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Label Char Prim Dim $A$ Field CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
136.1.e.a 136.e 136.e $1$ $0.068$ \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(-1\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{17}+\cdots\)
544.1.e.a 544.e 136.e $1$ $0.271$ \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}-q^{17}+2q^{19}-q^{25}-2q^{43}+\cdots\)
680.1.k.e 680.k 680.k $4$ $0.339$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots\)
952.1.bi.a 952.bi 952.ai $2$ $0.475$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-34}) \) None \(-1\) \(0\) \(-1\) \(1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{7}+\cdots\)
952.1.bi.b 952.bi 952.ai $2$ $0.475$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-34}) \) None \(-1\) \(0\) \(1\) \(-1\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+\zeta_{6}^{2}q^{7}+\cdots\)
952.1.bi.c 952.bi 952.ai $4$ $0.475$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-34}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
1224.1.n.a 1224.n 136.e $1$ $0.611$ \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{16}+q^{17}-2q^{19}+\cdots\)
1224.1.n.b 1224.n 136.e $2$ $0.611$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-34}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-\beta q^{5}-\beta q^{7}-q^{8}+\beta q^{10}+\cdots\)
1224.1.n.c 1224.n 136.e $2$ $0.611$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-34}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta q^{5}+\beta q^{7}+q^{8}-\beta q^{10}+\cdots\)
2176.1.e.a 2176.e 136.e $1$ $1.086$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{34}) \) \(0\) \(0\) \(-2\) \(0\) \(q-2q^{5}+q^{9}-q^{17}+3q^{25}+2q^{29}+\cdots\)
2176.1.e.b 2176.e 136.e $1$ $1.086$ \(\Q\) \(\Q(\sqrt{-17}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(-2\) \(q-2q^{7}+q^{9}+q^{17}+2q^{23}-q^{25}+\cdots\)
2176.1.e.c 2176.e 136.e $1$ $1.086$ \(\Q\) \(\Q(\sqrt{-17}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(2\) \(q+2q^{7}+q^{9}+q^{17}-2q^{23}-q^{25}+\cdots\)
2176.1.e.d 2176.e 136.e $1$ $1.086$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{34}) \) \(0\) \(0\) \(2\) \(0\) \(q+2q^{5}+q^{9}-q^{17}+3q^{25}-2q^{29}+\cdots\)
2312.1.f.a 2312.f 8.d $1$ $1.154$ \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}-q^{9}+q^{16}-q^{18}+\cdots\)
2312.1.j.a 2312.j 136.j $2$ $1.154$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{2}-q^{4}-iq^{8}+iq^{9}+q^{16}+\cdots\)
2312.1.p.c 2312.p 136.p $4$ $1.154$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}q^{8}-\zeta_{8}q^{9}+\cdots\)
2584.1.bi.a 2584.bi 2584.ai $2$ $1.290$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-34}) \) None \(-1\) \(0\) \(-1\) \(-4\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}-q^{7}+q^{8}+\cdots\)
2584.1.bi.b 2584.bi 2584.ai $2$ $1.290$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-34}) \) None \(-1\) \(0\) \(1\) \(4\) \(q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{7}+q^{8}+\cdots\)
2584.1.bi.e 2584.bi 2584.ai $4$ $1.290$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-34}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{4}q^{2}-\zeta_{12}^{2}q^{4}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
2584.1.ct.b 2584.ct 2584.bt $6$ $1.290$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(-6\) \(-3\) \(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(-1-\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
2584.1.ct.c 2584.ct 2584.bt $6$ $1.290$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(6\) \(3\) \(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{4}+(1+\zeta_{18}^{2}+\cdots)q^{5}+\cdots\)
2584.1.ct.e 2584.ct 2584.bt $12$ $1.290$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{36}^{8}q^{2}+\zeta_{36}^{16}q^{4}+(\zeta_{36}^{9}-\zeta_{36}^{13}+\cdots)q^{5}+\cdots\)
2720.1.k.e 2720.k 680.k $4$ $1.357$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{5}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}-q^{9}+\cdots\)
3128.1.bx.a 3128.bx 3128.ax $10$ $1.561$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-34}) \) None \(-1\) \(0\) \(-9\) \(2\) \(q-\zeta_{22}^{9}q^{2}-\zeta_{22}^{7}q^{4}+(-1+\zeta_{22}^{9}+\cdots)q^{5}+\cdots\)
3128.1.bx.b 3128.bx 3128.ax $10$ $1.561$ \(\Q(\zeta_{22})\) \(\Q(\sqrt{-34}) \) None \(-1\) \(0\) \(9\) \(-2\) \(q-\zeta_{22}^{9}q^{2}-\zeta_{22}^{7}q^{4}+(1-\zeta_{22}^{9}+\cdots)q^{5}+\cdots\)
3128.1.bx.c 3128.bx 3128.ax $20$ $1.561$ \(\Q(\zeta_{44})\) \(\Q(\sqrt{-34}) \) None \(2\) \(0\) \(0\) \(0\) \(q+\zeta_{44}^{10}q^{2}+\zeta_{44}^{20}q^{4}+(-\zeta_{44}^{11}+\cdots)q^{5}+\cdots\)
3400.1.g.a 3400.g 136.e $1$ $1.697$ \(\Q\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(1\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}+q^{8}+q^{9}+q^{16}+q^{17}+\cdots\)
3400.1.g.c 3400.g 136.e $2$ $1.697$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-34}) \) None \(-2\) \(0\) \(0\) \(0\) \(q-q^{2}+q^{4}-\beta q^{7}-q^{8}+q^{9}+\beta q^{14}+\cdots\)
3400.1.g.g 3400.g 136.e $2$ $1.697$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-34}) \) None \(2\) \(0\) \(0\) \(0\) \(q+q^{2}+q^{4}-\beta q^{7}+q^{8}+q^{9}-\beta q^{14}+\cdots\)
3400.1.k.a 3400.k 680.k $2$ $1.697$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-34}) \) \(\Q(\sqrt{17}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}+iq^{8}-q^{9}+q^{16}-iq^{17}+\cdots\)
3400.1.ch.a 3400.ch 3400.bh $16$ $1.697$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{40}^{18}q^{2}-\zeta_{40}^{16}q^{4}+\zeta_{40}^{15}q^{5}+\cdots\)
3400.1.cs.a 3400.cs 3400.bs $4$ $1.697$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-34}) \) None \(-1\) \(0\) \(-4\) \(2\) \(q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}-q^{5}+(-\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
3400.1.cs.b 3400.cs 3400.bs $4$ $1.697$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-34}) \) None \(-1\) \(0\) \(4\) \(-2\) \(q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+q^{5}+(\zeta_{10}^{2}+\cdots)q^{7}+\cdots\)
3400.1.cs.c 3400.cs 3400.bs $8$ $1.697$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-34}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{4}q^{2}+\zeta_{20}^{8}q^{4}+\zeta_{20}^{5}q^{5}+\cdots\)
3808.1.by.a 3808.by 952.ai $2$ $1.900$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(-1\) \(-1\) \(q+\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{17}+\cdots\)
3808.1.by.b 3808.by 952.ai $2$ $1.900$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(1\) \(1\) \(q-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{17}+\cdots\)
3808.1.by.c 3808.by 952.ai $4$ $1.900$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{2}q^{9}+\cdots\)
3944.1.p.a 3944.p 3944.p $4$ $1.968$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}-\zeta_{8}^{3})q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
3944.1.cf.a 3944.cf 3944.bf $24$ $1.968$ \(\Q(\zeta_{56})\) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{56}^{6}q^{2}+\zeta_{56}^{12}q^{4}+(\zeta_{56}^{15}+\zeta_{56}^{25}+\cdots)q^{5}+\cdots\)
3944.1.cn.a 3944.cn 3944.bn $6$ $1.968$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-34}) \) None \(-1\) \(0\) \(-2\) \(-2\) \(q+\zeta_{14}^{6}q^{2}-\zeta_{14}^{5}q^{4}+(-\zeta_{14}+\zeta_{14}^{4}+\cdots)q^{5}+\cdots\)
3944.1.cn.b 3944.cn 3944.bn $6$ $1.968$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-34}) \) None \(-1\) \(0\) \(2\) \(2\) \(q+\zeta_{14}^{6}q^{2}-\zeta_{14}^{5}q^{4}+(\zeta_{14}-\zeta_{14}^{4}+\cdots)q^{5}+\cdots\)
3944.1.cn.c 3944.cn 3944.bn $12$ $1.968$ \(\Q(\zeta_{28})\) \(\Q(\sqrt{-34}) \) None \(2\) \(0\) \(0\) \(0\) \(q-\zeta_{28}^{12}q^{2}-\zeta_{28}^{10}q^{4}+(\zeta_{28}-\zeta_{28}^{9}+\cdots)q^{5}+\cdots\)
136.3.e.a 136.e 136.e $2$ $3.706$ \(\Q(\sqrt{17}) \) \(\Q(\sqrt{-34}) \) None \(-4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-2q^{2}+4q^{4}+\beta q^{5}-\beta q^{7}-8q^{8}+\cdots\)
136.3.e.c 136.e 136.e $2$ $3.706$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-34}) \) None \(4\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+2q^{2}+4q^{4}+\beta q^{5}-2\beta q^{7}+8q^{8}+\cdots\)
680.2.u.b 680.u 680.u $8$ $5.430$ 8.0.\(\cdots\).13 \(\Q(\sqrt{-34}) \) None \(-8\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1+\beta _{2})q^{2}-2\beta _{2}q^{4}-\beta _{1}q^{5}+\cdots\)
680.2.u.c 680.u 680.u $8$ $5.430$ 8.0.\(\cdots\).13 \(\Q(\sqrt{-34}) \) None \(8\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+\beta _{2})q^{2}+2\beta _{2}q^{4}-\beta _{5}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
952.2.k.a 952.k 952.k $8$ $7.602$ 8.0.5473632256.3 \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{3}q^{2}+2q^{4}+(-\beta _{1}-\beta _{6})q^{5}+\beta _{4}q^{7}+\cdots\)
952.2.bf.a 952.bf 952.af $16$ $7.602$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(\beta _{2}+\beta _{6})q^{2}-2\beta _{5}q^{4}+(-\beta _{1}+\beta _{3}+\cdots)q^{5}+\cdots\)
1088.2.h.b 1088.h 136.h $8$ $8.688$ 8.0.342102016.5 \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{5}-\beta _{4}q^{7}-3q^{9}+\beta _{1}q^{17}+\cdots\)
1224.2.h.a 1224.h 408.h $8$ $9.774$ 8.0.\(\cdots\).11 \(\Q(\sqrt{-34}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}-\beta _{4}q^{7}+2\beta _{1}q^{8}+\cdots\)
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