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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
460.1.d.a 460.d 115.c $1$ $0.230$ \(\Q\) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(-1\) \(1\) \(q-q^{5}+q^{7}+q^{9}+q^{17}-q^{23}+q^{25}+\cdots\)
460.1.d.b 460.d 115.c $1$ $0.230$ \(\Q\) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(1\) \(-1\) \(q+q^{5}-q^{7}+q^{9}-q^{17}+q^{23}+q^{25}+\cdots\)
460.1.n.a 460.n 460.n $10$ $0.230$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-5}) \) None \(-1\) \(-2\) \(-1\) \(9\) \(q+\zeta_{22}^{10}q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{4})q^{3}-\zeta_{22}^{9}q^{4}+\cdots\)
460.1.n.b 460.n 460.n $10$ $0.230$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-5}) \) None \(1\) \(2\) \(-1\) \(-9\) \(q-\zeta_{22}^{10}q^{2}+(-\zeta_{22}^{2}-\zeta_{22}^{4})q^{3}+\cdots\)
460.2.a.a 460.a 1.a $1$ $3.673$ \(\Q\) None None \(0\) \(-1\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-2q^{7}-2q^{9}-4q^{11}+\cdots\)
460.2.a.b 460.a 1.a $1$ $3.673$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-q^{7}-3q^{9}+6q^{11}+6q^{13}+\cdots\)
460.2.a.c 460.a 1.a $1$ $3.673$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}-2q^{9}-6q^{11}+\cdots\)
460.2.a.d 460.a 1.a $1$ $3.673$ \(\Q\) None None \(0\) \(3\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}+2q^{7}+6q^{9}-3q^{13}+\cdots\)
460.2.a.e 460.a 1.a $2$ $3.673$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+(1-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
460.2.c.a 460.c 5.b $12$ $3.673$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{5}+\beta _{6})q^{3}+\beta _{9}q^{5}+(-\beta _{1}-\beta _{6}+\cdots)q^{7}+\cdots\)
460.2.e.a 460.e 92.b $16$ $3.673$ 16.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{2}+\beta _{8}q^{3}+(-\beta _{2}+\beta _{8})q^{4}+\cdots\)
460.2.e.b 460.e 92.b $32$ $3.673$ None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
460.2.g.a 460.g 460.g $4$ $3.673$ \(\Q(\sqrt{2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+2q^{6}+\cdots\)
460.2.g.b 460.g 460.g $8$ $3.673$ 8.0.207360000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{4})q^{3}+(-1-\beta _{3}+\cdots)q^{4}+\cdots\)
460.2.g.c 460.g 460.g $56$ $3.673$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
460.2.i.a 460.i 115.e $8$ $3.673$ 8.0.\(\cdots\).3 None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{3})q^{3}+(-\beta _{1}+\beta _{6})q^{5}-\beta _{2}q^{7}+\cdots\)
460.2.i.b 460.i 115.e $16$ $3.673$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{6}q^{3}-\beta _{3}q^{5}+(-\beta _{3}+\beta _{15})q^{7}+\cdots\)
460.2.j.a 460.j 20.e $132$ $3.673$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
460.2.m.a 460.m 23.c $30$ $3.673$ None None \(0\) \(0\) \(-3\) \(1\) $\mathrm{SU}(2)[C_{11}]$
460.2.m.b 460.m 23.c $50$ $3.673$ None None \(0\) \(0\) \(5\) \(-1\) $\mathrm{SU}(2)[C_{11}]$
460.2.o.a 460.o 460.o $40$ $3.673$ \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{22}]$
460.2.o.b 460.o 460.o $640$ $3.673$ None None \(0\) \(0\) \(-22\) \(0\) $\mathrm{SU}(2)[C_{22}]$
460.2.q.a 460.q 92.h $480$ $3.673$ None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
460.2.s.a 460.s 115.j $120$ $3.673$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
460.2.w.a 460.w 460.w $1360$ $3.673$ None None \(-18\) \(0\) \(-36\) \(0\) $\mathrm{SU}(2)[C_{44}]$
460.2.x.a 460.x 115.l $240$ $3.673$ None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{44}]$
460.3.b.a 460.b 4.b $88$ $12.534$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
460.3.d.a 460.d 115.c $2$ $12.534$ \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(-10\) \(-9\) $\mathrm{U}(1)[D_{2}]$ \(q-5q^{5}+(-4-\beta )q^{7}+9q^{9}+(4+3\beta )q^{17}+\cdots\)
460.3.d.b 460.d 115.c $2$ $12.534$ \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(10\) \(9\) $\mathrm{U}(1)[D_{2}]$ \(q+5q^{5}+(4+\beta )q^{7}+9q^{9}+(-4-3\beta )q^{17}+\cdots\)
460.3.d.c 460.d 115.c $20$ $12.534$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+\beta _{1}q^{5}-\beta _{16}q^{7}+(-4+\beta _{11}+\cdots)q^{9}+\cdots\)
460.3.f.a 460.f 23.b $16$ $12.534$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+\beta _{4}q^{5}-\beta _{7}q^{7}+(4+\beta _{2}+\cdots)q^{9}+\cdots\)
460.3.l.a 460.l 5.c $44$ $12.534$ None None \(0\) \(0\) \(8\) \(16\) $\mathrm{SU}(2)[C_{4}]$
460.4.a.a 460.a 1.a $5$ $27.141$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-7\) \(25\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{3})q^{3}+5q^{5}+(-5-\beta _{1}+\cdots)q^{7}+\cdots\)
460.4.a.b 460.a 1.a $5$ $27.141$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-3\) \(-25\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-5q^{5}+(2-\beta _{2}-\beta _{3}+\cdots)q^{7}+\cdots\)
460.4.a.c 460.a 1.a $6$ $27.141$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(-1\) \(30\) \(24\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+5q^{5}+(4+\beta _{3}-\beta _{4})q^{7}+\cdots\)
460.4.a.d 460.a 1.a $6$ $27.141$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None None \(0\) \(3\) \(-30\) \(20\) $+$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}-5q^{5}+(3+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
460.4.c.a 460.c 5.b $32$ $27.141$ None None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{2}]$
460.4.i.a 460.i 115.e $72$ $27.141$ None None \(0\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
460.5.d.a 460.d 115.c $2$ $47.550$ \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(-50\) \(-17\) $\mathrm{U}(1)[D_{2}]$ \(q-5^{2}q^{5}+(-10-3\beta )q^{7}+3^{4}q^{9}+\cdots\)
460.5.d.b 460.d 115.c $2$ $47.550$ \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(50\) \(17\) $\mathrm{U}(1)[D_{2}]$ \(q+5^{2}q^{5}+(10+3\beta )q^{7}+3^{4}q^{9}+(234+\cdots)q^{17}+\cdots\)
460.5.d.c 460.d 115.c $44$ $47.550$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
460.5.f.a 460.f 23.b $32$ $47.550$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
460.5.l.a 460.l 5.c $88$ $47.550$ None None \(0\) \(0\) \(48\) \(-160\) $\mathrm{SU}(2)[C_{4}]$
460.6.a.a 460.a 1.a $9$ $73.777$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(-31\) \(-225\) \(-319\) $+$ $\mathrm{SU}(2)$ \(q+(-3-\beta _{1})q^{3}-5^{2}q^{5}+(-35-\beta _{1}+\cdots)q^{7}+\cdots\)
460.6.a.b 460.a 1.a $9$ $73.777$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) None None \(0\) \(-9\) \(225\) \(-95\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}+5^{2}q^{5}+(-11+2\beta _{1}+\cdots)q^{7}+\cdots\)
460.6.a.c 460.a 1.a $10$ $73.777$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(-13\) \(-250\) \(-28\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta _{1})q^{3}-5^{2}q^{5}+(-3+2\beta _{1}+\cdots)q^{7}+\cdots\)
460.6.a.d 460.a 1.a $10$ $73.777$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(9\) \(250\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+5^{2}q^{5}+(1-\beta _{1}-\beta _{3}+\cdots)q^{7}+\cdots\)
460.6.c.a 460.c 5.b $56$ $73.777$ None None \(0\) \(0\) \(-60\) \(0\) $\mathrm{SU}(2)[C_{2}]$
460.7.d.a 460.d 115.c $2$ $105.825$ \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(-250\) \(594\) $\mathrm{U}(1)[D_{2}]$ \(q-5^{3}q^{5}+(297-4\beta )q^{7}+3^{6}q^{9}+(-4103+\cdots)q^{17}+\cdots\)
460.7.d.b 460.d 115.c $2$ $105.825$ \(\Q(\sqrt{345}) \) \(\Q(\sqrt{-115}) \) None \(0\) \(0\) \(250\) \(-594\) $\mathrm{U}(1)[D_{2}]$ \(q+5^{3}q^{5}+(-297-4\beta )q^{7}+3^{6}q^{9}+\cdots\)
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