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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1280.1.e.a 1280.e 40.e $2$ $0.639$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}+q^{9}-q^{25}-iq^{29}+q^{41}+\cdots\)
1280.1.h.a 1280.h 20.d $2$ $0.639$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-\beta q^{3}-q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots\)
1280.1.h.b 1280.h 20.d $2$ $0.639$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{10}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{5}-q^{9}-iq^{13}-q^{25}-iq^{37}+\cdots\)
1280.1.h.c 1280.h 20.d $2$ $0.639$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(2\) \(0\) \(q-\beta q^{3}+q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots\)
1280.1.m.a 1280.m 40.i $2$ $0.639$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots\)
1280.1.m.b 1280.m 40.i $2$ $0.639$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+q^{5}+iq^{9}+(1-i)q^{13}+(-1+i+\cdots)q^{17}+\cdots\)
1280.1.p.a 1280.p 5.c $2$ $0.639$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-2\) \(0\) \(q-q^{5}-iq^{9}+(1+i)q^{13}+(1-i)q^{17}+\cdots\)
1280.1.p.b 1280.p 5.c $2$ $0.639$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(2\) \(0\) \(q+q^{5}-iq^{9}+(-1-i)q^{13}+(1-i+\cdots)q^{17}+\cdots\)
1280.2.a.a 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}+(1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.b 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(-2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}-q^{5}+(3-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.c 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}+(-3+\beta )q^{7}+\cdots\)
1280.2.a.d 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None None \(0\) \(-2\) \(2\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta )q^{3}+q^{5}+(-1-\beta )q^{7}+\cdots\)
1280.2.a.e 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-\beta q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1280.2.a.f 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}-3\beta q^{7}-q^{9}+4\beta q^{11}+\cdots\)
1280.2.a.g 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+3\beta q^{7}-q^{9}+2\beta q^{11}+\cdots\)
1280.2.a.h 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{10}) \) None None \(0\) \(0\) \(-2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-q^{5}+\beta q^{7}+7q^{9}-6q^{13}+\cdots\)
1280.2.a.i 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(2\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-3\beta q^{7}-q^{9}+2\beta q^{11}+\cdots\)
1280.2.a.j 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+3\beta q^{7}-q^{9}+4\beta q^{11}+\cdots\)
1280.2.a.k 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}+\beta q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1280.2.a.l 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{10}) \) None None \(0\) \(0\) \(2\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+q^{5}-\beta q^{7}+7q^{9}+6q^{13}+\cdots\)
1280.2.a.m 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(-6\) $+$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+(-3-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.n 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(-2\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}-q^{5}+(-1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.o 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+(1-\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
1280.2.a.p 1280.a 1.a $2$ $10.221$ \(\Q(\sqrt{3}) \) None None \(0\) \(2\) \(2\) \(6\) $-$ $\mathrm{SU}(2)$ \(q+(1+\beta )q^{3}+q^{5}+(3+\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
1280.2.c.a 1280.c 5.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-4\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(-2+i)q^{5}+3q^{9}-6iq^{13}+8iq^{17}+\cdots\)
1280.2.c.b 1280.c 5.b $2$ $10.221$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{5}-2\beta q^{7}+3q^{9}-2q^{11}-2\beta q^{13}+\cdots\)
1280.2.c.c 1280.c 5.b $2$ $10.221$ \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{5}+2\beta q^{7}+3q^{9}+2q^{11}-2\beta q^{13}+\cdots\)
1280.2.c.d 1280.c 5.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(4\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+(2+i)q^{5}+3q^{9}-6iq^{13}-8iq^{17}+\cdots\)
1280.2.c.e 1280.c 5.b $4$ $10.221$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(-1-\beta _{1})q^{5}+\beta _{2}q^{7}-3q^{9}+\cdots\)
1280.2.c.f 1280.c 5.b $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{3}+\beta _{3}q^{5}+3\beta _{1}q^{7}-7q^{9}+\cdots\)
1280.2.c.g 1280.c 5.b $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
1280.2.c.h 1280.c 5.b $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}-3q^{9}+\cdots\)
1280.2.c.i 1280.c 5.b $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
1280.2.c.j 1280.c 5.b $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{5})\) \(\Q(\sqrt{-5}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+q^{9}+\beta _{2}q^{15}+\cdots\)
1280.2.c.k 1280.c 5.b $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{3})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+q^{9}+\cdots\)
1280.2.c.l 1280.c 5.b $4$ $10.221$ \(\Q(\sqrt{-2}, \sqrt{-5})\) \(\Q(\sqrt{-10}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{5}-\beta _{1}q^{7}+3q^{9}-\beta _{3}q^{11}+\cdots\)
1280.2.c.m 1280.c 5.b $4$ $10.221$ \(\Q(i, \sqrt{6})\) None None \(0\) \(0\) \(4\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}+(1+\beta _{1})q^{5}-\beta _{2}q^{7}-3q^{9}+\cdots\)
1280.2.d.a 1280.d 8.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}-4q^{7}+3q^{9}-4iq^{11}+2iq^{13}+\cdots\)
1280.2.d.b 1280.d 8.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+iq^{5}-2q^{7}-q^{9}-4iq^{11}+\cdots\)
1280.2.d.c 1280.d 8.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-iq^{5}-2q^{7}-q^{9}-2iq^{13}+\cdots\)
1280.2.d.d 1280.d 8.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q-iq^{5}-2q^{7}+3q^{9}-6iq^{11}+2iq^{13}+\cdots\)
1280.2.d.e 1280.d 8.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+iq^{5}-q^{9}-2iq^{11}+2iq^{13}+\cdots\)
1280.2.d.f 1280.d 8.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-iq^{5}-q^{9}-2iq^{11}-2iq^{13}+\cdots\)
1280.2.d.g 1280.d 8.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}+iq^{5}+2q^{7}-q^{9}+2iq^{13}+\cdots\)
1280.2.d.h 1280.d 8.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+2iq^{3}-iq^{5}+2q^{7}-q^{9}-4iq^{11}+\cdots\)
1280.2.d.i 1280.d 8.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+2q^{7}+3q^{9}-6iq^{11}-2iq^{13}+\cdots\)
1280.2.d.j 1280.d 8.b $2$ $10.221$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{5}+4q^{7}+3q^{9}+4iq^{11}+2iq^{13}+\cdots\)
1280.2.d.k 1280.d 8.b $4$ $10.221$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{3}-\beta _{1}q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
1280.2.d.l 1280.d 8.b $4$ $10.221$ \(\Q(\zeta_{8})\) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}-5q^{9}+\cdots\)
1280.2.d.m 1280.d 8.b $4$ $10.221$ \(\Q(i, \sqrt{5})\) None None \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}+\cdots\)
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