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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
450.2.a.a 450.a 1.a $1$ $3.593$ \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{7}-q^{8}-6q^{11}+4q^{13}+\cdots\)
450.2.a.b 450.a 1.a $1$ $3.593$ \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{7}-q^{8}-2q^{11}-6q^{13}+\cdots\)
450.2.a.c 450.a 1.a $1$ $3.593$ \(\Q\) None \(-1\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}-2q^{7}-q^{8}+3q^{11}+4q^{13}+\cdots\)
450.2.a.d 450.a 1.a $1$ $3.593$ \(\Q\) None \(-1\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{4}+4q^{7}-q^{8}-2q^{13}-4q^{14}+\cdots\)
450.2.a.e 450.a 1.a $1$ $3.593$ \(\Q\) None \(1\) \(0\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}-2q^{7}+q^{8}+6q^{11}+4q^{13}+\cdots\)
450.2.a.f 450.a 1.a $1$ $3.593$ \(\Q\) None \(1\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{7}+q^{8}-2q^{11}+6q^{13}+\cdots\)
450.2.a.g 450.a 1.a $1$ $3.593$ \(\Q\) None \(1\) \(0\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+2q^{7}+q^{8}+3q^{11}-4q^{13}+\cdots\)
450.2.c.a 450.c 5.b $2$ $3.593$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}-6q^{11}+\cdots\)
450.2.c.b 450.c 5.b $2$ $3.593$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-4iq^{7}-iq^{8}-2iq^{13}+\cdots\)
450.2.c.c 450.c 5.b $2$ $3.593$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+2iq^{7}-iq^{8}+3q^{11}+\cdots\)
450.2.c.d 450.c 5.b $2$ $3.593$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}-2iq^{7}-iq^{8}+6q^{11}+\cdots\)
450.2.e.a 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.b 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-3\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.c 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.d 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.e 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None \(1\) \(-3\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.f 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None \(1\) \(0\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.g 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(0\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.h 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.i 450.e 9.c $2$ $3.593$ \(\Q(\sqrt{-3}) \) None \(1\) \(3\) \(0\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\zeta_{6})q^{2}+(1+\zeta_{6})q^{3}-\zeta_{6}q^{4}+\cdots\)
450.2.e.j 450.e 9.c $4$ $3.593$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None \(-2\) \(-2\) \(0\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+(-\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
450.2.e.k 450.e 9.c $4$ $3.593$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(2\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(-\beta _{1}+\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
450.2.e.l 450.e 9.c $4$ $3.593$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(-2\) \(4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
450.2.e.m 450.e 9.c $4$ $3.593$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1-\beta _{2})q^{2}+(-1+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots\)
450.2.e.n 450.e 9.c $4$ $3.593$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None \(2\) \(-2\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{2}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3})q^{3}+(-1+\cdots)q^{4}+\cdots\)
450.2.f.a 450.f 15.e $4$ $3.593$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-3+3\zeta_{8}^{2})q^{7}+\cdots\)
450.2.f.b 450.f 15.e $4$ $3.593$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-2+2\zeta_{8}^{2})q^{7}+\cdots\)
450.2.f.c 450.f 15.e $4$ $3.593$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(12\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(3-3\zeta_{8}^{2})q^{7}+\cdots\)
450.2.h.a 450.h 25.d $4$ $3.593$ \(\Q(\zeta_{10})\) None \(-1\) \(0\) \(-5\) \(-12\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
450.2.h.b 450.h 25.d $4$ $3.593$ \(\Q(\zeta_{10})\) None \(-1\) \(0\) \(-5\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(-1+\zeta_{10}-\zeta_{10}^{2}+\zeta_{10}^{3})q^{2}+\cdots\)
450.2.h.c 450.h 25.d $4$ $3.593$ \(\Q(\zeta_{10})\) None \(1\) \(0\) \(-5\) \(6\) $\mathrm{SU}(2)[C_{5}]$ \(q+(1-\zeta_{10}+\zeta_{10}^{2}-\zeta_{10}^{3})q^{2}-\zeta_{10}^{3}q^{4}+\cdots\)
450.2.h.d 450.h 25.d $8$ $3.593$ 8.0.1064390625.3 None \(-2\) \(0\) \(4\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{3}q^{2}+(-1-\beta _{2}+\beta _{3}-\beta _{5})q^{4}+\cdots\)
450.2.h.e 450.h 25.d $8$ $3.593$ 8.0.58140625.2 None \(2\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{6}q^{2}-\beta _{3}q^{4}+(-\beta _{1}-\beta _{3})q^{5}+\cdots\)
450.2.h.f 450.h 25.d $12$ $3.593$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-3\) \(0\) \(1\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{7}q^{2}+(-1+\beta _{4}-\beta _{6}+\beta _{7})q^{4}+\cdots\)
450.2.h.g 450.h 25.d $12$ $3.593$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(3\) \(0\) \(-1\) \(-2\) $\mathrm{SU}(2)[C_{5}]$ \(q+\beta _{7}q^{2}+(-1+\beta _{4}-\beta _{6}+\beta _{7})q^{4}+\cdots\)
450.2.j.a 450.j 45.j $4$ $3.593$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}+2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.b 450.j 45.j $4$ $3.593$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-2\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.c 450.j 45.j $4$ $3.593$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.d 450.j 45.j $4$ $3.593$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.e 450.j 45.j $4$ $3.593$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(\zeta_{12}-2\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
450.2.j.f 450.j 45.j $8$ $3.593$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}+\zeta_{24}^{3})q^{2}+(\zeta_{24}^{3}+\zeta_{24}^{7})q^{3}+\cdots\)
450.2.j.g 450.j 45.j $8$ $3.593$ 8.0.303595776.1 None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{3}-\beta _{5}-\beta _{7})q^{3}+\cdots\)
450.2.l.a 450.l 25.e $8$ $3.593$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+(\zeta_{20}+\zeta_{20}^{2}+\cdots)q^{5}+\cdots\)
450.2.l.b 450.l 25.e $8$ $3.593$ \(\Q(\zeta_{20})\) None \(0\) \(0\) \(10\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q+\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}+(1-\zeta_{20}-\zeta_{20}^{3}+\cdots)q^{5}+\cdots\)
450.2.l.c 450.l 25.e $16$ $3.593$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{8}q^{2}-\beta _{10}q^{4}+(-1-\beta _{3}+\beta _{5}+\cdots)q^{5}+\cdots\)
450.2.l.d 450.l 25.e $16$ $3.593$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$ \(q-\beta _{11}q^{2}+(1+\beta _{3}+\beta _{4}+\beta _{5})q^{4}+\cdots\)
450.2.p.a 450.p 45.l $8$ $3.593$ \(\Q(\zeta_{24})\) None \(0\) \(-4\) \(0\) \(8\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}+(-1-\zeta_{24}^{2}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots\)
450.2.p.b 450.p 45.l $8$ $3.593$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}+(2\zeta_{24}-\zeta_{24}^{5})q^{3}-\zeta_{24}^{2}q^{4}+\cdots\)
450.2.p.c 450.p 45.l $8$ $3.593$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}+(\zeta_{24}^{3}-2\zeta_{24}^{7})q^{3}-\zeta_{24}^{2}q^{4}+\cdots\)
450.2.p.d 450.p 45.l $8$ $3.593$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{24}^{7}q^{2}+(-2\zeta_{24}+\zeta_{24}^{5})q^{3}+\cdots\)
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