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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
80.1.h.a 80.h 20.d $1$ $0.040$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots\)
80.2.a.a 80.a 1.a $1$ $0.639$ \(\Q\) None None \(0\) \(0\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-3q^{9}-4q^{11}-2q^{13}+\cdots\)
80.2.a.b 80.a 1.a $1$ $0.639$ \(\Q\) None None \(0\) \(2\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{5}-2q^{7}+q^{9}+2q^{13}+\cdots\)
80.2.c.a 80.c 5.b $2$ $0.639$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1+i)q^{5}-iq^{7}-q^{9}+\cdots\)
80.2.j.a 80.j 80.j $2$ $0.639$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(2\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{2}+2iq^{3}-2iq^{4}+(1+2i)q^{5}+\cdots\)
80.2.j.b 80.j 80.j $18$ $0.639$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(-4\) \(0\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{6}q^{2}-\beta _{16}q^{3}-\beta _{13}q^{4}+(-1+\cdots)q^{5}+\cdots\)
80.2.l.a 80.l 16.e $16$ $0.639$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{9}q^{2}+(\beta _{3}-\beta _{6}+\beta _{11})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
80.2.n.a 80.n 20.e $2$ $0.639$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(2+i)q^{5}-3iq^{9}+(-5+5i)q^{13}+\cdots\)
80.2.n.b 80.n 20.e $4$ $0.639$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{12}^{2}q^{3}+(-1-2\zeta_{12})q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
80.2.q.a 80.q 80.q $2$ $0.639$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+(1+i)q^{3}+2iq^{4}+\cdots\)
80.2.q.b 80.q 80.q $2$ $0.639$ \(\Q(\sqrt{-1}) \) None None \(2\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+(-1-i)q^{3}+2iq^{4}+\cdots\)
80.2.q.c 80.q 80.q $16$ $0.639$ 16.0.\(\cdots\).1 None None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{12}q^{2}+(-\beta _{3}-\beta _{11}-\beta _{13}+\beta _{14}+\cdots)q^{3}+\cdots\)
80.2.s.a 80.s 80.s $2$ $0.639$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-4\) \(-4\) \(-6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{2}-2q^{3}-2iq^{4}+(-2+\cdots)q^{5}+\cdots\)
80.2.s.b 80.s 80.s $18$ $0.639$ \(\mathbb{Q}[x]/(x^{18} + \cdots)\) None None \(0\) \(0\) \(2\) \(2\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{2}-\beta _{3}q^{3}+\beta _{13}q^{4}+\beta _{17}q^{5}+\cdots\)
80.3.b.a 80.b 4.b $4$ $2.180$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{1}q^{5}-\beta _{3}q^{7}+(-9+6\beta _{1}+\cdots)q^{9}+\cdots\)
80.3.h.a 80.h 20.d $2$ $2.180$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(10\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{3}+5q^{5}+3\beta q^{7}+11q^{9}-5\beta q^{15}+\cdots\)
80.3.h.b 80.h 20.d $4$ $2.180$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-1+\beta _{2})q^{5}+3\beta _{1}q^{7}+\cdots\)
80.3.i.a 80.i 80.i $44$ $2.180$ None None \(-2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$
80.3.k.a 80.k 80.k $44$ $2.180$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$
80.3.p.a 80.p 5.c $2$ $2.180$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(-6\) \(14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+(-3+4i)q^{5}+(7+7i)q^{7}+\cdots\)
80.3.p.b 80.p 5.c $2$ $2.180$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(10\) \(6\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{3}+5q^{5}+(3+3i)q^{7}+\cdots\)
80.3.p.c 80.p 5.c $2$ $2.180$ \(\Q(\sqrt{-1}) \) None None \(0\) \(4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2-2i)q^{3}-5iq^{5}+(-2-2i)q^{7}+\cdots\)
80.3.p.d 80.p 5.c $4$ $2.180$ \(\Q(i, \sqrt{41})\) None None \(0\) \(2\) \(-6\) \(-14\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots\)
80.3.r.a 80.r 16.f $32$ $2.180$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
80.3.t.a 80.t 80.t $44$ $2.180$ None None \(-2\) \(-4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$
80.4.a.a 80.a 1.a $1$ $4.720$ \(\Q\) None None \(0\) \(-10\) \(-5\) \(18\) $+$ $\mathrm{SU}(2)$ \(q-10q^{3}-5q^{5}+18q^{7}+73q^{9}+2^{4}q^{11}+\cdots\)
80.4.a.b 80.a 1.a $1$ $4.720$ \(\Q\) None None \(0\) \(-4\) \(5\) \(-16\) $-$ $\mathrm{SU}(2)$ \(q-4q^{3}+5q^{5}-2^{4}q^{7}-11q^{9}-6^{2}q^{11}+\cdots\)
80.4.a.c 80.a 1.a $1$ $4.720$ \(\Q\) None None \(0\) \(-4\) \(5\) \(16\) $+$ $\mathrm{SU}(2)$ \(q-4q^{3}+5q^{5}+2^{4}q^{7}-11q^{9}+60q^{11}+\cdots\)
80.4.a.d 80.a 1.a $1$ $4.720$ \(\Q\) None None \(0\) \(-2\) \(-5\) \(-6\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-5q^{5}-6q^{7}-23q^{9}-2^{5}q^{11}+\cdots\)
80.4.a.e 80.a 1.a $1$ $4.720$ \(\Q\) None None \(0\) \(6\) \(-5\) \(34\) $+$ $\mathrm{SU}(2)$ \(q+6q^{3}-5q^{5}+34q^{7}+9q^{9}-2^{4}q^{11}+\cdots\)
80.4.a.f 80.a 1.a $1$ $4.720$ \(\Q\) None None \(0\) \(8\) \(5\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+8q^{3}+5q^{5}+4q^{7}+37q^{9}-12q^{11}+\cdots\)
80.4.c.a 80.c 5.b $2$ $4.720$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-5-5i)q^{5}-13iq^{7}+23q^{9}+\cdots\)
80.4.c.b 80.c 5.b $2$ $4.720$ \(\Q(\sqrt{-19}) \) None None \(0\) \(0\) \(14\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{3}+(7-\beta )q^{5}+\beta q^{7}-7^{2}q^{9}+\cdots\)
80.4.c.c 80.c 5.b $4$ $4.720$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-1-\beta _{1}-\beta _{3})q^{5}+(2\beta _{1}+\cdots)q^{7}+\cdots\)
80.4.j.a 80.j 80.j $68$ $4.720$ None None \(-2\) \(0\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
80.4.l.a 80.l 16.e $48$ $4.720$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
80.4.n.a 80.n 20.e $2$ $4.720$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(2-11i)q^{5}-3^{3}iq^{9}+(55-55i)q^{13}+\cdots\)
80.4.n.b 80.n 20.e $4$ $4.720$ \(\Q(i, \sqrt{35})\) None None \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{3}+(-5+10\beta _{1})q^{5}+\beta _{3}q^{7}+\cdots\)
80.4.n.c 80.n 20.e $12$ $4.720$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(16\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{3}+(1+\beta _{1}+\beta _{4})q^{5}+(-2\beta _{2}+\cdots)q^{7}+\cdots\)
80.4.q.a 80.q 80.q $68$ $4.720$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$
80.4.s.a 80.s 80.s $68$ $4.720$ None None \(-2\) \(-4\) \(-2\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
80.5.b.a 80.b 4.b $4$ $8.270$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{2}q^{5}+\beta _{3}q^{7}+(-9-6\beta _{2}+\cdots)q^{9}+\cdots\)
80.5.b.b 80.b 4.b $4$ $8.270$ \(\Q(\sqrt{-3}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-5\beta _{1}q^{5}+(2\beta _{2}+7\beta _{3})q^{7}+\cdots\)
80.5.h.a 80.h 20.d $2$ $8.270$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-50\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{3}-5^{2}q^{5}-3\beta q^{7}+239q^{9}+\cdots\)
80.5.h.b 80.h 20.d $2$ $8.270$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(14\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(7+i)q^{5}-3^{4}q^{9}+10iq^{13}+20iq^{17}+\cdots\)
80.5.h.c 80.h 20.d $8$ $8.270$ 8.0.\(\cdots\).10 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{3}+\beta _{4}q^{5}+(2\beta _{3}-\beta _{7})q^{7}+(1+\cdots)q^{9}+\cdots\)
80.5.i.a 80.i 80.i $92$ $8.270$ None None \(-2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$
80.5.k.a 80.k 80.k $92$ $8.270$ None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$
80.5.p.a 80.p 5.c $2$ $8.270$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-20\) \(40\) \(84\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-10+10i)q^{3}+(20+15i)q^{5}+\cdots\)
80.5.p.b 80.p 5.c $2$ $8.270$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-18\) \(-30\) \(-58\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-9+9i)q^{3}+(-15+20i)q^{5}+\cdots\)
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