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Label Char Prim Dim $A$ Field CM RM Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1600.1.b.a 1600.b 4.b $1$ $0.799$ \(\Q\) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q+q^{9}+2q^{29}-2q^{41}+q^{49}+2q^{61}+\cdots\)
1600.1.m.a 1600.m 40.i $2$ $0.799$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}-iq^{11}-q^{19}+q^{41}-iq^{49}+\cdots\)
1600.1.m.b 1600.m 40.i $2$ $0.799$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \), \(\Q(\sqrt{-10}) \) \(\Q(\sqrt{5}) \) \(0\) \(0\) \(0\) \(0\) \(q-iq^{9}+iq^{11}+q^{19}+q^{41}-iq^{49}+\cdots\)
1600.1.m.c 1600.m 40.i $4$ $0.799$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+2\beta _{2}q^{9}-\beta _{2}q^{11}-\beta _{1}q^{17}+\cdots\)
1600.1.m.d 1600.m 40.i $4$ $0.799$ \(\Q(i, \sqrt{6})\) \(\Q(\sqrt{-2}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{3}+2\beta _{2}q^{9}+\beta _{2}q^{11}+\beta _{1}q^{17}+\cdots\)
1600.1.p.a 1600.p 5.c $2$ $0.799$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(-2\) \(q+(-1+i)q^{3}+(-1-i)q^{7}-iq^{9}+\cdots\)
1600.1.p.b 1600.p 5.c $2$ $0.799$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+iq^{9}+(-1+i)q^{13}+(1+i)q^{17}+\cdots\)
1600.1.p.c 1600.p 5.c $2$ $0.799$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(2\) \(q+(1-i)q^{3}+(1+i)q^{7}-iq^{9}+q^{21}+\cdots\)
1600.1.bd.a 1600.bd 200.n $8$ $0.799$ \(\Q(\zeta_{20})\) None None \(0\) \(-6\) \(0\) \(0\) \(q+(-1+\zeta_{20}^{6})q^{3}-\zeta_{20}^{3}q^{5}+\zeta_{20}^{5}q^{7}+\cdots\)
1600.1.bd.b 1600.bd 200.n $8$ $0.799$ \(\Q(\zeta_{20})\) None None \(0\) \(6\) \(0\) \(0\) \(q+(1-\zeta_{20}^{6})q^{3}-\zeta_{20}^{3}q^{5}-\zeta_{20}^{5}q^{7}+\cdots\)
1600.1.bf.a 1600.bf 100.h $4$ $0.799$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(-1\) \(0\) \(q-\zeta_{10}q^{5}+\zeta_{10}^{3}q^{9}+(\zeta_{10}^{2}-\zeta_{10}^{4}+\cdots)q^{13}+\cdots\)
1600.1.bh.a 1600.bh 100.j $4$ $0.799$ \(\Q(\zeta_{10})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(1\) \(0\) \(q+\zeta_{10}^{3}q^{5}+\zeta_{10}^{4}q^{9}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{13}+\cdots\)
1600.1.bh.b 1600.bh 100.j $8$ $0.799$ \(\Q(\zeta_{20})\) None None \(0\) \(0\) \(2\) \(0\) \(q-\zeta_{20}^{9}q^{3}-\zeta_{20}^{8}q^{5}+(-\zeta_{20}^{3}-\zeta_{20}^{7}+\cdots)q^{7}+\cdots\)
1600.1.bw.a 1600.bw 25.f $8$ $0.799$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{20}^{3}q^{5}-\zeta_{20}^{9}q^{9}+(\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{13}+\cdots\)
1600.2.a.a 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{7}+6q^{9}-q^{11}+4q^{13}+\cdots\)
1600.2.a.b 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(-3\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-3q^{3}-2q^{7}+6q^{9}+q^{11}-4q^{13}+\cdots\)
1600.2.a.c 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(-2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}-2q^{7}+q^{9}+2q^{13}+6q^{17}+\cdots\)
1600.2.a.d 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(-2\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots\)
1600.2.a.e 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(-2\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
1600.2.a.f 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(-2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-2q^{3}+2q^{7}+q^{9}+4q^{11}-4q^{13}+\cdots\)
1600.2.a.g 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}-2q^{9}-5q^{11}+5q^{17}+\cdots\)
1600.2.a.h 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(-1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q-q^{3}-2q^{7}-2q^{9}+5q^{11}-5q^{17}+\cdots\)
1600.2.a.i 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}-2q^{9}-3q^{11}-4q^{13}+\cdots\)
1600.2.a.j 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(-1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q-q^{3}+2q^{7}-2q^{9}+3q^{11}+4q^{13}+\cdots\)
1600.2.a.k 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(0\) \(0\) \(-4\) $-$ $\mathrm{SU}(2)$ \(q-4q^{7}-3q^{9}+4q^{11}-2q^{13}-2q^{17}+\cdots\)
1600.2.a.l 1600.a 1.a $1$ $12.776$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-3q^{9}-4q^{13}+8q^{17}-10q^{29}+\cdots\)
1600.2.a.m 1600.a 1.a $1$ $12.776$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q-3q^{9}+4q^{13}-8q^{17}-10q^{29}+\cdots\)
1600.2.a.n 1600.a 1.a $1$ $12.776$ \(\Q\) \(\Q(\sqrt{-1}) \) None \(0\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q-3q^{9}+6q^{13}-2q^{17}+10q^{29}+\cdots\)
1600.2.a.o 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(0\) \(0\) \(4\) $+$ $\mathrm{SU}(2)$ \(q+4q^{7}-3q^{9}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
1600.2.a.p 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}-2q^{9}-3q^{11}+4q^{13}+\cdots\)
1600.2.a.q 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(1\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}-2q^{7}-2q^{9}+3q^{11}-4q^{13}+\cdots\)
1600.2.a.r 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(1\) \(0\) \(2\) $+$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}-2q^{9}-5q^{11}-5q^{17}+\cdots\)
1600.2.a.s 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(1\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+q^{3}+2q^{7}-2q^{9}+5q^{11}+5q^{17}+\cdots\)
1600.2.a.t 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
1600.2.a.u 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(2\) \(0\) \(-2\) $+$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots\)
1600.2.a.v 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(2\) \(0\) \(-2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}-2q^{7}+q^{9}+4q^{11}+4q^{13}+\cdots\)
1600.2.a.w 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(2\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+2q^{3}+2q^{7}+q^{9}+2q^{13}+6q^{17}+\cdots\)
1600.2.a.x 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(3\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{7}+6q^{9}-q^{11}-4q^{13}+\cdots\)
1600.2.a.y 1600.a 1.a $1$ $12.776$ \(\Q\) None None \(0\) \(3\) \(0\) \(2\) $-$ $\mathrm{SU}(2)$ \(q+3q^{3}+2q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots\)
1600.2.a.z 1600.a 1.a $2$ $12.776$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(-2\) \(0\) \(6\) $-$ $N(\mathrm{U}(1))$ \(q+(-1-\beta )q^{3}+(3-\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
1600.2.a.ba 1600.a 1.a $2$ $12.776$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+2\beta q^{7}+2q^{9}-\beta q^{11}-4q^{13}+\cdots\)
1600.2.a.bb 1600.a 1.a $2$ $12.776$ \(\Q(\sqrt{5}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q-\beta q^{3}+2\beta q^{7}+2q^{9}+\beta q^{11}+4q^{13}+\cdots\)
1600.2.a.bc 1600.a 1.a $2$ $12.776$ \(\Q(\sqrt{2}) \) None None \(0\) \(0\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{7}+5q^{9}+2\beta q^{11}-2q^{13}+\cdots\)
1600.2.a.bd 1600.a 1.a $2$ $12.776$ \(\Q(\sqrt{5}) \) \(\Q(\sqrt{-5}) \) None \(0\) \(2\) \(0\) \(-6\) $-$ $N(\mathrm{U}(1))$ \(q+(1+\beta )q^{3}+(-3+\beta )q^{7}+(3+2\beta )q^{9}+\cdots\)
1600.2.c.a 1600.c 5.b $2$ $12.776$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-2iq^{7}-6q^{9}-q^{11}-4iq^{13}+\cdots\)
1600.2.c.b 1600.c 5.b $2$ $12.776$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+3iq^{3}-2iq^{7}-6q^{9}+q^{11}+4iq^{13}+\cdots\)
1600.2.c.c 1600.c 5.b $2$ $12.776$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}-4q^{11}-3iq^{13}+\cdots\)
1600.2.c.d 1600.c 5.b $2$ $12.776$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{7}-q^{9}-iq^{13}+3iq^{17}+\cdots\)
1600.2.c.e 1600.c 5.b $2$ $12.776$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}-iq^{7}-q^{9}+iq^{13}-3iq^{17}+\cdots\)
1600.2.c.f 1600.c 5.b $2$ $12.776$ \(\Q(\sqrt{-1}) \) None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+iq^{3}+iq^{7}-q^{9}+4q^{11}+3iq^{13}+\cdots\)
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