LMFDB - Newform search results

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Level	Weight	Analytic conductor	Analytic rank	Dim.

Bad $p$	Char.	Primitive character	Character order	Is maximal/largest

Coefficient field	Self-twists	CM/RM discriminant	Inner twist count	Is self-dual

Coefficient ring index	Coefficient ring gens.	Is twist minimal	Projective image

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				A-L signs					Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	2	3	5	13	19	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
7410.2.a.a	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.a	$1$	$0$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
7410.2.a.b	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.b	$1$	$0$	$-1$	$-1$	$-1$	$0$	$+$	$+$	$+$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
7410.2.a.c	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.c	$1$	$1$	$-1$	$-1$	$-1$	$3$	$+$	$+$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+3q^{7}+\cdots$
7410.2.a.d	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.d	$1$	$0$	$-1$	$-1$	$1$	$-5$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-5q^{7}+\cdots$
7410.2.a.e	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.e	$1$	$0$	$-1$	$-1$	$1$	$-2$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
7410.2.a.f	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.f	$1$	$0$	$-1$	$-1$	$1$	$0$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-q^{8}+\cdots$
7410.2.a.g	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.g	$1$	$0$	$-1$	$-1$	$1$	$4$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
7410.2.a.h	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.h	$1$	$0$	$-1$	$-1$	$1$	$4$	$+$	$+$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
7410.2.a.i	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.i	$1$	$0$	$-1$	$1$	$-1$	$0$	$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
7410.2.a.j	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.j	$1$	$1$	$-1$	$1$	$-1$	$1$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+q^{7}+\cdots$
7410.2.a.k	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.k	$1$	$0$	$-1$	$1$	$-1$	$4$	$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+4q^{7}+\cdots$
7410.2.a.l	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.l	$1$	$1$	$-1$	$1$	$1$	$0$	$+$	$-$	$-$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}-q^{8}+\cdots$
7410.2.a.m	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.m	$1$	$0$	$-1$	$1$	$1$	$2$	$+$	$-$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$
7410.2.a.n	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.n	$1$	$0$	$1$	$-1$	$1$	$-4$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-4q^{7}+\cdots$
7410.2.a.o	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.o	$1$	$0$	$1$	$-1$	$1$	$-3$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}-3q^{7}+\cdots$
7410.2.a.p	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.p	$1$	$1$	$1$	$-1$	$1$	$0$	$-$	$+$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
7410.2.a.q	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.q	$1$	$0$	$1$	$-1$	$1$	$0$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+q^{8}+\cdots$
7410.2.a.r	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.r	$1$	$0$	$1$	$-1$	$1$	$2$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+2q^{7}+\cdots$
7410.2.a.s	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.s	$1$	$1$	$1$	$1$	$-1$	$-4$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-4q^{7}+\cdots$
7410.2.a.t	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.t	$1$	$1$	$1$	$1$	$-1$	$-1$	$-$	$-$	$+$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}-q^{7}+\cdots$
7410.2.a.u	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.u	$1$	$1$	$1$	$1$	$-1$	$0$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+q^{8}+\cdots$
7410.2.a.v	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓	✓	✓	7410.2.a.v	$1$	$1$	$1$	$1$	$1$	$-2$	$-$	$-$	$-$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-2q^{7}+\cdots$
7410.2.a.w	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.w	$1$	$0$	$1$	$1$	$1$	$-1$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-q^{7}+\cdots$
7410.2.a.x	$7410$	$2$	7410.a	1.a	$1$	$1$	$1$	$59.169$	$\Q$	None	✓	✓			7410.2.a.x	$1$	$0$	$1$	$1$	$1$	$4$	$-$	$-$	$-$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+4q^{7}+\cdots$
7410.2.a.y	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{17}) $	None	✓	✓			7410.2.a.y	$1$	$0$	$-2$	$-2$	$-2$	$0$	$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}-q^{8}+\cdots$
7410.2.a.z	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{2}) $	None	✓	✓			7410.2.a.z	$1$	$0$	$-2$	$-2$	$-2$	$0$	$+$	$+$	$+$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+3\beta q^{7}+\cdots$
7410.2.a.ba	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{2}) $	None	✓	✓	✓		7410.2.a.ba	$1$	$1$	$-2$	$2$	$-2$	$-4$	$+$	$-$	$+$	$-$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots$
7410.2.a.bb	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{97}) $	None	✓	✓	✓		7410.2.a.bb	$1$	$0$	$-2$	$2$	$-2$	$0$	$+$	$-$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}-q^{8}+\cdots$
7410.2.a.bc	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{5}) $	None	✓	✓	✓		7410.2.a.bc	$1$	$1$	$-2$	$2$	$2$	$-2$	$+$	$-$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
7410.2.a.bd	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{3}) $	None	✓	✓	✓	✓	7410.2.a.bd	$1$	$1$	$-2$	$2$	$2$	$-2$	$+$	$-$	$-$	$-$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
7410.2.a.be	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{2}) $	None	✓	✓			7410.2.a.be	$1$	$0$	$2$	$-2$	$-2$	$0$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+3\beta q^{7}+\cdots$
7410.2.a.bf	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{17}) $	None	✓	✓			7410.2.a.bf	$1$	$0$	$2$	$-2$	$-2$	$0$	$-$	$+$	$+$	$+$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+q^{8}+\cdots$
7410.2.a.bg	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{5}) $	None	✓	✓			7410.2.a.bg	$1$	$1$	$2$	$-2$	$-2$	$4$	$-$	$+$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+2q^{7}+\cdots$
7410.2.a.bh	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{5}) $	None	✓	✓	✓		7410.2.a.bh	$1$	$1$	$2$	$-2$	$2$	$-2$	$-$	$+$	$-$	$-$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
7410.2.a.bi	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{17}) $	None	✓	✓			7410.2.a.bi	$1$	$0$	$2$	$-2$	$2$	$1$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+\beta q^{7}+\cdots$
7410.2.a.bj	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{57}) $	None	✓	✓	✓		7410.2.a.bj	$1$	$0$	$2$	$-2$	$2$	$8$	$-$	$+$	$-$	$-$	$+$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+4q^{7}+\cdots$
7410.2.a.bk	$7410$	$2$	7410.a	1.a	$1$	$2$	$2$	$59.169$	$\Q(\sqrt{2}) $	None	✓	✓	✓	✓	7410.2.a.bk	$1$	$1$	$2$	$2$	$2$	$-4$	$-$	$-$	$-$	$+$	$-$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
7410.2.a.bl	$7410$	$2$	7410.a	1.a	$1$	$3$	$3$	$59.169$	3.3.837.1	None	✓	✓	✓		7410.2.a.bl	$1$	$1$	$3$	$-3$	$-3$	$-3$	$-$	$+$	$+$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
7410.2.a.bm	$7410$	$2$	7410.a	1.a	$1$	$3$	$3$	$59.169$	3.3.3580.1	None	✓	✓	✓		7410.2.a.bm	$1$	$0$	$3$	$-3$	$3$	$-2$	$-$	$+$	$-$	$+$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-1+\cdots)q^{7}+\cdots$
7410.2.a.bn	$7410$	$2$	7410.a	1.a	$1$	$3$	$3$	$59.169$	3.3.568.1	None	✓	✓	✓		7410.2.a.bn	$1$	$1$	$3$	$3$	$-3$	$-5$	$-$	$-$	$+$	$+$	$+$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}-q^{5}+q^{6}+(-2+\cdots)q^{7}+\cdots$
7410.2.a.bo	$7410$	$2$	7410.a	1.a	$1$	$4$	$4$	$59.169$	4.4.85688.1	None	✓	✓	✓	✓	7410.2.a.bo	$1$	$0$	$-4$	$-4$	$4$	$-1$	$+$	$+$	$-$	$-$	$-$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}-\beta _{1}q^{7}+\cdots$
7410.2.a.bp	$7410$	$2$	7410.a	1.a	$1$	$4$	$4$	$59.169$	4.4.11344.1	None	✓	✓	✓	✓	7410.2.a.bp	$1$	$1$	$-4$	$-4$	$4$	$0$	$+$	$+$	$-$	$-$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+\beta _{1}q^{7}+\cdots$
7410.2.a.bq	$7410$	$2$	7410.a	1.a	$1$	$4$	$4$	$59.169$	4.4.15188.1	None	✓	✓	✓	✓	7410.2.a.bq	$1$	$0$	$4$	$-4$	$-4$	$-2$	$-$	$+$	$+$	$-$	$-$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+\beta _{3}q^{7}+\cdots$
7410.2.a.br	$7410$	$2$	7410.a	1.a	$1$	$4$	$4$	$59.169$	$\Q(\zeta_{16})^+$	None	✓	✓	✓	✓	7410.2.a.br	$1$	$1$	$4$	$-4$	$4$	$0$	$-$	$+$	$-$	$+$	$+$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}+q^{5}-q^{6}+(-\beta _{2}+\cdots)q^{7}+\cdots$
7410.2.a.bs	$7410$	$2$	7410.a	1.a	$1$	$4$	$4$	$59.169$	4.4.324176.1	None	✓	✓	✓		7410.2.a.bs	$1$	$0$	$4$	$4$	$4$	$0$	$-$	$-$	$-$	$+$	$+$	$-$	$2$	$\mathrm{SU}(2)$	$q+q^{2}+q^{3}+q^{4}+q^{5}+q^{6}-\beta _{1}q^{7}+\cdots$
7410.2.a.bt	$7410$	$2$	7410.a	1.a	$1$	$5$	$5$	$59.169$	5.5.4894544.1	None	✓	✓	✓		7410.2.a.bt	$1$	$1$	$-5$	$-5$	$-5$	$-2$	$+$	$+$	$+$	$-$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}-q^{5}+q^{6}+\beta _{4}q^{7}+\cdots$
7410.2.a.bu	$7410$	$2$	7410.a	1.a	$1$	$5$	$5$	$59.169$	5.5.394064.1	None	✓	✓	✓	✓	7410.2.a.bu	$1$	$1$	$-5$	$-5$	$5$	$4$	$+$	$+$	$-$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}-q^{3}+q^{4}+q^{5}+q^{6}+(1-\beta _{1}+\cdots)q^{7}+\cdots$
7410.2.a.bv	$7410$	$2$	7410.a	1.a	$1$	$5$	$5$	$59.169$	5.5.998068.1	None	✓	✓	✓	✓	7410.2.a.bv	$1$	$1$	$-5$	$5$	$-5$	$-9$	$+$	$-$	$+$	$+$	$-$	$+$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}-q^{5}-q^{6}+(-2+\cdots)q^{7}+\cdots$
7410.2.a.bw	$7410$	$2$	7410.a	1.a	$1$	$5$	$5$	$59.169$	5.5.9733193.1	None	✓	✓	✓		7410.2.a.bw	$1$	$0$	$-5$	$5$	$5$	$1$	$+$	$-$	$-$	$+$	$-$	$-$	$2^{2}$	$\mathrm{SU}(2)$	$q-q^{2}+q^{3}+q^{4}+q^{5}-q^{6}+\beta _{1}q^{7}+\cdots$
7410.2.a.bx	$7410$	$2$	7410.a	1.a	$1$	$5$	$5$	$59.169$	5.5.1493248.1	None	✓	✓	✓	✓	7410.2.a.bx	$1$	$1$	$5$	$-5$	$-5$	$1$	$-$	$+$	$+$	$+$	$-$	$+$	$2$	$\mathrm{SU}(2)$	$q+q^{2}-q^{3}+q^{4}-q^{5}-q^{6}+\beta _{2}q^{7}+\cdots$

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

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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.