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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
80.1.h.a	$80$	$1$	80.h	20.d	$2$	$1$	$1$	$0.040$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$-1$	$0$	$1$		$q-q^{5}-q^{9}+q^{25}+2q^{29}-2q^{41}+\cdots$
140.1.p.a	$140$	$1$	140.p	140.p	$6$	$2$	$1$	$0.070$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$1$	$-1$	$-1$	$1$		$q-\zeta_{6}q^{2}-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
140.1.p.b	$140$	$1$	140.p	140.p	$6$	$2$	$1$	$0.070$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$-1$	$-1$	$1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}-\zeta_{6}q^{5}+\cdots$
180.1.p.a	$180$	$1$	180.p	180.p	$6$	$2$	$1$	$0.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-1$	$-1$	$1$	$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
180.1.p.b	$180$	$1$	180.p	180.p	$6$	$2$	$1$	$0.090$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$1$	$-1$	$-1$	$1$		$q-\zeta_{6}^{2}q^{2}+\zeta_{6}q^{3}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
300.1.l.a	$300$	$1$	300.l	60.l	$4$	$4$	$2$	$0.150$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{3}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}q^{2}-\zeta_{8}^{3}q^{3}+\zeta_{8}^{2}q^{4}-q^{6}+\cdots$
320.1.h.a	$320$	$1$	320.h	20.d	$2$	$1$	$1$	$0.160$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{5}-q^{9}+q^{25}-2q^{29}-2q^{41}+\cdots$
400.1.b.a	$400$	$1$	400.b	4.b	$2$	$1$	$1$	$0.200$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+q^{9}-2q^{29}-2q^{41}+q^{49}-2q^{61}+\cdots$
420.1.o.a	$420$	$1$	420.o	420.o	$2$	$2$	$2$	$0.210$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{5}-q^{6}-iq^{7}+\cdots$
420.1.o.b	$420$	$1$	420.o	420.o	$2$	$2$	$2$	$0.210$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{105}) $		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+iq^{2}-iq^{3}-q^{4}+q^{5}+q^{6}-iq^{7}+\cdots$
420.1.be.a	$420$	$1$	420.be	420.ae	$6$	$4$	$2$	$0.210$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{12}q^{2}-\zeta_{12}q^{3}+\zeta_{12}^{2}q^{4}+\zeta_{12}^{4}q^{5}+\cdots$
420.1.be.b	$420$	$1$	420.be	420.ae	$6$	$4$	$2$	$0.210$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+\zeta_{12}q^{2}-\zeta_{12}^{3}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{4}q^{5}+\cdots$
460.1.n.a	$460$	$1$	460.n	460.n	$22$	$10$	$1$	$0.230$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-2$	$-1$	$9$	$1$		$q+\zeta_{22}^{10}q^{2}+(\zeta_{22}^{2}+\zeta_{22}^{4})q^{3}-\zeta_{22}^{9}q^{4}+\cdots$
460.1.n.b	$460$	$1$	460.n	460.n	$22$	$10$	$1$	$0.230$	$\Q(\zeta_{22})$	$D_{11}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$2$	$-1$	$-9$	$1$		$q-\zeta_{22}^{10}q^{2}+(-\zeta_{22}^{2}-\zeta_{22}^{4})q^{3}+\cdots$
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		$4$	$0$	$0$	$0$	$0$	$0$	$1$		$q+\beta _{3}q^{2}-\beta _{1}q^{3}-q^{4}+\beta _{2}q^{6}+(-\beta _{1}+\cdots)q^{7}+\cdots$
500.1.d.a	$500$	$1$	500.d	20.d	$2$	$2$	$2$	$0.250$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$-2$	$1$	$0$	$1$	$1$		$q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots$
500.1.d.b	$500$	$1$	500.d	20.d	$2$	$2$	$2$	$0.250$	$\Q(\sqrt{5}) $	$D_{5}$	$\Q(\sqrt{-5}) $	None	✓	$2$	$0$	$2$	$-1$	$0$	$-1$	$1$		$q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots$
540.1.p.a	$540$	$1$	540.p	180.p	$6$	$2$	$1$	$0.269$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$0$	$1$	$-1$	$1$		$q-\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}-\zeta_{6}q^{7}+\cdots$
540.1.p.b	$540$	$1$	540.p	180.p	$6$	$2$	$1$	$0.269$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$0$	$1$	$1$	$1$		$q+\zeta_{6}q^{2}+\zeta_{6}^{2}q^{4}-\zeta_{6}^{2}q^{5}+\zeta_{6}q^{7}+\cdots$
540.1.bf.a	$540$	$1$	540.bf	540.af	$18$	$6$	$1$	$0.269$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$-3$	$1$		$q-\zeta_{18}q^{2}-\zeta_{18}^{5}q^{3}+\zeta_{18}^{2}q^{4}-\zeta_{18}^{5}q^{5}+\cdots$
540.1.bf.b	$540$	$1$	540.bf	540.af	$18$	$6$	$1$	$0.269$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$3$	$1$		$q+\zeta_{18}q^{2}+\zeta_{18}^{5}q^{3}+\zeta_{18}^{2}q^{4}-\zeta_{18}^{5}q^{5}+\cdots$
560.1.bt.a	$560$	$1$	560.bt	140.p	$6$	$4$	$2$	$0.279$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q+(-\zeta_{12}^{3}-\zeta_{12}^{5})q^{3}+\zeta_{12}^{2}q^{5}+\cdots$
580.1.e.c	$580$	$1$	580.e	580.e	$2$	$2$	$2$	$0.289$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-29}) $	$\Q(\sqrt{145}) $		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q-iq^{2}-iq^{3}-q^{4}+q^{5}-2q^{6}+iq^{8}+\cdots$
580.1.v.a	$580$	$1$	580.v	580.v	$14$	$6$	$1$	$0.289$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-2$	$-1$	$5$	$1$		$q+\zeta_{14}^{2}q^{2}+(-\zeta_{14}-\zeta_{14}^{5})q^{3}+\zeta_{14}^{4}q^{4}+\cdots$
580.1.v.b	$580$	$1$	580.v	580.v	$14$	$6$	$1$	$0.289$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$2$	$-1$	$-5$	$1$		$q-\zeta_{14}^{2}q^{2}+(\zeta_{14}+\zeta_{14}^{5})q^{3}+\zeta_{14}^{4}q^{4}+\cdots$
580.1.y.c	$580$	$1$	580.y	580.y	$14$	$12$	$2$	$0.289$	$\Q(\zeta_{28})$	$D_{14}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$-2$	$0$	$1$		$q+\zeta_{28}^{9}q^{2}+(\zeta_{28}+\zeta_{28}^{5})q^{3}-\zeta_{28}^{4}q^{4}+\cdots$
640.1.e.c	$640$	$1$	640.e	40.e	$2$	$4$	$4$	$0.319$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$2$		$q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{5}+(\zeta_{8}-\zeta_{8}^{3}+\cdots)q^{7}+\cdots$
700.1.j.a	$700$	$1$	700.j	140.j	$4$	$4$	$2$	$0.349$	$\Q(\zeta_{8})$	$D_{2}$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{35}) $		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}-\zeta_{8}^{3}q^{7}-\zeta_{8}q^{8}+\cdots$
700.1.u.a	$700$	$1$	700.u	28.g	$6$	$4$	$2$	$0.349$	$\Q(\zeta_{12})$	$D_{3}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{12}q^{2}-\zeta_{12}^{5}q^{3}+\zeta_{12}^{2}q^{4}-q^{6}+\cdots$
700.1.bf.a	$700$	$1$	700.bf	140.x	$12$	$8$	$2$	$0.349$	$\Q(\zeta_{24})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		$16$	$0$	$0$	$0$	$0$	$0$	$1$		$q-\zeta_{24}^{11}q^{2}+(\zeta_{24}^{5}+\zeta_{24}^{9})q^{3}-\zeta_{24}^{10}q^{4}+\cdots$
720.1.j.a	$720$	$1$	720.j	20.d	$2$	$1$	$1$	$0.359$	$\Q$	$D_{2}$	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$	$1$		$q+q^{5}+q^{25}-2q^{29}+2q^{41}-q^{49}+\cdots$
720.1.bu.a	$720$	$1$	720.bu	180.p	$6$	$4$	$2$	$0.359$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-5}) $	None		$8$	$0$	$0$	$0$	$2$	$0$	$1$		$q-\zeta_{12}q^{3}-\zeta_{12}^{4}q^{5}+(\zeta_{12}+\zeta_{12}^{3}+\cdots)q^{7}+\cdots$
800.1.p.a	$800$	$1$	800.p	5.c	$4$	$2$	$1$	$0.399$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$-2$	$0$	$2$	$1$		$q+(-1+i)q^{3}+(1+i)q^{7}-iq^{9}-q^{21}+\cdots$
800.1.p.c	$800$	$1$	800.p	5.c	$4$	$2$	$1$	$0.399$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$2$	$0$	$-2$	$1$		$q+(1-i)q^{3}+(-1-i)q^{7}-iq^{9}-q^{21}+\cdots$
820.1.e.a	$820$	$1$	820.e	820.e	$2$	$1$	$1$	$0.409$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-205}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$-1$	$0$	$-1$	$0$	$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{9}+q^{10}+\cdots$
820.1.e.b	$820$	$1$	820.e	820.e	$2$	$1$	$1$	$0.409$	$\Q$	$D_{2}$	$\Q(\sqrt{-5}) $, $\Q(\sqrt{-205}) $	$\Q(\sqrt{41}) $	✓	$4$	$0$	$1$	$0$	$-1$	$0$	$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}+q^{9}-q^{10}+\cdots$
820.1.o.b	$820$	$1$	820.o	820.o	$4$	$2$	$1$	$0.409$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$-2$	$0$	$-2$	$1$		$q+iq^{2}+(-1+i)q^{3}-q^{4}+iq^{5}+\cdots$
820.1.o.c	$820$	$1$	820.o	820.o	$4$	$2$	$1$	$0.409$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$2$	$0$	$2$	$1$		$q-iq^{2}+(1-i)q^{3}-q^{4}+iq^{5}+(-1+\cdots)q^{6}+\cdots$
820.1.bd.a	$820$	$1$	820.bd	820.ad	$10$	$4$	$1$	$0.409$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$0$	$1$	$0$	$1$		$q+\zeta_{10}^{2}q^{2}+(-\zeta_{10}-\zeta_{10}^{4})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
820.1.bd.b	$820$	$1$	820.bd	820.ad	$10$	$4$	$1$	$0.409$	$\Q(\zeta_{10})$	$D_{10}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$0$	$1$	$0$	$1$		$q-\zeta_{10}^{2}q^{2}+(\zeta_{10}+\zeta_{10}^{4})q^{3}+\zeta_{10}^{4}q^{4}+\cdots$
820.1.bj.a	$820$	$1$	820.bj	820.aj	$10$	$4$	$1$	$0.409$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$-2$	$-1$	$-2$	$1$		$q-\zeta_{10}^{3}q^{2}+(-\zeta_{10}+\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+\cdots$
820.1.bj.b	$820$	$1$	820.bj	820.aj	$10$	$4$	$1$	$0.409$	$\Q(\zeta_{10})$	$D_{5}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$2$	$-1$	$2$	$1$		$q+\zeta_{10}^{3}q^{2}+(\zeta_{10}-\zeta_{10}^{4})q^{3}-\zeta_{10}q^{4}+\cdots$
820.1.bp.b	$820$	$1$	820.bp	820.ap	$20$	$8$	$1$	$0.409$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$-2$	$0$	$-2$	$1$		$q+\zeta_{20}q^{2}+(-\zeta_{20}^{2}-\zeta_{20}^{3})q^{3}+\zeta_{20}^{2}q^{4}+\cdots$
820.1.bp.c	$820$	$1$	820.bp	820.ap	$20$	$8$	$1$	$0.409$	$\Q(\zeta_{20})$	$D_{20}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$2$	$0$	$2$	$1$		$q-\zeta_{20}q^{2}+(\zeta_{20}^{2}+\zeta_{20}^{3})q^{3}+\zeta_{20}^{2}q^{4}+\cdots$
860.1.o.a	$860$	$1$	860.o	860.o	$6$	$2$	$1$	$0.429$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-2$	$-1$	$-1$	$2$	$1$		$q-q^{2}-\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots$
860.1.o.b	$860$	$1$	860.o	860.o	$6$	$2$	$1$	$0.429$	$\Q(\sqrt{-3}) $	$D_{3}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$2$	$1$	$-1$	$-2$	$1$		$q+q^{2}+\zeta_{6}q^{3}+q^{4}-\zeta_{6}q^{5}+\zeta_{6}q^{6}+\cdots$
860.1.bb.a	$860$	$1$	860.bb	860.ab	$14$	$6$	$1$	$0.429$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-1$	$5$	$-1$	$-2$	$1$		$q-\zeta_{14}^{3}q^{2}+(1-\zeta_{14})q^{3}+\zeta_{14}^{6}q^{4}+\cdots$
860.1.bb.b	$860$	$1$	860.bb	860.ab	$14$	$6$	$1$	$0.429$	$\Q(\zeta_{14})$	$D_{7}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$1$	$-5$	$-1$	$2$	$1$		$q+\zeta_{14}^{3}q^{2}+(-1+\zeta_{14})q^{3}+\zeta_{14}^{6}q^{4}+\cdots$
860.1.bq.a	$860$	$1$	860.bq	860.aq	$42$	$12$	$1$	$0.429$	$\Q(\zeta_{21})$	$D_{21}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$-2$	$-8$	$1$	$2$	$1$		$q+\zeta_{42}^{12}q^{2}+(\zeta_{42}^{14}+\zeta_{42}^{18})q^{3}+\cdots$

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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.