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 83 matches)

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Label	Dim.	$A$	Field	CM	Traces				Fricke sign	$q$-expansion
Label	Dim.	$A$	Field	CM	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	$q$-expansion
3330.2.a.a	$1$	$26.590$	$\Q$	None	$-1$	$0$	$-1$	$-3$	$+$	$q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots$
3330.2.a.b	$1$	$26.590$	$\Q$	None	$-1$	$0$	$-1$	$-3$	$-$	$q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots$
3330.2.a.c	$1$	$26.590$	$\Q$	None	$-1$	$0$	$-1$	$0$	$+$	$q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots$
3330.2.a.d	$1$	$26.590$	$\Q$	None	$-1$	$0$	$-1$	$2$	$+$	$q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots$
3330.2.a.e	$1$	$26.590$	$\Q$	None	$-1$	$0$	$-1$	$3$	$+$	$q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}+q^{10}+\cdots$
3330.2.a.f	$1$	$26.590$	$\Q$	None	$-1$	$0$	$1$	$-5$	$+$	$q-q^{2}+q^{4}+q^{5}-5q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.g	$1$	$26.590$	$\Q$	None	$-1$	$0$	$1$	$-3$	$+$	$q-q^{2}+q^{4}+q^{5}-3q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.h	$1$	$26.590$	$\Q$	None	$-1$	$0$	$1$	$-1$	$-$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.i	$1$	$26.590$	$\Q$	None	$-1$	$0$	$1$	$0$	$+$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots$
3330.2.a.j	$1$	$26.590$	$\Q$	None	$-1$	$0$	$1$	$0$	$+$	$q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+2q^{11}+\cdots$
3330.2.a.k	$1$	$26.590$	$\Q$	None	$-1$	$0$	$1$	$4$	$-$	$q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.l	$1$	$26.590$	$\Q$	None	$-1$	$0$	$1$	$4$	$-$	$q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.m	$1$	$26.590$	$\Q$	None	$1$	$0$	$-1$	$-4$	$-$	$q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.n	$1$	$26.590$	$\Q$	None	$1$	$0$	$-1$	$-3$	$+$	$q+q^{2}+q^{4}-q^{5}-3q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.o	$1$	$26.590$	$\Q$	None	$1$	$0$	$-1$	$0$	$+$	$q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+2q^{11}+\cdots$
3330.2.a.p	$1$	$26.590$	$\Q$	None	$1$	$0$	$-1$	$1$	$+$	$q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.q	$1$	$26.590$	$\Q$	None	$1$	$0$	$-1$	$3$	$-$	$q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.r	$1$	$26.590$	$\Q$	None	$1$	$0$	$-1$	$4$	$-$	$q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.s	$1$	$26.590$	$\Q$	None	$1$	$0$	$1$	$-4$	$-$	$q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.t	$1$	$26.590$	$\Q$	None	$1$	$0$	$1$	$-3$	$+$	$q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.u	$1$	$26.590$	$\Q$	None	$1$	$0$	$1$	$-1$	$+$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.v	$1$	$26.590$	$\Q$	None	$1$	$0$	$1$	$-1$	$+$	$q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.w	$1$	$26.590$	$\Q$	None	$1$	$0$	$1$	$0$	$-$	$q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots$
3330.2.a.x	$1$	$26.590$	$\Q$	None	$1$	$0$	$1$	$1$	$-$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.y	$1$	$26.590$	$\Q$	None	$1$	$0$	$1$	$1$	$-$	$q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.z	$1$	$26.590$	$\Q$	None	$1$	$0$	$1$	$3$	$-$	$q+q^{2}+q^{4}+q^{5}+3q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.ba	$1$	$26.590$	$\Q$	None	$1$	$0$	$1$	$4$	$-$	$q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots$
3330.2.a.bb	$2$	$26.590$	$\Q(\sqrt{33}) $	None	$-2$	$0$	$-2$	$-3$	$+$	$q-q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots$
3330.2.a.bc	$2$	$26.590$	$\Q(\sqrt{17}) $	None	$-2$	$0$	$2$	$-2$	$-$	$q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.bd	$2$	$26.590$	$\Q(\sqrt{3}) $	None	$2$	$0$	$-2$	$-6$	$-$	$q+q^{2}+q^{4}-q^{5}+(-3+\beta )q^{7}+q^{8}+\cdots$
3330.2.a.be	$2$	$26.590$	$\Q(\sqrt{33}) $	None	$2$	$0$	$-2$	$-1$	$+$	$q+q^{2}+q^{4}-q^{5}-\beta q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.bf	$2$	$26.590$	$\Q(\sqrt{113}) $	None	$2$	$0$	$-2$	$6$	$-$	$q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-q^{10}+\cdots$
3330.2.a.bg	$3$	$26.590$	3.3.892.1	None	$-3$	$0$	$3$	$-1$	$+$	$q-q^{2}+q^{4}+q^{5}-\beta _{1}q^{7}-q^{8}-q^{10}+\cdots$
3330.2.a.bh	$3$	$26.590$	3.3.316.1	None	$-3$	$0$	$3$	$-1$	$-$	$q-q^{2}+q^{4}+q^{5}+(-1+2\beta _{1})q^{7}+\cdots$
3330.2.a.bi	$3$	$26.590$	3.3.316.1	None	$3$	$0$	$-3$	$-1$	$-$	$q+q^{2}+q^{4}-q^{5}+(-1+2\beta _{1})q^{7}+\cdots$
3330.2.a.bj	$4$	$26.590$	4.4.54764.1	None	$-4$	$0$	$-4$	$4$	$-$	$q-q^{2}+q^{4}-q^{5}+(1+\beta _{2})q^{7}-q^{8}+\cdots$
3330.2.a.bk	$5$	$26.590$	5.5.23544108.1	None	$-5$	$0$	$-5$	$3$	$-$	$q-q^{2}+q^{4}-q^{5}+(1+\beta _{4})q^{7}-q^{8}+\cdots$
3330.2.a.bl	$5$	$26.590$	5.5.23544108.1	None	$5$	$0$	$5$	$3$	$-$	$q+q^{2}+q^{4}+q^{5}+(1+\beta _{4})q^{7}+q^{8}+\cdots$
3330.2.d.a	$2$	$26.590$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-4$	$0$	$-$	$q+iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots$
3330.2.d.b	$2$	$26.590$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-4$	$0$	$-$	$q-iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots$
3330.2.d.c	$2$	$26.590$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-2$	$0$	$-$	$q-iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots$
3330.2.d.d	$2$	$26.590$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-2$	$0$	$-$	$q-iq^{2}-q^{4}+(-1+2i)q^{5}+iq^{7}+\cdots$
3330.2.d.e	$2$	$26.590$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$2$	$0$	$-$	$q+iq^{2}-q^{4}+(1-2i)q^{5}+5iq^{7}+\cdots$
3330.2.d.f	$2$	$26.590$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$4$	$0$	$-$	$q+iq^{2}-q^{4}+(2-i)q^{5}+2iq^{7}-iq^{8}+\cdots$
3330.2.d.g	$2$	$26.590$	$\Q(\sqrt{-1}) $	None	$0$	$0$	$4$	$0$	$-$	$q-iq^{2}-q^{4}+(2+i)q^{5}+2iq^{7}+iq^{8}+\cdots$
3330.2.d.h	$4$	$26.590$	$\Q(i, \sqrt{6})$	None	$0$	$0$	$-4$	$0$	$-$	$q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots$
3330.2.d.i	$4$	$26.590$	$\Q(\zeta_{12})$	None	$0$	$0$	$-4$	$0$	$-$	$q+\zeta_{12}q^{2}-q^{4}+(-1-2\zeta_{12})q^{5}+\cdots$
3330.2.d.j	$4$	$26.590$	$\Q(i, \sqrt{5})$	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{7}-\beta _{1}q^{8}+\cdots$
3330.2.d.k	$4$	$26.590$	$\Q(\zeta_{8})$	None	$0$	$0$	$0$	$0$	$-$	$q-\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots$
3330.2.d.l	$4$	$26.590$	$\Q(\zeta_{12})$	None	$0$	$0$	$4$	$0$	$-$	$q-\zeta_{12}q^{2}-q^{4}+(1+2\zeta_{12})q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots$

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Classical	Maass
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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	Traces				Fricke sign	$q$-expansion
Label	Dim.	\(A\)	Field	CM	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Fricke sign	$q$-expansion
3330.2.a.a	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(-3\)	$+$	\(q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots\)
3330.2.a.b	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(-3\)	$-$	\(q-q^{2}+q^{4}-q^{5}-3q^{7}-q^{8}+q^{10}+\cdots\)
3330.2.a.c	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(0\)	$+$	\(q-q^{2}+q^{4}-q^{5}-q^{8}+q^{10}-4q^{11}+\cdots\)
3330.2.a.d	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(2\)	$+$	\(q-q^{2}+q^{4}-q^{5}+2q^{7}-q^{8}+q^{10}+\cdots\)
3330.2.a.e	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(-1\)	\(3\)	$+$	\(q-q^{2}+q^{4}-q^{5}+3q^{7}-q^{8}+q^{10}+\cdots\)
3330.2.a.f	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(-5\)	$+$	\(q-q^{2}+q^{4}+q^{5}-5q^{7}-q^{8}-q^{10}+\cdots\)
3330.2.a.g	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(-3\)	$+$	\(q-q^{2}+q^{4}+q^{5}-3q^{7}-q^{8}-q^{10}+\cdots\)
3330.2.a.h	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(-1\)	$-$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
3330.2.a.i	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(0\)	$+$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}-2q^{11}+\cdots\)
3330.2.a.j	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(0\)	$+$	\(q-q^{2}+q^{4}+q^{5}-q^{8}-q^{10}+2q^{11}+\cdots\)
3330.2.a.k	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(4\)	$-$	\(q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots\)
3330.2.a.l	$1$	$26.590$	\(\Q\)	None	\(-1\)	\(0\)	\(1\)	\(4\)	$-$	\(q-q^{2}+q^{4}+q^{5}+4q^{7}-q^{8}-q^{10}+\cdots\)
3330.2.a.m	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(-4\)	$-$	\(q+q^{2}+q^{4}-q^{5}-4q^{7}+q^{8}-q^{10}+\cdots\)
3330.2.a.n	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(-3\)	$+$	\(q+q^{2}+q^{4}-q^{5}-3q^{7}+q^{8}-q^{10}+\cdots\)
3330.2.a.o	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(0\)	$+$	\(q+q^{2}+q^{4}-q^{5}+q^{8}-q^{10}+2q^{11}+\cdots\)
3330.2.a.p	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(1\)	$+$	\(q+q^{2}+q^{4}-q^{5}+q^{7}+q^{8}-q^{10}+\cdots\)
3330.2.a.q	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(3\)	$-$	\(q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-q^{10}+\cdots\)
3330.2.a.r	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(-1\)	\(4\)	$-$	\(q+q^{2}+q^{4}-q^{5}+4q^{7}+q^{8}-q^{10}+\cdots\)
3330.2.a.s	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(-4\)	$-$	\(q+q^{2}+q^{4}+q^{5}-4q^{7}+q^{8}+q^{10}+\cdots\)
3330.2.a.t	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(-3\)	$+$	\(q+q^{2}+q^{4}+q^{5}-3q^{7}+q^{8}+q^{10}+\cdots\)
3330.2.a.u	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(-1\)	$+$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
3330.2.a.v	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(-1\)	$+$	\(q+q^{2}+q^{4}+q^{5}-q^{7}+q^{8}+q^{10}+\cdots\)
3330.2.a.w	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(0\)	$-$	\(q+q^{2}+q^{4}+q^{5}+q^{8}+q^{10}+4q^{11}+\cdots\)
3330.2.a.x	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(1\)	$-$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
3330.2.a.y	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(1\)	$-$	\(q+q^{2}+q^{4}+q^{5}+q^{7}+q^{8}+q^{10}+\cdots\)
3330.2.a.z	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(3\)	$-$	\(q+q^{2}+q^{4}+q^{5}+3q^{7}+q^{8}+q^{10}+\cdots\)
3330.2.a.ba	$1$	$26.590$	\(\Q\)	None	\(1\)	\(0\)	\(1\)	\(4\)	$-$	\(q+q^{2}+q^{4}+q^{5}+4q^{7}+q^{8}+q^{10}+\cdots\)
3330.2.a.bb	$2$	$26.590$	\(\Q(\sqrt{33}) \)	None	\(-2\)	\(0\)	\(-2\)	\(-3\)	$+$	\(q-q^{2}+q^{4}-q^{5}+(-1-\beta )q^{7}-q^{8}+\cdots\)
3330.2.a.bc	$2$	$26.590$	\(\Q(\sqrt{17}) \)	None	\(-2\)	\(0\)	\(2\)	\(-2\)	$-$	\(q-q^{2}+q^{4}+q^{5}-q^{7}-q^{8}-q^{10}+\cdots\)
3330.2.a.bd	$2$	$26.590$	\(\Q(\sqrt{3}) \)	None	\(2\)	\(0\)	\(-2\)	\(-6\)	$-$	\(q+q^{2}+q^{4}-q^{5}+(-3+\beta )q^{7}+q^{8}+\cdots\)
3330.2.a.be	$2$	$26.590$	\(\Q(\sqrt{33}) \)	None	\(2\)	\(0\)	\(-2\)	\(-1\)	$+$	\(q+q^{2}+q^{4}-q^{5}-\beta q^{7}+q^{8}-q^{10}+\cdots\)
3330.2.a.bf	$2$	$26.590$	\(\Q(\sqrt{113}) \)	None	\(2\)	\(0\)	\(-2\)	\(6\)	$-$	\(q+q^{2}+q^{4}-q^{5}+3q^{7}+q^{8}-q^{10}+\cdots\)
3330.2.a.bg	$3$	$26.590$	3.3.892.1	None	\(-3\)	\(0\)	\(3\)	\(-1\)	$+$	\(q-q^{2}+q^{4}+q^{5}-\beta _{1}q^{7}-q^{8}-q^{10}+\cdots\)
3330.2.a.bh	$3$	$26.590$	3.3.316.1	None	\(-3\)	\(0\)	\(3\)	\(-1\)	$-$	\(q-q^{2}+q^{4}+q^{5}+(-1+2\beta _{1})q^{7}+\cdots\)
3330.2.a.bi	$3$	$26.590$	3.3.316.1	None	\(3\)	\(0\)	\(-3\)	\(-1\)	$-$	\(q+q^{2}+q^{4}-q^{5}+(-1+2\beta _{1})q^{7}+\cdots\)
3330.2.a.bj	$4$	$26.590$	4.4.54764.1	None	\(-4\)	\(0\)	\(-4\)	\(4\)	$-$	\(q-q^{2}+q^{4}-q^{5}+(1+\beta _{2})q^{7}-q^{8}+\cdots\)
3330.2.a.bk	$5$	$26.590$	5.5.23544108.1	None	\(-5\)	\(0\)	\(-5\)	\(3\)	$-$	\(q-q^{2}+q^{4}-q^{5}+(1+\beta _{4})q^{7}-q^{8}+\cdots\)
3330.2.a.bl	$5$	$26.590$	5.5.23544108.1	None	\(5\)	\(0\)	\(5\)	\(3\)	$-$	\(q+q^{2}+q^{4}+q^{5}+(1+\beta _{4})q^{7}+q^{8}+\cdots\)
3330.2.d.a	$2$	$26.590$	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-4\)	\(0\)	$-$	\(q+iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots\)
3330.2.d.b	$2$	$26.590$	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-4\)	\(0\)	$-$	\(q-iq^{2}-q^{4}+(-2+i)q^{5}+2iq^{7}+\cdots\)
3330.2.d.c	$2$	$26.590$	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q-iq^{2}-q^{4}+(-1-2i)q^{5}+iq^{7}+\cdots\)
3330.2.d.d	$2$	$26.590$	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q-iq^{2}-q^{4}+(-1+2i)q^{5}+iq^{7}+\cdots\)
3330.2.d.e	$2$	$26.590$	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q+iq^{2}-q^{4}+(1-2i)q^{5}+5iq^{7}+\cdots\)
3330.2.d.f	$2$	$26.590$	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(4\)	\(0\)	$-$	\(q+iq^{2}-q^{4}+(2-i)q^{5}+2iq^{7}-iq^{8}+\cdots\)
3330.2.d.g	$2$	$26.590$	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(4\)	\(0\)	$-$	\(q-iq^{2}-q^{4}+(2+i)q^{5}+2iq^{7}+iq^{8}+\cdots\)
3330.2.d.h	$4$	$26.590$	\(\Q(i, \sqrt{6})\)	None	\(0\)	\(0\)	\(-4\)	\(0\)	$-$	\(q-\beta _{2}q^{2}-q^{4}+(-1-\beta _{2}-\beta _{3})q^{5}+\cdots\)
3330.2.d.i	$4$	$26.590$	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(-4\)	\(0\)	$-$	\(q+\zeta_{12}q^{2}-q^{4}+(-1-2\zeta_{12})q^{5}+\cdots\)
3330.2.d.j	$4$	$26.590$	\(\Q(i, \sqrt{5})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{1}q^{2}-q^{4}-\beta _{2}q^{5}-2\beta _{1}q^{7}-\beta _{1}q^{8}+\cdots\)
3330.2.d.k	$4$	$26.590$	\(\Q(\zeta_{8})\)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\zeta_{8}^{2}q^{2}-q^{4}+(\zeta_{8}+2\zeta_{8}^{3})q^{5}+(\zeta_{8}+\cdots)q^{7}+\cdots\)
3330.2.d.l	$4$	$26.590$	\(\Q(\zeta_{12})\)	None	\(0\)	\(0\)	\(4\)	\(0\)	$-$	\(q-\zeta_{12}q^{2}-q^{4}+(1+2\zeta_{12})q^{5}+(\zeta_{12}+\cdots)q^{7}+\cdots\)

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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.