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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
47.1.b.a	$47$	$1$	47.b	47.b	$2$	$2$	$2$	$0.023$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$
79.1.b.a	$79$	$1$	79.b	79.b	$2$	$2$	$2$	$0.039$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-79}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots$
95.1.d.b	$95$	$1$	95.d	95.d	$2$	$2$	$2$	$0.047$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-95}) $	None	✓	$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\beta q^{2}+\beta q^{3}+q^{4}-q^{5}-2q^{6}+q^{9}+\cdots$
103.1.b.a	$103$	$1$	103.b	103.b	$2$	$2$	$2$	$0.051$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-103}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots$
111.1.d.b	$111$	$1$	111.d	111.d	$2$	$2$	$2$	$0.055$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-111}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{5}+\beta q^{6}+q^{9}+\cdots$
119.1.d.a	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$2$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
119.1.d.b	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$-1$	$1$	$1$	$-2$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots$
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}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}+iq^{5}-q^{6}+iq^{8}+\cdots$
124.1.i.a	$124$	$1$	124.i	124.i	$6$	$4$	$2$	$0.062$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}-\zeta_{12}q^{3}-q^{4}-\zeta_{12}^{2}q^{5}+\cdots$
127.1.b.a	$127$	$1$	127.b	127.b	$2$	$2$	$2$	$0.063$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-127}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-q^{8}+q^{9}+\cdots$
131.1.b.a	$131$	$1$	131.b	131.b	$2$	$2$	$2$	$0.065$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}-\beta q^{7}+\cdots$
133.1.m.a	$133$	$1$	133.m	133.m	$6$	$4$	$2$	$0.066$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{2}q^{2}+\zeta_{12}^{5}q^{3}-\zeta_{12}^{5}q^{5}+\cdots$
143.1.d.a	$143$	$1$	143.d	143.d	$2$	$2$	$2$	$0.071$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-143}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
143.1.d.b	$143$	$1$	143.d	143.d	$2$	$2$	$2$	$0.071$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-143}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$1$	$1$		$q+(1-\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
155.1.c.b	$155$	$1$	155.c	155.c	$2$	$2$	$2$	$0.077$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{2}+(-1-\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{4}+\cdots$
159.1.d.a	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$-1$	$2$	$-1$	$-1$	$1$		$q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots$
159.1.d.b	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$1$	$-2$	$1$	$-1$	$1$		$q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+\beta q^{5}+\cdots$
164.1.d.b	$164$	$1$	164.d	164.d	$2$	$2$	$2$	$0.082$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-41}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}+\beta q^{7}-q^{8}+\cdots$
171.1.o.a	$171$	$1$	171.o	171.o	$6$	$4$	$2$	$0.085$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$-2$	$1$		$q+\zeta_{12}^{5}q^{2}+\zeta_{12}^{3}q^{3}+\zeta_{12}^{4}q^{5}+\cdots$
175.1.c.a	$175$	$1$	175.c	35.c	$2$	$2$	$2$	$0.087$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}+iq^{7}-iq^{8}-q^{9}-q^{11}+\cdots$
179.1.b.a	$179$	$1$	179.b	179.b	$2$	$2$	$2$	$0.089$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-179}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(1-\beta )q^{9}+\cdots$
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		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}-\zeta_{8}q^{8}+\cdots$
183.1.d.b	$183$	$1$	183.d	183.d	$2$	$2$	$2$	$0.091$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-183}) $	None	✓	$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-\beta q^{2}-q^{3}+q^{4}+\beta q^{6}+q^{9}+\beta q^{11}+\cdots$
184.1.e.b	$184$	$1$	184.e	184.e	$2$	$2$	$2$	$0.092$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}q^{4}+\cdots$
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}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{9}+iq^{19}-q^{25}+iq^{27}+\cdots$
200.1.e.a	$200$	$1$	200.e	40.e	$2$	$2$	$2$	$0.100$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{11}+\cdots$
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		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+\zeta_{12}^{5}q^{2}-\zeta_{12}^{2}q^{3}-\zeta_{12}^{2}q^{5}+\cdots$
219.1.j.b	$219$	$1$	219.j	219.j	$6$	$4$	$2$	$0.109$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots$
220.1.e.a	$220$	$1$	220.e	55.d	$2$	$2$	$2$	$0.110$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{6}+\zeta_{6}^{2})q^{3}-\zeta_{6}^{2}q^{5}+(-1-\zeta_{6}+\cdots)q^{9}+\cdots$
224.1.r.a	$224$	$1$	224.r	28.g	$6$	$4$	$2$	$0.112$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}^{5}q^{3}+\zeta_{12}^{4}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$
227.1.b.a	$227$	$1$	227.b	227.b	$2$	$2$	$2$	$0.113$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-227}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q+(-1+\beta )q^{3}+q^{4}-\beta q^{7}+(1-\beta )q^{9}+\cdots$
239.1.b.b	$239$	$1$	239.b	239.b	$2$	$2$	$2$	$0.119$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
240.1.bm.a	$240$	$1$	240.bm	240.am	$4$	$4$	$2$	$0.120$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots$
248.1.g.b	$248$	$1$	248.g	248.g	$2$	$2$	$2$	$0.124$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-62}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots$
248.1.g.c	$248$	$1$	248.g	248.g	$2$	$2$	$2$	$0.124$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$-1$	$0$	$0$	$2$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+(-\zeta_{6}-\zeta_{6}^{2})q^{5}+\cdots$
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		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{16}-\zeta_{16}^{3})q^{2}-\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
261.1.f.a	$261$	$1$	261.f	29.c	$4$	$4$	$2$	$0.130$	$\Q(\zeta_{8})$	$S_{4}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}-q^{7}+\zeta_{8}^{3}q^{8}+\cdots$
272.1.g.a	$272$	$1$	272.g	68.d	$2$	$2$	$2$	$0.136$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-17}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{3}+\beta q^{7}+q^{9}+\beta q^{11}-q^{17}+\cdots$
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		$4$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{5}+\zeta_{12}^{4}q^{6}+\cdots$
276.1.h.c	$276$	$1$	276.h	276.h	$2$	$2$	$2$	$0.138$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
276.1.h.d	$276$	$1$	276.h	276.h	$2$	$2$	$2$	$0.138$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-q^{8}+\cdots$
279.1.d.c	$279$	$1$	279.d	31.b	$2$	$2$	$2$	$0.139$	$\Q(\sqrt{3}) $	$D_{6}$	$\Q(\sqrt{-31}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\beta q^{2}+2q^{4}+\beta q^{5}-q^{7}-\beta q^{8}+\cdots$
283.1.b.b	$283$	$1$	283.b	283.b	$2$	$2$	$2$	$0.141$	$\Q(\sqrt{-2}) $	$S_{4}$	None	None		$2$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\beta q^{2}+\beta q^{3}-q^{4}+\beta q^{5}+2q^{6}+\cdots$
288.1.e.a	$288$	$1$	288.e	3.b	$2$	$2$	$2$	$0.144$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{5}+\beta q^{17}-q^{25}+\beta q^{29}-2q^{37}+\cdots$
288.1.o.a	$288$	$1$	288.o	36.f	$6$	$4$	$2$	$0.144$	$\Q(\zeta_{12})$	$A_{4}$	None	None		$4$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{5}+\zeta_{12}q^{7}-q^{9}+\cdots$

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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.