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Results (37 matches)

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Label Char Prim Dim $A$ Field CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
199.1.b.a 199.b 199.b $1$ $0.099$ \(\Q\) \(\Q(\sqrt{-199}) \) None \(-1\) \(0\) \(-1\) \(2\) \(q-q^{2}-q^{5}+2q^{7}+q^{8}+q^{9}+q^{10}+\cdots\)
199.1.b.b 199.b 199.b $3$ $0.099$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(-3\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}-\beta _{2})q^{5}+\cdots\)
995.1.c.a 995.c 995.c $1$ $0.497$ \(\Q\) \(\Q(\sqrt{-199}) \), \(\Q(\sqrt{-995}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+q^{4}+q^{5}-q^{9}+q^{16}+q^{20}+q^{25}+\cdots\)
995.1.c.b 995.c 995.c $2$ $0.497$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\)
995.1.c.d 995.c 995.c $6$ $0.497$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{18}-\zeta_{18}^{8})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{4}+\cdots\)
1393.1.n.a 1393.n 1393.n $18$ $0.695$ \(\Q(\zeta_{54})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{54}^{5}-\zeta_{54}^{13})q^{2}+(\zeta_{54}^{10}+\zeta_{54}^{18}+\cdots)q^{4}+\cdots\)
1592.1.g.a 1592.g 1592.g $1$ $0.795$ \(\Q\) \(\Q(\sqrt{-199}) \), \(\Q(\sqrt{-398}) \) \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(2\) \(q-q^{2}+q^{4}+2q^{7}-q^{8}-q^{9}-2q^{14}+\cdots\)
1592.1.g.b 1592.g 1592.g $2$ $0.795$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-199}) \) None \(1\) \(0\) \(0\) \(4\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{5}+\cdots\)
1592.1.g.f 1592.g 1592.g $6$ $0.795$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(-6\) \(q+\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{5}+\cdots)q^{5}+\cdots\)
1791.1.d.a 1791.d 199.b $1$ $0.894$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-199}) \) \(\Q(\sqrt{597}) \) \(0\) \(0\) \(0\) \(-2\) \(q-q^{4}-2q^{7}+2q^{13}+q^{16}-q^{25}+\cdots\)
1791.1.d.b 1791.d 199.b $1$ $0.894$ \(\Q\) \(\Q(\sqrt{-199}) \) None \(1\) \(0\) \(1\) \(2\) \(q+q^{2}+q^{5}+2q^{7}-q^{8}+q^{10}-q^{13}+\cdots\)
1791.1.d.c 1791.d 199.b $2$ $0.894$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(-4\) \(q-\beta q^{2}+2q^{4}-\beta q^{5}-2q^{7}-\beta q^{8}+\cdots\)
1791.1.d.d 1791.d 199.b $3$ $0.894$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(-3\) \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-\beta _{1}+\beta _{2})q^{5}+\cdots\)
1791.1.d.e 1791.d 199.b $6$ $0.894$ \(\Q(\zeta_{36})^+\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(6\) \(q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(\beta _{1}+\beta _{5})q^{5}+\cdots\)
2587.1.b.a 2587.b 2587.b $1$ $1.291$ \(\Q\) \(\Q(\sqrt{-199}) \), \(\Q(\sqrt{-2587}) \) \(\Q(\sqrt{13}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{4}+q^{9}+q^{13}+q^{16}-2q^{23}+\cdots\)
2587.1.b.b 2587.b 2587.b $2$ $1.291$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots\)
2587.1.b.d 2587.b 2587.b $6$ $1.291$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{18}-\zeta_{18}^{8})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{4}+\cdots\)
2587.1.n.a 2587.n 2587.n $18$ $1.291$ \(\Q(\zeta_{54})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{54}^{5}-\zeta_{54}^{13})q^{2}+(\zeta_{54}^{10}+\zeta_{54}^{18}+\cdots)q^{4}+\cdots\)
2587.1.t.a 2587.t 2587.t $18$ $1.291$ \(\Q(\zeta_{54})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{54}^{2}-\zeta_{54}^{16})q^{2}+(\zeta_{54}^{4}-\zeta_{54}^{5}+\cdots)q^{4}+\cdots\)
3184.1.e.a 3184.e 199.b $1$ $1.589$ \(\Q\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(-1\) \(-2\) \(q-q^{5}-2q^{7}+q^{9}-q^{13}+q^{23}+2q^{29}+\cdots\)
3184.1.e.b 3184.e 199.b $3$ $1.589$ \(\Q(\zeta_{18})^+\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(3\) \(q-\beta _{1}q^{5}+q^{7}+q^{9}+(\beta _{1}-\beta _{2})q^{13}+\cdots\)
3184.1.j.a 3184.j 3184.j $2$ $1.589$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(2\) \(0\) \(q+iq^{2}-q^{4}+(1+i)q^{5}-iq^{8}-iq^{9}+\cdots\)
3184.1.j.b 3184.j 3184.j $4$ $1.589$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(\zeta_{12}^{4}-\zeta_{12}^{5}+\cdots)q^{5}+\cdots\)
3184.1.j.c 3184.j 3184.j $12$ $1.589$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{36}^{13}q^{2}-\zeta_{36}^{8}q^{4}+(-\zeta_{36}^{11}+\cdots)q^{5}+\cdots\)
3980.1.l.a 3980.l 3980.l $2$ $1.986$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-199}) \) None \(-2\) \(0\) \(-2\) \(-2\) \(q-q^{2}+q^{4}-q^{5}+(-1-i)q^{7}-q^{8}+\cdots\)
3980.1.l.b 3980.l 3980.l $2$ $1.986$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(-2\) \(2\) \(q+iq^{2}-q^{4}-q^{5}+(1+i)q^{7}-iq^{8}+\cdots\)
3980.1.l.c 3980.l 3980.l $4$ $1.986$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(2\) \(4\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{2}q^{5}+(1+\cdots)q^{7}+\cdots\)
3980.1.l.d 3980.l 3980.l $4$ $1.986$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-199}) \) None \(2\) \(0\) \(2\) \(-4\) \(q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}+\zeta_{12}^{2}q^{5}+\cdots\)
3980.1.l.e 3980.l 3980.l $12$ $1.986$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(-6\) \(q+\zeta_{36}^{13}q^{2}-\zeta_{36}^{8}q^{4}+\zeta_{36}^{2}q^{5}+\cdots\)
3980.1.l.f 3980.l 3980.l $12$ $1.986$ \(\Q(\zeta_{36})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(6\) \(q+\zeta_{36}^{14}q^{2}-\zeta_{36}^{10}q^{4}+\zeta_{36}^{2}q^{5}+\cdots\)
199.3.b.a 199.b 199.b $9$ $5.422$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(4+\beta _{4}+\beta _{5})q^{4}-\beta _{8}q^{5}+\cdots\)
796.2.d.b 796.d 796.d $18$ $6.356$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{6}q^{2}+\beta _{5}q^{4}+\beta _{10}q^{5}-\beta _{13}q^{7}+\cdots\)
995.2.f.c 995.f 995.f $36$ $7.945$ \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$
1791.2.c.b 1791.c 597.c $36$ $14.301$ \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$
199.5.b.a 199.b 199.b $9$ $20.571$ \(\mathbb{Q}[x]/(x^{9} - \cdots)\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}+(2^{4}+4\beta _{1}+\beta _{8})q^{4}+(-4\beta _{3}+\cdots)q^{5}+\cdots\)
199.7.b.a 199.b 199.b $3$ $45.781$ 3.3.5373.1 \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(-330\) $\mathrm{U}(1)[D_{2}]$ \(q+(\beta _{1}-3\beta _{2})q^{2}+(2^{6}-8\beta _{1}-19\beta _{2})q^{4}+\cdots\)
199.7.b.b 199.b 199.b $6$ $45.781$ 6.6.\(\cdots\).2 \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(330\) $\mathrm{U}(1)[D_{2}]$ \(q+(2\beta _{2}+\beta _{3}+\beta _{4})q^{2}+(2^{6}-12\beta _{2}+\cdots)q^{4}+\cdots\)
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