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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
65.2.a.a 65.a 1.a $1$ $0.519$ \(\Q\) None \(-1\) \(-2\) \(-1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-q^{4}-q^{5}+2q^{6}-4q^{7}+\cdots\)
65.2.a.b 65.a 1.a $2$ $0.519$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+\beta q^{3}+(1-2\beta )q^{4}+\cdots\)
65.2.a.c 65.a 1.a $2$ $0.519$ \(\Q(\sqrt{3}) \) None \(0\) \(2\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(1-\beta )q^{3}+q^{4}-q^{5}+(-3+\cdots)q^{6}+\cdots\)
65.2.b.a 65.b 5.b $6$ $0.519$ 6.0.350464.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
65.2.c.a 65.c 13.b $6$ $0.519$ 6.0.5089536.1 None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(-1-\beta _{1})q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots\)
65.2.d.a 65.d 65.d $2$ $0.519$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+iq^{3}-q^{4}+(-1+i)q^{5}-iq^{6}+\cdots\)
65.2.d.b 65.d 65.d $2$ $0.519$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}-q^{4}+(1-i)q^{5}+iq^{6}+\cdots\)
65.2.e.a 65.e 13.c $4$ $0.519$ \(\Q(\sqrt{-3}, \sqrt{5})\) None \(-1\) \(0\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-1+2\beta _{1}-\beta _{3})q^{3}+(\beta _{1}+\cdots)q^{4}+\cdots\)
65.2.e.b 65.e 13.c $4$ $0.519$ \(\Q(\sqrt{-3}, \sqrt{13})\) None \(1\) \(-2\) \(-4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{2}+(-1-\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
65.2.f.a 65.f 65.f $2$ $0.519$ \(\Q(\sqrt{-1}) \) None \(0\) \(2\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+iq^{2}+(1-i)q^{3}+q^{4}+(-2-i)q^{5}+\cdots\)
65.2.f.b 65.f 65.f $8$ $0.519$ 8.0.619810816.2 None \(0\) \(-6\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{2}+(-1+\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
65.2.k.a 65.k 65.k $2$ $0.519$ \(\Q(\sqrt{-1}) \) None \(2\) \(2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+(1+i)q^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
65.2.k.b 65.k 65.k $8$ $0.519$ 8.0.619810816.2 None \(-4\) \(-6\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{5}q^{2}+(-1+\beta _{2}+\beta _{4}-\beta _{5})q^{3}+\cdots\)
65.2.l.a 65.l 65.l $8$ $0.519$ 8.0.49787136.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(\beta _{1}+\beta _{5})q^{2}+(\beta _{3}+\beta _{5})q^{3}+(\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
65.2.m.a 65.m 13.e $8$ $0.519$ 8.0.22581504.2 None \(0\) \(2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+\beta _{1}+\beta _{2}+\beta _{4}-\beta _{5})q^{2}+(\beta _{2}+\cdots)q^{3}+\cdots\)
65.2.n.a 65.n 65.n $12$ $0.519$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{4}q^{2}+(\beta _{4}-\beta _{11})q^{3}+(-\beta _{2}-\beta _{6}+\cdots)q^{4}+\cdots\)
65.2.o.a 65.o 65.o $20$ $0.519$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-4\) \(-2\) \(-6\) \(-6\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\beta _{3}+\beta _{4})q^{2}+(\beta _{2}+\beta _{4}+\beta _{8}-\beta _{12}+\cdots)q^{3}+\cdots\)
65.2.t.a 65.t 65.t $20$ $0.519$ \(\mathbb{Q}[x]/(x^{20} + \cdots)\) None \(-6\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{12}]$ \(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots\)
65.3.g.a 65.g 65.g $24$ $1.771$ None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$
65.3.h.a 65.h 65.h $24$ $1.771$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
65.3.i.a 65.i 5.c $24$ $1.771$ None \(0\) \(-4\) \(4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$
65.3.j.a 65.j 13.d $16$ $1.771$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(20\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}+\beta _{6}q^{3}+(\beta _{1}-\beta _{2}+\beta _{8}+\beta _{12}+\cdots)q^{4}+\cdots\)
65.3.p.a 65.p 13.f $40$ $1.771$ None \(0\) \(0\) \(0\) \(-40\) $\mathrm{SU}(2)[C_{12}]$
65.3.q.a 65.q 65.q $48$ $1.771$ None \(-6\) \(-2\) \(-16\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
65.3.r.a 65.r 65.r $48$ $1.771$ None \(-6\) \(-2\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{12}]$
65.3.s.a 65.s 65.s $48$ $1.771$ None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{12}]$
65.4.a.a 65.a 1.a $1$ $3.835$ \(\Q\) None \(5\) \(2\) \(-5\) \(-12\) $+$ $\mathrm{SU}(2)$ \(q+5q^{2}+2q^{3}+17q^{4}-5q^{5}+10q^{6}+\cdots\)
65.4.a.b 65.a 1.a $2$ $3.835$ \(\Q(\sqrt{6}) \) None \(-2\) \(-4\) \(10\) \(-20\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{2}+(-2-\beta )q^{3}+(-1+\cdots)q^{4}+\cdots\)
65.4.a.c 65.a 1.a $2$ $3.835$ \(\Q(\sqrt{17}) \) None \(1\) \(0\) \(-10\) \(58\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{2}+(-2+4\beta )q^{3}+(-4+\beta )q^{4}+\cdots\)
65.4.a.d 65.a 1.a $2$ $3.835$ \(\Q(\sqrt{3}) \) None \(4\) \(-10\) \(-10\) \(-36\) $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{2}+(-5-3\beta )q^{3}+(-1+4\beta )q^{4}+\cdots\)
65.4.a.e 65.a 1.a $5$ $3.835$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None \(0\) \(8\) \(25\) \(38\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+(2+\beta _{1}+\beta _{3})q^{3}+(7-\beta _{2}+\cdots)q^{4}+\cdots\)
65.4.b.a 65.b 5.b $2$ $3.835$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{2}-4iq^{3}-q^{4}+(2-11i)q^{5}+\cdots\)
65.4.b.b 65.b 5.b $16$ $3.835$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+\beta _{4}q^{3}+(-4+\beta _{1})q^{4}+(-1+\cdots)q^{5}+\cdots\)
65.4.c.a 65.c 13.b $14$ $3.835$ \(\mathbb{Q}[x]/(x^{14} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{4}q^{3}+(-4+\beta _{2})q^{4}-\beta _{7}q^{5}+\cdots\)
65.4.d.a 65.d 65.d $2$ $3.835$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(10\) \(48\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{2}+iq^{3}-7q^{4}+(5-5i)q^{5}-iq^{6}+\cdots\)
65.4.d.b 65.d 65.d $2$ $3.835$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(-10\) \(-48\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}-7q^{4}+(-5+5i)q^{5}+\cdots\)
65.4.d.c 65.d 65.d $16$ $3.835$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{2}-\beta _{6}q^{3}+(6+\beta _{2})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots\)
65.4.e.a 65.e 13.c $14$ $3.835$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(-2\) \(4\) \(-70\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{2}+(-\beta _{6}+\beta _{11})q^{3}+(-4-\beta _{5}+\cdots)q^{4}+\cdots\)
65.4.e.b 65.e 13.c $14$ $3.835$ \(\mathbb{Q}[x]/(x^{14} - \cdots)\) None \(2\) \(8\) \(70\) \(75\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(1+\beta _{4}-\beta _{6}-\beta _{11}+\cdots)q^{3}+\cdots\)
65.4.f.a 65.f 65.f $2$ $3.835$ \(\Q(\sqrt{-1}) \) None \(0\) \(-10\) \(20\) \(-52\) $\mathrm{SU}(2)[C_{4}]$ \(q+iq^{2}+(-5+5i)q^{3}+7q^{4}+(10+\cdots)q^{5}+\cdots\)
65.4.f.b 65.f 65.f $36$ $3.835$ None \(0\) \(6\) \(-30\) \(48\) $\mathrm{SU}(2)[C_{4}]$
65.4.k.a 65.k 65.k $2$ $3.835$ \(\Q(\sqrt{-1}) \) None \(2\) \(-10\) \(10\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+q^{2}+(-5-5i)q^{3}-7q^{4}+(5+10i)q^{5}+\cdots\)
65.4.k.b 65.k 65.k $36$ $3.835$ None \(-2\) \(6\) \(-26\) \(0\) $\mathrm{SU}(2)[C_{4}]$
65.4.l.a 65.l 65.l $40$ $3.835$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$
65.4.m.a 65.m 13.e $28$ $3.835$ None \(0\) \(-12\) \(0\) \(-36\) $\mathrm{SU}(2)[C_{6}]$
65.4.n.a 65.n 65.n $36$ $3.835$ None \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{6}]$
65.4.o.a 65.o 65.o $76$ $3.835$ None \(-6\) \(-2\) \(10\) \(-6\) $\mathrm{SU}(2)[C_{12}]$
65.4.t.a 65.t 65.t $76$ $3.835$ None \(-6\) \(-2\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{12}]$
65.5.g.a 65.g 65.g $52$ $6.719$ None \(0\) \(0\) \(58\) \(0\) $\mathrm{SU}(2)[C_{4}]$
65.5.h.a 65.h 65.h $52$ $6.719$ None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
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