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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
390.2.a.a 390.a 1.a $1$ $3.114$ \(\Q\) None \(-1\) \(-1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots\)
390.2.a.b 390.a 1.a $1$ $3.114$ \(\Q\) None \(-1\) \(-1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots\)
390.2.a.c 390.a 1.a $1$ $3.114$ \(\Q\) None \(-1\) \(1\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots\)
390.2.a.d 390.a 1.a $1$ $3.114$ \(\Q\) None \(-1\) \(1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots\)
390.2.a.e 390.a 1.a $1$ $3.114$ \(\Q\) None \(1\) \(-1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots\)
390.2.a.f 390.a 1.a $1$ $3.114$ \(\Q\) None \(1\) \(-1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots\)
390.2.a.g 390.a 1.a $1$ $3.114$ \(\Q\) None \(1\) \(1\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+2q^{7}+\cdots\)
390.2.a.h 390.a 1.a $2$ $3.114$ \(\Q(\sqrt{2}) \) None \(2\) \(2\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+\beta q^{7}+\cdots\)
390.2.b.a 390.b 13.b $2$ $3.114$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+iq^{8}+\cdots\)
390.2.b.b 390.b 13.b $2$ $3.114$ \(\Q(\sqrt{-1}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}+iq^{8}+\cdots\)
390.2.b.c 390.b 13.b $4$ $3.114$ \(\Q(i, \sqrt{13})\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)
390.2.b.d 390.b 13.b $4$ $3.114$ \(\Q(i, \sqrt{17})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+q^{3}-q^{4}+\beta _{1}q^{5}-\beta _{1}q^{6}+\cdots\)
390.2.e.a 390.e 5.b $2$ $3.114$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(-2-i)q^{5}+\cdots\)
390.2.e.b 390.e 5.b $2$ $3.114$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+iq^{3}-q^{4}+(2-i)q^{5}-q^{6}+\cdots\)
390.2.e.c 390.e 5.b $2$ $3.114$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+(2+i)q^{5}+q^{6}+\cdots\)
390.2.e.d 390.e 5.b $2$ $3.114$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-q^{4}+(2-i)q^{5}+q^{6}+\cdots\)
390.2.e.e 390.e 5.b $4$ $3.114$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}-\beta _{2}q^{5}-q^{6}+\cdots\)
390.2.f.a 390.f 65.d $6$ $3.114$ 6.0.350464.1 None \(-6\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}-\beta _{4}q^{3}+q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots\)
390.2.f.b 390.f 65.d $6$ $3.114$ 6.0.350464.1 None \(6\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{4}q^{3}+q^{4}+(-\beta _{1}-\beta _{5})q^{5}+\cdots\)
390.2.i.a 390.i 13.c $2$ $3.114$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.b 390.i 13.c $2$ $3.114$ \(\Q(\sqrt{-3}) \) None \(-1\) \(1\) \(2\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.c 390.i 13.c $2$ $3.114$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.d 390.i 13.c $2$ $3.114$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-2\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.e 390.i 13.c $2$ $3.114$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-2\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.f 390.i 13.c $2$ $3.114$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
390.2.i.g 390.i 13.c $4$ $3.114$ \(\Q(\sqrt{-3}, \sqrt{17})\) None \(-2\) \(-2\) \(4\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+(-1+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
390.2.j.a 390.j 65.k $12$ $3.114$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-q^{2}-\beta _{2}q^{3}+q^{4}+(\beta _{1}-\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
390.2.j.b 390.j 65.k $16$ $3.114$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(16\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+\beta _{8}q^{3}+q^{4}+\beta _{14}q^{5}+\beta _{8}q^{6}+\cdots\)
390.2.l.a 390.l 15.e $4$ $3.114$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(\zeta_{8}+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
390.2.l.b 390.l 15.e $4$ $3.114$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(1-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
390.2.l.c 390.l 15.e $20$ $3.114$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{9}q^{2}+\beta _{1}q^{3}-\beta _{11}q^{4}+(\beta _{2}+\beta _{4}+\cdots)q^{5}+\cdots\)
390.2.l.d 390.l 15.e $20$ $3.114$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(0\) \(4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{2}+\beta _{12}q^{3}+\beta _{11}q^{4}+(-\beta _{5}+\cdots)q^{5}+\cdots\)
390.2.n.a 390.n 195.n $56$ $3.114$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
390.2.p.a 390.p 39.f $4$ $3.114$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(-1+\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
390.2.p.b 390.p 39.f $4$ $3.114$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
390.2.p.c 390.p 39.f $4$ $3.114$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(-1-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
390.2.p.d 390.p 39.f $4$ $3.114$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(1+\zeta_{8}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
390.2.p.e 390.p 39.f $4$ $3.114$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
390.2.p.f 390.p 39.f $4$ $3.114$ \(\Q(\zeta_{8})\) None \(0\) \(4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+(1+\zeta_{8}-\zeta_{8}^{2})q^{3}+\zeta_{8}^{2}q^{4}+\cdots\)
390.2.p.g 390.p 39.f $8$ $3.114$ 8.0.40960000.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{7}q^{2}-\beta _{6}q^{3}-\beta _{2}q^{4}-\beta _{7}q^{5}+\cdots\)
390.2.s.a 390.s 195.s $8$ $3.114$ 8.0.40960000.1 None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+(1+\beta _{3})q^{3}+\beta _{2}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
390.2.s.b 390.s 195.s $24$ $3.114$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
390.2.s.c 390.s 195.s $24$ $3.114$ None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
390.2.t.a 390.t 65.f $12$ $3.114$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{2}-\beta _{7}q^{3}-q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
390.2.t.b 390.t 65.f $16$ $3.114$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{2}+\beta _{8}q^{3}-q^{4}-\beta _{10}q^{5}+\beta _{5}q^{6}+\cdots\)
390.2.x.a 390.x 65.l $12$ $3.114$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-6\) \(0\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\beta _{6})q^{2}+\beta _{4}q^{3}+\beta _{6}q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
390.2.x.b 390.x 65.l $12$ $3.114$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(6\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1+\beta _{6})q^{2}-\beta _{4}q^{3}+\beta _{6}q^{4}+(\beta _{3}+\cdots)q^{5}+\cdots\)
390.2.y.a 390.y 65.n $4$ $3.114$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
390.2.y.b 390.y 65.n $4$ $3.114$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(-1+\cdots)q^{5}+\cdots\)
390.2.y.c 390.y 65.n $4$ $3.114$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+(2\zeta_{12}+\cdots)q^{5}+\cdots\)
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