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Results (17 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
431.1.b.a 431.b 431.b $1$ $0.215$ \(\Q\) \(\Q(\sqrt{-431}) \) None \(2\) \(-1\) \(-1\) \(0\) \(q+2q^{2}-q^{3}+3q^{4}-q^{5}-2q^{6}+4q^{8}+\cdots\)
431.1.b.b 431.b 431.b $3$ $0.215$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-431}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{4}+\beta _{2}q^{5}+\cdots\)
431.1.b.c 431.b 431.b $6$ $0.215$ \(\Q(\zeta_{21})^+\) \(\Q(\sqrt{-431}) \) None \(-2\) \(1\) \(1\) \(0\) \(q+(-1-\beta _{3}+\beta _{5})q^{2}+\beta _{4}q^{3}+(1-\beta _{5})q^{4}+\cdots\)
2155.1.c.a 2155.c 2155.c $1$ $1.075$ \(\Q\) \(\Q(\sqrt{-431}) \), \(\Q(\sqrt{-2155}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-q^{5}+q^{9}-2q^{11}+q^{16}+2q^{19}+\cdots\)
2155.1.c.e 2155.c 2155.c $2$ $1.075$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-431}) \) None \(0\) \(0\) \(1\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{9}+\cdots\)
2155.1.c.f 2155.c 2155.c $6$ $1.075$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-431}) \) None \(0\) \(0\) \(1\) \(0\) \(q+(-\zeta_{14}^{3}-\zeta_{14}^{4})q^{2}+(\zeta_{14}^{2}+\zeta_{14}^{5}+\cdots)q^{3}+\cdots\)
2155.1.c.g 2155.c 2155.c $12$ $1.075$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-431}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+(-\zeta_{42}^{3}-\zeta_{42}^{18})q^{2}+(\zeta_{42}^{2}+\zeta_{42}^{19}+\cdots)q^{3}+\cdots\)
3448.1.b.a 3448.b 3448.b $1$ $1.721$ \(\Q\) \(\Q(\sqrt{-431}) \), \(\Q(\sqrt{-862}) \) \(\Q(\sqrt{2}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{9}+q^{16}+q^{18}+\cdots\)
3448.1.b.c 3448.b 3448.b $2$ $1.721$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-431}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}+q^{4}+(-\zeta_{6}+\cdots)q^{5}+\cdots\)
3448.1.b.e 3448.b 3448.b $6$ $1.721$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-431}) \) None \(-1\) \(0\) \(0\) \(0\) \(q-\zeta_{14}^{3}q^{2}+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{3}+\zeta_{14}^{6}q^{4}+\cdots\)
3448.1.b.f 3448.b 3448.b $12$ $1.721$ \(\Q(\zeta_{21})\) \(\Q(\sqrt{-431}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-\zeta_{42}^{3}q^{2}+(\zeta_{42}^{2}+\zeta_{42}^{19})q^{3}+\zeta_{42}^{6}q^{4}+\cdots\)
3879.1.d.a 3879.d 431.b $1$ $1.936$ \(\Q\) \(\Q(\sqrt{-431}) \) None \(-2\) \(0\) \(1\) \(0\) \(q-2q^{2}+3q^{4}+q^{5}-4q^{8}-2q^{10}+\cdots\)
3879.1.d.b 3879.d 431.b $3$ $1.936$ \(\Q(\zeta_{14})^+\) \(\Q(\sqrt{-431}) \) None \(1\) \(0\) \(1\) \(0\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{1}q^{5}+(1+\beta _{2})q^{8}+\cdots\)
3879.1.d.c 3879.d 431.b $6$ $1.936$ \(\Q(\zeta_{21})^+\) \(\Q(\sqrt{-431}) \) None \(2\) \(0\) \(-1\) \(0\) \(q+(1+\beta _{3}-\beta _{5})q^{2}+(1-\beta _{5})q^{4}+(-1+\cdots)q^{5}+\cdots\)
3879.1.g.b 3879.g 3879.g $6$ $1.936$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-431}) \) None \(-6\) \(0\) \(0\) \(0\) \(q+\zeta_{18}^{6}q^{2}+\zeta_{18}^{8}q^{3}-3\zeta_{18}^{3}q^{4}+\cdots\)
3879.1.g.c 3879.g 3879.g $36$ $1.936$ \(\Q(\zeta_{63})\) \(\Q(\sqrt{-431}) \) None \(6\) \(0\) \(0\) \(0\) \(q+(\zeta_{126}^{48}-\zeta_{126}^{57})q^{2}+\zeta_{126}^{4}q^{3}+\cdots\)
431.3.b.a 431.b 431.b $21$ $11.744$ \(\Q(\sqrt{-431}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$
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