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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
495.1.h.a 495.h 55.d $1$ $0.247$ \(\Q\) \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-55}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q-q^{4}+q^{5}+q^{11}+q^{16}-q^{20}+q^{25}+\cdots\)
495.1.h.b 495.h 55.d $2$ $0.247$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{2}+q^{4}-q^{5}-\beta q^{7}+\beta q^{10}+\cdots\)
495.1.h.c 495.h 55.d $2$ $0.247$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\beta q^{2}+q^{4}+q^{5}+\beta q^{7}-\beta q^{10}+\cdots\)
495.1.o.a 495.o 495.o $2$ $0.247$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(1\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}^{2}q^{9}+\cdots\)
495.1.o.b 495.o 495.o $2$ $0.247$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(-2\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}q^{4}-q^{5}+\zeta_{6}^{2}q^{9}-\zeta_{6}^{2}q^{11}+\cdots\)
495.1.bd.a 495.bd 495.ad $4$ $0.247$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{3}q^{5}+\zeta_{12}^{2}q^{9}+\cdots\)
495.1.bd.b 495.bd 495.ad $4$ $0.247$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-11}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}^{4}q^{3}-\zeta_{12}q^{4}-\zeta_{12}^{5}q^{5}-\zeta_{12}^{2}q^{9}+\cdots\)
495.2.a.a 495.a 1.a $1$ $3.953$ \(\Q\) None None \(-1\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{4}-q^{5}+3q^{8}+q^{10}+q^{11}+\cdots\)
495.2.a.b 495.a 1.a $2$ $3.953$ \(\Q(\sqrt{2}) \) None None \(-2\) \(0\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(1-2\beta )q^{4}+q^{5}-2q^{7}+\cdots\)
495.2.a.c 495.a 1.a $2$ $3.953$ \(\Q(\sqrt{3}) \) None None \(0\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+q^{4}+q^{5}+2q^{7}-\beta q^{8}+\beta q^{10}+\cdots\)
495.2.a.d 495.a 1.a $2$ $3.953$ \(\Q(\sqrt{2}) \) None None \(2\) \(0\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{2}+(1+2\beta )q^{4}+q^{5}+(-2+\cdots)q^{7}+\cdots\)
495.2.a.e 495.a 1.a $3$ $3.953$ 3.3.148.1 None None \(1\) \(0\) \(-3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(1+\beta _{1}+\beta _{2})q^{4}-q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
495.2.a.f 495.a 1.a $4$ $3.953$ 4.4.48704.2 None None \(-2\) \(0\) \(-4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}+(2+\beta _{2})q^{4}-q^{5}+\cdots\)
495.2.a.g 495.a 1.a $4$ $3.953$ 4.4.48704.2 None None \(2\) \(0\) \(4\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(2+\beta _{2})q^{4}+q^{5}+(1+\cdots)q^{7}+\cdots\)
495.2.c.a 495.c 5.b $4$ $3.953$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{2}+\beta _{3})q^{2}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
495.2.c.b 495.c 5.b $4$ $3.953$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}+\beta _{2}-\beta _{3})q^{5}+\cdots\)
495.2.c.c 495.c 5.b $4$ $3.953$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots\)
495.2.c.d 495.c 5.b $6$ $3.953$ 6.0.350464.1 None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}-\beta _{3}-\beta _{5})q^{2}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
495.2.c.e 495.c 5.b $6$ $3.953$ 6.0.350464.1 None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{2}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
495.2.d.a 495.d 165.d $4$ $3.953$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{2}+q^{4}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots\)
495.2.d.b 495.d 165.d $4$ $3.953$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
495.2.d.c 495.d 165.d $16$ $3.953$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{13}q^{2}+(-2-\beta _{3})q^{4}+\beta _{7}q^{5}+\cdots\)
495.2.f.a 495.f 33.d $16$ $3.953$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(1+\beta _{1}+\beta _{5})q^{4}+\beta _{7}q^{5}+\cdots\)
495.2.i.a 495.i 9.c $2$ $3.953$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
495.2.i.b 495.i 9.c $2$ $3.953$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
495.2.i.c 495.i 9.c $16$ $3.953$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-3\) \(0\) \(-8\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}-\beta _{4})q^{2}-\beta _{1}q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)
495.2.i.d 495.i 9.c $18$ $3.953$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(3\) \(0\) \(-9\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}-\beta _{10}q^{3}+(\beta _{1}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
495.2.i.e 495.i 9.c $20$ $3.953$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-3\) \(0\) \(10\) \(7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{10}+\beta _{14})q^{2}-\beta _{3}q^{3}+(-2-2\beta _{4}+\cdots)q^{4}+\cdots\)
495.2.i.f 495.i 9.c $22$ $3.953$ None None \(3\) \(0\) \(11\) \(-3\) $\mathrm{SU}(2)[C_{3}]$
495.2.k.a 495.k 55.e $4$ $3.953$ \(\Q(i, \sqrt{11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-2\beta _{2}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+(-2\beta _{1}+\cdots)q^{11}+\cdots\)
495.2.k.b 495.k 55.e $4$ $3.953$ \(\Q(i, \sqrt{10})\) None None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}+3\beta _{2}q^{4}+(2+\beta _{2})q^{5}+\beta _{3}q^{8}+\cdots\)
495.2.k.c 495.k 55.e $24$ $3.953$ None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
495.2.k.d 495.k 55.e $24$ $3.953$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
495.2.l.a 495.l 15.e $20$ $3.953$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{4}q^{2}+(\beta _{12}+\beta _{14})q^{4}-\beta _{9}q^{5}+\cdots\)
495.2.l.b 495.l 15.e $20$ $3.953$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{4}q^{2}+(\beta _{12}+\beta _{14})q^{4}+\beta _{9}q^{5}+\cdots\)
495.2.n.a 495.n 11.c $8$ $3.953$ 8.0.13140625.1 None None \(-4\) \(0\) \(2\) \(3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
495.2.n.b 495.n 11.c $8$ $3.953$ 8.0.819390625.1 None None \(-2\) \(0\) \(-2\) \(9\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{4}q^{2}+(1-\beta _{1}+2\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{4}+\cdots\)
495.2.n.c 495.n 11.c $8$ $3.953$ \(\Q(\zeta_{15})\) None None \(-2\) \(0\) \(2\) \(-5\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-2\zeta_{15}+\zeta_{15}^{3}-\zeta_{15}^{4}+\zeta_{15}^{5}+\cdots)q^{2}+\cdots\)
495.2.n.d 495.n 11.c $8$ $3.953$ 8.0.13140625.1 None None \(0\) \(0\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6})q^{2}+(-2\beta _{2}+\cdots)q^{4}+\cdots\)
495.2.n.e 495.n 11.c $8$ $3.953$ 8.0.13140625.1 None None \(2\) \(0\) \(-2\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{6}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{6}-\beta _{7})q^{4}+\cdots\)
495.2.n.f 495.n 11.c $8$ $3.953$ 8.0.159390625.1 None None \(4\) \(0\) \(2\) \(-3\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}+\beta _{2}-\beta _{4})q^{2}+(-2+\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
495.2.n.g 495.n 11.c $16$ $3.953$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(-2\) \(0\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\beta _{1}+\beta _{3}+\beta _{5}-\beta _{10}-\beta _{14}+\cdots)q^{2}+\cdots\)
495.2.n.h 495.n 11.c $16$ $3.953$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(2\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\beta _{1}-\beta _{3}-\beta _{5}+\beta _{10}+\beta _{14}+\cdots)q^{2}+\cdots\)
495.2.p.a 495.p 99.g $96$ $3.953$ None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
495.2.r.a 495.r 495.r $4$ $3.953$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(-1\) \(3\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q-\beta _{1}q^{3}+(-2+2\beta _{2})q^{4}+(2\beta _{2}+\beta _{3})q^{5}+\cdots\)
495.2.r.b 495.r 495.r $4$ $3.953$ \(\Q(\sqrt{-3}, \sqrt{-11})\) \(\Q(\sqrt{-11}) \) None \(0\) \(1\) \(6\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{3}+(-2+2\beta _{2})q^{4}+(1+\beta _{1}+\cdots)q^{5}+\cdots\)
495.2.r.c 495.r 495.r $128$ $3.953$ None None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$
495.2.u.a 495.u 45.j $52$ $3.953$ None None \(0\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{6}]$
495.2.u.b 495.u 45.j $68$ $3.953$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
495.2.x.a 495.x 33.f $64$ $3.953$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
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