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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
320.1.h.a 320.h 20.d $1$ $0.160$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+q^{5}-q^{9}+q^{25}-2q^{29}-2q^{41}+\cdots\)
320.1.p.a 320.p 5.c $2$ $0.160$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{5}+iq^{9}+(1-i)q^{13}+(-1-i+\cdots)q^{17}+\cdots\)
320.2.a.a 320.a 1.a $1$ $2.555$ \(\Q\) None None \(0\) \(-2\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}-2q^{7}+q^{9}-2q^{13}+\cdots\)
320.2.a.b 320.a 1.a $1$ $2.555$ \(\Q\) None None \(0\) \(-2\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots\)
320.2.a.c 320.a 1.a $1$ $2.555$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}-3q^{9}-4q^{11}+2q^{13}+\cdots\)
320.2.a.d 320.a 1.a $1$ $2.555$ \(\Q\) None None \(0\) \(0\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-3q^{9}+4q^{11}+2q^{13}+\cdots\)
320.2.a.e 320.a 1.a $1$ $2.555$ \(\Q\) None None \(0\) \(2\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots\)
320.2.a.f 320.a 1.a $1$ $2.555$ \(\Q\) None None \(0\) \(2\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots\)
320.2.a.g 320.a 1.a $2$ $2.555$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots\)
320.2.c.a 320.c 5.b $2$ $2.555$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1+i)q^{5}+3q^{9}+2iq^{13}+4iq^{17}+\cdots\)
320.2.c.b 320.c 5.b $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1+i)q^{5}+iq^{7}-q^{9}-4q^{11}+\cdots\)
320.2.c.c 320.c 5.b $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1-i)q^{5}+iq^{7}-q^{9}+4q^{11}+\cdots\)
320.2.c.d 320.c 5.b $4$ $2.555$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots\)
320.2.d.a 320.d 8.b $4$ $2.555$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}q^{5}+(-3+\cdots)q^{7}+\cdots\)
320.2.d.b 320.d 8.b $4$ $2.555$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}q^{5}+(3-\zeta_{12}^{3})q^{7}+\cdots\)
320.2.f.a 320.f 40.f $4$ $2.555$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{5}+\beta _{2}q^{7}-3q^{9}+\beta _{1}q^{11}+\cdots\)
320.2.f.b 320.f 40.f $8$ $2.555$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{4}q^{3}-\zeta_{24}^{6}q^{5}+\zeta_{24}^{2}q^{7}+\cdots\)
320.2.j.a 320.j 80.j $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q-2iq^{3}+(1+2i)q^{5}+(3+3i)q^{7}+\cdots\)
320.2.j.b 320.j 80.j $18$ $2.555$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(-4\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{12}q^{3}-\beta _{4}q^{5}+\beta _{10}q^{7}+(-1+\cdots)q^{9}+\cdots\)
320.2.l.a 320.l 16.e $16$ $2.555$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{5}+\beta _{7})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots\)
320.2.n.a 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-4\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2i)q^{3}+(2-i)q^{5}+(2-2i)q^{7}+\cdots\)
320.2.n.b 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-2\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(-1-2i)q^{5}+(-3+\cdots)q^{7}+\cdots\)
320.2.n.c 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(-1+2i)q^{5}+(1-i)q^{7}+\cdots\)
320.2.n.d 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-2-i)q^{5}-3iq^{9}+(5-5i)q^{13}+\cdots\)
320.2.n.e 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(2-i)q^{5}-3iq^{9}+(1-i)q^{13}+(3+\cdots)q^{17}+\cdots\)
320.2.n.f 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(-1+2i)q^{5}+(-1+i)q^{7}+\cdots\)
320.2.n.g 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(-1-2i)q^{5}+(3-3i)q^{7}+\cdots\)
320.2.n.h 320.n 20.e $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2i)q^{3}+(2-i)q^{5}+(-2+2i)q^{7}+\cdots\)
320.2.n.i 320.n 20.e $4$ $2.555$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{2}q^{3}+(1+2\zeta_{12})q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
320.2.o.a 320.o 40.k $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(-1-2i)q^{5}+(-1+\cdots)q^{7}+\cdots\)
320.2.o.b 320.o 40.k $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(1+2i)q^{5}+(1-i)q^{7}+\cdots\)
320.2.o.c 320.o 40.k $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(-1-2i)q^{5}+(1-i)q^{7}+\cdots\)
320.2.o.d 320.o 40.k $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{3}+(1+2i)q^{5}+(-1+i)q^{7}+\cdots\)
320.2.o.e 320.o 40.k $8$ $2.555$ 8.0.49787136.1 None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{2}-\beta _{7})q^{3}+\beta _{7}q^{5}-\beta _{6}q^{7}+\cdots\)
320.2.o.f 320.o 40.k $8$ $2.555$ 8.0.49787136.1 None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{2}-\beta _{7})q^{3}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots\)
320.2.q.a 320.q 80.q $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{3}+(1+2i)q^{5}-iq^{9}+\cdots\)
320.2.q.b 320.q 80.q $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{3}+(2+i)q^{5}-iq^{9}+(3+3i)q^{11}+\cdots\)
320.2.q.c 320.q 80.q $16$ $2.555$ 16.0.\(\cdots\).1 None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{11}q^{3}+(-1-\beta _{6}-\beta _{10})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
320.2.s.a 320.s 80.s $2$ $2.555$ \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(-4\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+2q^{3}+(-2+i)q^{5}+(3+3i)q^{7}+\cdots\)
320.2.s.b 320.s 80.s $18$ $2.555$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{3}+\beta _{7}q^{5}+\beta _{10}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots\)
320.2.bd.a 320.bd 320.ad $368$ $2.555$ None None \(-8\) \(-8\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
320.2.be.a 320.be 64.i $256$ $2.555$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
320.2.bf.a 320.bf 320.af $368$ $2.555$ None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{16}]$
320.2.bj.a 320.bj 320.aj $368$ $2.555$ None None \(-8\) \(-8\) \(-8\) \(-8\) $\mathrm{SU}(2)[C_{16}]$
320.3.b.a 320.b 4.b $4$ $8.719$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+(-9+6\beta _{1}+\cdots)q^{9}+\cdots\)
320.3.b.b 320.b 4.b $4$ $8.719$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-4\beta _{2})q^{7}+(-5+\cdots)q^{9}+\cdots\)
320.3.b.c 320.b 4.b $4$ $8.719$ \(\Q(\zeta_{10})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{5}+(-\zeta_{10}+\zeta_{10}^{3})q^{7}+\cdots\)
320.3.b.d 320.b 4.b $4$ $8.719$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(3+2\beta _{2}+\cdots)q^{9}+\cdots\)
320.3.e.a 320.e 40.e $8$ $8.719$ 8.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{3}+(-\beta _{4}-\beta _{6})q^{5}+\beta _{2}q^{7}+\cdots\)
320.3.e.b 320.e 40.e $16$ $8.719$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{11}q^{7}+(-6-\beta _{5}+\cdots)q^{9}+\cdots\)
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