LMFDB - Newform search results

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Level	Weight	Analytic conductor	$Nk^2$	Dim.

Bad $p$	Char.	Primitive character	Character order	Coefficient field

Self-twist	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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Results (1-50 of 157 matches)

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Label	Dim.	$A$	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	RM	$a_2$	$a_3$	$a_5$	$a_7$	Fricke sign	$q$-expansion
1089.1.c.a	$2$	$0.543$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q+q^{4}-\beta q^{7}+\beta q^{13}+q^{16}-\beta q^{19}+\cdots$
1089.1.h.a	$4$	$0.543$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$2$	$2$	$0$		$q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots$
1089.1.i.a	$2$	$0.543$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-11}) $	None	$0$	$1$	$3$	$0$		$q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+(1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots$
1089.1.k.a	$8$	$0.543$	8.0.64000000.1	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q-\beta _{2}q^{4}-\beta _{7}q^{7}-\beta _{1}q^{13}+\beta _{4}q^{16}+\cdots$
1089.1.r.a	$8$	$0.543$	$\Q(\zeta_{15})$	$\Q(\sqrt{-11}) $	None	$0$	$-1$	$-3$	$0$		$q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{11}+\cdots)q^{5}+\cdots$
1089.1.s.a	$8$	$0.543$	$\Q(\zeta_{15})$	$\Q(\sqrt{-11}) $	None	$0$	$1$	$-1$	$0$		$q-\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+\zeta_{30}q^{5}+\cdots$
1089.1.s.b	$16$	$0.543$	16.0.$\cdots$.1	None	None	$0$	$-2$	$-2$	$0$		$q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{15})q^{5}+\cdots$
1089.2.a.a	$1$	$8.696$	$\Q$	None	None	$-2$	$0$	$-4$	$-1$	$+$	$q-2q^{2}+2q^{4}-4q^{5}-q^{7}+8q^{10}+\cdots$
1089.2.a.b	$1$	$8.696$	$\Q$	None	None	$-2$	$0$	$-1$	$2$	$+$	$q-2q^{2}+2q^{4}-q^{5}+2q^{7}+2q^{10}+\cdots$
1089.2.a.c	$1$	$8.696$	$\Q$	None	None	$-1$	$0$	$-1$	$-2$	$+$	$q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots$
1089.2.a.d	$1$	$8.696$	$\Q$	None	None	$-1$	$0$	$4$	$2$	$-$	$q-q^{2}-q^{4}+4q^{5}+2q^{7}+3q^{8}-4q^{10}+\cdots$
1089.2.a.e	$1$	$8.696$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$-5$	$-$	$q-2q^{4}-5q^{7}-2q^{13}+4q^{16}+7q^{19}+\cdots$
1089.2.a.f	$1$	$8.696$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$5$	$-$	$q-2q^{4}+5q^{7}+2q^{13}+4q^{16}-7q^{19}+\cdots$
1089.2.a.g	$1$	$8.696$	$\Q$	$\Q(\sqrt{-11}) $	None	$0$	$0$	$3$	$0$	$-$	$q-2q^{4}+3q^{5}+4q^{16}-6q^{20}+9q^{23}+\cdots$
1089.2.a.h	$1$	$8.696$	$\Q$	None	None	$1$	$0$	$-4$	$2$	$-$	$q+q^{2}-q^{4}-4q^{5}+2q^{7}-3q^{8}-4q^{10}+\cdots$
1089.2.a.i	$1$	$8.696$	$\Q$	None	None	$1$	$0$	$-1$	$2$	$+$	$q+q^{2}-q^{4}-q^{5}+2q^{7}-3q^{8}-q^{10}+\cdots$
1089.2.a.j	$1$	$8.696$	$\Q$	None	None	$1$	$0$	$2$	$-4$	$+$	$q+q^{2}-q^{4}+2q^{5}-4q^{7}-3q^{8}+2q^{10}+\cdots$
1089.2.a.k	$1$	$8.696$	$\Q$	None	None	$2$	$0$	$-4$	$1$	$+$	$q+2q^{2}+2q^{4}-4q^{5}+q^{7}-8q^{10}+\cdots$
1089.2.a.l	$2$	$8.696$	$\Q(\sqrt{5}) $	None	None	$-3$	$0$	$-1$	$2$	$+$	$q+(-1-\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots$
1089.2.a.m	$2$	$8.696$	$\Q(\sqrt{5}) $	None	None	$-1$	$0$	$3$	$6$	$-$	$q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+3q^{7}+\cdots$
1089.2.a.n	$2$	$8.696$	$\Q(\sqrt{3}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$	$+$	$q-2q^{4}-\beta q^{7}+4\beta q^{13}+4q^{16}-3\beta q^{19}+\cdots$
1089.2.a.o	$2$	$8.696$	$\Q(\sqrt{3}) $	None	None	$0$	$0$	$6$	$0$	$-$	$q+\beta q^{2}+q^{4}+3q^{5}+2\beta q^{7}-\beta q^{8}+\cdots$
1089.2.a.p	$2$	$8.696$	$\Q(\sqrt{5}) $	None	None	$0$	$0$	$-4$	$0$	$-$	$q-\beta q^{2}+3q^{4}-2q^{5}-2\beta q^{7}-\beta q^{8}+\cdots$
1089.2.a.q	$2$	$8.696$	$\Q(\sqrt{7}) $	None	None	$0$	$0$	$0$	$-4$	$-$	$q+\beta q^{2}+5q^{4}+\beta q^{5}-2q^{7}+3\beta q^{8}+\cdots$
1089.2.a.r	$2$	$8.696$	$\Q(\sqrt{7}) $	None	None	$0$	$0$	$0$	$4$	$-$	$q+\beta q^{2}+5q^{4}-\beta q^{5}+2q^{7}+3\beta q^{8}+\cdots$
1089.2.a.s	$2$	$8.696$	$\Q(\sqrt{5}) $	None	None	$1$	$0$	$3$	$-6$	$+$	$q+\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}-3q^{7}+\cdots$
1089.2.a.t	$2$	$8.696$	$\Q(\sqrt{5}) $	None	None	$3$	$0$	$-1$	$-2$	$-$	$q+(1+\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots$
1089.2.a.u	$4$	$8.696$	$\Q(\sqrt{3}, \sqrt{11})$	None	None	$0$	$0$	$-2$	$0$	$-$	$q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots$
1089.2.a.v	$4$	$8.696$	4.4.4400.1	None	None	$0$	$0$	$0$	$-8$	$+$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{1}q^{5}+(-3+\cdots)q^{7}+\cdots$
1089.2.a.w	$4$	$8.696$	4.4.4400.1	None	None	$0$	$0$	$0$	$8$	$-$	$q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{1}q^{5}+(3+2\beta _{2}+\cdots)q^{7}+\cdots$
1089.2.d.a	$2$	$8.696$	$\Q(\sqrt{-2}) $	None	None	$-2$	$0$	$0$	$0$		$q-q^{2}-q^{4}-\beta q^{5}-2\beta q^{7}+3q^{8}+\cdots$
1089.2.d.b	$2$	$8.696$	$\Q(\sqrt{-2}) $	None	None	$2$	$0$	$0$	$0$		$q+q^{2}-q^{4}+\beta q^{5}-2\beta q^{7}-3q^{8}+\cdots$
1089.2.d.c	$4$	$8.696$	$\Q(\sqrt{-2}, \sqrt{3})$	None	None	$-4$	$0$	$0$	$0$		$q+(-1-\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots$
1089.2.d.d	$4$	$8.696$	$\Q(\sqrt{-2}, \sqrt{3})$	None	None	$0$	$0$	$0$	$0$		$q-\beta _{2}q^{2}+q^{4}+(-2\beta _{1}+\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots$
1089.2.d.e	$4$	$8.696$	$\Q(\sqrt{-2}, \sqrt{3})$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+q^{4}+(2\beta _{1}-\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots$
1089.2.d.f	$4$	$8.696$	$\Q(\sqrt{-2}, \sqrt{3})$	None	None	$4$	$0$	$0$	$0$		$q+(1+\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots$
1089.2.d.g	$16$	$8.696$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{15}q^{2}+(1+\beta _{4})q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$
1089.2.e.a	$2$	$8.696$	$\Q(\sqrt{-3}) $	None	None	$-2$	$0$	$2$	$4$		$q+(-2+2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots$
1089.2.e.b	$2$	$8.696$	$\Q(\sqrt{-3}) $	None	None	$0$	$-3$	$3$	$-4$		$q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots$
1089.2.e.c	$2$	$8.696$	$\Q(\sqrt{-3}) $	None	None	$1$	$-3$	$-1$	$4$		$q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots$
1089.2.e.d	$4$	$8.696$	$\Q(\sqrt{-3}, \sqrt{5})$	None	None	$-3$	$-6$	$-2$	$-2$		$q+(-1-\beta _{1}-\beta _{3})q^{2}+(-2-\beta _{3})q^{3}+\cdots$
1089.2.e.e	$4$	$8.696$	$\Q(\zeta_{12})$	None	None	$0$	$-6$	$6$	$0$		$q-\zeta_{12}^{2}q^{2}+(-1-\zeta_{12})q^{3}+(-1+\cdots)q^{4}+\cdots$
1089.2.e.f	$4$	$8.696$	$\Q(\sqrt{-3}, \sqrt{-11})$	$\Q(\sqrt{-11}) $	None	$0$	$1$	$-3$	$0$		$q-\beta _{3}q^{3}+2\beta _{2}q^{4}+(1-2\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots$
1089.2.e.g	$4$	$8.696$	$\Q(\sqrt{-3}, \sqrt{5})$	None	None	$3$	$-6$	$-2$	$2$		$q+(1+\beta _{1}+\beta _{3})q^{2}+(-2-\beta _{3})q^{3}+\cdots$
1089.2.e.h	$6$	$8.696$	$\Q(\zeta_{18})$	None	None	$0$	$0$	$-3$	$-3$		$q+(-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots$
1089.2.e.i	$8$	$8.696$	8.0.508277025.1	None	None	$1$	$5$	$-4$	$1$		$q+(\beta _{2}+\beta _{7})q^{2}+(1+\beta _{7})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots$
1089.2.e.j	$12$	$8.696$	$\mathbb{Q}[x]/(x^{12} + \cdots)$	None	None	$0$	$4$	$2$	$0$		$q+\beta _{7}q^{2}+(1+\beta _{2}-\beta _{6})q^{3}+(-1-2\beta _{4}+\cdots)q^{4}+\cdots$
1089.2.e.k	$16$	$8.696$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$-2$	$4$	$0$		$q+(-\beta _{1}-\beta _{2}-\beta _{6})q^{2}-\beta _{13}q^{3}+(2\beta _{5}+\cdots)q^{4}+\cdots$
1089.2.e.l	$20$	$8.696$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	None	$0$	$-1$	$-3$	$1$		$q-\beta _{3}q^{2}-\beta _{16}q^{3}+(-\beta _{12}+\beta _{17}+\cdots)q^{4}+\cdots$
1089.2.e.m	$20$	$8.696$	$\mathbb{Q}[x]/(x^{20} + \cdots)$	None	None	$0$	$-1$	$-3$	$-1$		$q+\beta _{3}q^{2}-\beta _{16}q^{3}+(-\beta _{12}+\beta _{17}+\cdots)q^{4}+\cdots$

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Degree 1	Degree 2
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$\zeta$ zeros

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

Label	Dim.	\(A\)	Field	CM	RM	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	RM	\(a_2\)	\(a_3\)	\(a_5\)	\(a_7\)	Fricke sign	$q$-expansion
1089.1.c.a	\(2\)	\(0.543\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+q^{4}-\beta q^{7}+\beta q^{13}+q^{16}-\beta q^{19}+\cdots\)
1089.1.h.a	\(4\)	\(0.543\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(2\)	\(2\)	\(0\)		\(q+(\beta _{1}-\beta _{3})q^{2}+(1-\beta _{2})q^{3}+(1-\beta _{2}+\cdots)q^{4}+\cdots\)
1089.1.i.a	\(2\)	\(0.543\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(1\)	\(3\)	\(0\)		\(q-\zeta_{6}^{2}q^{3}+\zeta_{6}^{2}q^{4}+(1+\zeta_{6})q^{5}-\zeta_{6}q^{9}+\cdots\)
1089.1.k.a	\(8\)	\(0.543\)	8.0.64000000.1	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{4}-\beta _{7}q^{7}-\beta _{1}q^{13}+\beta _{4}q^{16}+\cdots\)
1089.1.r.a	\(8\)	\(0.543\)	\(\Q(\zeta_{15})\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(-1\)	\(-3\)	\(0\)		\(q+\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+(\zeta_{30}^{6}+\zeta_{30}^{11}+\cdots)q^{5}+\cdots\)
1089.1.s.a	\(8\)	\(0.543\)	\(\Q(\zeta_{15})\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(1\)	\(-1\)	\(0\)		\(q-\zeta_{30}^{7}q^{3}-\zeta_{30}^{13}q^{4}+\zeta_{30}q^{5}+\cdots\)
1089.1.s.b	\(16\)	\(0.543\)	16.0.\(\cdots\).1	None	None	\(0\)	\(-2\)	\(-2\)	\(0\)		\(q+\beta _{1}q^{2}-\beta _{7}q^{3}+\beta _{2}q^{4}+(\beta _{3}+\beta _{15})q^{5}+\cdots\)
1089.2.a.a	\(1\)	\(8.696\)	\(\Q\)	None	None	\(-2\)	\(0\)	\(-4\)	\(-1\)	\(+\)	\(q-2q^{2}+2q^{4}-4q^{5}-q^{7}+8q^{10}+\cdots\)
1089.2.a.b	\(1\)	\(8.696\)	\(\Q\)	None	None	\(-2\)	\(0\)	\(-1\)	\(2\)	\(+\)	\(q-2q^{2}+2q^{4}-q^{5}+2q^{7}+2q^{10}+\cdots\)
1089.2.a.c	\(1\)	\(8.696\)	\(\Q\)	None	None	\(-1\)	\(0\)	\(-1\)	\(-2\)	\(+\)	\(q-q^{2}-q^{4}-q^{5}-2q^{7}+3q^{8}+q^{10}+\cdots\)
1089.2.a.d	\(1\)	\(8.696\)	\(\Q\)	None	None	\(-1\)	\(0\)	\(4\)	\(2\)	\(-\)	\(q-q^{2}-q^{4}+4q^{5}+2q^{7}+3q^{8}-4q^{10}+\cdots\)
1089.2.a.e	\(1\)	\(8.696\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(-5\)	\(-\)	\(q-2q^{4}-5q^{7}-2q^{13}+4q^{16}+7q^{19}+\cdots\)
1089.2.a.f	\(1\)	\(8.696\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(5\)	\(-\)	\(q-2q^{4}+5q^{7}+2q^{13}+4q^{16}-7q^{19}+\cdots\)
1089.2.a.g	\(1\)	\(8.696\)	\(\Q\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(0\)	\(3\)	\(0\)	\(-\)	\(q-2q^{4}+3q^{5}+4q^{16}-6q^{20}+9q^{23}+\cdots\)
1089.2.a.h	\(1\)	\(8.696\)	\(\Q\)	None	None	\(1\)	\(0\)	\(-4\)	\(2\)	\(-\)	\(q+q^{2}-q^{4}-4q^{5}+2q^{7}-3q^{8}-4q^{10}+\cdots\)
1089.2.a.i	\(1\)	\(8.696\)	\(\Q\)	None	None	\(1\)	\(0\)	\(-1\)	\(2\)	\(+\)	\(q+q^{2}-q^{4}-q^{5}+2q^{7}-3q^{8}-q^{10}+\cdots\)
1089.2.a.j	\(1\)	\(8.696\)	\(\Q\)	None	None	\(1\)	\(0\)	\(2\)	\(-4\)	\(+\)	\(q+q^{2}-q^{4}+2q^{5}-4q^{7}-3q^{8}+2q^{10}+\cdots\)
1089.2.a.k	\(1\)	\(8.696\)	\(\Q\)	None	None	\(2\)	\(0\)	\(-4\)	\(1\)	\(+\)	\(q+2q^{2}+2q^{4}-4q^{5}+q^{7}-8q^{10}+\cdots\)
1089.2.a.l	\(2\)	\(8.696\)	\(\Q(\sqrt{5}) \)	None	None	\(-3\)	\(0\)	\(-1\)	\(2\)	\(+\)	\(q+(-1-\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots\)
1089.2.a.m	\(2\)	\(8.696\)	\(\Q(\sqrt{5}) \)	None	None	\(-1\)	\(0\)	\(3\)	\(6\)	\(-\)	\(q-\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}+3q^{7}+\cdots\)
1089.2.a.n	\(2\)	\(8.696\)	\(\Q(\sqrt{3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	\(+\)	\(q-2q^{4}-\beta q^{7}+4\beta q^{13}+4q^{16}-3\beta q^{19}+\cdots\)
1089.2.a.o	\(2\)	\(8.696\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(0\)	\(6\)	\(0\)	\(-\)	\(q+\beta q^{2}+q^{4}+3q^{5}+2\beta q^{7}-\beta q^{8}+\cdots\)
1089.2.a.p	\(2\)	\(8.696\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)	\(-\)	\(q-\beta q^{2}+3q^{4}-2q^{5}-2\beta q^{7}-\beta q^{8}+\cdots\)
1089.2.a.q	\(2\)	\(8.696\)	\(\Q(\sqrt{7}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)	\(-\)	\(q+\beta q^{2}+5q^{4}+\beta q^{5}-2q^{7}+3\beta q^{8}+\cdots\)
1089.2.a.r	\(2\)	\(8.696\)	\(\Q(\sqrt{7}) \)	None	None	\(0\)	\(0\)	\(0\)	\(4\)	\(-\)	\(q+\beta q^{2}+5q^{4}-\beta q^{5}+2q^{7}+3\beta q^{8}+\cdots\)
1089.2.a.s	\(2\)	\(8.696\)	\(\Q(\sqrt{5}) \)	None	None	\(1\)	\(0\)	\(3\)	\(-6\)	\(+\)	\(q+\beta q^{2}+(-1+\beta )q^{4}+(2-\beta )q^{5}-3q^{7}+\cdots\)
1089.2.a.t	\(2\)	\(8.696\)	\(\Q(\sqrt{5}) \)	None	None	\(3\)	\(0\)	\(-1\)	\(-2\)	\(-\)	\(q+(1+\beta )q^{2}+3\beta q^{4}+(-1+\beta )q^{5}+\cdots\)
1089.2.a.u	\(4\)	\(8.696\)	\(\Q(\sqrt{3}, \sqrt{11})\)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	\(-\)	\(q+\beta _{1}q^{2}+(2+\beta _{3})q^{4}+\beta _{3}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
1089.2.a.v	\(4\)	\(8.696\)	4.4.4400.1	None	None	\(0\)	\(0\)	\(0\)	\(-8\)	\(+\)	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}-\beta _{1}q^{5}+(-3+\cdots)q^{7}+\cdots\)
1089.2.a.w	\(4\)	\(8.696\)	4.4.4400.1	None	None	\(0\)	\(0\)	\(0\)	\(8\)	\(-\)	\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{4}+\beta _{1}q^{5}+(3+2\beta _{2}+\cdots)q^{7}+\cdots\)
1089.2.d.a	\(2\)	\(8.696\)	\(\Q(\sqrt{-2}) \)	None	None	\(-2\)	\(0\)	\(0\)	\(0\)		\(q-q^{2}-q^{4}-\beta q^{5}-2\beta q^{7}+3q^{8}+\cdots\)
1089.2.d.b	\(2\)	\(8.696\)	\(\Q(\sqrt{-2}) \)	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+q^{2}-q^{4}+\beta q^{5}-2\beta q^{7}-3q^{8}+\cdots\)
1089.2.d.c	\(4\)	\(8.696\)	\(\Q(\sqrt{-2}, \sqrt{3})\)	None	None	\(-4\)	\(0\)	\(0\)	\(0\)		\(q+(-1-\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots\)
1089.2.d.d	\(4\)	\(8.696\)	\(\Q(\sqrt{-2}, \sqrt{3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}+q^{4}+(-2\beta _{1}+\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots\)
1089.2.d.e	\(4\)	\(8.696\)	\(\Q(\sqrt{-2}, \sqrt{3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+q^{4}+(2\beta _{1}-\beta _{3})q^{5}+2\beta _{3}q^{7}+\cdots\)
1089.2.d.f	\(4\)	\(8.696\)	\(\Q(\sqrt{-2}, \sqrt{3})\)	None	None	\(4\)	\(0\)	\(0\)	\(0\)		\(q+(1+\beta _{2})q^{2}+(2+2\beta _{2})q^{4}-2\beta _{1}q^{5}+\cdots\)
1089.2.d.g	\(16\)	\(8.696\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{15}q^{2}+(1+\beta _{4})q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
1089.2.e.a	\(2\)	\(8.696\)	\(\Q(\sqrt{-3}) \)	None	None	\(-2\)	\(0\)	\(2\)	\(4\)		\(q+(-2+2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
1089.2.e.b	\(2\)	\(8.696\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-3\)	\(3\)	\(-4\)		\(q+(-1-\zeta_{6})q^{3}+2\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
1089.2.e.c	\(2\)	\(8.696\)	\(\Q(\sqrt{-3}) \)	None	None	\(1\)	\(-3\)	\(-1\)	\(4\)		\(q+(1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
1089.2.e.d	\(4\)	\(8.696\)	\(\Q(\sqrt{-3}, \sqrt{5})\)	None	None	\(-3\)	\(-6\)	\(-2\)	\(-2\)		\(q+(-1-\beta _{1}-\beta _{3})q^{2}+(-2-\beta _{3})q^{3}+\cdots\)
1089.2.e.e	\(4\)	\(8.696\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(-6\)	\(6\)	\(0\)		\(q-\zeta_{12}^{2}q^{2}+(-1-\zeta_{12})q^{3}+(-1+\cdots)q^{4}+\cdots\)
1089.2.e.f	\(4\)	\(8.696\)	\(\Q(\sqrt{-3}, \sqrt{-11})\)	\(\Q(\sqrt{-11}) \)	None	\(0\)	\(1\)	\(-3\)	\(0\)		\(q-\beta _{3}q^{3}+2\beta _{2}q^{4}+(1-2\beta _{1}-2\beta _{2}+\cdots)q^{5}+\cdots\)
1089.2.e.g	\(4\)	\(8.696\)	\(\Q(\sqrt{-3}, \sqrt{5})\)	None	None	\(3\)	\(-6\)	\(-2\)	\(2\)		\(q+(1+\beta _{1}+\beta _{3})q^{2}+(-2-\beta _{3})q^{3}+\cdots\)
1089.2.e.h	\(6\)	\(8.696\)	\(\Q(\zeta_{18})\)	None	None	\(0\)	\(0\)	\(-3\)	\(-3\)		\(q+(-\zeta_{18}^{2}+\zeta_{18}^{3}+\zeta_{18}^{4}-\zeta_{18}^{5})q^{2}+\cdots\)
1089.2.e.i	\(8\)	\(8.696\)	8.0.508277025.1	None	None	\(1\)	\(5\)	\(-4\)	\(1\)		\(q+(\beta _{2}+\beta _{7})q^{2}+(1+\beta _{7})q^{3}+(-2+\beta _{1}+\cdots)q^{4}+\cdots\)
1089.2.e.j	\(12\)	\(8.696\)	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None	None	\(0\)	\(4\)	\(2\)	\(0\)		\(q+\beta _{7}q^{2}+(1+\beta _{2}-\beta _{6})q^{3}+(-1-2\beta _{4}+\cdots)q^{4}+\cdots\)
1089.2.e.k	\(16\)	\(8.696\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(-2\)	\(4\)	\(0\)		\(q+(-\beta _{1}-\beta _{2}-\beta _{6})q^{2}-\beta _{13}q^{3}+(2\beta _{5}+\cdots)q^{4}+\cdots\)
1089.2.e.l	\(20\)	\(8.696\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	None	\(0\)	\(-1\)	\(-3\)	\(1\)		\(q-\beta _{3}q^{2}-\beta _{16}q^{3}+(-\beta _{12}+\beta _{17}+\cdots)q^{4}+\cdots\)
1089.2.e.m	\(20\)	\(8.696\)	\(\mathbb{Q}[x]/(x^{20} + \cdots)\)	None	None	\(0\)	\(-1\)	\(-3\)	\(-1\)		\(q+\beta _{3}q^{2}-\beta _{16}q^{3}+(-\beta _{12}+\beta _{17}+\cdots)q^{4}+\cdots\)

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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.