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 127 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
1792.1.c.a	$1$	$0.894$	$\Q$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	$0$	$0$	$0$	$-1$		$q-q^{7}+q^{9}+2q^{23}+q^{25}+q^{49}+\cdots$
1792.1.c.b	$1$	$0.894$	$\Q$	$\Q(\sqrt{-7}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{2}) $	$0$	$0$	$0$	$1$		$q+q^{7}+q^{9}-2q^{23}+q^{25}+q^{49}+\cdots$
1792.1.c.c	$2$	$0.894$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-14}) $	None	$0$	$0$	$0$	$-2$		$q-\beta q^{3}-\beta q^{5}-q^{7}-q^{9}-\beta q^{13}+\cdots$
1792.1.c.d	$2$	$0.894$	$\Q(\sqrt{-2}) $	$\Q(\sqrt{-14}) $	None	$0$	$0$	$0$	$2$		$q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-\beta q^{13}+\cdots$
1792.1.o.a	$4$	$0.894$	$\Q(\zeta_{12})$	None	None	$0$	$-2$	$0$	$0$		$q+\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+\cdots$
1792.1.o.b	$4$	$0.894$	$\Q(\zeta_{12})$	None	None	$0$	$2$	$0$	$0$		$q-\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{7}+\cdots$
1792.1.v.a	$4$	$0.894$	$\Q(\zeta_{8})$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{9}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{11}+\cdots$
1792.1.v.b	$4$	$0.894$	$\Q(\zeta_{8})$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{9}+(-\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots$
1792.1.bf.a	$8$	$0.894$	$\Q(\zeta_{16})$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{16}^{7}q^{7}+\zeta_{16}q^{9}+(-\zeta_{16}^{2}-\zeta_{16}^{5}+\cdots)q^{11}+\cdots$
1792.1.bt.a	$32$	$0.894$	$\Q(\zeta_{64})$	$\Q(\sqrt{-7}) $	None	$0$	$0$	$0$	$0$		$q+\zeta_{64}^{3}q^{2}+\zeta_{64}^{6}q^{4}-\zeta_{64}^{7}q^{7}+\cdots$
1792.2.a.a	$1$	$14.309$	$\Q$	None	None	$0$	$-2$	$-4$	$1$	$+$	$q-2q^{3}-4q^{5}+q^{7}+q^{9}-2q^{11}+\cdots$
1792.2.a.b	$1$	$14.309$	$\Q$	None	None	$0$	$-2$	$-2$	$1$	$+$	$q-2q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}+\cdots$
1792.2.a.c	$1$	$14.309$	$\Q$	None	None	$0$	$-2$	$2$	$-1$	$+$	$q-2q^{3}+2q^{5}-q^{7}+q^{9}-2q^{13}+\cdots$
1792.2.a.d	$1$	$14.309$	$\Q$	None	None	$0$	$-2$	$4$	$-1$	$-$	$q-2q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+\cdots$
1792.2.a.e	$1$	$14.309$	$\Q$	None	None	$0$	$2$	$-4$	$-1$	$+$	$q+2q^{3}-4q^{5}-q^{7}+q^{9}+2q^{11}+\cdots$
1792.2.a.f	$1$	$14.309$	$\Q$	None	None	$0$	$2$	$-2$	$-1$	$-$	$q+2q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+\cdots$
1792.2.a.g	$1$	$14.309$	$\Q$	None	None	$0$	$2$	$2$	$1$	$-$	$q+2q^{3}+2q^{5}+q^{7}+q^{9}-2q^{13}+\cdots$
1792.2.a.h	$1$	$14.309$	$\Q$	None	None	$0$	$2$	$4$	$1$	$-$	$q+2q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+\cdots$
1792.2.a.i	$2$	$14.309$	$\Q(\sqrt{3}) $	None	None	$0$	$-2$	$-2$	$-2$	$+$	$q+(-1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots$
1792.2.a.j	$2$	$14.309$	$\Q(\sqrt{5}) $	None	None	$0$	$-2$	$-2$	$-2$	$+$	$q+(-1-\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+\cdots$
1792.2.a.k	$2$	$14.309$	$\Q(\sqrt{3}) $	None	None	$0$	$-2$	$2$	$2$	$-$	$q+(-1+\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots$
1792.2.a.l	$2$	$14.309$	$\Q(\sqrt{5}) $	None	None	$0$	$-2$	$2$	$2$	$+$	$q+(-1-\beta )q^{3}+(1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots$
1792.2.a.m	$2$	$14.309$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$0$	$-2$	$-$	$q+\beta q^{5}-q^{7}-3q^{9}+\beta q^{11}-\beta q^{13}+\cdots$
1792.2.a.n	$2$	$14.309$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$0$	$-2$	$+$	$q+\beta q^{3}+\beta q^{5}-q^{7}-q^{9}-2\beta q^{11}+\cdots$
1792.2.a.o	$2$	$14.309$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$0$	$2$	$+$	$q-\beta q^{5}+q^{7}-3q^{9}+\beta q^{11}+\beta q^{13}+\cdots$
1792.2.a.p	$2$	$14.309$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$0$	$2$	$+$	$q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-2\beta q^{11}+\cdots$
1792.2.a.q	$2$	$14.309$	$\Q(\sqrt{3}) $	None	None	$0$	$2$	$-2$	$2$	$+$	$q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots$
1792.2.a.r	$2$	$14.309$	$\Q(\sqrt{5}) $	None	None	$0$	$2$	$-2$	$2$	$-$	$q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots$
1792.2.a.s	$2$	$14.309$	$\Q(\sqrt{3}) $	None	None	$0$	$2$	$2$	$-2$	$-$	$q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots$
1792.2.a.t	$2$	$14.309$	$\Q(\sqrt{5}) $	None	None	$0$	$2$	$2$	$-2$	$-$	$q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots$
1792.2.a.u	$4$	$14.309$	$\Q(\zeta_{16})^+$	None	None	$0$	$0$	$0$	$-4$	$+$	$q+\beta _{1}q^{3}-\beta _{1}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots$
1792.2.a.v	$4$	$14.309$	4.4.9248.1	None	None	$0$	$0$	$0$	$-4$	$-$	$q+\beta _{2}q^{3}-\beta _{1}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots$
1792.2.a.w	$4$	$14.309$	$\Q(\zeta_{16})^+$	None	None	$0$	$0$	$0$	$4$	$-$	$q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots$
1792.2.a.x	$4$	$14.309$	4.4.9248.1	None	None	$0$	$0$	$0$	$4$	$-$	$q+\beta _{2}q^{3}+\beta _{1}q^{5}+q^{7}+(2-\beta _{3})q^{9}+\cdots$
1792.2.b.a	$2$	$14.309$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$-2$		$q+iq^{3}+2iq^{5}-q^{7}-q^{9}-8q^{15}+\cdots$
1792.2.b.b	$2$	$14.309$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$-2$		$q+iq^{3}-q^{7}-q^{9}-2iq^{11}-2iq^{13}+\cdots$
1792.2.b.c	$2$	$14.309$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$-2$		$q+iq^{3}-q^{7}-q^{9}+2iq^{13}+6q^{17}+\cdots$
1792.2.b.d	$2$	$14.309$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$-2$		$q-iq^{5}-q^{7}+3q^{9}-2iq^{11}+iq^{13}+\cdots$
1792.2.b.e	$2$	$14.309$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$-2$		$q-q^{7}+3q^{9}-iq^{11}+2iq^{13}-2q^{17}+\cdots$
1792.2.b.f	$2$	$14.309$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$2$		$q+iq^{3}+q^{7}-q^{9}-2iq^{11}+2iq^{13}+\cdots$
1792.2.b.g	$2$	$14.309$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$2$		$q+iq^{3}+q^{7}-q^{9}-2iq^{13}+6q^{17}+\cdots$
1792.2.b.h	$2$	$14.309$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$2$		$q+iq^{3}-2iq^{5}+q^{7}-q^{9}+8q^{15}+\cdots$
1792.2.b.i	$2$	$14.309$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$2$		$q-iq^{5}+q^{7}+3q^{9}+2iq^{11}+iq^{13}+\cdots$
1792.2.b.j	$2$	$14.309$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$2$		$q+q^{7}+3q^{9}+iq^{11}+2iq^{13}-2q^{17}+\cdots$
1792.2.b.k	$4$	$14.309$	$\Q(i, \sqrt{5})$	None	None	$0$	$0$	$0$	$-4$		$q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+(-3+\cdots)q^{9}+\cdots$
1792.2.b.l	$4$	$14.309$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$0$	$-4$		$q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-q^{7}+(-1+\zeta_{12}^{3})q^{9}+\cdots$
1792.2.b.m	$4$	$14.309$	$\Q(i, \sqrt{5})$	None	None	$0$	$0$	$0$	$4$		$q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+q^{7}+(-3+\cdots)q^{9}+\cdots$
1792.2.b.n	$4$	$14.309$	$\Q(\zeta_{12})$	None	None	$0$	$0$	$0$	$4$		$q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+q^{7}+(-1+\zeta_{12}^{3})q^{9}+\cdots$
1792.2.b.o	$6$	$14.309$	6.0.399424.1	None	None	$0$	$0$	$0$	$-6$		$q+\beta _{5}q^{3}+\beta _{4}q^{5}-q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots$
1792.2.b.p	$6$	$14.309$	6.0.399424.1	None	None	$0$	$0$	$0$	$6$		$q+\beta _{5}q^{3}-\beta _{4}q^{5}+q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots$

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Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ 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
1792.1.c.a	\(1\)	\(0.894\)	\(\Q\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{2}) \)	\(0\)	\(0\)	\(0\)	\(-1\)		\(q-q^{7}+q^{9}+2q^{23}+q^{25}+q^{49}+\cdots\)
1792.1.c.b	\(1\)	\(0.894\)	\(\Q\)	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{2}) \)	\(0\)	\(0\)	\(0\)	\(1\)		\(q+q^{7}+q^{9}-2q^{23}+q^{25}+q^{49}+\cdots\)
1792.1.c.c	\(2\)	\(0.894\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q-\beta q^{3}-\beta q^{5}-q^{7}-q^{9}-\beta q^{13}+\cdots\)
1792.1.c.d	\(2\)	\(0.894\)	\(\Q(\sqrt{-2}) \)	\(\Q(\sqrt{-14}) \)	None	\(0\)	\(0\)	\(0\)	\(2\)		\(q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-\beta q^{13}+\cdots\)
1792.1.o.a	\(4\)	\(0.894\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(-2\)	\(0\)	\(0\)		\(q+\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}-\zeta_{12}^{3}q^{7}+\cdots\)
1792.1.o.b	\(4\)	\(0.894\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(2\)	\(0\)	\(0\)		\(q-\zeta_{12}^{4}q^{3}+\zeta_{12}^{5}q^{5}+\zeta_{12}^{3}q^{7}+\cdots\)
1792.1.v.a	\(4\)	\(0.894\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{8}q^{7}+\zeta_{8}^{3}q^{9}+(\zeta_{8}^{2}+\zeta_{8}^{3})q^{11}+\cdots\)
1792.1.v.b	\(4\)	\(0.894\)	\(\Q(\zeta_{8})\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{8}q^{7}+\zeta_{8}^{3}q^{9}+(-\zeta_{8}^{2}-\zeta_{8}^{3}+\cdots)q^{11}+\cdots\)
1792.1.bf.a	\(8\)	\(0.894\)	\(\Q(\zeta_{16})\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{16}^{7}q^{7}+\zeta_{16}q^{9}+(-\zeta_{16}^{2}-\zeta_{16}^{5}+\cdots)q^{11}+\cdots\)
1792.1.bt.a	\(32\)	\(0.894\)	\(\Q(\zeta_{64})\)	\(\Q(\sqrt{-7}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q+\zeta_{64}^{3}q^{2}+\zeta_{64}^{6}q^{4}-\zeta_{64}^{7}q^{7}+\cdots\)
1792.2.a.a	\(1\)	\(14.309\)	\(\Q\)	None	None	\(0\)	\(-2\)	\(-4\)	\(1\)	\(+\)	\(q-2q^{3}-4q^{5}+q^{7}+q^{9}-2q^{11}+\cdots\)
1792.2.a.b	\(1\)	\(14.309\)	\(\Q\)	None	None	\(0\)	\(-2\)	\(-2\)	\(1\)	\(+\)	\(q-2q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}+\cdots\)
1792.2.a.c	\(1\)	\(14.309\)	\(\Q\)	None	None	\(0\)	\(-2\)	\(2\)	\(-1\)	\(+\)	\(q-2q^{3}+2q^{5}-q^{7}+q^{9}-2q^{13}+\cdots\)
1792.2.a.d	\(1\)	\(14.309\)	\(\Q\)	None	None	\(0\)	\(-2\)	\(4\)	\(-1\)	\(-\)	\(q-2q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+\cdots\)
1792.2.a.e	\(1\)	\(14.309\)	\(\Q\)	None	None	\(0\)	\(2\)	\(-4\)	\(-1\)	\(+\)	\(q+2q^{3}-4q^{5}-q^{7}+q^{9}+2q^{11}+\cdots\)
1792.2.a.f	\(1\)	\(14.309\)	\(\Q\)	None	None	\(0\)	\(2\)	\(-2\)	\(-1\)	\(-\)	\(q+2q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+\cdots\)
1792.2.a.g	\(1\)	\(14.309\)	\(\Q\)	None	None	\(0\)	\(2\)	\(2\)	\(1\)	\(-\)	\(q+2q^{3}+2q^{5}+q^{7}+q^{9}-2q^{13}+\cdots\)
1792.2.a.h	\(1\)	\(14.309\)	\(\Q\)	None	None	\(0\)	\(2\)	\(4\)	\(1\)	\(-\)	\(q+2q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+\cdots\)
1792.2.a.i	\(2\)	\(14.309\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(-2\)	\(-2\)	\(-2\)	\(+\)	\(q+(-1+\beta )q^{3}+(-1+\beta )q^{5}-q^{7}+\cdots\)
1792.2.a.j	\(2\)	\(14.309\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(-2\)	\(-2\)	\(-2\)	\(+\)	\(q+(-1-\beta )q^{3}+(-1-\beta )q^{5}-q^{7}+\cdots\)
1792.2.a.k	\(2\)	\(14.309\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(-2\)	\(2\)	\(2\)	\(-\)	\(q+(-1+\beta )q^{3}+(1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
1792.2.a.l	\(2\)	\(14.309\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(-2\)	\(2\)	\(2\)	\(+\)	\(q+(-1-\beta )q^{3}+(1+\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
1792.2.a.m	\(2\)	\(14.309\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(-\)	\(q+\beta q^{5}-q^{7}-3q^{9}+\beta q^{11}-\beta q^{13}+\cdots\)
1792.2.a.n	\(2\)	\(14.309\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)	\(+\)	\(q+\beta q^{3}+\beta q^{5}-q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1792.2.a.o	\(2\)	\(14.309\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(2\)	\(+\)	\(q-\beta q^{5}+q^{7}-3q^{9}+\beta q^{11}+\beta q^{13}+\cdots\)
1792.2.a.p	\(2\)	\(14.309\)	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(0\)	\(2\)	\(+\)	\(q+\beta q^{3}-\beta q^{5}+q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1792.2.a.q	\(2\)	\(14.309\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(2\)	\(-2\)	\(2\)	\(+\)	\(q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(1+\cdots)q^{9}+\cdots\)
1792.2.a.r	\(2\)	\(14.309\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(2\)	\(-2\)	\(2\)	\(-\)	\(q+(1+\beta )q^{3}+(-1-\beta )q^{5}+q^{7}+(3+\cdots)q^{9}+\cdots\)
1792.2.a.s	\(2\)	\(14.309\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(2\)	\(2\)	\(-2\)	\(-\)	\(q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(1+2\beta )q^{9}+\cdots\)
1792.2.a.t	\(2\)	\(14.309\)	\(\Q(\sqrt{5}) \)	None	None	\(0\)	\(2\)	\(2\)	\(-2\)	\(-\)	\(q+(1+\beta )q^{3}+(1+\beta )q^{5}-q^{7}+(3+2\beta )q^{9}+\cdots\)
1792.2.a.u	\(4\)	\(14.309\)	\(\Q(\zeta_{16})^+\)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)	\(+\)	\(q+\beta _{1}q^{3}-\beta _{1}q^{5}-q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1792.2.a.v	\(4\)	\(14.309\)	4.4.9248.1	None	None	\(0\)	\(0\)	\(0\)	\(-4\)	\(-\)	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}-q^{7}+(2-\beta _{3})q^{9}+\cdots\)
1792.2.a.w	\(4\)	\(14.309\)	\(\Q(\zeta_{16})^+\)	None	None	\(0\)	\(0\)	\(0\)	\(4\)	\(-\)	\(q+\beta _{1}q^{3}+\beta _{1}q^{5}+q^{7}+(1+\beta _{2})q^{9}+\cdots\)
1792.2.a.x	\(4\)	\(14.309\)	4.4.9248.1	None	None	\(0\)	\(0\)	\(0\)	\(4\)	\(-\)	\(q+\beta _{2}q^{3}+\beta _{1}q^{5}+q^{7}+(2-\beta _{3})q^{9}+\cdots\)
1792.2.b.a	\(2\)	\(14.309\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-8q^{15}+\cdots\)
1792.2.b.b	\(2\)	\(14.309\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q+iq^{3}-q^{7}-q^{9}-2iq^{11}-2iq^{13}+\cdots\)
1792.2.b.c	\(2\)	\(14.309\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q+iq^{3}-q^{7}-q^{9}+2iq^{13}+6q^{17}+\cdots\)
1792.2.b.d	\(2\)	\(14.309\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q-iq^{5}-q^{7}+3q^{9}-2iq^{11}+iq^{13}+\cdots\)
1792.2.b.e	\(2\)	\(14.309\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q-q^{7}+3q^{9}-iq^{11}+2iq^{13}-2q^{17}+\cdots\)
1792.2.b.f	\(2\)	\(14.309\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(2\)		\(q+iq^{3}+q^{7}-q^{9}-2iq^{11}+2iq^{13}+\cdots\)
1792.2.b.g	\(2\)	\(14.309\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(2\)		\(q+iq^{3}+q^{7}-q^{9}-2iq^{13}+6q^{17}+\cdots\)
1792.2.b.h	\(2\)	\(14.309\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(2\)		\(q+iq^{3}-2iq^{5}+q^{7}-q^{9}+8q^{15}+\cdots\)
1792.2.b.i	\(2\)	\(14.309\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(2\)		\(q-iq^{5}+q^{7}+3q^{9}+2iq^{11}+iq^{13}+\cdots\)
1792.2.b.j	\(2\)	\(14.309\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(2\)		\(q+q^{7}+3q^{9}+iq^{11}+2iq^{13}-2q^{17}+\cdots\)
1792.2.b.k	\(4\)	\(14.309\)	\(\Q(i, \sqrt{5})\)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}-q^{7}+(-3+\cdots)q^{9}+\cdots\)
1792.2.b.l	\(4\)	\(14.309\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)		\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-q^{7}+(-1+\zeta_{12}^{3})q^{9}+\cdots\)
1792.2.b.m	\(4\)	\(14.309\)	\(\Q(i, \sqrt{5})\)	None	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q+\beta _{1}q^{3}+(\beta _{1}+\beta _{2})q^{5}+q^{7}+(-3+\cdots)q^{9}+\cdots\)
1792.2.b.n	\(4\)	\(14.309\)	\(\Q(\zeta_{12})\)	None	None	\(0\)	\(0\)	\(0\)	\(4\)		\(q-\zeta_{12}^{2}q^{3}+\zeta_{12}q^{5}+q^{7}+(-1+\zeta_{12}^{3})q^{9}+\cdots\)
1792.2.b.o	\(6\)	\(14.309\)	6.0.399424.1	None	None	\(0\)	\(0\)	\(0\)	\(-6\)		\(q+\beta _{5}q^{3}+\beta _{4}q^{5}-q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots\)
1792.2.b.p	\(6\)	\(14.309\)	6.0.399424.1	None	None	\(0\)	\(0\)	\(0\)	\(6\)		\(q+\beta _{5}q^{3}-\beta _{4}q^{5}+q^{7}+(-2-\beta _{3}+\cdots)q^{9}+\cdots\)

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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.