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Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 2 5 31
9610.2.a.a 9610.a 1.a $1$ $76.736$ \(\Q\) None 310.2.a.b \(1\) \(-2\) \(-1\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{8}+\cdots\)
9610.2.a.b 9610.a 1.a $1$ $76.736$ \(\Q\) None 310.2.a.a \(1\) \(2\) \(-1\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots\)
9610.2.a.c 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{5}) \) None 310.2.h.a \(-2\) \(-2\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(-1+\cdots)q^{7}+\cdots\)
9610.2.a.d 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{5}) \) None 310.2.h.b \(-2\) \(-2\) \(2\) \(6\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+3q^{7}+\cdots\)
9610.2.a.e 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.e \(-2\) \(0\) \(-2\) \(-4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}-q^{5}-\beta q^{6}-2q^{7}+\cdots\)
9610.2.a.f 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{6}) \) None 310.2.a.d \(-2\) \(0\) \(2\) \(-4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}-2q^{7}+\cdots\)
9610.2.a.g 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.g \(-2\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-3q^{9}-q^{10}+\cdots\)
9610.2.a.h 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.h \(-2\) \(0\) \(2\) \(0\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2\beta q^{3}+q^{4}+q^{5}-2\beta q^{6}+\cdots\)
9610.2.a.i 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.i \(-2\) \(0\) \(2\) \(4\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta q^{3}+q^{4}+q^{5}-\beta q^{6}+2q^{7}+\cdots\)
9610.2.a.j 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{3}) \) None 310.2.a.c \(-2\) \(2\) \(-2\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta )q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
9610.2.a.k 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{5}) \) None 310.2.h.a \(-2\) \(2\) \(2\) \(-4\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots\)
9610.2.a.l 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{5}) \) None 310.2.h.b \(-2\) \(2\) \(2\) \(6\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+3q^{7}+\cdots\)
9610.2.a.m 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.m \(2\) \(0\) \(-2\) \(-4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}-2q^{7}+\cdots\)
9610.2.a.n 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.n \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+q^{8}-3q^{9}-q^{10}+\cdots\)
9610.2.a.o 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.o \(2\) \(0\) \(-2\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}-q^{5}+\beta q^{6}+q^{8}+\cdots\)
9610.2.a.p 9610.a 1.a $2$ $76.736$ \(\Q(\sqrt{2}) \) None 9610.2.a.p \(2\) \(0\) \(2\) \(-8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta q^{3}+q^{4}+q^{5}+\beta q^{6}-4q^{7}+\cdots\)
9610.2.a.q 9610.a 1.a $3$ $76.736$ 3.3.4065.1 None 310.2.e.b \(-3\) \(-1\) \(-3\) \(2\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
9610.2.a.r 9610.a 1.a $3$ $76.736$ 3.3.321.1 None 310.2.e.a \(-3\) \(-1\) \(3\) \(-2\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}+q^{5}-\beta _{2}q^{6}+\cdots\)
9610.2.a.s 9610.a 1.a $3$ $76.736$ 3.3.4065.1 None 310.2.e.b \(-3\) \(1\) \(-3\) \(2\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9610.2.a.t 9610.a 1.a $3$ $76.736$ 3.3.321.1 None 310.2.e.a \(-3\) \(1\) \(3\) \(-2\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+q^{5}+\beta _{2}q^{6}+\cdots\)
9610.2.a.u 9610.a 1.a $3$ $76.736$ 3.3.148.1 None 310.2.a.e \(3\) \(-2\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
9610.2.a.v 9610.a 1.a $3$ $76.736$ 3.3.321.1 None 310.2.e.c \(3\) \(-1\) \(-3\) \(4\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9610.2.a.w 9610.a 1.a $3$ $76.736$ 3.3.169.1 None 310.2.e.d \(3\) \(-1\) \(3\) \(0\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{1}q^{3}+q^{4}+q^{5}-\beta _{1}q^{6}+\cdots\)
9610.2.a.x 9610.a 1.a $3$ $76.736$ 3.3.321.1 None 310.2.e.c \(3\) \(1\) \(-3\) \(4\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}+\beta _{1}q^{6}+\cdots\)
9610.2.a.y 9610.a 1.a $3$ $76.736$ 3.3.169.1 None 310.2.e.d \(3\) \(1\) \(3\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1}+\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
9610.2.a.z 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.e \(-4\) \(-6\) \(-4\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-2-\beta _{3})q^{3}+q^{4}-q^{5}+(2+\cdots)q^{6}+\cdots\)
9610.2.a.ba 9610.a 1.a $4$ $76.736$ \(\Q(\sqrt{2}, \sqrt{5})\) None 310.2.h.e \(-4\) \(-4\) \(-4\) \(0\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1})q^{3}+q^{4}-q^{5}+(1+\cdots)q^{6}+\cdots\)
9610.2.a.bb 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.f \(-4\) \(-4\) \(-4\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{3}+q^{4}+\cdots\)
9610.2.a.bc 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.d \(-4\) \(-2\) \(-4\) \(-8\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
9610.2.a.bd 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.bd \(-4\) \(0\) \(-4\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9610.2.a.be 9610.a 1.a $4$ $76.736$ \(\Q(\sqrt{2}, \sqrt{5})\) None 9610.2.a.be \(-4\) \(0\) \(-4\) \(4\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}-q^{5}-\beta _{1}q^{6}+\cdots\)
9610.2.a.bf 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.bf \(-4\) \(0\) \(-4\) \(8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(\beta _{1}+\beta _{3})q^{3}+q^{4}-q^{5}+(-\beta _{1}+\cdots)q^{6}+\cdots\)
9610.2.a.bg 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.d \(-4\) \(2\) \(-4\) \(-8\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
9610.2.a.bh 9610.a 1.a $4$ $76.736$ \(\Q(\sqrt{2}, \sqrt{5})\) None 310.2.h.e \(-4\) \(4\) \(-4\) \(0\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{1})q^{3}+q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots\)
9610.2.a.bi 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.f \(-4\) \(4\) \(-4\) \(3\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+q^{4}-q^{5}+\cdots\)
9610.2.a.bj 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.e \(-4\) \(6\) \(-4\) \(3\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(2+\beta _{3})q^{3}+q^{4}-q^{5}+(-2+\cdots)q^{6}+\cdots\)
9610.2.a.bk 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.c \(4\) \(-4\) \(4\) \(-4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{3}+q^{4}+\cdots\)
9610.2.a.bl 9610.a 1.a $4$ $76.736$ \(\Q(\sqrt{2}, \sqrt{5})\) None 310.2.h.d \(4\) \(-4\) \(4\) \(4\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{3})q^{3}+q^{4}+q^{5}+(-1+\cdots)q^{6}+\cdots\)
9610.2.a.bm 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.a \(4\) \(-2\) \(4\) \(1\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
9610.2.a.bn 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.b \(4\) \(-2\) \(4\) \(3\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{3}q^{3}+q^{4}+q^{5}+\beta _{3}q^{6}+\cdots\)
9610.2.a.bo 9610.a 1.a $4$ $76.736$ 4.4.4400.1 None 310.2.h.c \(4\) \(0\) \(-4\) \(2\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{3}q^{3}+q^{4}-q^{5}-\beta _{3}q^{6}+\cdots\)
9610.2.a.bp 9610.a 1.a $4$ $76.736$ 4.4.4400.1 None 310.2.h.c \(4\) \(0\) \(-4\) \(2\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{3}q^{3}+q^{4}-q^{5}-\beta _{3}q^{6}+\cdots\)
9610.2.a.bq 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.bq \(4\) \(0\) \(4\) \(-8\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(\beta _{1}+\beta _{3})q^{3}+q^{4}+q^{5}+(\beta _{1}+\cdots)q^{6}+\cdots\)
9610.2.a.br 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.br \(4\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(-\beta _{2}+\beta _{3})q^{3}+q^{4}+q^{5}+\cdots\)
9610.2.a.bs 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.bs \(4\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+\beta _{1}q^{3}+q^{4}+q^{5}+\beta _{1}q^{6}+\cdots\)
9610.2.a.bt 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.br \(4\) \(0\) \(4\) \(0\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(\beta _{2}+\beta _{3})q^{3}+q^{4}+q^{5}+(\beta _{2}+\cdots)q^{6}+\cdots\)
9610.2.a.bu 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{16})^+\) None 9610.2.a.bu \(4\) \(0\) \(4\) \(16\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(\beta _{1}+2\beta _{3})q^{3}+q^{4}+q^{5}+(\beta _{1}+\cdots)q^{6}+\cdots\)
9610.2.a.bv 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.a \(4\) \(2\) \(4\) \(1\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
9610.2.a.bw 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.b \(4\) \(2\) \(4\) \(3\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+q^{2}-\beta _{3}q^{3}+q^{4}+q^{5}-\beta _{3}q^{6}+\cdots\)
9610.2.a.bx 9610.a 1.a $4$ $76.736$ \(\Q(\zeta_{15})^+\) None 310.2.q.c \(4\) \(4\) \(4\) \(-4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q+q^{2}+(1+\beta _{1}-\beta _{2})q^{3}+q^{4}+q^{5}+\cdots\)
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