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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twists	CM/RM discriminant	Inner twist count	Is self-dual	Analytic rank

Coefficient ring index	Coefficient ring gens.		Projective image	Projective image type
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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
647.1.b.a	$647$	$1$	647.b	647.b	$2$	$11$	$11$	$0.323$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-647}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q-\beta _{3}q^{2}-\beta _{5}q^{3}+(1+\beta _{6})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$
719.1.b.a	$719$	$1$	719.b	719.b	$2$	$15$	$15$	$0.359$	$\Q(\zeta_{62})^+$	$D_{31}$	$\Q(\sqrt{-719}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+\beta _{12}q^{2}+\beta _{10}q^{3}+(1-\beta _{7})q^{4}-\beta _{13}q^{5}+\cdots$
887.1.b.a	$887$	$1$	887.b	887.b	$2$	$14$	$14$	$0.443$	$\Q(\zeta_{58})^+$	$D_{29}$	$\Q(\sqrt{-887}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q-\beta _{11}q^{2}-\beta _{5}q^{3}+(1-\beta _{7})q^{4}+(\beta _{6}+\cdots)q^{6}+\cdots$
911.1.b.a	$911$	$1$	911.b	911.b	$2$	$15$	$15$	$0.455$	$\Q(\zeta_{62})^+$	$D_{31}$	$\Q(\sqrt{-911}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q+\beta _{12}q^{2}-\beta _{9}q^{3}+(1-\beta _{7})q^{4}+\beta _{8}q^{5}+\cdots$
955.1.c.b	$955$	$1$	955.c	955.c	$2$	$12$	$12$	$0.477$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-191}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{26}^{6}+\zeta_{26}^{7})q^{2}+(-\zeta_{26}^{2}-\zeta_{26}^{11}+\cdots)q^{3}+\cdots$
1031.1.b.c	$1031$	$1$	1031.b	1031.b	$2$	$12$	$12$	$0.515$	$\Q(\zeta_{35})^+$	$D_{35}$	$\Q(\sqrt{-1031}) $	None	✓	$2$	$0$	$1$	$-4$	$1$	$0$	$1$		$q+\beta _{9}q^{2}+\beta _{5}q^{3}+(-\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
1039.1.b.a	$1039$	$1$	1039.b	1039.b	$2$	$11$	$11$	$0.519$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1039}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}+\beta _{2}q^{5}-\beta _{7}q^{7}+\cdots$
1103.1.b.a	$1103$	$1$	1103.b	1103.b	$2$	$11$	$11$	$0.550$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1103}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\beta _{3}q^{2}+\beta _{4}q^{3}+(1+\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$
1151.1.b.a	$1151$	$1$	1151.b	1151.b	$2$	$20$	$20$	$0.574$	$\Q(\zeta_{82})^+$	$D_{41}$	$\Q(\sqrt{-1151}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+\beta _{10}q^{2}+\beta _{16}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
1223.1.b.c	$1223$	$1$	1223.b	1223.b	$2$	$12$	$12$	$0.610$	$\Q(\zeta_{35})^+$	$D_{35}$	$\Q(\sqrt{-1223}) $	None	✓	$2$	$0$	$1$	$1$	$0$	$1$	$1$		$q+\beta _{9}q^{2}+\beta _{2}q^{3}+(-\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
1279.1.b.a	$1279$	$1$	1279.b	1279.b	$2$	$11$	$11$	$0.638$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1279}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}-\beta _{5}q^{5}-\beta _{7}q^{7}+\cdots$
1319.1.b.e	$1319$	$1$	1319.b	1319.b	$2$	$12$	$12$	$0.658$	$\Q(\zeta_{45})^+$	$D_{45}$	$\Q(\sqrt{-1319}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$3$	$1$		$q+\beta _{9}q^{2}+\beta _{7}q^{3}+(1-\beta _{5}-\beta _{9})q^{4}+\cdots$
84.2.e.a	$84$	$2$	84.e	12.b	$2$	$12$	$12$	$0.671$	12.0.$\cdots$.2	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}-\beta _{9}q^{3}+(-\beta _{2}-\beta _{3})q^{4}+\cdots$
84.2.n.a	$84$	$2$	84.n	84.n	$6$	$24$	$12$	$0.671$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$
1439.1.b.c	$1439$	$1$	1439.b	1439.b	$2$	$12$	$12$	$0.718$	$\Q(\zeta_{39})^+$	$D_{39}$	$\Q(\sqrt{-1439}) $	None	✓	$2$	$0$	$-2$	$1$	$1$	$0$	$1$		$q+\beta _{3}q^{2}+\beta _{4}q^{3}+(1+\beta _{6})q^{4}+(-\beta _{4}+\cdots)q^{5}+\cdots$
1447.1.b.a	$1447$	$1$	1447.b	1447.b	$2$	$11$	$11$	$0.722$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1447}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}-\beta _{7}q^{7}+(-\beta _{3}+\cdots)q^{8}+\cdots$
1471.1.b.a	$1471$	$1$	1471.b	1471.b	$2$	$11$	$11$	$0.734$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1471}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}+\beta _{2}q^{5}+(-\beta _{3}+\cdots)q^{8}+\cdots$
1487.1.b.a	$1487$	$1$	1487.b	1487.b	$2$	$18$	$18$	$0.742$	$\Q(\zeta_{74})^+$	$D_{37}$	$\Q(\sqrt{-1487}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+\beta _{8}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
1528.1.b.c	$1528$	$1$	1528.b	1528.b	$2$	$12$	$12$	$0.763$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-191}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\zeta_{26}^{10}q^{2}+(\zeta_{26}+\zeta_{26}^{12})q^{3}-\zeta_{26}^{7}q^{4}+\cdots$
96.2.o.a	$96$	$2$	96.o	96.o	$8$	$56$	$14$	$0.767$		$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$-8$		$\mathrm{SU}(2)[C_{8}]$
1555.1.b.b	$1555$	$1$	1555.b	1555.b	$2$	$18$	$18$	$0.776$	$\Q(\zeta_{38})$	$D_{38}$	$\Q(\sqrt{-311}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(-\zeta_{38}^{3}-\zeta_{38}^{16})q^{2}+(-\zeta_{38}^{2}+\cdots)q^{3}+\cdots$
1559.1.b.c	$1559$	$1$	1559.b	1559.b	$2$	$16$	$16$	$0.778$	$\Q(\zeta_{51})^+$	$D_{51}$	$\Q(\sqrt{-1559}) $	None	✓	$2$	$0$	$-2$	$1$	$1$	$-2$	$1$		$q+\beta _{6}q^{2}+(-\beta _{8}-\beta _{9})q^{3}+(1+\beta _{12}+\cdots)q^{4}+\cdots$
100.2.l.b	$100$	$2$	100.l	100.l	$20$	$96$	$12$	$0.799$		$_{}$	None	None		$4$	$0$	$-10$	$0$	$-20$	$0$		$\mathrm{SU}(2)[C_{20}]$
104.2.r.a	$104$	$2$	104.r	104.r	$6$	$24$	$12$	$0.830$		$_{}$	None	None		$4$	$0$	$-1$	$0$	$0$	$-2$		$\mathrm{SU}(2)[C_{6}]$
104.2.u.a	$104$	$2$	104.u	104.u	$12$	$48$	$12$	$0.830$		$_{}$	None	None		$4$	$0$	$-4$	$-4$	$0$	$0$		$\mathrm{SU}(2)[C_{12}]$
1679.1.d.e	$1679$	$1$	1679.d	1679.d	$2$	$12$	$12$	$0.838$	$\Q(\zeta_{52})^+$	$D_{26}$	$\Q(\sqrt{-1679}) $	None	✓	$4$	$0$	$2$	$-2$	$0$	$0$	$1$		$q+\beta _{10}q^{2}+\beta _{4}q^{3}+(1-\beta _{6})q^{4}-\beta _{1}q^{5}+\cdots$
105.2.j.a	$105$	$2$	105.j	15.e	$4$	$24$	$12$	$0.838$		$_{}$	None	None		$4$	$0$	$0$	$-4$	$0$	$0$		$\mathrm{SU}(2)[C_{4}]$
105.2.p.a	$105$	$2$	105.p	105.p	$6$	$24$	$12$	$0.838$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{6}]$
105.2.x.a	$105$	$2$	105.x	105.x	$12$	$48$	$12$	$0.838$		$_{}$	None	None		$8$	$0$	$0$	$-2$	$0$	$-12$		$\mathrm{SU}(2)[C_{12}]$
1719.1.g.c	$1719$	$1$	1719.g	1719.g	$6$	$24$	$12$	$0.858$	$\Q(\zeta_{39})$	$D_{39}$	$\Q(\sqrt{-191}) $	None		$4$	$0$	$2$	$1$	$-1$	$0$	$1$		$q+(-\zeta_{78}^{7}-\zeta_{78}^{19})q^{2}-\zeta_{78}^{37}q^{3}+\cdots$
1720.1.g.g	$1720$	$1$	1720.g	1720.g	$2$	$12$	$12$	$0.858$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-215}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{9}q^{2}+(-\zeta_{28}^{3}-\zeta_{28}^{11})q^{3}+\cdots$
1725.1.l.c	$1725$	$1$	1725.l	345.l	$4$	$24$	$12$	$0.861$	$\Q(\zeta_{72})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{72}^{5}+\zeta_{72}^{13})q^{2}-\zeta_{72}^{19}q^{3}+\cdots$
108.2.l.a	$108$	$2$	108.l	108.l	$18$	$96$	$16$	$0.862$		$_{}$	None	None		$4$	$0$	$-6$	$0$	$-12$	$0$		$\mathrm{SU}(2)[C_{18}]$
112.2.v.a	$112$	$2$	112.v	112.v	$12$	$56$	$14$	$0.894$		$_{}$	None	None		$4$	$0$	$-2$	$-6$	$-6$	$-8$		$\mathrm{SU}(2)[C_{12}]$
112.2.w.c	$112$	$2$	112.w	112.w	$12$	$48$	$12$	$0.894$		$_{}$	None	None		$4$	$0$	$-4$	$0$	$4$	$0$		$\mathrm{SU}(2)[C_{12}]$
1795.1.c.c	$1795$	$1$	1795.c	1795.c	$2$	$18$	$18$	$0.896$	$\Q(\zeta_{38})$	$D_{38}$	$\Q(\sqrt{-359}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(-\zeta_{38}^{3}-\zeta_{38}^{16})q^{2}+(-\zeta_{38}^{4}+\cdots)q^{3}+\cdots$
1811.1.b.a	$1811$	$1$	1811.b	1811.b	$2$	$11$	$11$	$0.904$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1811}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q-\beta _{3}q^{3}+q^{4}-\beta _{5}q^{5}-\beta _{7}q^{7}+(1+\cdots)q^{9}+\cdots$
1823.1.b.f	$1823$	$1$	1823.b	1823.b	$2$	$12$	$12$	$0.910$	$\Q(\zeta_{45})^+$	$D_{45}$	$\Q(\sqrt{-1823}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-6$	$1$		$q+\beta _{9}q^{2}+\beta _{7}q^{3}+(1-\beta _{5}-\beta _{9})q^{4}+\cdots$
116.2.l.b	$116$	$2$	116.l	116.l	$28$	$144$	$12$	$0.926$		$_{}$	None	None		$4$	$0$	$-12$	$0$	$-28$	$0$		$\mathrm{SU}(2)[C_{28}]$
1871.1.b.e	$1871$	$1$	1871.b	1871.b	$2$	$12$	$12$	$0.934$	$\Q(\zeta_{45})^+$	$D_{45}$	$\Q(\sqrt{-1871}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{7}q^{2}+\beta _{1}q^{3}+(1+\beta _{11})q^{4}+(\beta _{1}+\cdots)q^{5}+\cdots$
117.2.f.a	$117$	$2$	117.f	117.f	$3$	$24$	$12$	$0.934$		$_{}$	None	None		$2$	$0$	$1$	$-1$	$-2$	$-6$		$\mathrm{SU}(2)[C_{3}]$
117.2.h.a	$117$	$2$	117.h	117.h	$3$	$24$	$12$	$0.934$		$_{}$	None	None		$2$	$0$	$-2$	$-1$	$-2$	$3$		$\mathrm{SU}(2)[C_{3}]$
117.2.l.b	$117$	$2$	117.l	117.l	$6$	$22$	$11$	$0.934$		$_{}$	None	None		$2$	$0$	$0$	$-1$	$-3$	$-6$		$\mathrm{SU}(2)[C_{6}]$
117.2.r.b	$117$	$2$	117.r	117.r	$6$	$22$	$11$	$0.934$		$_{}$	None	None		$2$	$0$	$0$	$2$	$3$	$0$		$\mathrm{SU}(2)[C_{6}]$
117.2.x.a	$117$	$2$	117.x	117.x	$12$	$48$	$12$	$0.934$		$_{}$	None	None		$2$	$0$	$-6$	$-2$	$-6$	$-4$		$\mathrm{SU}(2)[C_{12}]$
117.2.z.b	$117$	$2$	117.z	117.z	$12$	$44$	$11$	$0.934$		$_{}$	None	None		$4$	$0$	$0$	$-2$	$0$	$0$		$\mathrm{SU}(2)[C_{12}]$
117.2.bc.a	$117$	$2$	117.bc	117.ac	$12$	$48$	$12$	$0.934$		$_{}$	None	None		$2$	$0$	$-6$	$-2$	$-6$	$2$		$\mathrm{SU}(2)[C_{12}]$
120.2.m.b	$120$	$2$	120.m	120.m	$2$	$16$	$16$	$0.958$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$	$2^{13}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{13}q^{3}-\beta _{11}q^{4}+\beta _{7}q^{5}+\cdots$
120.2.v.a	$120$	$2$	120.v	40.k	$4$	$24$	$12$	$0.958$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{4}]$
120.2.w.c	$120$	$2$	120.w	120.w	$4$	$32$	$16$	$0.958$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{4}]$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.