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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
212.1.i.a	$212$	$1$	212.i	212.i	$26$	$12$	$1$	$0.106$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{26}^{6}q^{2}+\zeta_{26}^{12}q^{4}+(\zeta_{26}^{8}+\zeta_{26}^{10}+\cdots)q^{5}+\cdots$
237.1.k.a	$237$	$1$	237.k	237.k	$26$	$12$	$1$	$0.118$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{26}^{2}q^{3}-\zeta_{26}^{3}q^{4}+(\zeta_{26}^{8}-\zeta_{26}^{9}+\cdots)q^{7}+\cdots$
301.1.bc.a	$301$	$1$	301.bc	301.ac	$42$	$12$	$1$	$0.150$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$-6$	$1$		$q+(\zeta_{42}^{16}+\zeta_{42}^{20})q^{2}+(-\zeta_{42}^{11}+\cdots)q^{4}+\cdots$
309.1.l.a	$309$	$1$	309.l	309.l	$34$	$16$	$1$	$0.154$	$\Q(\zeta_{34})$	$D_{17}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{34}^{6}q^{3}-\zeta_{34}^{7}q^{4}+(\zeta_{34}^{4}-\zeta_{34}^{9}+\cdots)q^{7}+\cdots$
344.1.be.a	$344$	$1$	344.be	344.ae	$42$	$12$	$1$	$0.172$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-2$	$2$	$0$	$0$	$1$		$q-\zeta_{42}^{15}q^{2}+(\zeta_{42}^{8}-\zeta_{42}^{11})q^{3}+\cdots$
371.1.n.a	$371$	$1$	371.n	371.n	$26$	$12$	$1$	$0.185$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{26}+\zeta_{26}^{6})q^{2}+(\zeta_{26}^{2}-\zeta_{26}^{7}+\cdots)q^{4}+\cdots$
371.1.o.a	$371$	$1$	371.o	371.o	$26$	$12$	$1$	$0.185$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$0$	$0$	$0$	$-1$	$1$		$q+(-\zeta_{26}^{8}-\zeta_{26}^{9})q^{2}+(-\zeta_{26}^{3}-\zeta_{26}^{4}+\cdots)q^{4}+\cdots$
381.1.t.a	$381$	$1$	381.t	381.t	$42$	$12$	$1$	$0.190$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-5$	$1$		$q-\zeta_{42}^{11}q^{3}-\zeta_{42}^{9}q^{4}+(\zeta_{42}^{14}-\zeta_{42}^{17}+\cdots)q^{7}+\cdots$
404.1.o.a	$404$	$1$	404.o	404.o	$50$	$20$	$1$	$0.202$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{50}^{4}q^{2}+\zeta_{50}^{8}q^{4}+(\zeta_{50}^{18}+\zeta_{50}^{24}+\cdots)q^{5}+\cdots$
27.2.e.a	$27$	$2$	27.e	27.e	$9$	$12$	$2$	$0.216$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$-6$	$-6$	$-3$	$-6$	$3$	$\mathrm{SU}(2)[C_{9}]$	$q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots$
436.1.v.a	$436$	$1$	436.v	436.v	$54$	$18$	$1$	$0.218$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{15}q^{2}-\zeta_{54}^{3}q^{4}+(\zeta_{54}^{8}+\zeta_{54}^{14}+\cdots)q^{5}+\cdots$
452.1.p.a	$452$	$1$	452.p	452.p	$28$	$12$	$1$	$0.226$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$2$	$0$	$1$		$q+\zeta_{28}^{4}q^{2}+\zeta_{28}^{8}q^{4}+(-\zeta_{28}+\zeta_{28}^{10}+\cdots)q^{5}+\cdots$
453.1.t.a	$453$	$1$	453.t	453.t	$50$	$20$	$1$	$0.226$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{11}q^{3}-\zeta_{50}^{15}q^{4}+(\zeta_{50}^{6}-\zeta_{50}^{23}+\cdots)q^{7}+\cdots$
29.2.e.a	$29$	$2$	29.e	29.e	$14$	$12$	$2$	$0.232$	12.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$-7$	$-7$	$-1$	$-11$	$1$	$\mathrm{SU}(2)[C_{14}]$	$q+(-1+\beta _{3}+\beta _{7}+\beta _{9}+\beta _{10})q^{2}+\cdots$
469.1.bl.a	$469$	$1$	469.bl	469.al	$66$	$20$	$1$	$0.234$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$2$	$0$	$0$	$1$	$1$		$q+(\zeta_{66}^{10}+\zeta_{66}^{16})q^{2}+(\zeta_{66}^{20}+\zeta_{66}^{26}+\cdots)q^{4}+\cdots$
471.1.n.a	$471$	$1$	471.n	471.n	$26$	$12$	$1$	$0.235$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+\zeta_{26}^{2}q^{3}+\zeta_{26}^{11}q^{4}+(\zeta_{26}^{5}+\zeta_{26}^{12}+\cdots)q^{7}+\cdots$
471.1.o.a	$471$	$1$	471.o	471.o	$26$	$12$	$1$	$0.235$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{26}^{3}q^{3}+\zeta_{26}^{10}q^{4}+(-\zeta_{26}-\zeta_{26}^{5}+\cdots)q^{7}+\cdots$
489.1.p.a	$489$	$1$	489.p	489.p	$54$	$18$	$1$	$0.244$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{54}^{14}q^{3}-\zeta_{54}^{23}q^{4}+(\zeta_{54}^{12}+\cdots)q^{7}+\cdots$
31.2.g.a	$31$	$2$	31.g	31.g	$15$	$16$	$2$	$0.248$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$2$	$0$	$-6$	$-12$	$-3$	$2$	$1$	$\mathrm{SU}(2)[C_{15}]$	$q+(-1-\beta _{1}+\beta _{3}-\beta _{4}+\beta _{5}+\beta _{6}+\cdots)q^{2}+\cdots$
500.1.p.a	$500$	$1$	500.p	500.p	$50$	$20$	$1$	$0.250$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{50}^{13}q^{2}-\zeta_{50}q^{4}-\zeta_{50}^{9}q^{5}+\cdots$
507.1.n.a	$507$	$1$	507.n	507.n	$26$	$12$	$1$	$0.253$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+\zeta_{26}^{7}q^{3}-\zeta_{26}^{2}q^{4}+(\zeta_{26}^{9}+\zeta_{26}^{10}+\cdots)q^{7}+\cdots$
507.1.o.a	$507$	$1$	507.o	507.o	$26$	$12$	$1$	$0.253$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{26}^{7}q^{3}+\zeta_{26}^{2}q^{4}+(-\zeta_{26}^{9}+\zeta_{26}^{10}+\cdots)q^{7}+\cdots$
516.1.z.a	$516$	$1$	516.z	129.o	$42$	$12$	$1$	$0.258$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q-\zeta_{42}q^{3}+(\zeta_{42}^{10}+\zeta_{42}^{18})q^{7}+\zeta_{42}^{2}q^{9}+\cdots$
536.1.ba.a	$536$	$1$	536.ba	536.aa	$66$	$20$	$1$	$0.267$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$2$	$0$	$0$	$1$		$q-\zeta_{66}^{23}q^{2}+(\zeta_{66}^{14}-\zeta_{66}^{31})q^{3}+\cdots$
548.1.j.a	$548$	$1$	548.j	548.j	$34$	$16$	$1$	$0.273$	$\Q(\zeta_{34})$	$D_{34}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+\zeta_{34}^{10}q^{2}-\zeta_{34}^{3}q^{4}+(-\zeta_{34}+\zeta_{34}^{13}+\cdots)q^{5}+\cdots$
548.1.k.a	$548$	$1$	548.k	548.k	$34$	$16$	$1$	$0.273$	$\Q(\zeta_{34})$	$D_{17}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{34}^{7}q^{2}+\zeta_{34}^{14}q^{4}+(\zeta_{34}^{4}+\zeta_{34}^{16}+\cdots)q^{5}+\cdots$
553.1.x.a	$553$	$1$	553.x	553.x	$26$	$12$	$1$	$0.276$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(\zeta_{26}^{2}+\zeta_{26}^{12})q^{2}+(-\zeta_{26}+\zeta_{26}^{4}+\cdots)q^{4}+\cdots$
579.1.s.a	$579$	$1$	579.s	579.s	$32$	$16$	$1$	$0.289$	$\Q(\zeta_{32})$	$D_{32}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{32}^{10}q^{3}-\zeta_{32}^{2}q^{4}+(\zeta_{32}+\zeta_{32}^{7}+\cdots)q^{7}+\cdots$
580.1.y.c	$580$	$1$	580.y	580.y	$14$	$12$	$2$	$0.289$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{28}^{9}q^{2}+(\zeta_{28}+\zeta_{28}^{5})q^{3}-\zeta_{28}^{4}q^{4}+\cdots$
580.1.bd.a	$580$	$1$	580.bd	580.ad	$28$	$12$	$1$	$0.289$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-\zeta_{28}^{2}q^{2}+\zeta_{28}^{4}q^{4}-\zeta_{28}q^{5}-\zeta_{28}^{6}q^{8}+\cdots$
580.1.bm.a	$580$	$1$	580.bm	580.am	$28$	$12$	$1$	$0.289$	$\Q(\zeta_{28})$	$D_{28}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{28}^{3}q^{2}+\zeta_{28}^{6}q^{4}+\zeta_{28}q^{5}+\zeta_{28}^{9}q^{8}+\cdots$
583.1.n.a	$583$	$1$	583.n	583.n	$26$	$12$	$1$	$0.291$	$\Q(\zeta_{26})$	$D_{26}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{26}^{6}-\zeta_{26}^{11})q^{3}+\zeta_{26}q^{4}+\cdots$
583.1.o.a	$583$	$1$	583.o	583.o	$26$	$12$	$1$	$0.291$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(-\zeta_{26}^{9}+\zeta_{26}^{10})q^{3}+\zeta_{26}^{8}q^{4}+\cdots$
584.1.br.a	$584$	$1$	584.br	584.ar	$36$	$12$	$1$	$0.291$	$\Q(\zeta_{36})$	$D_{36}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{36}^{2}q^{2}+(\zeta_{36}^{5}-\zeta_{36}^{7})q^{3}+\zeta_{36}^{4}q^{4}+\cdots$
588.1.z.a	$588$	$1$	588.z	147.n	$42$	$12$	$1$	$0.293$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$1$	$1$		$q+\zeta_{42}^{10}q^{3}+\zeta_{42}^{8}q^{7}+\zeta_{42}^{20}q^{9}+\cdots$
589.1.bg.a	$589$	$1$	589.bg	589.ag	$18$	$18$	$3$	$0.294$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-31}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}^{17}-\zeta_{54}^{25})q^{2}+(-\zeta_{54}^{7}+\cdots)q^{4}+\cdots$
37.2.h.a	$37$	$2$	37.h	37.h	$18$	$18$	$3$	$0.295$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$-9$	$-9$	$-3$	$-3$	$1$	$\mathrm{SU}(2)[C_{18}]$	$q+(\beta _{4}-\beta _{11})q^{2}+(-1-\beta _{12}+\beta _{16}+\cdots)q^{3}+\cdots$
597.1.s.a	$597$	$1$	597.s	597.s	$66$	$20$	$1$	$0.298$	$\Q(\zeta_{33})$	$D_{33}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$-1$	$1$		$q-\zeta_{66}^{7}q^{3}+\zeta_{66}^{32}q^{4}+(\zeta_{66}^{12}-\zeta_{66}^{29}+\cdots)q^{7}+\cdots$
621.1.k.a	$621$	$1$	621.k	621.k	$18$	$18$	$3$	$0.310$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{54}+\zeta_{54}^{20})q^{2}-\zeta_{54}^{5}q^{3}+\cdots$
628.1.o.a	$628$	$1$	628.o	628.o	$26$	$12$	$1$	$0.313$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{26}^{5}q^{2}+\zeta_{26}^{10}q^{4}+(\zeta_{26}^{10}-\zeta_{26}^{11}+\cdots)q^{5}+\cdots$
639.1.g.b	$639$	$1$	639.g	639.g	$6$	$12$	$6$	$0.319$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-71}) $	None		$4$	$0$	$-1$	$1$	$2$	$0$	$1$		$q+(-\zeta_{42}^{3}+\zeta_{42}^{4})q^{2}-\zeta_{42}^{19}q^{3}+\cdots$
647.1.b.a	$647$	$1$	647.b	647.b	$2$	$11$	$11$	$0.323$	$\Q(\zeta_{46})^+$	$D_{23}$	$\Q(\sqrt{-647}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q-\beta _{3}q^{2}-\beta _{5}q^{3}+(1+\beta _{6})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots$
648.1.bf.a	$648$	$1$	648.bf	648.af	$54$	$18$	$1$	$0.323$	$\Q(\zeta_{54})$	$D_{27}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{54}^{7}q^{2}-\zeta_{54}^{19}q^{3}+\zeta_{54}^{14}q^{4}+\cdots$
667.1.i.b	$667$	$1$	667.i	667.i	$14$	$12$	$2$	$0.333$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$-5$	$2$	$0$	$0$	$1$		$q+(-\zeta_{42}+\zeta_{42}^{14})q^{2}+(\zeta_{42}^{16}-\zeta_{42}^{17}+\cdots)q^{3}+\cdots$
667.1.k.b	$667$	$1$	667.k	667.k	$14$	$12$	$2$	$0.333$	$\Q(\zeta_{21})$	$D_{42}$	$\Q(\sqrt{-23}) $	None		$4$	$0$	$7$	$0$	$0$	$0$	$1$		$q+(\zeta_{42}^{7}+\zeta_{42}^{8})q^{2}+(\zeta_{42}^{2}-\zeta_{42}^{10}+\cdots)q^{3}+\cdots$
676.1.o.a	$676$	$1$	676.o	676.o	$26$	$12$	$1$	$0.337$	$\Q(\zeta_{26})$	$D_{13}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q+\zeta_{26}^{8}q^{2}-\zeta_{26}^{3}q^{4}+(\zeta_{26}^{2}+\zeta_{26}^{12}+\cdots)q^{5}+\cdots$
687.1.n.a	$687$	$1$	687.n	687.n	$38$	$18$	$1$	$0.343$	$\Q(\zeta_{38})$	$D_{38}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{38}^{8}q^{3}-\zeta_{38}^{6}q^{4}+(-\zeta_{38}-\zeta_{38}^{16}+\cdots)q^{7}+\cdots$
687.1.p.a	$687$	$1$	687.p	687.p	$38$	$18$	$1$	$0.343$	$\Q(\zeta_{38})$	$D_{19}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q+\zeta_{38}^{16}q^{3}+\zeta_{38}^{12}q^{4}+(\zeta_{38}^{2}-\zeta_{38}^{13}+\cdots)q^{7}+\cdots$
693.1.bp.a	$693$	$1$	693.bp	231.r	$10$	$16$	$4$	$0.346$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{2}+\zeta_{40}^{8}+\cdots)q^{4}+\cdots$
696.1.bb.a	$696$	$1$	696.bb	696.ab	$14$	$12$	$2$	$0.347$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-6}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q+\zeta_{28}^{11}q^{2}+\zeta_{28}^{13}q^{3}-\zeta_{28}^{8}q^{4}+\cdots$

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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.