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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
740.1.g.a 740.g 740.g $1$ $0.369$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-185}) \) \(\Q(\sqrt{185}) \) 740.1.g.a \(-1\) \(0\) \(-1\) \(0\) \(q-q^{2}+q^{4}-q^{5}-q^{8}-q^{9}+q^{10}+\cdots\)
740.1.g.b 740.g 740.g $1$ $0.369$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-185}) \) \(\Q(\sqrt{185}) \) 740.1.g.a \(1\) \(0\) \(1\) \(0\) \(q+q^{2}+q^{4}+q^{5}+q^{8}-q^{9}+q^{10}+\cdots\)
740.1.g.c 740.g 740.g $2$ $0.369$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-185}) \) None 740.1.g.c \(-2\) \(0\) \(2\) \(0\) \(q-q^{2}-\beta q^{3}+q^{4}+q^{5}+\beta q^{6}+\beta q^{7}+\cdots\)
740.1.g.d 740.g 740.g $2$ $0.369$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-185}) \) None 740.1.g.c \(2\) \(0\) \(-2\) \(0\) \(q+q^{2}-\beta q^{3}+q^{4}-q^{5}-\beta q^{6}+\beta q^{7}+\cdots\)
740.1.p.a 740.p 740.p $2$ $0.369$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 740.1.p.a \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{5}+iq^{8}+iq^{9}+\cdots\)
740.1.s.a 740.s 740.s $2$ $0.369$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 740.1.p.a \(-2\) \(0\) \(-2\) \(0\) \(q-q^{2}+q^{4}-q^{5}-q^{8}+iq^{9}+q^{10}+\cdots\)
740.1.t.a 740.t 185.j $2$ $0.369$ \(\Q(\sqrt{-1}) \) None None 740.1.t.a \(0\) \(-2\) \(2\) \(0\) \(q-q^{3}+q^{5}-iq^{7}-iq^{11}-q^{15}+\cdots\)
740.1.t.b 740.t 185.j $2$ $0.369$ \(\Q(\sqrt{-1}) \) None None 740.1.t.a \(0\) \(2\) \(0\) \(0\) \(q+q^{3}+iq^{5}+iq^{7}-iq^{11}+iq^{15}+\cdots\)
740.1.v.a 740.v 740.v $2$ $0.369$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None 740.1.v.a \(-1\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+q^{8}+\zeta_{6}q^{9}+\cdots\)
740.1.v.b 740.v 740.v $2$ $0.369$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-1}) \) None 740.1.v.a \(1\) \(0\) \(-2\) \(0\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}-q^{8}+\zeta_{6}q^{9}+\cdots\)
740.1.bj.a 740.bj 740.aj $4$ $0.369$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None 740.1.bj.a \(2\) \(0\) \(2\) \(0\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots\)
740.1.bm.a 740.bm 740.am $4$ $0.369$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None 740.1.bj.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
740.1.bu.a 740.bu 740.au $6$ $0.369$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-1}) \) None 740.1.bu.a \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{8}q^{2}-\zeta_{18}^{7}q^{4}-\zeta_{18}^{5}q^{5}+\cdots\)
740.1.bu.b 740.bu 740.au $6$ $0.369$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-1}) \) None 740.1.bu.a \(0\) \(0\) \(3\) \(0\) \(q-\zeta_{18}^{8}q^{2}-\zeta_{18}^{7}q^{4}+\zeta_{18}^{3}q^{5}+\cdots\)
740.1.bw.a 740.bw 740.aw $12$ $0.369$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-1}) \) None 740.1.bw.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{7}q^{2}+\zeta_{36}^{14}q^{4}+\zeta_{36}^{15}q^{5}+\cdots\)
740.1.cb.a 740.cb 740.bb $12$ $0.369$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-1}) \) None 740.1.bw.a \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{8}q^{2}+\zeta_{36}^{16}q^{4}+\zeta_{36}^{14}q^{5}+\cdots\)
740.2.a.a 740.a 1.a $1$ $5.909$ \(\Q\) None None 740.2.a.a \(0\) \(-1\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}-2q^{9}-3q^{11}-6q^{13}+\cdots\)
740.2.a.b 740.a 1.a $1$ $5.909$ \(\Q\) None None 740.2.a.b \(0\) \(1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}-2q^{9}-3q^{11}-4q^{13}+\cdots\)
740.2.a.c 740.a 1.a $1$ $5.909$ \(\Q\) None None 740.2.a.c \(0\) \(3\) \(-1\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}-3q^{7}+6q^{9}+5q^{11}+\cdots\)
740.2.a.d 740.a 1.a $2$ $5.909$ \(\Q(\sqrt{3}) \) None None 740.2.a.d \(0\) \(-2\) \(2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}+(3+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
740.2.a.e 740.a 1.a $3$ $5.909$ 3.3.148.1 None None 740.2.a.e \(0\) \(0\) \(-3\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}-q^{5}+(2\beta _{1}-\beta _{2})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
740.2.a.f 740.a 1.a $4$ $5.909$ 4.4.286164.1 None None 740.2.a.f \(0\) \(3\) \(4\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+q^{5}+(-1-\beta _{1})q^{7}+\cdots\)
740.2.d.a 740.d 5.b $18$ $5.909$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None 740.2.d.a \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{13}q^{3}+\beta _{10}q^{5}-\beta _{8}q^{7}+(-2+\cdots)q^{9}+\cdots\)
740.2.e.a 740.e 185.d $20$ $5.909$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None None 740.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+\beta _{1}q^{5}-\beta _{4}q^{7}+(-1-\beta _{14}+\cdots)q^{9}+\cdots\)
740.2.h.a 740.h 37.b $2$ $5.909$ \(\Q(\sqrt{-1}) \) None None 740.2.h.a \(0\) \(6\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+3q^{3}+iq^{5}-q^{7}+6q^{9}+3q^{11}+\cdots\)
740.2.h.b 740.h 37.b $12$ $5.909$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None None 740.2.h.b \(0\) \(-6\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+\beta _{3})q^{3}-\beta _{6}q^{5}+\beta _{4}q^{7}+(1+\cdots)q^{9}+\cdots\)
740.2.i.a 740.i 37.c $14$ $5.909$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None 740.2.i.a \(0\) \(0\) \(-7\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{7}q^{3}+(-1+\beta _{10})q^{5}+(1+\beta _{5}+\cdots)q^{7}+\cdots\)
740.2.i.b 740.i 37.c $14$ $5.909$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None None 740.2.i.b \(0\) \(0\) \(7\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(1-\beta _{5})q^{5}+\beta _{11}q^{7}+(-\beta _{5}+\cdots)q^{9}+\cdots\)
740.2.k.a 740.k 740.k $2$ $5.909$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 740.2.k.a \(-2\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{2}-2iq^{4}+(-1-2i)q^{5}+\cdots\)
740.2.k.b 740.k 740.k $2$ $5.909$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 740.2.k.a \(2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-i)q^{2}-2iq^{4}+(2+i)q^{5}+(-2+\cdots)q^{8}+\cdots\)
740.2.k.c 740.k 740.k $216$ $5.909$ None None 740.2.k.c \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
740.2.l.a 740.l 185.f $6$ $5.909$ 6.0.79423744.1 None None 740.2.l.a \(0\) \(2\) \(-6\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(-1-2\beta _{4})q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
740.2.l.b 740.l 185.f $32$ $5.909$ None None 740.2.l.b \(0\) \(2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$
740.2.m.a 740.m 740.m $2$ $5.909$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 740.2.m.a \(-2\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+i)q^{2}-2iq^{4}+(-2-i)q^{5}+\cdots\)
740.2.m.b 740.m 740.m $2$ $5.909$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None 740.2.m.a \(2\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1-i)q^{2}-2iq^{4}+(2+i)q^{5}+(-2+\cdots)q^{8}+\cdots\)
740.2.m.c 740.m 740.m $216$ $5.909$ None None 740.2.m.c \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
740.2.n.a 740.n 20.e $216$ $5.909$ None None 740.2.n.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
740.2.o.a 740.o 185.k $6$ $5.909$ 6.0.79423744.1 None None 740.2.l.a \(0\) \(-2\) \(12\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(2+\beta _{4})q^{5}+(-1+\beta _{2}+\beta _{4}+\cdots)q^{7}+\cdots\)
740.2.o.b 740.o 185.k $32$ $5.909$ None None 740.2.l.b \(0\) \(-2\) \(-12\) \(4\) $\mathrm{SU}(2)[C_{4}]$
740.2.u.a 740.u 148.g $152$ $5.909$ None None 740.2.u.a \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
740.2.x.a 740.x 37.e $28$ $5.909$ None None 740.2.x.a \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{6}]$
740.2.ba.a 740.ba 185.l $40$ $5.909$ None None 740.2.ba.a \(0\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{6}]$
740.2.bb.a 740.bb 185.n $36$ $5.909$ None None 740.2.bb.a \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{6}]$
740.2.bc.a 740.bc 37.f $6$ $5.909$ \(\Q(\zeta_{18})\) None None 740.2.bc.a \(0\) \(-3\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-\zeta_{18}-\zeta_{18}^{2}-\zeta_{18}^{3})q^{3}+(-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
740.2.bc.b 740.bc 37.f $12$ $5.909$ 12.0.\(\cdots\).1 None None 740.2.bc.b \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{9}]$ \(q+(3+\beta _{1}+\beta _{2}-\beta _{4}-\beta _{5}-\beta _{6}+\beta _{8}+\cdots)q^{3}+\cdots\)
740.2.bc.c 740.bc 37.f $18$ $5.909$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None 740.2.bc.c \(0\) \(-9\) \(0\) \(3\) $\mathrm{SU}(2)[C_{9}]$ \(q+(-1+\beta _{5}-\beta _{6})q^{3}-\beta _{1}q^{5}+(\beta _{4}+\cdots)q^{7}+\cdots\)
740.2.bc.d 740.bc 37.f $36$ $5.909$ None None 740.2.bc.d \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{9}]$
740.2.be.a 740.be 148.l $304$ $5.909$ None None 740.2.be.a \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
740.2.bf.a 740.bf 185.p $76$ $5.909$ None None 740.2.bf.a \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
740.2.bg.a 740.bg 740.ag $4$ $5.909$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-1}) \) None 740.2.bg.a \(2\) \(0\) \(-8\) \(0\) $\mathrm{U}(1)[D_{12}]$ \(q+(-\zeta_{12}+\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}-2\zeta_{12}q^{4}+\cdots\)
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