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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
966.2.a.a 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(-1\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.b 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.c 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(-1\) \(2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.d 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(-1\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+3q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.e 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
966.2.a.f 966.a 1.a $1$ $7.714$ \(\Q\) None \(-1\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+q^{7}-q^{8}+\cdots\)
966.2.a.g 966.a 1.a $1$ $7.714$ \(\Q\) None \(1\) \(-1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-2q^{5}-q^{6}+q^{7}+\cdots\)
966.2.a.h 966.a 1.a $1$ $7.714$ \(\Q\) None \(1\) \(-1\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{7}+\cdots\)
966.2.a.i 966.a 1.a $1$ $7.714$ \(\Q\) None \(1\) \(1\) \(-3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-3q^{5}+q^{6}+q^{7}+\cdots\)
966.2.a.j 966.a 1.a $1$ $7.714$ \(\Q\) None \(1\) \(1\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.k 966.a 1.a $1$ $7.714$ \(\Q\) None \(1\) \(1\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+3q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.l 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{17}) \) None \(-2\) \(-2\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+\beta q^{5}+q^{6}-q^{7}+\cdots\)
966.2.a.m 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{41}) \) None \(-2\) \(2\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-\beta q^{5}-q^{6}-q^{7}+\cdots\)
966.2.a.n 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{41}) \) None \(-2\) \(2\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)
966.2.a.o 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{33}) \) None \(2\) \(-2\) \(-3\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+(-1-\beta )q^{5}-q^{6}+\cdots\)
966.2.a.p 966.a 1.a $2$ $7.714$ \(\Q(\sqrt{5}) \) None \(2\) \(2\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}+q^{7}+\cdots\)
966.2.f.a 966.f 21.c $4$ $7.714$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{3}-q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
966.2.f.b 966.f 21.c $24$ $7.714$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$
966.2.f.c 966.f 21.c $28$ $7.714$ None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$
966.2.g.a 966.g 161.c $4$ $7.714$ \(\Q(i, \sqrt{14})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+\beta _{2}q^{6}+\beta _{1}q^{7}+\cdots\)
966.2.g.b 966.g 161.c $4$ $7.714$ \(\Q(i, \sqrt{14})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{2}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
966.2.g.c 966.g 161.c $4$ $7.714$ \(\Q(i, \sqrt{7})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}+\beta _{3}q^{7}+\cdots\)
966.2.g.d 966.g 161.c $4$ $7.714$ \(\Q(i, \sqrt{7})\) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{1}q^{3}+q^{4}+\beta _{2}q^{5}-\beta _{1}q^{6}+\cdots\)
966.2.g.e 966.g 161.c $16$ $7.714$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{2}q^{3}+q^{4}-\beta _{8}q^{5}+\beta _{2}q^{6}+\cdots\)
966.2.h.a 966.h 69.c $24$ $7.714$ None \(0\) \(4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
966.2.h.b 966.h 69.c $24$ $7.714$ None \(0\) \(4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$
966.2.i.a 966.i 7.c $2$ $7.714$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(-4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.b 966.i 7.c $2$ $7.714$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-1\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.c 966.i 7.c $2$ $7.714$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.d 966.i 7.c $2$ $7.714$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.e 966.i 7.c $2$ $7.714$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.f 966.i 7.c $2$ $7.714$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.g 966.i 7.c $2$ $7.714$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
966.2.i.h 966.i 7.c $4$ $7.714$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(-2\) \(-2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
966.2.i.i 966.i 7.c $4$ $7.714$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(2\) \(-2\) \(1\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-1+\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
966.2.i.j 966.i 7.c $4$ $7.714$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(-2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
966.2.i.k 966.i 7.c $6$ $7.714$ 6.0.29428272.1 None \(3\) \(3\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{3})q^{2}-\beta _{3}q^{3}+\beta _{3}q^{4}+(-1+\cdots)q^{5}+\cdots\)
966.2.i.l 966.i 7.c $8$ $7.714$ 8.0.1768034304.4 None \(-4\) \(-4\) \(4\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(\beta _{2}+\cdots)q^{5}+\cdots\)
966.2.i.m 966.i 7.c $8$ $7.714$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-4\) \(4\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1})q^{2}-\beta _{1}q^{3}+\beta _{1}q^{4}+(-1+\cdots)q^{5}+\cdots\)
966.2.i.n 966.i 7.c $8$ $7.714$ 8.0.\(\cdots\).2 None \(4\) \(4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{5})q^{2}-\beta _{5}q^{3}+\beta _{5}q^{4}-\beta _{1}q^{5}+\cdots\)
966.2.j.a 966.j 483.m $128$ $7.714$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
966.2.k.a 966.k 161.g $32$ $7.714$ None \(-16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
966.2.k.b 966.k 161.g $32$ $7.714$ None \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
966.2.l.a 966.l 21.g $4$ $7.714$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{12}-\zeta_{12}^{3})q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\cdots\)
966.2.l.b 966.l 21.g $4$ $7.714$ \(\Q(\zeta_{12})\) None \(0\) \(6\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}+\zeta_{12}^{3})q^{2}+(1+\zeta_{12}^{2})q^{3}+\cdots\)
966.2.l.c 966.l 21.g $56$ $7.714$ None \(0\) \(-6\) \(0\) \(20\) $\mathrm{SU}(2)[C_{6}]$
966.2.l.d 966.l 21.g $56$ $7.714$ None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$
966.2.q.a 966.q 23.c $10$ $7.714$ \(\Q(\zeta_{22})\) None \(-1\) \(-1\) \(-14\) \(1\) $\mathrm{SU}(2)[C_{11}]$ \(q+\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
966.2.q.b 966.q 23.c $10$ $7.714$ \(\Q(\zeta_{22})\) None \(-1\) \(-1\) \(2\) \(1\) $\mathrm{SU}(2)[C_{11}]$ \(q+\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
966.2.q.c 966.q 23.c $10$ $7.714$ \(\Q(\zeta_{22})\) None \(1\) \(-1\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{11}]$ \(q-\zeta_{22}^{4}q^{2}+(-1+\zeta_{22}-\zeta_{22}^{2}+\zeta_{22}^{3}+\cdots)q^{3}+\cdots\)
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