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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
882.2.a.a 882.a 1.a $1$ $7.043$ \(\Q\) None \(-1\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-3q^{5}-q^{8}+3q^{10}+3q^{11}+\cdots\)
882.2.a.b 882.a 1.a $1$ $7.043$ \(\Q\) None \(-1\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{5}-q^{8}+2q^{10}+4q^{11}+\cdots\)
882.2.a.c 882.a 1.a $1$ $7.043$ \(\Q\) None \(-1\) \(0\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-5q^{11}+\cdots\)
882.2.a.d 882.a 1.a $1$ $7.043$ \(\Q\) None \(-1\) \(0\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-5q^{11}+\cdots\)
882.2.a.e 882.a 1.a $1$ $7.043$ \(\Q\) None \(-1\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+3q^{5}-q^{8}-3q^{10}+3q^{11}+\cdots\)
882.2.a.f 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(-4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-4q^{5}+q^{8}-4q^{10}+4q^{11}+\cdots\)
882.2.a.g 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
882.2.a.h 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(-3\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-3q^{5}+q^{8}-3q^{10}-3q^{11}+\cdots\)
882.2.a.i 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{8}+4q^{13}+q^{16}+6q^{17}+\cdots\)
882.2.a.j 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
882.2.a.k 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(3\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+3q^{5}+q^{8}+3q^{10}-3q^{11}+\cdots\)
882.2.a.l 882.a 1.a $1$ $7.043$ \(\Q\) None \(1\) \(0\) \(4\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+4q^{5}+q^{8}+4q^{10}+4q^{11}+\cdots\)
882.2.a.m 882.a 1.a $2$ $7.043$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+\beta q^{5}-q^{8}-\beta q^{10}-4q^{11}+\cdots\)
882.2.a.n 882.a 1.a $2$ $7.043$ \(\Q(\sqrt{2}) \) None \(-2\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+2\beta q^{5}-q^{8}-2\beta q^{10}+\cdots\)
882.2.a.o 882.a 1.a $2$ $7.043$ \(\Q(\sqrt{2}) \) None \(2\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+\beta q^{5}+q^{8}+\beta q^{10}+4q^{11}+\cdots\)
882.2.d.a 882.d 21.c $8$ $7.043$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{24}q^{2}-q^{4}+(-\zeta_{24}^{3}-\zeta_{24}^{4}+\cdots)q^{5}+\cdots\)
882.2.d.b 882.d 21.c $8$ $7.043$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{16}q^{2}-q^{4}-\zeta_{16}^{5}q^{5}+\zeta_{16}q^{8}+\cdots\)
882.2.e.a 882.e 63.h $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(-2+2\zeta_{6})q^{5}+\cdots\)
882.2.e.b 882.e 63.h $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-2\) \(-3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
882.2.e.c 882.e 63.h $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-2\) \(0\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(3-3\zeta_{6})q^{5}+\cdots\)
882.2.e.d 882.e 63.h $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
882.2.e.e 882.e 63.h $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-2\) \(3\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(2-2\zeta_{6})q^{5}+\cdots\)
882.2.e.f 882.e 63.h $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-1-\zeta_{6})q^{3}+q^{4}+(-1+\zeta_{6})q^{5}+\cdots\)
882.2.e.g 882.e 63.h $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(2\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-2+\zeta_{6})q^{3}+q^{4}+(-2+\zeta_{6})q^{6}+\cdots\)
882.2.e.h 882.e 63.h $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(2\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1-2\zeta_{6})q^{3}+q^{4}+(-3+3\zeta_{6})q^{5}+\cdots\)
882.2.e.i 882.e 63.h $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(2-\zeta_{6})q^{3}+q^{4}+(2-\zeta_{6})q^{6}+\cdots\)
882.2.e.j 882.e 63.h $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(2\) \(3\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(1+\zeta_{6})q^{3}+q^{4}+(1-\zeta_{6})q^{5}+\cdots\)
882.2.e.k 882.e 63.h $4$ $7.043$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-4\) \(-2\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(-\beta _{1}+\beta _{3})q^{3}+q^{4}+(-1+\cdots)q^{5}+\cdots\)
882.2.e.l 882.e 63.h $4$ $7.043$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-4\) \(2\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(\beta _{1}-\beta _{3})q^{3}+q^{4}+(1-2\beta _{1}+\cdots)q^{5}+\cdots\)
882.2.e.m 882.e 63.h $4$ $7.043$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(4\) \(-2\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+q^{4}+\cdots\)
882.2.e.n 882.e 63.h $4$ $7.043$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(4\) \(2\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
882.2.e.o 882.e 63.h $6$ $7.043$ 6.0.309123.1 None \(-6\) \(-2\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(\beta _{2}+\beta _{4})q^{3}+q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots\)
882.2.e.p 882.e 63.h $6$ $7.043$ 6.0.309123.1 None \(6\) \(2\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-\beta _{3}+\beta _{4}+\beta _{5})q^{3}+q^{4}+\cdots\)
882.2.e.q 882.e 63.h $8$ $7.043$ \(\Q(\zeta_{24})\) None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}+(\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+q^{4}-\zeta_{24}^{7}q^{5}+\cdots\)
882.2.e.r 882.e 63.h $8$ $7.043$ 8.0.\(\cdots\).2 None \(-8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-q^{2}-\beta _{3}q^{3}+q^{4}+(-\beta _{5}-\beta _{6})q^{5}+\cdots\)
882.2.e.s 882.e 63.h $8$ $7.043$ \(\Q(\zeta_{24})\) None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(-\zeta_{24}^{3}+2\zeta_{24}^{5}+\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
882.2.e.t 882.e 63.h $8$ $7.043$ 8.0.3317760000.3 None \(8\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+q^{2}+(\beta _{5}-\beta _{6})q^{3}+q^{4}+(2\beta _{1}-\beta _{3}+\cdots)q^{5}+\cdots\)
882.2.f.a 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.b 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.c 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.d 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.e 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.f 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-1-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.g 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.h 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.i 882.f 9.c $2$ $7.043$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(-3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
882.2.f.j 882.f 9.c $4$ $7.043$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(-4\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+(-1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
882.2.f.k 882.f 9.c $4$ $7.043$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(2\) \(1\) \(3\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{2}+(\beta _{2}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
882.2.f.l 882.f 9.c $6$ $7.043$ 6.0.309123.1 None \(-3\) \(-2\) \(-5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{4})q^{2}+(-1+\beta _{1}+\beta _{2})q^{3}+\cdots\)
882.2.f.m 882.f 9.c $6$ $7.043$ 6.0.309123.1 None \(-3\) \(2\) \(5\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\beta _{4})q^{2}+(1-\beta _{1}-\beta _{2})q^{3}+\cdots\)
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