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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1183.1.b.a 1183.b 91.b $6$ $0.590$ 6.0.153664.1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-1+\beta _{2})q^{4}-\beta _{5}q^{7}+(\beta _{1}+\cdots)q^{8}+\cdots\)
1183.1.d.a 1183.d 7.b $3$ $0.590$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(3\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{7}+(-1-\beta _{2})q^{8}+\cdots\)
1183.1.d.b 1183.d 7.b $3$ $0.590$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(-3\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{7}+(1+\beta _{2})q^{8}+\cdots\)
1183.1.n.a 1183.n 91.n $6$ $0.590$ 6.0.64827.1 \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(3\) \(q+(-1+\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-\beta _{3}+\cdots)q^{4}+\cdots\)
1183.1.n.b 1183.n 91.n $6$ $0.590$ 6.0.64827.1 \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(-3\) \(q+(1-\beta _{1}-\beta _{4}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
1183.1.t.a 1183.t 91.t $12$ $0.590$ 12.0.\(\cdots\).1 \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\beta _{1}+\beta _{2}-\beta _{6})q^{2}+(-1+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
1183.1.x.a 1183.x 91.x $8$ $0.590$ \(\Q(\zeta_{24})\) None None \(0\) \(-4\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{2}-\zeta_{24}^{4}q^{3}+\zeta_{24}^{7}q^{5}+\cdots\)
1183.1.z.a 1183.z 91.z $8$ $0.590$ \(\Q(\zeta_{24})\) None None \(0\) \(-4\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{4}q^{3}+\zeta_{24}^{11}q^{5}+\cdots\)
1183.1.bd.a 1183.bd 91.ad $8$ $0.590$ \(\Q(\zeta_{24})\) None None \(0\) \(8\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}+q^{3}-\zeta_{24}^{7}q^{5}-\zeta_{24}^{11}q^{6}+\cdots\)
1183.2.a.a 1183.a 1.a $1$ $9.446$ \(\Q\) None None \(0\) \(-2\) \(3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{4}+3q^{5}-q^{7}+q^{9}+4q^{12}+\cdots\)
1183.2.a.b 1183.a 1.a $1$ $9.446$ \(\Q\) None None \(2\) \(0\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}+2q^{4}+3q^{5}+q^{7}-3q^{9}+\cdots\)
1183.2.a.c 1183.a 1.a $2$ $9.446$ \(\Q(\sqrt{5}) \) None None \(-3\) \(-3\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1183.2.a.d 1183.a 1.a $2$ $9.446$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-6\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+\beta q^{3}+(-3+\beta )q^{5}+2q^{6}+\cdots\)
1183.2.a.e 1183.a 1.a $2$ $9.446$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(-3+\cdots)q^{6}+\cdots\)
1183.2.a.f 1183.a 1.a $2$ $9.446$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1+\beta )q^{3}+q^{4}+\beta q^{5}+(3+\cdots)q^{6}+\cdots\)
1183.2.a.g 1183.a 1.a $2$ $9.446$ \(\Q(\sqrt{5}) \) None None \(3\) \(-3\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(-1-\beta )q^{3}+3\beta q^{4}+\cdots\)
1183.2.a.h 1183.a 1.a $3$ $9.446$ 3.3.148.1 None None \(-2\) \(0\) \(-3\) \(3\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.i 1183.a 1.a $3$ $9.446$ 3.3.316.1 None None \(-1\) \(-2\) \(-2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(-1+\beta _{1}-\beta _{2})q^{3}+(1+\beta _{2})q^{4}+\cdots\)
1183.2.a.j 1183.a 1.a $3$ $9.446$ 3.3.148.1 None None \(2\) \(0\) \(3\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{2}q^{3}+(1-\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.k 1183.a 1.a $4$ $9.446$ 4.4.27004.1 None None \(-1\) \(1\) \(-7\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.l 1183.a 1.a $4$ $9.446$ 4.4.27004.1 None None \(1\) \(1\) \(7\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{2})q^{4}+\cdots\)
1183.2.a.m 1183.a 1.a $6$ $9.446$ 6.6.7674048.1 None None \(-4\) \(0\) \(-6\) \(6\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.2.a.n 1183.a 1.a $6$ $9.446$ 6.6.1279733.1 None None \(-2\) \(-4\) \(-2\) \(6\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{2}+\beta _{4})q^{2}+(-\beta _{1}+\beta _{3}+\cdots)q^{3}+\cdots\)
1183.2.a.o 1183.a 1.a $6$ $9.446$ 6.6.1279733.1 None None \(2\) \(-4\) \(2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{2}-\beta _{4})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+\cdots\)
1183.2.a.p 1183.a 1.a $6$ $9.446$ 6.6.7674048.1 None None \(4\) \(0\) \(6\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}-\beta _{4}q^{3}+(1-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
1183.2.a.q 1183.a 1.a $12$ $9.446$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-3\) \(8\) \(4\) \(-12\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
1183.2.a.r 1183.a 1.a $12$ $9.446$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(3\) \(8\) \(-4\) \(12\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{6})q^{3}+(2-\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots\)
1183.2.c.a 1183.c 13.b $2$ $9.446$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{3}+2q^{4}-3iq^{5}-iq^{7}+q^{9}+\cdots\)
1183.2.c.b 1183.c 13.b $2$ $9.446$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-2q^{4}+3iq^{5}-iq^{7}-3q^{9}+\cdots\)
1183.2.c.c 1183.c 13.b $4$ $9.446$ \(\Q(i, \sqrt{5})\) None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{2})q^{3}+3\beta _{2}q^{4}+\cdots\)
1183.2.c.d 1183.c 13.b $4$ $9.446$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}-\zeta_{8}^{3}q^{3}+(3\zeta_{8}+\zeta_{8}^{2})q^{5}+\cdots\)
1183.2.c.e 1183.c 13.b $4$ $9.446$ \(\Q(\zeta_{12})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{12}^{2}q^{2}+(1+\zeta_{12}^{3})q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots\)
1183.2.c.f 1183.c 13.b $6$ $9.446$ 6.0.399424.1 None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(-1-\beta _{1}-\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1183.2.c.g 1183.c 13.b $8$ $9.446$ 8.0.\(\cdots\).1 None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(-1+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
1183.2.c.h 1183.c 13.b $12$ $9.446$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{8}+\beta _{10}-\beta _{11})q^{2}+(-1-\beta _{4}+\cdots)q^{3}+\cdots\)
1183.2.c.i 1183.c 13.b $12$ $9.446$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{7})q^{2}-\beta _{2}q^{3}+(-1-\beta _{4}+\cdots)q^{4}+\cdots\)
1183.2.c.j 1183.c 13.b $24$ $9.446$ None None \(0\) \(16\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
1183.2.e.a 1183.e 7.c $2$ $9.446$ \(\Q(\sqrt{-3}) \) None None \(-1\) \(3\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
1183.2.e.b 1183.e 7.c $2$ $9.446$ \(\Q(\sqrt{-3}) \) None None \(1\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots\)
1183.2.e.c 1183.e 7.c $2$ $9.446$ \(\Q(\sqrt{-3}) \) None None \(1\) \(3\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
1183.2.e.d 1183.e 7.c $4$ $9.446$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(-3\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-2\beta _{1}-2\beta _{2}+\cdots)q^{3}+\cdots\)
1183.2.e.e 1183.e 7.c $4$ $9.446$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{2}+(1-\zeta_{12}^{2})q^{3}+\cdots\)
1183.2.e.f 1183.e 7.c $10$ $9.446$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(4\) \(0\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{7})q^{2}+(-\beta _{4}+\beta _{9})q^{3}+\cdots\)
1183.2.e.g 1183.e 7.c $12$ $9.446$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(-2\) \(1\) \(-1\) \(6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}+\beta _{5}-\beta _{11})q^{2}-\beta _{3}q^{3}+(\beta _{6}+\cdots)q^{4}+\cdots\)
1183.2.e.h 1183.e 7.c $12$ $9.446$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(2\) \(1\) \(1\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{5}+\beta _{11})q^{2}-\beta _{3}q^{3}+(\beta _{6}+\cdots)q^{4}+\cdots\)
1183.2.e.i 1183.e 7.c $16$ $9.446$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{9}q^{2}+(-1-\beta _{4}-\beta _{6})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1183.2.e.j 1183.e 7.c $24$ $9.446$ None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$
1183.2.e.k 1183.e 7.c $48$ $9.446$ None None \(-1\) \(0\) \(13\) \(-3\) $\mathrm{SU}(2)[C_{3}]$
1183.2.e.l 1183.e 7.c $48$ $9.446$ None None \(1\) \(0\) \(-13\) \(3\) $\mathrm{SU}(2)[C_{3}]$
1183.4.a.a 1183.a 1.a $1$ $69.799$ \(\Q\) None None \(-5\) \(2\) \(-19\) \(7\) $-$ $\mathrm{SU}(2)$ \(q-5q^{2}+2q^{3}+17q^{4}-19q^{5}-10q^{6}+\cdots\)
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