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 245 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
360.1.p.a	$1$	$0.180$	$\Q$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $	$-1$	$0$	$1$	$0$		$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots$
360.1.p.b	$1$	$0.180$	$\Q$	$\Q(\sqrt{-15}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{6}) $	$1$	$0$	$-1$	$0$		$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots$
360.1.u.a	$4$	$0.180$	$\Q(\zeta_{8})$	$\Q(\sqrt{-6}) $	None	$0$	$0$	$0$	$-4$		$q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots$
360.2.a.a	$1$	$2.875$	$\Q$	None	None	$0$	$0$	$-1$	$-4$	$+$	$q-q^{5}-4q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots$
360.2.a.b	$1$	$2.875$	$\Q$	None	None	$0$	$0$	$-1$	$0$	$-$	$q-q^{5}+4q^{11}+6q^{13}+6q^{17}-4q^{19}+\cdots$
360.2.a.c	$1$	$2.875$	$\Q$	None	None	$0$	$0$	$-1$	$2$	$-$	$q-q^{5}+2q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots$
360.2.a.d	$1$	$2.875$	$\Q$	None	None	$0$	$0$	$1$	$2$	$-$	$q+q^{5}+2q^{7}-2q^{11}+4q^{13}+2q^{17}+\cdots$
360.2.a.e	$1$	$2.875$	$\Q$	None	None	$0$	$0$	$1$	$4$	$-$	$q+q^{5}+4q^{7}-6q^{13}+2q^{17}+4q^{19}+\cdots$
360.2.b.a	$2$	$2.875$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$-2$	$0$		$q+\beta q^{2}-2q^{4}-q^{5}-3\beta q^{7}-2\beta q^{8}+\cdots$
360.2.b.b	$2$	$2.875$	$\Q(\sqrt{-2}) $	None	None	$0$	$0$	$2$	$0$		$q+\beta q^{2}-2q^{4}+q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots$
360.2.b.c	$6$	$2.875$	6.0.2580992.1	None	None	$-2$	$0$	$-6$	$0$		$q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots$
360.2.b.d	$6$	$2.875$	6.0.2580992.1	None	None	$2$	$0$	$6$	$0$		$q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+\beta _{2}q^{7}+\cdots$
360.2.d.a	$4$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-5})$	$\Q(\sqrt{-30}) $	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots$
360.2.d.b	$4$	$2.875$	$\Q(\sqrt{2}, \sqrt{-3})$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{1}q^{2}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots$
360.2.d.c	$4$	$2.875$	$\Q(\sqrt{-3}, \sqrt{5})$	$\Q(\sqrt{-15}) $	None	$0$	$0$	$0$	$0$		$q-\beta _{2}q^{2}+\beta _{3}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots$
360.2.d.d	$4$	$2.875$	$\Q(\sqrt{2}, \sqrt{-3})$	$\Q(\sqrt{-6}) $	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{2}+2q^{4}+(\beta _{1}+\beta _{2})q^{5}+2\beta _{3}q^{7}+\cdots$
360.2.d.e	$6$	$2.875$	6.0.839056.1	None	None	$-1$	$0$	$0$	$0$		$q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots$
360.2.d.f	$6$	$2.875$	6.0.839056.1	None	None	$1$	$0$	$0$	$0$		$q-\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots$
360.2.f.a	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$-4$	$0$		$q+(-2+i)q^{5}+2iq^{7}-2q^{11}+2iq^{13}+\cdots$
360.2.f.b	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$-4$	$0$		$q+(-2+i)q^{5}-4iq^{7}+4q^{11}-4iq^{13}+\cdots$
360.2.f.c	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$2$	$0$		$q+(1+i)q^{5}-iq^{7}+4q^{11}+2iq^{13}+\cdots$
360.2.f.d	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$4$	$0$		$q+(2+i)q^{5}+4iq^{7}-4q^{11}+4iq^{13}+\cdots$
360.2.k.a	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$-2$	$0$	$0$	$-8$		$q+(-1+i)q^{2}-2iq^{4}+iq^{5}-4q^{7}+\cdots$
360.2.k.b	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$-2$	$0$	$0$	$4$		$q+(-1+i)q^{2}-2iq^{4}+iq^{5}+2q^{7}+\cdots$
360.2.k.c	$2$	$2.875$	$\Q(\sqrt{-1}) $	None	None	$2$	$0$	$0$	$-8$		$q+(1+i)q^{2}+2iq^{4}+iq^{5}-4q^{7}+\cdots$
360.2.k.d	$4$	$2.875$	$\Q(i, \sqrt{7})$	None	None	$0$	$0$	$0$	$8$		$q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+2q^{7}+\cdots$
360.2.k.e	$4$	$2.875$	$\Q(\zeta_{12})$	None	None	$2$	$0$	$0$	$-4$		$q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots$
360.2.k.f	$6$	$2.875$	6.0.399424.1	None	None	$-2$	$0$	$0$	$4$		$q-\beta _{1}q^{2}+(\beta _{2}-\beta _{3})q^{4}+\beta _{3}q^{5}+(1+\cdots)q^{7}+\cdots$
360.2.m.a	$4$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-5})$	$\Q(\sqrt{-10}) $	None	$0$	$0$	$0$	$-8$		$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-2+\beta _{3})q^{7}+\cdots$
360.2.m.b	$4$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-5})$	$\Q(\sqrt{-10}) $	None	$0$	$0$	$0$	$8$		$q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(2-\beta _{3})q^{7}+\cdots$
360.2.m.c	$16$	$2.875$	$\mathbb{Q}[x]/(x^{16} - \cdots)$	None	None	$0$	$0$	$0$	$0$		$q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}-\beta _{12}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots$
360.2.q.a	$2$	$2.875$	$\Q(\sqrt{-3}) $	None	None	$0$	$-3$	$1$	$0$		$q+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+\cdots$
360.2.q.b	$4$	$2.875$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$2$	$-4$		$q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+(-2+2\zeta_{12}+\cdots)q^{7}+\cdots$
360.2.q.c	$4$	$2.875$	$\Q(\sqrt{-2}, \sqrt{-3})$	None	None	$0$	$2$	$2$	$-2$		$q+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots$
360.2.q.d	$6$	$2.875$	6.0.954288.1	None	None	$0$	$-1$	$-3$	$5$		$q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots$
360.2.q.e	$8$	$2.875$	8.0.856615824.2	None	None	$0$	$0$	$-4$	$1$		$q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\cdots$
360.2.s.a	$4$	$2.875$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$0$		$q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(4\zeta_{8}+4\zeta_{8}^{3})q^{11}+\cdots$
360.2.s.b	$8$	$2.875$	8.0.40960000.1	None	None	$0$	$0$	$0$	$-8$		$q+\beta _{7}q^{5}+(-1-\beta _{2}-\beta _{5})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots$
360.2.w.a	$4$	$2.875$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$4$		$q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots$
360.2.w.b	$4$	$2.875$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$-4$		$q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots$
360.2.w.c	$8$	$2.875$	$\Q(\zeta_{20})$	None	None	$2$	$0$	$0$	$0$		$q+\zeta_{20}^{7}q^{2}+\zeta_{20}q^{4}+(1+\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{5}+\cdots$
360.2.w.d	$16$	$2.875$	$\mathbb{Q}[x]/(x^{16} + \cdots)$	None	None	$0$	$0$	$0$	$0$		$q+\beta _{15}q^{2}-\beta _{2}q^{4}+(\beta _{10}-\beta _{15})q^{5}+\cdots$
360.2.w.e	$24$	$2.875$		None	None	$0$	$0$	$0$	$0$
360.2.x.a	$48$	$2.875$		None	None	$0$	$0$	$0$	$0$
360.2.bd.a	$8$	$2.875$	$\Q(\zeta_{24})$	None	None	$0$	$0$	$0$	$0$		$q+(-\zeta_{24}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}^{3}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots$
360.2.bd.b	$128$	$2.875$		None	None	$0$	$0$	$0$	$0$
360.2.bf.a	$4$	$2.875$	$\Q(\zeta_{12})$	None	None	$-2$	$0$	$0$	$8$		$q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots$
360.2.bf.b	$92$	$2.875$		None	None	$2$	$0$	$0$	$-8$
360.2.bi.a	$4$	$2.875$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$2$	$0$		$q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots$
360.2.bi.b	$32$	$2.875$		None	None	$0$	$0$	$-2$	$0$

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Classical	Maass
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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
360.1.p.a	\(1\)	\(0.180\)	\(\Q\)	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{6}) \)	\(-1\)	\(0\)	\(1\)	\(0\)		\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+q^{16}+\cdots\)
360.1.p.b	\(1\)	\(0.180\)	\(\Q\)	\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{6}) \)	\(1\)	\(0\)	\(-1\)	\(0\)		\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+q^{16}+\cdots\)
360.1.u.a	\(4\)	\(0.180\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q-\zeta_{8}^{3}q^{2}-\zeta_{8}^{2}q^{4}+\zeta_{8}q^{5}+(-1+\cdots)q^{7}+\cdots\)
360.2.a.a	\(1\)	\(2.875\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(-4\)	\(+\)	\(q-q^{5}-4q^{7}-4q^{11}-2q^{13}-2q^{17}+\cdots\)
360.2.a.b	\(1\)	\(2.875\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(0\)	\(-\)	\(q-q^{5}+4q^{11}+6q^{13}+6q^{17}-4q^{19}+\cdots\)
360.2.a.c	\(1\)	\(2.875\)	\(\Q\)	None	None	\(0\)	\(0\)	\(-1\)	\(2\)	\(-\)	\(q-q^{5}+2q^{7}+2q^{11}+4q^{13}-2q^{17}+\cdots\)
360.2.a.d	\(1\)	\(2.875\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(2\)	\(-\)	\(q+q^{5}+2q^{7}-2q^{11}+4q^{13}+2q^{17}+\cdots\)
360.2.a.e	\(1\)	\(2.875\)	\(\Q\)	None	None	\(0\)	\(0\)	\(1\)	\(4\)	\(-\)	\(q+q^{5}+4q^{7}-6q^{13}+2q^{17}+4q^{19}+\cdots\)
360.2.b.a	\(2\)	\(2.875\)	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)		\(q+\beta q^{2}-2q^{4}-q^{5}-3\beta q^{7}-2\beta q^{8}+\cdots\)
360.2.b.b	\(2\)	\(2.875\)	\(\Q(\sqrt{-2}) \)	None	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+\beta q^{2}-2q^{4}+q^{5}+3\beta q^{7}-2\beta q^{8}+\cdots\)
360.2.b.c	\(6\)	\(2.875\)	6.0.2580992.1	None	None	\(-2\)	\(0\)	\(-6\)	\(0\)		\(q+\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}-q^{5}+\beta _{2}q^{7}+\cdots\)
360.2.b.d	\(6\)	\(2.875\)	6.0.2580992.1	None	None	\(2\)	\(0\)	\(6\)	\(0\)		\(q-\beta _{4}q^{2}+(\beta _{2}+\beta _{5})q^{4}+q^{5}+\beta _{2}q^{7}+\cdots\)
360.2.d.a	\(4\)	\(2.875\)	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-30}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+2\beta _{1}q^{8}+\cdots\)
360.2.d.b	\(4\)	\(2.875\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{1}q^{2}+(-1+\beta _{3})q^{4}+(-\beta _{2}+\beta _{3})q^{5}+\cdots\)
360.2.d.c	\(4\)	\(2.875\)	\(\Q(\sqrt{-3}, \sqrt{5})\)	\(\Q(\sqrt{-15}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}+\beta _{3}q^{4}+(-\beta _{1}-\beta _{2})q^{5}+\cdots\)
360.2.d.d	\(4\)	\(2.875\)	\(\Q(\sqrt{2}, \sqrt{-3})\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{2}+2q^{4}+(\beta _{1}+\beta _{2})q^{5}+2\beta _{3}q^{7}+\cdots\)
360.2.d.e	\(6\)	\(2.875\)	6.0.839056.1	None	None	\(-1\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{3}q^{2}+(-\beta _{1}-\beta _{2})q^{4}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)
360.2.d.f	\(6\)	\(2.875\)	6.0.839056.1	None	None	\(1\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{2}q^{2}+(\beta _{1}-\beta _{3})q^{4}+(\beta _{2}-\beta _{3})q^{5}+\cdots\)
360.2.f.a	\(2\)	\(2.875\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+(-2+i)q^{5}+2iq^{7}-2q^{11}+2iq^{13}+\cdots\)
360.2.f.b	\(2\)	\(2.875\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)		\(q+(-2+i)q^{5}-4iq^{7}+4q^{11}-4iq^{13}+\cdots\)
360.2.f.c	\(2\)	\(2.875\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+(1+i)q^{5}-iq^{7}+4q^{11}+2iq^{13}+\cdots\)
360.2.f.d	\(2\)	\(2.875\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(4\)	\(0\)		\(q+(2+i)q^{5}+4iq^{7}-4q^{11}+4iq^{13}+\cdots\)
360.2.k.a	\(2\)	\(2.875\)	\(\Q(\sqrt{-1}) \)	None	None	\(-2\)	\(0\)	\(0\)	\(-8\)		\(q+(-1+i)q^{2}-2iq^{4}+iq^{5}-4q^{7}+\cdots\)
360.2.k.b	\(2\)	\(2.875\)	\(\Q(\sqrt{-1}) \)	None	None	\(-2\)	\(0\)	\(0\)	\(4\)		\(q+(-1+i)q^{2}-2iq^{4}+iq^{5}+2q^{7}+\cdots\)
360.2.k.c	\(2\)	\(2.875\)	\(\Q(\sqrt{-1}) \)	None	None	\(2\)	\(0\)	\(0\)	\(-8\)		\(q+(1+i)q^{2}+2iq^{4}+iq^{5}-4q^{7}+\cdots\)
360.2.k.d	\(4\)	\(2.875\)	\(\Q(i, \sqrt{7})\)	None	None	\(0\)	\(0\)	\(0\)	\(8\)		\(q+\beta _{1}q^{2}+(1+\beta _{2})q^{4}-\beta _{3}q^{5}+2q^{7}+\cdots\)
360.2.k.e	\(4\)	\(2.875\)	\(\Q(\zeta_{12})\)	None	None	\(2\)	\(0\)	\(0\)	\(-4\)		\(q+(\zeta_{12}-\zeta_{12}^{2})q^{2}+(\zeta_{12}+\zeta_{12}^{3})q^{4}+\cdots\)
360.2.k.f	\(6\)	\(2.875\)	6.0.399424.1	None	None	\(-2\)	\(0\)	\(0\)	\(4\)		\(q-\beta _{1}q^{2}+(\beta _{2}-\beta _{3})q^{4}+\beta _{3}q^{5}+(1+\cdots)q^{7}+\cdots\)
360.2.m.a	\(4\)	\(2.875\)	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(-2+\beta _{3})q^{7}+\cdots\)
360.2.m.b	\(4\)	\(2.875\)	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)	None	\(0\)	\(0\)	\(0\)	\(8\)		\(q-\beta _{1}q^{2}-2q^{4}+\beta _{2}q^{5}+(2-\beta _{3})q^{7}+\cdots\)
360.2.m.c	\(16\)	\(2.875\)	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\beta _{1}q^{2}+(1-\beta _{2})q^{4}-\beta _{12}q^{5}+(-\beta _{6}+\cdots)q^{7}+\cdots\)
360.2.q.a	\(2\)	\(2.875\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-3\)	\(1\)	\(0\)		\(q+(-1-\zeta_{6})q^{3}+\zeta_{6}q^{5}+3\zeta_{6}q^{9}+\cdots\)
360.2.q.b	\(4\)	\(2.875\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(2\)	\(-4\)		\(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+(-2+2\zeta_{12}+\cdots)q^{7}+\cdots\)
360.2.q.c	\(4\)	\(2.875\)	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None	None	\(0\)	\(2\)	\(2\)	\(-2\)		\(q+(\beta _{1}+\beta _{2}-\beta _{3})q^{3}+\beta _{2}q^{5}+(-1+\cdots)q^{7}+\cdots\)
360.2.q.d	\(6\)	\(2.875\)	6.0.954288.1	None	None	\(0\)	\(-1\)	\(-3\)	\(5\)		\(q-\beta _{1}q^{3}+(-1-\beta _{3})q^{5}+(-\beta _{1}-\beta _{2}+\cdots)q^{7}+\cdots\)
360.2.q.e	\(8\)	\(2.875\)	8.0.856615824.2	None	None	\(0\)	\(0\)	\(-4\)	\(1\)		\(q-\beta _{4}q^{3}-\beta _{1}q^{5}+(-\beta _{2}+\beta _{4})q^{7}+\cdots\)
360.2.s.a	\(4\)	\(2.875\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(2\zeta_{8}-\zeta_{8}^{3})q^{5}+(4\zeta_{8}+4\zeta_{8}^{3})q^{11}+\cdots\)
360.2.s.b	\(8\)	\(2.875\)	8.0.40960000.1	None	None	\(0\)	\(0\)	\(0\)	\(-8\)		\(q+\beta _{7}q^{5}+(-1-\beta _{2}-\beta _{5})q^{7}+(\beta _{1}+\cdots)q^{11}+\cdots\)
360.2.w.a	\(4\)	\(2.875\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q+(\zeta_{8}+\zeta_{8}^{3})q^{2}-2q^{4}+(-2\zeta_{8}+\zeta_{8}^{3})q^{5}+\cdots\)
360.2.w.b	\(4\)	\(2.875\)	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q+(-\zeta_{8}+\zeta_{8}^{3})q^{2}+2q^{4}+(-2\zeta_{8}+\cdots)q^{5}+\cdots\)
360.2.w.c	\(8\)	\(2.875\)	\(\Q(\zeta_{20})\)	None	None	\(2\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{20}^{7}q^{2}+\zeta_{20}q^{4}+(1+\zeta_{20}^{2}-\zeta_{20}^{5}+\cdots)q^{5}+\cdots\)
360.2.w.d	\(16\)	\(2.875\)	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\beta _{15}q^{2}-\beta _{2}q^{4}+(\beta _{10}-\beta _{15})q^{5}+\cdots\)
360.2.w.e	\(24\)	\(2.875\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
360.2.x.a	\(48\)	\(2.875\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
360.2.bd.a	\(8\)	\(2.875\)	\(\Q(\zeta_{24})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+(-\zeta_{24}+\zeta_{24}^{6})q^{2}+(-\zeta_{24}^{3}+\zeta_{24}^{4}+\cdots)q^{3}+\cdots\)
360.2.bd.b	\(128\)	\(2.875\)		None	None	\(0\)	\(0\)	\(0\)	\(0\)
360.2.bf.a	\(4\)	\(2.875\)	\(\Q(\zeta_{12})\)	None	None	\(-2\)	\(0\)	\(0\)	\(8\)		\(q+(-\zeta_{12}-\zeta_{12}^{2}+\zeta_{12}^{3})q^{2}+(-\zeta_{12}+\cdots)q^{3}+\cdots\)
360.2.bf.b	\(92\)	\(2.875\)		None	None	\(2\)	\(0\)	\(0\)	\(-8\)
360.2.bi.a	\(4\)	\(2.875\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(2\)	\(0\)		\(q+(-\zeta_{12}-\zeta_{12}^{3})q^{3}+(-2\zeta_{12}+\zeta_{12}^{2}+\cdots)q^{5}+\cdots\)
360.2.bi.b	\(32\)	\(2.875\)		None	None	\(0\)	\(0\)	\(-2\)	\(0\)

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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.