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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
47.1.b.a	$47$	$1$	47.b	47.b	$2$	$2$	$2$	$0.023$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}-\beta q^{3}+(1-\beta )q^{4}-q^{6}+\cdots$
77.1.j.a	$77$	$1$	77.j	77.j	$10$	$4$	$1$	$0.038$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-7}) $	None		$4$	$0$	$-2$	$0$	$0$	$-1$	$1$		$q+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{2}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{4}+\cdots$
79.1.b.a	$79$	$1$	79.b	79.b	$2$	$2$	$2$	$0.039$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-79}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{5}-q^{8}+\cdots$
88.1.l.a	$88$	$1$	88.l	88.l	$10$	$4$	$1$	$0.044$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q-\zeta_{10}q^{2}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{2}q^{4}+\cdots$
93.1.l.a	$93$	$1$	93.l	93.l	$10$	$4$	$1$	$0.046$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$-2$	$1$		$q-\zeta_{10}q^{3}-\zeta_{10}^{3}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4}+\cdots)q^{7}+\cdots$
100.1.j.a	$100$	$1$	100.j	100.j	$10$	$4$	$1$	$0.050$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-\zeta_{10}^{3}q^{2}-\zeta_{10}q^{4}+\zeta_{10}^{4}q^{5}+\zeta_{10}^{4}q^{8}+\cdots$
103.1.b.a	$103$	$1$	103.b	103.b	$2$	$2$	$2$	$0.051$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-103}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-\beta q^{7}-q^{8}+\cdots$
119.1.d.a	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$2$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
119.1.d.b	$119$	$1$	119.d	119.d	$2$	$2$	$2$	$0.059$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-119}) $	None	✓	$2$	$0$	$-1$	$1$	$1$	$-2$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{3}+(1-\beta )q^{4}+\cdots$
127.1.b.a	$127$	$1$	127.b	127.b	$2$	$2$	$2$	$0.063$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-127}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}-q^{8}+q^{9}+\cdots$
131.1.b.a	$131$	$1$	131.b	131.b	$2$	$2$	$2$	$0.065$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-131}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$-1$	$1$		$q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}-\beta q^{7}+\cdots$
143.1.d.a	$143$	$1$	143.d	143.d	$2$	$2$	$2$	$0.071$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-143}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
143.1.d.b	$143$	$1$	143.d	143.d	$2$	$2$	$2$	$0.071$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-143}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$1$	$1$		$q+(1-\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
159.1.d.a	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$-1$	$2$	$-1$	$-1$	$1$		$q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}-\beta q^{5}+\cdots$
159.1.d.b	$159$	$1$	159.d	159.d	$2$	$2$	$2$	$0.079$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-159}) $	None	✓	$2$	$0$	$1$	$-2$	$1$	$-1$	$1$		$q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+\beta q^{5}+\cdots$
164.1.j.a	$164$	$1$	164.j	164.j	$10$	$4$	$1$	$0.082$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}-\zeta_{10}^{3}+\cdots)q^{5}+\cdots$
179.1.b.a	$179$	$1$	179.b	179.b	$2$	$2$	$2$	$0.089$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-179}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(1-\beta )q^{9}+\cdots$
183.1.n.a	$183$	$1$	183.n	183.n	$10$	$4$	$1$	$0.091$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-3}) $	None		$4$	$0$	$0$	$-1$	$0$	$3$	$1$		$q+\zeta_{10}^{4}q^{3}-\zeta_{10}^{3}q^{4}+(1+\zeta_{10}^{2}+\cdots)q^{7}+\cdots$
209.1.m.a	$209$	$1$	209.m	209.m	$10$	$4$	$1$	$0.104$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-19}) $	None		$4$	$0$	$0$	$0$	$-2$	$3$	$1$		$q+\zeta_{10}^{4}q^{4}+(\zeta_{10}^{2}+\zeta_{10}^{4})q^{5}+(1+\cdots)q^{7}+\cdots$
227.1.b.a	$227$	$1$	227.b	227.b	$2$	$2$	$2$	$0.113$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-227}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$	$1$		$q+(-1+\beta )q^{3}+q^{4}-\beta q^{7}+(1-\beta )q^{9}+\cdots$
239.1.b.b	$239$	$1$	239.b	239.b	$2$	$2$	$2$	$0.119$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-239}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$0$	$1$		$q+(-1+\beta )q^{2}+(-1+\beta )q^{3}+(1-\beta )q^{4}+\cdots$
244.1.n.a	$244$	$1$	244.n	244.n	$10$	$4$	$1$	$0.122$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$3$	$0$	$1$		$q+\zeta_{10}^{4}q^{2}-\zeta_{10}^{3}q^{4}+(1-\zeta_{10})q^{5}+\cdots$
264.1.t.a	$264$	$1$	264.t	264.t	$10$	$4$	$1$	$0.132$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$-1$	$-1$	$-2$	$-2$	$1$		$q+\zeta_{10}^{4}q^{2}+\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
264.1.t.b	$264$	$1$	264.t	264.t	$10$	$4$	$1$	$0.132$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-6}) $	None		$4$	$0$	$1$	$1$	$2$	$-2$	$1$		$q-\zeta_{10}^{4}q^{2}-\zeta_{10}^{2}q^{3}-\zeta_{10}^{3}q^{4}+\cdots$
275.1.v.a	$275$	$1$	275.v	275.v	$10$	$4$	$1$	$0.137$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$4$	$0$	$1$		$q+(-\zeta_{10}^{3}+\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+q^{5}+\cdots$
296.1.h.a	$296$	$1$	296.h	296.h	$2$	$2$	$2$	$0.148$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-74}) $	None	✓	$2$	$0$	$-2$	$-1$	$1$	$0$	$1$		$q-q^{2}+(-1+\beta )q^{3}+q^{4}+\beta q^{5}+(1+\cdots)q^{6}+\cdots$
296.1.h.b	$296$	$1$	296.h	296.h	$2$	$2$	$2$	$0.148$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-74}) $	None	✓	$2$	$0$	$2$	$-1$	$-1$	$0$	$1$		$q+q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
303.1.d.a	$303$	$1$	303.d	303.d	$2$	$2$	$2$	$0.151$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-303}) $	None	✓	$2$	$0$	$-1$	$2$	$0$	$0$	$1$		$q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
303.1.d.b	$303$	$1$	303.d	303.d	$2$	$2$	$2$	$0.151$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-303}) $	None	✓	$2$	$0$	$1$	$-2$	$0$	$0$	$1$		$q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
319.1.d.a	$319$	$1$	319.d	319.d	$2$	$2$	$2$	$0.159$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-319}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
319.1.d.b	$319$	$1$	319.d	319.d	$2$	$2$	$2$	$0.159$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-319}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
328.1.x.a	$328$	$1$	328.x	328.x	$10$	$4$	$1$	$0.164$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-1$	$-2$	$0$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+(\zeta_{10}^{2}-\zeta_{10}^{3})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
341.1.z.a	$341$	$1$	341.z	341.z	$10$	$4$	$1$	$0.170$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-11}) $	None		$4$	$0$	$0$	$-2$	$-2$	$0$	$1$		$q+(-\zeta_{10}-\zeta_{10}^{3})q^{3}-\zeta_{10}q^{4}+(\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
344.1.h.a	$344$	$1$	344.h	344.h	$2$	$2$	$2$	$0.172$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-86}) $	None	✓	$2$	$0$	$-2$	$1$	$1$	$0$	$1$		$q-q^{2}+(1-\beta )q^{3}+q^{4}+\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
344.1.h.b	$344$	$1$	344.h	344.h	$2$	$2$	$2$	$0.172$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-86}) $	None	✓	$2$	$0$	$2$	$-1$	$-1$	$0$	$1$		$q+q^{2}+(-1+\beta )q^{3}+q^{4}-\beta q^{5}+(-1+\cdots)q^{6}+\cdots$
347.1.b.a	$347$	$1$	347.b	347.b	$2$	$2$	$2$	$0.173$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-347}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$	$1$		$q+(-1+\beta )q^{3}+q^{4}+(1-\beta )q^{9}-\beta q^{11}+\cdots$
352.1.t.a	$352$	$1$	352.t	88.l	$10$	$4$	$1$	$0.176$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$2$	$0$	$0$	$1$		$q+(\zeta_{10}^{3}-\zeta_{10}^{4})q^{3}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{9}+\cdots$
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		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\beta _{1}q^{2}+\beta _{3}q^{3}+\beta _{2}q^{4}+\beta _{2}q^{6}+\cdots$
375.1.d.a	$375$	$1$	375.d	15.d	$2$	$2$	$2$	$0.187$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$-1$	$2$	$0$	$0$	$1$		$q+(-1+\beta )q^{2}+q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
375.1.d.b	$375$	$1$	375.d	15.d	$2$	$2$	$2$	$0.187$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-15}) $	None	✓	$2$	$0$	$1$	$-2$	$0$	$0$	$1$		$q+(1-\beta )q^{2}-q^{3}+(1-\beta )q^{4}+(-1+\cdots)q^{6}+\cdots$
385.1.y.a	$385$	$1$	385.y	385.y	$10$	$4$	$1$	$0.192$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$-3$	$1$	$1$	$1$		$q+(-1+\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}-\zeta_{10}^{4}q^{5}+\cdots$
385.1.y.b	$385$	$1$	385.y	385.y	$10$	$4$	$1$	$0.192$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-35}) $	None		$4$	$0$	$0$	$3$	$-1$	$-1$	$1$		$q+(1-\zeta_{10})q^{3}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+\cdots$
404.1.j.a	$404$	$1$	404.j	404.j	$10$	$4$	$1$	$0.202$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$-1$	$0$	$-2$	$0$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+(-\zeta_{10}+\zeta_{10}^{2}+\cdots)q^{5}+\cdots$
415.1.d.a	$415$	$1$	415.d	415.d	$2$	$2$	$2$	$0.207$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-415}) $	None	✓	$2$	$0$	$-1$	$0$	$2$	$0$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}+q^{5}-q^{8}+\cdots$
415.1.d.b	$415$	$1$	415.d	415.d	$2$	$2$	$2$	$0.207$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-415}) $	None	✓	$2$	$0$	$1$	$0$	$-2$	$0$	$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}-q^{5}+q^{8}+\cdots$
423.1.d.a	$423$	$1$	423.d	47.b	$2$	$2$	$2$	$0.211$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-47}) $	None	✓	$2$	$0$	$1$	$0$	$0$	$-1$	$1$		$q+(1-\beta )q^{2}+(1-\beta )q^{4}+(-1+\beta )q^{7}+\cdots$
429.1.v.a	$429$	$1$	429.v	429.v	$10$	$4$	$1$	$0.214$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$-3$	$-1$	$2$	$0$	$1$		$q+(-1+\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
429.1.v.b	$429$	$1$	429.v	429.v	$10$	$4$	$1$	$0.214$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-39}) $	None		$4$	$0$	$3$	$-1$	$-2$	$0$	$1$		$q+(1-\zeta_{10}^{3})q^{2}+\zeta_{10}^{2}q^{3}+(1-\zeta_{10}+\cdots)q^{4}+\cdots$
439.1.b.b	$439$	$1$	439.b	439.b	$2$	$2$	$2$	$0.219$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-439}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$	$1$		$q+(-1+\beta )q^{2}+(1-\beta )q^{4}+(-1+\beta )q^{5}+\cdots$
440.1.bh.a	$440$	$1$	440.bh	440.ah	$10$	$4$	$1$	$0.220$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-1$	$0$	$-1$	$3$	$1$		$q-\zeta_{10}q^{2}+\zeta_{10}^{2}q^{4}+\zeta_{10}^{4}q^{5}+(1+\cdots)q^{7}+\cdots$

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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.