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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
760.1.b.a 760.b 760.b $8$ $0.379$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{2}+(\zeta_{16}^{3}+\zeta_{16}^{5})q^{3}+\zeta_{16}^{2}q^{4}+\cdots\)
760.1.bm.a 760.bm 760.am $2$ $0.379$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-10}) \) None \(-1\) \(0\) \(-1\) \(-2\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{7}+q^{8}+\cdots\)
760.1.bm.b 760.bm 760.am $2$ $0.379$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-10}) \) None \(1\) \(0\) \(1\) \(2\) \(q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{7}-q^{8}+\cdots\)
760.1.bt.a 760.bt 95.m $4$ $0.379$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(0\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{4})q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{9}+\cdots\)
760.1.bz.a 760.bz 760.az $6$ $0.379$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}-\zeta_{18}^{5}q^{5}+\cdots\)
760.1.bz.b 760.bz 760.az $6$ $0.379$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+\zeta_{18}^{5}q^{5}+\cdots\)
760.2.a.a 760.a 1.a $1$ $6.069$ \(\Q\) None None \(0\) \(-2\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+q^{9}-4q^{11}+4q^{13}+\cdots\)
760.2.a.b 760.a 1.a $1$ $6.069$ \(\Q\) None None \(0\) \(-2\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+\cdots\)
760.2.a.c 760.a 1.a $1$ $6.069$ \(\Q\) None None \(0\) \(0\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}-4q^{11}-6q^{13}-6q^{17}+\cdots\)
760.2.a.d 760.a 1.a $1$ $6.069$ \(\Q\) None None \(0\) \(2\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+4q^{7}+q^{9}-4q^{11}+\cdots\)
760.2.a.e 760.a 1.a $1$ $6.069$ \(\Q\) None None \(0\) \(3\) \(1\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}-q^{7}+6q^{9}+4q^{11}+\cdots\)
760.2.a.f 760.a 1.a $2$ $6.069$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+2\beta q^{7}-q^{9}+(2+2\beta )q^{11}+\cdots\)
760.2.a.g 760.a 1.a $2$ $6.069$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+(1+2\beta )q^{9}+2q^{11}+\cdots\)
760.2.a.h 760.a 1.a $3$ $6.069$ 3.3.568.1 None None \(0\) \(-1\) \(-3\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(-2-\beta _{2})q^{7}+(1+2\beta _{1}+\cdots)q^{9}+\cdots\)
760.2.a.i 760.a 1.a $3$ $6.069$ 3.3.316.1 None None \(0\) \(-1\) \(-3\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}-q^{5}+(-1+2\beta _{1}-\beta _{2})q^{7}+\cdots\)
760.2.a.j 760.a 1.a $3$ $6.069$ 3.3.229.1 None None \(0\) \(-1\) \(3\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}+q^{5}+\beta _{1}q^{7}+(1-\beta _{1})q^{9}+\cdots\)
760.2.d.a 760.d 5.b $2$ $6.069$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1+i)q^{5}+iq^{7}-q^{9}+\cdots\)
760.2.d.b 760.d 5.b $4$ $6.069$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
760.2.d.c 760.d 5.b $4$ $6.069$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(\zeta_{8}-2\zeta_{8}^{3})q^{5}+\cdots\)
760.2.d.d 760.d 5.b $4$ $6.069$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{3}+(1+\zeta_{8})q^{5}+(-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
760.2.d.e 760.d 5.b $12$ $6.069$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{11}q^{3}-\beta _{1}q^{5}+(\beta _{5}+\beta _{11})q^{7}+\cdots\)
760.2.e.a 760.e 152.b $80$ $6.069$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
760.2.f.a 760.f 8.b $28$ $6.069$ None None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$
760.2.f.b 760.f 8.b $44$ $6.069$ None None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$
760.2.k.a 760.k 40.f $108$ $6.069$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
760.2.p.a 760.p 760.p $4$ $6.069$ \(\Q(\sqrt{-2}, \sqrt{5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-2q^{4}-\beta _{3}q^{5}+2\beta _{3}q^{7}+\cdots\)
760.2.p.b 760.p 760.p $4$ $6.069$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots\)
760.2.p.c 760.p 760.p $4$ $6.069$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}+\beta _{2})q^{2}-2\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+\cdots\)
760.2.p.d 760.p 760.p $8$ $6.069$ 8.0.1499238400.2 None None \(-8\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{5})q^{2}-q^{3}+2\beta _{5}q^{4}+(\beta _{5}+\cdots)q^{5}+\cdots\)
760.2.p.e 760.p 760.p $8$ $6.069$ 8.0.5473632256.3 None None \(-4\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
760.2.p.f 760.p 760.p $8$ $6.069$ 8.0.5473632256.3 None None \(4\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}-q^{3}+(-1-\beta _{3}-\beta _{4}-\beta _{6}+\cdots)q^{4}+\cdots\)
760.2.p.g 760.p 760.p $8$ $6.069$ 8.0.1499238400.2 None None \(8\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+\beta _{5})q^{2}+q^{3}+2\beta _{5}q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
760.2.p.h 760.p 760.p $16$ $6.069$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+\beta _{4}q^{5}+\cdots\)
760.2.p.i 760.p 760.p $56$ $6.069$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
760.2.q.a 760.q 19.c $2$ $6.069$ \(\Q(\sqrt{-3}) \) None None \(0\) \(1\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}-2q^{7}+\cdots\)
760.2.q.b 760.q 19.c $2$ $6.069$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(-1\) \(8\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{5}+4q^{7}+\cdots\)
760.2.q.c 760.q 19.c $2$ $6.069$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-2\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
760.2.q.d 760.q 19.c $8$ $6.069$ 8.0.\(\cdots\).1 None None \(0\) \(-1\) \(-4\) \(-6\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}-\beta _{4}q^{5}+(-1+\beta _{3})q^{7}+(-4+\cdots)q^{9}+\cdots\)
760.2.q.e 760.q 19.c $8$ $6.069$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None None \(0\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(1-\beta _{5})q^{5}+(-1-\beta _{4}+2\beta _{7})q^{7}+\cdots\)
760.2.q.f 760.q 19.c $8$ $6.069$ 8.0.4601315889.1 None None \(0\) \(1\) \(-4\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{7}q^{3}-\beta _{5}q^{5}+(-\beta _{2}-\beta _{3}-\beta _{4}+\cdots)q^{7}+\cdots\)
760.2.q.g 760.q 19.c $10$ $6.069$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(0\) \(1\) \(5\) \(10\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(1-\beta _{6})q^{5}+(1+\beta _{5})q^{7}+\cdots\)
760.2.t.a 760.t 760.t $232$ $6.069$ None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$
760.2.v.a 760.v 95.g $12$ $6.069$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(-12\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{10}q^{3}+(-1-2\beta _{5})q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
760.2.v.b 760.v 95.g $48$ $6.069$ None None \(0\) \(0\) \(12\) \(4\) $\mathrm{SU}(2)[C_{4}]$
760.2.w.a 760.w 40.k $2$ $6.069$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(4\) \(2\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{2}+(2-2i)q^{3}-2iq^{4}+\cdots\)
760.2.w.b 760.w 40.k $2$ $6.069$ \(\Q(\sqrt{-1}) \) None None \(2\) \(4\) \(-2\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{2}+(2-2i)q^{3}-2iq^{4}+(-1+\cdots)q^{5}+\cdots\)
760.2.w.c 760.w 40.k $104$ $6.069$ None None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
760.2.w.d 760.w 40.k $108$ $6.069$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
760.2.z.a 760.z 760.z $232$ $6.069$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
760.2.bf.a 760.bf 760.af $8$ $6.069$ 8.0.207360000.2 \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+\beta _{1}q^{2}+(2+2\beta _{4})q^{4}-\beta _{6}q^{5}+(-2\beta _{1}+\cdots)q^{7}+\cdots\)
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