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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
72.1.p.a	$72$	$1$	72.p	72.p	$6$	$2$	$1$	$0.036$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}+\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{6}+\cdots$
88.1.l.a	$88$	$1$	88.l	88.l	$10$	$4$	$1$	$0.044$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
128.1.d.a	$128$	$1$	128.d	8.d	$2$	$1$	$1$	$0.064$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-q^{9}-2q^{17}+q^{25}+2q^{41}+q^{49}+\cdots$
136.1.e.a	$136$	$1$	136.e	136.e	$2$	$1$	$1$	$0.068$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-34}) $	$\Q(\sqrt{17}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{17}+\cdots$
136.1.j.a	$136$	$1$	136.j	136.j	$4$	$2$	$1$	$0.068$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q-iq^{2}+(-1-i)q^{3}-q^{4}+(-1+i+\cdots)q^{6}+\cdots$
136.1.p.a	$136$	$1$	136.p	136.p	$8$	$4$	$1$	$0.068$	$\Q(\zeta_{8})$	$D_{8}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{3}q^{2}+(\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-\zeta_{8}^{2}q^{4}+\cdots$
152.1.k.a	$152$	$1$	152.k	152.k	$6$	$2$	$1$	$0.076$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{4}+\zeta_{6}q^{6}+\cdots$
152.1.u.a	$152$	$1$	152.u	152.u	$18$	$6$	$1$	$0.076$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-3$	$0$	$0$	$1$		$q-\zeta_{18}^{5}q^{2}+(\zeta_{18}^{6}-\zeta_{18}^{7})q^{3}-\zeta_{18}q^{4}+\cdots$
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		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{11}+\cdots$
200.1.g.a	$200$	$1$	200.g	8.d	$2$	$1$	$1$	$0.100$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots$
200.1.g.b	$200$	$1$	200.g	8.d	$2$	$1$	$1$	$0.100$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots$
216.1.p.a	$216$	$1$	216.p	72.p	$6$	$2$	$1$	$0.108$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{8}+\zeta_{6}^{2}q^{11}+\cdots$
216.1.r.a	$216$	$1$	216.r	216.r	$18$	$6$	$1$	$0.108$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{2}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{4}q^{4}+\cdots$
256.1.c.a	$256$	$1$	256.c	4.b	$2$	$1$	$1$	$0.128$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{2}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-2q^{17}-q^{25}-2q^{41}+q^{49}+\cdots$
264.1.p.a	$264$	$1$	264.p	264.p	$2$	$1$	$1$	$0.132$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$-1$	$-1$	$0$	$0$	$1$		$q-q^{2}-q^{3}+q^{4}+q^{6}-q^{8}+q^{9}+\cdots$
264.1.p.b	$264$	$1$	264.p	264.p	$2$	$1$	$1$	$0.132$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-66}) $	$\Q(\sqrt{33}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
264.1.r.a	$264$	$1$	264.r	264.r	$10$	$4$	$1$	$0.132$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+\zeta_{10}^{3}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
264.1.r.b	$264$	$1$	264.r	264.r	$10$	$4$	$1$	$0.132$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$1$	$0$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}-\zeta_{10}^{4}q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
288.1.t.a	$288$	$1$	288.t	72.p	$6$	$2$	$1$	$0.144$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+\zeta_{6}^{2}q^{11}-q^{17}+\cdots$
328.1.c.a	$328$	$1$	328.c	328.c	$2$	$1$	$1$	$0.164$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-82}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-q^{2}+q^{4}-q^{8}+q^{9}+q^{16}-q^{18}+\cdots$
328.1.k.a	$328$	$1$	328.k	328.k	$4$	$2$	$1$	$0.164$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q-iq^{2}+(1-i)q^{3}-q^{4}+(-1-i+\cdots)q^{6}+\cdots$
328.1.t.a	$328$	$1$	328.t	328.t	$10$	$4$	$1$	$0.164$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
328.1.x.a	$328$	$1$	328.x	328.x	$10$	$4$	$1$	$0.164$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+(\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
328.1.z.a	$328$	$1$	328.z	328.z	$20$	$8$	$1$	$0.164$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$		$q+\zeta_{20}^{7}q^{2}+(-\zeta_{20}^{2}+\zeta_{20}^{3})q^{3}+\cdots$
344.1.l.a	$344$	$1$	344.l	344.l	$6$	$2$	$1$	$0.172$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$2$	$-2$	$0$	$0$	$1$		$q+q^{2}-\zeta_{6}q^{3}+q^{4}-2\zeta_{6}q^{6}+q^{8}+\cdots$
344.1.s.a	$344$	$1$	344.s	344.s	$14$	$6$	$1$	$0.172$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{14}^{2}q^{2}+(-\zeta_{14}+\zeta_{14}^{2})q^{3}+\zeta_{14}^{4}q^{4}+\cdots$
344.1.be.a	$344$	$1$	344.be	344.ae	$42$	$12$	$1$	$0.172$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-2$	$2$	$0$	$0$	$1$		$q-\zeta_{42}^{15}q^{2}+(\zeta_{42}^{8}-\zeta_{42}^{11})q^{3}+\cdots$
352.1.t.a	$352$	$1$	352.t	88.l	$10$	$4$	$1$	$0.176$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(\zeta_{10}^{3}-\zeta_{10}^{4})q^{3}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{9}+\cdots$
24.2.f.a	$24$	$2$	24.f	24.f	$2$	$2$	$2$	$0.192$	$\Q(\sqrt{-2}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$-2$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta q^{2}+(-1-\beta )q^{3}-2q^{4}+(2-\beta )q^{6}+\cdots$
384.1.h.a	$384$	$1$	384.h	24.h	$2$	$1$	$1$	$0.192$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$-1$	$0$	$0$	$1$		$q-q^{3}+q^{9}+2q^{11}-q^{25}-q^{27}+\cdots$
384.1.h.b	$384$	$1$	384.h	24.h	$2$	$1$	$1$	$0.192$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-6}) $	$\Q(\sqrt{3}) $	✓	$4$	$0$	$0$	$1$	$0$	$0$	$1$		$q+q^{3}+q^{9}-2q^{11}-q^{25}+q^{27}+\cdots$
392.1.g.a	$392$	$1$	392.g	8.d	$2$	$1$	$1$	$0.196$	$\Q$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $	✓	$4$	$0$	$1$	$0$	$0$	$0$	$1$		$q+q^{2}+q^{4}+q^{8}-q^{9}-2q^{11}+q^{16}+\cdots$
392.1.g.b	$392$	$1$	392.g	8.d	$2$	$2$	$2$	$0.196$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None	✓	$4$	$0$	$-2$	$0$	$0$	$0$	$1$		$q-q^{2}-\beta q^{3}+q^{4}+\beta q^{6}-q^{8}+q^{9}+\cdots$
392.1.k.a	$392$	$1$	392.k	56.k	$6$	$2$	$1$	$0.196$	$\Q(\sqrt{-3}) $	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-2}) $	$\Q(\sqrt{14}) $		$8$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}+q^{8}+\zeta_{6}q^{9}-\zeta_{6}^{2}q^{11}+\cdots$
392.1.k.b	$392$	$1$	392.k	56.k	$6$	$4$	$2$	$0.196$	$\Q(\sqrt{2}, \sqrt{-3})$	$D_{4}$	$\Q(\sqrt{-2}) $	None		$8$	$0$	$2$	$0$	$0$	$0$	$1$		$q-\beta _{2}q^{2}-\beta _{1}q^{3}+(-1-\beta _{2})q^{4}+\beta _{3}q^{6}+\cdots$
408.1.bg.a	$408$	$1$	408.bg	408.ag	$16$	$8$	$1$	$0.204$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{16}q^{2}+\zeta_{16}^{6}q^{3}+\zeta_{16}^{2}q^{4}-\zeta_{16}^{7}q^{6}+\cdots$
408.1.bg.b	$408$	$1$	408.bg	408.ag	$16$	$8$	$1$	$0.204$	$\Q(\zeta_{16})$	$D_{16}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}q^{2}+\zeta_{16}^{5}q^{3}+\zeta_{16}^{2}q^{4}+\zeta_{16}^{6}q^{6}+\cdots$
8.3.d.a	$8$	$3$	8.d	8.d	$2$	$1$	$1$	$0.218$	$\Q$	$_{}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$-2$	$-2$	$0$	$0$	$1$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}-2q^{3}+4q^{4}+4q^{6}-8q^{8}+\cdots$
456.1.l.a	$456$	$1$	456.l	456.l	$2$	$1$	$1$	$0.228$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-114}) $	$\Q(\sqrt{57}) $	✓	$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}+q^{9}+\cdots$
456.1.l.b	$456$	$1$	456.l	456.l	$2$	$1$	$1$	$0.228$	$\Q$	$D_{2}$	$\Q(\sqrt{-2}) $, $\Q(\sqrt{-114}) $	$\Q(\sqrt{57}) $	✓	$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}+q^{9}+\cdots$
456.1.s.a	$456$	$1$	456.s	456.s	$6$	$2$	$1$	$0.228$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{6}^{2}q^{2}-q^{3}-\zeta_{6}q^{4}-\zeta_{6}^{2}q^{6}+\cdots$
456.1.s.b	$456$	$1$	456.s	456.s	$6$	$2$	$1$	$0.228$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-q^{6}-q^{8}+\cdots$
456.1.bt.a	$456$	$1$	456.bt	456.at	$18$	$6$	$1$	$0.228$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{18}^{5}q^{2}-\zeta_{18}^{7}q^{3}-\zeta_{18}q^{4}+\zeta_{18}^{3}q^{6}+\cdots$
456.1.bt.b	$456$	$1$	456.bt	456.at	$18$	$6$	$1$	$0.228$	$\Q(\zeta_{18})$	$D_{18}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$3$	$0$	$0$	$1$		$q-\zeta_{18}^{5}q^{2}-\zeta_{18}^{6}q^{3}-\zeta_{18}q^{4}-\zeta_{18}^{2}q^{6}+\cdots$
472.1.k.a	$472$	$1$	472.k	472.k	$58$	$28$	$1$	$0.236$	$\Q(\zeta_{58})$	$D_{29}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{58}^{4}q^{2}+(-\zeta_{58}^{5}+\zeta_{58}^{18})q^{3}+\cdots$
512.1.c.a	$512$	$1$	512.c	4.b	$2$	$2$	$2$	$0.256$	$\Q(\sqrt{-2}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{3}-q^{9}-\beta q^{11}+\beta q^{19}-q^{25}+\cdots$
512.1.d.a	$512$	$1$	512.d	8.d	$2$	$2$	$2$	$0.256$	$\Q(\sqrt{2}) $	$D_{4}$	$\Q(\sqrt{-2}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta q^{3}+q^{9}+\beta q^{11}+\beta q^{19}+q^{25}+\cdots$
536.1.o.a	$536$	$1$	536.o	536.o	$6$	$2$	$1$	$0.267$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{6}q^{2}-q^{3}+\zeta_{6}^{2}q^{4}+\zeta_{6}q^{6}+q^{8}+\cdots$
536.1.t.a	$536$	$1$	536.t	536.t	$22$	$10$	$1$	$0.267$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{22}^{7}q^{2}+(\zeta_{22}^{8}+\zeta_{22}^{10})q^{3}-\zeta_{22}^{3}q^{4}+\cdots$

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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.