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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
552.1.h.a 552.h 552.h $1$ $0.275$ \(\Q\) \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-138}) \) \(\Q(\sqrt{6}) \) \(-1\) \(-1\) \(0\) \(0\) \(q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots\)
552.1.h.b 552.h 552.h $1$ $0.275$ \(\Q\) \(\Q(\sqrt{-23}) \), \(\Q(\sqrt{-138}) \) \(\Q(\sqrt{6}) \) \(1\) \(-1\) \(0\) \(0\) \(q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots\)
552.1.h.c 552.h 552.h $2$ $0.275$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-23}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}+q^{8}+\cdots\)
552.1.h.d 552.h 552.h $2$ $0.275$ \(\Q(\sqrt{-3}) \) \(\Q(\sqrt{-23}) \) None \(1\) \(1\) \(0\) \(0\) \(q-\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots\)
552.2.a.a 552.a 1.a $1$ $4.408$ \(\Q\) None None \(0\) \(-1\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{5}+2q^{7}+q^{9}-2q^{11}+\cdots\)
552.2.a.b 552.a 1.a $1$ $4.408$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}+q^{9}+2q^{13}+8q^{17}+\cdots\)
552.2.a.c 552.a 1.a $1$ $4.408$ \(\Q\) None None \(0\) \(-1\) \(2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{5}-4q^{7}+q^{9}-4q^{11}+\cdots\)
552.2.a.d 552.a 1.a $1$ $4.408$ \(\Q\) None None \(0\) \(-1\) \(4\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+4q^{5}+2q^{7}+q^{9}+2q^{13}+\cdots\)
552.2.a.e 552.a 1.a $1$ $4.408$ \(\Q\) None None \(0\) \(1\) \(-2\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{5}-4q^{7}+q^{9}-2q^{13}+\cdots\)
552.2.a.f 552.a 1.a $2$ $4.408$ \(\Q(\sqrt{5}) \) None None \(0\) \(2\) \(2\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+(1+\beta )q^{5}+2q^{7}+q^{9}+(1+\beta )q^{11}+\cdots\)
552.2.a.g 552.a 1.a $3$ $4.408$ 3.3.148.1 None None \(0\) \(3\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+\beta _{2}q^{5}+(1+\beta _{1})q^{7}+q^{9}+(1+\cdots)q^{11}+\cdots\)
552.2.b.a 552.b 552.b $6$ $4.408$ 6.0.8869743.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+\beta _{4}q^{3}+(\beta _{2}+\beta _{5})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
552.2.b.b 552.b 552.b $6$ $4.408$ 6.0.8869743.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{2}+\beta _{2}q^{3}+(\beta _{2}+\beta _{5})q^{4}+(1+\cdots)q^{6}+\cdots\)
552.2.b.c 552.b 552.b $80$ $4.408$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
552.2.f.a 552.f 8.b $2$ $4.408$ \(\Q(\sqrt{-1}) \) None None \(2\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+iq^{3}+2iq^{4}+2iq^{5}+\cdots\)
552.2.f.b 552.f 8.b $4$ $4.408$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{3}q^{2}+\zeta_{8}q^{3}+2q^{4}+(2\zeta_{8}+\zeta_{8}^{2}+\cdots)q^{5}+\cdots\)
552.2.f.c 552.f 8.b $18$ $4.408$ \(\mathbb{Q}[x]/(x^{18} - \cdots)\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{3}q^{2}-\beta _{4}q^{3}-\beta _{2}q^{4}+\beta _{9}q^{5}+\cdots\)
552.2.f.d 552.f 8.b $20$ $4.408$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(-2\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{2}+\beta _{5}q^{3}+\beta _{2}q^{4}+\beta _{11}q^{5}+\cdots\)
552.2.j.a 552.j 24.f $2$ $4.408$ \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-1+\beta )q^{3}-2q^{4}-4q^{5}+\cdots\)
552.2.j.b 552.j 24.f $2$ $4.408$ \(\Q(\sqrt{-2}) \) None None \(0\) \(-2\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{2}+(-1+\beta )q^{3}-2q^{4}+4q^{5}+\cdots\)
552.2.j.c 552.j 24.f $42$ $4.408$ None None \(0\) \(2\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{2}]$
552.2.j.d 552.j 24.f $42$ $4.408$ None None \(0\) \(2\) \(8\) \(0\) $\mathrm{SU}(2)[C_{2}]$
552.2.m.a 552.m 69.c $8$ $4.408$ 8.0.40960000.1 None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-\beta _{2})q^{3}+\beta _{3}q^{5}+\beta _{5}q^{7}+(1+\cdots)q^{9}+\cdots\)
552.2.m.b 552.m 69.c $16$ $4.408$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{7}q^{3}-\beta _{5}q^{5}-\beta _{1}q^{7}+(\beta _{2}+\beta _{4}+\cdots)q^{9}+\cdots\)
552.2.n.a 552.n 184.h $24$ $4.408$ None None \(-4\) \(24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
552.2.n.b 552.n 184.h $24$ $4.408$ None None \(0\) \(-24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
552.2.q.a 552.q 23.c $30$ $4.408$ None None \(0\) \(-3\) \(0\) \(-2\) $\mathrm{SU}(2)[C_{11}]$
552.2.q.b 552.q 23.c $30$ $4.408$ None None \(0\) \(-3\) \(0\) \(0\) $\mathrm{SU}(2)[C_{11}]$
552.2.q.c 552.q 23.c $30$ $4.408$ None None \(0\) \(3\) \(-2\) \(-2\) $\mathrm{SU}(2)[C_{11}]$
552.2.q.d 552.q 23.c $30$ $4.408$ None None \(0\) \(3\) \(2\) \(4\) $\mathrm{SU}(2)[C_{11}]$
552.2.t.a 552.t 184.j $240$ $4.408$ None None \(0\) \(24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
552.2.t.b 552.t 184.j $240$ $4.408$ None None \(4\) \(-24\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
552.2.u.a 552.u 69.g $240$ $4.408$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
552.2.x.a 552.x 552.x $920$ $4.408$ None None \(0\) \(-18\) \(0\) \(0\) $\mathrm{SU}(2)[C_{22}]$
552.2.bb.a 552.bb 184.p $480$ $4.408$ None None \(4\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{22}]$
552.2.bf.a 552.bf 552.af $920$ $4.408$ None None \(0\) \(0\) \(0\) \(-44\) $\mathrm{SU}(2)[C_{22}]$
552.3.c.a 552.c 23.b $24$ $15.041$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
552.3.d.a 552.d 8.d $88$ $15.041$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
552.3.g.a 552.g 3.b $44$ $15.041$ None None \(0\) \(-4\) \(0\) \(24\) $\mathrm{SU}(2)[C_{2}]$
552.3.l.a 552.l 184.e $96$ $15.041$ None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
552.4.a.a 552.a 1.a $1$ $32.569$ \(\Q\) None None \(0\) \(3\) \(-14\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-14q^{5}+2q^{7}+9q^{9}+58q^{11}+\cdots\)
552.4.a.b 552.a 1.a $1$ $32.569$ \(\Q\) None None \(0\) \(3\) \(8\) \(-22\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+8q^{5}-22q^{7}+9q^{9}-4q^{11}+\cdots\)
552.4.a.c 552.a 1.a $2$ $32.569$ \(\Q(\sqrt{2}) \) None None \(0\) \(-6\) \(-8\) \(4\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-4+4\beta )q^{5}+(2+9\beta )q^{7}+\cdots\)
552.4.a.d 552.a 1.a $2$ $32.569$ \(\Q(\sqrt{93}) \) None None \(0\) \(-6\) \(2\) \(10\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(1+\beta )q^{5}+(5-\beta )q^{7}+9q^{9}+\cdots\)
552.4.a.e 552.a 1.a $2$ $32.569$ \(\Q(\sqrt{5}) \) None None \(0\) \(6\) \(-14\) \(10\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-7-\beta )q^{5}+(5+\beta )q^{7}+9q^{9}+\cdots\)
552.4.a.f 552.a 1.a $2$ $32.569$ \(\Q(\sqrt{2}) \) None None \(0\) \(6\) \(-4\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+(-2+\beta )q^{5}+(-4+3\beta )q^{7}+\cdots\)
552.4.a.g 552.a 1.a $4$ $32.569$ 4.4.1623576.1 None None \(0\) \(-12\) \(-14\) \(14\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(-3+\beta _{3})q^{5}+(4-\beta _{1}+\beta _{2}+\cdots)q^{7}+\cdots\)
552.4.a.h 552.a 1.a $4$ $32.569$ 4.4.2239521.1 None None \(0\) \(12\) \(2\) \(50\) $+$ $\mathrm{SU}(2)$ \(q+3q^{3}+(1+\beta _{3})q^{5}+(12-\beta _{2})q^{7}+\cdots\)
552.4.a.i 552.a 1.a $5$ $32.569$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-15\) \(4\) \(-14\) $-$ $\mathrm{SU}(2)$ \(q-3q^{3}+(1-\beta _{1})q^{5}+(-3-\beta _{2})q^{7}+\cdots\)
552.4.a.j 552.a 1.a $5$ $32.569$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None None \(0\) \(-15\) \(16\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}+(3-\beta _{2})q^{5}-\beta _{3}q^{7}+9q^{9}+\cdots\)
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