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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
440.1.o.a 440.o 440.o $1$ $0.220$ \(\Q\) \(\Q(\sqrt{-110}) \) None \(-1\) \(-1\) \(1\) \(1\) \(q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+q^{7}+\cdots\)
440.1.o.b 440.o 440.o $1$ $0.220$ \(\Q\) \(\Q(\sqrt{-110}) \) None \(-1\) \(1\) \(-1\) \(1\) \(q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots\)
440.1.o.c 440.o 440.o $1$ $0.220$ \(\Q\) \(\Q(\sqrt{-110}) \) None \(1\) \(-1\) \(1\) \(-1\) \(q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-q^{7}+\cdots\)
440.1.o.d 440.o 440.o $1$ $0.220$ \(\Q\) \(\Q(\sqrt{-110}) \) None \(1\) \(1\) \(-1\) \(-1\) \(q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots\)
440.1.o.e 440.o 440.o $4$ $0.220$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots\)
440.1.bh.a 440.bh 440.ah $4$ $0.220$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-10}) \) None \(-1\) \(0\) \(-1\) \(3\) \(q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+(1+\cdots)q^{7}+\cdots\)
440.1.bh.b 440.bh 440.ah $4$ $0.220$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-10}) \) None \(1\) \(0\) \(1\) \(-3\) \(q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+(-1+\cdots)q^{7}+\cdots\)
440.2.a.a 440.a 1.a $1$ $3.513$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{9}-q^{11}-8q^{19}+\cdots\)
440.2.a.b 440.a 1.a $1$ $3.513$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-3q^{9}+q^{11}-4q^{13}+\cdots\)
440.2.a.c 440.a 1.a $1$ $3.513$ \(\Q\) None None \(0\) \(0\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}-3q^{9}-q^{11}+6q^{13}+\cdots\)
440.2.a.d 440.a 1.a $1$ $3.513$ \(\Q\) None None \(0\) \(3\) \(1\) \(1\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+q^{5}+q^{7}+6q^{9}-q^{11}-6q^{13}+\cdots\)
440.2.a.e 440.a 1.a $2$ $3.513$ \(\Q(\sqrt{17}) \) None None \(0\) \(-1\) \(2\) \(-1\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+q^{5}-\beta q^{7}+(1+\beta )q^{9}+q^{11}+\cdots\)
440.2.a.f 440.a 1.a $2$ $3.513$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(-2\) \(3\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(2-\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
440.2.a.g 440.a 1.a $2$ $3.513$ \(\Q(\sqrt{17}) \) None None \(0\) \(1\) \(-2\) \(5\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+(2+\beta )q^{7}+(1+\beta )q^{9}+\cdots\)
440.2.b.a 440.b 5.b $2$ $3.513$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(-1+i)q^{5}+iq^{7}-q^{9}+\cdots\)
440.2.b.b 440.b 5.b $2$ $3.513$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(1-i)q^{5}-2iq^{7}-q^{9}+q^{11}+\cdots\)
440.2.b.c 440.b 5.b $2$ $3.513$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+(2+i)q^{5}+iq^{7}+2q^{9}-q^{11}+\cdots\)
440.2.b.d 440.b 5.b $8$ $3.513$ 8.0.\(\cdots\).2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-\beta _{3}-\beta _{4})q^{7}+\cdots\)
440.2.c.a 440.c 440.c $4$ $3.513$ \(\Q(\sqrt{-2}, \sqrt{5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}-2q^{4}+\beta _{3}q^{5}-2\beta _{1}q^{7}+\cdots\)
440.2.c.b 440.c 440.c $8$ $3.513$ 8.0.\(\cdots\).19 \(\Q(\sqrt{-55}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{2}-\beta _{5})q^{5}+\cdots\)
440.2.c.c 440.c 440.c $56$ $3.513$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
440.2.g.a 440.g 8.b $4$ $3.513$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{3}q^{2}+(-\zeta_{8}+\zeta_{8}^{2})q^{3}+2q^{4}+\cdots\)
440.2.g.b 440.g 8.b $12$ $3.513$ 12.0.\(\cdots\).1 None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{9}q^{2}+(\beta _{1}+\beta _{3})q^{3}-\beta _{5}q^{4}-\beta _{8}q^{5}+\cdots\)
440.2.g.c 440.g 8.b $24$ $3.513$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
440.2.l.a 440.l 40.f $2$ $3.513$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-4\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{2}-2q^{3}-2iq^{4}+(-1+\cdots)q^{5}+\cdots\)
440.2.l.b 440.l 40.f $2$ $3.513$ \(\Q(\sqrt{-1}) \) None None \(2\) \(4\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{2}+2q^{3}+2iq^{4}+(1+2i)q^{5}+\cdots\)
440.2.l.c 440.l 40.f $56$ $3.513$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
440.2.p.a 440.p 88.g $48$ $3.513$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$
440.2.r.a 440.r 40.k $2$ $3.513$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(-4\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1+i)q^{2}+(-1+i)q^{3}-2iq^{4}+\cdots\)
440.2.r.b 440.r 40.k $2$ $3.513$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots\)
440.2.r.c 440.r 40.k $2$ $3.513$ \(\Q(\sqrt{-1}) \) None None \(-2\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-i)q^{2}+(-1+i)q^{3}+2iq^{4}+\cdots\)
440.2.r.d 440.r 40.k $2$ $3.513$ \(\Q(\sqrt{-1}) \) None None \(2\) \(-2\) \(4\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1-i)q^{2}+(-1+i)q^{3}-2iq^{4}+\cdots\)
440.2.r.e 440.r 40.k $4$ $3.513$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}+\zeta_{8}^{3})q^{3}+\cdots\)
440.2.r.f 440.r 40.k $4$ $3.513$ \(\Q(\zeta_{8})\) None None \(0\) \(-4\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+(-1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}+\cdots\)
440.2.r.g 440.r 40.k $48$ $3.513$ None None \(0\) \(12\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
440.2.r.h 440.r 40.k $56$ $3.513$ None None \(4\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
440.2.t.a 440.t 440.t $4$ $3.513$ \(\Q(i, \sqrt{10})\) None None \(-4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-1-\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}+\cdots\)
440.2.t.b 440.t 440.t $4$ $3.513$ \(\Q(i, \sqrt{10})\) None None \(4\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\beta _{2})q^{2}+\beta _{1}q^{3}+2\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
440.2.t.c 440.t 440.t $128$ $3.513$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
440.2.v.a 440.v 55.e $4$ $3.513$ \(\Q(\zeta_{8})\) None None \(0\) \(4\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(1+\zeta_{8})q^{3}+(-2-\zeta_{8})q^{5}+(2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
440.2.v.b 440.v 55.e $32$ $3.513$ None None \(0\) \(-4\) \(8\) \(0\) $\mathrm{SU}(2)[C_{4}]$
440.2.y.a 440.y 11.c $8$ $3.513$ 8.0.13140625.1 None None \(0\) \(1\) \(-2\) \(1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}-\beta _{5})q^{3}+\beta _{7}q^{5}+(-1-\beta _{2}+\cdots)q^{7}+\cdots\)
440.2.y.b 440.y 11.c $12$ $3.513$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-1\) \(3\) \(-8\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{1}+\beta _{4})q^{3}+(1-\beta _{6}+\beta _{7}-\beta _{8}+\cdots)q^{5}+\cdots\)
440.2.y.c 440.y 11.c $12$ $3.513$ \(\mathbb{Q}[x]/(x^{12} - \cdots)\) None None \(0\) \(-1\) \(3\) \(-1\) $\mathrm{SU}(2)[C_{5}]$ \(q+(\beta _{3}+\beta _{8})q^{3}-\beta _{6}q^{5}+(1+\beta _{2}+\beta _{5}+\cdots)q^{7}+\cdots\)
440.2.y.d 440.y 11.c $16$ $3.513$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(-3\) \(-4\) \(8\) $\mathrm{SU}(2)[C_{5}]$ \(q-\beta _{1}q^{3}+(-1+\beta _{4}-\beta _{10}+\beta _{12}+\cdots)q^{5}+\cdots\)
440.2.z.a 440.z 88.k $192$ $3.513$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
440.2.bd.a 440.bd 440.ad $272$ $3.513$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{10}]$
440.2.bi.a 440.bi 88.o $8$ $3.513$ \(\Q(\zeta_{20})\) None None \(-2\) \(0\) \(0\) \(-6\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
440.2.bi.b 440.bi 88.o $8$ $3.513$ \(\Q(\zeta_{20})\) None None \(-2\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{10}]$ \(q+(-1+\zeta_{20}^{2}-\zeta_{20}^{3}-\zeta_{20}^{4}+\zeta_{20}^{6}+\cdots)q^{2}+\cdots\)
440.2.bi.c 440.bi 88.o $176$ $3.513$ None None \(8\) \(0\) \(0\) \(18\) $\mathrm{SU}(2)[C_{10}]$
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