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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
720.1.j.a 720.j 20.d $1$ $0.359$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(1\) \(0\) \(q+q^{5}+q^{25}-2q^{29}+2q^{41}-q^{49}+\cdots\)
720.1.r.a 720.r 80.k $4$ $0.359$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}-\zeta_{8}^{3}q^{8}+\cdots\)
720.1.bk.a 720.bk 60.l $4$ $0.359$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{5}+(1-\zeta_{8}^{2})q^{13}-\zeta_{8}^{3}q^{17}+\cdots\)
720.1.bu.a 720.bu 180.p $4$ $0.359$ \(\Q(\zeta_{12})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{5}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{7}+\cdots\)
720.2.a.a 720.a 1.a $1$ $5.749$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}-2q^{11}+4q^{13}-2q^{17}+\cdots\)
720.2.a.b 720.a 1.a $1$ $5.749$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+6q^{11}-4q^{13}+6q^{17}+\cdots\)
720.2.a.c 720.a 1.a $1$ $5.749$ \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{11}-2q^{13}-2q^{17}-4q^{19}+\cdots\)
720.2.a.d 720.a 1.a $1$ $5.749$ \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{11}+6q^{13}+6q^{17}+4q^{19}+\cdots\)
720.2.a.e 720.a 1.a $1$ $5.749$ \(\Q\) None None \(0\) \(0\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
720.2.a.f 720.a 1.a $1$ $5.749$ \(\Q\) None None \(0\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-6q^{13}+2q^{17}-4q^{19}+\cdots\)
720.2.a.g 720.a 1.a $1$ $5.749$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-6q^{11}-4q^{13}-6q^{17}+\cdots\)
720.2.a.h 720.a 1.a $1$ $5.749$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+2q^{13}+6q^{17}+4q^{19}+\cdots\)
720.2.a.i 720.a 1.a $1$ $5.749$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+2q^{11}+4q^{13}+2q^{17}+\cdots\)
720.2.a.j 720.a 1.a $1$ $5.749$ \(\Q\) None None \(0\) \(0\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}+2q^{13}-6q^{17}+4q^{19}+\cdots\)
720.2.f.a 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+i)q^{5}+4iq^{7}-4q^{11}-4iq^{13}+\cdots\)
720.2.f.b 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-2+i)q^{5}-2iq^{7}+2q^{11}+2iq^{13}+\cdots\)
720.2.f.c 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{5}-2iq^{7}-4q^{11}-2iq^{17}+\cdots\)
720.2.f.d 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{5}+2\beta q^{17}+4q^{19}+4\beta q^{23}+\cdots\)
720.2.f.e 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(1+i)q^{5}+iq^{7}-4q^{11}+2iq^{13}+\cdots\)
720.2.f.f 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+i)q^{5}-2iq^{7}+2q^{11}-6iq^{13}+\cdots\)
720.2.f.g 720.f 5.b $2$ $5.749$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+i)q^{5}-4iq^{7}+4q^{11}+4iq^{13}+\cdots\)
720.2.h.a 720.h 12.b $8$ $5.749$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}q^{5}+\zeta_{24}^{5}q^{7}+(\zeta_{24}^{2}-\zeta_{24}^{4}+\cdots)q^{11}+\cdots\)
720.2.o.a 720.o 60.h $4$ $5.749$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\zeta_{8}^{3}q^{5}+2\zeta_{8}q^{13}+(\zeta_{8}^{2}-2\zeta_{8}^{3})q^{17}+\cdots\)
720.2.o.b 720.o 60.h $8$ $5.749$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\zeta_{24}-\zeta_{24}^{2})q^{5}-\zeta_{24}^{6}q^{7}+\zeta_{24}^{3}q^{11}+\cdots\)
720.2.q.a 720.q 9.c $2$ $5.749$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(-1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
720.2.q.b 720.q 9.c $2$ $5.749$ \(\Q(\sqrt{-3}) \) None None \(0\) \(-3\) \(1\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-1+\zeta_{6})q^{7}+\cdots\)
720.2.q.c 720.q 9.c $2$ $5.749$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(-1\) \(-4\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\zeta_{6})q^{3}-\zeta_{6}q^{5}+(-4+4\zeta_{6})q^{7}+\cdots\)
720.2.q.d 720.q 9.c $2$ $5.749$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(1\) \(-3\) $\mathrm{SU}(2)[C_{3}]$ \(q+(2-\zeta_{6})q^{3}+\zeta_{6}q^{5}+(-3+3\zeta_{6})q^{7}+\cdots\)
720.2.q.e 720.q 9.c $2$ $5.749$ \(\Q(\sqrt{-3}) \) None None \(0\) \(3\) \(1\) \(0\) $\mathrm{SU}(2)[C_{3}]$ \(q+(1+\zeta_{6})q^{3}+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+(-5+\cdots)q^{11}+\cdots\)
720.2.q.f 720.q 9.c $4$ $5.749$ \(\Q(\sqrt{-3}, \sqrt{-11})\) None None \(0\) \(-2\) \(2\) \(1\) $\mathrm{SU}(2)[C_{3}]$ \(q+(-\beta _{1}+\beta _{3})q^{3}+(1-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
720.2.q.g 720.q 9.c $4$ $5.749$ \(\Q(\sqrt{-2}, \sqrt{-3})\) None None \(0\) \(-2\) \(2\) \(2\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{1}-\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+(1+\beta _{1}+\cdots)q^{7}+\cdots\)
720.2.q.h 720.q 9.c $4$ $5.749$ \(\Q(\zeta_{12})\) None None \(0\) \(0\) \(2\) \(4\) $\mathrm{SU}(2)[C_{3}]$ \(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+(2-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots\)
720.2.q.i 720.q 9.c $6$ $5.749$ 6.0.954288.1 None None \(0\) \(-1\) \(-3\) \(5\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{3}+\beta _{3}q^{5}+(2-\beta _{1}+\beta _{2}+2\beta _{3}+\cdots)q^{7}+\cdots\)
720.2.q.j 720.q 9.c $6$ $5.749$ 6.0.954288.1 None None \(0\) \(1\) \(-3\) \(-5\) $\mathrm{SU}(2)[C_{3}]$ \(q+(\beta _{2}-\beta _{5})q^{3}+\beta _{3}q^{5}+(-2-2\beta _{3}+\cdots)q^{7}+\cdots\)
720.2.q.k 720.q 9.c $6$ $5.749$ 6.0.954288.1 None None \(0\) \(1\) \(3\) \(3\) $\mathrm{SU}(2)[C_{3}]$ \(q-\beta _{4}q^{3}+(1+\beta _{2})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
720.2.q.l 720.q 9.c $8$ $5.749$ 8.0.856615824.2 None None \(0\) \(0\) \(-4\) \(-1\) $\mathrm{SU}(2)[C_{3}]$ \(q+\beta _{4}q^{3}-\beta _{1}q^{5}+(\beta _{2}-\beta _{4})q^{7}+(-\beta _{1}+\cdots)q^{9}+\cdots\)
720.2.t.a 720.t 16.e $4$ $5.749$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+\zeta_{8}q^{5}+\cdots\)
720.2.t.b 720.t 16.e $8$ $5.749$ 8.0.18939904.2 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta _{4}-\beta _{5})q^{2}+(-1+\beta _{2}-\beta _{3}-\beta _{6}+\cdots)q^{4}+\cdots\)
720.2.t.c 720.t 16.e $16$ $5.749$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta _{9}q^{2}+(\beta _{1}-\beta _{5}-\beta _{14})q^{4}-\beta _{4}q^{5}+\cdots\)
720.2.t.d 720.t 16.e $20$ $5.749$ \(\mathbb{Q}[x]/(x^{20} - \cdots)\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{3}q^{5}+(-1+\beta _{2}+\cdots)q^{7}+\cdots\)
720.2.t.e 720.t 16.e $32$ $5.749$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
720.2.u.a 720.u 240.t $96$ $5.749$ None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$
720.2.w.a 720.w 15.e $4$ $5.749$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-2-2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
720.2.w.b 720.w 15.e $4$ $5.749$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-2+2\zeta_{8}^{2}+\cdots)q^{7}+\cdots\)
720.2.w.c 720.w 15.e $4$ $5.749$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(-4\zeta_{8}-4\zeta_{8}^{3})q^{11}+\cdots\)
720.2.w.d 720.w 15.e $4$ $5.749$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(2+2\zeta_{8}^{2})q^{7}+(2\zeta_{8}+\cdots)q^{11}+\cdots\)
720.2.w.e 720.w 15.e $8$ $5.749$ 8.0.40960000.1 None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{4}]$ \(q-\beta _{7}q^{5}+(1+\beta _{2}+\beta _{5})q^{7}+(\beta _{1}+\beta _{6}+\cdots)q^{11}+\cdots\)
720.2.x.a 720.x 20.e $2$ $5.749$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-2-i)q^{5}+(-5+5i)q^{13}+(5+\cdots)q^{17}+\cdots\)
720.2.x.b 720.x 20.e $2$ $5.749$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-1-2i)q^{5}+(1-i)q^{13}+(-5+\cdots)q^{17}+\cdots\)
720.2.x.c 720.x 20.e $2$ $5.749$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(1+2i)q^{5}+(1-i)q^{13}+(5+5i)q^{17}+\cdots\)
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