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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
462.2.a.a 462.a 1.a $1$ $3.689$ \(\Q\) None \(-1\) \(-1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-2q^{5}+q^{6}+q^{7}+\cdots\)
462.2.a.b 462.a 1.a $1$ $3.689$ \(\Q\) None \(-1\) \(-1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{7}-q^{8}+\cdots\)
462.2.a.c 462.a 1.a $1$ $3.689$ \(\Q\) None \(-1\) \(-1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
462.2.a.d 462.a 1.a $1$ $3.689$ \(\Q\) None \(-1\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{7}-q^{8}+\cdots\)
462.2.a.e 462.a 1.a $1$ $3.689$ \(\Q\) None \(1\) \(-1\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-q^{3}+q^{4}-4q^{5}-q^{6}+q^{7}+\cdots\)
462.2.a.f 462.a 1.a $1$ $3.689$ \(\Q\) None \(1\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+q^{6}+q^{7}+q^{8}+\cdots\)
462.2.a.g 462.a 1.a $1$ $3.689$ \(\Q\) None \(1\) \(1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}+2q^{5}+q^{6}-q^{7}+\cdots\)
462.2.a.h 462.a 1.a $2$ $3.689$ \(\Q(\sqrt{3}) \) None \(-2\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}+\beta q^{5}-q^{6}+q^{7}+\cdots\)
462.2.c.a 462.c 33.d $12$ $3.689$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(-12\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+\beta _{6}q^{3}+q^{4}-\beta _{11}q^{5}-\beta _{6}q^{6}+\cdots\)
462.2.c.b 462.c 33.d $12$ $3.689$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(12\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+\beta _{6}q^{3}+q^{4}-\beta _{11}q^{5}+\beta _{6}q^{6}+\cdots\)
462.2.e.a 462.e 77.b $8$ $3.689$ 8.0.6679465984.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
462.2.e.b 462.e 77.b $8$ $3.689$ 8.0.6679465984.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
462.2.g.a 462.g 21.c $4$ $3.689$ \(\Q(i, \sqrt{5})\) None \(0\) \(-2\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{1})q^{3}-q^{4}+(-2+\cdots)q^{5}+\cdots\)
462.2.g.b 462.g 21.c $4$ $3.689$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
462.2.g.c 462.g 21.c $4$ $3.689$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{3}q^{3}-q^{4}+\zeta_{12}^{2}q^{6}+\cdots\)
462.2.g.d 462.g 21.c $4$ $3.689$ \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(4\) \(6\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{2}+\beta _{3})q^{3}-q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
462.2.g.e 462.g 21.c $8$ $3.689$ 8.0.342102016.5 None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}-q^{4}+(\beta _{4}-\beta _{5})q^{5}+\cdots\)
462.2.i.a 462.i 7.c $2$ $3.689$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.b 462.i 7.c $2$ $3.689$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.c 462.i 7.c $2$ $3.689$ \(\Q(\sqrt{-3}) \) None \(1\) \(-1\) \(3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-1+\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.d 462.i 7.c $2$ $3.689$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
462.2.i.e 462.i 7.c $4$ $3.689$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
462.2.i.f 462.i 7.c $6$ $3.689$ 6.0.1156923.1 None \(-3\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{2}q^{3}+\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
462.2.i.g 462.i 7.c $6$ $3.689$ 6.0.21870000.1 None \(-3\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1-\beta _{2})q^{4}+\cdots\)
462.2.j.a 462.j 11.c $4$ $3.689$ \(\Q(\zeta_{10})\) None \(-1\) \(-1\) \(3\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
462.2.j.b 462.j 11.c $4$ $3.689$ \(\Q(\zeta_{10})\) None \(-1\) \(1\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
462.2.j.c 462.j 11.c $4$ $3.689$ \(\Q(\zeta_{10})\) None \(1\) \(-1\) \(5\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+\cdots\)
462.2.j.d 462.j 11.c $4$ $3.689$ \(\Q(\zeta_{10})\) None \(1\) \(1\) \(-3\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{2}q^{3}+\cdots\)
462.2.j.e 462.j 11.c $8$ $3.689$ 8.0.484000000.9 None \(-2\) \(-2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{2}q^{2}+(-1-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+\cdots\)
462.2.j.f 462.j 11.c $8$ $3.689$ 8.0.64000000.1 None \(-2\) \(2\) \(-6\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{6}q^{2}+(1-\beta _{2}+\beta _{4}-\beta _{6})q^{3}-\beta _{2}q^{4}+\cdots\)
462.2.j.g 462.j 11.c $8$ $3.689$ 8.0.324000000.3 None \(2\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{2}q^{2}+\beta _{6}q^{3}+\beta _{4}q^{4}+(-\beta _{1}-\beta _{5}+\cdots)q^{5}+\cdots\)
462.2.j.h 462.j 11.c $8$ $3.689$ 8.0.\(\cdots\).8 None \(2\) \(2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-1-\beta _{2}-\beta _{3}+\cdots)q^{4}+\cdots\)
462.2.k.a 462.k 21.g $4$ $3.689$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
462.2.k.b 462.k 21.g $4$ $3.689$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
462.2.k.c 462.k 21.g $4$ $3.689$ \(\Q(\zeta_{12})\) None \(0\) \(6\) \(0\) \(2\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(2-\zeta_{12}^{2})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
462.2.k.d 462.k 21.g $8$ $3.689$ \(\Q(\zeta_{24})\) None \(0\) \(-12\) \(0\) \(4\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(-1-\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
462.2.k.e 462.k 21.g $8$ $3.689$ \(\Q(\zeta_{24})\) None \(0\) \(4\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}^{2}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}-\zeta_{24}^{2}+\cdots)q^{3}+\cdots\)
462.2.k.f 462.k 21.g $8$ $3.689$ \(\Q(\zeta_{24})\) None \(0\) \(8\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\zeta_{24}^{2}-\zeta_{24}^{6})q^{2}+(1-\zeta_{24}^{3}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
462.2.k.g 462.k 21.g $20$ $3.689$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(-6\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{7}q^{2}-\beta _{12}q^{3}-\beta _{3}q^{4}+(2\beta _{6}+\beta _{7}+\cdots)q^{5}+\cdots\)
462.2.n.a 462.n 231.l $4$ $3.689$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(-2\) \(-6\) \(3\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
462.2.n.b 462.n 231.l $4$ $3.689$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(-2\) \(6\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
462.2.n.c 462.n 231.l $4$ $3.689$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(2\) \(-6\) \(3\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(1-\beta _{2})q^{2}+(-2+\beta _{2})q^{3}-\beta _{2}q^{4}+\cdots\)
462.2.n.d 462.n 231.l $4$ $3.689$ \(\Q(\sqrt{-3}, \sqrt{-19})\) None \(2\) \(6\) \(-3\) \(3\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(1+\beta _{2})q^{3}+(-1+\beta _{2})q^{4}+\cdots\)
462.2.n.e 462.n 231.l $24$ $3.689$ None \(-12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
462.2.n.f 462.n 231.l $24$ $3.689$ None \(12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
462.2.p.a 462.p 77.i $16$ $3.689$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(12\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{11}q^{2}-\beta _{12}q^{3}-\beta _{13}q^{4}+(1+\beta _{8}+\cdots)q^{5}+\cdots\)
462.2.p.b 462.p 77.i $16$ $3.689$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(12\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{12}q^{2}+\beta _{11}q^{3}+(1+\beta _{13})q^{4}+\cdots\)
462.2.s.a 462.s 231.u $128$ $3.689$ None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{10}]$
462.2.u.a 462.u 77.l $32$ $3.689$ None \(0\) \(0\) \(-10\) \(-10\) $\mathrm{SU}(2)[C_{10}]$
462.2.u.b 462.u 77.l $32$ $3.689$ None \(0\) \(0\) \(10\) \(-10\) $\mathrm{SU}(2)[C_{10}]$
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