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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
195.1.e.a	$195$	$1$	195.e	195.e	$2$	$4$	$4$	$0.097$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{2}+\zeta_{8}^{2}q^{3}-q^{4}+\cdots$
239.1.b.c	$239$	$1$	239.b	239.b	$2$	$4$	$4$	$0.119$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$1$	$-2$	$1$	$0$	$1$		$q+\beta _{1}q^{2}+(-1-\beta _{3})q^{3}+(1+\beta _{2})q^{4}+\cdots$
252.1.h.a	$252$	$1$	252.h	84.h	$2$	$4$	$4$	$0.126$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
280.1.c.a	$280$	$1$	280.c	280.c	$2$	$4$	$4$	$0.140$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-14}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots$
312.1.b.a	$312$	$1$	312.b	312.b	$2$	$4$	$4$	$0.156$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{2}q^{3}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}+\cdots)q^{5}+\cdots$
329.1.f.b	$329$	$1$	329.f	329.f	$6$	$8$	$4$	$0.164$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-1$	$2$	$0$	$1$	$1$		$q+(\zeta_{30}^{8}+\zeta_{30}^{12})q^{2}+(-\zeta_{30}^{11}+\zeta_{30}^{14}+\cdots)q^{3}+\cdots$
375.1.c.a	$375$	$1$	375.c	3.b	$2$	$4$	$4$	$0.187$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-15}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+\beta _{2}q^{6}+\cdots$
376.1.e.c	$376$	$1$	376.e	376.e	$2$	$4$	$4$	$0.188$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-1$	$0$	$0$	$2$	$1$		$q-\zeta_{10}^{3}q^{2}+(-\zeta_{10}-\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+\cdots$
395.1.c.c	$395$	$1$	395.c	395.c	$2$	$4$	$4$	$0.197$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{2}+(-1+\zeta_{10}^{2}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
396.1.d.a	$396$	$1$	396.d	132.d	$2$	$4$	$4$	$0.198$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{11}) $		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+\zeta_{8}^{2}q^{2}-q^{4}+(-\zeta_{8}-\zeta_{8}^{3})q^{5}+\cdots$
407.1.d.c	$407$	$1$	407.d	407.d	$2$	$4$	$4$	$0.203$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-407}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}-\beta _{2}q^{3}+(1+\beta _{2})q^{4}+(\beta _{1}+\cdots)q^{6}+\cdots$
423.1.f.b	$423$	$1$	423.f	423.f	$6$	$8$	$4$	$0.211$	$\Q(\zeta_{15})$	$D_{15}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$2$	$-2$	$0$	$-1$	$1$		$q+(-\zeta_{30}^{11}+\zeta_{30}^{14})q^{2}+\zeta_{30}^{12}q^{3}+\cdots$
435.1.b.a	$435$	$1$	435.b	435.b	$2$	$4$	$4$	$0.217$	$\Q(\zeta_{8})$	$D_{4}$	None	$\Q(\sqrt{145}) $		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-\zeta_{8}q^{3}-q^{4}+\zeta_{8}^{2}q^{5}+\cdots$
439.1.b.c	$439$	$1$	439.b	439.b	$2$	$4$	$4$	$0.219$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-439}) $	None	✓	$2$	$0$	$1$	$0$	$-2$	$1$	$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}+(-1-\beta _{3})q^{5}+\cdots$
440.1.o.e	$440$	$1$	440.o	440.o	$2$	$4$	$4$	$0.220$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-55}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}-\zeta_{8}^{2}q^{5}+(-\zeta_{8}+\cdots)q^{7}+\cdots$
471.1.d.c	$471$	$1$	471.d	471.d	$2$	$4$	$4$	$0.235$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-471}) $	None	✓	$4$	$0$	$0$	$-4$	$0$	$0$	$1$		$q-\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\cdots$
480.1.c.a	$480$	$1$	480.c	15.d	$2$	$4$	$4$	$0.240$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}+\zeta_{8}^{3})q^{7}+\cdots$
500.1.b.a	$500$	$1$	500.b	4.b	$2$	$4$	$4$	$0.250$	$\Q(i, \sqrt{5})$	$D_{5}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{3}q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{2}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
504.1.e.a	$504$	$1$	504.e	168.e	$2$	$4$	$4$	$0.252$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{8}+\cdots$
520.1.b.b	$520$	$1$	520.b	520.b	$2$	$4$	$4$	$0.260$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-26}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}+\cdots$
524.1.d.b	$524$	$1$	524.d	131.b	$2$	$4$	$4$	$0.262$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$1$	$-2$	$1$	$1$		$q+\beta _{1}q^{3}+\beta _{3}q^{5}+(-\beta _{2}-\beta _{3})q^{7}+\cdots$
540.1.f.a	$540$	$1$	540.f	20.d	$2$	$4$	$4$	$0.269$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
559.1.d.c	$559$	$1$	559.d	559.d	$2$	$4$	$4$	$0.279$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-559}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+\beta _{3}q^{5}+\beta _{1}q^{7}+\cdots$
564.1.f.c	$564$	$1$	564.f	564.f	$2$	$4$	$4$	$0.281$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$-1$	$1$	$0$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}+\zeta_{10}q^{3}-\zeta_{10}q^{4}-\zeta_{10}^{4}q^{6}+\cdots$
564.1.f.d	$564$	$1$	564.f	564.f	$2$	$4$	$4$	$0.281$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-47}) $	None		$4$	$0$	$1$	$-1$	$0$	$0$	$1$		$q+\zeta_{10}q^{2}-\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{6}+\cdots$
36.2.h.a	$36$	$2$	36.h	36.h	$6$	$8$	$4$	$0.287$	8.0.170772624.1	$_{}$	None	None		$4$	$0$	$-3$	$0$	$-6$	$0$	$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(1-\beta _{1}+\beta _{4}+\beta _{7})q^{2}+(-\beta _{2}-\beta _{3}+\cdots)q^{3}+\cdots$
580.1.e.d	$580$	$1$	580.e	580.e	$2$	$4$	$4$	$0.289$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-29}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}^{3}q^{2}-\zeta_{12}^{3}q^{3}-q^{4}+\zeta_{12}^{4}q^{5}+\cdots$
584.1.h.c	$584$	$1$	584.h	584.h	$2$	$4$	$4$	$0.291$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-146}) $	None	✓	$4$	$0$	$-4$	$0$	$0$	$0$	$1$		$q-q^{2}-\beta _{2}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{2}q^{6}+\cdots$
585.1.o.a	$585$	$1$	585.o	65.h	$4$	$8$	$4$	$0.292$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{2}+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\cdots)q^{4}+\cdots$
600.1.q.b	$600$	$1$	600.q	120.q	$4$	$8$	$4$	$0.299$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-2}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{24}^{3}q^{2}-\zeta_{24}q^{3}+\zeta_{24}^{6}q^{4}-\zeta_{24}^{4}q^{6}+\cdots$
624.1.bi.a	$624$	$1$	624.bi	624.ai	$4$	$8$	$4$	$0.311$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-39}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{16}^{3}q^{2}-\zeta_{16}^{2}q^{3}+\zeta_{16}^{6}q^{4}+\cdots$
632.1.f.c	$632$	$1$	632.f	632.f	$2$	$4$	$4$	$0.315$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$-1$	$0$	$0$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+(-\zeta_{10}-\zeta_{10}^{4}+\cdots)q^{5}+\cdots$
40.2.d.a	$40$	$2$	40.d	8.b	$2$	$4$	$4$	$0.319$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-4$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}+\cdots)q^{3}+\cdots$
40.2.f.a	$40$	$2$	40.f	40.f	$2$	$4$	$4$	$0.319$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
40.2.k.a	$40$	$2$	40.k	40.k	$4$	$8$	$4$	$0.319$	$\Q(\zeta_{20})$	$_{}$	None	None		$4$	$0$	$-2$	$-4$	$0$	$0$	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{20}^{7}q^{2}+(-1+\zeta_{20}^{3}+\zeta_{20}^{5}+\cdots)q^{3}+\cdots$
640.1.e.c	$640$	$1$	640.e	40.e	$2$	$4$	$4$	$0.319$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
655.1.d.e	$655$	$1$	655.d	655.d	$2$	$4$	$4$	$0.327$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-131}) $	None		$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+(\zeta_{10}+\zeta_{10}^{4})q^{3}-q^{4}-\zeta_{10}^{2}q^{5}+\cdots$
656.1.h.a	$656$	$1$	656.h	164.d	$2$	$4$	$4$	$0.327$	$\Q(\zeta_{16})^+$	$D_{8}$	$\Q(\sqrt{-41}) $	None	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{3}q^{7}+(1+\beta _{2}+\cdots)q^{9}+\cdots$
671.1.d.e	$671$	$1$	671.d	671.d	$2$	$4$	$4$	$0.335$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-671}) $	None	✓	$2$	$0$	$-1$	$1$	$-2$	$4$	$1$		$q-\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
671.1.d.f	$671$	$1$	671.d	671.d	$2$	$4$	$4$	$0.335$	$\Q(\zeta_{15})^+$	$D_{15}$	$\Q(\sqrt{-671}) $	None	✓	$2$	$0$	$1$	$1$	$-2$	$-4$	$1$		$q+\beta _{1}q^{2}+(-\beta _{2}-\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
42.2.d.a	$42$	$2$	42.d	21.c	$2$	$4$	$4$	$0.335$	$\Q(i, \sqrt{6})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$	$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{2}q^{2}+\beta _{1}q^{3}-q^{4}+(-\beta _{1}+\beta _{3})q^{5}+\cdots$
680.1.k.e	$680$	$1$	680.k	680.k	$2$	$4$	$4$	$0.339$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-34}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\zeta_{8}^{2}q^{2}-q^{4}-\zeta_{8}q^{5}+(-\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
684.1.q.a	$684$	$1$	684.q	76.g	$6$	$8$	$4$	$0.341$	$\Q(\zeta_{24})$	$S_{4}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}+(\zeta_{24}^{5}+\zeta_{24}^{11}+\cdots)q^{5}+\cdots$
693.1.h.a	$693$	$1$	693.h	231.h	$2$	$4$	$4$	$0.346$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{8}-\zeta_{8}^{3})q^{2}+q^{4}+\zeta_{8}^{2}q^{7}-\zeta_{8}^{3}q^{11}+\cdots$
693.1.bp.a	$693$	$1$	693.bp	231.r	$10$	$16$	$4$	$0.346$	$\Q(\zeta_{40})$	$D_{20}$	$\Q(\sqrt{-7}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q+(\zeta_{40}+\zeta_{40}^{7})q^{2}+(\zeta_{40}^{2}+\zeta_{40}^{8}+\cdots)q^{4}+\cdots$
695.1.d.g	$695$	$1$	695.d	695.d	$2$	$4$	$4$	$0.347$	$\Q(\zeta_{24})^+$	$D_{12}$	$\Q(\sqrt{-695}) $	None	✓	$4$	$0$	$0$	$0$	$-4$	$0$	$1$		$q-\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{2})q^{4}-q^{5}+\cdots$
696.1.n.f	$696$	$1$	696.n	696.n	$2$	$4$	$4$	$0.347$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-87}) $	None		$8$	$0$	$0$	$0$	$0$	$4$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{6}+\cdots$
700.1.j.b	$700$	$1$	700.j	140.j	$4$	$8$	$4$	$0.349$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-7}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{7}q^{2}-\zeta_{24}^{2}q^{4}+\zeta_{24}^{3}q^{7}+\cdots$
44.2.c.a	$44$	$2$	44.c	44.c	$2$	$4$	$4$	$0.351$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$-4$	$0$	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+(-1+\beta _{2})q^{4}-q^{5}+\cdots$
44.2.g.a	$44$	$2$	44.g	44.g	$10$	$16$	$4$	$0.351$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$-5$	$0$	$-6$	$0$	$1$	$\mathrm{SU}(2)[C_{10}]$	$q+\beta _{2}q^{2}+(-1-\beta _{1}-\beta _{2}-\beta _{13}-\beta _{14}+\cdots)q^{3}+\cdots$

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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.