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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
595.1.b.a	$595$	$1$	595.b	595.b	$2$	$2$	$2$	$0.297$	$\Q(\sqrt{-1}) $	$D_{2}$	$\Q(\sqrt{-35}) $, $\Q(\sqrt{-119}) $	$\Q(\sqrt{85}) $		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{3}+q^{4}+iq^{5}-iq^{7}-3q^{9}+\cdots$
595.1.b.b	$595$	$1$	595.b	595.b	$2$	$8$	$8$	$0.297$	$\Q(\zeta_{20})$	$D_{10}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{20}^{2}+\zeta_{20}^{8})q^{2}+(-\zeta_{20}^{3}-\zeta_{20}^{7}+\cdots)q^{3}+\cdots$
595.1.u.a	$595$	$1$	595.u	595.u	$4$	$4$	$2$	$0.297$	$\Q(\zeta_{8})$	$D_{4}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-q^{4}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{9}+\cdots$
595.1.be.a	$595$	$1$	595.be	595.ae	$8$	$8$	$2$	$0.297$	$\Q(\zeta_{16})$	$D_{8}$	$\Q(\sqrt{-35}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q+(\zeta_{16}-\zeta_{16}^{5})q^{3}+\zeta_{16}^{4}q^{4}-\zeta_{16}^{3}q^{5}+\cdots$
595.2.a.a	$595$	$2$	595.a	1.a	$1$	$1$	$1$	$4.751$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$-2$	$2$	$-1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{3}+2q^{4}-q^{5}-4q^{6}+\cdots$
595.2.a.b	$595$	$2$	595.a	1.a	$1$	$1$	$1$	$4.751$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$-1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}-q^{5}+4q^{6}+\cdots$
595.2.a.c	$595$	$2$	595.a	1.a	$1$	$1$	$1$	$4.751$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$1$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{3}+2q^{4}+q^{5}+4q^{6}+\cdots$
595.2.a.d	$595$	$2$	595.a	1.a	$1$	$3$	$3$	$4.751$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$-4$	$-2$	$3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{1})q^{2}+(-1-\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots$
595.2.a.e	$595$	$2$	595.a	1.a	$1$	$3$	$3$	$4.751$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$1$	$-2$	$-4$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1-\beta _{2})q^{2}+(-2+\beta _{1}-\beta _{2})q^{3}+\cdots$
595.2.a.f	$595$	$2$	595.a	1.a	$1$	$3$	$3$	$4.751$	3.3.169.1	$_{}$	None	None	✓	$1$	$1$	$-2$	$-2$	$-3$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+(-1+\beta _{1})q^{2}+(-\beta _{1}+\beta _{2})q^{3}+(2+\cdots)q^{4}+\cdots$
595.2.a.g	$595$	$2$	595.a	1.a	$1$	$3$	$3$	$4.751$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}-\beta _{2}q^{3}+\beta _{2}q^{4}-q^{5}+(-1+\cdots)q^{6}+\cdots$
595.2.a.h	$595$	$2$	595.a	1.a	$1$	$3$	$3$	$4.751$	$\Q(\zeta_{14})^+$	$_{}$	None	None	✓	$1$	$0$	$2$	$0$	$-3$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{1})q^{2}+(1-2\beta _{1}+\beta _{2})q^{3}+(1+\cdots)q^{4}+\cdots$
595.2.a.i	$595$	$2$	595.a	1.a	$1$	$4$	$4$	$4.751$	4.4.10889.1	$_{}$	None	None	✓	$1$	$0$	$1$	$-2$	$4$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(-1+\beta _{3})q^{3}+(1+\beta _{1}+\beta _{2}+\cdots)q^{4}+\cdots$
595.2.a.j	$595$	$2$	595.a	1.a	$1$	$4$	$4$	$4.751$	4.4.2777.1	$_{}$	None	None	✓	$1$	$0$	$2$	$2$	$4$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q+(1-\beta _{3})q^{2}+(1+\beta _{2}-\beta _{3})q^{3}+(1+\cdots)q^{4}+\cdots$
595.2.a.k	$595$	$2$	595.a	1.a	$1$	$5$	$5$	$4.751$	5.5.1034856.1	$_{}$	None	None	✓	$1$	$0$	$2$	$-2$	$-5$	$5$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{3}q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots$
595.2.c.a	$595$	$2$	595.c	5.b	$2$	$14$	$14$	$4.751$	$\mathbb{Q}[x]/(x^{14} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(\beta _{9}+\beta _{11})q^{3}+(\beta _{4}+\beta _{5}+\cdots)q^{4}+\cdots$
595.2.c.b	$595$	$2$	595.c	5.b	$2$	$34$	$34$	$4.751$		$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{2}]$
595.2.d.a	$595$	$2$	595.d	85.c	$2$	$26$	$26$	$4.751$		$_{}$	None	None		$2$	$0$	$0$	$-6$	$0$	$26$			$\mathrm{SU}(2)[C_{2}]$
595.2.d.b	$595$	$2$	595.d	85.c	$2$	$26$	$26$	$4.751$		$_{}$	None	None		$2$	$0$	$0$	$6$	$0$	$-26$			$\mathrm{SU}(2)[C_{2}]$
595.2.f.a	$595$	$2$	595.f	17.b	$2$	$2$	$2$	$4.751$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-2q^{4}+iq^{5}-iq^{7}+3q^{9}+2iq^{11}+\cdots$
595.2.f.b	$595$	$2$	595.f	17.b	$2$	$12$	$12$	$4.751$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		$2$	$0$	$4$	$0$	$0$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{7}q^{2}+\beta _{8}q^{3}+(1+\beta _{2})q^{4}-\beta _{4}q^{5}+\cdots$
595.2.f.c	$595$	$2$	595.f	17.b	$2$	$22$	$22$	$4.751$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
595.2.i.a	$595$	$2$	595.i	7.c	$3$	$2$	$1$	$4.751$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$0$	$-1$	$1$	$5$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{3}+(2-2\zeta_{6})q^{4}+\zeta_{6}q^{5}+\cdots$
595.2.i.b	$595$	$2$	595.i	7.c	$3$	$2$	$1$	$4.751$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$1$	$-1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
595.2.i.c	$595$	$2$	595.i	7.c	$3$	$2$	$1$	$4.751$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$1$	$1$	$1$	$-4$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots$
595.2.i.d	$595$	$2$	595.i	7.c	$3$	$2$	$1$	$4.751$	$\Q(\sqrt{-3}) $	$_{}$	None	None		$2$	$0$	$2$	$1$	$1$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{2}+(1-\zeta_{6})q^{3}+(-2+2\zeta_{6})q^{4}+\cdots$
595.2.i.e	$595$	$2$	595.i	7.c	$3$	$4$	$2$	$4.751$	$\Q(\sqrt{-3}, \sqrt{7})$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1-\beta _{2})q^{2}+(\beta _{1}+\beta _{3})q^{3}-\beta _{2}q^{4}+\cdots$
595.2.i.f	$595$	$2$	595.i	7.c	$3$	$4$	$2$	$4.751$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		$2$	$0$	$-1$	$3$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{1}-2\beta _{2}+\beta _{3})q^{3}+\cdots$
595.2.i.g	$595$	$2$	595.i	7.c	$3$	$4$	$2$	$4.751$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		$2$	$0$	$1$	$1$	$2$	$2$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(\beta _{2}-\beta _{3})q^{3}+(3\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
595.2.i.h	$595$	$2$	595.i	7.c	$3$	$12$	$6$	$4.751$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$2$	$0$	$-1$	$1$	$6$	$5$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-\beta _{1}+\beta _{4})q^{3}+(-2+\beta _{2}+\cdots)q^{4}+\cdots$
595.2.i.i	$595$	$2$	595.i	7.c	$3$	$14$	$7$	$4.751$	$\mathbb{Q}[x]/(x^{14} - \cdots)$	$_{}$	None	None		$2$	$0$	$1$	$6$	$-7$	$-1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-\beta _{8}+\beta _{13})q^{3}+\beta _{12}q^{4}+\cdots$
595.2.i.j	$595$	$2$	595.i	7.c	$3$	$18$	$9$	$4.751$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$-4$	$9$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{1}+\beta _{3})q^{2}+\beta _{8}q^{3}+(\beta _{4}+\beta _{7}+\cdots)q^{4}+\cdots$
595.2.i.k	$595$	$2$	595.i	7.c	$3$	$24$	$12$	$4.751$		$_{}$	None	None		$2$	$0$	$2$	$-5$	$-12$	$-4$			$\mathrm{SU}(2)[C_{3}]$
595.2.k.a	$595$	$2$	595.k	17.c	$4$	$28$	$14$	$4.751$		$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
595.2.k.b	$595$	$2$	595.k	17.c	$4$	$44$	$22$	$4.751$		$_{}$	None	None		$2$	$0$	$0$	$4$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
595.2.l.a	$595$	$2$	595.l	595.l	$4$	$136$	$68$	$4.751$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
595.2.o.a	$595$	$2$	595.o	35.f	$4$	$128$	$64$	$4.751$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{4}]$
595.2.p.a	$595$	$2$	595.p	595.p	$4$	$40$	$20$	$4.751$		$_{}$	$\Q(\sqrt{-119}) $	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{U}(1)[D_{4}]$
595.2.p.b	$595$	$2$	595.p	595.p	$4$	$96$	$48$	$4.751$		$_{}$	None	None		$8$	$0$	$-8$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
595.2.r.a	$595$	$2$	595.r	595.r	$4$	$136$	$68$	$4.751$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{4}]$
595.2.t.a	$595$	$2$	595.t	85.j	$4$	$104$	$52$	$4.751$		$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{4}]$
595.2.x.a	$595$	$2$	595.x	119.j	$6$	$4$	$2$	$4.751$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+3\zeta_{12}q^{3}+(2-2\zeta_{12}^{2})q^{4}+(\zeta_{12}+\cdots)q^{5}+\cdots$
595.2.x.b	$595$	$2$	595.x	119.j	$6$	$92$	$46$	$4.751$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
595.2.z.a	$595$	$2$	595.z	595.z	$6$	$136$	$68$	$4.751$		$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{6}]$
595.2.ba.a	$595$	$2$	595.ba	35.j	$6$	$4$	$2$	$4.751$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{6}]$	$q+\zeta_{12}q^{3}+(-2+2\zeta_{12}^{2})q^{4}+(-\zeta_{12}+\cdots)q^{5}+\cdots$
595.2.ba.b	$595$	$2$	595.ba	35.j	$6$	$124$	$62$	$4.751$		$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$			$\mathrm{SU}(2)[C_{6}]$
595.2.bd.a	$595$	$2$	595.bd	595.ad	$8$	$272$	$68$	$4.751$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-8$			$\mathrm{SU}(2)[C_{8}]$
595.2.bf.a	$595$	$2$	595.bf	17.d	$8$	$56$	$14$	$4.751$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
595.2.bf.b	$595$	$2$	595.bf	17.d	$8$	$88$	$22$	$4.751$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$
595.2.bg.a	$595$	$2$	595.bg	85.m	$8$	$224$	$56$	$4.751$		$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{8}]$

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Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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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.