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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
120.1.i.a	$120$	$1$	120.i	120.i	$2$	$2$	$2$	$0.060$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}+iq^{5}-q^{6}+iq^{8}+\cdots$
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		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots$
192.1.h.a	$192$	$1$	192.h	24.h	$2$	$2$	$2$	$0.096$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{6}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{9}+iq^{19}-q^{25}+iq^{27}+\cdots$
195.1.e.a	$195$	$1$	195.e	195.e	$2$	$4$	$4$	$0.097$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots$
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}) $		$8$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{9}+\cdots$
225.1.g.a	$225$	$1$	225.g	5.c	$4$	$2$	$1$	$0.112$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-15}) $	$\Q(\sqrt{5}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{4}-q^{16}-iq^{19}-q^{31}+iq^{49}+\cdots$
240.1.bm.a	$240$	$1$	240.bm	240.am	$4$	$4$	$2$	$0.120$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots$
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.h.e	$255$	$1$	255.h	255.h	$2$	$2$	$2$	$0.127$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-51}) $	$\Q(\sqrt{85}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{4}-iq^{5}-q^{9}+iq^{12}+\cdots$
255.1.i.a	$255$	$1$	255.i	255.i	$4$	$4$	$2$	$0.127$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{3}q^{3}-q^{4}+\cdots$
255.1.y.a	$255$	$1$	255.y	255.y	$8$	$8$	$2$	$0.127$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{16}-\zeta_{16}^{3})q^{2}-\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
280.1.c.a	$280$	$1$	280.c	280.c	$2$	$4$	$4$	$0.140$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
312.1.b.a	$312$	$1$	312.b	312.b	$2$	$4$	$4$	$0.156$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
325.1.u.a	$325$	$1$	325.u	65.q	$12$	$8$	$2$	$0.162$	$\Q(\zeta_{24})$	$A_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{5}q^{2}-\zeta_{24}^{11}q^{3}-\zeta_{24}^{4}q^{6}+\cdots$
360.1.u.a	$360$	$1$	360.u	40.i	$4$	$4$	$2$	$0.180$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots$
385.1.q.c	$385$	$1$	385.q	385.q	$6$	$4$	$2$	$0.192$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{2}+(-1-\zeta_{12}^{2}+\cdots)q^{4}+\cdots$
392.1.j.a	$392$	$1$	392.j	56.j	$6$	$2$	$1$	$0.196$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $		$8$	$0$	$1$	$0$	$0$	$0$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-q^{8}+\zeta_{6}q^{9}-\zeta_{6}q^{16}+\cdots$
392.1.k.a	$392$	$1$	392.k	56.k	$6$	$2$	$1$	$0.196$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $		$8$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
392.1.k.b	$392$	$1$	392.k	56.k	$6$	$4$	$2$	$0.196$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\beta _{3}q^{6}+\cdots$
396.1.d.a	$396$	$1$	396.d	132.d	$2$	$4$	$4$	$0.198$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{11}) $		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+\zeta_{8}^{2}q^{2}-q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
420.1.o.a	$420$	$1$	420.o	420.o	$2$	$2$	$2$	$0.210$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}-iq^{7}+\cdots$
420.1.o.b	$420$	$1$	420.o	420.o	$2$	$2$	$2$	$0.210$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{2}-iq^{3}-q^{4}+q^{5}+q^{6}-iq^{7}+\cdots$
420.1.be.a	$420$	$1$	420.be	420.ae	$6$	$4$	$2$	$0.210$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{5}+\cdots$
420.1.be.b	$420$	$1$	420.be	420.ae	$6$	$4$	$2$	$0.210$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$
429.1.v.c	$429$	$1$	429.v	429.v	$10$	$8$	$2$	$0.214$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(-\zeta_{20}+\zeta_{20}^{5})q^{2}-\zeta_{20}^{4}q^{3}+(-1+\cdots)q^{4}+\cdots$
435.1.b.a	$435$	$1$	435.b	435.b	$2$	$4$	$4$	$0.217$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{145}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+\cdots$
440.1.o.e	$440$	$1$	440.o	440.o	$2$	$4$	$4$	$0.220$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$
441.1.m.a	$441$	$1$	441.m	7.d	$6$	$2$	$1$	$0.220$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{16}+\zeta_{6}^{2}q^{25}+\zeta_{6}q^{37}+\cdots$
441.1.q.a	$441$	$1$	441.q	21.h	$6$	$4$	$2$	$0.220$	$\Q(\sqrt{-2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{1}q^{2}+\beta _{2}q^{4}+(-\beta _{1}+\beta _{3})q^{11}+\cdots$
455.1.h.c	$455$	$1$	455.h	455.h	$2$	$2$	$2$	$0.227$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-91}) $	$\Q(\sqrt{65}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{4}-iq^{5}-iq^{7}-q^{9}-iq^{13}+\cdots$
455.1.be.a	$455$	$1$	455.be	455.ae	$6$	$4$	$2$	$0.227$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{12}+\zeta_{12}^{3})q^{3}-\zeta_{12}^{4}q^{4}+\zeta_{12}^{3}q^{5}+\cdots$
468.1.e.c	$468$	$1$	468.e	52.b	$2$	$2$	$2$	$0.234$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{39}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-q^{4}+iq^{5}+iq^{8}+2q^{10}+\cdots$
468.1.o.a	$468$	$1$	468.o	156.l	$4$	$4$	$2$	$0.234$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{8}+q^{13}+\cdots$
468.1.q.a	$468$	$1$	468.q	52.i	$6$	$4$	$2$	$0.234$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
468.1.bx.a	$468$	$1$	468.bx	156.v	$12$	$8$	$2$	$0.234$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+(-\zeta_{24}-\zeta_{24}^{5}+\cdots)q^{5}+\cdots$
476.1.o.c	$476$	$1$	476.o	476.o	$6$	$4$	$2$	$0.238$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-17}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+\zeta_{12}^{2}q^{2}+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\cdots$
480.1.c.a	$480$	$1$	480.c	15.d	$2$	$4$	$4$	$0.240$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots$
480.1.i.a	$480$	$1$	480.i	120.i	$2$	$2$	$2$	$0.240$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{10}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-iq^{5}-q^{9}-q^{15}-q^{25}+\cdots$
480.1.bu.a	$480$	$1$	480.bu	480.au	$8$	$8$	$2$	$0.240$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{7}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
484.1.f.a	$484$	$1$	484.f	11.d	$10$	$4$	$1$	$0.242$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$1$	$1$	$0$	$1$		$q-\zeta_{10}^{4}q^{3}-\zeta_{10}^{2}q^{5}-\zeta_{10}q^{15}+\cdots$
484.1.h.a	$484$	$1$	484.h	44.h	$10$	$4$	$1$	$0.242$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$-1$	$0$	$1$	$0$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}-\zeta_{10}^{3}q^{8}+\cdots$
484.1.h.b	$484$	$1$	484.h	44.h	$10$	$4$	$1$	$0.242$	$\Q(\zeta_{10})$	$D_{3}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$1$	$0$	$1$	$0$	$1$		$q+\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+\zeta_{10}^{3}q^{8}+\cdots$
500.1.h.a	$500$	$1$	500.h	100.h	$10$	$8$	$2$	$0.250$	$\Q(\zeta_{20})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{20}q^{2}+\zeta_{20}^{2}q^{4}-\zeta_{20}^{3}q^{8}-\zeta_{20}^{4}q^{9}+\cdots$
504.1.e.a	$504$	$1$	504.e	168.e	$2$	$4$	$4$	$0.252$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
504.1.l.b	$504$	$1$	504.l	56.h	$2$	$2$	$2$	$0.252$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{42}) $		$8$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{2}-q^{4}+q^{7}+iq^{8}-iq^{11}+\cdots$
504.1.bn.c	$504$	$1$	504.bn	504.an	$6$	$4$	$2$	$0.252$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$2$	$0$	$0$	$2$	$1$		$q+\zeta_{12}^{2}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{4}+\cdots$
504.1.bw.a	$504$	$1$	504.bw	56.j	$6$	$4$	$2$	$0.252$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{4}q^{4}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{5}+\cdots$
507.1.h.a	$507$	$1$	507.h	39.h	$6$	$2$	$1$	$0.253$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$1$	$0$	$0$	$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{4}+\zeta_{6}^{2}q^{9}+q^{12}+\cdots$
507.1.i.a	$507$	$1$	507.i	39.i	$6$	$2$	$1$	$0.253$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $		$8$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{9}-q^{12}+\cdots$

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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.