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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
580.1.e.a 580.e 580.e $1$ $0.289$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-145}) \) \(\Q(\sqrt{145}) \) 580.1.e.a \(-1\) \(0\) \(-1\) \(0\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{9}+q^{10}+\cdots\)
580.1.e.b 580.e 580.e $1$ $0.289$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-145}) \) \(\Q(\sqrt{145}) \) 580.1.e.a \(1\) \(0\) \(-1\) \(0\) \(q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots\)
580.1.e.c 580.e 580.e $2$ $0.289$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-29}) \) \(\Q(\sqrt{145}) \) 580.1.e.c \(0\) \(0\) \(2\) \(0\) \(q-iq^{2}-iq^{3}-q^{4}+q^{5}-2q^{6}+iq^{8}+\cdots\)
580.1.e.d 580.e 580.e $4$ $0.289$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-29}) \) None 580.1.e.d \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{12}^{3}q^{2}-\zeta_{12}^{3}q^{3}-q^{4}+\zeta_{12}^{4}q^{5}+\cdots\)
580.1.i.a 580.i 580.i $2$ $0.289$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 580.1.i.a \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{5}+iq^{8}+q^{9}+q^{10}+\cdots\)
580.1.t.a 580.t 580.t $2$ $0.289$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 580.1.i.a \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+iq^{5}+q^{8}-q^{9}+iq^{10}+\cdots\)
580.1.v.a 580.v 580.v $6$ $0.289$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-5}) \) None 580.1.v.a \(-1\) \(-2\) \(-1\) \(5\) \(q+\zeta_{14}^{2}q^{2}+(-\zeta_{14}-\zeta_{14}^{5})q^{3}+\zeta_{14}^{4}q^{4}+\cdots\)
580.1.v.b 580.v 580.v $6$ $0.289$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-5}) \) None 580.1.v.a \(1\) \(2\) \(-1\) \(-5\) \(q-\zeta_{14}^{2}q^{2}+(\zeta_{14}+\zeta_{14}^{5})q^{3}+\zeta_{14}^{4}q^{4}+\cdots\)
580.1.y.a 580.y 580.y $6$ $0.289$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-1}) \) None 580.1.y.a \(-1\) \(0\) \(1\) \(0\) \(q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}-\zeta_{14}^{4}q^{5}-\zeta_{14}^{3}q^{8}+\cdots\)
580.1.y.b 580.y 580.y $6$ $0.289$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-1}) \) None 580.1.y.a \(1\) \(0\) \(1\) \(0\) \(q+\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+\zeta_{14}^{5}q^{5}+\zeta_{14}^{3}q^{8}+\cdots\)
580.1.y.c 580.y 580.y $12$ $0.289$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-5}) \) None 580.1.y.c \(0\) \(0\) \(-2\) \(0\) \(q+\zeta_{28}^{9}q^{2}+(\zeta_{28}+\zeta_{28}^{5})q^{3}-\zeta_{28}^{4}q^{4}+\cdots\)
580.1.bd.a 580.bd 580.ad $12$ $0.289$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-1}) \) None 580.1.bd.a \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{28}^{2}q^{2}+\zeta_{28}^{4}q^{4}-\zeta_{28}q^{5}-\zeta_{28}^{6}q^{8}+\cdots\)
580.1.bm.a 580.bm 580.am $12$ $0.289$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-1}) \) None 580.1.bd.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}+\zeta_{28}q^{5}+\zeta_{28}^{9}q^{8}+\cdots\)
580.2.a.a 580.a 1.a $1$ $4.631$ \(\Q\) None None 580.2.a.a \(0\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-3q^{9}-2q^{11}-2q^{13}-2q^{19}+\cdots\)
580.2.a.b 580.a 1.a $1$ $4.631$ \(\Q\) None None 580.2.a.b \(0\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-3q^{9}-4q^{11}-6q^{13}+\cdots\)
580.2.a.c 580.a 1.a $3$ $4.631$ 3.3.564.1 None None 580.2.a.c \(0\) \(2\) \(-3\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta _{2})q^{3}-q^{5}+(-1+\beta _{2})q^{7}+\cdots\)
580.2.a.d 580.a 1.a $3$ $4.631$ 3.3.148.1 None None 580.2.a.d \(0\) \(2\) \(3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+(1-\beta _{2})q^{7}+(1+\cdots)q^{9}+\cdots\)
580.2.c.a 580.c 5.b $4$ $4.631$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None 580.2.c.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{1}q^{7}+\cdots\)
580.2.c.b 580.c 5.b $10$ $4.631$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None 580.2.c.b \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{7}q^{5}+(-\beta _{1}+\beta _{8}+\beta _{9})q^{7}+\cdots\)
580.2.d.a 580.d 29.b $2$ $4.631$ \(\Q(\sqrt{-7}) \) None None 580.2.d.a \(0\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{5}-2q^{7}+3q^{9}-\beta q^{11}-2q^{13}+\cdots\)
580.2.d.b 580.d 29.b $4$ $4.631$ 4.0.7168.1 None None 580.2.d.b \(0\) \(0\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-q^{5}+(2+\beta _{3})q^{7}+(-3+2\beta _{3})q^{9}+\cdots\)
580.2.d.c 580.d 29.b $4$ $4.631$ \(\Q(\sqrt{-2}, \sqrt{11})\) None None 580.2.d.c \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+q^{5}+(-1+\beta _{3})q^{7}+q^{9}+\cdots\)
580.2.f.a 580.f 145.d $16$ $4.631$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None 580.2.f.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{9}q^{5}+\beta _{10}q^{7}+(2+\beta _{5}+\cdots)q^{9}+\cdots\)
580.2.j.a 580.j 145.j $30$ $4.631$ None None 580.2.j.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
580.2.k.a 580.k 116.e $60$ $4.631$ None None 580.2.k.a \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
580.2.k.b 580.k 116.e $60$ $4.631$ None None 580.2.k.b \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
580.2.n.a 580.n 20.e $2$ $4.631$ \(\Q(\sqrt{-1}) \) None None 580.2.n.a \(-2\) \(-2\) \(2\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{2}+(-1-i)q^{3}-2iq^{4}+\cdots\)
580.2.n.b 580.n 20.e $2$ $4.631$ \(\Q(\sqrt{-1}) \) None None 580.2.n.a \(2\) \(2\) \(2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{2}+(1+i)q^{3}-2iq^{4}+(1+\cdots)q^{5}+\cdots\)
580.2.n.c 580.n 20.e $8$ $4.631$ 8.0.18939904.2 None None 580.2.n.c \(4\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{3}+\beta _{6})q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots\)
580.2.n.d 580.n 20.e $76$ $4.631$ None None 580.2.n.d \(-4\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{4}]$
580.2.n.e 580.n 20.e $80$ $4.631$ None None 580.2.n.e \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
580.2.o.a 580.o 580.o $2$ $4.631$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 580.2.o.a \(-2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{2}-2iq^{4}+(2+i)q^{5}+\cdots\)
580.2.o.b 580.o 580.o $2$ $4.631$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 580.2.o.a \(2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-i)q^{2}-2iq^{4}+(2+i)q^{5}+(-2+\cdots)q^{8}+\cdots\)
580.2.o.c 580.o 580.o $12$ $4.631$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) \(\Q(\sqrt{-29}) \) None 580.2.o.c \(-12\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-\beta _{3})q^{2}-\beta _{7}q^{3}+2\beta _{3}q^{4}+\cdots\)
580.2.o.d 580.o 580.o $12$ $4.631$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) \(\Q(\sqrt{-29}) \) None 580.2.o.c \(12\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-\beta _{1})q^{2}+\beta _{5}q^{3}-2\beta _{1}q^{4}+\beta _{2}q^{5}+\cdots\)
580.2.o.e 580.o 580.o $144$ $4.631$ None None 580.2.o.e \(0\) \(0\) \(-16\) \(0\) $\mathrm{SU}(2)[C_{4}]$
580.2.r.a 580.r 580.r $2$ $4.631$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 580.2.r.a \(-2\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{2}-2iq^{4}+(-1+2i)q^{5}+\cdots\)
580.2.r.b 580.r 580.r $2$ $4.631$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 580.2.r.a \(2\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-i)q^{2}-2iq^{4}+(1+2i)q^{5}+(-2+\cdots)q^{8}+\cdots\)
580.2.r.c 580.r 580.r $4$ $4.631$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) None 580.2.r.c \(-4\) \(-4\) \(0\) \(-12\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-\beta _{1})q^{2}+(-1-\beta _{1})q^{3}+2\beta _{1}q^{4}+\cdots\)
580.2.r.d 580.r 580.r $4$ $4.631$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) None 580.2.r.c \(4\) \(4\) \(0\) \(12\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+\beta _{1})q^{2}+(1+\beta _{1})q^{3}+2\beta _{1}q^{4}+\cdots\)
580.2.r.e 580.r 580.r $160$ $4.631$ None None 580.2.r.e \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
580.2.s.a 580.s 145.e $30$ $4.631$ None None 580.2.j.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
580.2.u.a 580.u 29.d $24$ $4.631$ None None 580.2.u.a \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{7}]$
580.2.u.b 580.u 29.d $36$ $4.631$ None None 580.2.u.b \(0\) \(2\) \(6\) \(0\) $\mathrm{SU}(2)[C_{7}]$
580.2.x.a 580.x 145.l $96$ $4.631$ None None 580.2.x.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{14}]$
580.2.z.a 580.z 29.e $24$ $4.631$ None None 580.2.z.a \(0\) \(0\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{14}]$
580.2.z.b 580.z 29.e $36$ $4.631$ None None 580.2.z.b \(0\) \(0\) \(6\) \(-4\) $\mathrm{SU}(2)[C_{14}]$
580.2.ba.a 580.ba 145.n $84$ $4.631$ None None 580.2.ba.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{14}]$
580.2.bc.a 580.bc 145.t $180$ $4.631$ None None 580.2.bc.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{28}]$
580.2.be.a 580.be 580.ae $12$ $4.631$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-1}) \) None 580.2.be.a \(-2\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{28}]$ \(q+(\zeta_{28}+\zeta_{28}^{8})q^{2}+2\zeta_{28}^{9}q^{4}+(-1+\cdots)q^{5}+\cdots\)
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