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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
1011.1.y.a	$1011$	$1$	1011.y	1011.y	$28$	$12$	$1$	$0.505$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{28}^{3}q^{3}-\zeta_{28}^{10}q^{4}+(-\zeta_{28}^{4}+\cdots)q^{7}+\cdots$
1012.1.r.a	$1012$	$1$	1012.r	253.k	$22$	$20$	$2$	$0.505$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$2$	$2$	$0$	$1$		$q+(\zeta_{66}^{2}-\zeta_{66}^{19})q^{3}+(-\zeta_{66}^{25}+\zeta_{66}^{32}+\cdots)q^{5}+\cdots$
1020.1.cl.a	$1020$	$1$	1020.cl	1020.bl	$16$	$16$	$2$	$0.509$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{32}^{11}q^{2}-\zeta_{32}^{15}q^{3}-\zeta_{32}^{6}q^{4}+\cdots$
1020.1.cl.b	$1020$	$1$	1020.cl	1020.bl	$16$	$16$	$2$	$0.509$	$\Q(\zeta_{32})$	$D_{16}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{32}^{9}q^{2}-\zeta_{32}^{15}q^{3}-\zeta_{32}^{2}q^{4}+\cdots$
1028.1.l.a	$1028$	$1$	1028.l	1028.l	$32$	$16$	$1$	$0.513$	$\Q(\zeta_{32})$	$D_{32}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{32}^{8}q^{2}-q^{4}+(\zeta_{32}^{2}+\zeta_{32}^{13}+\cdots)q^{5}+\cdots$
1029.1.n.a	$1029$	$1$	1029.n	147.n	$42$	$12$	$1$	$0.514$	$\Q(\zeta_{21})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\zeta_{42}^{13}q^{3}+\zeta_{42}^{4}q^{4}-\zeta_{42}^{5}q^{9}+\cdots$
1029.1.n.b	$1029$	$1$	1029.n	147.n	$42$	$12$	$1$	$0.514$	$\Q(\zeta_{21})$	$D_{7}$	$\Q(\sqrt{-3}) $	None		$8$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{42}^{13}q^{3}+\zeta_{42}^{4}q^{4}-\zeta_{42}^{5}q^{9}+\cdots$
1031.1.b.c	$1031$	$1$	1031.b	1031.b	$2$	$12$	$12$	$0.515$	$\Q(\zeta_{35})^+$	$D_{35}$	$\Q(\sqrt{-1031}) $	None	✓	$2$	$0$	$1$	$-4$	$1$	$0$	$1$		$q+\beta _{9}q^{2}+\beta _{5}q^{3}+(-\beta _{3}-\beta _{5}+\beta _{6}+\cdots)q^{4}+\cdots$
1032.1.bx.a	$1032$	$1$	1032.bx	1032.ax	$42$	$12$	$1$	$0.515$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-2$	$-1$	$0$	$0$	$1$		$q-\zeta_{42}^{15}q^{2}+\zeta_{42}q^{3}-\zeta_{42}^{9}q^{4}+\cdots$
1032.1.bx.b	$1032$	$1$	1032.bx	1032.ax	$42$	$12$	$1$	$0.515$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$2$	$1$	$0$	$0$	$1$		$q+\zeta_{42}^{15}q^{2}+\zeta_{42}^{4}q^{3}-\zeta_{42}^{9}q^{4}+\cdots$
1036.1.dl.a	$1036$	$1$	1036.dl	1036.cl	$36$	$12$	$1$	$0.517$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{36}^{4}q^{2}+\zeta_{36}^{8}q^{4}+\zeta_{36}^{13}q^{7}+\cdots$
1036.1.dl.b	$1036$	$1$	1036.dl	1036.cl	$36$	$12$	$1$	$0.517$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{36}^{3}q^{2}+\zeta_{36}^{6}q^{4}-\zeta_{36}^{13}q^{7}+\cdots$
1039.1.b.a	$1039$	$1$	1039.b	1039.b	$2$	$11$	$11$	$0.519$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1039}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q-\beta _{3}q^{2}+(1+\beta _{6})q^{4}+\beta _{2}q^{5}-\beta _{7}q^{7}+\cdots$
1044.1.ba.a	$1044$	$1$	1044.ba	116.h	$14$	$12$	$2$	$0.521$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-1}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}+(-\zeta_{28}+\zeta_{28}^{5}+\cdots)q^{5}+\cdots$
1045.1.w.f	$1045$	$1$	1045.w	1045.w	$10$	$16$	$4$	$0.522$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-95}) $	None		$8$	$0$	$0$	$0$	$4$	$0$	$1$		$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{11}+\zeta_{40}^{13}+\cdots)q^{3}+\cdots$
1048.1.s.a	$1048$	$1$	1048.s	1048.s	$26$	$12$	$1$	$0.523$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{26}^{5}q^{2}+(\zeta_{26}^{2}-\zeta_{26}^{3})q^{3}+\zeta_{26}^{10}q^{4}+\cdots$
1057.1.bq.a	$1057$	$1$	1057.bq	1057.aq	$50$	$20$	$1$	$0.528$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{50}^{12}-\zeta_{50}^{23})q^{2}+(\zeta_{50}^{10}-\zeta_{50}^{21}+\cdots)q^{4}+\cdots$
1060.1.z.a	$1060$	$1$	1060.z	1060.z	$26$	$12$	$1$	$0.529$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+\zeta_{26}^{10}q^{2}-\zeta_{26}^{7}q^{4}+\zeta_{26}^{9}q^{5}+\cdots$
1060.1.z.b	$1060$	$1$	1060.z	1060.z	$26$	$12$	$1$	$0.529$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q-\zeta_{26}^{10}q^{2}-\zeta_{26}^{7}q^{4}+\zeta_{26}^{8}q^{5}+\cdots$
1064.1.ef.c	$1064$	$1$	1064.ef	1064.df	$18$	$12$	$2$	$0.531$	$\Q(\zeta_{36})$	$D_{18}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$6$	$1$		$q+\zeta_{36}^{10}q^{2}+(-\zeta_{36}-\zeta_{36}^{7})q^{3}+\cdots$
1065.1.l.c	$1065$	$1$	1065.l	1065.l	$4$	$12$	$6$	$0.532$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(\zeta_{28}^{9}+\zeta_{28}^{12})q^{2}+\zeta_{28}q^{3}+(-\zeta_{28}^{4}+\cdots)q^{4}+\cdots$
1065.1.l.d	$1065$	$1$	1065.l	1065.l	$4$	$12$	$6$	$0.532$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$2$	$-2$	$0$	$0$	$1$		$q+(\zeta_{28}^{9}-\zeta_{28}^{12})q^{2}-\zeta_{28}^{6}q^{3}+(-\zeta_{28}^{4}+\cdots)q^{4}+\cdots$
1067.1.bg.a	$1067$	$1$	1067.bg	1067.ag	$48$	$16$	$1$	$0.533$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{48}^{5}-\zeta_{48}^{9})q^{3}+\zeta_{48}^{2}q^{4}+(-\zeta_{48}^{3}+\cdots)q^{5}+\cdots$
1083.1.p.a	$1083$	$1$	1083.p	1083.p	$38$	$18$	$1$	$0.540$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{38}^{6}q^{3}+\zeta_{38}^{2}q^{4}+(\zeta_{38}^{6}-\zeta_{38}^{9}+\cdots)q^{7}+\cdots$
1085.1.cp.a	$1085$	$1$	1085.cp	1085.bp	$12$	$12$	$3$	$0.541$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{36}^{7}+\zeta_{36}^{8})q^{2}+(\zeta_{36}^{14}+\zeta_{36}^{15}+\cdots)q^{4}+\cdots$
1085.1.cp.b	$1085$	$1$	1085.cp	1085.bp	$12$	$12$	$3$	$0.541$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{36}^{5}-\zeta_{36}^{10})q^{2}+(-\zeta_{36}^{2}+\cdots)q^{4}+\cdots$
1089.1.s.b	$1089$	$1$	1089.s	99.o	$30$	$16$	$2$	$0.543$	16.0.$\cdots$.1	$S_{4}$	None	None		$16$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{15})q^{5}+\cdots$
1096.1.s.a	$1096$	$1$	1096.s	1096.s	$34$	$16$	$1$	$0.547$	$\Q(\zeta_{34})$	$D_{17}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{34}^{7}q^{2}+(-\zeta_{34}^{3}+\zeta_{34}^{12})q^{3}+\cdots$
1096.1.u.a	$1096$	$1$	1096.u	1096.u	$34$	$16$	$1$	$0.547$	$\Q(\zeta_{34})$	$D_{34}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+\zeta_{34}q^{2}+(\zeta_{34}^{9}-\zeta_{34}^{15})q^{3}+\zeta_{34}^{2}q^{4}+\cdots$
1103.1.b.a	$1103$	$1$	1103.b	1103.b	$2$	$11$	$11$	$0.550$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-1103}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-\beta _{3}q^{2}+\beta _{4}q^{3}+(1+\beta _{6})q^{4}+(-\beta _{1}+\cdots)q^{6}+\cdots$
1121.1.l.a	$1121$	$1$	1121.l	1121.l	$18$	$18$	$3$	$0.559$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-59}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}^{7}-\zeta_{54}^{17})q^{3}+\zeta_{54}^{6}q^{4}+\cdots$
1127.1.v.a	$1127$	$1$	1127.v	161.n	$66$	$20$	$1$	$0.562$	$\Q(\zeta_{33})$	$D_{11}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q+(-\zeta_{66}^{23}-\zeta_{66}^{29})q^{2}+(-\zeta_{66}^{13}+\cdots)q^{4}+\cdots$
1127.1.x.a	$1127$	$1$	1127.x	161.p	$66$	$20$	$1$	$0.562$	$\Q(\zeta_{33})$	$D_{22}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$-2$	$0$	$0$	$0$	$1$		$q+(\zeta_{66}^{5}+\zeta_{66}^{29})q^{2}+(-\zeta_{66}+\zeta_{66}^{10}+\cdots)q^{4}+\cdots$
1133.1.s.a	$1133$	$1$	1133.s	1133.s	$34$	$16$	$1$	$0.565$	$\Q(\zeta_{34})$	$D_{17}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(-\zeta_{34}^{5}-\zeta_{34}^{9})q^{3}-\zeta_{34}^{11}q^{4}+\cdots$
1136.1.l.b	$1136$	$1$	1136.l	1136.l	$4$	$12$	$6$	$0.567$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$0$	$2$	$-2$	$0$	$1$		$q+\zeta_{28}^{3}q^{2}+(\zeta_{28}^{9}-\zeta_{28}^{12})q^{3}+\zeta_{28}^{6}q^{4}+\cdots$
1137.1.t.a	$1137$	$1$	1137.t	1137.t	$42$	$12$	$1$	$0.567$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$2$	$1$		$q+\zeta_{42}^{4}q^{3}+\zeta_{42}^{16}q^{4}+(\zeta_{42}^{4}-\zeta_{42}^{19}+\cdots)q^{7}+\cdots$
1141.1.bm.a	$1141$	$1$	1141.bm	1141.am	$54$	$18$	$1$	$0.569$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{54}^{6}+\zeta_{54}^{14})q^{2}+(-\zeta_{54}+\zeta_{54}^{12}+\cdots)q^{4}+\cdots$
1143.1.bo.a	$1143$	$1$	1143.bo	127.j	$42$	$12$	$1$	$0.570$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$-7$	$1$		$q+\zeta_{42}^{9}q^{4}+(-\zeta_{42}^{7}-\zeta_{42}^{10})q^{7}+\cdots$
1151.1.b.a	$1151$	$1$	1151.b	1151.b	$2$	$20$	$20$	$0.574$	$\Q(\zeta_{82})^+$	$D_{41}$	$\Q(\sqrt{-1151}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$	$1$		$q+\beta _{10}q^{2}+\beta _{16}q^{3}+(\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{4}+\cdots$
1156.1.l.a	$1156$	$1$	1156.l	1156.l	$34$	$16$	$1$	$0.577$	$\Q(\zeta_{34})$	$D_{34}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$1$	$0$	$-17$	$0$	$1$		$q-\zeta_{34}^{10}q^{2}-\zeta_{34}^{3}q^{4}+(-1+\zeta_{34}^{8}+\cdots)q^{5}+\cdots$
1156.1.m.a	$1156$	$1$	1156.m	1156.m	$34$	$16$	$1$	$0.577$	$\Q(\zeta_{34})$	$D_{17}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$15$	$0$	$1$		$q+\zeta_{34}^{6}q^{2}+\zeta_{34}^{12}q^{4}+(1-\zeta_{34}^{15}+\cdots)q^{5}+\cdots$
1161.1.by.a	$1161$	$1$	1161.by	129.o	$42$	$12$	$1$	$0.579$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$2$	$1$		$q+\zeta_{42}^{12}q^{4}+(-\zeta_{42}^{11}-\zeta_{42}^{17}+\cdots)q^{7}+\cdots$
1161.1.bz.a	$1161$	$1$	1161.bz	43.h	$42$	$12$	$1$	$0.579$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{42}^{3}q^{4}+(-\zeta_{42}+\zeta_{42}^{13})q^{7}+\cdots$
1164.1.br.a	$1164$	$1$	1164.br	291.v	$48$	$16$	$1$	$0.581$	$\Q(\zeta_{48})$	$D_{48}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{48}^{19}q^{3}+(\zeta_{48}^{3}-\zeta_{48}^{20})q^{7}+\cdots$
1168.1.cn.a	$1168$	$1$	1168.cn	292.u	$36$	$12$	$1$	$0.583$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{36}^{4}-\zeta_{36}^{7})q^{5}-\zeta_{36}^{12}q^{9}+(-\zeta_{36}^{9}+\cdots)q^{13}+\cdots$
1169.1.f.c	$1169$	$1$	1169.f	1169.f	$6$	$20$	$10$	$0.583$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-167}) $	None		$4$	$0$	$2$	$-1$	$0$	$1$	$1$		$q+(\zeta_{66}^{16}+\zeta_{66}^{28})q^{2}+(-\zeta_{66}^{9}-\zeta_{66}^{13}+\cdots)q^{3}+\cdots$
1176.1.be.a	$1176$	$1$	1176.be	168.ae	$6$	$16$	$8$	$0.587$	$\Q(\zeta_{48})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{48}^{4}q^{2}+\zeta_{48}^{5}q^{3}+\zeta_{48}^{8}q^{4}+\cdots$
1176.1.ck.a	$1176$	$1$	1176.ck	1176.bk	$42$	$12$	$1$	$0.587$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$1$	$1$	$1$		$q+\zeta_{42}^{13}q^{2}+\zeta_{42}^{11}q^{3}-\zeta_{42}^{5}q^{4}+\cdots$
1176.1.ck.b	$1176$	$1$	1176.ck	1176.bk	$42$	$12$	$1$	$0.587$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$-1$	$1$	$1$		$q-\zeta_{42}^{13}q^{2}-\zeta_{42}^{11}q^{3}-\zeta_{42}^{5}q^{4}+\cdots$
1183.1.t.a	$1183$	$1$	1183.t	91.t	$6$	$12$	$6$	$0.590$	12.0.$\cdots$.1	$D_{7}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\beta _{1}+\beta _{2}-\beta _{6})q^{2}+(-1+\beta _{3}+\beta _{5}+\cdots)q^{4}+\cdots$

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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.