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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
60.2.d.a 60.d 5.b $2$ $0.479$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1+2i)q^{5}-4iq^{7}-q^{9}+\cdots\)
60.2.e.a 60.e 12.b $8$ $0.479$ 8.0.342102016.5 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-\beta _{4}-\beta _{7})q^{3}+(\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
60.2.h.a 60.h 60.h $4$ $0.479$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}-\beta _{1}q^{3}-2q^{4}-\beta _{3}q^{5}+(-1+\cdots)q^{6}+\cdots\)
60.2.h.b 60.h 60.h $4$ $0.479$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2})q^{3}+\beta _{3}q^{4}+\cdots\)
60.2.i.a 60.i 15.e $4$ $0.479$ \(\Q(i, \sqrt{5})\) None \(0\) \(2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{1})q^{3}+(-1-\beta _{1}+\beta _{3})q^{5}+\cdots\)
60.2.j.a 60.j 20.e $12$ $0.479$ 12.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{2}-\beta _{2}q^{3}+(\beta _{2}+\beta _{4}-\beta _{7})q^{4}+\cdots\)
60.3.b.a 60.b 15.d $4$ $1.635$ \(\Q(i, \sqrt{5})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{5}+(-2\beta _{2}+2\beta _{3})q^{7}+\cdots\)
60.3.c.a 60.c 4.b $8$ $1.635$ 8.0.85100625.1 None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{2}+\beta _{4}q^{3}+(1+\beta _{2}+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots\)
60.3.f.a 60.f 20.d $4$ $1.635$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{12}+\zeta_{12}^{3})q^{2}+\zeta_{12}^{3}q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{4}+\cdots\)
60.3.f.b 60.f 20.d $8$ $1.635$ 8.0.\(\cdots\).4 None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{4})q^{4}+(1+\cdots)q^{5}+\cdots\)
60.3.g.a 60.g 3.b $2$ $1.635$ \(\Q(\sqrt{-5}) \) None \(0\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+\beta )q^{3}+\beta q^{5}+2q^{7}+(-1+4\beta )q^{9}+\cdots\)
60.3.k.a 60.k 5.c $4$ $1.635$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(12\) \(20\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{1}q^{3}+(3+\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+\cdots\)
60.3.l.a 60.l 60.l $40$ $1.635$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
60.4.a.a 60.a 1.a $1$ $3.540$ \(\Q\) None \(0\) \(-3\) \(-5\) \(-28\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-5q^{5}-28q^{7}+9q^{9}-24q^{11}+\cdots\)
60.4.a.b 60.a 1.a $1$ $3.540$ \(\Q\) None \(0\) \(-3\) \(5\) \(32\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+5q^{5}+2^{5}q^{7}+9q^{9}+6^{2}q^{11}+\cdots\)
60.4.d.a 60.d 5.b $2$ $3.540$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+(-10+5i)q^{5}+22iq^{7}+\cdots\)
60.4.e.a 60.e 12.b $24$ $3.540$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
60.4.h.a 60.h 60.h $4$ $3.540$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2\beta _{2}q^{2}+(\beta _{1}-4\beta _{2})q^{3}-8q^{4}-5\beta _{3}q^{5}+\cdots\)
60.4.h.b 60.h 60.h $4$ $3.540$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{2}+(-\beta _{1}+2\beta _{2})q^{3}+\cdots\)
60.4.h.c 60.h 60.h $24$ $3.540$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
60.4.i.a 60.i 15.e $4$ $3.540$ \(\Q(\zeta_{8})\) None \(0\) \(-4\) \(0\) \(92\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\zeta_{8}+\zeta_{8}^{2})q^{3}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
60.4.i.b 60.i 15.e $8$ $3.540$ 8.0.\(\cdots\).7 None \(0\) \(0\) \(0\) \(-80\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{3}+(\beta _{2}-\beta _{3}-\beta _{5}-\beta _{6}+\beta _{7})q^{5}+\cdots\)
60.4.j.a 60.j 20.e $8$ $3.540$ 8.0.157351936.1 None \(0\) \(0\) \(-24\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{2}+\beta _{4})q^{2}+3\beta _{5}q^{3}+(6\beta _{3}+2\beta _{6}+\cdots)q^{4}+\cdots\)
60.4.j.b 60.j 20.e $28$ $3.540$ None \(0\) \(0\) \(24\) \(0\) $\mathrm{SU}(2)[C_{4}]$
60.5.b.a 60.b 15.d $8$ $6.202$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+\beta _{2}q^{5}+\beta _{6}q^{7}+(6+\beta _{2}+\cdots)q^{9}+\cdots\)
60.5.c.a 60.c 4.b $16$ $6.202$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(-12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{3})q^{2}+\beta _{2}q^{3}+(2+\beta _{3}+\beta _{7}+\cdots)q^{4}+\cdots\)
60.5.f.a 60.f 20.d $24$ $6.202$ None \(0\) \(0\) \(-24\) \(0\) $\mathrm{SU}(2)[C_{2}]$
60.5.g.a 60.g 3.b $2$ $6.202$ \(\Q(\sqrt{-5}) \) None \(0\) \(12\) \(0\) \(148\) $\mathrm{SU}(2)[C_{2}]$ \(q+(6+3\beta )q^{3}-5\beta q^{5}+74q^{7}+(-9+\cdots)q^{9}+\cdots\)
60.5.g.b 60.g 3.b $4$ $6.202$ \(\Q(\sqrt{-5}, \sqrt{34})\) None \(0\) \(-20\) \(0\) \(-40\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-5+\beta _{1})q^{3}-\beta _{3}q^{5}+(-10-\beta _{1}+\cdots)q^{7}+\cdots\)
60.5.k.a 60.k 5.c $8$ $6.202$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(0\) \(12\) \(-140\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+(2+2\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\cdots)q^{5}+\cdots\)
60.5.l.a 60.l 60.l $88$ $6.202$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
60.6.a.a 60.a 1.a $1$ $9.623$ \(\Q\) None \(0\) \(-9\) \(-25\) \(44\) $-$ $\mathrm{SU}(2)$ \(q-9q^{3}-5^{2}q^{5}+44q^{7}+3^{4}q^{9}+6^{3}q^{11}+\cdots\)
60.6.a.b 60.a 1.a $1$ $9.623$ \(\Q\) None \(0\) \(-9\) \(25\) \(-16\) $+$ $\mathrm{SU}(2)$ \(q-9q^{3}+5^{2}q^{5}-2^{4}q^{7}+3^{4}q^{9}-564q^{11}+\cdots\)
60.6.a.c 60.a 1.a $1$ $9.623$ \(\Q\) None \(0\) \(9\) \(-25\) \(-244\) $+$ $\mathrm{SU}(2)$ \(q+9q^{3}-5^{2}q^{5}-244q^{7}+3^{4}q^{9}+\cdots\)
60.6.a.d 60.a 1.a $1$ $9.623$ \(\Q\) None \(0\) \(9\) \(25\) \(56\) $-$ $\mathrm{SU}(2)$ \(q+9q^{3}+5^{2}q^{5}+56q^{7}+3^{4}q^{9}+156q^{11}+\cdots\)
60.6.d.a 60.d 5.b $6$ $9.623$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(0\) \(0\) \(-38\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-6-\beta _{1}-\beta _{2})q^{5}+(-3\beta _{1}+\cdots)q^{7}+\cdots\)
60.6.e.a 60.e 12.b $40$ $9.623$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
60.6.h.a 60.h 60.h $4$ $9.623$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-5}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4\beta _{1}q^{2}+(10\beta _{1}+\beta _{2})q^{3}-2^{5}q^{4}+\cdots\)
60.6.h.b 60.h 60.h $4$ $9.623$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+9\beta _{1}q^{3}+(31-\beta _{3})q^{4}+(-5\beta _{1}+\cdots)q^{5}+\cdots\)
60.6.h.c 60.h 60.h $48$ $9.623$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
60.6.i.a 60.i 15.e $20$ $9.623$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(2\) \(0\) \(76\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{6}q^{3}-\beta _{5}q^{5}+(4+4\beta _{1}+\beta _{8})q^{7}+\cdots\)
60.6.j.a 60.j 20.e $60$ $9.623$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
60.7.b.a 60.b 15.d $12$ $13.803$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}-\beta _{3}q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots\)
60.7.c.a 60.c 4.b $24$ $13.803$ None \(20\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
60.7.f.a 60.f 20.d $36$ $13.803$ None \(0\) \(0\) \(44\) \(0\) $\mathrm{SU}(2)[C_{2}]$
60.7.g.a 60.g 3.b $8$ $13.803$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(0\) \(-20\) \(0\) \(-560\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-3-\beta _{1})q^{3}+\beta _{2}q^{5}+(-71-\beta _{4}+\cdots)q^{7}+\cdots\)
60.7.k.a 60.k 5.c $12$ $13.803$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(312\) \(120\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{3}+(26-4\beta _{1}+\beta _{2}+2\beta _{3}-\beta _{4}+\cdots)q^{5}+\cdots\)
60.7.l.a 60.l 60.l $136$ $13.803$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
60.8.a.a 60.a 1.a $1$ $18.743$ \(\Q\) None \(0\) \(-27\) \(-125\) \(1028\) $-$ $\mathrm{SU}(2)$ \(q-3^{3}q^{3}-5^{3}q^{5}+1028q^{7}+3^{6}q^{9}+\cdots\)
60.8.a.b 60.a 1.a $1$ $18.743$ \(\Q\) None \(0\) \(-27\) \(125\) \(-832\) $+$ $\mathrm{SU}(2)$ \(q-3^{3}q^{3}+5^{3}q^{5}-832q^{7}+3^{6}q^{9}+\cdots\)
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