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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
576.1.b.a 576.b 8.d $2$ $0.287$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{2}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{7}+q^{25}+iq^{31}-3q^{49}-q^{73}+\cdots\)
576.1.e.a 576.e 3.b $2$ $0.287$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}-\beta q^{17}-q^{25}+\beta q^{29}+2q^{37}+\cdots\)
576.1.g.a 576.g 4.b $1$ $0.287$ \(\Q\) \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{3}) \) \(0\) \(0\) \(0\) \(0\) \(q+2q^{13}-q^{25}-2q^{37}+q^{49}-2q^{61}+\cdots\)
576.1.n.a 576.n 72.j $4$ $0.287$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{9}+(-\zeta_{12}^{3}-\zeta_{12}^{5}+\cdots)q^{11}+\cdots\)
576.1.o.a 576.o 36.f $4$ $0.287$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) \(q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-q^{9}+\cdots\)
576.2.a.a 576.a 1.a $1$ $4.599$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-4q^{5}+6q^{13}+8q^{17}+11q^{25}+\cdots\)
576.2.a.b 576.a 1.a $1$ $4.599$ \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-2q^{5}-4q^{11}+2q^{13}-2q^{17}-4q^{19}+\cdots\)
576.2.a.c 576.a 1.a $1$ $4.599$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-2q^{5}-6q^{13}-2q^{17}-q^{25}-10q^{29}+\cdots\)
576.2.a.d 576.a 1.a $1$ $4.599$ \(\Q\) None None \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-2q^{5}+4q^{11}+2q^{13}-2q^{17}+4q^{19}+\cdots\)
576.2.a.e 576.a 1.a $1$ $4.599$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(-4\) $+$ $N(\mathrm{U}(1))$ \(q-4q^{7}-2q^{13}-8q^{19}-5q^{25}-4q^{31}+\cdots\)
576.2.a.f 576.a 1.a $1$ $4.599$ \(\Q\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(4\) $-$ $N(\mathrm{U}(1))$ \(q+4q^{7}-2q^{13}+8q^{19}-5q^{25}+4q^{31}+\cdots\)
576.2.a.g 576.a 1.a $1$ $4.599$ \(\Q\) None None \(0\) \(0\) \(2\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}-4q^{7}+4q^{11}+2q^{13}+6q^{17}+\cdots\)
576.2.a.h 576.a 1.a $1$ $4.599$ \(\Q\) None None \(0\) \(0\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+2q^{5}+4q^{7}-4q^{11}+2q^{13}+6q^{17}+\cdots\)
576.2.a.i 576.a 1.a $1$ $4.599$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+4q^{5}+6q^{13}-8q^{17}+11q^{25}+\cdots\)
576.2.c.a 576.c 12.b $2$ $4.599$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{5}-4q^{13}+\beta q^{17}-13q^{25}+\cdots\)
576.2.c.b 576.c 12.b $2$ $4.599$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{5}+4q^{13}+5\beta q^{17}+3q^{25}+\cdots\)
576.2.c.c 576.c 12.b $4$ $4.599$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{11}-4q^{13}+\cdots\)
576.2.d.a 576.d 8.b $2$ $4.599$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+3iq^{11}+6q^{17}+iq^{19}+5q^{25}+\cdots\)
576.2.d.b 576.d 8.b $4$ $4.599$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{12}^{2}q^{5}-\zeta_{12}q^{7}-6q^{17}-\zeta_{12}^{3}q^{19}+\cdots\)
576.2.d.c 576.d 8.b $4$ $4.599$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-3}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{12}q^{7}-\zeta_{12}^{2}q^{13}-\zeta_{12}^{3}q^{19}+\cdots\)
576.2.f.a 576.f 24.f $8$ $4.599$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{2}q^{5}-\zeta_{24}q^{7}-\zeta_{24}^{6}q^{11}+\cdots\)
576.2.i.a 576.i 9.c $2$ $4.599$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\zeta_{6})q^{3}+(2-2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
576.2.i.b 576.i 9.c $2$ $4.599$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(4\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1-\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(2-2\zeta_{6})q^{7}+\cdots\)
576.2.i.c 576.i 9.c $2$ $4.599$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots\)
576.2.i.d 576.i 9.c $2$ $4.599$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots\)
576.2.i.e 576.i 9.c $2$ $4.599$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
576.2.i.f 576.i 9.c $2$ $4.599$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(3\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-2\zeta_{6})q^{3}+3\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+\cdots\)
576.2.i.g 576.i 9.c $2$ $4.599$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{7}+3\zeta_{6}q^{9}+\cdots\)
576.2.i.h 576.i 9.c $2$ $4.599$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}+(-2+2\zeta_{6})q^{7}+\cdots\)
576.2.i.i 576.i 9.c $4$ $4.599$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-4\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{3})q^{3}-\beta _{2}q^{5}+(-1+\beta _{1}+\cdots)q^{7}+\cdots\)
576.2.i.j 576.i 9.c $4$ $4.599$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-1\) \(-1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
576.2.i.k 576.i 9.c $4$ $4.599$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{3}q^{3}+(-1+\zeta_{12})q^{5}-\zeta_{12}^{2}q^{7}+\cdots\)
576.2.i.l 576.i 9.c $4$ $4.599$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(1\) \(-1\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{1}q^{3}+(-\beta _{1}+\beta _{2}+2\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
576.2.i.m 576.i 9.c $4$ $4.599$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(4\) \(-2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{3})q^{3}+(-1+\beta _{2})q^{5}+(\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
576.2.i.n 576.i 9.c $8$ $4.599$ 8.0.170772624.1 None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{5})q^{3}+(-1+\beta _{4}-\beta _{7})q^{5}+\cdots\)
576.2.k.a 576.k 16.e $2$ $4.599$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+i)q^{5}+2iq^{7}+(1+i)q^{11}+(-1+\cdots)q^{13}+\cdots\)
576.2.k.b 576.k 16.e $8$ $4.599$ 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{4}+\beta _{6})q^{5}+(\beta _{1}+\beta _{3}-\beta _{4}-\beta _{5}+\cdots)q^{7}+\cdots\)
576.2.k.c 576.k 16.e $8$ $4.599$ 8.0.629407744.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{2}q^{5}+(\beta _{3}-\beta _{7})q^{7}+(-\beta _{1}-\beta _{2}+\cdots)q^{11}+\cdots\)
576.2.l.a 576.l 48.k $16$ $4.599$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{3}q^{5}-\beta _{9}q^{7}+(\beta _{2}+\beta _{14})q^{11}+\cdots\)
576.2.p.a 576.p 72.l $16$ $4.599$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{12}q^{3}+(\beta _{3}-\beta _{4}-\beta _{7})q^{5}+(\beta _{6}+\cdots)q^{7}+\cdots\)
576.2.p.b 576.p 72.l $16$ $4.599$ 16.0.\(\cdots\).3 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{4}q^{3}+(\beta _{3}+\beta _{6})q^{5}+(-\beta _{14}-\beta _{15})q^{7}+\cdots\)
576.2.p.c 576.p 72.l $16$ $4.599$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\beta _{12}q^{3}+(-\beta _{3}+\beta _{4}+\beta _{7})q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
576.2.r.a 576.r 72.n $4$ $4.599$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(-12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2-2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
576.2.r.b 576.r 72.n $4$ $4.599$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(2+2\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
576.2.r.c 576.r 72.n $8$ $4.599$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{6}]$ \(q+(-\zeta_{24}^{4}+\zeta_{24}^{6})q^{3}+(-1+\zeta_{24}+\cdots)q^{9}+\cdots\)
576.2.r.d 576.r 72.n $8$ $4.599$ 8.0.12960000.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-2\beta _{1}-\beta _{3})q^{3}-\beta _{4}q^{5}+(-\beta _{5}+\cdots)q^{7}+\cdots\)
576.2.r.e 576.r 72.n $12$ $4.599$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(-18\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{4}+\beta _{5})q^{3}+(-2-\beta _{6})q^{5}+(\beta _{1}+\cdots)q^{7}+\cdots\)
576.2.r.f 576.r 72.n $12$ $4.599$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(0\) \(18\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\beta _{4}+\beta _{5})q^{3}+(2+\beta _{6})q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
576.2.s.a 576.s 36.h $2$ $4.599$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(6\) \(6\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1-\zeta_{6})q^{3}+(4-2\zeta_{6})q^{5}+(2+2\zeta_{6})q^{7}+\cdots\)
576.2.s.b 576.s 36.h $2$ $4.599$ \(\Q(\sqrt{-3}) \) None None \(0\) \(0\) \(-3\) \(-3\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-1+2\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
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