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Label Char Prim Dim $A$ Field CM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1386.2.a.a 1386.a 1.a $1$ $11.067$ \(\Q\) None 462.2.a.g \(-1\) \(0\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
1386.2.a.b 1386.a 1.a $1$ $11.067$ \(\Q\) None 154.2.a.c \(-1\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{7}-q^{8}+2q^{10}+\cdots\)
1386.2.a.c 1386.a 1.a $1$ $11.067$ \(\Q\) None 462.2.a.f \(-1\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{7}-q^{8}+q^{11}+2q^{13}+\cdots\)
1386.2.a.d 1386.a 1.a $1$ $11.067$ \(\Q\) None 1386.2.a.d \(-1\) \(0\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2q^{5}-q^{7}-q^{8}-2q^{10}+\cdots\)
1386.2.a.e 1386.a 1.a $1$ $11.067$ \(\Q\) None 462.2.a.e \(-1\) \(0\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{5}+q^{7}-q^{8}-4q^{10}+\cdots\)
1386.2.a.f 1386.a 1.a $1$ $11.067$ \(\Q\) None 154.2.a.b \(1\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
1386.2.a.g 1386.a 1.a $1$ $11.067$ \(\Q\) None 462.2.a.c \(1\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
1386.2.a.h 1386.a 1.a $1$ $11.067$ \(\Q\) None 1386.2.a.d \(1\) \(0\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{5}-q^{7}+q^{8}-2q^{10}+\cdots\)
1386.2.a.i 1386.a 1.a $1$ $11.067$ \(\Q\) None 462.2.a.b \(1\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}-2q^{13}+\cdots\)
1386.2.a.j 1386.a 1.a $1$ $11.067$ \(\Q\) None 462.2.a.d \(1\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{11}+6q^{13}+\cdots\)
1386.2.a.k 1386.a 1.a $1$ $11.067$ \(\Q\) None 462.2.a.a \(1\) \(0\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{5}+q^{7}+q^{8}+2q^{10}+\cdots\)
1386.2.a.l 1386.a 1.a $1$ $11.067$ \(\Q\) None 154.2.a.a \(1\) \(0\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}-q^{7}+q^{8}+4q^{10}+\cdots\)
1386.2.a.m 1386.a 1.a $2$ $11.067$ \(\Q(\sqrt{5}) \) None 154.2.a.d \(-2\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta )q^{5}+q^{7}-q^{8}+\cdots\)
1386.2.a.n 1386.a 1.a $2$ $11.067$ \(\Q(\sqrt{10}) \) None 1386.2.a.n \(-2\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-q^{7}-q^{8}-\beta q^{10}+\cdots\)
1386.2.a.o 1386.a 1.a $2$ $11.067$ \(\Q(\sqrt{10}) \) None 1386.2.a.n \(2\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}-q^{7}+q^{8}+\beta q^{10}+\cdots\)
1386.2.a.p 1386.a 1.a $2$ $11.067$ \(\Q(\sqrt{3}) \) None 462.2.a.h \(2\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{7}+q^{8}+\beta q^{10}+\cdots\)
1386.2.a.q 1386.a 1.a $3$ $11.067$ 3.3.1304.1 None 1386.2.a.q \(-3\) \(0\) \(-2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+(-1-\beta _{2})q^{5}+q^{7}-q^{8}+\cdots\)
1386.2.a.r 1386.a 1.a $3$ $11.067$ 3.3.1304.1 None 1386.2.a.q \(3\) \(0\) \(2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+(1+\beta _{2})q^{5}+q^{7}+q^{8}+\cdots\)
1386.2.c.a 1386.c 33.d $12$ $11.067$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 1386.2.c.a \(-12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+q^{4}+(\beta _{1}-\beta _{5})q^{5}-\beta _{1}q^{7}+\cdots\)
1386.2.c.b 1386.c 33.d $12$ $11.067$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None 1386.2.c.a \(12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+q^{4}+(\beta _{1}-\beta _{5})q^{5}+\beta _{1}q^{7}+\cdots\)
1386.2.e.a 1386.e 77.b $8$ $11.067$ 8.0.6679465984.1 None 462.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1386.2.e.b 1386.e 77.b $8$ $11.067$ 8.0.\(\cdots\).1 None 154.2.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\beta _{3}+\cdots)q^{7}+\cdots\)
1386.2.e.c 1386.e 77.b $8$ $11.067$ 8.0.157351936.1 None 1386.2.e.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}-q^{4}-\beta _{5}q^{5}+\beta _{1}q^{7}-\beta _{2}q^{8}+\cdots\)
1386.2.e.d 1386.e 77.b $8$ $11.067$ 8.0.40960000.1 None 1386.2.e.d \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}-\beta _{4}q^{5}+(\beta _{2}-\beta _{7})q^{7}+\cdots\)
1386.2.e.e 1386.e 77.b $8$ $11.067$ 8.0.6679465984.1 None 462.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}-q^{4}+(\beta _{1}+\beta _{3})q^{5}+(\beta _{1}+\beta _{4}+\cdots)q^{7}+\cdots\)
1386.2.g.a 1386.g 21.c $16$ $11.067$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 1386.2.g.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{4}-\beta _{4}q^{5}+\beta _{7}q^{7}-\beta _{1}q^{8}+\cdots\)
1386.2.g.b 1386.g 21.c $16$ $11.067$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None 1386.2.g.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}-q^{4}+\beta _{1}q^{5}-\beta _{10}q^{7}-\beta _{5}q^{8}+\cdots\)
1386.2.k.a 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 154.2.e.d \(-1\) \(0\) \(-4\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-4\zeta_{6}q^{5}+\cdots\)
1386.2.k.b 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 1386.2.k.b \(-1\) \(0\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
1386.2.k.c 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 462.2.i.c \(-1\) \(0\) \(-3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-3\zeta_{6}q^{5}+\cdots\)
1386.2.k.d 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 462.2.i.b \(-1\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-3+2\zeta_{6})q^{7}+\cdots\)
1386.2.k.e 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 154.2.e.c \(-1\) \(0\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(-2+3\zeta_{6})q^{7}+\cdots\)
1386.2.k.f 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 462.2.i.d \(-1\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(3-2\zeta_{6})q^{7}+\cdots\)
1386.2.k.g 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 1386.2.k.g \(-1\) \(0\) \(1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1386.2.k.h 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 1386.2.k.h \(-1\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
1386.2.k.i 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 1386.2.k.i \(-1\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
1386.2.k.j 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 462.2.i.a \(-1\) \(0\) \(3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
1386.2.k.k 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 1386.2.k.i \(1\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1386.2.k.l 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 1386.2.k.h \(1\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-2\zeta_{6}q^{5}+\cdots\)
1386.2.k.m 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 1386.2.k.g \(1\) \(0\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+(-2+\cdots)q^{7}+\cdots\)
1386.2.k.n 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 154.2.e.b \(1\) \(0\) \(0\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+(2+\zeta_{6})q^{7}+\cdots\)
1386.2.k.o 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 154.2.e.a \(1\) \(0\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+2\zeta_{6}q^{5}+\cdots\)
1386.2.k.p 1386.k 7.c $2$ $11.067$ \(\Q(\sqrt{-3}) \) None 1386.2.k.b \(1\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+3\zeta_{6}q^{5}+\cdots\)
1386.2.k.q 1386.k 7.c $4$ $11.067$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 1386.2.k.q \(-2\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
1386.2.k.r 1386.k 7.c $4$ $11.067$ \(\Q(\sqrt{-3}, \sqrt{7})\) None 462.2.i.e \(-2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+\beta _{1}q^{5}-\beta _{1}q^{7}+\cdots\)
1386.2.k.s 1386.k 7.c $4$ $11.067$ \(\Q(\sqrt{-3}, \sqrt{7})\) None 154.2.e.f \(-2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1386.2.k.t 1386.k 7.c $4$ $11.067$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 154.2.e.e \(2\) \(0\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-\beta _{1}+2\beta _{2}+\cdots)q^{5}+\cdots\)
1386.2.k.u 1386.k 7.c $4$ $11.067$ \(\Q(\sqrt{2}, \sqrt{-3})\) None 1386.2.k.q \(2\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+\beta _{2}q^{4}+(1+\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
1386.2.k.v 1386.k 7.c $6$ $11.067$ 6.0.21870000.1 None 462.2.i.g \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)
1386.2.k.w 1386.k 7.c $6$ $11.067$ 6.0.1156923.1 None 462.2.i.f \(3\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+\beta _{4}q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
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