q^15 - q^16 
        + a*q^19 + a*q^22 + (-a + 1)*q^24 - a*q^31 - q^33 + (-a + 1)*q^37 - q^40
        + (a - 1)*q^42 - a*q^43 + q^49 + q^54 + a*q^55 + (-a + 1)*q^58 - a*q^63 
        - q^64 + q^67 + q^70 + a*q^78 - q^79 + (a - 1)*q^81 + a*q^82 + a*q^87 + 
        a*q^88 - a*q^90 + (-a + 1)*q^91 + 2*a*q^94 - a*q^97 + O(q^100),
    q^2 + (a - 1)*q^3 + q^5 + q^8 - a*q^11 - q^14 + a*q^18 + (-a + 1)*q^21 + (a 
        - 1)*q^26 - q^27 + (a - 1)*q^29 + (-a + 1)*q^30 - q^35 + a*q^38 - a*q^39
        - a*q^41 + a*q^45 - 2*a*q^47 + (-a + 1)*q^48 + q^53 - q^56 - q^57 - 
        a*q^62 + (a - 1)*q^65 - q^66 + a*q^71 + a*q^72 + (-a + 1)*q^74 + a*q^77 
        - q^80 - a*q^86 + q^93 + a*q^95 + q^98 + (-a + 1)*q^99 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^2 - q^8 + (a - 1)*q^15 + a*q^16 + a*q^21 + (a - 1)*q^23 + (-a + 
        1)*q^29 + q^30 - a*q^35 - q^39 + (-a + 1)*q^42 - a*q^43 + q^46 - q^49 + 
        (-a + 1)*q^51 + (-a + 1)*q^53 - a*q^57 - q^58 + q^64 + q^65 + (a - 
        1)*q^67 + (a - 1)*q^70 + a*q^71 + a*q^78 - a*q^79 + a*q^81 + (a - 
        1)*q^85 + (a - 1)*q^86 + (-a + 1)*q^91 + a*q^95 + a*q^98 + O(q^100),
    q^3 - a*q^6 - q^24 + (a - 1)*q^45 + a*q^48 + a*q^63 + (a - 1)*q^69 + (-a + 
        1)*q^87 + q^90 + O(q^100),
    q^5 + (-a + 1)*q^7 - a*q^10 + a*q^13 - q^14 - q^17 + (a - 1)*q^19 + (-a + 
        1)*q^26 + (-a + 1)*q^27 + a*q^34 + q^38 - q^40 - q^41 + (a - 1)*q^45 + 
        a*q^47 - q^54 + (a - 1)*q^56 + q^59 - a*q^61 + a*q^63 + q^73 + a*q^80 + 
        a*q^82 - a*q^89 + q^90 + (-a + 1)*q^94 - q^97 + O(q^100),
    q^9 - q^15 - a*q^18 + (a - 1)*q^21 + a*q^30 - a*q^39 + q^42 + q^51 + (-a + 
        1)*q^57 - q^72 + (a - 1)*q^78 + (a - 1)*q^81 + O(q^100)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a + 1)*q^6 - q^7 - q^9 + a*q^10 + (a - 1)*q^13 + (-a + 1)*q^15 + (-a +
        1)*q^16 - q^19 + a*q^22 - q^24 + (a - 1)*q^31 + (-a + 1)*q^33 + a*q^37 +
        (-a + 1)*q^40 + (a - 1)*q^42 - a*q^43 + q^49 + (a - 1)*q^54 + a*q^55 + 
        a*q^58 + q^63 - q^64 - a*q^67 - a*q^70 + a*q^78 + (-a + 1)*q^79 + q^81 -
        q^82 + (-a + 1)*q^87 + (-a + 1)*q^88 - a*q^90 + (-a + 1)*q^91 + (-2*a + 
        2)*q^94 - a*q^97 + O(q^100),
    q^2 - a*q^3 + q^5 - a*q^8 + q^11 - q^14 - q^18 + a*q^21 + (a - 1)*q^26 + 
        a*q^27 + q^29 + (-a + 1)*q^30 - q^35 - q^38 + q^39 + (a - 1)*q^41 - q^45
        - 2*a*q^47 - q^48 + (a - 1)*q^53 + a*q^56 + a*q^57 + (a - 1)*q^62 + (a -
        1)*q^65 + (-a + 1)*q^66 + (-a + 1)*q^71 + a*q^72 + a*q^74 - q^77 + (-a +
        1)*q^80 - a*q^86 + q^93 - q^95 + q^98 - q^99 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
9*H.3
;
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(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - a*q^4 + (-a + 1)*q^5 + (a - 1)*q^7 + (a - 1)*q^9 + a*q^11 + (a - 1)*q^16
        - 2*a*q^17 + (a - 1)*q^19 - q^20 + (-a + 1)*q^23 + q^28 + a*q^35 + q^36 
        - q^43 + (-a + 1)*q^44 + a*q^45 + (-a + 1)*q^47 - a*q^49 + q^55 + (-a + 
        1)*q^61 - a*q^63 + q^64 + (2*a - 2)*q^68 + a*q^73 + q^76 - q^77 + a*q^80
        - a*q^81 - q^83 - 2*q^85 - q^92 + a*q^95 - q^99 + O(q^100),
    q^3 - a*q^12 + (-a + 1)*q^15 + (a - 1)*q^21 + (a - 1)*q^27 + a*q^33 + (a - 
        1)*q^48 - 2*a*q^51 + (a - 1)*q^57 - q^60 + (-a + 1)*q^69 + q^84 + 
        O(q^100)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
399
);
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:=
100
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - q^28 - q^30 - q^39 - q^43 + q^49 - q^58 - q^64 + q^81 - q^85 - 
        q^93 + O(q^100),
    q^2 - q^14 - q^15 + q^18 - q^29 - q^32 + q^50 + q^51 + q^53 - q^60 + q^71 + 
        q^95 + q^98 + O(q^100),
    q^3 - q^12 - 2*q^13 + q^19 + q^21 + q^27 - 2*q^31 + q^48 + 2*q^52 - q^75 - 
        q^76 - q^84 - 2*q^91 + 2*q^97 + O(q^100),
    q^4 - q^7 - q^16 + q^25 - q^30 + q^36 + q^39 + q^43 - q^57 - q^58 - q^63 - 
        q^85 + q^93 + O(q^100),
    q^5 - q^6 - q^17 + q^20 - q^35 + q^38 + q^42 + q^45 - q^47 - q^54 - q^68 - 
        q^80 + q^83 + q^87 + q^96 + O(q^100),
    q^10 - q^12 - q^13 + q^19 + q^21 - q^31 - q^34 + q^48 + q^52 - q^70 - q^75 +
        q^90 - q^91 - q^94 + 2*q^97 + O(q^100)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + q^9 - 2*q^29 - 2*q^41 + q^49 - 2*q^61 + q^81 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^11 - q^19 - q^41 + q^49 + q^51 + 2*q^59 - q^81 + O(q^86),
    q^2 + q^8 - q^12 - q^22 + q^32 - q^38 - q^48 - q^68 - q^82 + O(q^86),
    q^3 + q^17 - q^27 - q^33 - 2*q^43 - q^57 + q^67 + q^73 + q^83 + O(q^86),
    q^4 - q^6 + q^16 - q^24 - q^34 - q^44 + q^54 + q^64 + q^66 - q^76 + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.2 + H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C<a>:=CyclotomicField(
20
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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(
20
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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(
20
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[
    q + (-a^3 + a^2 - a + 1)*q^5 - a^2*q^9 + (a^3 - a)*q^13 + (a^2 + a)*q^17 - 
        a^3*q^25 + (-a^2 + a - 1)*q^29 + (a^3 - a^2 + a - 2)*q^37 + (a^3 + 
        a)*q^41 - a*q^45 - q^49 + (a^2 - 1)*q^53 + (-a^3 - a + 1)*q^61 + (a^2 - 
        1)*q^65 + (a^3 - 2*a^2 + a - 1)*q^73 + (a^3 - a^2 + a - 1)*q^81 + (a + 
        1)*q^85 + O(q^86)
]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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(
20
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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(
10
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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:=
86
;
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 + O(q^86),
    q^2 - a^3*q^10 + (a^3 - a^2 + a - 1)*q^18 + (a^2 - a)*q^26 + (a^3 + a - 
        1)*q^34 - a*q^50 + (-a^3 - a)*q^58 + (-a^3 + 1)*q^74 + (a^2 - a)*q^82 + 
        O(q^86),
    q^4 - a*q^8 + a^2*q^16 - a^3*q^20 - a^3*q^32 + (a^3 - a^2 + a - 1)*q^36 + 
        (a^3 - a^2 + a - 1)*q^40 + (a^2 - a)*q^52 + (a^3 - a^2 + a - 1)*q^64 + 
        (a^3 + a - 1)*q^68 + q^72 + q^80 + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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(
20
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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(
10
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
5*H.3
;
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(
400
);
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(
4
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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(
4
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
3*H.2 + 5*H.3
;
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(
400
);
H,m:=AbelianGroup(G);
m_inv:=m^-1;
eps_H:=
H.1 + 10*H.3
;
eps:=m(eps_H);
EPS:=MinimalBaseRingCharacter(eps);
C:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^9 + 2*q^29 - 2*q^41 - q^49 - 2*q^61 + q^81 + O(q^86),
    q^5 - q^25 - q^45 + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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(
4
);
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
G:=FullDirichletGroup(
400
);
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:=Rationals();
qprec:=
86
;
Cq<q>:=PowerSeriesRing(C,qprec);
Bn:=
[]
;
Bo:=
[
    q - q^11 + q^19 - q^41 - q^49 + q^51 - 2*q^59 - q^81 + O(q^86),
    q^2 - q^8 - q^12 - q^22 + q^32 + q^38 + q^48 + q^68 - q^82 + O(q^86),
    q^3 - q^17 + q^27 - q^33 - 2*q^43 + q^57 - q^67 + q^73 + q^83 + O(q^86),
    q^4 + q^6 - q^16 - q^24 - q^34 - q^44 + q^54 + q^64 - q^66 + q^76 + O(q^86)
]
;
Append(~basis_list,[*eps,EPS,Bn,Bo*]);
