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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
7.3.b.a 7.b 7.b $1$ $0.191$ \(\Q\) \(\Q(\sqrt{-7}) \) \(-3\) \(0\) \(0\) \(-7\) $\mathrm{U}(1)[D_{2}]$ \(q-3q^{2}+5q^{4}-7q^{7}-3q^{8}+9q^{9}+\cdots\)
8.3.d.a 8.d 8.d $1$ $0.218$ \(\Q\) \(\Q(\sqrt{-2}) \) \(-2\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots\)
9.3.d.a 9.d 9.d $2$ $0.245$ \(\Q(\sqrt{-3}) \) None \(-3\) \(-3\) \(6\) \(-2\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{2}+(-3+3\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
10.3.c.a 10.c 5.c $2$ $0.272$ \(\Q(\sqrt{-1}) \) None \(-2\) \(-4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots\)
5.4.a.a 5.a 1.a $1$ $0.295$ \(\Q\) None \(-4\) \(2\) \(-5\) \(6\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+2q^{3}+8q^{4}-5q^{5}-8q^{6}+\cdots\)
6.4.a.a 6.a 1.a $1$ $0.354$ \(\Q\) None \(-2\) \(-3\) \(6\) \(-16\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}+6q^{5}+6q^{6}+\cdots\)
7.4.a.a 7.a 1.a $1$ $0.413$ \(\Q\) None \(-1\) \(-2\) \(16\) \(-7\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}-7q^{4}+2^{4}q^{5}+2q^{6}+\cdots\)
7.4.c.a 7.c 7.c $2$ $0.413$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-7\) \(-7\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}-7\zeta_{6}q^{3}+4\zeta_{6}q^{4}+\cdots\)
4.5.b.a 4.b 4.b $1$ $0.413$ \(\Q\) \(\Q(\sqrt{-1}) \) \(-4\) \(0\) \(-14\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-4q^{2}+2^{4}q^{4}-14q^{5}-2^{6}q^{8}+3^{4}q^{9}+\cdots\)
8.4.a.a 8.a 1.a $1$ $0.472$ \(\Q\) None \(0\) \(-4\) \(-2\) \(24\) $+$ $\mathrm{SU}(2)$ \(q-4q^{3}-2q^{5}+24q^{7}-11q^{9}-44q^{11}+\cdots\)
8.4.b.a 8.b 8.b $2$ $0.472$ \(\Q(\sqrt{-7}) \) None \(-2\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta )q^{2}+2\beta q^{3}+(-6+2\beta )q^{4}+\cdots\)
3.6.a.a 3.a 1.a $1$ $0.481$ \(\Q\) None \(-6\) \(9\) \(6\) \(-40\) $-$ $\mathrm{SU}(2)$ \(q-6q^{2}+9q^{3}+4q^{4}+6q^{5}-54q^{6}+\cdots\)
5.5.c.a 5.c 5.c $2$ $0.517$ \(\Q(\sqrt{-1}) \) None \(-2\) \(-12\) \(40\) \(-52\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+(-6+6i)q^{3}-14iq^{4}+\cdots\)
9.4.a.a 9.a 1.a $1$ $0.531$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(0\) \(0\) \(20\) $+$ $N(\mathrm{U}(1))$ \(q-8q^{4}+20q^{7}-70q^{13}+2^{6}q^{16}+\cdots\)
9.4.c.a 9.c 9.c $4$ $0.531$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-3\) \(-3\) \(-15\) \(-7\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
10.4.a.a 10.a 1.a $1$ $0.590$ \(\Q\) None \(2\) \(-8\) \(5\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-8q^{3}+4q^{4}+5q^{5}-2^{4}q^{6}+\cdots\)
10.4.b.a 10.b 5.b $2$ $0.590$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-iq^{3}-4q^{4}+(-5-5i)q^{5}+\cdots\)
6.5.b.a 6.b 3.b $2$ $0.620$ \(\Q(\sqrt{-2}) \) None \(0\) \(-6\) \(0\) \(52\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-3-3\beta )q^{3}-8q^{4}+6\beta q^{5}+\cdots\)
2.8.a.a 2.a 1.a $1$ $0.625$ \(\Q\) None \(-8\) \(12\) \(-210\) \(1016\) $+$ $\mathrm{SU}(2)$ \(q-8q^{2}+12q^{3}+2^{6}q^{4}-210q^{5}+\cdots\)
4.6.a.a 4.a 1.a $1$ $0.642$ \(\Q\) None \(0\) \(-12\) \(54\) \(-88\) $-$ $\mathrm{SU}(2)$ \(q-12q^{3}+54q^{5}-88q^{7}-99q^{9}+\cdots\)
3.7.b.a 3.b 3.b $1$ $0.690$ \(\Q\) \(\Q(\sqrt{-3}) \) \(0\) \(-27\) \(0\) \(-286\) $\mathrm{U}(1)[D_{2}]$ \(q-3^{3}q^{3}+2^{6}q^{4}-286q^{7}+3^{6}q^{9}+\cdots\)
7.5.b.a 7.b 7.b $1$ $0.724$ \(\Q\) \(\Q(\sqrt{-7}) \) \(1\) \(0\) \(0\) \(49\) $\mathrm{U}(1)[D_{2}]$ \(q+q^{2}-15q^{4}+7^{2}q^{7}-31q^{8}+3^{4}q^{9}+\cdots\)
7.5.d.a 7.d 7.d $4$ $0.724$ \(\Q(\sqrt{-3}, \sqrt{22})\) None \(-4\) \(6\) \(-30\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2+\beta _{1}-2\beta _{2})q^{2}+(2-\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
5.6.a.a 5.a 1.a $1$ $0.802$ \(\Q\) None \(2\) \(-4\) \(25\) \(192\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-4q^{3}-28q^{4}+5^{2}q^{5}-8q^{6}+\cdots\)
5.6.b.a 5.b 5.b $2$ $0.802$ \(\Q(\sqrt{-11}) \) None \(0\) \(0\) \(-90\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta q^{2}+3\beta q^{3}-12q^{4}+(-45-5\beta )q^{5}+\cdots\)
8.5.d.a 8.d 8.d $1$ $0.827$ \(\Q\) \(\Q(\sqrt{-2}) \) \(4\) \(-14\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+4q^{2}-14q^{3}+2^{4}q^{4}-56q^{6}+2^{6}q^{8}+\cdots\)
8.5.d.b 8.d 8.d $2$ $0.827$ \(\Q(\sqrt{-15}) \) None \(-2\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta )q^{2}+6q^{3}+(-14+2\beta )q^{4}+\cdots\)
4.7.b.a 4.b 4.b $2$ $0.920$ \(\Q(\sqrt{-15}) \) None \(4\) \(0\) \(20\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+\beta )q^{2}-4\beta q^{3}+(-56+4\beta )q^{4}+\cdots\)
9.5.b.a 9.b 3.b $2$ $0.930$ \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(-56\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}-2q^{4}-7\beta q^{5}-28q^{7}+14\beta q^{8}+\cdots\)
9.5.d.a 9.d 9.d $6$ $0.930$ 6.0.39400128.1 None \(-3\) \(-3\) \(-12\) \(12\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{2}q^{2}+(-3+\beta _{1}-3\beta _{3}+\beta _{4})q^{3}+\cdots\)
3.8.a.a 3.a 1.a $1$ $0.937$ \(\Q\) None \(6\) \(-27\) \(390\) \(-64\) $+$ $\mathrm{SU}(2)$ \(q+6q^{2}-3^{3}q^{3}-92q^{4}+390q^{5}+\cdots\)
6.6.a.a 6.a 1.a $1$ $0.962$ \(\Q\) None \(4\) \(-9\) \(-66\) \(176\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}-66q^{5}-6^{2}q^{6}+\cdots\)
2.10.a.a 2.a 1.a $1$ $1.030$ \(\Q\) None \(16\) \(-156\) \(870\) \(-952\) $-$ $\mathrm{SU}(2)$ \(q+2^{4}q^{2}-156q^{3}+2^{8}q^{4}+870q^{5}+\cdots\)
10.5.c.a 10.c 5.c $2$ $1.034$ \(\Q(\sqrt{-1}) \) None \(-4\) \(18\) \(-30\) \(58\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2i)q^{2}+(9-9i)q^{3}+8iq^{4}+\cdots\)
10.5.c.b 10.c 5.c $2$ $1.034$ \(\Q(\sqrt{-1}) \) None \(4\) \(2\) \(-30\) \(-38\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2i)q^{2}+(1-i)q^{3}+8iq^{4}+(-15+\cdots)q^{5}+\cdots\)
7.6.a.a 7.a 1.a $1$ $1.123$ \(\Q\) None \(-10\) \(-14\) \(-56\) \(-49\) $+$ $\mathrm{SU}(2)$ \(q-10q^{2}-14q^{3}+68q^{4}-56q^{5}+\cdots\)
7.6.a.b 7.a 1.a $2$ $1.123$ \(\Q(\sqrt{57}) \) None \(9\) \(-6\) \(-18\) \(98\) $-$ $\mathrm{SU}(2)$ \(q+(5-\beta )q^{2}+(-6+6\beta )q^{3}+(7-9\beta )q^{4}+\cdots\)
7.6.c.a 7.c 7.c $4$ $1.123$ \(\Q(\sqrt{-3}, \sqrt{37})\) None \(-2\) \(8\) \(38\) \(-168\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}-\beta _{2})q^{2}+(4-4\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
5.7.c.a 5.c 5.c $4$ $1.150$ \(\Q(i, \sqrt{201})\) None \(-10\) \(30\) \(-70\) \(550\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2+2\beta _{1}+\beta _{3})q^{2}+(7+8\beta _{1}+\beta _{2}+\cdots)q^{3}+\cdots\)
3.9.b.a 3.b 3.b $2$ $1.222$ \(\Q(\sqrt{-14}) \) None \(0\) \(90\) \(0\) \(-3500\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(45-3\beta )q^{3}-248q^{4}-10\beta q^{5}+\cdots\)
8.6.a.a 8.a 1.a $1$ $1.283$ \(\Q\) None \(0\) \(20\) \(-74\) \(-24\) $-$ $\mathrm{SU}(2)$ \(q+20q^{3}-74q^{5}-24q^{7}+157q^{9}+\cdots\)
8.6.b.a 8.b 8.b $4$ $1.283$ 4.0.218489.1 None \(-2\) \(0\) \(0\) \(96\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{1})q^{2}+(-\beta _{1}+\beta _{3})q^{3}+(5+\cdots)q^{4}+\cdots\)
6.7.b.a 6.b 3.b $2$ $1.380$ \(\Q(\sqrt{-2}) \) None \(0\) \(42\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(21+3\beta )q^{3}-2^{5}q^{4}-30\beta q^{5}+\cdots\)
9.6.a.a 9.a 1.a $1$ $1.443$ \(\Q\) None \(6\) \(0\) \(-6\) \(-40\) $-$ $\mathrm{SU}(2)$ \(q+6q^{2}+4q^{4}-6q^{5}-40q^{7}-168q^{8}+\cdots\)
9.6.c.a 9.c 9.c $8$ $1.443$ \(\mathbb{Q}[x]/(x^{8} + \cdots)\) None \(3\) \(-12\) \(78\) \(28\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{1}+\beta _{4}+\beta _{5})q^{2}+(-3+3\beta _{1}+\cdots)q^{3}+\cdots\)
3.10.a.a 3.a 1.a $1$ $1.545$ \(\Q\) None \(-36\) \(-81\) \(-1314\) \(-4480\) $+$ $\mathrm{SU}(2)$ \(q-6^{2}q^{2}-3^{4}q^{3}+28^{2}q^{4}-1314q^{5}+\cdots\)
3.10.a.b 3.a 1.a $1$ $1.545$ \(\Q\) None \(18\) \(81\) \(-1530\) \(9128\) $-$ $\mathrm{SU}(2)$ \(q+18q^{2}+3^{4}q^{3}-188q^{4}-1530q^{5}+\cdots\)
5.8.a.a 5.a 1.a $1$ $1.562$ \(\Q\) None \(-14\) \(-48\) \(125\) \(-1644\) $-$ $\mathrm{SU}(2)$ \(q-14q^{2}-48q^{3}+68q^{4}+5^{3}q^{5}+\cdots\)
5.8.a.b 5.a 1.a $2$ $1.562$ \(\Q(\sqrt{19}) \) None \(20\) \(20\) \(-250\) \(-100\) $+$ $\mathrm{SU}(2)$ \(q+(10+\beta )q^{2}+(10-8\beta )q^{3}+(48+20\beta )q^{4}+\cdots\)
5.8.b.a 5.b 5.b $2$ $1.562$ \(\Q(\sqrt{-29}) \) None \(0\) \(0\) \(150\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+3\beta q^{3}+12q^{4}+(75-5^{2}\beta )q^{5}+\cdots\)
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