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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
968.1.f.a 968.f 8.d $2$ $0.483$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-2}) \) None \(-2\) \(-1\) \(0\) \(0\) \(q-q^{2}+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{6}+\cdots\)
968.1.f.b 968.f 8.d $2$ $0.483$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-2}) \) None \(2\) \(-1\) \(0\) \(0\) \(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
968.1.h.a 968.h 11.b $2$ $0.483$ \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(2\) \(0\) \(q-q^{3}+q^{5}-\beta q^{7}-q^{15}-\beta q^{17}+\cdots\)
968.1.j.a 968.j 11.d $8$ $0.483$ 8.0.64000000.1 None None \(0\) \(2\) \(-2\) \(0\) \(q+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+\cdots\)
968.1.l.a 968.l 88.l $4$ $0.483$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-2}) \) None \(-1\) \(3\) \(0\) \(0\) \(q-\zeta_{10}q^{2}+(1-\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}+\cdots\)
968.1.l.b 968.l 88.l $4$ $0.483$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-2}) \) None \(1\) \(-2\) \(0\) \(0\) \(q+\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots\)
968.1.l.c 968.l 88.l $4$ $0.483$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-2}) \) None \(1\) \(3\) \(0\) \(0\) \(q+\zeta_{10}q^{2}+(1-\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}+\cdots\)
968.1.x.a 968.x 968.x $10$ $0.483$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-2}) \) None \(-1\) \(-2\) \(0\) \(0\) \(q+\zeta_{22}^{8}q^{2}+(-\zeta_{22}^{5}+\zeta_{22}^{6})q^{3}+\cdots\)
968.1.z.a 968.z 968.z $40$ $0.483$ \(\Q(\zeta_{55})\) \(\Q(\sqrt{-2}) \) None \(1\) \(2\) \(0\) \(0\) \(q-\zeta_{110}^{49}q^{2}+(-\zeta_{110}^{21}-\zeta_{110}^{23}+\cdots)q^{3}+\cdots\)
968.2.a.a 968.a 1.a $1$ $7.730$ \(\Q\) None None \(0\) \(-3\) \(-3\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-3q^{5}+2q^{7}+6q^{9}+9q^{15}+\cdots\)
968.2.a.b 968.a 1.a $1$ $7.730$ \(\Q\) None None \(0\) \(0\) \(3\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+3q^{5}-4q^{7}-3q^{9}-3q^{13}-3q^{17}+\cdots\)
968.2.a.c 968.a 1.a $1$ $7.730$ \(\Q\) None None \(0\) \(0\) \(3\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+3q^{5}+4q^{7}-3q^{9}+3q^{13}+3q^{17}+\cdots\)
968.2.a.d 968.a 1.a $1$ $7.730$ \(\Q\) None None \(0\) \(1\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-4q^{7}-2q^{9}-4q^{13}+\cdots\)
968.2.a.e 968.a 1.a $1$ $7.730$ \(\Q\) None None \(0\) \(1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}-2q^{9}+4q^{13}+\cdots\)
968.2.a.f 968.a 1.a $2$ $7.730$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+\beta q^{5}+(-1-\beta )q^{7}+\cdots\)
968.2.a.g 968.a 1.a $2$ $7.730$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+\beta q^{5}+(1+\beta )q^{7}+(3+\cdots)q^{9}+\cdots\)
968.2.a.h 968.a 1.a $2$ $7.730$ \(\Q(\sqrt{5}) \) None None \(0\) \(-1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{5}-\beta q^{7}+(-2+\cdots)q^{9}+\cdots\)
968.2.a.i 968.a 1.a $2$ $7.730$ \(\Q(\sqrt{5}) \) None None \(0\) \(-1\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+(-1+\beta )q^{5}+\beta q^{7}+(-2+\cdots)q^{9}+\cdots\)
968.2.a.j 968.a 1.a $2$ $7.730$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+(2-\beta )q^{5}+2\beta q^{7}+(1+\beta )q^{9}+\cdots\)
968.2.a.k 968.a 1.a $2$ $7.730$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-2-\beta )q^{5}+(-1-\beta )q^{7}+\cdots\)
968.2.a.l 968.a 1.a $2$ $7.730$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-2-\beta )q^{5}+(1+\beta )q^{7}+\cdots\)
968.2.a.m 968.a 1.a $4$ $7.730$ 4.4.5225.1 None None \(0\) \(2\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
968.2.a.n 968.a 1.a $4$ $7.730$ 4.4.5225.1 None None \(0\) \(2\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{3}q^{3}+(-1+\beta _{1}-\beta _{2}+\beta _{3})q^{5}+\cdots\)
968.2.c.a 968.c 8.b $2$ $7.730$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-22}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}-2q^{4}-2\beta q^{8}+3q^{9}+2\beta q^{13}+\cdots\)
968.2.c.b 968.c 8.b $4$ $7.730$ \(\Q(\sqrt{3}, \sqrt{-5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+(-1-\beta _{2})q^{4}+(-1-2\beta _{2}+\cdots)q^{5}+\cdots\)
968.2.c.c 968.c 8.b $8$ $7.730$ 8.0.\(\cdots\).10 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+(-\beta _{2}+\beta _{3})q^{3}+(1+\beta _{3}+\cdots)q^{4}+\cdots\)
968.2.c.d 968.c 8.b $10$ $7.730$ 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-\beta _{1}q^{3}+(\beta _{2}-\beta _{4}-\beta _{6})q^{4}+\cdots\)
968.2.c.e 968.c 8.b $10$ $7.730$ 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}-\beta _{6}q^{3}-\beta _{2}q^{4}+\beta _{7}q^{5}+\cdots\)
968.2.c.f 968.c 8.b $10$ $7.730$ 10.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{4}q^{2}-\beta _{6}q^{3}-\beta _{2}q^{4}+\beta _{7}q^{5}+\cdots\)
968.2.c.g 968.c 8.b $16$ $7.730$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{8}q^{2}+\beta _{5}q^{3}-\beta _{11}q^{4}-\beta _{7}q^{5}+\cdots\)
968.2.c.h 968.c 8.b $20$ $7.730$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(10\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{15}q^{2}+\beta _{10}q^{3}-\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots\)
968.2.c.i 968.c 8.b $20$ $7.730$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(-10\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{15}q^{2}+\beta _{10}q^{3}-\beta _{4}q^{4}+\beta _{6}q^{5}+\cdots\)
968.2.g.a 968.g 88.g $8$ $7.730$ 8.0.64000000.1 \(\Q(\sqrt{-2}) \) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}-2q^{4}-\beta _{5}q^{6}-2\beta _{1}q^{8}+\cdots\)
968.2.g.b 968.g 88.g $8$ $7.730$ \(\Q(\zeta_{24})\) None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{4}q^{2}+(1-\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
968.2.g.c 968.g 88.g $20$ $7.730$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{12}q^{2}-\beta _{5}q^{3}-\beta _{6}q^{4}-\beta _{9}q^{5}+\cdots\)
968.2.g.d 968.g 88.g $32$ $7.730$ None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
968.2.g.e 968.g 88.g $32$ $7.730$ None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
968.2.i.a 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(-4\) \(-5\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2\zeta_{10}-2\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.b 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(-4\) \(-5\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-2\zeta_{10}-2\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.c 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(-2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(-1+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.d 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(-2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}+(-1+\zeta_{10}+\cdots)q^{5}+\cdots\)
968.2.i.e 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(-1\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}-\zeta_{10}q^{5}-4\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.f 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(-1\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+\zeta_{10}^{2}q^{3}-\zeta_{10}q^{5}+4\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.g 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(0\) \(-3\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q-3\zeta_{10}q^{5}-4\zeta_{10}^{3}q^{7}+(3-3\zeta_{10}+\cdots)q^{9}+\cdots\)
968.2.i.h 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(0\) \(-3\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q-3\zeta_{10}q^{5}+4\zeta_{10}^{3}q^{7}+(3-3\zeta_{10}+\cdots)q^{9}+\cdots\)
968.2.i.i 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(3\) \(3\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-3\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}-2\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.j 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(3\) \(3\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-3\zeta_{10}^{2}q^{3}+3\zeta_{10}q^{5}+2\zeta_{10}^{3}q^{7}+\cdots\)
968.2.i.k 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(3\) \(3\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+(1+\zeta_{10}^{2}+\cdots)q^{5}+\cdots\)
968.2.i.l 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(6\) \(5\) \(-6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+(2+\cdots)q^{5}+\cdots\)
968.2.i.m 968.i 11.c $4$ $7.730$ \(\Q(\zeta_{10})\) None None \(0\) \(6\) \(5\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(2\zeta_{10}-2\zeta_{10}^{2}+2\zeta_{10}^{3})q^{3}+(2+\cdots)q^{5}+\cdots\)
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