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 225 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
1280.1.e.a	$2$	$0.639$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-5}) $	$\Q(\sqrt{5}) $	$0$	$0$	$0$	$0$	$-$	$q-iq^{5}+q^{9}-q^{25}-iq^{29}+q^{41}+\cdots$
1280.1.h.a	$2$	$0.639$	$\Q(\sqrt{2}) $	$\Q(\sqrt{-5}) $	None	$0$	$0$	$-2$	$0$	$-$	$q-\beta q^{3}-q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots$
1280.1.h.b	$2$	$0.639$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $, $\Q(\sqrt{-10}) $	$\Q(\sqrt{10}) $	$0$	$0$	$0$	$0$	$-$	$q-iq^{5}-q^{9}-iq^{13}-q^{25}-iq^{37}+\cdots$
1280.1.h.c	$2$	$0.639$	$\Q(\sqrt{2}) $	$\Q(\sqrt{-5}) $	None	$0$	$0$	$2$	$0$	$-$	$q-\beta q^{3}+q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots$
1280.1.m.a	$2$	$0.639$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-2$	$0$	$-$	$q-q^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots$
1280.1.m.b	$2$	$0.639$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$2$	$0$	$-$	$q+q^{5}+iq^{9}+(1-i)q^{13}+(-1+i+\cdots)q^{17}+\cdots$
1280.1.p.a	$2$	$0.639$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-2$	$0$	$-$	$q-q^{5}-iq^{9}+(1+i)q^{13}+(1-i)q^{17}+\cdots$
1280.1.p.b	$2$	$0.639$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$2$	$0$	$-$	$q+q^{5}-iq^{9}+(-1-i)q^{13}+(1-i+\cdots)q^{17}+\cdots$
1280.2.a.a	$2$	$10.221$	$\Q(\sqrt{3}) $	None	None	$0$	$-2$	$-2$	$2$	$+$	$q+(-1+\beta )q^{3}-q^{5}+(1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1280.2.a.b	$2$	$10.221$	$\Q(\sqrt{3}) $	None	None	$0$	$-2$	$-2$	$6$	$-$	$q+(-1+\beta )q^{3}-q^{5}+(3-\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1280.2.a.c	$2$	$10.221$	$\Q(\sqrt{3}) $	None	None	$0$	$-2$	$2$	$-6$	$+$	$q+(-1+\beta )q^{3}+q^{5}+(-3+\beta )q^{7}+\cdots$
1280.2.a.d	$2$	$10.221$	$\Q(\sqrt{3}) $	None	None	$0$	$-2$	$2$	$-2$	$+$	$q+(-1+\beta )q^{3}+q^{5}+(-1-\beta )q^{7}+\cdots$
1280.2.a.e	$2$	$10.221$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$-2$	$0$	$+$	$q+\beta q^{3}-q^{5}-\beta q^{7}-q^{9}-2\beta q^{11}+\cdots$
1280.2.a.f	$2$	$10.221$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$-2$	$0$	$-$	$q+\beta q^{3}-q^{5}-3\beta q^{7}-q^{9}+4\beta q^{11}+\cdots$
1280.2.a.g	$2$	$10.221$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$-2$	$0$	$-$	$q+\beta q^{3}-q^{5}+3\beta q^{7}-q^{9}+2\beta q^{11}+\cdots$
1280.2.a.h	$2$	$10.221$	$\Q(\sqrt{10}) $	None	None	$0$	$0$	$-2$	$0$	$-$	$q+\beta q^{3}-q^{5}+\beta q^{7}+7q^{9}-6q^{13}+\cdots$
1280.2.a.i	$2$	$10.221$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$2$	$0$	$+$	$q+\beta q^{3}+q^{5}-3\beta q^{7}-q^{9}+2\beta q^{11}+\cdots$
1280.2.a.j	$2$	$10.221$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$2$	$0$	$-$	$q+\beta q^{3}+q^{5}+3\beta q^{7}-q^{9}+4\beta q^{11}+\cdots$
1280.2.a.k	$2$	$10.221$	$\Q(\sqrt{2}) $	None	None	$0$	$0$	$2$	$0$	$-$	$q+\beta q^{3}+q^{5}+\beta q^{7}-q^{9}-2\beta q^{11}+\cdots$
1280.2.a.l	$2$	$10.221$	$\Q(\sqrt{10}) $	None	None	$0$	$0$	$2$	$0$	$-$	$q+\beta q^{3}+q^{5}-\beta q^{7}+7q^{9}+6q^{13}+\cdots$
1280.2.a.m	$2$	$10.221$	$\Q(\sqrt{3}) $	None	None	$0$	$2$	$-2$	$-6$	$+$	$q+(1+\beta )q^{3}-q^{5}+(-3-\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1280.2.a.n	$2$	$10.221$	$\Q(\sqrt{3}) $	None	None	$0$	$2$	$-2$	$-2$	$-$	$q+(1+\beta )q^{3}-q^{5}+(-1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots$
1280.2.a.o	$2$	$10.221$	$\Q(\sqrt{3}) $	None	None	$0$	$2$	$2$	$2$	$-$	$q+(1+\beta )q^{3}+q^{5}+(1-\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
1280.2.a.p	$2$	$10.221$	$\Q(\sqrt{3}) $	None	None	$0$	$2$	$2$	$6$	$-$	$q+(1+\beta )q^{3}+q^{5}+(3+\beta )q^{7}+(1+2\beta )q^{9}+\cdots$
1280.2.c.a	$2$	$10.221$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$-4$	$0$	$-$	$q+(-2+i)q^{5}+3q^{9}-6iq^{13}+8iq^{17}+\cdots$
1280.2.c.b	$2$	$10.221$	$\Q(\sqrt{-5}) $	$\Q(\sqrt{-10}) $	None	$0$	$0$	$0$	$0$	$-$	$q+\beta q^{5}-2\beta q^{7}+3q^{9}-2q^{11}-2\beta q^{13}+\cdots$
1280.2.c.c	$2$	$10.221$	$\Q(\sqrt{-5}) $	$\Q(\sqrt{-10}) $	None	$0$	$0$	$0$	$0$	$-$	$q+\beta q^{5}+2\beta q^{7}+3q^{9}+2q^{11}-2\beta q^{13}+\cdots$
1280.2.c.d	$2$	$10.221$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-1}) $	None	$0$	$0$	$4$	$0$	$-$	$q+(2+i)q^{5}+3q^{9}-6iq^{13}-8iq^{17}+\cdots$
1280.2.c.e	$4$	$10.221$	$\Q(i, \sqrt{6})$	None	None	$0$	$0$	$-4$	$0$	$-$	$q+\beta _{2}q^{3}+(-1-\beta _{1})q^{5}+\beta _{2}q^{7}-3q^{9}+\cdots$
1280.2.c.f	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{5})$	$\Q(\sqrt{-5}) $	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{2}q^{3}+\beta _{3}q^{5}+3\beta _{1}q^{7}-7q^{9}+\cdots$
1280.2.c.g	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{3})$	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots$
1280.2.c.h	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{3})$	None	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}-3q^{9}+\cdots$
1280.2.c.i	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{3})$	None	None	$0$	$0$	$0$	$0$	$-$	$q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots$
1280.2.c.j	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{5})$	$\Q(\sqrt{-5}) $	None	$0$	$0$	$0$	$0$	$-$	$q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+q^{9}+\beta _{2}q^{15}+\cdots$
1280.2.c.k	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{3})$	None	None	$0$	$0$	$0$	$0$	$-$	$q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+q^{9}+\cdots$
1280.2.c.l	$4$	$10.221$	$\Q(\sqrt{-2}, \sqrt{-5})$	$\Q(\sqrt{-10}) $	None	$0$	$0$	$0$	$0$	$-$	$q+\beta _{2}q^{5}-\beta _{1}q^{7}+3q^{9}-\beta _{3}q^{11}+\cdots$
1280.2.c.m	$4$	$10.221$	$\Q(i, \sqrt{6})$	None	None	$0$	$0$	$4$	$0$	$-$	$q+\beta _{2}q^{3}+(1+\beta _{1})q^{5}-\beta _{2}q^{7}-3q^{9}+\cdots$
1280.2.d.a	$2$	$10.221$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$-8$	$-$	$q+iq^{5}-4q^{7}+3q^{9}-4iq^{11}+2iq^{13}+\cdots$
1280.2.d.b	$2$	$10.221$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$-4$	$-$	$q+2iq^{3}+iq^{5}-2q^{7}-q^{9}-4iq^{11}+\cdots$
1280.2.d.c	$2$	$10.221$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$-4$	$-$	$q+2iq^{3}-iq^{5}-2q^{7}-q^{9}-2iq^{13}+\cdots$
1280.2.d.d	$2$	$10.221$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$-4$	$-$	$q-iq^{5}-2q^{7}+3q^{9}-6iq^{11}+2iq^{13}+\cdots$
1280.2.d.e	$2$	$10.221$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$0$	$-$	$q+2iq^{3}+iq^{5}-q^{9}-2iq^{11}+2iq^{13}+\cdots$
1280.2.d.f	$2$	$10.221$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$0$	$-$	$q+2iq^{3}-iq^{5}-q^{9}-2iq^{11}-2iq^{13}+\cdots$
1280.2.d.g	$2$	$10.221$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$4$	$-$	$q+2iq^{3}+iq^{5}+2q^{7}-q^{9}+2iq^{13}+\cdots$
1280.2.d.h	$2$	$10.221$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$4$	$-$	$q+2iq^{3}-iq^{5}+2q^{7}-q^{9}-4iq^{11}+\cdots$
1280.2.d.i	$2$	$10.221$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$4$	$-$	$q+iq^{5}+2q^{7}+3q^{9}-6iq^{11}-2iq^{13}+\cdots$
1280.2.d.j	$2$	$10.221$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$8$	$-$	$q+iq^{5}+4q^{7}+3q^{9}+4iq^{11}+2iq^{13}+\cdots$
1280.2.d.k	$4$	$10.221$	$\Q(i, \sqrt{5})$	None	None	$0$	$0$	$0$	$-4$	$-$	$q+(-\beta _{1}+\beta _{2})q^{3}-\beta _{1}q^{5}+(-1-\beta _{3})q^{7}+\cdots$
1280.2.d.l	$4$	$10.221$	$\Q(\zeta_{8})$	None	None	$0$	$0$	$0$	$0$	$-$	$q+\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}-5q^{9}+\cdots$
1280.2.d.m	$4$	$10.221$	$\Q(i, \sqrt{5})$	None	None	$0$	$0$	$0$	$4$	$-$	$q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}+\cdots$

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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
1280.1.e.a	$2$	$0.639$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{5}) \)	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-iq^{5}+q^{9}-q^{25}-iq^{29}+q^{41}+\cdots\)
1280.1.h.a	$2$	$0.639$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-5}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q-\beta q^{3}-q^{5}-\beta q^{7}+q^{9}+\beta q^{15}+\cdots\)
1280.1.h.b	$2$	$0.639$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-10}) \)	\(\Q(\sqrt{10}) \)	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-iq^{5}-q^{9}-iq^{13}-q^{25}-iq^{37}+\cdots\)
1280.1.h.c	$2$	$0.639$	\(\Q(\sqrt{2}) \)	\(\Q(\sqrt{-5}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q-\beta q^{3}+q^{5}+\beta q^{7}+q^{9}-\beta q^{15}+\cdots\)
1280.1.m.a	$2$	$0.639$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q-q^{5}+iq^{9}+(-1+i)q^{13}+(-1+\cdots)q^{17}+\cdots\)
1280.1.m.b	$2$	$0.639$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q+q^{5}+iq^{9}+(1-i)q^{13}+(-1+i+\cdots)q^{17}+\cdots\)
1280.1.p.a	$2$	$0.639$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q-q^{5}-iq^{9}+(1+i)q^{13}+(1-i)q^{17}+\cdots\)
1280.1.p.b	$2$	$0.639$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q+q^{5}-iq^{9}+(-1-i)q^{13}+(1-i+\cdots)q^{17}+\cdots\)
1280.2.a.a	$2$	$10.221$	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(-2\)	\(-2\)	\(2\)	$+$	\(q+(-1+\beta )q^{3}-q^{5}+(1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.b	$2$	$10.221$	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(-2\)	\(-2\)	\(6\)	$-$	\(q+(-1+\beta )q^{3}-q^{5}+(3-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.c	$2$	$10.221$	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(-2\)	\(2\)	\(-6\)	$+$	\(q+(-1+\beta )q^{3}+q^{5}+(-3+\beta )q^{7}+\cdots\)
1280.2.a.d	$2$	$10.221$	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(-2\)	\(2\)	\(-2\)	$+$	\(q+(-1+\beta )q^{3}+q^{5}+(-1-\beta )q^{7}+\cdots\)
1280.2.a.e	$2$	$10.221$	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	$+$	\(q+\beta q^{3}-q^{5}-\beta q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1280.2.a.f	$2$	$10.221$	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q+\beta q^{3}-q^{5}-3\beta q^{7}-q^{9}+4\beta q^{11}+\cdots\)
1280.2.a.g	$2$	$10.221$	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q+\beta q^{3}-q^{5}+3\beta q^{7}-q^{9}+2\beta q^{11}+\cdots\)
1280.2.a.h	$2$	$10.221$	\(\Q(\sqrt{10}) \)	None	None	\(0\)	\(0\)	\(-2\)	\(0\)	$-$	\(q+\beta q^{3}-q^{5}+\beta q^{7}+7q^{9}-6q^{13}+\cdots\)
1280.2.a.i	$2$	$10.221$	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	$+$	\(q+\beta q^{3}+q^{5}-3\beta q^{7}-q^{9}+2\beta q^{11}+\cdots\)
1280.2.a.j	$2$	$10.221$	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q+\beta q^{3}+q^{5}+3\beta q^{7}-q^{9}+4\beta q^{11}+\cdots\)
1280.2.a.k	$2$	$10.221$	\(\Q(\sqrt{2}) \)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q+\beta q^{3}+q^{5}+\beta q^{7}-q^{9}-2\beta q^{11}+\cdots\)
1280.2.a.l	$2$	$10.221$	\(\Q(\sqrt{10}) \)	None	None	\(0\)	\(0\)	\(2\)	\(0\)	$-$	\(q+\beta q^{3}+q^{5}-\beta q^{7}+7q^{9}+6q^{13}+\cdots\)
1280.2.a.m	$2$	$10.221$	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(2\)	\(-2\)	\(-6\)	$+$	\(q+(1+\beta )q^{3}-q^{5}+(-3-\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.n	$2$	$10.221$	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(2\)	\(-2\)	\(-2\)	$-$	\(q+(1+\beta )q^{3}-q^{5}+(-1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)
1280.2.a.o	$2$	$10.221$	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(2\)	\(2\)	\(2\)	$-$	\(q+(1+\beta )q^{3}+q^{5}+(1-\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
1280.2.a.p	$2$	$10.221$	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(2\)	\(2\)	\(6\)	$-$	\(q+(1+\beta )q^{3}+q^{5}+(3+\beta )q^{7}+(1+2\beta )q^{9}+\cdots\)
1280.2.c.a	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(-4\)	\(0\)	$-$	\(q+(-2+i)q^{5}+3q^{9}-6iq^{13}+8iq^{17}+\cdots\)
1280.2.c.b	$2$	$10.221$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-10}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta q^{5}-2\beta q^{7}+3q^{9}-2q^{11}-2\beta q^{13}+\cdots\)
1280.2.c.c	$2$	$10.221$	\(\Q(\sqrt{-5}) \)	\(\Q(\sqrt{-10}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta q^{5}+2\beta q^{7}+3q^{9}+2q^{11}-2\beta q^{13}+\cdots\)
1280.2.c.d	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-1}) \)	None	\(0\)	\(0\)	\(4\)	\(0\)	$-$	\(q+(2+i)q^{5}+3q^{9}-6iq^{13}-8iq^{17}+\cdots\)
1280.2.c.e	$4$	$10.221$	\(\Q(i, \sqrt{6})\)	None	None	\(0\)	\(0\)	\(-4\)	\(0\)	$-$	\(q+\beta _{2}q^{3}+(-1-\beta _{1})q^{5}+\beta _{2}q^{7}-3q^{9}+\cdots\)
1280.2.c.f	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{2}q^{3}+\beta _{3}q^{5}+3\beta _{1}q^{7}-7q^{9}+\cdots\)
1280.2.c.g	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{3}q^{3}+(-\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}+\cdots\)
1280.2.c.h	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{3}q^{3}+(\beta _{1}+\beta _{2})q^{5}-\beta _{1}q^{7}-3q^{9}+\cdots\)
1280.2.c.i	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\beta _{1}q^{3}+(-\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+\cdots\)
1280.2.c.j	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{5})\)	\(\Q(\sqrt{-5}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\beta _{1}q^{3}-\beta _{3}q^{5}-\beta _{2}q^{7}+q^{9}+\beta _{2}q^{15}+\cdots\)
1280.2.c.k	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{3})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+\beta _{3}q^{7}+q^{9}+\cdots\)
1280.2.c.l	$4$	$10.221$	\(\Q(\sqrt{-2}, \sqrt{-5})\)	\(\Q(\sqrt{-10}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\beta _{2}q^{5}-\beta _{1}q^{7}+3q^{9}-\beta _{3}q^{11}+\cdots\)
1280.2.c.m	$4$	$10.221$	\(\Q(i, \sqrt{6})\)	None	None	\(0\)	\(0\)	\(4\)	\(0\)	$-$	\(q+\beta _{2}q^{3}+(1+\beta _{1})q^{5}-\beta _{2}q^{7}-3q^{9}+\cdots\)
1280.2.d.a	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-8\)	$-$	\(q+iq^{5}-4q^{7}+3q^{9}-4iq^{11}+2iq^{13}+\cdots\)
1280.2.d.b	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)	$-$	\(q+2iq^{3}+iq^{5}-2q^{7}-q^{9}-4iq^{11}+\cdots\)
1280.2.d.c	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)	$-$	\(q+2iq^{3}-iq^{5}-2q^{7}-q^{9}-2iq^{13}+\cdots\)
1280.2.d.d	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)	$-$	\(q-iq^{5}-2q^{7}+3q^{9}-6iq^{11}+2iq^{13}+\cdots\)
1280.2.d.e	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+2iq^{3}+iq^{5}-q^{9}-2iq^{11}+2iq^{13}+\cdots\)
1280.2.d.f	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+2iq^{3}-iq^{5}-q^{9}-2iq^{11}-2iq^{13}+\cdots\)
1280.2.d.g	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(4\)	$-$	\(q+2iq^{3}+iq^{5}+2q^{7}-q^{9}+2iq^{13}+\cdots\)
1280.2.d.h	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(4\)	$-$	\(q+2iq^{3}-iq^{5}+2q^{7}-q^{9}-4iq^{11}+\cdots\)
1280.2.d.i	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(4\)	$-$	\(q+iq^{5}+2q^{7}+3q^{9}-6iq^{11}-2iq^{13}+\cdots\)
1280.2.d.j	$2$	$10.221$	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(8\)	$-$	\(q+iq^{5}+4q^{7}+3q^{9}+4iq^{11}+2iq^{13}+\cdots\)
1280.2.d.k	$4$	$10.221$	\(\Q(i, \sqrt{5})\)	None	None	\(0\)	\(0\)	\(0\)	\(-4\)	$-$	\(q+(-\beta _{1}+\beta _{2})q^{3}-\beta _{1}q^{5}+(-1-\beta _{3})q^{7}+\cdots\)
1280.2.d.l	$4$	$10.221$	\(\Q(\zeta_{8})\)	None	None	\(0\)	\(0\)	\(0\)	\(0\)	$-$	\(q+\zeta_{8}^{2}q^{3}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}-5q^{9}+\cdots\)
1280.2.d.m	$4$	$10.221$	\(\Q(i, \sqrt{5})\)	None	None	\(0\)	\(0\)	\(0\)	\(4\)	$-$	\(q+(-\beta _{1}+\beta _{2})q^{3}+\beta _{1}q^{5}+(1+\beta _{3})q^{7}+\cdots\)

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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.