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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 5
405.4.a.l 405.a 1.a $6$ $23.896$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None \(4\) \(0\) \(30\) \(40\) $-$ $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{2}+(6-\beta _{1}+\beta _{3})q^{4}+5q^{5}+\cdots\)
405.4.a.n 405.a 1.a $7$ $23.896$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None \(2\) \(0\) \(35\) \(22\) $-$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+(5+\beta _{2})q^{4}+5q^{5}+(3-\beta _{5}+\cdots)q^{7}+\cdots\)
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