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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
832.1.c.a 832.c 52.b $1$ $0.415$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-13}) \) \(\Q(\sqrt{13}) \) 208.1.c.a \(0\) \(0\) \(0\) \(0\) \(q+q^{9}+q^{13}-2q^{17}+q^{25}+2q^{29}+\cdots\)
832.1.t.a 832.t 13.d $2$ $0.415$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 416.1.t.a \(0\) \(0\) \(-2\) \(0\) \(q+(-1+i)q^{5}-q^{9}+iq^{13}+iq^{17}+\cdots\)
832.1.y.a 832.y 52.i $2$ $0.415$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None 208.1.y.a \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{13}+\cdots\)
832.1.bb.a 832.bb 52.j $2$ $0.415$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None 52.1.j.a \(0\) \(0\) \(2\) \(0\) \(q+q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+\zeta_{6}q^{17}+\cdots\)
832.1.bb.b 832.bb 52.j $4$ $0.415$ \(\Q(\zeta_{12})\) None None 416.1.bb.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{5}q^{11}+\cdots\)
832.1.bl.a 832.bl 13.f $4$ $0.415$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None 416.1.bl.a \(0\) \(0\) \(2\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{2})q^{5}-\zeta_{12}^{4}q^{9}-\zeta_{12}^{5}q^{13}+\cdots\)
832.2.a.a 832.a 1.a $1$ $6.644$ \(\Q\) None None 26.2.a.b \(0\) \(-3\) \(1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}-q^{7}+6q^{9}-2q^{11}+\cdots\)
832.2.a.b 832.a 1.a $1$ $6.644$ \(\Q\) None None 416.2.a.a \(0\) \(-1\) \(-1\) \(3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+3q^{7}-2q^{9}-2q^{11}+\cdots\)
832.2.a.c 832.a 1.a $1$ $6.644$ \(\Q\) None None 104.2.a.a \(0\) \(-1\) \(1\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+5q^{7}-2q^{9}+2q^{11}+\cdots\)
832.2.a.d 832.a 1.a $1$ $6.644$ \(\Q\) None None 26.2.a.a \(0\) \(-1\) \(3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}-q^{7}-2q^{9}-6q^{11}+\cdots\)
832.2.a.e 832.a 1.a $1$ $6.644$ \(\Q\) None None 52.2.a.a \(0\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}-3q^{9}+2q^{11}+q^{13}+\cdots\)
832.2.a.f 832.a 1.a $1$ $6.644$ \(\Q\) None None 52.2.a.a \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}-3q^{9}-2q^{11}+q^{13}+\cdots\)
832.2.a.g 832.a 1.a $1$ $6.644$ \(\Q\) None None 416.2.a.a \(0\) \(1\) \(-1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-3q^{7}-2q^{9}+2q^{11}+\cdots\)
832.2.a.h 832.a 1.a $1$ $6.644$ \(\Q\) None None 104.2.a.a \(0\) \(1\) \(1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-5q^{7}-2q^{9}-2q^{11}+\cdots\)
832.2.a.i 832.a 1.a $1$ $6.644$ \(\Q\) None None 26.2.a.a \(0\) \(1\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{5}+q^{7}-2q^{9}+6q^{11}+\cdots\)
832.2.a.j 832.a 1.a $1$ $6.644$ \(\Q\) None None 26.2.a.b \(0\) \(3\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}+q^{7}+6q^{9}+2q^{11}+\cdots\)
832.2.a.k 832.a 1.a $2$ $6.644$ \(\Q(\sqrt{17}) \) None None 104.2.a.b \(0\) \(-1\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-2+\beta )q^{5}-\beta q^{7}+(1+\beta )q^{9}+\cdots\)
832.2.a.l 832.a 1.a $2$ $6.644$ \(\Q(\sqrt{17}) \) None None 416.2.a.c \(0\) \(-1\) \(3\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(2-\beta )q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
832.2.a.m 832.a 1.a $2$ $6.644$ \(\Q(\sqrt{5}) \) None None 416.2.a.d \(0\) \(0\) \(-6\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-3q^{5}+\beta q^{7}+2q^{9}+2\beta q^{11}+\cdots\)
832.2.a.n 832.a 1.a $2$ $6.644$ \(\Q(\sqrt{17}) \) None None 104.2.a.b \(0\) \(1\) \(-3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(-2+\beta )q^{5}+\beta q^{7}+(1+\beta )q^{9}+\cdots\)
832.2.a.o 832.a 1.a $2$ $6.644$ \(\Q(\sqrt{17}) \) None None 416.2.a.c \(0\) \(1\) \(3\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2-\beta )q^{5}+(-2+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
832.2.a.p 832.a 1.a $4$ $6.644$ 4.4.13448.1 None None 416.2.a.f \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
832.2.b.a 832.b 8.b $4$ $6.644$ \(\Q(\zeta_{8})\) None None 832.2.b.a \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(-\zeta_{8}+2\zeta_{8}^{2})q^{5}+\cdots\)
832.2.b.b 832.b 8.b $4$ $6.644$ \(\Q(\zeta_{8})\) None None 832.2.b.a \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2})q^{3}+(\zeta_{8}-2\zeta_{8}^{2})q^{5}+(3+\cdots)q^{7}+\cdots\)
832.2.b.c 832.b 8.b $8$ $6.644$ 8.0.195105024.2 None None 832.2.b.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}-\beta _{4}q^{5}+(-\beta _{1}-\beta _{7})q^{7}+\cdots\)
832.2.b.d 832.b 8.b $8$ $6.644$ 8.0.195105024.2 None None 832.2.b.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+\beta _{4}q^{5}+(\beta _{1}+\beta _{7})q^{7}+(-1+\cdots)q^{9}+\cdots\)
832.2.e.a 832.e 104.e $4$ $6.644$ \(\Q(\zeta_{12})\) None None 832.2.e.a \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{3}-3q^{5}-\zeta_{12}q^{7}+2q^{9}+\cdots\)
832.2.e.b 832.e 104.e $4$ $6.644$ \(\Q(\zeta_{12})\) None None 832.2.e.a \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{3}+3q^{5}+\zeta_{12}q^{7}+2q^{9}+\cdots\)
832.2.e.c 832.e 104.e $8$ $6.644$ 8.0.3317760000.2 None None 832.2.e.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{2}q^{7}-q^{9}-\beta _{4}q^{11}+(\beta _{5}+\cdots)q^{13}+\cdots\)
832.2.e.d 832.e 104.e $12$ $6.644$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) \(\Q(\sqrt{-26}) \) None 832.2.e.d \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{3}-\beta _{5}q^{5}-\beta _{3}q^{7}+(-3-\beta _{7}+\cdots)q^{9}+\cdots\)
832.2.f.a 832.f 13.b $2$ $6.644$ \(\Q(\sqrt{-1}) \) None None 416.2.f.a \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-3q^{3}-3iq^{5}+iq^{7}+6q^{9}+4iq^{11}+\cdots\)
832.2.f.b 832.f 13.b $2$ $6.644$ \(\Q(\sqrt{-1}) \) None None 26.2.b.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}-iq^{7}-2q^{9}+(-2-i)q^{13}+\cdots\)
832.2.f.c 832.f 13.b $2$ $6.644$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 416.2.f.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2iq^{5}-3q^{9}+(3-i)q^{13}-2q^{17}+\cdots\)
832.2.f.d 832.f 13.b $2$ $6.644$ \(\Q(\sqrt{-1}) \) None None 26.2.b.a \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+iq^{5}+iq^{7}-2q^{9}+(-2-i)q^{13}+\cdots\)
832.2.f.e 832.f 13.b $2$ $6.644$ \(\Q(\sqrt{-1}) \) None None 416.2.f.a \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3q^{3}-3iq^{5}-iq^{7}+6q^{9}-4iq^{11}+\cdots\)
832.2.f.f 832.f 13.b $4$ $6.644$ \(\Q(i, \sqrt{17})\) None None 104.2.f.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{3})q^{3}-\beta _{1}q^{5}+(-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
832.2.f.g 832.f 13.b $4$ $6.644$ \(\Q(i, \sqrt{13})\) \(\Q(\sqrt{-13}) \) None 416.2.f.d \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{7}-3q^{9}+(-\beta _{1}-\beta _{2})q^{11}+\cdots\)
832.2.f.h 832.f 13.b $4$ $6.644$ \(\Q(i, \sqrt{5})\) None None 416.2.f.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+\beta _{1}q^{5}+\beta _{2}q^{7}+2q^{9}+(-2+\cdots)q^{13}+\cdots\)
832.2.f.i 832.f 13.b $4$ $6.644$ \(\Q(i, \sqrt{17})\) None None 104.2.f.a \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1-\beta _{3})q^{3}-\beta _{1}q^{5}+(\beta _{1}-\beta _{2})q^{7}+\cdots\)
832.2.i.a 832.i 13.c $2$ $6.644$ \(\Q(\sqrt{-3}) \) None None 52.2.e.a \(0\) \(-3\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-3+3\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
832.2.i.b 832.i 13.c $2$ $6.644$ \(\Q(\sqrt{-3}) \) None None 416.2.i.a \(0\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}-q^{5}-\zeta_{6}q^{9}+(-4+\cdots)q^{11}+\cdots\)
832.2.i.c 832.i 13.c $2$ $6.644$ \(\Q(\sqrt{-3}) \) None None 52.2.e.b \(0\) \(-2\) \(6\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+3q^{5}+4\zeta_{6}q^{7}+\cdots\)
832.2.i.d 832.i 13.c $2$ $6.644$ \(\Q(\sqrt{-3}) \) None None 104.2.i.a \(0\) \(-1\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{3}-2q^{5}-\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
832.2.i.e 832.i 13.c $2$ $6.644$ \(\Q(\sqrt{-3}) \) None None 26.2.c.a \(0\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{5}-4\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
832.2.i.f 832.i 13.c $2$ $6.644$ \(\Q(\sqrt{-3}) \) None None 26.2.c.a \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{5}+4\zeta_{6}q^{7}+3\zeta_{6}q^{9}+(-4+4\zeta_{6})q^{11}+\cdots\)
832.2.i.g 832.i 13.c $2$ $6.644$ \(\Q(\sqrt{-3}) \) None None 104.2.i.a \(0\) \(1\) \(-4\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}-2q^{5}+\zeta_{6}q^{7}+2\zeta_{6}q^{9}+\cdots\)
832.2.i.h 832.i 13.c $2$ $6.644$ \(\Q(\sqrt{-3}) \) None None 416.2.i.a \(0\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}-q^{5}-\zeta_{6}q^{9}+(4-4\zeta_{6})q^{11}+\cdots\)
832.2.i.i 832.i 13.c $2$ $6.644$ \(\Q(\sqrt{-3}) \) None None 52.2.e.b \(0\) \(2\) \(6\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+3q^{5}-4\zeta_{6}q^{7}-\zeta_{6}q^{9}+\cdots\)
832.2.i.j 832.i 13.c $2$ $6.644$ \(\Q(\sqrt{-3}) \) None None 52.2.e.a \(0\) \(3\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(3-3\zeta_{6})q^{3}-2q^{5}-\zeta_{6}q^{7}-6\zeta_{6}q^{9}+\cdots\)
832.2.i.k 832.i 13.c $4$ $6.644$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None 416.2.i.c \(0\) \(-2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{1}-\beta _{2})q^{3}-2\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
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