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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
39.1.d.a	$39$	$1$	39.d	39.d	$2$	$1$	$1$	$0.019$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-39}) $	$\Q(\sqrt{13}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}-q^{4}+q^{9}+q^{12}-q^{13}+q^{16}+\cdots$
57.1.h.a	$57$	$1$	57.h	57.h	$6$	$2$	$1$	$0.028$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-q^{7}-\zeta_{6}q^{9}+q^{12}+\cdots$
63.1.d.a	$63$	$1$	63.d	7.b	$2$	$1$	$1$	$0.031$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-7}) $	$\Q(\sqrt{21}) $	✓	$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q-q^{4}-q^{7}+q^{16}+q^{25}+q^{28}-2q^{37}+\cdots$
84.1.p.a	$84$	$1$	84.p	21.h	$6$	$2$	$1$	$0.042$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}-q^{13}+\cdots$
93.1.l.a	$93$	$1$	93.l	93.l	$10$	$4$	$1$	$0.046$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
108.1.c.a	$108$	$1$	108.c	3.b	$2$	$1$	$1$	$0.054$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-1$	$1$		$q-q^{7}-q^{13}-q^{19}+q^{25}+2q^{31}+\cdots$
111.1.d.a	$111$	$1$	111.d	111.d	$2$	$1$	$1$	$0.055$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-111}) $	$\Q(\sqrt{37}) $	✓	$4$	$0$	$0$	$1$	$0$	$-2$	$1$		$q+q^{3}-q^{4}-2q^{7}+q^{9}-q^{12}+q^{16}+\cdots$
111.1.h.a	$111$	$1$	111.h	111.h	$6$	$2$	$1$	$0.055$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q-\zeta_{6}q^{3}+\zeta_{6}q^{4}-\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
111.1.i.a	$111$	$1$	111.i	111.i	$6$	$2$	$1$	$0.055$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-\zeta_{6}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
117.1.j.a	$117$	$1$	117.j	13.d	$4$	$2$	$1$	$0.058$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+iq^{4}+(-1-i)q^{7}-iq^{13}-q^{16}+\cdots$
129.1.l.a	$129$	$1$	129.l	129.l	$14$	$6$	$1$	$0.064$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{14}^{5}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$
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}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-2q^{13}-q^{25}+2q^{37}+q^{49}+2q^{61}+\cdots$
147.1.l.a	$147$	$1$	147.l	147.l	$14$	$6$	$1$	$0.073$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}-\zeta_{14}^{3}q^{7}+\cdots$
156.1.o.a	$156$	$1$	156.o	39.i	$6$	$2$	$1$	$0.078$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$1$	$1$		$q-\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+\zeta_{6}^{2}q^{13}+\cdots$
156.1.s.a	$156$	$1$	156.s	39.h	$6$	$2$	$1$	$0.078$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-3$	$1$		$q+\zeta_{6}q^{3}+(-1-\zeta_{6})q^{7}+\zeta_{6}^{2}q^{9}+\cdots$
171.1.c.a	$171$	$1$	171.c	19.b	$2$	$1$	$1$	$0.085$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-19}) $	$\Q(\sqrt{57}) $	✓	$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+q^{4}-2q^{7}+q^{16}-q^{19}-q^{25}+\cdots$
171.1.p.a	$171$	$1$	171.p	19.d	$6$	$2$	$1$	$0.085$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-\zeta_{6}q^{4}+q^{7}+(-1+\zeta_{6}^{2})q^{13}+\zeta_{6}^{2}q^{16}+\cdots$
183.1.d.a	$183$	$1$	183.d	183.d	$2$	$1$	$1$	$0.091$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-183}) $	$\Q(\sqrt{61}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}-q^{4}+q^{9}-q^{12}-2q^{13}+q^{16}+\cdots$
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		$4$	$0$	$0$	$-1$	$0$	$3$	$1$		$q+\zeta_{10}^{4}q^{3}-\zeta_{10}^{3}q^{4}+(1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
189.1.m.a	$189$	$1$	189.m	7.d	$6$	$2$	$1$	$0.094$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{6}q^{4}-q^{7}+(-\zeta_{6}-\zeta_{6}^{2})q^{13}+\cdots$
189.1.q.a	$189$	$1$	189.q	21.h	$6$	$2$	$1$	$0.094$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{6}^{2}q^{4}+q^{7}-q^{13}-\zeta_{6}q^{16}-\zeta_{6}q^{19}+\cdots$
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}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-q^{9}+iq^{19}-q^{25}+iq^{27}+\cdots$
201.1.k.a	$201$	$1$	201.k	201.k	$22$	$10$	$1$	$0.100$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{22}^{7}q^{3}+\zeta_{22}^{6}q^{4}+(\zeta_{22}^{8}-\zeta_{22}^{9}+\cdots)q^{7}+\cdots$
219.1.c.a	$219$	$1$	219.c	219.c	$2$	$1$	$1$	$0.109$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-219}) $	$\Q(\sqrt{73}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}-2q^{19}+\cdots$
219.1.f.a	$219$	$1$	219.f	219.f	$4$	$2$	$1$	$0.109$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-iq^{3}+q^{4}+(-1+i)q^{7}-q^{9}-iq^{12}+\cdots$
219.1.i.a	$219$	$1$	219.i	219.i	$6$	$2$	$1$	$0.109$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-q^{3}+\zeta_{6}^{2}q^{4}+(\zeta_{6}+\zeta_{6}^{2})q^{7}+q^{9}+\cdots$
219.1.j.a	$219$	$1$	219.j	219.j	$6$	$2$	$1$	$0.109$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$-2$	$1$		$q+q^{3}+\zeta_{6}^{2}q^{4}-q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots$
219.1.o.a	$219$	$1$	219.o	219.o	$12$	$4$	$1$	$0.109$	$\Q(\zeta_{12})$	$D_{12}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{12}^{3}q^{3}-\zeta_{12}^{2}q^{4}+(\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{7}+\cdots$
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}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{4}-q^{16}-iq^{19}-q^{31}+iq^{49}+\cdots$
228.1.s.a	$228$	$1$	228.s	57.l	$18$	$6$	$1$	$0.114$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+(\zeta_{18}^{2}+\zeta_{18}^{4})q^{7}-\zeta_{18}^{7}q^{9}+\cdots$
237.1.k.a	$237$	$1$	237.k	237.k	$26$	$12$	$1$	$0.118$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{26}^{2}q^{3}-\zeta_{26}^{3}q^{4}+(\zeta_{26}^{8}-\zeta_{26}^{9}+\cdots)q^{7}+\cdots$
243.1.b.a	$243$	$1$	243.b	3.b	$2$	$1$	$1$	$0.121$	$\Q$	$D_{3}$	$\Q(\sqrt{-3}) $	None	✓	$2$	$0$	$0$	$0$	$0$	$-1$	$1$		$q+q^{4}-q^{7}-q^{13}+q^{16}-q^{19}+q^{25}+\cdots$
243.1.d.a	$243$	$1$	243.d	9.d	$6$	$2$	$1$	$0.121$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{7}-\zeta_{6}^{2}q^{13}-\zeta_{6}q^{16}+\cdots$
252.1.z.a	$252$	$1$	252.z	7.d	$6$	$2$	$1$	$0.126$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q-\zeta_{6}^{2}q^{7}+(\zeta_{6}+\zeta_{6}^{2})q^{13}+(-1-\zeta_{6}+\cdots)q^{19}+\cdots$
273.1.o.a	$273$	$1$	273.o	273.o	$4$	$2$	$1$	$0.136$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+iq^{3}+iq^{4}-iq^{7}-q^{9}-q^{12}+\cdots$
273.1.o.b	$273$	$1$	273.o	273.o	$4$	$2$	$1$	$0.136$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{3}+iq^{4}+q^{7}-q^{9}+q^{12}-iq^{13}+\cdots$
273.1.s.a	$273$	$1$	273.s	273.s	$6$	$2$	$1$	$0.136$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q+\zeta_{6}^{2}q^{3}+q^{4}+\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
273.1.x.a	$273$	$1$	273.x	273.x	$6$	$2$	$1$	$0.136$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-2$	$0$	$-1$	$1$		$q-q^{3}-\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots$
273.1.bm.a	$273$	$1$	273.bm	273.am	$6$	$2$	$1$	$0.136$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$2$	$0$	$-1$	$1$		$q+q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{7}+q^{9}+\zeta_{6}^{2}q^{12}+\cdots$
273.1.bp.a	$273$	$1$	273.bp	273.ap	$6$	$2$	$1$	$0.136$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q-\zeta_{6}^{2}q^{3}-q^{4}-\zeta_{6}^{2}q^{7}-\zeta_{6}q^{9}+\cdots$
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		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q-\zeta_{12}^{3}q^{3}-\zeta_{12}^{5}q^{4}+\zeta_{12}^{4}q^{7}+\cdots$
279.1.d.a	$279$	$1$	279.d	31.b	$2$	$1$	$1$	$0.139$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-31}) $	$\Q(\sqrt{93}) $	✓	$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-q^{4}+2q^{7}+q^{16}-2q^{19}-q^{25}+\cdots$
279.1.v.a	$279$	$1$	279.v	31.f	$10$	$4$	$1$	$0.139$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-2$	$1$		$q+\zeta_{10}q^{4}+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{7}+(-\zeta_{10}+\cdots)q^{13}+\cdots$
291.1.c.a	$291$	$1$	291.c	291.c	$2$	$1$	$1$	$0.145$	$\Q$	$D_{2}$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-291}) $	$\Q(\sqrt{97}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{4}+q^{9}-q^{12}+q^{16}-q^{25}+\cdots$
291.1.g.a	$291$	$1$	291.g	291.g	$4$	$2$	$1$	$0.145$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q-iq^{3}-q^{4}+(1-i)q^{7}-q^{9}+iq^{12}+\cdots$
291.1.k.a	$291$	$1$	291.k	291.k	$8$	$4$	$1$	$0.145$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$		$q-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{3})q^{7}+\cdots$
291.1.o.a	$291$	$1$	291.o	291.o	$16$	$8$	$1$	$0.145$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}q^{3}+\zeta_{16}^{6}q^{4}+(-\zeta_{16}+\zeta_{16}^{4}+\cdots)q^{7}+\cdots$
300.1.b.a	$300$	$1$	300.b	15.d	$2$	$2$	$2$	$0.150$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{3}-iq^{7}-q^{9}+iq^{13}+q^{19}+\cdots$

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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.