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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
116.1.j.a	$116$	$1$	116.j	116.j	$14$	$6$	$1$	$0.058$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+(\zeta_{14}^{4}-\zeta_{14}^{5}+\cdots)q^{5}+\cdots$
129.1.l.a	$129$	$1$	129.l	129.l	$14$	$6$	$1$	$0.064$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{14}^{5}q^{3}+\zeta_{14}^{4}q^{4}+(-\zeta_{14}+\zeta_{14}^{6}+\cdots)q^{7}+\cdots$
147.1.l.a	$147$	$1$	147.l	147.l	$14$	$6$	$1$	$0.073$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q+\zeta_{14}^{2}q^{3}+\zeta_{14}^{6}q^{4}-\zeta_{14}^{3}q^{7}+\cdots$
148.1.p.a	$148$	$1$	148.p	148.p	$18$	$6$	$1$	$0.074$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q-\zeta_{18}q^{2}+\zeta_{18}^{2}q^{4}+(\zeta_{18}^{4}+\zeta_{18}^{6}+\cdots)q^{5}+\cdots$
152.1.u.a	$152$	$1$	152.u	152.u	$18$	$6$	$1$	$0.076$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots$
161.1.l.a	$161$	$1$	161.l	161.l	$22$	$10$	$1$	$0.080$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{22}+\zeta_{22}^{8})q^{2}+(\zeta_{22}^{2}-\zeta_{22}^{5}+\cdots)q^{4}+\cdots$
191.1.b.a	$191$	$1$	191.b	191.b	$2$	$6$	$6$	$0.095$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-191}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q-\beta _{3}q^{2}-\beta _{1}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
201.1.k.a	$201$	$1$	201.k	201.k	$22$	$10$	$1$	$0.100$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{22}^{7}q^{3}+\zeta_{22}^{6}q^{4}+(\zeta_{22}^{8}-\zeta_{22}^{9}+\cdots)q^{7}+\cdots$
203.1.n.a	$203$	$1$	203.n	203.n	$14$	$6$	$1$	$0.101$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{14}^{3}+\zeta_{14}^{6})q^{2}+(\zeta_{14}^{2}-\zeta_{14}^{5}+\cdots)q^{4}+\cdots$
203.1.o.a	$203$	$1$	203.o	203.o	$14$	$6$	$1$	$0.101$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$1$	$1$		$q+(\zeta_{14}^{5}+\zeta_{14}^{6})q^{2}+(-\zeta_{14}^{3}-\zeta_{14}^{4}+\cdots)q^{4}+\cdots$
207.1.f.a	$207$	$1$	207.f	207.f	$6$	$6$	$3$	$0.103$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+\zeta_{18}^{2}q^{3}+(-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
216.1.r.a	$216$	$1$	216.r	216.r	$18$	$6$	$1$	$0.108$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\cdots$
217.1.n.a	$217$	$1$	217.n	217.n	$6$	$6$	$3$	$0.108$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(-\zeta_{18}+\zeta_{18}^{2}+\cdots)q^{4}+\cdots$
228.1.s.a	$228$	$1$	228.s	57.l	$18$	$6$	$1$	$0.114$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+(\zeta_{18}^{2}+\zeta_{18}^{4})q^{7}-\zeta_{18}^{7}q^{9}+\cdots$
244.1.u.a	$244$	$1$	244.u	244.u	$30$	$8$	$1$	$0.122$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-6$	$0$	$1$		$q+\zeta_{30}^{14}q^{2}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{10}+\cdots)q^{5}+\cdots$
253.1.k.a	$253$	$1$	253.k	253.k	$22$	$10$	$1$	$0.126$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(\zeta_{22}^{8}+\zeta_{22}^{10})q^{3}-\zeta_{22}^{5}q^{4}+(-\zeta_{22}+\cdots)q^{5}+\cdots$
255.1.y.a	$255$	$1$	255.y	255.y	$8$	$8$	$2$	$0.127$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{16}-\zeta_{16}^{3})q^{2}-\zeta_{16}^{7}q^{3}+(\zeta_{16}^{2}+\cdots)q^{4}+\cdots$
259.1.bi.a	$259$	$1$	259.bi	259.ai	$18$	$6$	$1$	$0.129$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}^{3}+\zeta_{18}^{4})q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
259.1.bo.a	$259$	$1$	259.bo	259.ao	$18$	$6$	$1$	$0.129$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{3}-\zeta_{18}^{7})q^{2}+(\zeta_{18}-\zeta_{18}^{5}+\cdots)q^{4}+\cdots$
263.1.b.a	$263$	$1$	263.b	263.b	$2$	$6$	$6$	$0.131$	$\Q(\zeta_{26})^+$	$D_{13}$	$\Q(\sqrt{-263}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\beta _{3}q^{2}+\beta _{2}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\cdots)q^{4}+\cdots$
285.1.bd.a	$285$	$1$	285.bd	285.ad	$18$	$6$	$1$	$0.142$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-3$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}+\zeta_{18}^{6})q^{2}+\zeta_{18}^{2}q^{3}+(-\zeta_{18}+\cdots)q^{4}+\cdots$
285.1.bd.b	$285$	$1$	285.bd	285.ad	$18$	$6$	$1$	$0.142$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$3$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}^{4}-\zeta_{18}^{6})q^{2}-\zeta_{18}^{2}q^{3}+\cdots$
291.1.o.a	$291$	$1$	291.o	291.o	$16$	$8$	$1$	$0.145$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}q^{3}+\zeta_{16}^{6}q^{4}+(-\zeta_{16}+\zeta_{16}^{4}+\cdots)q^{7}+\cdots$
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		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{18}^{7}q^{2}-\zeta_{18}^{5}q^{4}-\zeta_{18}^{2}q^{5}+\cdots$
297.1.q.a	$297$	$1$	297.q	297.q	$18$	$6$	$1$	$0.148$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$-3$	$0$	$1$		$q+\zeta_{18}^{8}q^{3}+\zeta_{18}^{2}q^{4}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{5}+\cdots$
299.1.h.a	$299$	$1$	299.h	299.h	$6$	$6$	$3$	$0.149$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{18}-\zeta_{18}^{5})q^{2}+(\zeta_{18}^{2}+\zeta_{18}^{4}+\cdots)q^{3}+\cdots$
299.1.j.a	$299$	$1$	299.j	299.j	$6$	$6$	$3$	$0.149$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{18}^{4}-\zeta_{18}^{8})q^{2}+(\zeta_{18}^{5}+\zeta_{18}^{7}+\cdots)q^{3}+\cdots$
301.1.v.a	$301$	$1$	301.v	301.v	$14$	$6$	$1$	$0.150$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$6$	$1$		$q+(-\zeta_{14}-\zeta_{14}^{3})q^{2}+(\zeta_{14}^{2}+\zeta_{14}^{4}+\cdots)q^{4}+\cdots$
311.1.b.a	$311$	$1$	311.b	311.b	$2$	$9$	$9$	$0.155$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-311}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
325.1.u.a	$325$	$1$	325.u	65.q	$12$	$8$	$2$	$0.162$	$\Q(\zeta_{24})$	$A_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{5}q^{2}-\zeta_{24}^{11}q^{3}-\zeta_{24}^{4}q^{6}+\cdots$
327.1.n.a	$327$	$1$	327.n	327.n	$18$	$6$	$1$	$0.163$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q+\zeta_{18}^{7}q^{3}-\zeta_{18}^{6}q^{4}+(\zeta_{18}^{2}+\zeta_{18}^{6}+\cdots)q^{7}+\cdots$
327.1.o.a	$327$	$1$	327.o	327.o	$18$	$6$	$1$	$0.163$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q+\zeta_{18}^{4}q^{3}+\zeta_{18}^{6}q^{4}+(-\zeta_{18}^{5}+\zeta_{18}^{6}+\cdots)q^{7}+\cdots$
328.1.z.a	$328$	$1$	328.z	328.z	$20$	$8$	$1$	$0.164$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{20}^{7}q^{2}+(-\zeta_{20}^{2}+\zeta_{20}^{3})q^{3}+\cdots$
329.1.f.b	$329$	$1$	329.f	329.f	$6$	$8$	$4$	$0.164$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-1$	$2$	$0$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}^{11}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$
340.1.bc.a	$340$	$1$	340.bc	340.ac	$16$	$8$	$1$	$0.170$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}-\zeta_{16}^{6}q^{5}+\cdots$
340.1.bj.a	$340$	$1$	340.bj	340.aj	$16$	$8$	$1$	$0.170$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+\zeta_{16}^{3}q^{5}+\cdots$
341.1.by.a	$341$	$1$	341.by	341.ay	$30$	$8$	$1$	$0.170$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$-1$	$0$	$1$		$q+(\zeta_{30}^{2}+\zeta_{30}^{14})q^{3}-\zeta_{30}^{9}q^{4}+(\zeta_{30}^{8}+\cdots)q^{5}+\cdots$
343.1.d.a	$343$	$1$	343.d	7.d	$6$	$6$	$3$	$0.171$	6.0.64827.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{2}+(-1+\cdots)q^{4}+\cdots$
344.1.s.a	$344$	$1$	344.s	344.s	$14$	$6$	$1$	$0.172$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{14}^{2}q^{2}+(-\zeta_{14}+\zeta_{14}^{2})q^{3}+\zeta_{14}^{4}q^{4}+\cdots$
345.1.p.a	$345$	$1$	345.p	345.p	$22$	$10$	$1$	$0.172$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$0$	$1$		$q+(-\zeta_{22}^{3}-\zeta_{22}^{5})q^{2}+\zeta_{22}^{10}q^{3}+\cdots$
345.1.p.b	$345$	$1$	345.p	345.p	$22$	$10$	$1$	$0.172$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$2$	$1$	$1$	$0$	$1$		$q+(\zeta_{22}^{3}+\zeta_{22}^{5})q^{2}-\zeta_{22}^{10}q^{3}+(\zeta_{22}^{6}+\cdots)q^{4}+\cdots$
355.1.c.b	$355$	$1$	355.c	355.c	$2$	$6$	$6$	$0.177$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{14}^{2}+\zeta_{14}^{5})q^{2}+(-\zeta_{14}-\zeta_{14}^{6}+\cdots)q^{3}+\cdots$
356.1.j.a	$356$	$1$	356.j	356.j	$22$	$10$	$1$	$0.178$	$\Q(\zeta_{22})$	$D_{22}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-2$	$0$	$1$		$q+\zeta_{22}^{3}q^{2}+\zeta_{22}^{6}q^{4}+(\zeta_{22}^{8}+\zeta_{22}^{10}+\cdots)q^{5}+\cdots$
356.1.l.a	$356$	$1$	356.l	356.l	$22$	$10$	$1$	$0.178$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{22}^{6}q^{2}-\zeta_{22}q^{4}+(-\zeta_{22}^{5}-\zeta_{22}^{9}+\cdots)q^{5}+\cdots$
359.1.b.a	$359$	$1$	359.b	359.b	$2$	$9$	$9$	$0.179$	$\Q(\zeta_{38})^+$	$D_{19}$	$\Q(\sqrt{-359}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5}+\cdots)q^{2}+\cdots$
372.1.be.a	$372$	$1$	372.be	93.o	$30$	$8$	$1$	$0.186$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q-\zeta_{30}^{7}q^{3}+(\zeta_{30}^{4}-\zeta_{30}^{13})q^{7}+\zeta_{30}^{14}q^{9}+\cdots$
381.1.m.a	$381$	$1$	381.m	381.m	$14$	$6$	$1$	$0.190$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$5$	$1$		$q+\zeta_{14}^{6}q^{3}-\zeta_{14}^{3}q^{4}+(1-\zeta_{14})q^{7}+\cdots$
383.1.b.a	$383$	$1$	383.b	383.b	$2$	$8$	$8$	$0.191$	$\Q(\zeta_{34})^+$	$D_{17}$	$\Q(\sqrt{-383}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+\beta _{6}q^{2}+\beta _{4}q^{3}+(1-\beta _{5})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$
387.1.w.a	$387$	$1$	387.w	43.f	$14$	$6$	$1$	$0.193$	$\Q(\zeta_{14})$	$D_{14}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{14}q^{4}+(-\zeta_{14}^{2}-\zeta_{14}^{5})q^{7}+(-\zeta_{14}^{4}+\cdots)q^{13}+\cdots$

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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.