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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1152.1.b.a 1152.b 8.d $1$ $0.575$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q+2q^{17}+q^{25}-2q^{41}+q^{49}-2q^{73}+\cdots\)
1152.1.b.b 1152.b 8.d $2$ $0.575$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}-3q^{25}-iq^{29}+q^{49}+iq^{53}+\cdots\)
1152.1.h.a 1152.h 24.h $4$ $0.575$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{13}+(\zeta_{8}+\cdots)q^{17}+\cdots\)
1152.1.n.a 1152.n 72.j $2$ $0.575$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(-1\) \(0\) \(0\) \(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{9}-\zeta_{6}q^{11}+(-\zeta_{6}+\cdots)q^{17}+\cdots\)
1152.1.n.b 1152.n 72.j $2$ $0.575$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(1\) \(0\) \(0\) \(q+\zeta_{6}q^{3}+\zeta_{6}^{2}q^{9}+\zeta_{6}q^{11}+(-\zeta_{6}+\cdots)q^{17}+\cdots\)
1152.1.t.a 1152.t 72.p $4$ $0.575$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{9}+(\zeta_{12}^{3}+\zeta_{12}^{5}+\cdots)q^{11}+\cdots\)
1152.2.a.a 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(-4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-4q^{5}-2q^{7}-4q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.b 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(-4\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-4q^{5}+2q^{7}+4q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.c 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{7}+2q^{11}+2q^{13}+2q^{17}+\cdots\)
1152.2.a.d 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}+4q^{11}-2q^{13}+4q^{17}+\cdots\)
1152.2.a.e 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(-2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-2q^{7}+4q^{11}+2q^{13}-4q^{17}+\cdots\)
1152.2.a.f 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}-4q^{11}-2q^{13}+4q^{17}+\cdots\)
1152.2.a.g 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}+2q^{7}-4q^{11}+2q^{13}-4q^{17}+\cdots\)
1152.2.a.h 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(-2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{7}-2q^{11}+2q^{13}+2q^{17}+\cdots\)
1152.2.a.i 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}-4q^{11}+6q^{13}-6q^{17}+4q^{23}+\cdots\)
1152.2.a.j 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{7}+4q^{11}-6q^{13}-6q^{17}+4q^{23}+\cdots\)
1152.2.a.k 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{7}-4q^{11}-6q^{13}-6q^{17}-4q^{23}+\cdots\)
1152.2.a.l 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{7}+4q^{11}+6q^{13}-6q^{17}-4q^{23}+\cdots\)
1152.2.a.m 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}-2q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.n 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-4q^{11}-2q^{13}-4q^{17}+\cdots\)
1152.2.a.o 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-2q^{7}-4q^{11}+2q^{13}+4q^{17}+\cdots\)
1152.2.a.p 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}+4q^{11}-2q^{13}-4q^{17}+\cdots\)
1152.2.a.q 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+2q^{7}+4q^{11}+2q^{13}+4q^{17}+\cdots\)
1152.2.a.r 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}+2q^{11}-2q^{13}+2q^{17}+\cdots\)
1152.2.a.s 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(4\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+4q^{5}-2q^{7}+4q^{11}+2q^{13}+2q^{17}+\cdots\)
1152.2.a.t 1152.a 1.a $1$ $9.199$ \(\Q\) None None \(0\) \(0\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+4q^{5}+2q^{7}-4q^{11}+2q^{13}+2q^{17}+\cdots\)
1152.2.c.a 1152.c 12.b $4$ $9.199$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(\zeta_{8}-2\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots\)
1152.2.c.b 1152.c 12.b $4$ $9.199$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-\zeta_{8}+2\zeta_{8}^{2})q^{7}+\cdots\)
1152.2.c.c 1152.c 12.b $4$ $9.199$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(\zeta_{8}-2\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots\)
1152.2.c.d 1152.c 12.b $4$ $9.199$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\zeta_{8}-\zeta_{8}^{2})q^{5}+(-\zeta_{8}+2\zeta_{8}^{2})q^{7}+\cdots\)
1152.2.d.a 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-4q^{7}+iq^{11}-iq^{13}+2q^{17}-iq^{19}+\cdots\)
1152.2.d.b 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}+2iq^{13}-8q^{17}+q^{25}+5iq^{29}+\cdots\)
1152.2.d.c 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{11}-6q^{17}-3\beta q^{19}+5q^{25}+\cdots\)
1152.2.d.d 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}+iq^{13}+2q^{17}-11q^{25}+\cdots\)
1152.2.d.e 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+iq^{5}-2iq^{13}+8q^{17}+q^{25}+5iq^{29}+\cdots\)
1152.2.d.f 1152.d 8.b $2$ $9.199$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+4q^{7}+iq^{11}+iq^{13}+2q^{17}-iq^{19}+\cdots\)
1152.2.d.g 1152.d 8.b $4$ $9.199$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{5}+\beta _{1}q^{7}-\beta _{3}q^{11}-7q^{25}+\cdots\)
1152.2.d.h 1152.d 8.b $4$ $9.199$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}q^{11}-2\zeta_{8}^{2}q^{13}+\cdots\)
1152.2.f.a 1152.f 24.f $4$ $9.199$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{3}q^{5}-2\zeta_{8}^{2}q^{7}+2\zeta_{8}q^{11}-\zeta_{8}q^{13}+\cdots\)
1152.2.f.b 1152.f 24.f $4$ $9.199$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{8}^{2}q^{5}+\zeta_{8}q^{13}+\zeta_{8}^{3}q^{17}-3q^{25}+\cdots\)
1152.2.f.c 1152.f 24.f $4$ $9.199$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{13}-5\zeta_{8}^{2}q^{17}+13q^{25}+\cdots\)
1152.2.f.d 1152.f 24.f $4$ $9.199$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{3}q^{5}-2\zeta_{8}^{2}q^{7}+2\zeta_{8}q^{11}+\zeta_{8}q^{13}+\cdots\)
1152.2.i.a 1152.i 9.c $2$ $9.199$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
1152.2.i.b 1152.i 9.c $2$ $9.199$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
1152.2.i.c 1152.i 9.c $2$ $9.199$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
1152.2.i.d 1152.i 9.c $2$ $9.199$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\zeta_{6})q^{3}+2\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
1152.2.i.e 1152.i 9.c $10$ $9.199$ 10.0.\(\cdots\).1 None None \(0\) \(-1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{5}-\beta _{7})q^{3}-\beta _{8}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
1152.2.i.f 1152.i 9.c $10$ $9.199$ 10.0.\(\cdots\).1 None None \(0\) \(-1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{5}-\beta _{7})q^{3}+\beta _{8}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
1152.2.i.g 1152.i 9.c $10$ $9.199$ 10.0.\(\cdots\).1 None None \(0\) \(1\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{5}+\beta _{7})q^{3}+\beta _{8}q^{5}+(-1-\beta _{1}+\cdots)q^{7}+\cdots\)
1152.2.i.h 1152.i 9.c $10$ $9.199$ 10.0.\(\cdots\).1 None None \(0\) \(1\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{5}+\beta _{7})q^{3}-\beta _{8}q^{5}+(1+\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
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