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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
200.1.e.a	$200$	$1$	200.e	40.e	$2$	$2$	$2$	$0.100$	$\Q(\sqrt{-1}) $	$D_{3}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-iq^{2}-iq^{3}-q^{4}-q^{6}+iq^{8}-q^{11}+\cdots$
200.1.g.a	$200$	$1$	200.g	8.d	$2$	$1$	$1$	$0.100$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$-1$	$1$	$0$	$0$		$1$		$q-q^{2}+q^{3}+q^{4}-q^{6}-q^{8}-q^{11}+\cdots$
200.1.g.b	$200$	$1$	200.g	8.d	$2$	$1$	$1$	$0.100$	$\Q$	$D_{3}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$1$	$-1$	$0$	$0$		$1$		$q+q^{2}-q^{3}+q^{4}-q^{6}+q^{8}-q^{11}+\cdots$
200.2.a.a	$200$	$2$	200.a	1.a	$1$	$1$	$1$	$1.597$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$-3$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-3q^{3}+2q^{7}+6q^{9}+q^{11}+4q^{13}+\cdots$
200.2.a.b	$200$	$2$	200.a	1.a	$1$	$1$	$1$	$1.597$	$\Q$	$_{}$	None	None	✓	$1$	$1$	$0$	$-2$	$0$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{3}-2q^{7}+q^{9}-4q^{11}-4q^{13}+\cdots$
200.2.a.c	$200$	$2$	200.a	1.a	$1$	$1$	$1$	$1.597$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$0$	$0$	$4$	$-$	$1$	$\mathrm{SU}(2)$	$q+4q^{7}-3q^{9}+4q^{11}+2q^{13}-2q^{17}+\cdots$
200.2.a.d	$200$	$2$	200.a	1.a	$1$	$1$	$1$	$1.597$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$2$	$0$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{3}+2q^{7}+q^{9}-4q^{11}+4q^{13}+\cdots$
200.2.a.e	$200$	$2$	200.a	1.a	$1$	$1$	$1$	$1.597$	$\Q$	$_{}$	None	None	✓	$1$	$0$	$0$	$3$	$0$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q+3q^{3}-2q^{7}+6q^{9}+q^{11}-4q^{13}+\cdots$
200.2.c.a	$200$	$2$	200.c	5.b	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+3iq^{3}+2iq^{7}-6q^{9}+q^{11}-4iq^{13}+\cdots$
200.2.c.b	$200$	$2$	200.c	5.b	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+2iq^{7}+3q^{9}+4q^{11}-iq^{13}-iq^{17}+\cdots$
200.2.d.a	$200$	$2$	200.d	8.b	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$-4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{2}-iq^{3}-2iq^{4}+(1+i)q^{6}+\cdots$
200.2.d.b	$200$	$2$	200.d	8.b	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{-7}) $	$_{}$	None	None		$2$	$0$	$-1$	$0$	$0$	$-8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta q^{2}+(1-2\beta )q^{3}+(-2+\beta )q^{4}+\cdots$
200.2.d.c	$200$	$2$	200.d	8.b	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{-7}) $	$_{}$	None	None		$2$	$0$	$1$	$0$	$0$	$8$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}+(-1+2\beta )q^{3}+(-2+\beta )q^{4}+\cdots$
200.2.d.d	$200$	$2$	200.d	8.b	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$4$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{2}-iq^{3}+2iq^{4}+(1-i)q^{6}+\cdots$
200.2.d.e	$200$	$2$	200.d	8.b	$2$	$4$	$4$	$1.597$	$\Q(\sqrt{-2}, \sqrt{-3})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{3}+(1+\beta _{3})q^{4}+(-1+\cdots)q^{6}+\cdots$
200.2.d.f	$200$	$2$	200.d	8.b	$2$	$4$	$4$	$1.597$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$2$	$0$	$0$	$4$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(1-\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
200.2.f.a	$200$	$2$	200.f	40.f	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$-2$	$-2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+i)q^{2}-q^{3}-2iq^{4}+(1-i)q^{6}+\cdots$
200.2.f.b	$200$	$2$	200.f	40.f	$2$	$2$	$2$	$1.597$	$\Q(\sqrt{-1}) $	$_{}$	None	None		$2$	$0$	$2$	$2$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots$
200.2.f.c	$200$	$2$	200.f	40.f	$2$	$4$	$4$	$1.597$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$-2$	$4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(1-\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
200.2.f.d	$200$	$2$	200.f	40.f	$2$	$4$	$4$	$1.597$	$\Q(i, \sqrt{7})$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+(-2\beta _{1}+\beta _{3})q^{3}+(1+\beta _{2}+\cdots)q^{4}+\cdots$
200.2.f.e	$200$	$2$	200.f	40.f	$2$	$4$	$4$	$1.597$	$\Q(\zeta_{12})$	$_{}$	None	None		$2$	$0$	$2$	$-4$	$0$	$0$		$2$	$\mathrm{SU}(2)[C_{2}]$	$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(-1+\zeta_{12}-\zeta_{12}^{2}+\cdots)q^{3}+\cdots$
200.2.k.a	$200$	$2$	200.k	40.k	$4$	$2$	$1$	$1.597$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$1$	$-2$	$-4$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1-i)q^{2}+(-2+2i)q^{3}+2iq^{4}+\cdots$
200.2.k.b	$200$	$2$	200.k	40.k	$4$	$2$	$1$	$1.597$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$-2$	$0$	$0$	$-4$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1+i)q^{2}-2iq^{4}+(-2+2i)q^{7}+\cdots$
200.2.k.c	$200$	$2$	200.k	40.k	$4$	$2$	$1$	$1.597$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$2$	$0$	$0$	$4$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1-i)q^{2}-2iq^{4}+(2-2i)q^{7}+(-2+\cdots)q^{8}+\cdots$
200.2.k.d	$200$	$2$	200.k	40.k	$4$	$2$	$1$	$1.597$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$2$	$4$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1+i)q^{2}+(2-2i)q^{3}+2iq^{4}+4q^{6}+\cdots$
200.2.k.e	$200$	$2$	200.k	40.k	$4$	$4$	$2$	$1.597$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$-4$	$4$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(-1-\beta _{2})q^{2}+(1-\beta _{2}+\beta _{3})q^{3}+\cdots$
200.2.k.f	$200$	$2$	200.k	40.k	$4$	$4$	$2$	$1.597$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$4$	$-4$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{4}]$	$q+(1+\beta _{2})q^{2}+(-1+\beta _{2}-\beta _{3})q^{3}+\cdots$
200.2.k.g	$200$	$2$	200.k	40.k	$4$	$8$	$4$	$1.597$	8.0.3317760000.5	$_{}$	None	None		$8$	$0$	$0$	$0$	$0$	$0$		$1$	$\mathrm{SU}(2)[C_{4}]$	$q+\beta _{1}q^{2}+(\beta _{4}+\beta _{6})q^{3}+\beta _{2}q^{4}+(2+\cdots)q^{6}+\cdots$
200.2.k.h	$200$	$2$	200.k	40.k	$4$	$8$	$4$	$1.597$	$\Q(\zeta_{20})$	$_{}$	None	None		$4$	$0$	$2$	$4$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	$q+\zeta_{20}^{7}q^{2}+(1-\zeta_{20}^{3}-\zeta_{20}^{5}+\zeta_{20}^{6}+\cdots)q^{3}+\cdots$
200.2.m.a	$200$	$2$	200.m	25.d	$5$	$4$	$1$	$1.597$	$\Q(\zeta_{10})$	$_{}$	None	None		$2$	$0$	$0$	$5$	$-5$	$6$		$1$	$\mathrm{SU}(2)[C_{5}]$	$q+(2-2\zeta_{10}-\zeta_{10}^{3})q^{3}+(-2+\zeta_{10}+\cdots)q^{5}+\cdots$
200.2.m.b	$200$	$2$	200.m	25.d	$5$	$8$	$2$	$1.597$	8.0.58140625.2	$_{}$	None	None		$2$	$0$	$0$	$-6$	$5$	$4$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+(-1+\beta _{2})q^{3}+(1+\beta _{5})q^{5}+(\beta _{1}-\beta _{4}+\cdots)q^{7}+\cdots$
200.2.m.c	$200$	$2$	200.m	25.d	$5$	$16$	$4$	$1.597$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$2$	$0$	$0$	$1$	$-1$	$-6$		$5$	$\mathrm{SU}(2)[C_{5}]$	$q+\beta _{1}q^{3}+(-1+\beta _{2}-\beta _{4}+\beta _{5}+\beta _{14}+\cdots)q^{5}+\cdots$
200.2.o.a	$200$	$2$	200.o	200.o	$10$	$112$	$28$	$1.597$		$_{}$	None	None		$4$	$0$	$-5$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{10}]$
200.2.q.a	$200$	$2$	200.q	25.e	$10$	$32$	$8$	$1.597$		$_{}$	None	None		$2$	$0$	$0$	$0$	$2$	$0$			$\mathrm{SU}(2)[C_{10}]$
200.2.t.a	$200$	$2$	200.t	200.t	$10$	$112$	$28$	$1.597$		$_{}$	None	None		$4$	$0$	$-3$	$0$	$0$	$-16$			$\mathrm{SU}(2)[C_{10}]$
200.2.v.a	$200$	$2$	200.v	200.v	$20$	$8$	$1$	$1.597$	$\Q(\zeta_{20})$	$_{}$	None	None		$2$	$0$	$-8$	$0$	$10$	$4$		$1$	$\mathrm{SU}(2)[C_{20}]$	$q+(-1+\zeta_{20}^{5})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$
200.2.v.b	$200$	$2$	200.v	200.v	$20$	$8$	$1$	$1.597$	$\Q(\zeta_{20})$	$_{}$	None	None		$2$	$0$	$-2$	$0$	$-10$	$-4$		$1$	$\mathrm{SU}(2)[C_{20}]$	$q+(-\zeta_{20}-\zeta_{20}^{6})q^{2}+(1-\zeta_{20}-\zeta_{20}^{2}+\cdots)q^{3}+\cdots$
200.2.v.c	$200$	$2$	200.v	200.v	$20$	$208$	$26$	$1.597$		$_{}$	None	None		$4$	$0$	$2$	$-16$	$0$	$0$			$\mathrm{SU}(2)[C_{20}]$
200.3.e.a	$200$	$3$	200.e	40.e	$2$	$2$	$2$	$5.450$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{2}-iq^{3}-4q^{4}+4q^{6}-4iq^{8}+\cdots$
200.3.e.b	$200$	$3$	200.e	40.e	$2$	$4$	$4$	$5.450$	$\Q(i, \sqrt{6})$	$_{}$	$\Q(\sqrt{-2}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{3}$	$\mathrm{U}(1)[D_{2}]$	$q+2\beta _{1}q^{2}+(\beta _{1}+\beta _{2})q^{3}-4q^{4}+(-2+\cdots)q^{6}+\cdots$
200.3.e.c	$200$	$3$	200.e	40.e	$2$	$12$	$12$	$5.450$	$\mathbb{Q}[x]/(x^{12} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}-\beta _{3}q^{3}+(1+\beta _{6}+\beta _{9})q^{4}+\cdots$
200.3.e.d	$200$	$3$	200.e	40.e	$2$	$16$	$16$	$5.450$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{27}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{2}q^{3}+(1+\beta _{11})q^{4}+(-2+\cdots)q^{6}+\cdots$
200.3.g.a	$200$	$3$	200.g	8.d	$2$	$1$	$1$	$5.450$	$\Q$	$_{}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$2$	$2$	$0$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+2q^{3}+4q^{4}+4q^{6}+8q^{8}+\cdots$
200.3.g.b	$200$	$3$	200.g	8.d	$2$	$2$	$2$	$5.450$	$\Q(\sqrt{6}) $	$_{}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$-4$	$2$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-2q^{2}+(1+\beta )q^{3}+4q^{4}+(-2-2\beta )q^{6}+\cdots$
200.3.g.c	$200$	$3$	200.g	8.d	$2$	$2$	$2$	$5.450$	$\Q(\sqrt{-1}) $	$_{}$	$\Q(\sqrt{-10}) $	None		$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+iq^{2}-4q^{4}-3iq^{7}-4iq^{8}-9q^{9}+\cdots$
200.3.g.d	$200$	$3$	200.g	8.d	$2$	$2$	$2$	$5.450$	$\Q(\sqrt{6}) $	$_{}$	$\Q(\sqrt{-2}) $	None	✓	$2$	$0$	$4$	$-2$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+2q^{2}+(-1+\beta )q^{3}+4q^{4}+(-2+\cdots)q^{6}+\cdots$
200.3.g.e	$200$	$3$	200.g	8.d	$2$	$6$	$6$	$5.450$	6.0.189974000.1	$_{}$	None	None		$2$	$0$	$-3$	$2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1+\beta _{1})q^{2}+\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
200.3.g.f	$200$	$3$	200.g	8.d	$2$	$6$	$6$	$5.450$	6.0.189974000.1	$_{}$	None	None		$2$	$0$	$3$	$-2$	$0$	$0$		$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+(1-\beta _{1})q^{2}-\beta _{2}q^{3}+(-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
200.3.g.g	$200$	$3$	200.g	8.d	$2$	$8$	$8$	$5.450$	8.0.$\cdots$.1	$_{}$	None	None		$2$	$0$	$-2$	$0$	$0$	$0$		$2^{6}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{4}q^{2}+\beta _{6}q^{3}+(-1+\beta _{1})q^{4}+(-1+\cdots)q^{6}+\cdots$
200.3.g.h	$200$	$3$	200.g	8.d	$2$	$8$	$8$	$5.450$	8.0.$\cdots$.1	$_{}$	None	None		$4$	$0$	$0$	$0$	$0$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{4}q^{2}+\beta _{6}q^{3}+(2+\beta _{5})q^{4}+(2-\beta _{2}+\cdots)q^{6}+\cdots$

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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.