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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
464.1.h.a 464.h 116.d $1$ $0.232$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-29}) \) \(\Q(\sqrt{29}) \) \(0\) \(0\) \(2\) \(0\) \(q+2q^{5}-q^{9}-2q^{13}+3q^{25}-q^{29}+\cdots\)
464.1.h.b 464.h 116.d $2$ $0.232$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-29}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{3}-q^{5}+2q^{9}+\beta q^{11}+q^{13}+\cdots\)
464.1.v.a 464.v 116.h $6$ $0.232$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q+(-\zeta_{14}-\zeta_{14}^{3})q^{5}-\zeta_{14}^{6}q^{9}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots\)
464.2.a.a 464.a 1.a $1$ $3.705$ \(\Q\) None None \(0\) \(-2\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{5}-4q^{7}+q^{9}+6q^{11}+\cdots\)
464.2.a.b 464.a 1.a $1$ $3.705$ \(\Q\) None None \(0\) \(-1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}-2q^{9}-3q^{11}+\cdots\)
464.2.a.c 464.a 1.a $1$ $3.705$ \(\Q\) None None \(0\) \(-1\) \(3\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+3q^{5}+4q^{7}-2q^{9}-3q^{11}+\cdots\)
464.2.a.d 464.a 1.a $1$ $3.705$ \(\Q\) None None \(0\) \(1\) \(-3\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-3q^{5}-2q^{7}-2q^{9}+3q^{11}+\cdots\)
464.2.a.e 464.a 1.a $1$ $3.705$ \(\Q\) None None \(0\) \(1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+2q^{7}-2q^{9}+3q^{11}+\cdots\)
464.2.a.f 464.a 1.a $1$ $3.705$ \(\Q\) None None \(0\) \(3\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-3q^{5}+2q^{7}+6q^{9}+q^{11}+\cdots\)
464.2.a.g 464.a 1.a $1$ $3.705$ \(\Q\) None None \(0\) \(3\) \(3\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+3q^{5}-4q^{7}+6q^{9}+q^{11}+\cdots\)
464.2.a.h 464.a 1.a $2$ $3.705$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}-2\beta q^{7}-2\beta q^{9}+\cdots\)
464.2.a.i 464.a 1.a $2$ $3.705$ \(\Q(\sqrt{2}) \) None None \(0\) \(2\) \(-2\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+(-1+2\beta )q^{5}+4q^{7}+\cdots\)
464.2.a.j 464.a 1.a $3$ $3.705$ 3.3.568.1 None None \(0\) \(-2\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+(1-\beta _{2})q^{5}+(2+\beta _{2})q^{9}+\cdots\)
464.2.e.a 464.e 29.b $2$ $3.705$ \(\Q(\sqrt{-5}) \) None None \(0\) \(0\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-3q^{5}-2q^{7}-2q^{9}-\beta q^{11}+\cdots\)
464.2.e.b 464.e 29.b $2$ $3.705$ \(\Q(\sqrt{-7}) \) None None \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+q^{5}+2q^{7}-4q^{9}-\beta q^{11}+\cdots\)
464.2.e.c 464.e 29.b $2$ $3.705$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+q^{5}+2q^{7}+2q^{9}-5iq^{11}+\cdots\)
464.2.e.d 464.e 29.b $8$ $3.705$ 8.0.4589249536.2 None None \(0\) \(0\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+\beta _{4}q^{5}+(-1+\beta _{6})q^{7}+(-1+\cdots)q^{9}+\cdots\)
464.2.j.a 464.j 464.j $116$ $3.705$ None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
464.2.k.a 464.k 116.e $2$ $3.705$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-4iq^{5}+3iq^{9}-6iq^{13}+(-3-3i)q^{17}+\cdots\)
464.2.k.b 464.k 116.e $8$ $3.705$ 8.0.1024000000.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+(-\beta _{1}-\beta _{5})q^{7}+\cdots\)
464.2.k.c 464.k 116.e $20$ $3.705$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{13}q^{3}+\beta _{18}q^{5}+\beta _{9}q^{7}+(\beta _{1}-\beta _{8}+\cdots)q^{9}+\cdots\)
464.2.m.a 464.m 464.m $2$ $3.705$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+(1+i)q^{3}+2iq^{4}+\cdots\)
464.2.m.b 464.m 464.m $2$ $3.705$ \(\Q(\sqrt{-1}) \) None None \(2\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+(-1-i)q^{3}+2iq^{4}+\cdots\)
464.2.m.c 464.m 464.m $112$ $3.705$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
464.2.n.a 464.n 16.e $112$ $3.705$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
464.2.t.a 464.t 464.t $116$ $3.705$ None None \(-4\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
464.2.u.a 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None None \(0\) \(-5\) \(7\) \(3\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\zeta_{14}^{5})q^{3}+(1-\zeta_{14}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots\)
464.2.u.b 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None None \(0\) \(-3\) \(-4\) \(5\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\zeta_{14}-\zeta_{14}^{4}+\zeta_{14}^{5})q^{3}+\cdots\)
464.2.u.c 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None None \(0\) \(-3\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-2\zeta_{14}+2\zeta_{14}^{2}-2\zeta_{14}^{3}+2\zeta_{14}^{4}+\cdots)q^{3}+\cdots\)
464.2.u.d 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None None \(0\) \(1\) \(-1\) \(-5\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1+2\zeta_{14}^{2}-2\zeta_{14}^{3}-\zeta_{14}^{5})q^{3}+\cdots\)
464.2.u.e 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None None \(0\) \(3\) \(2\) \(3\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-\zeta_{14}+\zeta_{14}^{4}-\zeta_{14}^{5})q^{3}+(\zeta_{14}^{3}+\cdots)q^{5}+\cdots\)
464.2.u.f 464.u 29.d $6$ $3.705$ \(\Q(\zeta_{14})\) None None \(0\) \(5\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-\zeta_{14}^{5})q^{3}+(1-\zeta_{14}-2\zeta_{14}^{3}+\cdots)q^{5}+\cdots\)
464.2.u.g 464.u 29.d $12$ $3.705$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(3\) \(-1\) \(7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(\beta _{1}+\beta _{8})q^{3}+(-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5}+\cdots)q^{5}+\cdots\)
464.2.u.h 464.u 29.d $12$ $3.705$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(3\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{7}]$ \(q-\beta _{11}q^{3}+(\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}-\beta _{7}+\cdots)q^{5}+\cdots\)
464.2.u.i 464.u 29.d $24$ $3.705$ None None \(0\) \(1\) \(-8\) \(-5\) $\mathrm{SU}(2)[C_{7}]$
464.2.y.a 464.y 29.e $6$ $3.705$ \(\Q(\zeta_{14})\) None None \(0\) \(-7\) \(-1\) \(5\) $\mathrm{SU}(2)[C_{14}]$ \(q+(-1-\zeta_{14}^{3})q^{3}+(1-2\zeta_{14}+\zeta_{14}^{2}+\cdots)q^{5}+\cdots\)
464.2.y.b 464.y 29.e $6$ $3.705$ \(\Q(\zeta_{14})\) None None \(0\) \(7\) \(-1\) \(-9\) $\mathrm{SU}(2)[C_{14}]$ \(q+(1+\zeta_{14}^{3})q^{3}+(-1-\zeta_{14}^{2}-2\zeta_{14}^{4}+\cdots)q^{5}+\cdots\)
464.2.y.c 464.y 29.e $12$ $3.705$ \(\Q(\zeta_{28})\) None None \(0\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{14}]$ \(q+(\zeta_{28}-\zeta_{28}^{5}+\zeta_{28}^{11})q^{3}+(2\zeta_{28}+\cdots)q^{5}+\cdots\)
464.2.y.d 464.y 29.e $12$ $3.705$ 12.0.\(\cdots\).1 None None \(0\) \(7\) \(-1\) \(11\) $\mathrm{SU}(2)[C_{14}]$ \(q+(2+\beta _{1}+\beta _{5}+\beta _{7}+\beta _{8}-\beta _{9})q^{3}+\cdots\)
464.2.y.e 464.y 29.e $48$ $3.705$ None None \(0\) \(0\) \(-2\) \(4\) $\mathrm{SU}(2)[C_{14}]$
464.2.bc.a 464.bc 464.ac $696$ $3.705$ None None \(-10\) \(-10\) \(-14\) \(-20\) $\mathrm{SU}(2)[C_{28}]$
464.2.bi.a 464.bi 464.ai $696$ $3.705$ None None \(-10\) \(-10\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{28}]$
464.2.bj.a 464.bj 464.aj $696$ $3.705$ None None \(-14\) \(-14\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{28}]$
464.2.bl.a 464.bl 116.l $12$ $3.705$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{28}]$ \(q+(1-\zeta_{28}^{2}+2\zeta_{28}^{4}+2\zeta_{28}^{5}-\zeta_{28}^{6}+\cdots)q^{5}+\cdots\)
464.2.bl.b 464.bl 116.l $48$ $3.705$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{28}]$
464.2.bl.c 464.bl 116.l $120$ $3.705$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{28}]$
464.2.bm.a 464.bm 464.am $696$ $3.705$ None None \(-14\) \(-14\) \(-14\) \(-20\) $\mathrm{SU}(2)[C_{28}]$
464.3.d.a 464.d 4.b $8$ $12.643$ 8.0.\(\cdots\).2 None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(1-\beta _{6})q^{5}+\beta _{7}q^{7}+(-5+\cdots)q^{9}+\cdots\)
464.3.d.b 464.d 4.b $20$ $12.643$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{11}q^{3}-\beta _{3}q^{5}-\beta _{12}q^{7}+(-3+\cdots)q^{9}+\cdots\)
464.3.h.a 464.h 116.d $4$ $12.643$ \(\Q(\sqrt{5}, \sqrt{-6})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-q^{5}-\beta _{2}q^{7}-4q^{9}-3\beta _{1}q^{11}+\cdots\)
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