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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
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}) $	✓	$4$	$0$	$0$	$0$	$1$	$0$		$1$		$q+q^{5}-q^{9}+q^{25}-2q^{29}-2q^{41}+\cdots$
320.1.p.a	$320$	$1$	320.p	5.c	$4$	$2$	$1$	$0.160$	$\Q(\sqrt{-1}) $	$D_{4}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q+iq^{5}+iq^{9}+(1-i)q^{13}+(-1-i+\cdots)q^{17}+\cdots$
320.2.a.a	$320$	$2$	320.a	1.a	$1$	$1$	$1$	$2.555$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}-2q^{7}+q^{9}-2q^{13}+\cdots$
320.2.a.b	$320$	$2$	320.a	1.a	$1$	$1$	$1$	$2.555$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}+q^{5}+2q^{7}+q^{9}-4q^{11}+\cdots$
320.2.a.c	$320$	$2$	320.a	1.a	$1$	$1$	$1$	$2.555$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$0$	$-1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}-3q^{9}-4q^{11}+2q^{13}+\cdots$
320.2.a.d	$320$	$2$	320.a	1.a	$1$	$1$	$1$	$2.555$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$-1$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+4q^{7}-3q^{9}+4q^{11}+2q^{13}+\cdots$
320.2.a.e	$320$	$2$	320.a	1.a	$1$	$1$	$1$	$2.555$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}-2q^{7}+q^{9}+4q^{11}+\cdots$
320.2.a.f	$320$	$2$	320.a	1.a	$1$	$1$	$1$	$2.555$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+q^{5}+2q^{7}+q^{9}-2q^{13}+\cdots$
320.2.a.g	$320$	$2$	320.a	1.a	$1$	$2$	$2$	$2.555$	$\Q(\sqrt{2}) $	$_{}$	None	None	✓	$2$	$0$	$0$	$0$	$-2$	$0$	$-$	$2$	$\mathrm{SU}(2)$	$q+\beta q^{3}-q^{5}+\beta q^{7}+5q^{9}-2\beta q^{11}+\cdots$
320.2.c.a	$320$	$2$	320.c	5.b	$2$	$2$	$2$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-2$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-1+i)q^{5}+3q^{9}+2iq^{13}+4iq^{17}+\cdots$
320.2.c.b	$320$	$2$	320.c	5.b	$2$	$2$	$2$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(1+i)q^{5}+iq^{7}-q^{9}-4q^{11}+\cdots$
320.2.c.c	$320$	$2$	320.c	5.b	$2$	$2$	$2$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+iq^{3}+(1-i)q^{5}+iq^{7}-q^{9}+4q^{11}+\cdots$
320.2.c.d	$320$	$2$	320.c	5.b	$2$	$4$	$4$	$2.555$	$\Q(i, \sqrt{5})$	$_{}$	$\Q(\sqrt{-5}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{3}+\beta _{2}q^{5}-\beta _{3}q^{7}+(-3+2\beta _{2}+\cdots)q^{9}+\cdots$
320.2.d.a	$320$	$2$	320.d	8.b	$2$	$4$	$4$	$2.555$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$-12$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}-\zeta_{12}q^{5}+(-3+\cdots)q^{7}+\cdots$
320.2.d.b	$320$	$2$	320.d	8.b	$2$	$4$	$4$	$2.555$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$12$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{3}+\zeta_{12}q^{5}+(3-\zeta_{12}^{3})q^{7}+\cdots$
320.2.f.a	$320$	$2$	320.f	40.f	$2$	$4$	$4$	$2.555$	$\Q(i, \sqrt{5})$	$_{}$	$\Q(\sqrt{-10}) $	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{5}+\beta _{2}q^{7}-3q^{9}+\beta _{1}q^{11}+\cdots$
320.2.f.b	$320$	$2$	320.f	40.f	$2$	$8$	$8$	$2.555$	$\Q(\zeta_{24})$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\zeta_{24}^{4}q^{3}-\zeta_{24}^{6}q^{5}+\zeta_{24}^{2}q^{7}+\cdots$
320.2.j.a	$320$	$2$	320.j	80.j	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q-2iq^{3}+(1+2i)q^{5}+(3+3i)q^{7}+\cdots$
320.2.j.b	$320$	$2$	320.j	80.j	$4$	$18$	$9$	$2.555$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$-4$	$-2$		$2^{13}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{12}q^{3}-\beta _{4}q^{5}+\beta _{10}q^{7}+(-1+\cdots)q^{9}+\cdots$
320.2.l.a	$320$	$2$	320.l	16.e	$4$	$16$	$8$	$2.555$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{5}+\beta _{7})q^{3}+\beta _{1}q^{5}+(\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots$
320.2.n.a	$320$	$2$	320.n	20.e	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-4$	$4$	$4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-2-2i)q^{3}+(2-i)q^{5}+(2-2i)q^{7}+\cdots$
320.2.n.b	$320$	$2$	320.n	20.e	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$-2$	$-6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{3}+(-1-2i)q^{5}+(-3+\cdots)q^{7}+\cdots$
320.2.n.c	$320$	$2$	320.n	20.e	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{3}+(-1+2i)q^{5}+(1-i)q^{7}+\cdots$
320.2.n.d	$320$	$2$	320.n	20.e	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-2-i)q^{5}-3iq^{9}+(5-5i)q^{13}+\cdots$
320.2.n.e	$320$	$2$	320.n	20.e	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-1}) $	None		$4$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(2-i)q^{5}-3iq^{9}+(1-i)q^{13}+(3+\cdots)q^{17}+\cdots$
320.2.n.f	$320$	$2$	320.n	20.e	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{3}+(-1+2i)q^{5}+(-1+i)q^{7}+\cdots$
320.2.n.g	$320$	$2$	320.n	20.e	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$-2$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{3}+(-1-2i)q^{5}+(3-3i)q^{7}+\cdots$
320.2.n.h	$320$	$2$	320.n	20.e	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$4$	$4$	$-4$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(2+2i)q^{3}+(2-i)q^{5}+(-2+2i)q^{7}+\cdots$
320.2.n.i	$320$	$2$	320.n	20.e	$4$	$4$	$2$	$2.555$	$\Q(\zeta_{12})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$4$	$0$		$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	$q-\zeta_{12}^{2}q^{3}+(1+2\zeta_{12})q^{5}-\zeta_{12}^{3}q^{7}+\cdots$
320.2.o.a	$320$	$2$	320.o	40.k	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$1$	$0$	$-2$	$-2$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{3}+(-1-2i)q^{5}+(-1+\cdots)q^{7}+\cdots$
320.2.o.b	$320$	$2$	320.o	40.k	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$2$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1+i)q^{3}+(1+2i)q^{5}+(1-i)q^{7}+\cdots$
320.2.o.c	$320$	$2$	320.o	40.k	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$-2$	$2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{3}+(-1-2i)q^{5}+(1-i)q^{7}+\cdots$
320.2.o.d	$320$	$2$	320.o	40.k	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$2$	$-2$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1-i)q^{3}+(1+2i)q^{5}+(-1+i)q^{7}+\cdots$
320.2.o.e	$320$	$2$	320.o	40.k	$4$	$8$	$4$	$2.555$	8.0.49787136.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$-4$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{2}-\beta _{7})q^{3}+\beta _{7}q^{5}-\beta _{6}q^{7}+\cdots$
320.2.o.f	$320$	$2$	320.o	40.k	$4$	$8$	$4$	$2.555$	8.0.49787136.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$4$		$2^{6}$	$\mathrm{SU}(2)[C_{4}]$	$q+(-\beta _{2}-\beta _{7})q^{3}-\beta _{7}q^{5}+\beta _{6}q^{7}+\cdots$
320.2.q.a	$320$	$2$	320.q	80.q	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$-2$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(-1-i)q^{3}+(1+2i)q^{5}-iq^{9}+\cdots$
320.2.q.b	$320$	$2$	320.q	80.q	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$2$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+(1+i)q^{3}+(2+i)q^{5}-iq^{9}+(3+3i)q^{11}+\cdots$
320.2.q.c	$320$	$2$	320.q	80.q	$4$	$16$	$8$	$2.555$	16.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$		$2^{12}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{11}q^{3}+(-1-\beta _{6}-\beta _{10})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots$
320.2.s.a	$320$	$2$	320.s	80.s	$4$	$2$	$1$	$2.555$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$4$	$-4$	$6$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+2q^{3}+(-2+i)q^{5}+(3+3i)q^{7}+\cdots$
320.2.s.b	$320$	$2$	320.s	80.s	$4$	$18$	$9$	$2.555$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$-2$		$2^{13}$	$\mathrm{SU}(2)[C_{4}]$	$q-\beta _{1}q^{3}+\beta _{7}q^{5}+\beta _{10}q^{7}+(1-\beta _{1}+\cdots)q^{9}+\cdots$
320.2.bd.a	$320$	$2$	320.bd	320.ad	$16$	$368$	$46$	$2.555$		$_{}$	None	None		$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
320.2.be.a	$320$	$2$	320.be	64.i	$16$	$256$	$32$	$2.555$		$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{16}]$
320.2.bf.a	$320$	$2$	320.bf	320.af	$16$	$368$	$46$	$2.555$		$_{}$	None	None		$4$	$0$	$0$	$0$	$-8$	$0$			$\mathrm{SU}(2)[C_{16}]$
320.2.bj.a	$320$	$2$	320.bj	320.aj	$16$	$368$	$46$	$2.555$		$_{}$	None	None		$2$	$0$	$-8$	$-8$	$-8$	$-8$			$\mathrm{SU}(2)[C_{16}]$
320.3.b.a	$320$	$3$	320.b	4.b	$2$	$4$	$4$	$8.719$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{3}-\beta _{1}q^{5}+\beta _{3}q^{7}+(-9+6\beta _{1}+\cdots)q^{9}+\cdots$
320.3.b.b	$320$	$3$	320.b	4.b	$2$	$4$	$4$	$8.719$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{3}+\beta _{3}q^{5}+(\beta _{1}-4\beta _{2})q^{7}+(-5+\cdots)q^{9}+\cdots$
320.3.b.c	$320$	$3$	320.b	4.b	$2$	$4$	$4$	$8.719$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\zeta_{10}^{3}q^{3}+\zeta_{10}^{2}q^{5}+(-\zeta_{10}+\zeta_{10}^{3})q^{7}+\cdots$
320.3.b.d	$320$	$3$	320.b	4.b	$2$	$4$	$4$	$8.719$	$\Q(i, \sqrt{5})$	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}-\beta _{2}q^{5}-\beta _{1}q^{7}+(3+2\beta _{2}+\cdots)q^{9}+\cdots$
320.3.e.a	$320$	$3$	320.e	40.e	$2$	$8$	$8$	$8.719$	8.0.$\cdots$.3	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{5}q^{3}+(-\beta _{4}-\beta _{6})q^{5}+\beta _{2}q^{7}+\cdots$
320.3.e.b	$320$	$3$	320.e	40.e	$2$	$16$	$16$	$8.719$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$2^{34}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{3}+\beta _{4}q^{5}-\beta _{11}q^{7}+(-6-\beta _{5}+\cdots)q^{9}+\cdots$

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Elliptic curves over $\Q$
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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.