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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				Fricke sign	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*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
167.1.b.a	$167$	$1$	167.b	167.b	$2$	$5$	$5$	$0.083$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-167}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$-1$		$1$		$q+\beta _{4}q^{2}+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{3}+\cdots$
271.1.b.a	$271$	$1$	271.b	271.b	$2$	$5$	$5$	$0.135$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-271}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
591.1.d.a	$591$	$1$	591.d	591.d	$2$	$5$	$5$	$0.295$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-591}) $	None	✓	$2$	$0$	$-1$	$5$	$-1$	$-1$		$1$		$q+\beta _{4}q^{2}+q^{3}+(1-\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots$
591.1.d.b	$591$	$1$	591.d	591.d	$2$	$5$	$5$	$0.295$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-591}) $	None	✓	$2$	$0$	$1$	$-5$	$1$	$-1$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-q^{3}+\cdots$
623.1.d.a	$623$	$1$	623.d	623.d	$2$	$5$	$5$	$0.311$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-623}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$5$		$1$		$q+(-1+\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots$
623.1.d.b	$623$	$1$	623.d	623.d	$2$	$5$	$5$	$0.311$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-623}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$-5$		$1$		$q+\beta _{2}q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
659.1.b.a	$659$	$1$	659.b	659.b	$2$	$5$	$5$	$0.329$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-659}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
767.1.d.a	$767$	$1$	767.d	767.d	$2$	$5$	$5$	$0.383$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-767}) $	None	✓	$2$	$0$	$-1$	$-1$	$0$	$0$		$1$		$q+\beta _{4}q^{2}+\beta _{2}q^{3}+(1-\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$
767.1.d.b	$767$	$1$	767.d	767.d	$2$	$5$	$5$	$0.383$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-767}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-\beta _{3}q^{3}+\cdots$
839.1.b.b	$839$	$1$	839.b	839.b	$2$	$5$	$5$	$0.419$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-839}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$		$1$		$q+\beta _{4}q^{2}+\beta _{4}q^{3}+(1-\beta _{3})q^{4}+\beta _{2}q^{5}+\cdots$
869.1.j.a	$869$	$1$	869.j	869.j	$10$	$20$	$5$	$0.434$	$\Q(\zeta_{50})$	$D_{25}$	$\Q(\sqrt{-79}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(-\zeta_{50}^{9}-\zeta_{50}^{21})q^{2}+(-\zeta_{50}^{5}+\cdots)q^{4}+\cdots$
871.1.d.a	$871$	$1$	871.d	871.d	$2$	$5$	$5$	$0.435$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-871}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}-\beta _{3}q^{5}+\beta _{2}q^{7}+\cdots$
871.1.d.b	$871$	$1$	871.d	871.d	$2$	$5$	$5$	$0.435$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-871}) $	None	✓	$2$	$0$	$1$	$0$	$1$	$1$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
879.1.d.a	$879$	$1$	879.d	879.d	$2$	$5$	$5$	$0.439$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-879}) $	None	✓	$2$	$0$	$-1$	$5$	$-1$	$0$		$1$		$q+\beta _{4}q^{2}+q^{3}+(1-\beta _{3})q^{4}+(-1+\beta _{1}+\cdots)q^{5}+\cdots$
879.1.d.b	$879$	$1$	879.d	879.d	$2$	$5$	$5$	$0.439$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-879}) $	None	✓	$2$	$0$	$1$	$-5$	$1$	$0$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-q^{3}+\cdots$
59.2.a.a	$59$	$2$	59.a	1.a	$1$	$5$	$5$	$0.471$	5.5.138136.1	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$2$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+(\beta _{1}-\beta _{3})q^{2}+(-1-\beta _{2}+\beta _{4})q^{3}+\cdots$
967.1.b.a	$967$	$1$	967.b	967.b	$2$	$5$	$5$	$0.483$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-967}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(-\beta _{1}+\beta _{4})q^{8}+\cdots$
61.2.k.a	$61$	$2$	61.k	61.k	$30$	$40$	$5$	$0.487$		$_{}$	None	None		$2$	$0$	$-7$	$-4$	$-18$	$-11$			$\mathrm{SU}(2)[C_{30}]$
63.2.g.b	$63$	$2$	63.g	63.g	$3$	$10$	$5$	$0.503$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$2$	$2$	$-8$	$-1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots$
63.2.h.b	$63$	$2$	63.h	63.h	$3$	$10$	$5$	$0.503$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$-4$	$-1$	$4$	$-4$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{5})q^{2}-\beta _{8}q^{3}+(1-\beta _{4}+\cdots)q^{4}+\cdots$
63.2.i.b	$63$	$2$	63.i	63.i	$6$	$10$	$5$	$0.503$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$-3$	$0$	$-6$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(-\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots$
63.2.s.b	$63$	$2$	63.s	63.s	$6$	$10$	$5$	$0.503$	10.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$3$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+(\beta _{4}+\beta _{7}+\beta _{8})q^{2}+(-\beta _{1}+\beta _{2}-\beta _{4}+\cdots)q^{3}+\cdots$
65.2.o.a	$65$	$2$	65.o	65.o	$12$	$20$	$5$	$0.519$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$-4$	$-2$	$-6$	$-6$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+(-\beta _{3}+\beta _{4})q^{2}+(\beta _{2}+\beta _{4}+\beta _{8}-\beta _{12}+\cdots)q^{3}+\cdots$
65.2.t.a	$65$	$2$	65.t	65.t	$12$	$20$	$5$	$0.519$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$-6$	$-2$	$0$	$-2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{6}+\cdots)q^{3}+\cdots$
67.2.c.a	$67$	$2$	67.c	67.c	$3$	$10$	$5$	$0.535$	$\mathbb{Q}[x]/(x^{10} - \cdots)$	$_{}$	None	None		$2$	$0$	$2$	$-8$	$-6$	$2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}-\beta _{5})q^{2}+(-1+\beta _{3}-\beta _{4}+\cdots)q^{3}+\cdots$
67.2.g.a	$67$	$2$	67.g	67.g	$33$	$100$	$5$	$0.535$		$_{}$	None	None		$2$	$0$	$-24$	$-14$	$-16$	$-24$			$\mathrm{SU}(2)[C_{33}]$
1076.1.d.a	$1076$	$1$	1076.d	1076.d	$2$	$5$	$5$	$0.537$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-269}) $	None	✓	$2$	$0$	$-5$	$1$	$-1$	$1$		$1$		$q-q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
1076.1.d.b	$1076$	$1$	1076.d	1076.d	$2$	$5$	$5$	$0.537$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-269}) $	None	✓	$2$	$0$	$5$	$-1$	$-1$	$-1$		$1$		$q+q^{2}+\beta _{4}q^{3}+q^{4}-\beta _{1}q^{5}+\beta _{4}q^{6}+\cdots$
1111.1.d.a	$1111$	$1$	1111.d	1111.d	$2$	$5$	$5$	$0.554$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1111}) $	None	✓	$2$	$0$	$-1$	$0$	$-1$	$-1$		$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+\beta _{2}q^{5}-\beta _{3}q^{7}+\cdots$
1111.1.d.b	$1111$	$1$	1111.d	1111.d	$2$	$5$	$5$	$0.554$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1111}) $	None	✓	$2$	$0$	$1$	$0$	$-1$	$1$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots$
71.2.c.a	$71$	$2$	71.c	71.c	$5$	$20$	$5$	$0.567$	$\mathbb{Q}[x]/(x^{20} - \cdots)$	$_{}$	None	None		$2$	$0$	$-6$	$-1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q-\beta _{14}q^{2}+\beta _{17}q^{3}+(-\beta _{2}-\beta _{4}-\beta _{5}+\cdots)q^{4}+\cdots$
71.2.d.a	$71$	$2$	71.d	71.d	$7$	$30$	$5$	$0.567$		$_{}$	None	None		$2$	$0$	$-3$	$-10$	$-10$	$-3$			$\mathrm{SU}(2)[C_{7}]$
71.2.g.a	$71$	$2$	71.g	71.g	$35$	$120$	$5$	$0.567$		$_{}$	None	None		$2$	$0$	$-22$	$-20$	$-20$	$-27$			$\mathrm{SU}(2)[C_{35}]$
1167.1.d.a	$1167$	$1$	1167.d	1167.d	$2$	$5$	$5$	$0.582$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1167}) $	None	✓	$2$	$0$	$-1$	$5$	$0$	$-1$		$1$		$q+\beta _{4}q^{2}+q^{3}+(1-\beta _{3})q^{4}+\beta _{4}q^{6}+\cdots$
1167.1.d.b	$1167$	$1$	1167.d	1167.d	$2$	$5$	$5$	$0.582$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1167}) $	None	✓	$2$	$0$	$1$	$-5$	$0$	$-1$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}-q^{3}+\cdots$
73.2.g.a	$73$	$2$	73.g	73.g	$9$	$30$	$5$	$0.583$		$_{}$	None	None		$2$	$0$	$-6$	$0$	$-12$	$3$			$\mathrm{SU}(2)[C_{9}]$
73.2.h.a	$73$	$2$	73.h	73.h	$12$	$20$	$5$	$0.583$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	$_{}$	None	None		$2$	$0$	$-4$	$0$	$-4$	$-2$		$1$	$\mathrm{SU}(2)[C_{12}]$	$q-\beta _{9}q^{2}+(\beta _{2}+\beta _{6}-\beta _{8}-\beta _{11}+\beta _{13}+\cdots)q^{3}+\cdots$
73.2.i.a	$73$	$2$	73.i	73.i	$18$	$30$	$5$	$0.583$		$_{}$	None	None		$2$	$0$	$-6$	$-6$	$0$	$-9$			$\mathrm{SU}(2)[C_{18}]$
77.2.m.b	$77$	$2$	77.m	77.m	$15$	$40$	$5$	$0.615$		$_{}$	None	None		$4$	$0$	$-3$	$-4$	$4$	$-2$			$\mathrm{SU}(2)[C_{15}]$
79.2.a.b	$79$	$2$	79.a	1.a	$1$	$5$	$5$	$0.631$	5.5.81589.1	$_{}$	None	None	✓	$1$	$0$	$0$	$1$	$7$	$-5$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1-\beta _{2}-\beta _{4})q^{3}+\beta _{2}q^{4}+\cdots$
79.2.e.a	$79$	$2$	79.e	79.e	$13$	$60$	$5$	$0.631$		$_{}$	None	None		$2$	$0$	$-9$	$-9$	$-11$	$1$			$\mathrm{SU}(2)[C_{13}]$
1283.1.b.a	$1283$	$1$	1283.b	1283.b	$2$	$5$	$5$	$0.640$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1283}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$0$		$1$		$q+\beta _{4}q^{3}+q^{4}+(1-\beta _{3})q^{9}+\beta _{2}q^{11}+\cdots$
1303.1.b.a	$1303$	$1$	1303.b	1303.b	$2$	$5$	$5$	$0.650$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1303}) $	None	✓	$2$	$0$	$-1$	$0$	$0$	$0$		$1$		$q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}+(-\beta _{1}+\beta _{4})q^{8}+\cdots$
1304.1.h.a	$1304$	$1$	1304.h	1304.h	$2$	$5$	$5$	$0.651$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-326}) $	None	✓	$2$	$0$	$-5$	$1$	$1$	$0$		$1$		$q-q^{2}+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{3}+\cdots$
1304.1.h.b	$1304$	$1$	1304.h	1304.h	$2$	$5$	$5$	$0.651$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-326}) $	None	✓	$2$	$0$	$5$	$-1$	$-1$	$0$		$1$		$q+q^{2}+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
1307.1.b.a	$1307$	$1$	1307.b	1307.b	$2$	$5$	$5$	$0.652$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1307}) $	None	✓	$2$	$0$	$0$	$-1$	$0$	$-1$		$1$		$q+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{7}+\cdots$
1331.1.b.a	$1331$	$1$	1331.b	11.b	$2$	$5$	$5$	$0.664$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-11}) $	None	✓	$2$	$0$	$0$	$-1$	$-1$	$0$		$1$		$q+\beta _{4}q^{3}+q^{4}+(-1+\beta _{1}-\beta _{2}+\beta _{3}+\cdots)q^{5}+\cdots$
1331.1.d.a	$1331$	$1$	1331.d	11.d	$10$	$20$	$5$	$0.664$	20.0.$\cdots$.1	$D_{11}$	$\Q(\sqrt{-11}) $	None		$8$	$0$	$0$	$1$	$1$	$0$		$1$		$q-\beta _{13}q^{3}+\beta _{9}q^{4}+(\beta _{8}+\beta _{11}+\beta _{12}+\cdots)q^{5}+\cdots$
1391.1.d.c	$1391$	$1$	1391.d	1391.d	$2$	$5$	$5$	$0.694$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1391}) $	None	✓	$2$	$0$	$-1$	$-1$	$-1$	$-1$		$1$		$q+\beta _{4}q^{2}-\beta _{1}q^{3}+(1-\beta _{3})q^{4}-\beta _{3}q^{5}+\cdots$
1391.1.d.d	$1391$	$1$	1391.d	1391.d	$2$	$5$	$5$	$0.694$	$\Q(\zeta_{22})^+$	$D_{11}$	$\Q(\sqrt{-1391}) $	None	✓	$2$	$0$	$1$	$-1$	$1$	$1$		$1$		$q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+\beta _{4}q^{3}+\cdots$

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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.