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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 133 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
1080.1.c.a	$1080$	$1$	1080.c	15.d	$2$	$4$	$4$	$0.539$	$\Q(\zeta_{8})$	$S_{4}$	None	None		✓	✓	✓	1080.1.c.a	$4$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{8}q^{5}+\zeta_{8}^{2}q^{7}+(\zeta_{8}+\zeta_{8}^{3})q^{11}+\cdots$
1080.1.i.a	$1080$	$1$	1080.i	120.i	$2$	$1$	$1$	$0.539$	$\Q$	$D_{3}$	$\Q(\sqrt{-30}) $	None	✓	✓			1080.1.i.a	$2$	$0$	$-1$	$0$	$-1$	$0$		$1$		$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}+q^{11}+\cdots$
1080.1.i.b	$1080$	$1$	1080.i	120.i	$2$	$1$	$1$	$0.539$	$\Q$	$D_{3}$	$\Q(\sqrt{-30}) $	None	✓	✓			1080.1.i.a	$2$	$0$	$-1$	$0$	$1$	$0$		$1$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-q^{11}+\cdots$
1080.1.i.c	$1080$	$1$	1080.i	120.i	$2$	$1$	$1$	$0.539$	$\Q$	$D_{3}$	$\Q(\sqrt{-30}) $	None	✓	✓			1080.1.i.a	$2$	$0$	$1$	$0$	$-1$	$0$		$1$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{11}+\cdots$
1080.1.i.d	$1080$	$1$	1080.i	120.i	$2$	$1$	$1$	$0.539$	$\Q$	$D_{3}$	$\Q(\sqrt{-30}) $	None	✓	✓			1080.1.i.a	$2$	$0$	$1$	$0$	$1$	$0$		$1$		$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}-q^{11}+\cdots$
1080.1.i.e	$1080$	$1$	1080.i	120.i	$2$	$4$	$4$	$0.539$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-6}) $	None		✓			1080.1.i.e	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}^{3}q^{2}-q^{4}-\zeta_{12}q^{5}+(\zeta_{12}^{2}+\cdots)q^{7}+\cdots$
1080.1.i.f	$1080$	$1$	1080.i	120.i	$2$	$4$	$4$	$0.539$	$\Q(\zeta_{12})$	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1080.1.i.f	$8$	$0$	$0$	$0$	$0$	$0$		$1$		$q-\zeta_{12}q^{2}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}-\zeta_{12}^{3}q^{8}+\cdots$
1080.1.p.a	$1080$	$1$	1080.p	40.e	$2$	$2$	$2$	$0.539$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1080.1.p.a	$4$	$0$	$-1$	$0$	$-2$	$0$		$1$		$q+\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}-q^{5}+q^{8}-\zeta_{6}^{2}q^{10}+\cdots$
1080.1.p.b	$1080$	$1$	1080.p	40.e	$2$	$2$	$2$	$0.539$	$\Q(\sqrt{-3}) $	$D_{6}$	$\Q(\sqrt{-15}) $	None		✓			1080.1.p.a	$4$	$0$	$1$	$0$	$2$	$0$		$1$		$q-\zeta_{6}^{2}q^{2}-\zeta_{6}q^{4}+q^{5}-q^{8}-\zeta_{6}^{2}q^{10}+\cdots$
1080.1.u.a	$1080$	$1$	1080.u	40.i	$4$	$8$	$4$	$0.539$	$\Q(\zeta_{24})$	$D_{12}$	$\Q(\sqrt{-6}) $	None		✓	✓	✓	1080.1.u.a	$8$	$0$	$0$	$0$	$0$	$4$		$1$		$q+\zeta_{24}^{3}q^{2}+\zeta_{24}^{6}q^{4}-\zeta_{24}q^{5}+(-\zeta_{24}^{2}+\cdots)q^{7}+\cdots$
1080.2.a.a	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓			1080.2.a.a	$1$	$0$	$0$	$0$	$-1$	$-4$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-4q^{7}+2q^{11}+4q^{13}+q^{17}+\cdots$
1080.2.a.b	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓			1080.2.a.b	$1$	$0$	$0$	$0$	$-1$	$-2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{7}-6q^{13}+7q^{17}+7q^{19}+\cdots$
1080.2.a.c	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓			1080.2.a.c	$1$	$1$	$0$	$0$	$-1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-q^{7}+2q^{11}-5q^{13}+4q^{17}+\cdots$
1080.2.a.d	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1080.2.a.d	$1$	$1$	$0$	$0$	$-1$	$0$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}-2q^{11}-3q^{17}-q^{19}-3q^{23}+\cdots$
1080.2.a.e	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓			1080.2.a.e	$1$	$1$	$0$	$0$	$-1$	$2$	$+$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-4q^{11}-2q^{13}-5q^{17}+\cdots$
1080.2.a.f	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓			1080.2.a.f	$1$	$0$	$0$	$0$	$-1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+2q^{7}-q^{11}+q^{13}+q^{17}+\cdots$
1080.2.a.g	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓			1080.2.a.a	$1$	$1$	$0$	$0$	$1$	$-4$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-4q^{7}-2q^{11}+4q^{13}-q^{17}+\cdots$
1080.2.a.h	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓	✓	✓	1080.2.a.b	$1$	$1$	$0$	$0$	$1$	$-2$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-2q^{7}-6q^{13}-7q^{17}+7q^{19}+\cdots$
1080.2.a.i	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓			1080.2.a.c	$1$	$1$	$0$	$0$	$1$	$-1$	$+$	$1$	$\mathrm{SU}(2)$	$q+q^{5}-q^{7}-2q^{11}-5q^{13}-4q^{17}+\cdots$
1080.2.a.j	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓			1080.2.a.d	$1$	$0$	$0$	$0$	$1$	$0$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{11}+3q^{17}-q^{19}+3q^{23}+\cdots$
1080.2.a.k	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓			1080.2.a.f	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+q^{11}+q^{13}-q^{17}+\cdots$
1080.2.a.l	$1080$	$2$	1080.a	1.a	$1$	$1$	$1$	$8.624$	$\Q$	$_{}$	None	None	✓	✓			1080.2.a.e	$1$	$0$	$0$	$0$	$1$	$2$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+2q^{7}+4q^{11}-2q^{13}+5q^{17}+\cdots$
1080.2.a.m	$1080$	$2$	1080.a	1.a	$1$	$2$	$2$	$8.624$	$\Q(\sqrt{73}) $	$_{}$	None	None	✓	✓	✓		1080.2.a.m	$1$	$0$	$0$	$0$	$-2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q-q^{5}+\beta q^{7}+(1-\beta )q^{11}+3q^{13}+\cdots$
1080.2.a.n	$1080$	$2$	1080.a	1.a	$1$	$2$	$2$	$8.624$	$\Q(\sqrt{73}) $	$_{}$	None	None	✓	✓	✓		1080.2.a.m	$1$	$0$	$0$	$0$	$2$	$1$	$-$	$1$	$\mathrm{SU}(2)$	$q+q^{5}+\beta q^{7}+(-1+\beta )q^{11}+3q^{13}+\cdots$
1080.2.b.a	$1080$	$2$	1080.b	24.f	$2$	$16$	$16$	$8.624$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1080.2.b.a	$2$	$0$	$-2$	$0$	$16$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{2}-\beta _{6}q^{4}+q^{5}-\beta _{4}q^{7}-\beta _{7}q^{8}+\cdots$
1080.2.b.b	$1080$	$2$	1080.b	24.f	$2$	$16$	$16$	$8.624$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1080.2.b.b	$2$	$0$	$-1$	$0$	$-16$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{6}q^{2}+\beta _{4}q^{4}-q^{5}-\beta _{2}q^{7}+\beta _{1}q^{8}+\cdots$
1080.2.b.c	$1080$	$2$	1080.b	24.f	$2$	$16$	$16$	$8.624$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1080.2.b.b	$2$	$0$	$1$	$0$	$16$	$0$		$2^{10}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{6}q^{2}+\beta _{4}q^{4}+q^{5}-\beta _{2}q^{7}-\beta _{1}q^{8}+\cdots$
1080.2.b.d	$1080$	$2$	1080.b	24.f	$2$	$16$	$16$	$8.624$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1080.2.b.a	$2$	$0$	$2$	$0$	$-16$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}-\beta _{6}q^{4}-q^{5}-\beta _{4}q^{7}+\beta _{7}q^{8}+\cdots$
1080.2.d.a	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		✓			1080.2.d.a	$4$	$0$	$-3$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(-1+\beta _{3})q^{2}+(\beta _{2}-\beta _{3})q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
1080.2.d.b	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-30}) $	None		✓			1080.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots$
1080.2.d.c	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	$\Q(\sqrt{-2}, \sqrt{-5})$	$_{}$	$\Q(\sqrt{-30}) $	None		✓			1080.2.d.b	$4$	$0$	$0$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{1}q^{2}-2q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{8}+\cdots$
1080.2.d.d	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-6}) $	None		✓			1080.2.d.d	$4$	$0$	$0$	$0$	$-6$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{2}+2q^{4}+(-2-\beta _{1}-\beta _{2}-\beta _{3})q^{5}+\cdots$
1080.2.d.e	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	$\Q(\sqrt{2}, \sqrt{-3})$	$_{}$	$\Q(\sqrt{-6}) $	None		✓			1080.2.d.d	$4$	$0$	$0$	$0$	$6$	$0$		$1$	$\mathrm{U}(1)[D_{2}]$	$q+\beta _{3}q^{2}+2q^{4}+(2+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+\cdots$
1080.2.d.f	$1080$	$2$	1080.d	40.f	$2$	$4$	$4$	$8.624$	$\Q(\sqrt{-3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		✓			1080.2.d.a	$4$	$0$	$3$	$0$	$0$	$0$		$2$	$\mathrm{U}(1)[D_{2}]$	$q+(1-\beta _{3})q^{2}+(\beta _{2}-\beta _{3})q^{4}+(\beta _{1}-\beta _{2}+\cdots)q^{5}+\cdots$
1080.2.d.g	$1080$	$2$	1080.d	40.f	$2$	$16$	$16$	$8.624$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1080.2.d.g	$4$	$0$	$-2$	$0$	$-6$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{12}q^{2}+(-1+\beta _{3}+\beta _{5})q^{4}-\beta _{10}q^{5}+\cdots$
1080.2.d.h	$1080$	$2$	1080.d	40.f	$2$	$16$	$16$	$8.624$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	$_{}$	None	None		✓			1080.2.d.g	$4$	$0$	$2$	$0$	$6$	$0$		$2^{6}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{12}q^{2}+(-1+\beta _{3}+\beta _{5})q^{4}+\beta _{10}q^{5}+\cdots$
1080.2.d.i	$1080$	$2$	1080.d	40.f	$2$	$20$	$20$	$8.624$	20.0.$\cdots$.1	$_{}$	None	None		✓			1080.2.d.i	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{8}q^{2}+\beta _{11}q^{4}+\beta _{14}q^{5}+(\beta _{12}+\cdots)q^{7}+\cdots$
1080.2.d.j	$1080$	$2$	1080.d	40.f	$2$	$20$	$20$	$8.624$	20.0.$\cdots$.1	$_{}$	None	None		✓			1080.2.d.i	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{1}q^{2}+\beta _{2}q^{4}+\beta _{14}q^{5}+(1-\beta _{3}+\cdots)q^{7}+\cdots$
1080.2.f.a	$1080$	$2$	1080.f	5.b	$2$	$2$	$2$	$8.624$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1080.2.f.a	$2$	$1$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(i-2)q^{5}+2 i q^{7}-2 q^{11}+2 i q^{13}+\cdots$
1080.2.f.b	$1080$	$2$	1080.f	5.b	$2$	$2$	$2$	$8.624$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1080.2.f.b	$2$	$0$	$0$	$0$	$-2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-2 i-1)q^{5}+4 i q^{7}-q^{11}+\cdots$
1080.2.f.c	$1080$	$2$	1080.f	5.b	$2$	$2$	$2$	$8.624$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1080.2.f.b	$2$	$0$	$0$	$0$	$2$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(2 i+1)q^{5}+4 i q^{7}+q^{11}+i q^{13}+\cdots$
1080.2.f.d	$1080$	$2$	1080.f	5.b	$2$	$2$	$2$	$8.624$	$\Q(\sqrt{-1}) $	$_{}$	None	None		✓			1080.2.f.a	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-i+2)q^{5}+2 i q^{7}+2 q^{11}+\cdots$
1080.2.f.e	$1080$	$2$	1080.f	5.b	$2$	$4$	$4$	$8.624$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			1080.2.f.e	$2$	$0$	$0$	$0$	$-4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(-1-\beta _{2}+\beta _{3})q^{5}-\beta _{2}q^{7}+(2-\beta _{1}+\cdots)q^{11}+\cdots$
1080.2.f.f	$1080$	$2$	1080.f	5.b	$2$	$4$	$4$	$8.624$	$\Q(i, \sqrt{6})$	$_{}$	None	None		✓			1080.2.f.e	$2$	$0$	$0$	$0$	$4$	$0$		$1$	$\mathrm{SU}(2)[C_{2}]$	$q+(1+\beta _{2}-\beta _{3})q^{5}-\beta _{2}q^{7}+(-2+\beta _{1}+\cdots)q^{11}+\cdots$
1080.2.f.g	$1080$	$2$	1080.f	5.b	$2$	$8$	$8$	$8.624$	$\Q(i, \sqrt{3}, \sqrt{19})$	$_{}$	None	None		✓	✓		1080.2.f.g	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{3}q^{5}-\beta _{1}q^{7}+(-2\beta _{3}-\beta _{6}+2\beta _{7})q^{11}+\cdots$
1080.2.k.a	$1080$	$2$	1080.k	8.b	$2$	$12$	$12$	$8.624$	12.0.$\cdots$.1	$_{}$	None	None		✓			1080.2.k.a	$4$	$0$	$0$	$0$	$0$	$0$		$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}-\beta _{8}q^{4}-\beta _{7}q^{5}+(-\beta _{3}+\beta _{5}+\cdots)q^{7}+\cdots$
1080.2.k.b	$1080$	$2$	1080.k	8.b	$2$	$16$	$16$	$8.624$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			1080.2.k.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{9}q^{2}-\beta _{2}q^{4}-\beta _{7}q^{5}-\beta _{14}q^{7}+\cdots$
1080.2.k.c	$1080$	$2$	1080.k	8.b	$2$	$16$	$16$	$8.624$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	$_{}$	None	None		✓			1080.2.k.b	$2$	$0$	$0$	$0$	$0$	$0$		$2^{5}$	$\mathrm{SU}(2)[C_{2}]$	$q+\beta _{1}q^{2}+\beta _{2}q^{4}-\beta _{8}q^{5}-\beta _{11}q^{7}+\cdots$
1080.2.k.d	$1080$	$2$	1080.k	8.b	$2$	$20$	$20$	$8.624$	20.0.$\cdots$.1	$_{}$	None	None		✓	✓		1080.2.k.d	$4$	$0$	$0$	$0$	$0$	$0$		$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{2}+\beta _{4}q^{4}-\beta _{6}q^{5}-\beta _{12}q^{7}+\cdots$
1080.2.m.a	$1080$	$2$	1080.m	120.m	$2$	$8$	$8$	$8.624$	$\Q(i, \sqrt{3}, \sqrt{5})$	$_{}$	$\Q(\sqrt{-15}) $	None		✓			1080.2.m.a	$8$	$0$	$0$	$0$	$0$	$0$		$2^{2}\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{3}q^{2}+\beta _{1}q^{4}+(\beta _{3}+\beta _{6})q^{5}+(-\beta _{2}+\cdots)q^{8}+\cdots$

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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.