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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1440.1.c.a 1440.c 15.d $4$ $0.719$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{8}q^{5}-\zeta_{8}^{2}q^{13}+(-\zeta_{8}+\zeta_{8}^{3}+\cdots)q^{17}+\cdots\)
1440.1.p.a 1440.p 40.e $1$ $0.719$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(-1\) \(0\) \(q-q^{5}+2q^{19}+2q^{23}+q^{25}-2q^{47}+\cdots\)
1440.1.p.b 1440.p 40.e $1$ $0.719$ \(\Q\) \(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{6}) \) \(0\) \(0\) \(1\) \(0\) \(q+q^{5}+2q^{19}-2q^{23}+q^{25}+2q^{47}+\cdots\)
1440.1.y.a 1440.y 40.i $4$ $0.719$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(4\) \(q+\zeta_{8}^{3}q^{5}+(1-\zeta_{8}^{2})q^{7}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)
1440.1.bh.a 1440.bh 5.c $2$ $0.719$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}+(1+i)q^{13}+(1-i)q^{17}+q^{25}+\cdots\)
1440.1.bh.b 1440.bh 5.c $2$ $0.719$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}+(-1-i)q^{13}+(1-i)q^{17}+\cdots\)
1440.1.bh.c 1440.bh 5.c $2$ $0.719$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+q^{5}+(1+i)q^{13}+(-1+i)q^{17}+\cdots\)
1440.1.cd.a 1440.cd 45.h $8$ $0.719$ \(\Q(\zeta_{24})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{24}^{7}q^{3}-\zeta_{24}^{10}q^{5}+(-\zeta_{24}-\zeta_{24}^{3}+\cdots)q^{7}+\cdots\)
1440.1.cm.a 1440.cm 160.y $8$ $0.719$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{3}q^{2}+\zeta_{16}^{6}q^{4}-\zeta_{16}^{5}q^{5}+\cdots\)
1440.2.a.a 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-4q^{7}-2q^{13}+6q^{17}+4q^{23}+\cdots\)
1440.2.a.b 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(-1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}-2q^{7}+2q^{11}+2q^{17}-4q^{19}+\cdots\)
1440.2.a.c 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{13}-6q^{17}-4q^{19}-8q^{23}+\cdots\)
1440.2.a.d 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(-1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{13}-6q^{17}+4q^{19}+8q^{23}+\cdots\)
1440.2.a.e 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(-1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+2q^{7}-2q^{11}+2q^{17}+4q^{19}+\cdots\)
1440.2.a.f 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(-1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}+4q^{7}-2q^{13}+6q^{17}-4q^{23}+\cdots\)
1440.2.a.g 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(1\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{7}-4q^{11}+6q^{13}-2q^{17}+\cdots\)
1440.2.a.h 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}-2q^{11}-2q^{17}-4q^{19}+\cdots\)
1440.2.a.i 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(1\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-2q^{7}+4q^{11}-6q^{13}-2q^{17}+\cdots\)
1440.2.a.j 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-4q^{11}+2q^{13}+2q^{17}+8q^{19}+\cdots\)
1440.2.a.k 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(1\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{11}+2q^{13}+2q^{17}-8q^{19}+\cdots\)
1440.2.a.l 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(1\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}-4q^{11}-6q^{13}-2q^{17}+\cdots\)
1440.2.a.m 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(1\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+2q^{7}+2q^{11}-2q^{17}+4q^{19}+\cdots\)
1440.2.a.n 1440.a 1.a $1$ $11.498$ \(\Q\) None None \(0\) \(0\) \(1\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}+4q^{7}+4q^{11}+6q^{13}-2q^{17}+\cdots\)
1440.2.a.o 1440.a 1.a $2$ $11.498$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-q^{5}+\beta q^{7}-2\beta q^{11}-2q^{13}-2q^{17}+\cdots\)
1440.2.a.p 1440.a 1.a $2$ $11.498$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-q^{5}-\beta q^{7}-\beta q^{11}+4q^{13}-2q^{17}+\cdots\)
1440.2.a.q 1440.a 1.a $2$ $11.498$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+q^{5}-\beta q^{7}+\beta q^{11}+4q^{13}+2q^{17}+\cdots\)
1440.2.b.a 1440.b 24.f $2$ $11.498$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{5}+3\beta q^{7}+\beta q^{11}-3\beta q^{13}+2\beta q^{17}+\cdots\)
1440.2.b.b 1440.b 24.f $2$ $11.498$ \(\Q(\sqrt{-2}) \) None None \(0\) \(0\) \(2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{5}+3\beta q^{7}-\beta q^{11}-3\beta q^{13}-2\beta q^{17}+\cdots\)
1440.2.b.c 1440.b 24.f $6$ $11.498$ 6.0.2580992.1 None None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-q^{5}-\beta _{1}q^{7}+(\beta _{1}+\beta _{3})q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots\)
1440.2.b.d 1440.b 24.f $6$ $11.498$ 6.0.2580992.1 None None \(0\) \(0\) \(6\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+q^{5}-\beta _{1}q^{7}+(-\beta _{1}-\beta _{3})q^{11}+(\beta _{1}+\cdots)q^{13}+\cdots\)
1440.2.d.a 1440.d 40.f $4$ $11.498$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-30}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{5}-2\beta _{2}q^{11}-\beta _{3}q^{13}+\beta _{1}q^{17}+\cdots\)
1440.2.d.b 1440.d 40.f $4$ $11.498$ \(\Q(\sqrt{2}, \sqrt{-3})\) \(\Q(\sqrt{-6}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{5}-\beta _{3}q^{7}+(\beta _{1}+\beta _{2})q^{11}+(-1+\cdots)q^{25}+\cdots\)
1440.2.d.c 1440.d 40.f $4$ $11.498$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{1}-\beta _{2})q^{5}-\beta _{3}q^{7}-2\beta _{2}q^{11}+\cdots\)
1440.2.d.d 1440.d 40.f $4$ $11.498$ \(\Q(\sqrt{-3}, \sqrt{5})\) \(\Q(\sqrt{-15}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{1}q^{5}+2\beta _{2}q^{17}-\beta _{3}q^{19}-\beta _{2}q^{23}+\cdots\)
1440.2.d.e 1440.d 40.f $6$ $11.498$ 6.0.839056.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{5}-\beta _{1}q^{7}+(-\beta _{1}-\beta _{5})q^{11}+\cdots\)
1440.2.d.f 1440.d 40.f $6$ $11.498$ 6.0.839056.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{5}-\beta _{1}q^{7}+(\beta _{1}+\beta _{5})q^{11}+(1+\cdots)q^{13}+\cdots\)
1440.2.f.a 1440.f 5.b $2$ $11.498$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-2-i)q^{5}+4iq^{13}-2iq^{17}+\cdots\)
1440.2.f.b 1440.f 5.b $2$ $11.498$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1-i)q^{5}+2iq^{7}-2iq^{13}-8q^{19}+\cdots\)
1440.2.f.c 1440.f 5.b $2$ $11.498$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-1-i)q^{5}+2iq^{13}+4iq^{17}+\cdots\)
1440.2.f.d 1440.f 5.b $2$ $11.498$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(-2\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-1+i)q^{5}+2iq^{7}+2iq^{13}+8q^{19}+\cdots\)
1440.2.f.e 1440.f 5.b $2$ $11.498$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2-i)q^{5}+2iq^{7}-6q^{11}-2iq^{13}+\cdots\)
1440.2.f.f 1440.f 5.b $2$ $11.498$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(2+i)q^{5}+4iq^{13}+2iq^{17}+(3+\cdots)q^{25}+\cdots\)
1440.2.f.g 1440.f 5.b $2$ $11.498$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+i)q^{5}+2iq^{7}+6q^{11}+2iq^{13}+\cdots\)
1440.2.f.h 1440.f 5.b $4$ $11.498$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{5}+\beta _{2}q^{7}-\beta _{3}q^{11}+2\beta _{1}q^{13}+\cdots\)
1440.2.f.i 1440.f 5.b $4$ $11.498$ \(\Q(i, \sqrt{5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{3}q^{5}-\beta _{1}q^{7}+(-\beta _{1}+2\beta _{2})q^{23}+\cdots\)
1440.2.f.j 1440.f 5.b $8$ $11.498$ \(\Q(\zeta_{24})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{24}^{4}q^{5}+\zeta_{24}^{5}q^{7}-\zeta_{24}^{6}q^{11}+\cdots\)
1440.2.h.a 1440.h 12.b $4$ $11.498$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+(-4-\zeta_{8}^{3})q^{11}+\cdots\)
1440.2.h.b 1440.h 12.b $4$ $11.498$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}-\zeta_{8}^{3}q^{11}+\cdots\)
1440.2.h.c 1440.h 12.b $4$ $11.498$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+\zeta_{8}^{3}q^{11}+\cdots\)
1440.2.h.d 1440.h 12.b $4$ $11.498$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\zeta_{8}q^{5}+(2\zeta_{8}-\zeta_{8}^{2})q^{7}+(4+\zeta_{8}^{3})q^{11}+\cdots\)
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