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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1560.1.y.a 1560.y 1560.y $1$ $0.779$ \(\Q\) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-390}) \) \(\Q(\sqrt{10}) \) \(-1\) \(-1\) \(1\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
1560.1.y.b 1560.y 1560.y $1$ $0.779$ \(\Q\) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-390}) \) \(\Q(\sqrt{10}) \) \(-1\) \(1\) \(1\) \(0\) \(q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots\)
1560.1.y.c 1560.y 1560.y $1$ $0.779$ \(\Q\) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-390}) \) \(\Q(\sqrt{10}) \) \(1\) \(-1\) \(-1\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots\)
1560.1.y.d 1560.y 1560.y $1$ $0.779$ \(\Q\) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-390}) \) \(\Q(\sqrt{10}) \) \(1\) \(1\) \(-1\) \(0\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots\)
1560.1.y.e 1560.y 1560.y $2$ $0.779$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-30}) \) \(\Q(\sqrt{130}) \) \(0\) \(-2\) \(0\) \(0\) \(q-iq^{2}-q^{3}-q^{4}-iq^{5}+iq^{6}+iq^{8}+\cdots\)
1560.1.y.f 1560.y 1560.y $2$ $0.779$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-39}) \), \(\Q(\sqrt{-30}) \) \(\Q(\sqrt{130}) \) \(0\) \(2\) \(0\) \(0\) \(q-iq^{2}+q^{3}-q^{4}+iq^{5}-iq^{6}+iq^{8}+\cdots\)
1560.1.cs.a 1560.cs 1560.bs $4$ $0.779$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots\)
1560.1.cs.b 1560.cs 1560.bs $4$ $0.779$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-26}) \) None \(0\) \(4\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+q^{3}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\cdots\)
1560.1.cs.c 1560.cs 1560.bs $8$ $0.779$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-26}) \) None \(0\) \(-4\) \(0\) \(0\) \(q+\zeta_{24}^{9}q^{2}+\zeta_{24}^{8}q^{3}-\zeta_{24}^{6}q^{4}+\cdots\)
1560.1.cs.d 1560.cs 1560.bs $8$ $0.779$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{3}-\zeta_{16}^{2}q^{4}+\cdots\)
1560.1.cs.e 1560.cs 1560.bs $8$ $0.779$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-39}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots\)
1560.1.cs.f 1560.cs 1560.bs $8$ $0.779$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-26}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{9}q^{2}+\zeta_{24}^{2}q^{3}-\zeta_{24}^{6}q^{4}+\cdots\)
1560.1.dk.a 1560.dk 1560.ck $4$ $0.779$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-30}) \) None \(0\) \(-2\) \(0\) \(0\) \(q+\zeta_{12}q^{2}+\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\cdots\)
1560.1.dk.b 1560.dk 1560.ck $4$ $0.779$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-30}) \) None \(0\) \(2\) \(0\) \(0\) \(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}+\cdots\)
1560.1.du.a 1560.du 1560.cu $2$ $0.779$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-30}) \) None \(-1\) \(-1\) \(2\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots\)
1560.1.du.b 1560.du 1560.cu $2$ $0.779$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-30}) \) None \(-1\) \(1\) \(-2\) \(0\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots\)
1560.1.du.c 1560.du 1560.cu $2$ $0.779$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-30}) \) None \(1\) \(-1\) \(-2\) \(0\) \(q-\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{5}+\cdots\)
1560.1.du.d 1560.du 1560.cu $2$ $0.779$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-30}) \) None \(1\) \(1\) \(2\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+q^{5}+\cdots\)
1560.2.a.a 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+q^{13}+q^{15}-6q^{17}+\cdots\)
1560.2.a.b 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(-1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+q^{9}+4q^{11}+q^{13}+q^{15}+\cdots\)
1560.2.a.c 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(-1\) \(1\) \(-5\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-5q^{7}+q^{9}+q^{11}+q^{13}+\cdots\)
1560.2.a.d 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(-1\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{9}-4q^{11}+q^{13}-q^{15}+\cdots\)
1560.2.a.e 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(-1\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+2q^{7}+q^{9}+4q^{11}-q^{13}+\cdots\)
1560.2.a.f 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(-1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+4q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
1560.2.a.g 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-4q^{7}+q^{9}+4q^{11}+q^{13}+\cdots\)
1560.2.a.h 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(1\) \(-1\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}-q^{7}+q^{9}-5q^{11}+q^{13}+\cdots\)
1560.2.a.i 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(1\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{9}-q^{13}-q^{15}+2q^{17}+\cdots\)
1560.2.a.j 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(1\) \(1\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-3q^{7}+q^{9}-3q^{11}-q^{13}+\cdots\)
1560.2.a.k 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(1\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}-2q^{7}+q^{9}+q^{13}+q^{15}+\cdots\)
1560.2.a.l 1560.a 1.a $1$ $12.457$ \(\Q\) None None \(0\) \(1\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+4q^{7}+q^{9}+q^{13}+q^{15}+\cdots\)
1560.2.a.m 1560.a 1.a $2$ $12.457$ \(\Q(\sqrt{41}) \) None None \(0\) \(-2\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}-\beta q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
1560.2.a.n 1560.a 1.a $2$ $12.457$ \(\Q(\sqrt{33}) \) None None \(0\) \(-2\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-q^{5}+\beta q^{7}+q^{9}-\beta q^{11}-q^{13}+\cdots\)
1560.2.a.o 1560.a 1.a $2$ $12.457$ \(\Q(\sqrt{17}) \) None None \(0\) \(-2\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}-\beta q^{7}+q^{9}+(-4+\beta )q^{11}+\cdots\)
1560.2.a.p 1560.a 1.a $3$ $12.457$ 3.3.1849.1 None None \(0\) \(3\) \(-3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+(2-\beta _{1})q^{7}+q^{9}+(1+\beta _{2})q^{11}+\cdots\)
1560.2.a.q 1560.a 1.a $3$ $12.457$ 3.3.940.1 None None \(0\) \(3\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{5}+\beta _{2}q^{7}+q^{9}+(2+\beta _{1}+\cdots)q^{11}+\cdots\)
1560.2.g.a 1560.g 13.b $2$ $12.457$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+iq^{5}+2iq^{7}+q^{9}+(-3+2i)q^{13}+\cdots\)
1560.2.g.b 1560.g 13.b $2$ $12.457$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-iq^{5}+2iq^{7}+q^{9}-4iq^{11}+\cdots\)
1560.2.g.c 1560.g 13.b $2$ $12.457$ \(\Q(\sqrt{-1}) \) None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-iq^{5}+4iq^{7}+q^{9}+4iq^{11}+\cdots\)
1560.2.g.d 1560.g 13.b $2$ $12.457$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-iq^{5}+3iq^{7}+q^{9}-3iq^{11}+\cdots\)
1560.2.g.e 1560.g 13.b $2$ $12.457$ \(\Q(\sqrt{-1}) \) None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-iq^{5}+q^{9}+6iq^{11}+(-2+\cdots)q^{13}+\cdots\)
1560.2.g.f 1560.g 13.b $4$ $12.457$ \(\Q(i, \sqrt{41})\) None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
1560.2.g.g 1560.g 13.b $4$ $12.457$ \(\Q(\zeta_{12})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\zeta_{12}q^{5}+\zeta_{12}^{2}q^{7}+q^{9}+(1+\cdots)q^{13}+\cdots\)
1560.2.g.h 1560.g 13.b $4$ $12.457$ \(\Q(i, \sqrt{17})\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\beta _{2}q^{5}+(\beta _{1}-\beta _{2})q^{7}+q^{9}+\cdots\)
1560.2.g.i 1560.g 13.b $6$ $12.457$ 6.0.3356224.1 None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{1}q^{5}+(-2\beta _{1}+\beta _{4})q^{7}+q^{9}+\cdots\)
1560.2.l.a 1560.l 5.b $2$ $12.457$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1+2i)q^{5}+5iq^{7}-q^{9}+\cdots\)
1560.2.l.b 1560.l 5.b $2$ $12.457$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+(1+2i)q^{5}+iq^{7}-q^{9}+3q^{11}+\cdots\)
1560.2.l.c 1560.l 5.b $6$ $12.457$ 6.0.5161984.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}-\beta _{5}q^{5}-q^{9}+(-2+\beta _{4}+\cdots)q^{11}+\cdots\)
1560.2.l.d 1560.l 5.b $8$ $12.457$ 8.0.\(\cdots\).2 None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}-\beta _{7}q^{5}+(-\beta _{1}+2\beta _{2})q^{7}+\cdots\)
1560.2.l.e 1560.l 5.b $8$ $12.457$ 8.0.1698758656.6 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{3}+(-\beta _{2}-\beta _{3})q^{5}-\beta _{4}q^{7}+\cdots\)
1560.2.l.f 1560.l 5.b $10$ $12.457$ \(\mathbb{Q}[x]/(x^{10} + \cdots)\) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{3}+\beta _{2}q^{5}-\beta _{9}q^{7}-q^{9}+(1+\cdots)q^{11}+\cdots\)
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