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 240 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
588.1.c.a	$1$	$0.293$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$0$		$q-q^{3}+q^{9}+q^{13}+q^{19}+q^{25}-q^{27}+\cdots$
588.1.c.b	$1$	$0.293$	$\Q$	$\Q(\sqrt{-3}) $	None	$0$	$1$	$0$	$0$		$q+q^{3}+q^{9}-q^{13}-q^{19}+q^{25}+q^{27}+\cdots$
588.1.p.a	$2$	$0.293$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$1$	$0$	$0$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+q^{13}-\zeta_{6}q^{19}+\cdots$
588.1.z.a	$12$	$0.293$	$\Q(\zeta_{21})$	$\Q(\sqrt{-3}) $	None	$0$	$1$	$0$	$1$		$q+\zeta_{42}^{10}q^{3}+\zeta_{42}^{8}q^{7}+\zeta_{42}^{20}q^{9}+\cdots$
588.2.a.a	$1$	$4.695$	$\Q$	None	None	$0$	$-1$	$-2$	$0$	$-$	$q-q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots$
588.2.a.b	$1$	$4.695$	$\Q$	None	None	$0$	$-1$	$-2$	$0$	$+$	$q-q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots$
588.2.a.c	$1$	$4.695$	$\Q$	None	None	$0$	$-1$	$0$	$0$	$+$	$q-q^{3}+q^{9}-6q^{11}-2q^{13}+4q^{19}+\cdots$
588.2.a.d	$1$	$4.695$	$\Q$	None	None	$0$	$1$	$-4$	$0$	$-$	$q+q^{3}-4q^{5}+q^{9}+2q^{11}+6q^{13}+\cdots$
588.2.a.e	$1$	$4.695$	$\Q$	None	None	$0$	$1$	$2$	$0$	$-$	$q+q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots$
588.2.a.f	$1$	$4.695$	$\Q$	None	None	$0$	$1$	$2$	$0$	$-$	$q+q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots$
588.2.b.a	$8$	$4.695$	8.0.562828176.1	None	None	$-2$	$-8$	$0$	$0$		$q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots$
588.2.b.b	$8$	$4.695$	8.0.562828176.1	None	None	$-2$	$8$	$0$	$0$		$q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$
588.2.b.c	$12$	$4.695$	12.0.$\cdots$.1	None	None	$4$	$-12$	$0$	$0$		$q+\beta _{1}q^{2}-q^{3}+(\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots$
588.2.b.d	$12$	$4.695$	12.0.$\cdots$.1	None	None	$4$	$12$	$0$	$0$		$q+\beta _{1}q^{2}+q^{3}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots$
588.2.e.a	$4$	$4.695$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-21}) $	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+\beta _{3}q^{6}+\cdots$
588.2.e.b	$8$	$4.695$	8.0.3317760000.1	None	None	$0$	$0$	$0$	$0$		$q-\beta _{6}q^{2}-\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
588.2.e.c	$12$	$4.695$	12.0.$\cdots$.2	None	None	$0$	$0$	$0$	$0$		$q+\beta _{2}q^{2}+\beta _{10}q^{3}+(-\beta _{3}+\beta _{5})q^{4}+\cdots$
588.2.e.d	$12$	$4.695$	12.0.$\cdots$.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots$
588.2.e.e	$12$	$4.695$	12.0.$\cdots$.1	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+\beta _{8}q^{3}+\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots$
588.2.e.f	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$
588.2.f.a	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$-3$	$6$	$0$		$q+(-1-\zeta_{6})q^{3}+3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots$
588.2.f.b	$2$	$4.695$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{6}q^{3}-3q^{9}-3\zeta_{6}q^{13}-5\zeta_{6}q^{19}+\cdots$
588.2.f.c	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$3$	$-6$	$0$		$q+(1+\zeta_{6})q^{3}-3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots$
588.2.f.d	$8$	$4.695$	8.0.3288334336.2	None	None	$0$	$0$	$0$	$0$		$q+(-\beta _{1}+\beta _{6})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots$
588.2.i.a	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-2$	$0$		$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
588.2.i.b	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$-2$	$0$		$q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
588.2.i.c	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$0$	$0$		$q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots$
588.2.i.d	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$-1$	$4$	$0$		$q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots$
588.2.i.e	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$-4$	$0$		$q+(1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots$
588.2.i.f	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$0$	$0$		$q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots$
588.2.i.g	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$1$	$2$	$0$		$q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots$
588.2.k.a	$2$	$4.695$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$-3$	$0$	$0$		$q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(4-8\zeta_{6})q^{13}+\cdots$
588.2.k.b	$2$	$4.695$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$-3$	$0$	$0$		$q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-3+6\zeta_{6})q^{13}+\cdots$
588.2.k.c	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$0$	$3$	$0$		$q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}-3q^{9}+\cdots$
588.2.k.d	$2$	$4.695$	$\Q(\sqrt{-3}) $	None	None	$0$	$3$	$-3$	$0$		$q+(2-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-3\zeta_{6})q^{9}+\cdots$
588.2.k.e	$2$	$4.695$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$3$	$0$	$0$		$q+(1+\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-4+8\zeta_{6})q^{13}+\cdots$
588.2.k.f	$16$	$4.695$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+(-\beta _{1}-\beta _{5}-\beta _{8})q^{3}+(\beta _{1}-2\beta _{7}+\cdots)q^{5}+\cdots$
588.2.n.a	$4$	$4.695$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-21}) $	None	$0$	$-6$	$0$	$0$		$q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots$
588.2.n.b	$4$	$4.695$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-21}) $	None	$0$	$6$	$0$	$0$		$q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots$
588.2.n.c	$16$	$4.695$	16.0.$\cdots$.1	None	None	$0$	$0$	$0$	$0$		$q-\beta _{9}q^{2}+(-\beta _{1}+\beta _{5}+\beta _{15})q^{3}-\beta _{3}q^{4}+\cdots$
588.2.n.d	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$
588.2.n.e	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$
588.2.n.f	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$
588.2.n.g	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$
588.2.n.h	$24$	$4.695$		None	None	$0$	$0$	$0$	$0$
588.2.o.a	$8$	$4.695$	8.0.432972864.2	None	None	$1$	$-4$	$0$	$0$		$q+(-\beta _{1}-\beta _{6})q^{2}+\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots$
588.2.o.b	$8$	$4.695$	8.0.562828176.1	None	None	$1$	$-4$	$0$	$0$		$q+\beta _{6}q^{2}-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots$
588.2.o.c	$8$	$4.695$	8.0.432972864.2	None	None	$1$	$4$	$0$	$0$		$q+(-\beta _{1}-\beta _{6})q^{2}-\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots$
588.2.o.d	$8$	$4.695$	8.0.562828176.1	None	None	$1$	$4$	$0$	$0$		$q-\beta _{4}q^{2}+(1-\beta _{3})q^{3}+(\beta _{2}+\beta _{5}-\beta _{7})q^{4}+\cdots$
588.2.o.e	$24$	$4.695$		None	None	$-4$	$-12$	$0$	$0$

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Elliptic curves over $\Q$
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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
588.1.c.a	\(1\)	\(0.293\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(0\)		\(q-q^{3}+q^{9}+q^{13}+q^{19}+q^{25}-q^{27}+\cdots\)
588.1.c.b	\(1\)	\(0.293\)	\(\Q\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(1\)	\(0\)	\(0\)		\(q+q^{3}+q^{9}-q^{13}-q^{19}+q^{25}+q^{27}+\cdots\)
588.1.p.a	\(2\)	\(0.293\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(1\)	\(0\)	\(0\)		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{9}+q^{13}-\zeta_{6}q^{19}+\cdots\)
588.1.z.a	\(12\)	\(0.293\)	\(\Q(\zeta_{21})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(1\)	\(0\)	\(1\)		\(q+\zeta_{42}^{10}q^{3}+\zeta_{42}^{8}q^{7}+\zeta_{42}^{20}q^{9}+\cdots\)
588.2.a.a	\(1\)	\(4.695\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(-\)	\(q-q^{3}-2q^{5}+q^{9}+2q^{11}-3q^{13}+\cdots\)
588.2.a.b	\(1\)	\(4.695\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(-2\)	\(0\)	\(+\)	\(q-q^{3}-2q^{5}+q^{9}+2q^{11}+4q^{13}+\cdots\)
588.2.a.c	\(1\)	\(4.695\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(0\)	\(0\)	\(+\)	\(q-q^{3}+q^{9}-6q^{11}-2q^{13}+4q^{19}+\cdots\)
588.2.a.d	\(1\)	\(4.695\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-4\)	\(0\)	\(-\)	\(q+q^{3}-4q^{5}+q^{9}+2q^{11}+6q^{13}+\cdots\)
588.2.a.e	\(1\)	\(4.695\)	\(\Q\)	None	None	\(0\)	\(1\)	\(2\)	\(0\)	\(-\)	\(q+q^{3}+2q^{5}+q^{9}+2q^{11}-4q^{13}+\cdots\)
588.2.a.f	\(1\)	\(4.695\)	\(\Q\)	None	None	\(0\)	\(1\)	\(2\)	\(0\)	\(-\)	\(q+q^{3}+2q^{5}+q^{9}+2q^{11}+3q^{13}+\cdots\)
588.2.b.a	\(8\)	\(4.695\)	8.0.562828176.1	None	None	\(-2\)	\(-8\)	\(0\)	\(0\)		\(q-\beta _{1}q^{2}-q^{3}+\beta _{2}q^{4}+(\beta _{2}-\beta _{5})q^{5}+\cdots\)
588.2.b.b	\(8\)	\(4.695\)	8.0.562828176.1	None	None	\(-2\)	\(8\)	\(0\)	\(0\)		\(q-\beta _{1}q^{2}+q^{3}+\beta _{2}q^{4}+(-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
588.2.b.c	\(12\)	\(4.695\)	12.0.\(\cdots\).1	None	None	\(4\)	\(-12\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}-q^{3}+(\beta _{5}+\beta _{6})q^{4}+(-1+\cdots)q^{5}+\cdots\)
588.2.b.d	\(12\)	\(4.695\)	12.0.\(\cdots\).1	None	None	\(4\)	\(12\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+q^{3}+(\beta _{5}+\beta _{6})q^{4}+(1-\beta _{1}+\cdots)q^{5}+\cdots\)
588.2.e.a	\(4\)	\(4.695\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-21}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}-\beta _{2}q^{3}+2q^{4}+\beta _{3}q^{5}+\beta _{3}q^{6}+\cdots\)
588.2.e.b	\(8\)	\(4.695\)	8.0.3317760000.1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{6}q^{2}-\beta _{2}q^{3}+(-1-\beta _{3})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
588.2.e.c	\(12\)	\(4.695\)	12.0.\(\cdots\).2	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{2}q^{2}+\beta _{10}q^{3}+(-\beta _{3}+\beta _{5})q^{4}+\cdots\)
588.2.e.d	\(12\)	\(4.695\)	12.0.\(\cdots\).1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}-\beta _{8}q^{3}+\beta _{2}q^{4}-\beta _{3}q^{5}+\cdots\)
588.2.e.e	\(12\)	\(4.695\)	12.0.\(\cdots\).1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+\beta _{8}q^{3}+\beta _{2}q^{4}+\beta _{3}q^{5}+\cdots\)
588.2.e.f	\(24\)	\(4.695\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
588.2.f.a	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-3\)	\(6\)	\(0\)		\(q+(-1-\zeta_{6})q^{3}+3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
588.2.f.b	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{6}q^{3}-3q^{9}-3\zeta_{6}q^{13}-5\zeta_{6}q^{19}+\cdots\)
588.2.f.c	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(3\)	\(-6\)	\(0\)		\(q+(1+\zeta_{6})q^{3}-3q^{5}+3\zeta_{6}q^{9}+(-3+\cdots)q^{11}+\cdots\)
588.2.f.d	\(8\)	\(4.695\)	8.0.3288334336.2	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{1}+\beta _{6})q^{3}+(-\beta _{1}-\beta _{2}+\beta _{5}+\cdots)q^{5}+\cdots\)
588.2.i.a	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-2\)	\(0\)		\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.b	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(-2\)	\(0\)		\(q+(-1+\zeta_{6})q^{3}-2\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.c	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(0\)	\(0\)		\(q+(-1+\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots\)
588.2.i.d	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-1\)	\(4\)	\(0\)		\(q+(-1+\zeta_{6})q^{3}+4\zeta_{6}q^{5}-\zeta_{6}q^{9}+\cdots\)
588.2.i.e	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(-4\)	\(0\)		\(q+(1-\zeta_{6})q^{3}-4\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
588.2.i.f	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(0\)	\(0\)		\(q+(1-\zeta_{6})q^{3}-\zeta_{6}q^{9}+(6-6\zeta_{6})q^{11}+\cdots\)
588.2.i.g	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(1\)	\(2\)	\(0\)		\(q+(1-\zeta_{6})q^{3}+2\zeta_{6}q^{5}-\zeta_{6}q^{9}+(-2+\cdots)q^{11}+\cdots\)
588.2.k.a	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-3\)	\(0\)	\(0\)		\(q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(4-8\zeta_{6})q^{13}+\cdots\)
588.2.k.b	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-3\)	\(0\)	\(0\)		\(q+(-1-\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-3+6\zeta_{6})q^{13}+\cdots\)
588.2.k.c	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(0\)	\(3\)	\(0\)		\(q+(-1+2\zeta_{6})q^{3}+3\zeta_{6}q^{5}-3q^{9}+\cdots\)
588.2.k.d	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(3\)	\(-3\)	\(0\)		\(q+(2-\zeta_{6})q^{3}-3\zeta_{6}q^{5}+(3-3\zeta_{6})q^{9}+\cdots\)
588.2.k.e	\(2\)	\(4.695\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(3\)	\(0\)	\(0\)		\(q+(1+\zeta_{6})q^{3}+3\zeta_{6}q^{9}+(-4+8\zeta_{6})q^{13}+\cdots\)
588.2.k.f	\(16\)	\(4.695\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\beta _{1}-\beta _{5}-\beta _{8})q^{3}+(\beta _{1}-2\beta _{7}+\cdots)q^{5}+\cdots\)
588.2.n.a	\(4\)	\(4.695\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-21}) \)	None	\(0\)	\(-6\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(-2-\beta _{2})q^{3}+2\beta _{2}q^{4}+\cdots\)
588.2.n.b	\(4\)	\(4.695\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-21}) \)	None	\(0\)	\(6\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(2+\beta _{2})q^{3}+2\beta _{2}q^{4}+(-\beta _{1}+\cdots)q^{5}+\cdots\)
588.2.n.c	\(16\)	\(4.695\)	16.0.\(\cdots\).1	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{9}q^{2}+(-\beta _{1}+\beta _{5}+\beta _{15})q^{3}-\beta _{3}q^{4}+\cdots\)
588.2.n.d	\(24\)	\(4.695\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
588.2.n.e	\(24\)	\(4.695\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
588.2.n.f	\(24\)	\(4.695\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
588.2.n.g	\(24\)	\(4.695\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
588.2.n.h	\(24\)	\(4.695\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
588.2.o.a	\(8\)	\(4.695\)	8.0.432972864.2	None	None	\(1\)	\(-4\)	\(0\)	\(0\)		\(q+(-\beta _{1}-\beta _{6})q^{2}+\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots\)
588.2.o.b	\(8\)	\(4.695\)	8.0.562828176.1	None	None	\(1\)	\(-4\)	\(0\)	\(0\)		\(q+\beta _{6}q^{2}-\beta _{3}q^{3}+(\beta _{1}-\beta _{2})q^{4}+(-\beta _{2}+\cdots)q^{5}+\cdots\)
588.2.o.c	\(8\)	\(4.695\)	8.0.432972864.2	None	None	\(1\)	\(4\)	\(0\)	\(0\)		\(q+(-\beta _{1}-\beta _{6})q^{2}-\beta _{2}q^{3}+\beta _{5}q^{4}+\cdots\)
588.2.o.d	\(8\)	\(4.695\)	8.0.562828176.1	None	None	\(1\)	\(4\)	\(0\)	\(0\)		\(q-\beta _{4}q^{2}+(1-\beta _{3})q^{3}+(\beta _{2}+\beta _{5}-\beta _{7})q^{4}+\cdots\)
588.2.o.e	\(24\)	\(4.695\)		None	None	\(-4\)	\(-12\)	\(0\)	\(0\)

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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.