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Label Char Prim Dim $A$ Field CM RM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
191.1.b.a 191.b 191.b $6$ $0.095$ \(\Q(\zeta_{26})^+\) \(\Q(\sqrt{-191}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q-\beta _{3}q^{2}-\beta _{1}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
263.1.b.a 263.b 263.b $6$ $0.131$ \(\Q(\zeta_{26})^+\) \(\Q(\sqrt{-263}) \) None \(-1\) \(-1\) \(0\) \(0\) \(q-\beta _{3}q^{2}+\beta _{2}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
311.1.b.a 311.b 311.b $9$ $0.155$ \(\Q(\zeta_{38})^+\) \(\Q(\sqrt{-311}) \) None \(-1\) \(-1\) \(-1\) \(-1\) \(q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
355.1.c.b 355.c 355.c $6$ $0.177$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-71}) \) None \(0\) \(0\) \(1\) \(0\) \(q+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{2}+(-\zeta_{14}-\zeta_{14}^{6}+\cdots)q^{3}+\cdots\)
359.1.b.a 359.b 359.b $9$ $0.179$ \(\Q(\zeta_{38})^+\) \(\Q(\sqrt{-359}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
383.1.b.a 383.b 383.b $8$ $0.191$ \(\Q(\zeta_{34})^+\) \(\Q(\sqrt{-383}) \) None \(-1\) \(-1\) \(0\) \(-1\) \(q+\beta _{6}q^{2}+\beta _{4}q^{3}+(1-\beta _{5})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)
431.1.b.c 431.b 431.b $6$ $0.215$ \(\Q(\zeta_{21})^+\) \(\Q(\sqrt{-431}) \) None \(-2\) \(1\) \(1\) \(0\) \(q+(-1-\beta _{3}+\beta _{5})q^{2}+\beta _{4}q^{3}+(1-\beta _{5})q^{4}+\cdots\)
479.1.b.b 479.b 479.b $10$ $0.239$ \(\Q(\zeta_{50})^+\) \(\Q(\sqrt{-479}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}-\beta _{9}q^{5}+\cdots\)
503.1.b.c 503.b 503.b $6$ $0.251$ \(\Q(\zeta_{21})^+\) \(\Q(\sqrt{-503}) \) None \(-2\) \(1\) \(0\) \(1\) \(q+\beta _{3}q^{2}+\beta _{4}q^{3}+(-\beta _{3}+\beta _{5})q^{4}+\cdots\)
551.1.d.a 551.d 551.d $6$ $0.275$ \(\Q(\zeta_{26})^+\) \(\Q(\sqrt{-551}) \) None \(-1\) \(-1\) \(-1\) \(-1\) \(q-\beta _{3}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots\)
551.1.d.b 551.d 551.d $6$ $0.275$ \(\Q(\zeta_{26})^+\) \(\Q(\sqrt{-551}) \) None \(1\) \(1\) \(-1\) \(-1\) \(q+\beta _{3}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4}+\cdots)q^{3}+\cdots\)
555.1.b.a 555.b 555.b $8$ $0.277$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-111}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{16}-\zeta_{16}^{7})q^{2}+\zeta_{16}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots\)
568.1.b.b 568.b 568.b $6$ $0.283$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-71}) \) None \(1\) \(0\) \(0\) \(0\) \(q-\zeta_{14}^{4}q^{2}+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{3}-\zeta_{14}q^{4}+\cdots\)
575.1.c.b 575.c 115.c $6$ $0.287$ 6.0.419904.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{1}-\beta _{5})q^{3}+(-1+\beta _{2}+\cdots)q^{4}+\cdots\)
595.1.b.b 595.b 595.b $8$ $0.297$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-119}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{20}^{2}+\zeta_{20}^{8})q^{2}+(-\zeta_{20}^{3}-\zeta_{20}^{7}+\cdots)q^{3}+\cdots\)
599.1.b.b 599.b 599.b $10$ $0.299$ \(\Q(\zeta_{50})^+\) \(\Q(\sqrt{-599}) \) None \(0\) \(0\) \(-5\) \(0\) \(q-\beta _{1}q^{2}+\beta _{6}q^{3}+(1+\beta _{2})q^{4}+(-1+\cdots)q^{5}+\cdots\)
607.1.b.a 607.b 607.b $6$ $0.303$ \(\Q(\zeta_{26})^+\) \(\Q(\sqrt{-607}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
631.1.b.a 631.b 631.b $6$ $0.315$ \(\Q(\zeta_{26})^+\) \(\Q(\sqrt{-631}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
727.1.b.a 727.b 727.b $6$ $0.363$ \(\Q(\zeta_{26})^+\) \(\Q(\sqrt{-727}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
743.1.b.c 743.b 743.b $6$ $0.371$ \(\Q(\zeta_{21})^+\) \(\Q(\sqrt{-743}) \) None \(1\) \(-2\) \(0\) \(0\) \(q+\beta _{4}q^{2}+\beta _{3}q^{3}+(2-\beta _{1}+\beta _{3}-\beta _{5})q^{4}+\cdots\)
755.1.c.e 755.c 755.c $6$ $0.377$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-151}) \) None \(0\) \(0\) \(1\) \(0\) \(q+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{2}+(-1-\zeta_{14}^{3}+\cdots)q^{4}+\cdots\)
760.1.b.a 760.b 760.b $8$ $0.379$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-95}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{2}+(\zeta_{16}^{3}+\zeta_{16}^{5})q^{3}+\zeta_{16}^{2}q^{4}+\cdots\)
791.1.d.d 791.d 791.d $8$ $0.395$ \(\Q(\zeta_{32})^+\) \(\Q(\sqrt{-791}) \) None \(0\) \(0\) \(0\) \(-8\) \(q+\beta _{2}q^{2}+\beta _{5}q^{3}+(1+\beta _{4})q^{4}-\beta _{3}q^{5}+\cdots\)
795.1.b.b 795.b 795.b $8$ $0.397$ \(\Q(\zeta_{20})\) \(\Q(\sqrt{-159}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(\zeta_{20}^{3}+\zeta_{20}^{7})q^{2}-\zeta_{20}^{5}q^{3}+(-1+\cdots)q^{4}+\cdots\)
820.1.e.c 820.e 820.e $8$ $0.409$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-41}) \) None \(0\) \(0\) \(0\) \(0\) \(q+\zeta_{16}^{4}q^{2}+(-\zeta_{16}-\zeta_{16}^{7})q^{3}-q^{4}+\cdots\)
831.1.d.d 831.d 831.d $6$ $0.415$ \(\Q(\zeta_{28})^+\) \(\Q(\sqrt{-831}) \) None \(0\) \(-6\) \(0\) \(2\) \(q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{5}q^{5}+\cdots\)
839.1.b.c 839.b 839.b $10$ $0.419$ \(\Q(\zeta_{33})^+\) \(\Q(\sqrt{-839}) \) None \(1\) \(1\) \(-2\) \(-2\) \(q+(-\beta _{2}-\beta _{9})q^{2}+\beta _{2}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots\)
852.1.d.c 852.d 852.d $6$ $0.425$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-71}) \) None \(-1\) \(1\) \(0\) \(0\) \(q+\zeta_{14}^{2}q^{2}+\zeta_{14}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}^{3}+\cdots)q^{5}+\cdots\)
852.1.d.d 852.d 852.d $6$ $0.425$ \(\Q(\zeta_{14})\) \(\Q(\sqrt{-71}) \) None \(1\) \(-1\) \(0\) \(0\) \(q-\zeta_{14}^{4}q^{2}-\zeta_{14}^{5}q^{3}-\zeta_{14}q^{4}+(-\zeta_{14}+\cdots)q^{5}+\cdots\)
863.1.b.c 863.b 863.b $6$ $0.431$ \(\Q(\zeta_{21})^+\) \(\Q(\sqrt{-863}) \) None \(1\) \(1\) \(0\) \(0\) \(q+\beta _{4}q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(2-\beta _{1}+\cdots)q^{4}+\cdots\)
888.1.i.e 888.i 888.i $8$ $0.443$ \(\Q(\zeta_{16})\) \(\Q(\sqrt{-111}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\zeta_{16}q^{2}-\zeta_{16}^{4}q^{3}+\zeta_{16}^{2}q^{4}+(\zeta_{16}^{3}+\cdots)q^{5}+\cdots\)
919.1.b.a 919.b 919.b $9$ $0.459$ \(\Q(\zeta_{38})^+\) \(\Q(\sqrt{-919}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
951.1.d.a 951.d 951.d $6$ $0.475$ \(\Q(\zeta_{26})^+\) \(\Q(\sqrt{-951}) \) None \(-1\) \(6\) \(-1\) \(-1\) \(q-\beta _{3}q^{2}+q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
951.1.d.b 951.d 951.d $6$ $0.475$ \(\Q(\zeta_{26})^+\) \(\Q(\sqrt{-951}) \) None \(1\) \(-6\) \(1\) \(-1\) \(q+\beta _{3}q^{2}-q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots\)
959.1.d.g 959.d 959.d $6$ $0.479$ \(\Q(\zeta_{36})^+\) \(\Q(\sqrt{-959}) \) None \(0\) \(0\) \(0\) \(-6\) \(q-\beta _{4}q^{2}-\beta _{1}q^{3}+(1-\beta _{2})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
60.2.e.a 60.e 12.b $8$ $0.479$ 8.0.342102016.5 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{2}q^{2}+(-\beta _{4}-\beta _{7})q^{3}+(\beta _{3}-\beta _{5}+\cdots)q^{4}+\cdots\)
983.1.b.c 983.b 983.b $9$ $0.491$ \(\Q(\zeta_{54})^+\) \(\Q(\sqrt{-983}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{2}+\beta _{7})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots\)
991.1.b.a 991.b 991.b $8$ $0.495$ \(\Q(\zeta_{34})^+\) \(\Q(\sqrt{-991}) \) None \(-1\) \(0\) \(-1\) \(0\) \(q+\beta _{6}q^{2}+(1-\beta _{5})q^{4}+\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
995.1.c.d 995.c 995.c $6$ $0.497$ \(\Q(\zeta_{18})\) \(\Q(\sqrt{-199}) \) None \(0\) \(0\) \(0\) \(0\) \(q+(-\zeta_{18}-\zeta_{18}^{8})q^{2}+(-1+\zeta_{18}^{2}+\cdots)q^{4}+\cdots\)
1004.1.d.b 1004.d 251.b $6$ $0.501$ \(\Q(\zeta_{21})^+\) \(\Q(\sqrt{-251}) \) None \(0\) \(-2\) \(1\) \(1\) \(q+(-1-\beta _{3}+\beta _{5})q^{3}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)
1019.1.b.a 1019.b 1019.b $6$ $0.509$ \(\Q(\zeta_{26})^+\) \(\Q(\sqrt{-1019}) \) None \(0\) \(-1\) \(-1\) \(0\) \(q-\beta _{3}q^{3}+q^{4}+\beta _{2}q^{5}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{9}+\cdots\)
65.2.b.a 65.b 5.b $6$ $0.519$ 6.0.350464.1 None None \(0\) \(0\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q+(\beta _{3}-\beta _{5})q^{2}+(-\beta _{3}-\beta _{4})q^{3}+(-2+\cdots)q^{4}+\cdots\)
65.2.c.a 65.c 13.b $6$ $0.519$ 6.0.5089536.1 None None \(0\) \(-4\) \(0\) \(0\) $\mathrm{SU}(2)[C_{2}]$ \(q-\beta _{5}q^{2}+(-1-\beta _{1})q^{3}+(-2+\beta _{3}+\cdots)q^{4}+\cdots\)
1055.1.d.h 1055.d 1055.d $6$ $0.527$ \(\Q(\zeta_{36})^+\) \(\Q(\sqrt{-1055}) \) None \(0\) \(0\) \(-6\) \(0\) \(q+\beta _{3}q^{2}-\beta _{1}q^{3}+2q^{4}-q^{5}+(-2\beta _{2}+\cdots)q^{6}+\cdots\)
1063.1.b.a 1063.b 1063.b $9$ $0.531$ \(\Q(\zeta_{38})^+\) \(\Q(\sqrt{-1063}) \) None \(-1\) \(0\) \(0\) \(-1\) \(q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots\)
1075.1.c.c 1075.c 43.b $6$ $0.536$ 6.0.153664.1 \(\Q(\sqrt{-215}) \) None \(0\) \(0\) \(0\) \(0\) \(q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1079.1.d.a 1079.d 1079.d $8$ $0.538$ \(\Q(\zeta_{34})^+\) \(\Q(\sqrt{-1079}) \) None \(-1\) \(-1\) \(-1\) \(0\) \(q+\beta _{6}q^{2}-\beta _{1}q^{3}+(1-\beta _{5})q^{4}-\beta _{3}q^{5}+\cdots\)
1079.1.d.b 1079.d 1079.d $8$ $0.538$ \(\Q(\zeta_{34})^+\) \(\Q(\sqrt{-1079}) \) None \(1\) \(-1\) \(1\) \(0\) \(q-\beta _{2}q^{2}+\beta _{6}q^{3}+(1+\beta _{4})q^{4}+\beta _{1}q^{5}+\cdots\)
1091.1.b.a 1091.b 1091.b $8$ $0.544$ \(\Q(\zeta_{34})^+\) \(\Q(\sqrt{-1091}) \) None \(0\) \(-1\) \(-1\) \(-1\) \(q+\beta _{6}q^{3}+q^{4}-\beta _{7}q^{5}+\beta _{2}q^{7}+(1+\cdots)q^{9}+\cdots\)
69.2.c.a 69.c 69.c $6$ $0.551$ 6.0.8869743.1 \(\Q(\sqrt{-23}) \) None \(0\) \(0\) \(0\) \(0\) $\mathrm{U}(1)[D_{2}]$ \(q+\beta _{2}q^{2}-\beta _{1}q^{3}+(-2+\beta _{1}+\beta _{3}+\cdots)q^{4}+\cdots\)
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