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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
124.1.i.a	$124$	$1$	124.i	124.i	$6$	$4$	$2$	$0.062$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
133.1.m.a	$133$	$1$	133.m	133.m	$6$	$4$	$2$	$0.066$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{5}q^{5}+\cdots$
136.1.p.a	$136$	$1$	136.p	136.p	$8$	$4$	$1$	$0.068$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
164.1.j.a	$164$	$1$	164.j	164.j	$10$	$4$	$1$	$0.082$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{5}+\cdots$
164.1.l.a	$164$	$1$	164.l	164.l	$10$	$4$	$1$	$0.082$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
171.1.o.a	$171$	$1$	171.o	171.o	$6$	$4$	$2$	$0.085$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\cdots$
180.1.m.a	$180$	$1$	180.m	60.l	$4$	$4$	$2$	$0.090$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots$
183.1.l.a	$183$	$1$	183.l	183.l	$10$	$4$	$1$	$0.091$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-5$	$1$		$q-\zeta_{10}q^{3}-\zeta_{10}^{2}q^{4}+(-1-\zeta_{10}^{3}+\cdots)q^{7}+\cdots$
183.1.n.a	$183$	$1$	183.n	183.n	$10$	$4$	$1$	$0.091$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$3$	$1$		$q+\zeta_{10}^{4}q^{3}-\zeta_{10}^{3}q^{4}+(1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
195.1.e.a	$195$	$1$	195.e	195.e	$2$	$4$	$4$	$0.097$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots$
201.1.g.a	$201$	$1$	201.g	201.g	$6$	$4$	$2$	$0.100$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{6}+\cdots$
209.1.h.a	$209$	$1$	209.h	209.h	$6$	$4$	$2$	$0.104$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{5}+\cdots$
209.1.m.a	$209$	$1$	209.m	209.m	$10$	$4$	$1$	$0.104$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$3$	$1$		$q+\zeta_{10}^{4}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{5}+(1+\cdots)q^{7}+\cdots$
219.1.j.b	$219$	$1$	219.j	219.j	$6$	$4$	$2$	$0.109$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots$
219.1.o.a	$219$	$1$	219.o	219.o	$12$	$4$	$1$	$0.109$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots$
224.1.r.a	$224$	$1$	224.r	28.g	$6$	$4$	$2$	$0.112$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$
224.1.v.a	$224$	$1$	224.v	224.v	$8$	$4$	$1$	$0.112$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
239.1.b.c	$239$	$1$	239.b	239.b	$2$	$4$	$4$	$0.119$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$1$	$-2$	$1$	$0$	$1$		$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
240.1.bm.a	$240$	$1$	240.bm	240.am	$4$	$4$	$2$	$0.120$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots$
244.1.n.a	$244$	$1$	244.n	244.n	$10$	$4$	$1$	$0.122$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$3$	$0$	$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+(1-\zeta_{10})q^{5}+\cdots$
252.1.h.a	$252$	$1$	252.h	84.h	$2$	$4$	$4$	$0.126$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
255.1.i.a	$255$	$1$	255.i	255.i	$4$	$4$	$2$	$0.127$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}-q^{4}+\cdots$
260.1.be.a	$260$	$1$	260.be	260.ae	$12$	$4$	$1$	$0.130$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}+\zeta_{12}^{4}q^{4}-\zeta_{12}^{5}q^{5}+\cdots$
260.1.bl.a	$260$	$1$	260.bl	260.al	$12$	$4$	$1$	$0.130$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
261.1.f.a	$261$	$1$	261.f	29.c	$4$	$4$	$2$	$0.130$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
264.1.r.a	$264$	$1$	264.r	264.r	$10$	$4$	$1$	$0.132$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
264.1.r.b	$264$	$1$	264.r	264.r	$10$	$4$	$1$	$0.132$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}-\zeta_{10}^{4}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
264.1.t.a	$264$	$1$	264.t	264.t	$10$	$4$	$1$	$0.132$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$-2$	$-2$	$1$		$q+\zeta_{10}^{4}q^{2}+\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
264.1.t.b	$264$	$1$	264.t	264.t	$10$	$4$	$1$	$0.132$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$2$	$-2$	$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
272.1.u.a	$272$	$1$	272.u	68.g	$8$	$4$	$1$	$0.136$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{13}+\cdots$
273.1.s.b	$273$	$1$	273.s	273.s	$6$	$4$	$2$	$0.136$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{5}q^{5}+\cdots$
273.1.bm.b	$273$	$1$	273.bm	273.am	$6$	$4$	$2$	$0.136$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots$
273.1.bs.a	$273$	$1$	273.bs	273.as	$12$	$4$	$1$	$0.136$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{12}q^{3}-\zeta_{12}^{3}q^{4}-\zeta_{12}q^{7}+\zeta_{12}^{2}q^{9}+\cdots$
273.1.ch.a	$273$	$1$	273.ch	273.bh	$12$	$4$	$1$	$0.136$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}+\zeta_{12}^{4}q^{7}+\cdots$
275.1.s.a	$275$	$1$	275.s	275.s	$10$	$4$	$1$	$0.137$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+(\zeta_{10}-\zeta_{10}^{3})q^{3}-\zeta_{10}^{2}q^{4}-q^{5}+\cdots$
275.1.v.a	$275$	$1$	275.v	275.v	$10$	$4$	$1$	$0.137$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$4$	$0$	$1$		$q+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+q^{5}+\cdots$
279.1.v.a	$279$	$1$	279.v	31.f	$10$	$4$	$1$	$0.139$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{10}q^{4}+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{7}+(-\zeta_{10}+\cdots)q^{13}+\cdots$
280.1.c.a	$280$	$1$	280.c	280.c	$2$	$4$	$4$	$0.140$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
288.1.o.a	$288$	$1$	288.o	36.f	$6$	$4$	$2$	$0.144$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}-q^{9}+\cdots$
291.1.k.a	$291$	$1$	291.k	291.k	$8$	$4$	$1$	$0.145$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{3})q^{7}+\cdots$
300.1.l.a	$300$	$1$	300.l	60.l	$4$	$4$	$2$	$0.150$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{3}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots$
301.1.r.a	$301$	$1$	301.r	301.r	$6$	$4$	$2$	$0.150$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{5}-q^{6}+\cdots$
308.1.s.a	$308$	$1$	308.s	308.s	$10$	$4$	$1$	$0.154$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-1$	$0$	$0$	$1$	$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}-\zeta_{10}^{2}q^{7}+\cdots$
308.1.s.b	$308$	$1$	308.s	308.s	$10$	$4$	$1$	$0.154$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{2}q^{7}-\zeta_{10}^{4}q^{8}+\cdots$
309.1.h.a	$309$	$1$	309.h	309.h	$6$	$4$	$2$	$0.154$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$-4$	$0$	$2$	$1$		$q-\zeta_{12}q^{2}-q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}q^{6}+\cdots$
312.1.b.a	$312$	$1$	312.b	312.b	$2$	$4$	$4$	$0.156$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
323.1.l.a	$323$	$1$	323.l	323.l	$8$	$4$	$1$	$0.161$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{3})q^{5}+(\zeta_{8}^{2}+\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
328.1.n.a	$328$	$1$	328.n	328.n	$8$	$4$	$1$	$0.164$	$\Q(\zeta_{8})$	$D_{8}$	None	$\Q(\sqrt{2}) $		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\zeta_{8}^{2})q^{7}+\cdots$
328.1.t.a	$328$	$1$	328.t	328.t	$10$	$4$	$1$	$0.164$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
328.1.x.a	$328$	$1$	328.x	328.x	$10$	$4$	$1$	$0.164$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+(\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$

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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.