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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
600.1.n.a 600.n 24.h $1$ $0.299$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(-1\) \(1\) \(0\) \(0\) \(q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots\)
600.1.n.b 600.n 24.h $1$ $0.299$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-6}) \) \(\Q(\sqrt{10}) \) \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
600.1.q.a 600.q 120.q $4$ $0.299$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-15}) \) \(\Q(\sqrt{30}) \) \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{8}^{3}q^{2}-\zeta_{8}q^{3}-\zeta_{8}^{2}q^{4}+q^{6}+\cdots\)
600.1.q.b 600.q 120.q $8$ $0.299$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{6}q^{4}-\zeta_{24}^{4}q^{6}+\cdots\)
600.1.z.a 600.z 600.z $8$ $0.299$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{20}q^{2}+\zeta_{20}^{7}q^{3}+\zeta_{20}^{2}q^{4}+\zeta_{20}q^{5}+\cdots\)
600.1.bj.a 600.bj 600.aj $4$ $0.299$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-6}) \) None \(-1\) \(-1\) \(-1\) \(-2\) \(q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}q^{5}+\cdots\)
600.1.bj.b 600.bj 600.aj $4$ $0.299$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-6}) \) None \(1\) \(1\) \(1\) \(-2\) \(q+\zeta_{10}q^{2}-\zeta_{10}^{2}q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}q^{5}+\cdots\)
600.2.a.a 600.a 1.a $1$ $4.791$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-4q^{7}+q^{9}+6q^{13}+2q^{17}+\cdots\)
600.2.a.b 600.a 1.a $1$ $4.791$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-3\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-3q^{7}+q^{9}+2q^{11}+3q^{13}+\cdots\)
600.2.a.c 600.a 1.a $1$ $4.791$ \(\Q\) None None \(0\) \(-1\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+q^{9}-4q^{11}-6q^{13}+6q^{17}+\cdots\)
600.2.a.d 600.a 1.a $1$ $4.791$ \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}+q^{9}+2q^{11}-2q^{13}+\cdots\)
600.2.a.e 600.a 1.a $1$ $4.791$ \(\Q\) None None \(0\) \(-1\) \(0\) \(5\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+5q^{7}+q^{9}-6q^{11}+3q^{13}+\cdots\)
600.2.a.f 600.a 1.a $1$ $4.791$ \(\Q\) None None \(0\) \(1\) \(0\) \(-5\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-5q^{7}+q^{9}-6q^{11}-3q^{13}+\cdots\)
600.2.a.g 600.a 1.a $1$ $4.791$ \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
600.2.a.h 600.a 1.a $1$ $4.791$ \(\Q\) None None \(0\) \(1\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots\)
600.2.a.i 600.a 1.a $1$ $4.791$ \(\Q\) None None \(0\) \(1\) \(0\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+3q^{7}+q^{9}+2q^{11}-3q^{13}+\cdots\)
600.2.b.a 600.b 24.f $2$ $4.791$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{2}+(1-\beta )q^{3}-2q^{4}+(2+\beta )q^{6}+\cdots\)
600.2.b.b 600.b 24.f $4$ $4.791$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(-2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+(-1-\beta _{2})q^{3}-2q^{4}+(-1+\cdots)q^{6}+\cdots\)
600.2.b.c 600.b 24.f $4$ $4.791$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{2})q^{3}+\beta _{3}q^{4}+(-2+\cdots)q^{6}+\cdots\)
600.2.b.d 600.b 24.f $4$ $4.791$ \(\Q(\sqrt{-2}, \sqrt{-3})\) \(\Q(\sqrt{-2}) \) None \(0\) \(2\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+(1+\beta _{2})q^{3}-2q^{4}+(-1+\cdots)q^{6}+\cdots\)
600.2.b.e 600.b 24.f $8$ $4.791$ 8.0.1649659456.5 None None \(-1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{4}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
600.2.b.f 600.b 24.f $8$ $4.791$ 8.0.1649659456.5 None None \(1\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+(\beta _{1}+\beta _{3}+\beta _{4})q^{4}+\cdots\)
600.2.b.g 600.b 24.f $12$ $4.791$ 12.0.\(\cdots\).1 None None \(0\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{8}q^{2}-\beta _{5}q^{3}+(1+\beta _{4})q^{4}+(-\beta _{4}+\cdots)q^{6}+\cdots\)
600.2.b.h 600.b 24.f $12$ $4.791$ 12.0.\(\cdots\).1 None None \(0\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{6}+\cdots\)
600.2.b.i 600.b 24.f $16$ $4.791$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{10}q^{2}+\beta _{5}q^{3}-\beta _{14}q^{4}+(\beta _{7}+\beta _{12}+\cdots)q^{6}+\cdots\)
600.2.d.a 600.d 40.f $2$ $4.791$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-q^{3}-2iq^{4}+(1-i)q^{6}+\cdots\)
600.2.d.b 600.d 40.f $2$ $4.791$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}+q^{3}-2iq^{4}+(-1+\cdots)q^{6}+\cdots\)
600.2.d.c 600.d 40.f $2$ $4.791$ \(\Q(\sqrt{-1}) \) None None \(2\) \(-2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}-q^{3}+2iq^{4}+(-1-i)q^{6}+\cdots\)
600.2.d.d 600.d 40.f $2$ $4.791$ \(\Q(\sqrt{-1}) \) None None \(2\) \(2\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots\)
600.2.d.e 600.d 40.f $6$ $4.791$ 6.0.399424.1 None None \(0\) \(-6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}-q^{3}-\beta _{2}q^{4}-\beta _{3}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
600.2.d.f 600.d 40.f $6$ $4.791$ 6.0.399424.1 None None \(0\) \(6\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+q^{3}-\beta _{1}q^{4}-\beta _{2}q^{6}+(\beta _{1}+\cdots)q^{7}+\cdots\)
600.2.d.g 600.d 40.f $8$ $4.791$ 8.0.214798336.3 None None \(-2\) \(-8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{6}q^{2}-q^{3}+(-1-\beta _{1}+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
600.2.d.h 600.d 40.f $8$ $4.791$ 8.0.214798336.3 None None \(2\) \(8\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{6}q^{2}+q^{3}+(-1-\beta _{1}+\beta _{3}+\beta _{6}+\cdots)q^{4}+\cdots\)
600.2.f.a 600.f 5.b $2$ $4.791$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+5iq^{7}-q^{9}-6q^{11}-3iq^{13}+\cdots\)
600.2.f.b 600.f 5.b $2$ $4.791$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{9}-4q^{11}+6iq^{13}+6iq^{17}+\cdots\)
600.2.f.c 600.f 5.b $2$ $4.791$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-4iq^{7}-q^{9}-6iq^{13}+2iq^{17}+\cdots\)
600.2.f.d 600.f 5.b $2$ $4.791$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-3iq^{7}-q^{9}+2q^{11}-3iq^{13}+\cdots\)
600.2.f.e 600.f 5.b $2$ $4.791$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-q^{9}+4q^{11}+2iq^{13}+2iq^{17}+\cdots\)
600.2.k.a 600.k 8.b $2$ $4.791$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-iq^{3}-2iq^{4}+(1+i)q^{6}+\cdots\)
600.2.k.b 600.k 8.b $2$ $4.791$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+iq^{3}+2iq^{4}+(-1+i)q^{6}+\cdots\)
600.2.k.c 600.k 8.b $6$ $4.791$ 6.0.399424.1 None None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{3}q^{3}+(\beta _{2}-\beta _{3})q^{4}+\beta _{4}q^{6}+\cdots\)
600.2.k.d 600.k 8.b $8$ $4.791$ 8.0.214798336.3 None None \(-2\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{2}+\beta _{2}q^{3}+(-\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
600.2.k.e 600.k 8.b $8$ $4.791$ 8.0.214798336.3 None None \(2\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{2}q^{3}+(-\beta _{4}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots\)
600.2.k.f 600.k 8.b $12$ $4.791$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}-\beta _{5}q^{6}+\cdots\)
600.2.m.a 600.m 120.m $4$ $4.791$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{8}^{3}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+2q^{4}+\cdots\)
600.2.m.b 600.m 120.m $8$ $4.791$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{24}^{2}q^{2}-\zeta_{24}^{3}q^{3}+2q^{4}+(-1+\cdots)q^{6}+\cdots\)
600.2.m.c 600.m 120.m $16$ $4.791$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(-1+\beta _{11}+\cdots)q^{6}+\cdots\)
600.2.m.d 600.m 120.m $16$ $4.791$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{2}+\beta _{6}q^{3}+\beta _{2}q^{4}-\beta _{14}q^{6}+\cdots\)
600.2.m.e 600.m 120.m $24$ $4.791$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
600.2.r.a 600.r 15.e $4$ $4.791$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+(-2+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
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