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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
200.1.e.a 200.e 40.e $2$ $0.100$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{11}+\cdots\)
200.1.g.a 200.g 8.d $1$ $0.100$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(-1\) \(1\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots\)
200.1.g.b 200.g 8.d $1$ $0.100$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots\)
200.2.a.a 200.a 1.a $1$ $1.597$ \(\Q\) None None \(0\) \(-3\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+2q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots\)
200.2.a.b 200.a 1.a $1$ $1.597$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots\)
200.2.a.c 200.a 1.a $1$ $1.597$ \(\Q\) None None \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
200.2.a.d 200.a 1.a $1$ $1.597$ \(\Q\) None None \(0\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
200.2.a.e 200.a 1.a $1$ $1.597$ \(\Q\) None None \(0\) \(3\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-2q^{7}+6q^{9}+q^{11}-4q^{13}+\cdots\)
200.2.c.a 200.c 5.b $2$ $1.597$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+2iq^{7}-6q^{9}+q^{11}-4iq^{13}+\cdots\)
200.2.c.b 200.c 5.b $2$ $1.597$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{7}+3q^{9}+4q^{11}-iq^{13}-iq^{17}+\cdots\)
200.2.d.a 200.d 8.b $2$ $1.597$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-iq^{3}-2iq^{4}+(1+i)q^{6}+\cdots\)
200.2.d.b 200.d 8.b $2$ $1.597$ \(\Q(\sqrt{-7}) \) None None \(-1\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}+(1-2\beta )q^{3}+(-2+\beta )q^{4}+\cdots\)
200.2.d.c 200.d 8.b $2$ $1.597$ \(\Q(\sqrt{-7}) \) None None \(1\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-1+2\beta )q^{3}+(-2+\beta )q^{4}+\cdots\)
200.2.d.d 200.d 8.b $2$ $1.597$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}-iq^{3}+2iq^{4}+(1-i)q^{6}+\cdots\)
200.2.d.e 200.d 8.b $4$ $1.597$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots\)
200.2.d.f 200.d 8.b $4$ $1.597$ \(\Q(\zeta_{12})\) None None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
200.2.f.a 200.f 40.f $2$ $1.597$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-q^{3}-2iq^{4}+(1-i)q^{6}+\cdots\)
200.2.f.b 200.f 40.f $2$ $1.597$ \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots\)
200.2.f.c 200.f 40.f $4$ $1.597$ \(\Q(\zeta_{12})\) None None \(-2\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
200.2.f.d 200.f 40.f $4$ $1.597$ \(\Q(i, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(-2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
200.2.f.e 200.f 40.f $4$ $1.597$ \(\Q(\zeta_{12})\) None None \(2\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots\)
200.2.k.a 200.k 40.k $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(-2\) \(-4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots\)
200.2.k.b 200.k 40.k $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{2}-2iq^{4}+(-2+2i)q^{7}+\cdots\)
200.2.k.c 200.k 40.k $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) None \(2\) \(0\) \(0\) \(4\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-i)q^{2}-2iq^{4}+(2-2i)q^{7}+(-2+\cdots)q^{8}+\cdots\)
200.2.k.d 200.k 40.k $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(2\) \(4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+i)q^{2}+(2-2i)q^{3}+2iq^{4}+4q^{6}+\cdots\)
200.2.k.e 200.k 40.k $4$ $1.597$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) None \(-4\) \(4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-\beta _{2})q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+\cdots\)
200.2.k.f 200.k 40.k $4$ $1.597$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) None \(4\) \(-4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+\beta _{2})q^{2}+(-1+\beta _{2}-\beta _{3})q^{3}+\cdots\)
200.2.k.g 200.k 40.k $8$ $1.597$ 8.0.3317760000.5 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots\)
200.2.k.h 200.k 40.k $8$ $1.597$ \(\Q(\zeta_{20})\) None None \(2\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{20}^{7}q^{2}+(1-\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{6}+\cdots)q^{3}+\cdots\)
200.2.m.a 200.m 25.d $4$ $1.597$ \(\Q(\zeta_{10})\) None None \(0\) \(5\) \(-5\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2-2\zeta_{10}-\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots\)
200.2.m.b 200.m 25.d $8$ $1.597$ 8.0.58140625.2 None None \(0\) \(-6\) \(5\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\beta _{2})q^{3}+(1+\beta _{5})q^{5}+(\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
200.2.m.c 200.m 25.d $16$ $1.597$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(1\) \(-1\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{1}q^{3}+(-1+\beta _{2}-\beta _{4}+\beta _{5}+\beta _{14}+\cdots)q^{5}+\cdots\)
200.2.o.a 200.o 200.o $112$ $1.597$ None None \(-5\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
200.2.q.a 200.q 25.e $32$ $1.597$ None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{10}]$
200.2.t.a 200.t 200.t $112$ $1.597$ None None \(-3\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{10}]$
200.2.v.a 200.v 200.v $8$ $1.597$ \(\Q(\zeta_{20})\) None None \(-8\) \(0\) \(10\) \(4\) $\mathrm{SU}(2)[C_{20}]$ \(q+(-1+\zeta_{20}^{5})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
200.2.v.b 200.v 200.v $8$ $1.597$ \(\Q(\zeta_{20})\) None None \(-2\) \(0\) \(-10\) \(-4\) $\mathrm{SU}(2)[C_{20}]$ \(q+(-\zeta_{20}-\zeta_{20}^{6})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots\)
200.2.v.c 200.v 200.v $208$ $1.597$ None None \(2\) \(-16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{20}]$
200.3.e.a 200.e 40.e $2$ $5.450$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{2}-iq^{3}-4q^{4}+4q^{6}-4iq^{8}+\cdots\)
200.3.e.b 200.e 40.e $4$ $5.450$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}-4q^{4}+(-2+\cdots)q^{6}+\cdots\)
200.3.e.c 200.e 40.e $12$ $5.450$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{6}+\beta _{9})q^{4}+\cdots\)
200.3.e.d 200.e 40.e $16$ $5.450$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{2}q^{3}+(1+\beta _{11})q^{4}+(-2+\cdots)q^{6}+\cdots\)
200.3.g.a 200.g 8.d $1$ $5.450$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(2\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+2q^{3}+4q^{4}+4q^{6}+8q^{8}+\cdots\)
200.3.g.b 200.g 8.d $2$ $5.450$ \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-2}) \) None \(-4\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+(1+\beta )q^{3}+4q^{4}+(-2-2\beta )q^{6}+\cdots\)
200.3.g.c 200.g 8.d $2$ $5.450$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{2}-4q^{4}-3iq^{7}-4iq^{8}-9q^{9}+\cdots\)
200.3.g.d 200.g 8.d $2$ $5.450$ \(\Q(\sqrt{6}) \) \(\Q(\sqrt{-2}) \) None \(4\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+(-1+\beta )q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots\)
200.3.g.e 200.g 8.d $6$ $5.450$ 6.0.189974000.1 None None \(-3\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
200.3.g.f 200.g 8.d $6$ $5.450$ 6.0.189974000.1 None None \(3\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots\)
200.3.g.g 200.g 8.d $8$ $5.450$ 8.0.\(\cdots\).1 None None \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}+\beta _{6}q^{3}+(-1+\beta _{1})q^{4}+(-1+\cdots)q^{6}+\cdots\)
200.3.g.h 200.g 8.d $8$ $5.450$ 8.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{6}q^{3}+(2+\beta _{5})q^{4}+(2-\beta _{2}+\cdots)q^{6}+\cdots\)
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