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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1520.1.m.a 1520.m 95.d $1$ $0.759$ \(\Q\) \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-95}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+q^{5}-q^{9}+2q^{11}-q^{19}+q^{25}+\cdots\)
1520.1.m.b 1520.m 95.d $2$ $0.759$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{3}-q^{5}+q^{9}-\beta q^{13}+\beta q^{15}+\cdots\)
1520.1.m.c 1520.m 95.d $2$ $0.759$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}+(\zeta_{6}+\zeta_{6}^{2})q^{7}-q^{9}-q^{11}+\cdots\)
1520.1.ba.a 1520.ba 380.j $2$ $0.759$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(-2\) \(q-q^{5}+(-1-i)q^{7}-iq^{9}+iq^{11}+\cdots\)
1520.1.ba.b 1520.ba 380.j $2$ $0.759$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-2\) \(2\) \(q-q^{5}+(1+i)q^{7}-iq^{9}-iq^{11}+(-1+\cdots)q^{17}+\cdots\)
1520.1.ba.c 1520.ba 380.j $4$ $0.759$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(-2\) \(q+\zeta_{12}^{2}q^{5}+(-\zeta_{12}-\zeta_{12}^{2})q^{7}-\zeta_{12}^{3}q^{9}+\cdots\)
1520.1.ba.d 1520.ba 380.j $4$ $0.759$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(2\) \(2\) \(q+\zeta_{12}^{2}q^{5}+(-\zeta_{12}+\zeta_{12}^{2})q^{7}+\zeta_{12}^{3}q^{9}+\cdots\)
1520.1.bh.a 1520.bh 1520.ah $4$ $0.759$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-4\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}+\cdots\)
1520.1.bh.b 1520.bh 1520.ah $4$ $0.759$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(4\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{5}+\cdots\)
1520.1.bh.c 1520.bh 1520.ah $16$ $0.759$ \(\Q(\zeta_{32})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{32}^{3}q^{2}+(\zeta_{32}-\zeta_{32}^{7})q^{3}+\zeta_{32}^{6}q^{4}+\cdots\)
1520.1.br.a 1520.br 95.h $2$ $0.759$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}-q^{11}-\zeta_{6}^{2}q^{19}+\cdots\)
1520.1.bu.a 1520.bu 380.p $2$ $0.759$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2})q^{11}+\cdots\)
1520.1.bu.b 1520.bu 380.p $2$ $0.759$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{6}q^{5}-\zeta_{6}^{2}q^{9}+(-\zeta_{6}-\zeta_{6}^{2})q^{11}+\cdots\)
1520.1.cr.a 1520.cr 95.m $4$ $0.759$ \(\Q(\zeta_{12})\) None None \(0\) \(-2\) \(0\) \(0\) \(q+(-\zeta_{12}+\zeta_{12}^{4})q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{9}+\cdots\)
1520.1.cr.b 1520.cr 95.m $4$ $0.759$ \(\Q(\zeta_{12})\) None None \(0\) \(2\) \(2\) \(0\) \(q+(\zeta_{12}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{4}q^{5}-\zeta_{12}^{5}q^{9}+\cdots\)
1520.2.a.a 1520.a 1.a $1$ $12.137$ \(\Q\) None None \(0\) \(-3\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+q^{5}+q^{7}+6q^{9}-4q^{11}+\cdots\)
1520.2.a.b 1520.a 1.a $1$ $12.137$ \(\Q\) None None \(0\) \(-2\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{5}-2q^{7}+q^{9}+6q^{13}+\cdots\)
1520.2.a.c 1520.a 1.a $1$ $12.137$ \(\Q\) None None \(0\) \(-2\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{5}-4q^{7}+q^{9}+4q^{11}+\cdots\)
1520.2.a.d 1520.a 1.a $1$ $12.137$ \(\Q\) None None \(0\) \(-1\) \(1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{5}+q^{7}-2q^{9}-q^{13}-q^{15}+\cdots\)
1520.2.a.e 1520.a 1.a $1$ $12.137$ \(\Q\) None None \(0\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-3q^{9}+4q^{11}-4q^{13}+\cdots\)
1520.2.a.f 1520.a 1.a $1$ $12.137$ \(\Q\) None None \(0\) \(0\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-3q^{9}+4q^{11}-6q^{13}-6q^{17}+\cdots\)
1520.2.a.g 1520.a 1.a $1$ $12.137$ \(\Q\) None None \(0\) \(1\) \(-1\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{5}+q^{7}-2q^{9}-3q^{13}-q^{15}+\cdots\)
1520.2.a.h 1520.a 1.a $1$ $12.137$ \(\Q\) None None \(0\) \(2\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
1520.2.a.i 1520.a 1.a $1$ $12.137$ \(\Q\) None None \(0\) \(2\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{5}+q^{9}+4q^{11}+4q^{13}+\cdots\)
1520.2.a.j 1520.a 1.a $1$ $12.137$ \(\Q\) None None \(0\) \(3\) \(-1\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{5}+5q^{7}+6q^{9}+4q^{11}+\cdots\)
1520.2.a.k 1520.a 1.a $2$ $12.137$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}+(1-2\beta )q^{9}-2q^{11}+\cdots\)
1520.2.a.l 1520.a 1.a $2$ $12.137$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}-2q^{7}+(1-2\beta )q^{9}+\cdots\)
1520.2.a.m 1520.a 1.a $2$ $12.137$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+2\beta q^{7}-q^{9}+(-2+2\beta )q^{11}+\cdots\)
1520.2.a.n 1520.a 1.a $2$ $12.137$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+\beta q^{7}+(1+\beta )q^{9}-4q^{11}+\cdots\)
1520.2.a.o 1520.a 1.a $2$ $12.137$ \(\Q(\sqrt{2}) \) None None \(0\) \(4\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+(2+\beta )q^{3}+q^{5}+(2-2\beta )q^{7}+(3+4\beta )q^{9}+\cdots\)
1520.2.a.p 1520.a 1.a $3$ $12.137$ 3.3.148.1 None None \(0\) \(-2\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}+q^{5}+(-\beta _{1}+\beta _{2})q^{7}+\cdots\)
1520.2.a.q 1520.a 1.a $3$ $12.137$ 3.3.316.1 None None \(0\) \(1\) \(-3\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(1-2\beta _{1}+\beta _{2})q^{7}+\cdots\)
1520.2.a.r 1520.a 1.a $3$ $12.137$ 3.3.568.1 None None \(0\) \(1\) \(-3\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{5}+(2+\beta _{2})q^{7}+(1+2\beta _{1}+\cdots)q^{9}+\cdots\)
1520.2.a.s 1520.a 1.a $3$ $12.137$ 3.3.229.1 None None \(0\) \(1\) \(3\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{2}q^{3}+q^{5}-\beta _{1}q^{7}+(1-\beta _{1})q^{9}+\cdots\)
1520.2.a.t 1520.a 1.a $4$ $12.137$ 4.4.11344.1 None None \(0\) \(-2\) \(-4\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{2}q^{3}-q^{5}+(-1+\beta _{1})q^{7}+(2-\beta _{3})q^{9}+\cdots\)
1520.2.d.a 1520.d 5.b $2$ $12.137$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1-i)q^{5}+iq^{7}-q^{9}+\cdots\)
1520.2.d.b 1520.d 5.b $2$ $12.137$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-i)q^{5}-iq^{7}+3q^{9}+4q^{11}+\cdots\)
1520.2.d.c 1520.d 5.b $4$ $12.137$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+(-1-\beta _{2})q^{5}+(2\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
1520.2.d.d 1520.d 5.b $4$ $12.137$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
1520.2.d.e 1520.d 5.b $4$ $12.137$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots\)
1520.2.d.f 1520.d 5.b $4$ $12.137$ \(\Q(\sqrt{-2}, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{5}+(\beta _{1}-\beta _{3})q^{7}+\beta _{2}q^{9}+\cdots\)
1520.2.d.g 1520.d 5.b $4$ $12.137$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{3}+(1-\zeta_{8})q^{5}+(-\zeta_{8}-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
1520.2.d.h 1520.d 5.b $6$ $12.137$ 6.0.16516096.1 None None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{4}q^{3}+\beta _{3}q^{5}+(\beta _{1}+\beta _{4})q^{7}+(-3+\cdots)q^{9}+\cdots\)
1520.2.d.i 1520.d 5.b $6$ $12.137$ 6.0.14077504.2 None None \(0\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+\beta _{5}q^{5}+(-\beta _{3}-\beta _{4})q^{7}+\cdots\)
1520.2.d.j 1520.d 5.b $6$ $12.137$ 6.0.5161984.1 None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{5}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(-\beta _{4}+\beta _{5})q^{7}+\cdots\)
1520.2.d.k 1520.d 5.b $12$ $12.137$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{11}q^{3}-\beta _{6}q^{5}+(\beta _{5}+\beta _{11})q^{7}+\cdots\)
1520.2.g.a 1520.g 380.d $2$ $12.137$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(-6\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{5}-3q^{7}+3q^{9}+(1-2\beta )q^{11}+\cdots\)
1520.2.g.b 1520.g 380.d $2$ $12.137$ \(\Q(\sqrt{-19}) \) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(-1\) \(6\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1+\beta )q^{5}+3q^{7}+3q^{9}+(1-2\beta )q^{11}+\cdots\)
1520.2.g.c 1520.g 380.d $4$ $12.137$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(-6\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{5}+(-2-\beta _{1}-\beta _{3})q^{7}+3q^{9}+\cdots\)
1520.2.g.d 1520.g 380.d $4$ $12.137$ \(\Q(\sqrt{-3}, \sqrt{-19})\) \(\Q(\sqrt{-19}) \) None \(0\) \(0\) \(1\) \(6\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{5}+(2+\beta _{1}+\beta _{3})q^{7}+3q^{9}+\cdots\)
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