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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
90.2.a.a 90.a 1.a $1$ $0.719$ \(\Q\) None \(-1\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}+2q^{7}-q^{8}-q^{10}+\cdots\)
90.2.a.b 90.a 1.a $1$ $0.719$ \(\Q\) None \(1\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-q^{5}+2q^{7}+q^{8}-q^{10}+\cdots\)
90.2.a.c 90.a 1.a $1$ $0.719$ \(\Q\) None \(1\) \(0\) \(1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
90.2.c.a 90.c 5.b $2$ $0.719$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(2+i)q^{5}+2iq^{7}-iq^{8}+\cdots\)
90.2.e.a 90.e 9.c $2$ $0.719$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(1\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
90.2.e.b 90.e 9.c $2$ $0.719$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(-1\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
90.2.e.c 90.e 9.c $4$ $0.719$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(2\) \(2\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{3})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
90.2.f.a 90.f 15.e $4$ $0.719$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+\cdots\)
90.2.i.a 90.i 45.j $4$ $0.719$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
90.2.i.b 90.i 45.j $8$ $0.719$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{2}q^{2}+(\zeta_{24}^{2}+\zeta_{24}^{3}-\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
90.2.l.a 90.l 45.l $8$ $0.719$ \(\Q(\zeta_{24})\) None \(0\) \(4\) \(12\) \(-8\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}+(1+\zeta_{24}^{2}-\zeta_{24}^{4}+\zeta_{24}^{5}+\cdots)q^{3}+\cdots\)
90.2.l.b 90.l 45.l $16$ $0.719$ 16.0.\(\cdots\).9 None \(0\) \(0\) \(-12\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q-\beta _{11}q^{2}+(-\beta _{3}-\beta _{4}-\beta _{5}+\beta _{8}+\cdots)q^{3}+\cdots\)
90.3.b.a 90.b 15.d $4$ $2.452$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+2q^{4}+5\zeta_{8}q^{5}-4\zeta_{8}^{2}q^{7}+\cdots\)
90.3.g.a 90.g 5.c $2$ $2.452$ \(\Q(\sqrt{-1}) \) None \(-2\) \(0\) \(-6\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+2iq^{4}+(-3+4i)q^{5}+\cdots\)
90.3.g.b 90.g 5.c $2$ $2.452$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+2iq^{4}+5iq^{5}+(2+2i)q^{7}+\cdots\)
90.3.g.c 90.g 5.c $2$ $2.452$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(6\) \(16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{2}+2iq^{4}+(3-4i)q^{5}+(8+\cdots)q^{7}+\cdots\)
90.3.g.d 90.g 5.c $4$ $2.452$ \(\Q(i, \sqrt{6})\) None \(-4\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{1})q^{2}+2\beta _{1}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
90.3.h.a 90.h 9.d $16$ $2.452$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{5}q^{2}+(-1-\beta _{2}-\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{3}+\cdots\)
90.3.j.a 90.j 45.h $8$ $2.452$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}^{4}q^{2}+3\zeta_{24}q^{3}+(-2+2\zeta_{24}^{2}+\cdots)q^{4}+\cdots\)
90.3.j.b 90.j 45.h $16$ $2.452$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(30\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{7}q^{2}+\beta _{13}q^{3}+2\beta _{6}q^{4}+(2-\beta _{1}+\cdots)q^{5}+\cdots\)
90.3.k.a 90.k 45.k $24$ $2.452$ None \(-12\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{12}]$
90.3.k.b 90.k 45.k $24$ $2.452$ None \(12\) \(4\) \(0\) \(6\) $\mathrm{SU}(2)[C_{12}]$
90.4.a.a 90.a 1.a $1$ $5.310$ \(\Q\) None \(-2\) \(0\) \(-5\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-5q^{5}-4q^{7}-8q^{8}+\cdots\)
90.4.a.b 90.a 1.a $1$ $5.310$ \(\Q\) None \(-2\) \(0\) \(-5\) \(14\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}-5q^{5}+14q^{7}-8q^{8}+\cdots\)
90.4.a.c 90.a 1.a $1$ $5.310$ \(\Q\) None \(-2\) \(0\) \(5\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+4q^{4}+5q^{5}-4q^{7}-8q^{8}+\cdots\)
90.4.a.d 90.a 1.a $1$ $5.310$ \(\Q\) None \(2\) \(0\) \(-5\) \(32\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}-5q^{5}+2^{5}q^{7}+8q^{8}+\cdots\)
90.4.a.e 90.a 1.a $1$ $5.310$ \(\Q\) None \(2\) \(0\) \(5\) \(14\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+4q^{4}+5q^{5}+14q^{7}+8q^{8}+\cdots\)
90.4.c.a 90.c 5.b $2$ $5.310$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{2}-4q^{4}+(-2+11i)q^{5}+2iq^{7}+\cdots\)
90.4.c.b 90.c 5.b $2$ $5.310$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-4q^{4}+(5-5i)q^{5}-13iq^{7}+\cdots\)
90.4.c.c 90.c 5.b $4$ $5.310$ \(\Q(i, \sqrt{31})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}-4q^{4}-\beta _{1}q^{5}-\beta _{3}q^{7}+4\beta _{2}q^{8}+\cdots\)
90.4.e.a 90.e 9.c $2$ $5.310$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-9\) \(5\) \(16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{2}+(-3-3\zeta_{6})q^{3}+\cdots\)
90.4.e.b 90.e 9.c $4$ $5.310$ \(\Q(\sqrt{-3}, \sqrt{-5})\) None \(-4\) \(12\) \(10\) \(-16\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\beta _{1})q^{2}+(4-2\beta _{1}+\beta _{2})q^{3}+\cdots\)
90.4.e.c 90.e 9.c $4$ $5.310$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(4\) \(6\) \(10\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+2\beta _{1}q^{2}+(3-3\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\cdots\)
90.4.e.d 90.e 9.c $6$ $5.310$ 6.0.41783472.1 None \(6\) \(-9\) \(-15\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2+2\beta _{1})q^{2}+(-2-\beta _{4})q^{3}+4\beta _{1}q^{4}+\cdots\)
90.4.e.e 90.e 9.c $8$ $5.310$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(-8\) \(2\) \(-20\) \(-23\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2-2\beta _{3})q^{2}-\beta _{1}q^{3}+4\beta _{3}q^{4}+\cdots\)
90.4.f.a 90.f 15.e $4$ $5.310$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{4}]$ \(q+2\zeta_{8}q^{2}+4\zeta_{8}^{2}q^{4}+(5\zeta_{8}+10\zeta_{8}^{3})q^{5}+\cdots\)
90.4.f.b 90.f 15.e $8$ $5.310$ 8.0.\(\cdots\).8 None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta _{2}-\beta _{3})q^{2}-4\beta _{1}q^{4}+(3\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
90.4.i.a 90.i 45.j $36$ $5.310$ None \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{6}]$
90.4.l.a 90.l 45.l $72$ $5.310$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
90.5.b.a 90.b 15.d $8$ $9.303$ 8.0.\(\cdots\).1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+8q^{4}+(2\beta _{2}-\beta _{3}+\beta _{4})q^{5}+\cdots\)
90.5.d.a 90.d 3.b $4$ $9.303$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(32\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{1}q^{2}-8q^{4}+\beta _{2}q^{5}+(8+3\beta _{3})q^{7}+\cdots\)
90.5.d.b 90.d 3.b $4$ $9.303$ \(\Q(\sqrt{-2}, \sqrt{-5})\) None \(0\) \(0\) \(0\) \(128\) $\mathrm{SU}(2)[C_{2}]$ \(q-2\beta _{1}q^{2}-8q^{4}+\beta _{2}q^{5}+(2^{5}-3\beta _{3})q^{7}+\cdots\)
90.5.g.a 90.g 5.c $2$ $9.303$ \(\Q(\sqrt{-1}) \) None \(-4\) \(0\) \(30\) \(-38\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2i)q^{2}+8iq^{4}+(15+20i)q^{5}+\cdots\)
90.5.g.b 90.g 5.c $2$ $9.303$ \(\Q(\sqrt{-1}) \) None \(4\) \(0\) \(30\) \(58\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2i)q^{2}+8iq^{4}+(15-20i)q^{5}+\cdots\)
90.5.g.c 90.g 5.c $4$ $9.303$ \(\Q(i, \sqrt{6})\) None \(-8\) \(0\) \(-36\) \(68\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2+2\beta _{2})q^{2}-8\beta _{2}q^{4}+(-9-11\beta _{1}+\cdots)q^{5}+\cdots\)
90.5.g.d 90.g 5.c $4$ $9.303$ \(\Q(i, \sqrt{26})\) None \(-8\) \(0\) \(-24\) \(-100\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2\beta _{2})q^{2}+8\beta _{2}q^{4}+(-6-2\beta _{1}+\cdots)q^{5}+\cdots\)
90.5.g.e 90.g 5.c $4$ $9.303$ \(\Q(i, \sqrt{6})\) None \(8\) \(0\) \(-84\) \(-28\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2-2\beta _{2})q^{2}-8\beta _{2}q^{4}+(-21+\beta _{1}+\cdots)q^{5}+\cdots\)
90.5.g.f 90.g 5.c $4$ $9.303$ \(\Q(i, \sqrt{26})\) None \(8\) \(0\) \(24\) \(-100\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2\beta _{2})q^{2}+8\beta _{2}q^{4}+(6-2\beta _{1}+\cdots)q^{5}+\cdots\)
90.5.h.a 90.h 9.d $32$ $9.303$ None \(0\) \(8\) \(0\) \(52\) $\mathrm{SU}(2)[C_{6}]$
90.5.j.a 90.j 45.h $48$ $9.303$ None \(0\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{6}]$
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