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Label Char Prim Dim $A$ Field CM RM Minimal twist Traces Fricke sign Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
1024.1.c.a 1024.c 4.b $2$ $0.511$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None 512.1.f.a \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}+q^{9}+\beta q^{13}+q^{25}+\beta q^{29}+\cdots\)
1024.1.d.a 1024.d 8.d $2$ $0.511$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None 512.1.f.a \(0\) \(0\) \(0\) \(0\) \(q-\beta q^{5}-q^{9}-\beta q^{13}-q^{25}-\beta q^{29}+\cdots\)
1024.1.f.a 1024.f 16.f $2$ $0.511$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None 512.1.c.a \(0\) \(-2\) \(0\) \(0\) \(q+(-i-1)q^{3}+i q^{9}+(-i+1)q^{11}+\cdots\)
1024.1.f.b 1024.f 16.f $2$ $0.511$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{2}) \) 128.1.d.a \(0\) \(0\) \(0\) \(0\) \(q-i q^{9}+2 q^{17}-i q^{25}+2 i q^{41}+\cdots\)
1024.1.f.c 1024.f 16.f $2$ $0.511$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None 512.1.c.a \(0\) \(2\) \(0\) \(0\) \(q+(i+1)q^{3}+i q^{9}+(i-1)q^{11}+\cdots\)
1024.2.a.a 1024.a 1.a $2$ $8.177$ \(\Q(\sqrt{2}) \) None None 512.2.e.a \(0\) \(0\) \(0\) \(-8\) $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}+\beta q^{5}-4q^{7}+5q^{9}+2\beta q^{11}+\cdots\)
1024.2.a.b 1024.a 1.a $2$ $8.177$ \(\Q(\sqrt{2}) \) None None 16.2.e.a \(0\) \(0\) \(0\) \(-4\) $+$ $\mathrm{SU}(2)$ \(q+\beta q^{3}-\beta q^{5}-2q^{7}-q^{9}-\beta q^{11}+\cdots\)
1024.2.a.c 1024.a 1.a $2$ $8.177$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None 512.2.e.d \(0\) \(0\) \(0\) \(0\) $+$ $N(\mathrm{U}(1))$ \(q+\beta q^{5}-3q^{9}-5\beta q^{13}-8q^{17}-3q^{25}+\cdots\)
1024.2.a.d 1024.a 1.a $2$ $8.177$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None 512.2.e.c \(0\) \(0\) \(0\) \(0\) $-$ $N(\mathrm{U}(1))$ \(q+3\beta q^{5}-3q^{9}+\beta q^{13}+8q^{17}+13q^{25}+\cdots\)
1024.2.a.e 1024.a 1.a $2$ $8.177$ \(\Q(\sqrt{2}) \) None None 16.2.e.a \(0\) \(0\) \(0\) \(4\) $-$ $\mathrm{SU}(2)$ \(q+\beta q^{3}+\beta q^{5}+2q^{7}-q^{9}-\beta q^{11}+\cdots\)
1024.2.a.f 1024.a 1.a $2$ $8.177$ \(\Q(\sqrt{2}) \) None None 512.2.e.a \(0\) \(0\) \(0\) \(8\) $-$ $\mathrm{SU}(2)$ \(q+2\beta q^{3}-\beta q^{5}+4q^{7}+5q^{9}+2\beta q^{11}+\cdots\)
1024.2.a.g 1024.a 1.a $4$ $8.177$ \(\Q(\zeta_{24})^+\) None None 256.2.e.a \(0\) \(-4\) \(0\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{3}-\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+\cdots\)
1024.2.a.h 1024.a 1.a $4$ $8.177$ \(\Q(\zeta_{16})^+\) None None 512.2.e.i \(0\) \(0\) \(-8\) \(0\) $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(-2-\beta _{2})q^{5}+(-\beta _{1}+\beta _{3})q^{7}+\cdots\)
1024.2.a.i 1024.a 1.a $4$ $8.177$ \(\Q(\zeta_{16})^+\) None None 512.2.e.i \(0\) \(0\) \(8\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{3}+(2+\beta _{2})q^{5}+(\beta _{1}-\beta _{3})q^{7}+\cdots\)
1024.2.a.j 1024.a 1.a $4$ $8.177$ \(\Q(\zeta_{24})^+\) None None 256.2.e.a \(0\) \(4\) \(0\) \(0\) $-$ $\mathrm{SU}(2)$ \(q+(1-\beta _{1})q^{3}+\beta _{3}q^{5}+(\beta _{2}+\beta _{3})q^{7}+\cdots\)
1024.2.b.a 1024.b 8.b $2$ $8.177$ \(\Q(\sqrt{-2}) \) None None 512.2.e.a \(0\) \(0\) \(0\) \(-8\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{3}+\beta q^{5}-4q^{7}-5q^{9}-2\beta q^{11}+\cdots\)
1024.2.b.b 1024.b 8.b $2$ $8.177$ \(\Q(\sqrt{-2}) \) None None 16.2.e.a \(0\) \(0\) \(0\) \(-4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}-\beta q^{5}-2q^{7}+q^{9}+\beta q^{11}+\cdots\)
1024.2.b.c 1024.b 8.b $2$ $8.177$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None 512.2.e.d \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-\beta q^{5}+3q^{9}-5\beta q^{13}-8q^{17}+3q^{25}+\cdots\)
1024.2.b.d 1024.b 8.b $2$ $8.177$ \(\Q(\sqrt{-2}) \) \(\Q(\sqrt{-1}) \) None 512.2.e.c \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-3\beta q^{5}+3q^{9}+\beta q^{13}+8q^{17}-13q^{25}+\cdots\)
1024.2.b.e 1024.b 8.b $2$ $8.177$ \(\Q(\sqrt{-2}) \) None None 16.2.e.a \(0\) \(0\) \(0\) \(4\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta q^{3}+\beta q^{5}+2q^{7}+q^{9}+\beta q^{11}+\cdots\)
1024.2.b.f 1024.b 8.b $2$ $8.177$ \(\Q(\sqrt{-2}) \) None None 512.2.e.a \(0\) \(0\) \(0\) \(8\) $\mathrm{SU}(2)[C_{2}]$ \(q+2\beta q^{3}-\beta q^{5}+4q^{7}-5q^{9}-2\beta q^{11}+\cdots\)
1024.2.b.g 1024.b 8.b $8$ $8.177$ \(\Q(\zeta_{16})\) None None 512.2.e.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta_{2} q^{3}+\beta_1 q^{5}-\beta_{3} q^{7}+(-\beta_{5}-1)q^{9}+\cdots\)
1024.2.b.h 1024.b 8.b $8$ $8.177$ \(\Q(\zeta_{24})\) None None 256.2.e.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta_1 q^{3}+\beta_{5} q^{5}+\beta_{4} q^{7}+(-\beta_{2}-1)q^{9}+\cdots\)
1024.2.e.a 1024.e 16.e $2$ $8.177$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None 128.2.b.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(2 i-2)q^{3}-5 i q^{9}+(2 i+2)q^{11}+\cdots\)
1024.2.e.b 1024.e 16.e $2$ $8.177$ \(\Q(\sqrt{-1}) \) None None 512.2.a.c \(0\) \(-2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(i-1)q^{3}+(-2 i-2)q^{5}-4 i q^{7}+\cdots\)
1024.2.e.c 1024.e 16.e $2$ $8.177$ \(\Q(\sqrt{-1}) \) None None 512.2.a.c \(0\) \(-2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(i-1)q^{3}+(2 i+2)q^{5}+4 i q^{7}+\cdots\)
1024.2.e.d 1024.e 16.e $2$ $8.177$ \(\Q(\sqrt{-1}) \) None None 512.2.a.c \(0\) \(2\) \(-4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-i+1)q^{3}+(-2 i-2)q^{5}+4 i q^{7}+\cdots\)
1024.2.e.e 1024.e 16.e $2$ $8.177$ \(\Q(\sqrt{-1}) \) None None 512.2.a.c \(0\) \(2\) \(4\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-i+1)q^{3}+(2 i+2)q^{5}-4 i q^{7}+\cdots\)
1024.2.e.f 1024.e 16.e $2$ $8.177$ \(\Q(\sqrt{-1}) \) \(\Q(\sqrt{-2}) \) None 128.2.b.a \(0\) \(4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-2 i+2)q^{3}-5 i q^{9}+(-2 i-2)q^{11}+\cdots\)
1024.2.e.g 1024.e 16.e $4$ $8.177$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None 512.2.a.a \(0\) \(-4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(-\beta_{2}+\beta_1-1)q^{3}+(-2\beta_{3}+3\beta_{2}-2\beta_1)q^{9}+\cdots\)
1024.2.e.h 1024.e 16.e $4$ $8.177$ \(\Q(\zeta_{8})\) None None 512.2.a.b \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(\beta_{2}-1)q^{3}-\beta_1 q^{5}+(-\beta_{3}-\beta_1)q^{7}+\cdots\)
1024.2.e.i 1024.e 16.e $4$ $8.177$ \(\Q(\zeta_{8})\) None None 128.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta_1 q^{3}+\beta_{3} q^{5}+4\beta_{2} q^{7}+\beta_{2} q^{9}+\cdots\)
1024.2.e.j 1024.e 16.e $4$ $8.177$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None 32.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q-\beta_1 q^{5}+3\beta_{2} q^{9}-3\beta_{3} q^{13}-2 q^{17}+\cdots\)
1024.2.e.k 1024.e 16.e $4$ $8.177$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-1}) \) None 128.2.b.b \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta_1 q^{5}+3\beta_{2} q^{9}-\beta_{3} q^{13}+2 q^{17}+\cdots\)
1024.2.e.l 1024.e 16.e $4$ $8.177$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None 64.2.b.a \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+\beta_1 q^{3}+\beta_{2} q^{9}-3\beta_{3} q^{11}+6 q^{17}+\cdots\)
1024.2.e.m 1024.e 16.e $4$ $8.177$ \(\Q(\zeta_{8})\) None None 128.2.a.a \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta_1 q^{3}-\beta_{3} q^{5}-4\beta_{2} q^{7}+\beta_{2} q^{9}+\cdots\)
1024.2.e.n 1024.e 16.e $4$ $8.177$ \(\Q(\zeta_{8})\) None None 512.2.a.b \(0\) \(4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-\beta_{2}+1)q^{3}-\beta_1 q^{5}+(\beta_{3}+\beta_1)q^{7}+\cdots\)
1024.2.e.o 1024.e 16.e $4$ $8.177$ \(\Q(\zeta_{8})\) \(\Q(\sqrt{-2}) \) None 512.2.a.a \(0\) \(4\) \(0\) \(0\) $\mathrm{U}(1)[D_{4}]$ \(q+(\beta_{2}+\beta_1+1)q^{3}+(2\beta_{3}+3\beta_{2}+2\beta_1)q^{9}+\cdots\)
1024.2.e.p 1024.e 16.e $8$ $8.177$ \(\Q(\zeta_{24})\) None None 512.2.a.g \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{4}]$ \(q+\beta_{7} q^{3}+\beta_1 q^{5}-\beta_{6} q^{7}-3\beta_{2} q^{9}+\cdots\)
1024.2.g.a 1024.g 32.g $16$ $8.177$ \(\Q(\zeta_{48})\) None None 1024.2.g.a \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta_{15} q^{3}+(-\beta_{9}-\beta_{8}+\beta_{3}-1)q^{5}+\cdots\)
1024.2.g.b 1024.g 32.g $16$ $8.177$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 1024.2.g.b \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{2}q^{3}+(\beta _{3}+\beta _{10})q^{5}+(-\beta _{4}-\beta _{9}+\cdots)q^{7}+\cdots\)
1024.2.g.c 1024.g 32.g $16$ $8.177$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 1024.2.g.b \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{13}q^{3}+(-1-\beta _{3}+\beta _{5}+\beta _{8})q^{5}+\cdots\)
1024.2.g.d 1024.g 32.g $16$ $8.177$ \(\Q(\zeta_{48})\) None None 1024.2.g.a \(0\) \(0\) \(-8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\beta_{14}+\beta_{11})q^{3}+(-\beta_{13}-\beta_{10}+\cdots-\beta_1)q^{5}+\cdots\)
1024.2.g.e 1024.g 32.g $16$ $8.177$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 1024.2.g.b \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{2}q^{3}+(-\beta _{3}-\beta _{10})q^{5}+(\beta _{4}+\beta _{9}+\cdots)q^{7}+\cdots\)
1024.2.g.f 1024.g 32.g $16$ $8.177$ \(\Q(\zeta_{48})\) None None 1024.2.g.a \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta_{15} q^{3}+(\beta_{13}+\beta_{8}+1)q^{5}+(-\beta_{15}+\beta_{12}+\cdots+\beta_{5})q^{7}+\cdots\)
1024.2.g.g 1024.g 32.g $16$ $8.177$ \(\Q(\zeta_{48})\) None None 1024.2.g.a \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+(\beta_{14}+\beta_{11})q^{3}+(\beta_{13}+\beta_{10}+\cdots+\beta_1)q^{5}+\cdots\)
1024.2.g.h 1024.g 32.g $16$ $8.177$ \(\mathbb{Q}[x]/(x^{16} - \cdots)\) None None 1024.2.g.b \(0\) \(0\) \(8\) \(0\) $\mathrm{SU}(2)[C_{8}]$ \(q+\beta _{13}q^{3}+(1+\beta _{3}-\beta _{5}-\beta _{8})q^{5}+\cdots\)
1024.3.c.a 1024.c 4.b $2$ $27.902$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None 512.3.f.c \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q-7\beta q^{5}+9q^{9}-17\beta q^{13}-2^{4}q^{17}+\cdots\)
1024.3.c.b 1024.c 4.b $2$ $27.902$ \(\Q(\sqrt{2}) \) \(\Q(\sqrt{-1}) \) None 512.3.f.d \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta q^{5}+9q^{9}+7\beta q^{13}+2^{4}q^{17}+\cdots\)
1024.3.c.c 1024.c 4.b $4$ $27.902$ \(\Q(\sqrt{2}, \sqrt{-3})\) None None 512.3.f.i \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+\beta _{2}q^{3}-5\beta _{1}q^{5}-\beta _{3}q^{7}-15q^{9}+\cdots\)
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