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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1400.1.c.a 1400.c 280.c $2$ $0.699$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{2}-q^{4}-iq^{7}+iq^{8}+q^{9}-q^{14}+\cdots\)
1400.1.c.b 1400.c 280.c $4$ $0.699$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{7}-\zeta_{12}^{3}q^{8}+\cdots\)
1400.1.m.a 1400.m 56.h $1$ $0.699$ \(\Q\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{2}) \) \(1\) \(0\) \(0\) \(1\) \(q+q^{2}+q^{4}+q^{7}+q^{8}-q^{9}+q^{14}+\cdots\)
1400.1.m.b 1400.m 56.h $2$ $0.699$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-14}) \) None \(-2\) \(0\) \(0\) \(2\) \(q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+q^{7}-q^{8}+\cdots\)
1400.1.m.c 1400.m 56.h $2$ $0.699$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(-1\) \(0\) \(0\) \(2\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{7}+q^{8}-q^{9}+\cdots\)
1400.1.m.d 1400.m 56.h $2$ $0.699$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-7}) \) None \(1\) \(0\) \(0\) \(-2\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{7}-q^{8}-q^{9}+\cdots\)
1400.1.m.e 1400.m 56.h $2$ $0.699$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-14}) \) None \(2\) \(0\) \(0\) \(-2\) \(q+q^{2}-\beta q^{3}+q^{4}-\beta q^{6}-q^{7}+q^{8}+\cdots\)
1400.1.y.a 1400.y 280.y $4$ $0.699$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{70}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots\)
1400.1.y.b 1400.y 280.y $8$ $0.699$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-7}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots\)
1400.1.ba.a 1400.ba 56.k $4$ $0.699$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}-\zeta_{12}^{3}q^{7}+\cdots\)
1400.1.bf.a 1400.bf 56.j $2$ $0.699$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{2}) \) \(-1\) \(0\) \(0\) \(-1\) \(q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}^{2}q^{7}+q^{8}+\cdots\)
1400.1.bf.b 1400.bf 56.j $2$ $0.699$ \(\Q(\sqrt{-3}) \) None \(\Q(\sqrt{2}) \) \(1\) \(0\) \(0\) \(1\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{7}-q^{8}+\cdots\)
1400.1.bl.a 1400.bl 280.ak $4$ $0.699$ \(\Q(\zeta_{12})\) None \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{5}q^{7}+\cdots\)
1400.1.bs.a 1400.bs 1400.as $4$ $0.699$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-14}) \) None \(-1\) \(-3\) \(1\) \(4\) \(q+\zeta_{10}^{4}q^{2}+(-1+\zeta_{10})q^{3}-\zeta_{10}^{3}q^{4}+\cdots\)
1400.1.bs.b 1400.bs 1400.as $4$ $0.699$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-14}) \) None \(-1\) \(3\) \(-1\) \(4\) \(q+\zeta_{10}^{4}q^{2}+(1-\zeta_{10})q^{3}-\zeta_{10}^{3}q^{4}+\cdots\)
1400.1.bs.c 1400.bs 1400.as $8$ $0.699$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-14}) \) None \(2\) \(0\) \(0\) \(-8\) \(q-\zeta_{20}^{8}q^{2}+(\zeta_{20}^{5}+\zeta_{20}^{7})q^{3}-\zeta_{20}^{6}q^{4}+\cdots\)
1400.1.cc.a 1400.cc 1400.bc $16$ $0.699$ \(\Q(\zeta_{40})\) \(\Q(\sqrt{-14}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{40}^{6}q^{2}+(\zeta_{40}^{9}-\zeta_{40}^{15})q^{3}+\zeta_{40}^{12}q^{4}+\cdots\)
1400.1.cf.a 1400.cf 280.ap $8$ $0.699$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}-\zeta_{24}^{3}q^{7}+\cdots\)
1400.2.a.a 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}+2q^{17}-2q^{19}+\cdots\)
1400.2.a.b 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-q^{7}+q^{9}+5q^{11}-8q^{17}+\cdots\)
1400.2.a.c 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(-2\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{7}+q^{9}+q^{11}-4q^{13}+\cdots\)
1400.2.a.d 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}-2q^{9}-q^{11}+q^{13}+3q^{17}+\cdots\)
1400.2.a.e 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}-2q^{9}-q^{11}+6q^{13}+\cdots\)
1400.2.a.f 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(0\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{7}-3q^{9}+q^{11}+2q^{13}+4q^{17}+\cdots\)
1400.2.a.g 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}-4q^{11}-2q^{13}+6q^{17}+\cdots\)
1400.2.a.h 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(0\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{7}-3q^{9}+q^{11}-2q^{13}-4q^{17}+\cdots\)
1400.2.a.i 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}-2q^{9}-q^{11}-6q^{13}+\cdots\)
1400.2.a.j 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}-2q^{9}-q^{11}-q^{13}-3q^{17}+\cdots\)
1400.2.a.k 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(1\) \(0\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{7}-2q^{9}-5q^{11}-q^{13}+\cdots\)
1400.2.a.l 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(2\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-q^{7}+q^{9}+q^{11}+4q^{13}+\cdots\)
1400.2.a.m 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(2\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{7}+q^{9}+5q^{11}+8q^{17}+\cdots\)
1400.2.a.n 1400.a 1.a $1$ $11.179$ \(\Q\) None None \(0\) \(3\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-q^{7}+6q^{9}-5q^{11}+5q^{13}+\cdots\)
1400.2.a.o 1400.a 1.a $2$ $11.179$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{7}+(1+\beta )q^{9}+(-3+2\beta )q^{11}+\cdots\)
1400.2.a.p 1400.a 1.a $2$ $11.179$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}-q^{7}+(1+\beta )q^{9}-\beta q^{11}+(-2+\cdots)q^{13}+\cdots\)
1400.2.a.q 1400.a 1.a $2$ $11.179$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{7}+(1+\beta )q^{9}+(-3+2\beta )q^{11}+\cdots\)
1400.2.a.r 1400.a 1.a $2$ $11.179$ \(\Q(\sqrt{33}) \) None None \(0\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{7}+(5+\beta )q^{9}+(4-\beta )q^{11}+\cdots\)
1400.2.a.s 1400.a 1.a $3$ $11.179$ 3.3.568.1 None None \(0\) \(-1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{3}+q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots\)
1400.2.a.t 1400.a 1.a $3$ $11.179$ 3.3.568.1 None None \(0\) \(1\) \(0\) \(-3\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}-q^{7}+(1+2\beta _{1}+\beta _{2})q^{9}+\cdots\)
1400.2.g.a 1400.g 5.b $2$ $11.179$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}+iq^{7}-6q^{9}-5q^{11}+5iq^{13}+\cdots\)
1400.2.g.b 1400.g 5.b $2$ $11.179$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-iq^{7}-q^{9}+2iq^{17}+2q^{19}+\cdots\)
1400.2.g.c 1400.g 5.b $2$ $11.179$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+iq^{7}-q^{9}+q^{11}+4iq^{13}+\cdots\)
1400.2.g.d 1400.g 5.b $2$ $11.179$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-iq^{7}-q^{9}+5q^{11}-8iq^{17}+\cdots\)
1400.2.g.e 1400.g 5.b $2$ $11.179$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{7}+2q^{9}-5q^{11}-iq^{13}+\cdots\)
1400.2.g.f 1400.g 5.b $2$ $11.179$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}+2q^{9}-q^{11}-6iq^{13}+\cdots\)
1400.2.g.g 1400.g 5.b $2$ $11.179$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{7}+3q^{9}-4q^{11}+2iq^{13}+6iq^{17}+\cdots\)
1400.2.g.h 1400.g 5.b $2$ $11.179$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{7}+3q^{9}+q^{11}-2iq^{13}+4iq^{17}+\cdots\)
1400.2.g.i 1400.g 5.b $4$ $11.179$ \(\Q(i, \sqrt{33})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-6+\beta _{3})q^{9}+(3+\cdots)q^{11}+\cdots\)
1400.2.g.j 1400.g 5.b $4$ $11.179$ \(\Q(i, \sqrt{17})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
1400.2.g.k 1400.g 5.b $4$ $11.179$ \(\Q(i, \sqrt{17})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{2}q^{7}+(-2+\beta _{3})q^{9}+(-1+\cdots)q^{11}+\cdots\)
1400.2.q.a 1400.q 7.c $2$ $11.179$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+2\zeta_{6})q^{3}+(-3+2\zeta_{6})q^{7}+\cdots\)
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