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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1344.1.e.a 1344.e 168.e $2$ $0.671$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{21}) \) \(0\) \(-2\) \(0\) \(0\) \(q-q^{3}-iq^{5}-iq^{7}+q^{9}+2iq^{15}+\cdots\)
1344.1.e.b 1344.e 168.e $2$ $0.671$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{42}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{3}-iq^{7}-q^{9}-q^{13}-iq^{19}+\cdots\)
1344.1.e.c 1344.e 168.e $2$ $0.671$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{42}) \) \(0\) \(0\) \(0\) \(0\) \(q+iq^{3}-iq^{7}-q^{9}+q^{13}+iq^{19}+\cdots\)
1344.1.e.d 1344.e 168.e $2$ $0.671$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-14}) \) \(\Q(\sqrt{21}) \) \(0\) \(2\) \(0\) \(0\) \(q+q^{3}-iq^{5}+iq^{7}+q^{9}-2iq^{15}+\cdots\)
1344.1.o.a 1344.o 84.h $1$ $0.671$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \) \(\Q(\sqrt{7}) \) \(0\) \(-1\) \(0\) \(-1\) \(q-q^{3}-q^{7}+q^{9}+2q^{19}+q^{21}-q^{25}+\cdots\)
1344.1.o.b 1344.o 84.h $1$ $0.671$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \) \(\Q(\sqrt{7}) \) \(0\) \(1\) \(0\) \(1\) \(q+q^{3}+q^{7}+q^{9}-2q^{19}+q^{21}-q^{25}+\cdots\)
1344.1.z.a 1344.z 84.j $2$ $0.671$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(-1\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots\)
1344.1.z.b 1344.z 84.j $2$ $0.671$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(1\) \(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots\)
1344.1.ba.a 1344.ba 168.s $4$ $0.671$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+(-\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
1344.1.ba.b 1344.ba 168.s $4$ $0.671$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+(\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
1344.1.bm.a 1344.bm 168.ae $4$ $0.671$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(-2\) \(0\) \(0\) \(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
1344.1.bm.b 1344.bm 168.ae $4$ $0.671$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}-q^{13}+\cdots\)
1344.1.bm.c 1344.bm 168.ae $4$ $0.671$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+q^{13}+\cdots\)
1344.1.bm.d 1344.bm 168.ae $4$ $0.671$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-6}) \) None \(0\) \(2\) \(0\) \(0\) \(q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
1344.1.bn.a 1344.bn 21.h $2$ $0.671$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(0\) \(1\) \(q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots\)
1344.1.bn.b 1344.bn 21.h $2$ $0.671$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(-1\) \(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots\)
1344.2.a.a 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(-1\) \(-4\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{5}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
1344.2.a.b 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-q^{7}+q^{9}-6q^{13}+2q^{15}+\cdots\)
1344.2.a.c 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots\)
1344.2.a.d 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots\)
1344.2.a.e 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1344.2.a.f 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(-1\) \(0\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
1344.2.a.g 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(-1\) \(2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
1344.2.a.h 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(-1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
1344.2.a.i 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(-1\) \(2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
1344.2.a.j 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(-1\) \(4\) \(1\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1344.2.a.k 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(1\) \(-4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
1344.2.a.l 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(1\) \(-2\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
1344.2.a.m 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(1\) \(-2\) \(1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}+q^{9}-6q^{13}-2q^{15}+\cdots\)
1344.2.a.n 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(1\) \(-2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
1344.2.a.o 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
1344.2.a.p 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(1\) \(0\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1344.2.a.q 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
1344.2.a.r 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
1344.2.a.s 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(1\) \(2\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
1344.2.a.t 1344.a 1.a $1$ $10.732$ \(\Q\) None None \(0\) \(1\) \(4\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1344.2.a.u 1344.a 1.a $2$ $10.732$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
1344.2.a.v 1344.a 1.a $2$ $10.732$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
1344.2.b.a 1344.b 28.d $2$ $10.732$ \(\Q(\sqrt{-6}) \) None None \(0\) \(-2\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
1344.2.b.b 1344.b 28.d $2$ $10.732$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(2-\zeta_{6})q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots\)
1344.2.b.c 1344.b 28.d $2$ $10.732$ \(\Q(\sqrt{-3}) \) None None \(0\) \(2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-2+\zeta_{6})q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
1344.2.b.d 1344.b 28.d $2$ $10.732$ \(\Q(\sqrt{-6}) \) None None \(0\) \(2\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+\beta q^{5}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
1344.2.b.e 1344.b 28.d $4$ $10.732$ 4.0.2312.1 None None \(0\) \(-4\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1344.2.b.f 1344.b 28.d $4$ $10.732$ 4.0.2312.1 None None \(0\) \(4\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
1344.2.b.g 1344.b 28.d $8$ $10.732$ 8.0.836829184.2 None None \(0\) \(-8\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{3}-\beta _{1}q^{5}-\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
1344.2.b.h 1344.b 28.d $8$ $10.732$ 8.0.836829184.2 None None \(0\) \(8\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{3}-\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(\beta _{2}+\beta _{4}+\cdots)q^{11}+\cdots\)
1344.2.c.a 1344.c 8.b $2$ $10.732$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
1344.2.c.b 1344.c 8.b $2$ $10.732$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
1344.2.c.c 1344.c 8.b $2$ $10.732$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)
1344.2.c.d 1344.c 8.b $2$ $10.732$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)
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