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Label Char Prim Dim $A$ Field CM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
490.2.a.a 490.a 1.a $1$ $3.913$ \(\Q\) None \(-1\) \(-2\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}-2q^{3}+q^{4}+q^{5}+2q^{6}-q^{8}+\cdots\)
490.2.a.b 490.a 1.a $1$ $3.913$ \(\Q\) None \(-1\) \(-1\) \(1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots\)
490.2.a.c 490.a 1.a $1$ $3.913$ \(\Q\) None \(-1\) \(1\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots\)
490.2.a.d 490.a 1.a $1$ $3.913$ \(\Q\) None \(-1\) \(2\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+2q^{3}+q^{4}-q^{5}-2q^{6}-q^{8}+\cdots\)
490.2.a.e 490.a 1.a $1$ $3.913$ \(\Q\) None \(1\) \(-3\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-3q^{3}+q^{4}+q^{5}-3q^{6}+q^{8}+\cdots\)
490.2.a.f 490.a 1.a $1$ $3.913$ \(\Q\) None \(1\) \(-2\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{8}+\cdots\)
490.2.a.g 490.a 1.a $1$ $3.913$ \(\Q\) None \(1\) \(-2\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}-2q^{3}+q^{4}-q^{5}-2q^{6}+q^{8}+\cdots\)
490.2.a.h 490.a 1.a $1$ $3.913$ \(\Q\) None \(1\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+q^{4}+q^{5}+q^{8}-3q^{9}+q^{10}+\cdots\)
490.2.a.i 490.a 1.a $1$ $3.913$ \(\Q\) None \(1\) \(2\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{8}+\cdots\)
490.2.a.j 490.a 1.a $1$ $3.913$ \(\Q\) None \(1\) \(2\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+2q^{3}+q^{4}+q^{5}+2q^{6}+q^{8}+\cdots\)
490.2.a.k 490.a 1.a $1$ $3.913$ \(\Q\) None \(1\) \(3\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{2}+3q^{3}+q^{4}-q^{5}+3q^{6}+q^{8}+\cdots\)
490.2.a.l 490.a 1.a $2$ $3.913$ \(\Q(\sqrt{2}) \) None \(-2\) \(-4\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{2}+(-2+\beta )q^{3}+q^{4}-q^{5}+(2+\cdots)q^{6}+\cdots\)
490.2.a.m 490.a 1.a $2$ $3.913$ \(\Q(\sqrt{2}) \) None \(-2\) \(4\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{2}+(2+\beta )q^{3}+q^{4}+q^{5}+(-2+\cdots)q^{6}+\cdots\)
490.2.c.a 490.c 5.b $2$ $3.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(-2-i)q^{5}-iq^{8}+\cdots\)
490.2.c.b 490.c 5.b $2$ $3.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-3iq^{3}-q^{4}+(-1-2i)q^{5}+\cdots\)
490.2.c.c 490.c 5.b $2$ $3.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}+3iq^{3}-q^{4}+(1+2i)q^{5}+\cdots\)
490.2.c.d 490.c 5.b $2$ $3.913$ \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{2}-q^{4}+(2+i)q^{5}-iq^{8}+3q^{9}+\cdots\)
490.2.c.e 490.c 5.b $4$ $3.913$ \(\Q(i, \sqrt{6})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{2}+(\beta _{1}+\beta _{3})q^{3}-q^{4}+(-1+\cdots)q^{5}+\cdots\)
490.2.c.f 490.c 5.b $4$ $3.913$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{2}+(\zeta_{8}+\zeta_{8}^{3})q^{3}-q^{4}+(\zeta_{8}+\cdots)q^{5}+\cdots\)
490.2.c.g 490.c 5.b $4$ $3.913$ \(\Q(\zeta_{8})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}^{2}q^{2}-q^{4}+(2\zeta_{8}+\zeta_{8}^{3})q^{5}+\zeta_{8}^{2}q^{8}+\cdots\)
490.2.e.a 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.b 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(-2\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.c 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}-\zeta_{6}q^{5}+q^{8}+\cdots\)
490.2.e.d 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(0\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(-1+\zeta_{6})q^{4}+\zeta_{6}q^{5}+q^{8}+\cdots\)
490.2.e.e 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(2-2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.f 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(-1\) \(3\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{6}q^{2}+(3-3\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.g 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(1\) \(-2\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(-2+2\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.h 490.e 7.c $2$ $3.913$ \(\Q(\sqrt{-3}) \) None \(1\) \(1\) \(-1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-1+\zeta_{6})q^{4}+\cdots\)
490.2.e.i 490.e 7.c $4$ $3.913$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(-4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\beta _{2})q^{2}+(\beta _{1}+2\beta _{2}+\beta _{3})q^{3}+\cdots\)
490.2.e.j 490.e 7.c $4$ $3.913$ \(\Q(\sqrt{2}, \sqrt{-3})\) None \(2\) \(4\) \(2\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{2}q^{2}+(2+\beta _{1}+2\beta _{2})q^{3}+(-1+\cdots)q^{4}+\cdots\)
490.2.g.a 490.g 35.f $8$ $3.913$ \(\Q(\zeta_{16})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\zeta_{16}^{2}q^{2}+(-\zeta_{16}-\zeta_{16}^{3}-\zeta_{16}^{5}+\cdots)q^{3}+\cdots\)
490.2.g.b 490.g 35.f $16$ $3.913$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{9}q^{2}+(-\beta _{11}-\beta _{12}+\beta _{13})q^{3}+\cdots\)
490.2.g.c 490.g 35.f $16$ $3.913$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{5}q^{2}+(-\beta _{8}+\beta _{14})q^{3}-\beta _{9}q^{4}+\cdots\)
490.2.i.a 490.i 35.j $4$ $3.913$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+(-2+\zeta_{12}+\cdots)q^{5}+\cdots\)
490.2.i.b 490.i 35.j $4$ $3.913$ \(\Q(\zeta_{12})\) None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{12}q^{2}+(3\zeta_{12}-3\zeta_{12}^{3})q^{3}+\zeta_{12}^{2}q^{4}+\cdots\)
490.2.i.c 490.i 35.j $8$ $3.913$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}+\zeta_{24}^{4})q^{2}+(-\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
490.2.i.d 490.i 35.j $8$ $3.913$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q-\zeta_{24}^{2}q^{2}+\zeta_{24}^{4}q^{4}+(\zeta_{24}^{3}+2\zeta_{24}^{5}+\cdots)q^{5}+\cdots\)
490.2.i.e 490.i 35.j $8$ $3.913$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+\zeta_{24}^{2}q^{2}+(-\zeta_{24}+\zeta_{24}^{7})q^{3}+\zeta_{24}^{4}q^{4}+\cdots\)
490.2.i.f 490.i 35.j $8$ $3.913$ \(\Q(\zeta_{24})\) None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{6}]$ \(q+(-\zeta_{24}+\zeta_{24}^{4})q^{2}+(-\zeta_{24}^{5}-\zeta_{24}^{6}+\cdots)q^{3}+\cdots\)
490.2.k.a 490.k 49.e $6$ $3.913$ \(\Q(\zeta_{14})\) None \(-1\) \(0\) \(-1\) \(7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(-1+\zeta_{14}-\zeta_{14}^{2}+\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{2}+\cdots\)
490.2.k.b 490.k 49.e $6$ $3.913$ \(\Q(\zeta_{14})\) None \(1\) \(-1\) \(1\) \(-7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{2}+\cdots\)
490.2.k.c 490.k 49.e $6$ $3.913$ \(\Q(\zeta_{14})\) None \(1\) \(6\) \(1\) \(7\) $\mathrm{SU}(2)[C_{7}]$ \(q+(1-\zeta_{14}+\zeta_{14}^{2}-\zeta_{14}^{3}+\zeta_{14}^{4}+\cdots)q^{2}+\cdots\)
490.2.k.d 490.k 49.e $12$ $3.913$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(-2\) \(-4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{7}]$ \(q-\beta _{6}q^{2}+(-1-\beta _{3}-\beta _{4}-\beta _{7}-\beta _{10}+\cdots)q^{3}+\cdots\)
490.2.k.e 490.k 49.e $12$ $3.913$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None \(2\) \(-4\) \(2\) \(0\) $\mathrm{SU}(2)[C_{7}]$ \(q-\beta _{2}q^{2}+(\beta _{2}-\beta _{6})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
490.2.k.f 490.k 49.e $24$ $3.913$ None \(4\) \(6\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{7}]$
490.2.k.g 490.k 49.e $30$ $3.913$ None \(-5\) \(1\) \(5\) \(1\) $\mathrm{SU}(2)[C_{7}]$
490.2.l.a 490.l 35.k $16$ $3.913$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q-\zeta_{48}^{10}q^{2}+(-\zeta_{48}^{5}-\zeta_{48}^{7}+\zeta_{48}^{15})q^{3}+\cdots\)
490.2.l.b 490.l 35.k $16$ $3.913$ \(\Q(\zeta_{48})\) None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+\zeta_{48}^{14}q^{2}+(-\zeta_{48}-\zeta_{48}^{3}+\zeta_{48}^{7}+\cdots)q^{3}+\cdots\)
490.2.l.c 490.l 35.k $16$ $3.913$ \(\mathbb{Q}[x]/(x^{16} + \cdots)\) None \(0\) \(0\) \(12\) \(0\) $\mathrm{SU}(2)[C_{12}]$ \(q+(-\beta _{7}-\beta _{15})q^{2}+(\beta _{4}-\beta _{13})q^{3}+\cdots\)
490.2.l.d 490.l 35.k $32$ $3.913$ None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{12}]$
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