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Results (19 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
503.1.b.a 503.b 503.b $1$ $0.251$ \(\Q\) \(\Q(\sqrt{-503}) \) None \(2\) \(-1\) \(0\) \(-1\) \(q+2q^{2}-q^{3}+3q^{4}-2q^{6}-q^{7}+4q^{8}+\cdots\)
503.1.b.b 503.b 503.b $3$ $0.251$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-503}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q-\beta _{1}q^{2}-\beta _{1}q^{3}+(1+\beta _{2})q^{4}+(2+\beta _{2})q^{6}+\cdots\)
503.1.b.c 503.b 503.b $6$ $0.251$ \(\Q(\zeta_{21})^+\) \(\Q(\sqrt{-503}) \) None \(-2\) \(1\) \(0\) \(1\) \(q+\beta _{3}q^{2}+\beta _{4}q^{3}+(-\beta _{3}+\beta _{5})q^{4}+\cdots\)
503.2.a.a 503.a 1.a $1$ $4.016$ \(\Q\) None None \(-1\) \(1\) \(-4\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}-q^{4}-4q^{5}-q^{6}-3q^{7}+\cdots\)
503.2.a.b 503.a 1.a $1$ $4.016$ \(\Q\) None None \(1\) \(1\) \(-2\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{3}-q^{4}-2q^{5}+q^{6}-3q^{7}+\cdots\)
503.2.a.c 503.a 1.a $1$ $4.016$ \(\Q\) None None \(1\) \(3\) \(-2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}-q^{4}-2q^{5}+3q^{6}+3q^{7}+\cdots\)
503.2.a.d 503.a 1.a $3$ $4.016$ 3.3.257.1 None None \(0\) \(1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{2}+\beta _{1}q^{3}+(1+\beta _{1}-\beta _{2})q^{4}+\cdots\)
503.2.a.e 503.a 1.a $10$ $4.016$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None None \(-4\) \(-8\) \(-1\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q-\beta _{9}q^{2}+(-1+\beta _{1})q^{3}+\beta _{5}q^{4}-\beta _{2}q^{5}+\cdots\)
503.2.a.f 503.a 1.a $26$ $4.016$ None None \(4\) \(4\) \(9\) \(11\) $-$ $\mathrm{SU}(2)$
503.2.c.a 503.c 503.c $10250$ $4.016$ None None \(-249\) \(-249\) \(-245\) \(-247\) $\mathrm{SU}(2)[C_{251}]$
503.3.b.a 503.b 503.b $21$ $13.706$ \(\Q(\sqrt{-503}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$
503.3.b.b 503.b 503.b $62$ $13.706$ None None \(-2\) \(-2\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$
503.4.a.a 503.a 1.a $1$ $29.678$ \(\Q\) None None \(5\) \(7\) \(-4\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+5q^{2}+7q^{3}+17q^{4}-4q^{5}+35q^{6}+\cdots\)
503.4.a.b 503.a 1.a $52$ $29.678$ None None \(-11\) \(-31\) \(-22\) \(-101\) $-$ $\mathrm{SU}(2)$
503.4.a.c 503.a 1.a $72$ $29.678$ None None \(4\) \(22\) \(42\) \(98\) $+$ $\mathrm{SU}(2)$
503.6.a.a 503.a 1.a $94$ $80.673$ None None \(-21\) \(-91\) \(-187\) \(-628\) $+$ $\mathrm{SU}(2)$
503.6.a.b 503.a 1.a $115$ $80.673$ None None \(19\) \(89\) \(113\) \(744\) $-$ $\mathrm{SU}(2)$
503.8.a.a 503.a 1.a $136$ $157.130$ None None \(-41\) \(-271\) \(-627\) \(-5000\) $-$ $\mathrm{SU}(2)$
503.8.a.b 503.a 1.a $157$ $157.130$ None None \(39\) \(269\) \(873\) \(4604\) $+$ $\mathrm{SU}(2)$
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