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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
102.2.a.a 102.a 1.a $1$ $0.814$ \(\Q\) None \(-1\) \(-1\) \(-4\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}-4q^{5}+q^{6}-2q^{7}+\cdots\)
102.2.a.b 102.a 1.a $1$ $0.814$ \(\Q\) None \(-1\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{6}+2q^{7}-q^{8}+\cdots\)
102.2.a.c 102.a 1.a $1$ $0.814$ \(\Q\) None \(1\) \(1\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}+q^{4}-2q^{5}+q^{6}+q^{8}+\cdots\)
102.2.b.a 102.b 17.b $2$ $0.814$ \(\Q(\sqrt{-1}) \) None \(2\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{2}+iq^{3}+q^{4}-2iq^{5}+iq^{6}+\cdots\)
102.2.f.a 102.f 17.c $4$ $0.814$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+(-1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
102.2.h.a 102.h 17.d $8$ $0.814$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{3}q^{3}+\zeta_{16}^{4}q^{4}+\cdots\)
102.2.h.b 102.h 17.d $8$ $0.814$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\zeta_{16}^{6}q^{2}+\zeta_{16}q^{3}-\zeta_{16}^{4}q^{4}+(1+\cdots)q^{5}+\cdots\)
102.2.i.a 102.i 51.i $24$ $0.814$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
102.2.i.b 102.i 51.i $24$ $0.814$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
102.3.c.a 102.c 3.b $12$ $2.779$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{9}q^{3}-2q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
102.3.d.a 102.d 51.c $12$ $2.779$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}+\beta _{1}q^{3}-2q^{4}-\beta _{8}q^{5}+\beta _{10}q^{6}+\cdots\)
102.3.e.a 102.e 51.f $4$ $2.779$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-20\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}-3\zeta_{8}^{3}q^{3}+2q^{4}+\cdots\)
102.3.e.b 102.e 51.f $20$ $2.779$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(4\) \(0\) \(20\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{2}q^{2}+\beta _{13}q^{3}+2q^{4}+(-\beta _{2}-\beta _{5}+\cdots)q^{5}+\cdots\)
102.3.g.a 102.g 51.g $24$ $2.779$ None \(-24\) \(-4\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$
102.3.g.b 102.g 51.g $24$ $2.779$ None \(24\) \(4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$
102.3.j.a 102.j 17.e $16$ $2.779$ 16.0.\(\cdots\).2 None \(0\) \(0\) \(0\) \(16\) $\mathrm{SU}(2)[C_{16}]$ \(q+(\beta _{2}-\beta _{10})q^{2}-\beta _{9}q^{3}-2\beta _{12}q^{4}+\cdots\)
102.3.j.b 102.j 17.e $32$ $2.779$ None \(0\) \(0\) \(0\) \(-16\) $\mathrm{SU}(2)[C_{16}]$
102.4.a.a 102.a 1.a $1$ $6.018$ \(\Q\) None \(-2\) \(-3\) \(-3\) \(20\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}+4q^{4}-3q^{5}+6q^{6}+\cdots\)
102.4.a.b 102.a 1.a $1$ $6.018$ \(\Q\) None \(-2\) \(3\) \(-5\) \(-32\) $-$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}-5q^{5}-6q^{6}+\cdots\)
102.4.a.c 102.a 1.a $1$ $6.018$ \(\Q\) None \(2\) \(-3\) \(-12\) \(-22\) $-$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}-12q^{5}-6q^{6}+\cdots\)
102.4.a.d 102.a 1.a $1$ $6.018$ \(\Q\) None \(2\) \(-3\) \(5\) \(12\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}-3q^{3}+4q^{4}+5q^{5}-6q^{6}+\cdots\)
102.4.a.e 102.a 1.a $2$ $6.018$ \(\Q(\sqrt{15}) \) None \(-4\) \(6\) \(12\) \(16\) $+$ $\mathrm{SU}(2)$ \(q-2q^{2}+3q^{3}+4q^{4}+(6+\beta )q^{5}-6q^{6}+\cdots\)
102.4.a.f 102.a 1.a $2$ $6.018$ \(\Q(\sqrt{393}) \) None \(4\) \(6\) \(3\) \(22\) $+$ $\mathrm{SU}(2)$ \(q+2q^{2}+3q^{3}+4q^{4}+(2-\beta )q^{5}+6q^{6}+\cdots\)
102.4.b.a 102.b 17.b $4$ $6.018$ \(\Q(i, \sqrt{569})\) None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-2q^{2}-\beta _{2}q^{3}+4q^{4}+(\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
102.4.b.b 102.b 17.b $6$ $6.018$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(12\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2q^{2}+\beta _{2}q^{3}+4q^{4}+(-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots\)
102.4.f.a 102.f 17.c $4$ $6.018$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(4\) \(-48\) $\mathrm{SU}(2)[C_{4}]$ \(q+2\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-4q^{4}+(1+2\zeta_{8}+\cdots)q^{5}+\cdots\)
102.4.f.b 102.f 17.c $4$ $6.018$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(32\) \(76\) $\mathrm{SU}(2)[C_{4}]$ \(q+2\zeta_{8}^{2}q^{2}-\zeta_{8}q^{3}-4q^{4}+(8-3\zeta_{8}+\cdots)q^{5}+\cdots\)
102.4.f.c 102.f 17.c $12$ $6.018$ \(\mathbb{Q}[x]/(x^{12} + \cdots)\) None \(0\) \(0\) \(16\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q-2\beta _{3}q^{2}+\beta _{5}q^{3}-4q^{4}+(1+\beta _{3}+\cdots)q^{5}+\cdots\)
102.4.h.a 102.h 17.d $16$ $6.018$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(-64\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q-2\beta _{3}q^{2}+\beta _{8}q^{3}+4\beta _{9}q^{4}+(-4+\cdots)q^{5}+\cdots\)
102.4.h.b 102.h 17.d $16$ $6.018$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+2\beta _{1}q^{2}+\beta _{8}q^{3}-4\beta _{3}q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
102.4.i.a 102.i 51.i $72$ $6.018$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
102.4.i.b 102.i 51.i $72$ $6.018$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{16}]$
102.5.c.a 102.c 3.b $20$ $10.544$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None \(0\) \(20\) \(0\) \(-104\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+(1-\beta _{4})q^{3}-8q^{4}+\beta _{2}q^{5}+\cdots\)
102.5.d.a 102.d 51.c $24$ $10.544$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
102.5.e.a 102.e 51.f $48$ $10.544$ None \(0\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
102.5.g.a 102.g 51.g $4$ $10.544$ \(\Q(\zeta_{8})\) None \(-8\) \(24\) \(8\) \(-132\) $\mathrm{SU}(2)[C_{8}]$ \(q+(-2-2\zeta_{8}^{2})q^{2}+(6+3\zeta_{8}-6\zeta_{8}^{2}+\cdots)q^{3}+\cdots\)
102.5.g.b 102.g 51.g $4$ $10.544$ \(\Q(\zeta_{8})\) None \(8\) \(12\) \(-8\) \(-132\) $\mathrm{SU}(2)[C_{8}]$ \(q+(2+2\zeta_{8}^{2})q^{2}+(3+6\zeta_{8}+6\zeta_{8}^{3})q^{3}+\cdots\)
102.5.g.c 102.g 51.g $44$ $10.544$ None \(-88\) \(-32\) \(-72\) \(132\) $\mathrm{SU}(2)[C_{8}]$
102.5.g.d 102.g 51.g $44$ $10.544$ None \(88\) \(-4\) \(72\) \(132\) $\mathrm{SU}(2)[C_{8}]$
102.5.j.a 102.j 17.e $48$ $10.544$ None \(0\) \(0\) \(0\) \(-192\) $\mathrm{SU}(2)[C_{16}]$
102.5.j.b 102.j 17.e $48$ $10.544$ None \(0\) \(0\) \(0\) \(192\) $\mathrm{SU}(2)[C_{16}]$
102.6.a.a 102.a 1.a $1$ $16.359$ \(\Q\) None \(-4\) \(-9\) \(81\) \(92\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+3^{4}q^{5}+6^{2}q^{6}+\cdots\)
102.6.a.b 102.a 1.a $1$ $16.359$ \(\Q\) None \(-4\) \(9\) \(9\) \(-88\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+9q^{5}-6^{2}q^{6}+\cdots\)
102.6.a.c 102.a 1.a $1$ $16.359$ \(\Q\) None \(4\) \(-9\) \(-9\) \(-52\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}-9q^{5}-6^{2}q^{6}+\cdots\)
102.6.a.d 102.a 1.a $1$ $16.359$ \(\Q\) None \(4\) \(-9\) \(25\) \(-188\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}-9q^{3}+2^{4}q^{4}+5^{2}q^{5}-6^{2}q^{6}+\cdots\)
102.6.a.e 102.a 1.a $1$ $16.359$ \(\Q\) None \(4\) \(9\) \(-81\) \(-88\) $+$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}-3^{4}q^{5}+6^{2}q^{6}+\cdots\)
102.6.a.f 102.a 1.a $2$ $16.359$ \(\Q(\sqrt{769}) \) None \(-8\) \(-18\) \(-53\) \(130\) $+$ $\mathrm{SU}(2)$ \(q-4q^{2}-9q^{3}+2^{4}q^{4}+(-5^{2}-3\beta )q^{5}+\cdots\)
102.6.a.g 102.a 1.a $2$ $16.359$ \(\Q(\sqrt{20209}) \) None \(-8\) \(18\) \(-25\) \(146\) $-$ $\mathrm{SU}(2)$ \(q-4q^{2}+9q^{3}+2^{4}q^{4}+(-12-\beta )q^{5}+\cdots\)
102.6.a.h 102.a 1.a $3$ $16.359$ \(\mathbb{Q}[x]/(x^{3} - \cdots)\) None \(12\) \(27\) \(53\) \(168\) $-$ $\mathrm{SU}(2)$ \(q+4q^{2}+9q^{3}+2^{4}q^{4}+(18+\beta _{2})q^{5}+\cdots\)
102.6.b.a 102.b 17.b $6$ $16.359$ \(\mathbb{Q}[x]/(x^{6} + \cdots)\) None \(24\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+4q^{2}-\beta _{2}q^{3}+2^{4}q^{4}+(\beta _{1}-3\beta _{2}+\cdots)q^{5}+\cdots\)
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