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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1792.1.c.a 1792.c 7.b $1$ $0.894$ \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) 56.1.h.a \(0\) \(0\) \(0\) \(-1\) \(q-q^{7}+q^{9}+2q^{23}+q^{25}+q^{49}+\cdots\)
1792.1.c.b 1792.c 7.b $1$ $0.894$ \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) 56.1.h.a \(0\) \(0\) \(0\) \(1\) \(q+q^{7}+q^{9}-2q^{23}+q^{25}+q^{49}+\cdots\)
1792.1.c.c 1792.c 7.b $2$ $0.894$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-14}) \) None 896.1.h.a \(0\) \(0\) \(0\) \(-2\) \(q-\beta q^{3}-\beta q^{5}-q^{7}-q^{9}-\beta q^{13}+\cdots\)
1792.1.c.d 1792.c 7.b $2$ $0.894$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-14}) \) None 896.1.h.a \(0\) \(0\) \(0\) \(2\) \(q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-\beta q^{13}+\cdots\)
1792.1.o.a 1792.o 56.k $4$ $0.894$ \(\Q(\zeta_{12})\) None None 224.1.r.a \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1792.1.o.b 1792.o 56.k $4$ $0.894$ \(\Q(\zeta_{12})\) None None 224.1.r.a \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1792.1.v.a 1792.v 224.v $4$ $0.894$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None 224.1.v.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{9}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{11}+\cdots\)
1792.1.v.b 1792.v 224.v $4$ $0.894$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \) None 224.1.v.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{9}+(-\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)
1792.1.bf.a 1792.bf 448.af $8$ $0.894$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-7}) \) None 448.1.bf.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}^{7}q^{7}+\zeta_{16}q^{9}+(-\zeta_{16}^{2}-\zeta_{16}^{5}+\cdots)q^{11}+\cdots\)
1792.1.bt.a 1792.bt 1792.at $32$ $0.894$ \(\Q(\zeta_{64})\) \(\Q(\sqrt{-7}) \) None 1792.1.bt.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{64}^{3}q^{2}+\zeta_{64}^{6}q^{4}-\zeta_{64}^{7}q^{7}+\cdots\)
1792.2.a.a 1792.a 1.a $1$ $14.309$ \(\Q\) None None 448.2.b.a \(0\) \(-2\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{5}+q^{7}+q^{9}-2q^{11}+\cdots\)
1792.2.a.b 1792.a 1.a $1$ $14.309$ \(\Q\) None None 896.2.b.a \(0\) \(-2\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}+\cdots\)
1792.2.a.c 1792.a 1.a $1$ $14.309$ \(\Q\) None None 896.2.b.a \(0\) \(-2\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{5}-q^{7}+q^{9}-2q^{13}+\cdots\)
1792.2.a.d 1792.a 1.a $1$ $14.309$ \(\Q\) None None 448.2.b.a \(0\) \(-2\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
1792.2.a.e 1792.a 1.a $1$ $14.309$ \(\Q\) None None 448.2.b.a \(0\) \(2\) \(-4\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
1792.2.a.f 1792.a 1.a $1$ $14.309$ \(\Q\) None None 896.2.b.a \(0\) \(2\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+\cdots\)
1792.2.a.g 1792.a 1.a $1$ $14.309$ \(\Q\) None None 896.2.b.a \(0\) \(2\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{5}+q^{7}+q^{9}-2q^{13}+\cdots\)
1792.2.a.h 1792.a 1.a $1$ $14.309$ \(\Q\) None None 448.2.b.a \(0\) \(2\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+\cdots\)
1792.2.a.i 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{3}) \) None None 448.2.b.c \(0\) \(-2\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots\)
1792.2.a.j 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{5}) \) None None 896.2.b.e \(0\) \(-2\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+\cdots\)
1792.2.a.k 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{3}) \) None None 448.2.b.c \(0\) \(-2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
1792.2.a.l 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{5}) \) None None 896.2.b.e \(0\) \(-2\) \(2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
1792.2.a.m 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{2}) \) None None 896.2.b.b \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{5}-q^{7}-3q^{9}+\beta q^{11}-\beta q^{13}+\cdots\)
1792.2.a.n 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{2}) \) None None 56.2.b.a \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{5}-q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1792.2.a.o 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{2}) \) None None 896.2.b.b \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{5}+q^{7}-3q^{9}+\beta q^{11}+\beta q^{13}+\cdots\)
1792.2.a.p 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{2}) \) None None 56.2.b.a \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1792.2.a.q 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{3}) \) None None 448.2.b.c \(0\) \(2\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
1792.2.a.r 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{5}) \) None None 896.2.b.e \(0\) \(2\) \(-2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
1792.2.a.s 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{3}) \) None None 448.2.b.c \(0\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots\)
1792.2.a.t 1792.a 1.a $2$ $14.309$ \(\Q(\sqrt{5}) \) None None 896.2.b.e \(0\) \(2\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots\)
1792.2.a.u 1792.a 1.a $4$ $14.309$ \(\Q(\zeta_{16})^+\) None None 896.2.b.f \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-\beta _{1}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1792.2.a.v 1792.a 1.a $4$ $14.309$ 4.4.9248.1 None None 56.2.b.b \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-\beta _{1}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots\)
1792.2.a.w 1792.a 1.a $4$ $14.309$ \(\Q(\zeta_{16})^+\) None None 896.2.b.f \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1792.2.a.x 1792.a 1.a $4$ $14.309$ 4.4.9248.1 None None 56.2.b.b \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+\beta _{1}q^{5}+q^{7}+(2-\beta _{3})q^{9}+\cdots\)
1792.2.b.a 1792.b 8.b $2$ $14.309$ \(\Q(\sqrt{-1}) \) None None 56.2.a.b \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+2\beta q^{5}-q^{7}-q^{9}-8 q^{15}+\cdots\)
1792.2.b.b 1792.b 8.b $2$ $14.309$ \(\Q(\sqrt{-1}) \) None None 224.2.a.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-q^{7}-q^{9}-2\beta q^{11}-2\beta q^{13}+\cdots\)
1792.2.b.c 1792.b 8.b $2$ $14.309$ \(\Q(\sqrt{-1}) \) None None 14.2.a.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-q^{7}-q^{9}+2\beta q^{13}+6 q^{17}+\cdots\)
1792.2.b.d 1792.b 8.b $2$ $14.309$ \(\Q(\sqrt{-1}) \) None None 56.2.a.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{5}-q^{7}+3 q^{9}-2\beta q^{11}+\beta q^{13}+\cdots\)
1792.2.b.e 1792.b 8.b $2$ $14.309$ \(\Q(\sqrt{-1}) \) None None 896.2.a.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{7}+3 q^{9}-\beta q^{11}+2\beta q^{13}-2 q^{17}+\cdots\)
1792.2.b.f 1792.b 8.b $2$ $14.309$ \(\Q(\sqrt{-1}) \) None None 224.2.a.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+q^{7}-q^{9}-2\beta q^{11}+2\beta q^{13}+\cdots\)
1792.2.b.g 1792.b 8.b $2$ $14.309$ \(\Q(\sqrt{-1}) \) None None 14.2.a.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+q^{7}-q^{9}-2\beta q^{13}+6 q^{17}+\cdots\)
1792.2.b.h 1792.b 8.b $2$ $14.309$ \(\Q(\sqrt{-1}) \) None None 56.2.a.b \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-2\beta q^{5}+q^{7}-q^{9}+8 q^{15}+\cdots\)
1792.2.b.i 1792.b 8.b $2$ $14.309$ \(\Q(\sqrt{-1}) \) None None 56.2.a.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{5}+q^{7}+3 q^{9}+2\beta q^{11}+\beta q^{13}+\cdots\)
1792.2.b.j 1792.b 8.b $2$ $14.309$ \(\Q(\sqrt{-1}) \) None None 896.2.a.a \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{7}+3 q^{9}+\beta q^{11}+2\beta q^{13}-2 q^{17}+\cdots\)
1792.2.b.k 1792.b 8.b $4$ $14.309$ \(\Q(i, \sqrt{5})\) None None 224.2.a.c \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+(-3+\cdots)q^{9}+\cdots\)
1792.2.b.l 1792.b 8.b $4$ $14.309$ \(\Q(\zeta_{12})\) None None 896.2.a.e \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_{2} q^{3}-\beta_1 q^{5}-q^{7}+(\beta_{3}-1)q^{9}+\cdots\)
1792.2.b.m 1792.b 8.b $4$ $14.309$ \(\Q(i, \sqrt{5})\) None None 224.2.a.c \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+q^{7}+(-3+\cdots)q^{9}+\cdots\)
1792.2.b.n 1792.b 8.b $4$ $14.309$ \(\Q(\zeta_{12})\) None None 896.2.a.e \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_{2} q^{3}+\beta_1 q^{5}+q^{7}+(\beta_{3}-1)q^{9}+\cdots\)
1792.2.b.o 1792.b 8.b $6$ $14.309$ 6.0.399424.1 None None 896.2.a.i \(0\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}+\beta _{4}q^{5}-q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots\)
1792.2.b.p 1792.b 8.b $6$ $14.309$ 6.0.399424.1 None None 896.2.a.i \(0\) \(0\) \(0\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}-\beta _{4}q^{5}+q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots\)
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