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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Results (1-50 of 91 matches)

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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	Coefficient ring index	Sato-Tate	$q$-expansion
1215.1.d.a	$1215$	$1$	1215.d	15.d	$2$	$3$	$3$	$0.606$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-15}) $	None	✓	✓			1215.1.d.a	$2$	$0$	$0$	$0$	$-3$	$0$		$1$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{1}+\cdots)q^{8}+\cdots$
1215.1.d.b	$1215$	$1$	1215.d	15.d	$2$	$3$	$3$	$0.606$	$\Q(\zeta_{18})^+$	$D_{9}$	$\Q(\sqrt{-15}) $	None	✓	✓			1215.1.d.a	$2$	$0$	$0$	$0$	$3$	$0$		$1$		$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(-1-\beta _{1}+\cdots)q^{8}+\cdots$
1215.1.h.a	$1215$	$1$	1215.h	45.h	$6$	$6$	$3$	$0.606$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		✓			1215.1.d.a	$4$	$0$	$0$	$0$	$-3$	$0$		$3$		$q+(\zeta_{18}^{4}+\zeta_{18}^{8})q^{2}+(-\zeta_{18}^{3}-\zeta_{18}^{7}+\cdots)q^{4}+\cdots$
1215.1.h.b	$1215$	$1$	1215.h	45.h	$6$	$6$	$3$	$0.606$	$\Q(\zeta_{18})$	$D_{9}$	$\Q(\sqrt{-15}) $	None		✓			1215.1.d.a	$4$	$0$	$0$	$0$	$3$	$0$		$3$		$q+(\zeta_{18}-\zeta_{18}^{2})q^{2}+(\zeta_{18}^{2}-\zeta_{18}^{3}+\cdots)q^{4}+\cdots$
1215.2.a.a	$1215$	$2$	1215.a	1.a	$1$	$1$	$1$	$9.702$	$\Q$	$_{}$	None	None	✓	✓			1215.2.a.a	$1$	$1$	$-2$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{2}+2q^{4}-q^{5}+2q^{10}-2q^{11}+\cdots$
1215.2.a.b	$1215$	$2$	1215.a	1.a	$1$	$1$	$1$	$9.702$	$\Q$	$_{}$	None	None	✓	✓			1215.2.a.b	$1$	$1$	$-1$	$0$	$1$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}-3q^{7}+3q^{8}-q^{10}+\cdots$
1215.2.a.c	$1215$	$2$	1215.a	1.a	$1$	$1$	$1$	$9.702$	$\Q$	$_{}$	None	None	✓	✓			1215.2.a.c	$1$	$1$	$-1$	$0$	$1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+3q^{7}+3q^{8}-q^{10}+\cdots$
1215.2.a.d	$1215$	$2$	1215.a	1.a	$1$	$1$	$1$	$9.702$	$\Q$	$_{}$	None	None	✓	✓			1215.2.a.d	$1$	$0$	$-1$	$0$	$1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{2}-q^{4}+q^{5}+3q^{7}+3q^{8}-q^{10}+\cdots$
1215.2.a.e	$1215$	$2$	1215.a	1.a	$1$	$1$	$1$	$9.702$	$\Q$	$_{}$	None	None	✓	✓			1215.2.a.e	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}-q^{5}-q^{7}+6q^{11}+2q^{13}+\cdots$
1215.2.a.f	$1215$	$2$	1215.a	1.a	$1$	$1$	$1$	$9.702$	$\Q$	$_{}$	None	None	✓	✓			1215.2.a.e	$1$	$0$	$0$	$0$	$1$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q-2q^{4}+q^{5}-q^{7}-6q^{11}+2q^{13}+\cdots$
1215.2.a.g	$1215$	$2$	1215.a	1.a	$1$	$1$	$1$	$9.702$	$\Q$	$_{}$	None	None	✓	✓			1215.2.a.b	$1$	$0$	$1$	$0$	$-1$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}-3q^{7}-3q^{8}-q^{10}+\cdots$
1215.2.a.h	$1215$	$2$	1215.a	1.a	$1$	$1$	$1$	$9.702$	$\Q$	$_{}$	None	None	✓	✓			1215.2.a.d	$1$	$1$	$1$	$0$	$-1$	$3$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}+3q^{7}-3q^{8}-q^{10}+\cdots$
1215.2.a.i	$1215$	$2$	1215.a	1.a	$1$	$1$	$1$	$9.702$	$\Q$	$_{}$	None	None	✓	✓			1215.2.a.c	$1$	$0$	$1$	$0$	$-1$	$3$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{2}-q^{4}-q^{5}+3q^{7}-3q^{8}-q^{10}+\cdots$
1215.2.a.j	$1215$	$2$	1215.a	1.a	$1$	$1$	$1$	$9.702$	$\Q$	$_{}$	None	None	✓	✓			1215.2.a.a	$1$	$0$	$2$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+2q^{2}+2q^{4}+q^{5}+2q^{10}+2q^{11}+\cdots$
1215.2.a.k	$1215$	$2$	1215.a	1.a	$1$	$2$	$2$	$9.702$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			1215.2.a.k	$1$	$1$	$-1$	$0$	$2$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(1+\beta )q^{4}+q^{5}+(-1+\beta )q^{7}+\cdots$
1215.2.a.l	$1215$	$2$	1215.a	1.a	$1$	$2$	$2$	$9.702$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	✓			1215.2.a.l	$1$	$1$	$-1$	$0$	$-2$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta q^{2}+(3+\beta )q^{4}-q^{5}+(-1-\beta )q^{7}+\cdots$
1215.2.a.m	$1215$	$2$	1215.a	1.a	$1$	$2$	$2$	$9.702$	$\Q(\sqrt{13}) $	$_{}$	None	None	✓	✓			1215.2.a.k	$1$	$0$	$1$	$0$	$-2$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(1+\beta )q^{4}-q^{5}+(-1+\beta )q^{7}+\cdots$
1215.2.a.n	$1215$	$2$	1215.a	1.a	$1$	$2$	$2$	$9.702$	$\Q(\sqrt{21}) $	$_{}$	None	None	✓	✓			1215.2.a.l	$1$	$0$	$1$	$0$	$2$	$-3$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta q^{2}+(3+\beta )q^{4}+q^{5}+(-1-\beta )q^{7}+\cdots$
1215.2.a.o	$1215$	$2$	1215.a	1.a	$1$	$3$	$3$	$9.702$	3.3.564.1	$_{}$	None	None	✓	✓			1215.2.a.o	$1$	$1$	$-1$	$0$	$-3$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(2+\beta _{2})q^{4}-q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots$
1215.2.a.p	$1215$	$2$	1215.a	1.a	$1$	$3$	$3$	$9.702$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓			1215.2.a.p	$1$	$1$	$0$	$0$	$-3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-q^{5}+(-1-\beta _{2})q^{7}+\cdots$
1215.2.a.q	$1215$	$2$	1215.a	1.a	$1$	$3$	$3$	$9.702$	$\Q(\zeta_{18})^+$	$_{}$	None	None	✓	✓	✓		1215.2.a.p	$1$	$1$	$0$	$0$	$3$	$-3$	$+$	$1$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+q^{5}+(-1-\beta _{2})q^{7}+\cdots$
1215.2.a.r	$1215$	$2$	1215.a	1.a	$1$	$3$	$3$	$9.702$	3.3.564.1	$_{}$	None	None	✓	✓			1215.2.a.o	$1$	$0$	$1$	$0$	$3$	$-1$	$-$	$1$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+q^{5}+(-1+2\beta _{1}+\cdots)q^{7}+\cdots$
1215.2.a.s	$1215$	$2$	1215.a	1.a	$1$	$9$	$9$	$9.702$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓		1215.2.a.s	$1$	$0$	$0$	$0$	$-9$	$9$	$-$	$3^{3}$	$\mathrm{SU}(2)$	$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-q^{5}+(1+\beta _{8})q^{7}+\cdots$
1215.2.a.t	$1215$	$2$	1215.a	1.a	$1$	$9$	$9$	$9.702$	$\mathbb{Q}[x]/(x^{9} - \cdots)$	$_{}$	None	None	✓	✓	✓		1215.2.a.s	$1$	$0$	$0$	$0$	$9$	$9$	$-$	$3^{3}$	$\mathrm{SU}(2)$	$q-\beta _{1}q^{2}+(1+\beta _{2})q^{4}+q^{5}+(1+\beta _{8})q^{7}+\cdots$
1215.2.b.a	$1215$	$2$	1215.b	5.b	$2$	$12$	$12$	$9.702$	12.0.$\cdots$.1	$_{}$	$\Q(\sqrt{-15}) $	None		✓			1215.2.b.a	$4$	$0$	$0$	$0$	$0$	$0$		$3^{12}$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{2}+(-2+\beta _{7})q^{4}-\beta _{6}q^{5}+(-2\beta _{3}+\cdots)q^{8}+\cdots$
1215.2.b.b	$1215$	$2$	1215.b	5.b	$2$	$12$	$12$	$9.702$	12.0.$\cdots$.1	$_{}$	None	None		✓			1215.2.b.b	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}+(-1+\beta _{1})q^{4}+\beta _{3}q^{5}-\beta _{5}q^{7}+\cdots$
1215.2.b.c	$1215$	$2$	1215.b	5.b	$2$	$12$	$12$	$9.702$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1215.2.b.c	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{2}q^{2}+(-1-\beta _{3})q^{4}+(-\beta _{4}-\beta _{7}+\cdots)q^{5}+\cdots$
1215.2.b.d	$1215$	$2$	1215.b	5.b	$2$	$12$	$12$	$9.702$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	$_{}$	None	None		✓			1215.2.b.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+(-1-\beta _{1})q^{4}-\beta _{4}q^{5}+(\beta _{9}+\cdots)q^{7}+\cdots$
1215.2.b.e	$1215$	$2$	1215.b	5.b	$2$	$24$	$24$	$9.702$		$_{}$	None	None		✓	✓		1215.2.b.e	$4$	$0$	$0$	$0$	$0$	$0$			$\mathrm{SU}(2)[C_{2}]$
1215.2.e.a	$1215$	$2$	1215.e	9.c	$3$	$2$	$1$	$9.702$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1215.2.a.a	$2$	$0$	$-2$	$0$	$-1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-2+2\zeta_{6})q^{2}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots$
1215.2.e.b	$1215$	$2$	1215.e	9.c	$3$	$2$	$1$	$9.702$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1215.2.a.c	$2$	$0$	$-1$	$0$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
1215.2.e.c	$1215$	$2$	1215.e	9.c	$3$	$2$	$1$	$9.702$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1215.2.a.d	$2$	$1$	$-1$	$0$	$1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
1215.2.e.d	$1215$	$2$	1215.e	9.c	$3$	$2$	$1$	$9.702$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1215.2.a.b	$2$	$0$	$-1$	$0$	$1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(-1+\zeta_{6})q^{2}+\zeta_{6}q^{4}+\zeta_{6}q^{5}+(3+\cdots)q^{7}+\cdots$
1215.2.e.e	$1215$	$2$	1215.e	9.c	$3$	$2$	$1$	$9.702$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1215.2.a.e	$2$	$0$	$0$	$0$	$-1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(6+\cdots)q^{11}+\cdots$
1215.2.e.f	$1215$	$2$	1215.e	9.c	$3$	$2$	$1$	$9.702$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1215.2.a.e	$2$	$0$	$0$	$0$	$1$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(1-\zeta_{6})q^{7}+(-6+\cdots)q^{11}+\cdots$
1215.2.e.g	$1215$	$2$	1215.e	9.c	$3$	$2$	$1$	$9.702$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1215.2.a.d	$2$	$0$	$1$	$0$	$-1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
1215.2.e.h	$1215$	$2$	1215.e	9.c	$3$	$2$	$1$	$9.702$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1215.2.a.c	$2$	$0$	$1$	$0$	$-1$	$-3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots$
1215.2.e.i	$1215$	$2$	1215.e	9.c	$3$	$2$	$1$	$9.702$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1215.2.a.b	$2$	$0$	$1$	$0$	$-1$	$3$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(1-\zeta_{6})q^{2}+\zeta_{6}q^{4}-\zeta_{6}q^{5}+(3-3\zeta_{6})q^{7}+\cdots$
1215.2.e.j	$1215$	$2$	1215.e	9.c	$3$	$2$	$1$	$9.702$	$\Q(\sqrt{-3}) $	$_{}$	None	None		✓			1215.2.a.a	$2$	$0$	$2$	$0$	$1$	$0$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+2q^{10}+\cdots$
1215.2.e.k	$1215$	$2$	1215.e	9.c	$3$	$4$	$2$	$9.702$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			1215.2.a.l	$2$	$0$	$-1$	$0$	$-2$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{3}q^{2}+(3\beta _{1}-\beta _{2}+\beta _{3})q^{4}+\beta _{1}q^{5}+\cdots$
1215.2.e.l	$1215$	$2$	1215.e	9.c	$3$	$4$	$2$	$9.702$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		✓			1215.2.a.k	$2$	$0$	$-1$	$0$	$2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
1215.2.e.m	$1215$	$2$	1215.e	9.c	$3$	$4$	$2$	$9.702$	$\Q(\sqrt{-3}, \sqrt{-7})$	$_{}$	None	None		✓			1215.2.a.l	$2$	$0$	$1$	$0$	$2$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{3}q^{2}+(3\beta _{1}-\beta _{2}+\beta _{3})q^{4}-\beta _{1}q^{5}+\cdots$
1215.2.e.n	$1215$	$2$	1215.e	9.c	$3$	$4$	$2$	$9.702$	$\Q(\sqrt{-3}, \sqrt{13})$	$_{}$	None	None		✓			1215.2.a.k	$2$	$0$	$1$	$0$	$-2$	$1$		$1$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots$
1215.2.e.o	$1215$	$2$	1215.e	9.c	$3$	$6$	$3$	$9.702$	6.0.954288.1	$_{}$	None	None		✓			1215.2.a.o	$2$	$0$	$-1$	$0$	$-3$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta _{4}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots$
1215.2.e.p	$1215$	$2$	1215.e	9.c	$3$	$6$	$3$	$9.702$	$\Q(\zeta_{18})$	$_{}$	None	None		✓			1215.2.a.p	$2$	$0$	$0$	$0$	$-3$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(\beta_{5}-\beta_{4}+\cdots+\beta_{2})q^{2}+\cdots+\beta_{5} q^{4}+\cdots$
1215.2.e.q	$1215$	$2$	1215.e	9.c	$3$	$6$	$3$	$9.702$	$\Q(\zeta_{18})$	$_{}$	None	None		✓			1215.2.a.p	$2$	$0$	$0$	$0$	$3$	$3$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta_{5}+\beta_{4}+\cdots-\beta_{2})q^{2}+\cdots+\beta_{5} q^{4}+\cdots$
1215.2.e.r	$1215$	$2$	1215.e	9.c	$3$	$6$	$3$	$9.702$	6.0.954288.1	$_{}$	None	None		✓			1215.2.a.o	$2$	$0$	$1$	$0$	$3$	$1$		$3$	$\mathrm{SU}(2)[C_{3}]$	$q+(-\beta _{4}+\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2}+\cdots)q^{4}+\cdots$
1215.2.e.s	$1215$	$2$	1215.e	9.c	$3$	$18$	$9$	$9.702$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓			1215.2.a.s	$2$	$0$	$0$	$0$	$-9$	$-9$		$3^{9}$	$\mathrm{SU}(2)[C_{3}]$	$q-\beta _{1}q^{2}+(-1+\beta _{4}+\beta _{6}+\beta _{12})q^{4}+\cdots$
1215.2.e.t	$1215$	$2$	1215.e	9.c	$3$	$18$	$9$	$9.702$	$\mathbb{Q}[x]/(x^{18} + \cdots)$	$_{}$	None	None		✓			1215.2.a.s	$2$	$0$	$0$	$0$	$9$	$-9$		$3^{9}$	$\mathrm{SU}(2)[C_{3}]$	$q+\beta _{1}q^{2}+(-1+\beta _{4}+\beta _{6}+\beta _{12})q^{4}+\cdots$
1215.3.c.a	$1215$	$3$	1215.c	3.b	$2$	$2$	$2$	$33.106$	$\Q(\sqrt{-5}) $	$_{}$	None	None		✓			1215.3.c.a	$2$	$0$	$0$	$0$	$0$	$-24$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta q^{2}-q^{4}-\beta q^{5}-12q^{7}+3\beta q^{8}+\cdots$

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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.