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Results (14 matches)

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Label Char Prim Dim $A$ Field Image CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
759.1.h.c 759.h 759.h $1$ $0.379$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-759}) \) \(\Q(\sqrt{69}) \) \(0\) \(-1\) \(-2\) \(0\) \(q-q^{3}-q^{4}-2q^{5}+q^{9}+q^{11}+q^{12}+\cdots\)
759.1.h.d 759.h 759.h $1$ $0.379$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-759}) \) \(\Q(\sqrt{69}) \) \(0\) \(-1\) \(2\) \(0\) \(q-q^{3}-q^{4}+2q^{5}+q^{9}-q^{11}+q^{12}+\cdots\)
897.1.m.b 897.m 897.m $2$ $0.448$ \(\Q(\sqrt{-1}) \) $D_{4}$ None \(\Q(\sqrt{69}) \) \(0\) \(-2\) \(-2\) \(0\) \(q-q^{3}-iq^{4}+(-1+i)q^{5}+q^{9}+(-1+\cdots)q^{11}+\cdots\)
897.1.m.c 897.m 897.m $2$ $0.448$ \(\Q(\sqrt{-1}) \) $D_{4}$ None \(\Q(\sqrt{69}) \) \(0\) \(-2\) \(2\) \(0\) \(q-q^{3}-iq^{4}+(1-i)q^{5}+q^{9}+(1+i+\cdots)q^{11}+\cdots\)
1035.1.d.a 1035.d 115.c $1$ $0.517$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-115}) \) \(\Q(\sqrt{69}) \) \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}-q^{5}+q^{16}+2q^{17}-q^{20}+\cdots\)
1035.1.d.b 1035.d 115.c $1$ $0.517$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-115}) \) \(\Q(\sqrt{69}) \) \(0\) \(0\) \(1\) \(0\) \(q+q^{4}+q^{5}+q^{16}-2q^{17}+q^{20}+\cdots\)
1587.1.b.a 1587.b 3.b $1$ $0.792$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-23}) \) \(\Q(\sqrt{69}) \) \(0\) \(1\) \(0\) \(0\) \(q+q^{3}+q^{4}+q^{9}+q^{12}-2q^{13}+q^{16}+\cdots\)
1587.1.h.a 1587.h 69.h $10$ $0.792$ \(\Q(\zeta_{22})\) $D_{2}$ \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-23}) \) \(\Q(\sqrt{69}) \) \(0\) \(-1\) \(0\) \(0\) \(q+\zeta_{22}^{4}q^{3}-\zeta_{22}q^{4}+\zeta_{22}^{8}q^{9}-\zeta_{22}^{5}q^{12}+\cdots\)
3105.1.d.c 3105.d 115.c $2$ $1.550$ \(\Q(\sqrt{-3}) \) $D_{6}$ None \(\Q(\sqrt{69}) \) \(0\) \(0\) \(-1\) \(0\) \(q+q^{4}+\zeta_{6}^{2}q^{5}+(-\zeta_{6}-\zeta_{6}^{2})q^{11}+\cdots\)
3105.1.d.d 3105.d 115.c $2$ $1.550$ \(\Q(\sqrt{-3}) \) $D_{6}$ None \(\Q(\sqrt{69}) \) \(0\) \(0\) \(1\) \(0\) \(q+q^{4}-\zeta_{6}^{2}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{11}+(-\zeta_{6}+\cdots)q^{13}+\cdots\)
3519.1.h.a 3519.h 391.c $1$ $1.756$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-391}) \) \(\Q(\sqrt{69}) \) \(0\) \(0\) \(-2\) \(0\) \(q-q^{4}-2q^{5}-2q^{11}-2q^{13}+q^{16}+\cdots\)
3519.1.h.b 3519.h 391.c $1$ $1.756$ \(\Q\) $D_{2}$ \(\Q(\sqrt{-51}) \), \(\Q(\sqrt{-391}) \) \(\Q(\sqrt{69}) \) \(0\) \(0\) \(2\) \(0\) \(q-q^{4}+2q^{5}+2q^{11}-2q^{13}+q^{16}+\cdots\)
3588.1.bw.a 3588.bw 897.w $4$ $1.791$ \(\Q(\zeta_{12})\) $D_{12}$ None \(\Q(\sqrt{69}) \) \(0\) \(2\) \(-2\) \(0\) \(q-\zeta_{12}^{4}q^{3}+(\zeta_{12}-\zeta_{12}^{2})q^{5}-\zeta_{12}^{2}q^{9}+\cdots\)
3588.1.bw.b 3588.bw 897.w $4$ $1.791$ \(\Q(\zeta_{12})\) $D_{12}$ None \(\Q(\sqrt{69}) \) \(0\) \(2\) \(2\) \(0\) \(q-\zeta_{12}^{4}q^{3}+(-\zeta_{12}+\zeta_{12}^{2})q^{5}-\zeta_{12}^{2}q^{9}+\cdots\)
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