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Label Char Prim Dim $A$ Field CM Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 59
177.4.a.c 177.a 1.a $8$ $10.443$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(2\) \(-24\) \(-12\) \(53\) $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(5+\beta _{2})q^{4}+(-2+\cdots)q^{5}+\cdots\)
177.4.a.d 177.a 1.a $8$ $10.443$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None \(6\) \(24\) \(42\) \(53\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+3q^{3}+(5-\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots\)
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