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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
800.1.e.a 800.e 40.e $2$ $0.399$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}+q^{11}-iq^{17}-q^{19}-iq^{27}+\cdots\)
800.1.g.a 800.g 8.d $1$ $0.399$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-q^{3}+q^{11}+q^{17}+q^{19}+q^{27}+\cdots\)
800.1.g.b 800.g 8.d $1$ $0.399$ \(\Q\) \(\Q(\sqrt{-2}) \) None \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{11}-q^{17}+q^{19}-q^{27}+\cdots\)
800.1.p.a 800.p 5.c $2$ $0.399$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(2\) \(q+(-1+i)q^{3}+(1+i)q^{7}-iq^{9}-q^{21}+\cdots\)
800.1.p.b 800.p 5.c $2$ $0.399$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{9}+(1-i)q^{13}+(1+i)q^{17}+(-1+\cdots)q^{37}+\cdots\)
800.1.p.c 800.p 5.c $2$ $0.399$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(-2\) \(q+(1-i)q^{3}+(-1-i)q^{7}-iq^{9}-q^{21}+\cdots\)
800.1.bh.a 800.bh 100.j $8$ $0.399$ \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{20}^{7}q^{3}+\zeta_{20}^{4}q^{5}+(\zeta_{20}+\zeta_{20}^{9}+\cdots)q^{7}+\cdots\)
800.1.bo.a 800.bo 25.f $8$ $0.399$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{7}q^{5}+\zeta_{20}q^{9}+(-\zeta_{20}^{8}+\zeta_{20}^{9}+\cdots)q^{13}+\cdots\)
800.2.a.a 800.a 1.a $1$ $6.388$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
800.2.a.b 800.a 1.a $1$ $6.388$ \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}-2q^{9}-5q^{11}+5q^{17}+\cdots\)
800.2.a.c 800.a 1.a $1$ $6.388$ \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}-2q^{9}+5q^{11}-5q^{17}+\cdots\)
800.2.a.d 800.a 1.a $1$ $6.388$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-3q^{9}-6q^{13}-2q^{17}-10q^{29}+\cdots\)
800.2.a.e 800.a 1.a $1$ $6.388$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-3q^{9}-4q^{13}-8q^{17}+10q^{29}+\cdots\)
800.2.a.f 800.a 1.a $1$ $6.388$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-3q^{9}+4q^{13}+8q^{17}+10q^{29}+\cdots\)
800.2.a.g 800.a 1.a $1$ $6.388$ \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}-2q^{9}-5q^{11}-5q^{17}+\cdots\)
800.2.a.h 800.a 1.a $1$ $6.388$ \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}-2q^{9}+5q^{11}+5q^{17}+\cdots\)
800.2.a.i 800.a 1.a $1$ $6.388$ \(\Q\) None None \(0\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
800.2.a.j 800.a 1.a $2$ $6.388$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(-6\) $+$ $N(\mathrm{U}(1))$ \(q+(-1-\beta )q^{3}+(-3+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
800.2.a.k 800.a 1.a $2$ $6.388$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-2\beta q^{7}+2q^{9}+\beta q^{11}-4q^{13}+\cdots\)
800.2.a.l 800.a 1.a $2$ $6.388$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-2\beta q^{7}+2q^{9}-\beta q^{11}+4q^{13}+\cdots\)
800.2.a.m 800.a 1.a $2$ $6.388$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-\beta q^{7}+5q^{9}+2\beta q^{11}+2q^{13}+\cdots\)
800.2.a.n 800.a 1.a $2$ $6.388$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(6\) $-$ $N(\mathrm{U}(1))$ \(q+(1+\beta )q^{3}+(3-\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
800.2.c.a 800.c 5.b $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{7}-q^{9}-4q^{11}+3iq^{13}+\cdots\)
800.2.c.b 800.c 5.b $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{7}-q^{9}+4q^{11}-3iq^{13}+\cdots\)
800.2.c.c 800.c 5.b $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{7}+2q^{9}-5q^{11}+5iq^{17}+\cdots\)
800.2.c.d 800.c 5.b $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{7}+2q^{9}+5q^{11}-5iq^{17}+\cdots\)
800.2.c.e 800.c 5.b $2$ $6.388$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3q^{9}+3iq^{13}-iq^{17}+10q^{29}+\cdots\)
800.2.c.f 800.c 5.b $4$ $6.388$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{7}-5q^{9}+\zeta_{8}^{3}q^{11}+\cdots\)
800.2.c.g 800.c 5.b $4$ $6.388$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-2\beta _{2}q^{7}-2q^{9}+\beta _{3}q^{11}+\cdots\)
800.2.d.a 800.d 8.b $2$ $6.388$ \(\Q(\sqrt{-7}) \) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}-4q^{7}-4q^{9}+\beta q^{11}-3q^{17}+\cdots\)
800.2.d.b 800.d 8.b $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-2q^{7}+2q^{9}-5iq^{11}-6iq^{13}+\cdots\)
800.2.d.c 800.d 8.b $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2q^{7}+2q^{9}+5iq^{11}-6iq^{13}+\cdots\)
800.2.d.d 800.d 8.b $2$ $6.388$ \(\Q(\sqrt{-7}) \) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+4q^{7}-4q^{9}-\beta q^{11}+3q^{17}+\cdots\)
800.2.d.e 800.d 8.b $4$ $6.388$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{3}q^{3}+(-1-\zeta_{12})q^{7}+(-1+\cdots)q^{9}+\cdots\)
800.2.d.f 800.d 8.b $4$ $6.388$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{7}+q^{9}+\beta _{3}q^{11}-2\beta _{2}q^{17}+\cdots\)
800.2.f.a 800.f 40.f $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-2iq^{7}-2q^{9}+5iq^{11}+6q^{13}+\cdots\)
800.2.f.b 800.f 40.f $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+2iq^{7}-2q^{9}+5iq^{11}-6q^{13}+\cdots\)
800.2.f.c 800.f 40.f $4$ $6.388$ \(\Q(\zeta_{12})\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\zeta_{12})q^{3}+\zeta_{12}^{3}q^{7}+(1+2\zeta_{12}+\cdots)q^{9}+\cdots\)
800.2.f.d 800.f 40.f $4$ $6.388$ \(\Q(i, \sqrt{7})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+4\beta _{1}q^{7}+4q^{9}-\beta _{3}q^{11}+\cdots\)
800.2.f.e 800.f 40.f $4$ $6.388$ \(\Q(\zeta_{12})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\zeta_{12})q^{3}-\zeta_{12}^{3}q^{7}+(1+2\zeta_{12}+\cdots)q^{9}+\cdots\)
800.2.n.a 800.n 20.e $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2i)q^{3}+(-2+2i)q^{7}+5iq^{9}+\cdots\)
800.2.n.b 800.n 20.e $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(-1+i)q^{7}-iq^{9}+\cdots\)
800.2.n.c 800.n 20.e $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(-1+i)q^{7}-iq^{9}+\cdots\)
800.2.n.d 800.n 20.e $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(-1+i)q^{7}-iq^{9}+\cdots\)
800.2.n.e 800.n 20.e $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(3-3i)q^{7}-iq^{9}+\cdots\)
800.2.n.f 800.n 20.e $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(-3+3i)q^{7}-iq^{9}+\cdots\)
800.2.n.g 800.n 20.e $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(1-i)q^{7}-iq^{9}+4iq^{11}+\cdots\)
800.2.n.h 800.n 20.e $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(1-i)q^{7}-iq^{9}-6iq^{11}+\cdots\)
800.2.n.i 800.n 20.e $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(1-i)q^{7}-iq^{9}-4iq^{11}+\cdots\)
800.2.n.j 800.n 20.e $2$ $6.388$ \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2i)q^{3}+(2-2i)q^{7}+5iq^{9}+\cdots\)
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