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Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 5 23
115.4.a.e 115.a 1.a $5$ $6.785$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 115.4.a.e \(6\) \(4\) \(-25\) \(-3\) $+$ $+$ $\mathrm{SU}(2)$ \(q+(1+\beta _{1})q^{2}+(1+\beta _{1}-\beta _{2}+\beta _{3})q^{3}+\cdots\)
115.4.a.f 115.a 1.a $8$ $6.785$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 115.4.a.f \(6\) \(0\) \(40\) \(11\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+\beta _{6}q^{3}+(5+\beta _{2})q^{4}+\cdots\)
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