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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
3200.1.e.a 3200.e 40.e $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}-iq^{17}+q^{41}-q^{49}+iq^{73}+\cdots\)
3200.1.e.b 3200.e 40.e $4$ $1.597$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}+(-1-\zeta_{12}^{2}+\cdots)q^{9}+\cdots\)
3200.1.g.a 3200.g 8.d $1$ $1.597$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}+2q^{17}+2q^{41}+q^{49}+2q^{73}+\cdots\)
3200.1.g.b 3200.g 8.d $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-q^{9}-iq^{13}-iq^{37}-q^{41}+q^{49}+\cdots\)
3200.1.g.c 3200.g 8.d $2$ $1.597$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{3}+2q^{9}-\beta q^{11}-q^{17}+\beta q^{19}+\cdots\)
3200.1.g.d 3200.g 8.d $2$ $1.597$ \(\Q(\sqrt{3}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\beta q^{3}+2q^{9}-\beta q^{11}+q^{17}+\beta q^{19}+\cdots\)
3200.1.g.e 3200.g 8.d $4$ $1.597$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{3}+(-\zeta_{8}-\zeta_{8}^{3})q^{7}+\cdots\)
3200.1.m.a 3200.m 40.i $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}+(-1-i)q^{13}+(-1-i)q^{17}+\cdots\)
3200.1.m.b 3200.m 40.i $2$ $1.597$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}+(1+i)q^{13}+(-1-i)q^{17}+\cdots\)
3200.1.m.c 3200.m 40.i $4$ $1.597$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-5}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{9}+\zeta_{8}q^{23}-q^{41}+\cdots\)
3200.1.m.d 3200.m 40.i $4$ $1.597$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}^{3}q^{3}-3\zeta_{8}^{2}q^{9}+2\zeta_{8}q^{27}+q^{41}+\cdots\)
3200.1.m.e 3200.m 40.i $8$ $1.597$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{3}+(-\zeta_{24}^{4}-\zeta_{24}^{8})q^{11}+\cdots\)
3200.1.bd.a 3200.bd 200.n $4$ $1.597$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-1\) \(0\) \(q+\zeta_{10}^{4}q^{5}-\zeta_{10}^{2}q^{9}+(-\zeta_{10}+\zeta_{10}^{3}+\cdots)q^{13}+\cdots\)
3200.1.bd.b 3200.bd 200.n $4$ $1.597$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q-\zeta_{10}^{4}q^{5}-\zeta_{10}^{2}q^{9}+(\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{13}+\cdots\)
3200.1.bi.a 3200.bi 200.s $4$ $1.597$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)
3200.1.bi.b 3200.bi 200.s $4$ $1.597$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)
3200.1.bz.a 3200.bz 200.x $8$ $1.597$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}^{9}q^{5}-\zeta_{20}^{7}q^{9}+(\zeta_{20}^{3}-\zeta_{20}^{6}+\cdots)q^{13}+\cdots\)
3200.1.bz.b 3200.bz 200.x $8$ $1.597$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{9}q^{5}-\zeta_{20}^{7}q^{9}+(-\zeta_{20}^{3}+\zeta_{20}^{6}+\cdots)q^{13}+\cdots\)
3200.2.a.a 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-4q^{7}+6q^{9}-3q^{11}-2q^{13}+\cdots\)
3200.2.a.b 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}-4q^{7}+6q^{9}+3q^{11}+2q^{13}+\cdots\)
3200.2.a.c 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-3\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+4q^{7}+6q^{9}-3q^{11}+2q^{13}+\cdots\)
3200.2.a.d 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-3\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+4q^{7}+6q^{9}+3q^{11}-2q^{13}+\cdots\)
3200.2.a.e 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-4q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
3200.2.a.f 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}+2q^{11}-2q^{13}-6q^{17}+\cdots\)
3200.2.a.g 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-2\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+q^{9}+2q^{11}+2q^{13}-6q^{17}+\cdots\)
3200.2.a.h 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-2\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+4q^{7}+q^{9}-2q^{11}-2q^{13}+\cdots\)
3200.2.a.i 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{9}-q^{11}-2q^{13}-3q^{17}+\cdots\)
3200.2.a.j 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{9}-q^{11}+2q^{13}-3q^{17}+\cdots\)
3200.2.a.k 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{9}+q^{11}-2q^{13}+3q^{17}+\cdots\)
3200.2.a.l 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{9}+q^{11}+2q^{13}+3q^{17}+\cdots\)
3200.2.a.m 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}-6q^{11}+2q^{13}+6q^{17}+\cdots\)
3200.2.a.n 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{7}-3q^{9}+6q^{11}-2q^{13}+6q^{17}+\cdots\)
3200.2.a.o 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}-6q^{11}-2q^{13}+6q^{17}+\cdots\)
3200.2.a.p 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}-3q^{9}+6q^{11}+2q^{13}+6q^{17}+\cdots\)
3200.2.a.q 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{9}-q^{11}-2q^{13}+3q^{17}+\cdots\)
3200.2.a.r 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{9}-q^{11}+2q^{13}+3q^{17}+\cdots\)
3200.2.a.s 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{9}+q^{11}-2q^{13}-3q^{17}+\cdots\)
3200.2.a.t 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{9}+q^{11}+2q^{13}-3q^{17}+\cdots\)
3200.2.a.u 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(2\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-4q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
3200.2.a.v 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}-2q^{11}-2q^{13}-6q^{17}+\cdots\)
3200.2.a.w 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(2\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}+q^{9}-2q^{11}+2q^{13}-6q^{17}+\cdots\)
3200.2.a.x 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(2\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+4q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
3200.2.a.y 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(3\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}-4q^{7}+6q^{9}-3q^{11}-2q^{13}+\cdots\)
3200.2.a.z 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(3\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-4q^{7}+6q^{9}+3q^{11}+2q^{13}+\cdots\)
3200.2.a.ba 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(3\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+4q^{7}+6q^{9}-3q^{11}+2q^{13}+\cdots\)
3200.2.a.bb 3200.a 1.a $1$ $25.552$ \(\Q\) None None \(0\) \(3\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+4q^{7}+6q^{9}+3q^{11}-2q^{13}+\cdots\)
3200.2.a.bc 3200.a 1.a $2$ $25.552$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(-2-2\beta )q^{7}-2\beta q^{9}+\cdots\)
3200.2.a.bd 3200.a 1.a $2$ $25.552$ \(\Q(\sqrt{2}) \) None None \(0\) \(-2\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+(-2-2\beta )q^{7}-2\beta q^{9}+\cdots\)
3200.2.a.be 3200.a 1.a $2$ $25.552$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(-1+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
3200.2.a.bf 3200.a 1.a $2$ $25.552$ \(\Q(\sqrt{5}) \) None None \(0\) \(-2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(-1-\beta )q^{3}+(1-\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
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