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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
52.1.j.a	$52$	$1$	52.j	52.j	$6$	$2$	$1$	$0.026$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
68.1.d.a	$68$	$1$	68.d	68.d	$2$	$1$	$1$	$0.034$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-17}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}-q^{9}-2q^{13}+q^{16}+\cdots$
68.1.f.a	$68$	$1$	68.f	68.f	$4$	$2$	$1$	$0.034$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+iq^{2}-q^{4}+(-1-i)q^{5}-iq^{8}+\cdots$
80.1.h.a	$80$	$1$	80.h	20.d	$2$	$1$	$1$	$0.040$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots$
100.1.j.a	$100$	$1$	100.j	100.j	$10$	$4$	$1$	$0.050$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots$
116.1.j.a	$116$	$1$	116.j	116.j	$14$	$6$	$1$	$0.058$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+(\zeta_{14}^{4}-\zeta_{14}^{5}+\cdots)q^{5}+\cdots$
128.1.d.a	$128$	$1$	128.d	8.d	$2$	$1$	$1$	$0.064$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots$
144.1.g.a	$144$	$1$	144.g	4.b	$2$	$1$	$1$	$0.072$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-1}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-2q^{13}-q^{25}+2q^{37}+q^{49}+2q^{61}+\cdots$
148.1.i.a	$148$	$1$	148.i	148.i	$6$	$2$	$1$	$0.074$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
148.1.p.a	$148$	$1$	148.p	148.p	$18$	$6$	$1$	$0.074$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q-\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{6}+\cdots)q^{5}+\cdots$
160.1.p.a	$160$	$1$	160.p	5.c	$4$	$2$	$1$	$0.080$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots$
164.1.d.a	$164$	$1$	164.d	164.d	$2$	$1$	$1$	$0.082$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-41}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$1$	$0$	$-2$	$0$	$1$		$q+q^{2}+q^{4}-2q^{5}+q^{8}-q^{9}-2q^{10}+\cdots$
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		$4$	$0$	$-1$	$0$	$2$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{4}q^{4}+(\zeta_{10}-\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
180.1.f.a	$180$	$1$	180.f	20.d	$2$	$2$	$2$	$0.090$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{15}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}-iq^{5}+iq^{8}-q^{10}+\cdots$
180.1.m.a	$180$	$1$	180.m	60.l	$4$	$4$	$2$	$0.090$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots$
196.1.c.a	$196$	$1$	196.c	4.b	$2$	$1$	$1$	$0.098$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{7}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots$
196.1.g.a	$196$	$1$	196.g	28.g	$6$	$2$	$1$	$0.098$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{7}) $		$8$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
208.1.c.a	$208$	$1$	208.c	52.b	$2$	$1$	$1$	$0.104$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-13}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-q^{13}-2q^{17}+q^{25}-2q^{29}+\cdots$
208.1.y.a	$208$	$1$	208.y	52.i	$6$	$2$	$1$	$0.104$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{5}-\zeta_{6}q^{9}-\zeta_{6}^{2}q^{13}+\cdots$
212.1.i.a	$212$	$1$	212.i	212.i	$26$	$12$	$1$	$0.106$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{26}^{6}q^{2}+\zeta_{26}^{12}q^{4}+(\zeta_{26}^{8}+\zeta_{26}^{10}+\cdots)q^{5}+\cdots$
244.1.j.a	$244$	$1$	244.j	244.j	$6$	$2$	$1$	$0.122$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{5}+q^{8}+q^{9}+\cdots$
244.1.n.a	$244$	$1$	244.n	244.n	$10$	$4$	$1$	$0.122$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$3$	$0$	$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+(1-\zeta_{10})q^{5}+\cdots$
244.1.u.a	$244$	$1$	244.u	244.u	$30$	$8$	$1$	$0.122$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-6$	$0$	$1$		$q+\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{10}+\cdots)q^{5}+\cdots$
256.1.c.a	$256$	$1$	256.c	4.b	$2$	$1$	$1$	$0.128$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-2q^{17}-q^{25}-2q^{41}+q^{49}+\cdots$
260.1.g.a	$260$	$1$	260.g	260.g	$2$	$1$	$1$	$0.130$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $	✓	$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{9}-q^{10}+\cdots$
260.1.g.b	$260$	$1$	260.g	260.g	$2$	$1$	$1$	$0.130$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-65}) $	$\Q(\sqrt{65}) $	✓	$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{9}-q^{10}+\cdots$
260.1.l.a	$260$	$1$	260.l	260.l	$4$	$2$	$1$	$0.130$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-q^{4}+q^{5}+iq^{8}-iq^{9}-iq^{10}+\cdots$
260.1.s.a	$260$	$1$	260.s	260.s	$4$	$2$	$1$	$0.130$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}+iq^{5}-q^{8}+iq^{9}-iq^{10}+\cdots$
260.1.w.a	$260$	$1$	260.w	260.w	$6$	$2$	$1$	$0.130$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{5}+q^{8}+\cdots$
260.1.w.b	$260$	$1$	260.w	260.w	$6$	$2$	$1$	$0.130$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-q^{8}+\zeta_{6}q^{9}+\cdots$
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		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{2}q^{5}+\zeta_{12}^{3}q^{8}+\cdots$
272.1.u.a	$272$	$1$	272.u	68.g	$8$	$4$	$1$	$0.136$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{5}+\zeta_{8}q^{9}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{13}+\cdots$
288.1.e.a	$288$	$1$	288.e	3.b	$2$	$2$	$2$	$0.144$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{5}+\beta q^{17}-q^{25}+\beta q^{29}-2q^{37}+\cdots$
292.1.b.a	$292$	$1$	292.b	292.b	$2$	$1$	$1$	$0.146$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-73}) $	$\Q(\sqrt{73}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots$
292.1.h.a	$292$	$1$	292.h	292.h	$6$	$2$	$1$	$0.146$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+q^{8}+q^{9}+\cdots$
292.1.i.a	$292$	$1$	292.i	292.i	$6$	$2$	$1$	$0.146$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+q^{9}+(-1+\cdots)q^{13}+\cdots$
292.1.q.a	$292$	$1$	292.q	292.q	$18$	$6$	$1$	$0.146$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{2}q^{2}+\zeta_{18}^{4}q^{4}+(-\zeta_{18}-\zeta_{18}^{4}+\cdots)q^{5}+\cdots$
292.1.r.a	$292$	$1$	292.r	292.r	$18$	$6$	$1$	$0.146$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{7}q^{2}-\zeta_{18}^{5}q^{4}-\zeta_{18}^{2}q^{5}+\cdots$
20.2.e.a	$20$	$2$	20.e	20.e	$4$	$2$	$1$	$0.160$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$-4$	$0$	$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1-i)q^{2}+2iq^{4}+(-2+i)q^{5}+\cdots$
320.1.h.a	$320$	$1$	320.h	20.d	$2$	$1$	$1$	$0.160$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{5}-q^{9}+q^{25}-2q^{29}-2q^{41}+\cdots$
320.1.p.a	$320$	$1$	320.p	5.c	$4$	$2$	$1$	$0.160$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{5}+iq^{9}+(1-i)q^{13}+(-1-i+\cdots)q^{17}+\cdots$
324.1.d.a	$324$	$1$	324.d	4.b	$2$	$1$	$1$	$0.162$	$\Q$	$D_{3}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{13}+\cdots$
324.1.d.b	$324$	$1$	324.d	4.b	$2$	$1$	$1$	$0.162$	$\Q$	$D_{3}$	$\Q(\sqrt{-1}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}-q^{13}+\cdots$
324.1.f.a	$324$	$1$	324.f	36.f	$6$	$2$	$1$	$0.162$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}+q^{8}-q^{10}+\cdots$
324.1.f.b	$324$	$1$	324.f	36.f	$6$	$2$	$1$	$0.162$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}-q^{8}-q^{10}+\cdots$
340.1.ba.a	$340$	$1$	340.ba	340.aa	$8$	$4$	$1$	$0.170$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}-\zeta_{8}^{3}q^{8}+\cdots$
340.1.ba.b	$340$	$1$	340.ba	340.aa	$8$	$4$	$1$	$0.170$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{5}+\zeta_{8}^{3}q^{8}+\cdots$
340.1.bc.a	$340$	$1$	340.bc	340.ac	$16$	$8$	$1$	$0.170$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}-\zeta_{16}^{6}q^{5}+\cdots$

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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.