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 275 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
1344.1.e.a	$2$	$0.671$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{21}) $	$0$	$-2$	$0$	$0$		$q-q^{3}-iq^{5}-iq^{7}+q^{9}+2iq^{15}+\cdots$
1344.1.e.b	$2$	$0.671$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{42}) $	$0$	$0$	$0$	$0$		$q-iq^{3}-iq^{7}-q^{9}-q^{13}-iq^{19}+\cdots$
1344.1.e.c	$2$	$0.671$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{42}) $	$0$	$0$	$0$	$0$		$q+iq^{3}-iq^{7}-q^{9}+q^{13}+iq^{19}+\cdots$
1344.1.e.d	$2$	$0.671$	$\Q(\sqrt{-1}) $	$\Q(\sqrt{-6}) $, $\Q(\sqrt{-14}) $	$\Q(\sqrt{21}) $	$0$	$2$	$0$	$0$		$q+q^{3}-iq^{5}+iq^{7}+q^{9}-2iq^{15}+\cdots$
1344.1.o.a	$1$	$0.671$	$\Q$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{7}) $	$0$	$-1$	$0$	$-1$		$q-q^{3}-q^{7}+q^{9}+2q^{19}+q^{21}-q^{25}+\cdots$
1344.1.o.b	$1$	$0.671$	$\Q$	$\Q(\sqrt{-3}) $, $\Q(\sqrt{-21}) $	$\Q(\sqrt{7}) $	$0$	$1$	$0$	$1$		$q+q^{3}+q^{7}+q^{9}-2q^{19}+q^{21}-q^{25}+\cdots$
1344.1.z.a	$2$	$0.671$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$-1$		$q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots$
1344.1.z.b	$2$	$0.671$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$1$	$0$	$1$		$q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots$
1344.1.ba.a	$4$	$0.671$	$\Q(\zeta_{12})$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+(-\zeta_{12}^{2}+\cdots)q^{13}+\cdots$
1344.1.ba.b	$4$	$0.671$	$\Q(\zeta_{12})$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+(\zeta_{12}^{2}+\cdots)q^{13}+\cdots$
1344.1.bm.a	$4$	$0.671$	$\Q(\zeta_{12})$	$\Q(\sqrt{-6}) $	None	$0$	$-2$	$0$	$0$		$q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
1344.1.bm.b	$4$	$0.671$	$\Q(\zeta_{12})$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}-q^{13}+\cdots$
1344.1.bm.c	$4$	$0.671$	$\Q(\zeta_{12})$	$\Q(\sqrt{-3}) $	None	$0$	$0$	$0$	$0$		$q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+q^{13}+\cdots$
1344.1.bm.d	$4$	$0.671$	$\Q(\zeta_{12})$	$\Q(\sqrt{-6}) $	None	$0$	$2$	$0$	$0$		$q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{4}q^{9}+\cdots$
1344.1.bn.a	$2$	$0.671$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$-1$	$0$	$1$		$q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots$
1344.1.bn.b	$2$	$0.671$	$\Q(\sqrt{-3}) $	$\Q(\sqrt{-3}) $	None	$0$	$1$	$0$	$-1$		$q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots$
1344.2.a.a	$1$	$10.732$	$\Q$	None	None	$0$	$-1$	$-4$	$1$	$+$	$q-q^{3}-4q^{5}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots$
1344.2.a.b	$1$	$10.732$	$\Q$	None	None	$0$	$-1$	$-2$	$-1$	$-$	$q-q^{3}-2q^{5}-q^{7}+q^{9}-6q^{13}+2q^{15}+\cdots$
1344.2.a.c	$1$	$10.732$	$\Q$	None	None	$0$	$-1$	$-2$	$-1$	$+$	$q-q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots$
1344.2.a.d	$1$	$10.732$	$\Q$	None	None	$0$	$-1$	$-2$	$1$	$+$	$q-q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots$
1344.2.a.e	$1$	$10.732$	$\Q$	None	None	$0$	$-1$	$0$	$1$	$-$	$q-q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
1344.2.a.f	$1$	$10.732$	$\Q$	None	None	$0$	$-1$	$0$	$1$	$-$	$q-q^{3}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots$
1344.2.a.g	$1$	$10.732$	$\Q$	None	None	$0$	$-1$	$2$	$-1$	$+$	$q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots$
1344.2.a.h	$1$	$10.732$	$\Q$	None	None	$0$	$-1$	$2$	$-1$	$-$	$q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots$
1344.2.a.i	$1$	$10.732$	$\Q$	None	None	$0$	$-1$	$2$	$1$	$+$	$q-q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots$
1344.2.a.j	$1$	$10.732$	$\Q$	None	None	$0$	$-1$	$4$	$1$	$-$	$q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
1344.2.a.k	$1$	$10.732$	$\Q$	None	None	$0$	$1$	$-4$	$-1$	$-$	$q+q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots$
1344.2.a.l	$1$	$10.732$	$\Q$	None	None	$0$	$1$	$-2$	$-1$	$+$	$q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots$
1344.2.a.m	$1$	$10.732$	$\Q$	None	None	$0$	$1$	$-2$	$1$	$+$	$q+q^{3}-2q^{5}+q^{7}+q^{9}-6q^{13}-2q^{15}+\cdots$
1344.2.a.n	$1$	$10.732$	$\Q$	None	None	$0$	$1$	$-2$	$1$	$-$	$q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots$
1344.2.a.o	$1$	$10.732$	$\Q$	None	None	$0$	$1$	$0$	$-1$	$+$	$q+q^{3}-q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots$
1344.2.a.p	$1$	$10.732$	$\Q$	None	None	$0$	$1$	$0$	$-1$	$-$	$q+q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots$
1344.2.a.q	$1$	$10.732$	$\Q$	None	None	$0$	$1$	$2$	$-1$	$-$	$q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots$
1344.2.a.r	$1$	$10.732$	$\Q$	None	None	$0$	$1$	$2$	$1$	$-$	$q+q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots$
1344.2.a.s	$1$	$10.732$	$\Q$	None	None	$0$	$1$	$2$	$1$	$-$	$q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots$
1344.2.a.t	$1$	$10.732$	$\Q$	None	None	$0$	$1$	$4$	$-1$	$-$	$q+q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots$
1344.2.a.u	$2$	$10.732$	$\Q(\sqrt{3}) $	None	None	$0$	$-2$	$0$	$-2$	$-$	$q-q^{3}+\beta q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots$
1344.2.a.v	$2$	$10.732$	$\Q(\sqrt{3}) $	None	None	$0$	$2$	$0$	$2$	$-$	$q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2+\beta )q^{11}+\cdots$
1344.2.b.a	$2$	$10.732$	$\Q(\sqrt{-6}) $	None	None	$0$	$-2$	$0$	$-2$		$q-q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots$
1344.2.b.b	$2$	$10.732$	$\Q(\sqrt{-3}) $	None	None	$0$	$-2$	$0$	$4$		$q-q^{3}+(2-\zeta_{6})q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots$
1344.2.b.c	$2$	$10.732$	$\Q(\sqrt{-3}) $	None	None	$0$	$2$	$0$	$-4$		$q+q^{3}+(-2+\zeta_{6})q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots$
1344.2.b.d	$2$	$10.732$	$\Q(\sqrt{-6}) $	None	None	$0$	$2$	$0$	$2$		$q+q^{3}+\beta q^{5}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots$
1344.2.b.e	$4$	$10.732$	4.0.2312.1	None	None	$0$	$-4$	$0$	$-2$		$q-q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots$
1344.2.b.f	$4$	$10.732$	4.0.2312.1	None	None	$0$	$4$	$0$	$2$		$q+q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots$
1344.2.b.g	$8$	$10.732$	8.0.836829184.2	None	None	$0$	$-8$	$0$	$4$		$q-q^{3}-\beta _{1}q^{5}-\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots$
1344.2.b.h	$8$	$10.732$	8.0.836829184.2	None	None	$0$	$8$	$0$	$-4$		$q+q^{3}-\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(\beta _{2}+\beta _{4}+\cdots)q^{11}+\cdots$
1344.2.c.a	$2$	$10.732$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$-2$		$q+iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots$
1344.2.c.b	$2$	$10.732$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$-2$		$q-iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots$
1344.2.c.c	$2$	$10.732$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$2$		$q+iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots$
1344.2.c.d	$2$	$10.732$	$\Q(\sqrt{-1}) $	None	None	$0$	$0$	$0$	$2$		$q-iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots$

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Elliptic curves over $\Q$
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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
1344.1.e.a	\(2\)	\(0.671\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{21}) \)	\(0\)	\(-2\)	\(0\)	\(0\)		\(q-q^{3}-iq^{5}-iq^{7}+q^{9}+2iq^{15}+\cdots\)
1344.1.e.b	\(2\)	\(0.671\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{42}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q-iq^{3}-iq^{7}-q^{9}-q^{13}-iq^{19}+\cdots\)
1344.1.e.c	\(2\)	\(0.671\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{42}) \)	\(0\)	\(0\)	\(0\)	\(0\)		\(q+iq^{3}-iq^{7}-q^{9}+q^{13}+iq^{19}+\cdots\)
1344.1.e.d	\(2\)	\(0.671\)	\(\Q(\sqrt{-1}) \)	\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-14}) \)	\(\Q(\sqrt{21}) \)	\(0\)	\(2\)	\(0\)	\(0\)		\(q+q^{3}-iq^{5}+iq^{7}+q^{9}-2iq^{15}+\cdots\)
1344.1.o.a	\(1\)	\(0.671\)	\(\Q\)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{7}) \)	\(0\)	\(-1\)	\(0\)	\(-1\)		\(q-q^{3}-q^{7}+q^{9}+2q^{19}+q^{21}-q^{25}+\cdots\)
1344.1.o.b	\(1\)	\(0.671\)	\(\Q\)	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-21}) \)	\(\Q(\sqrt{7}) \)	\(0\)	\(1\)	\(0\)	\(1\)		\(q+q^{3}+q^{7}+q^{9}-2q^{19}+q^{21}-q^{25}+\cdots\)
1344.1.z.a	\(2\)	\(0.671\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(-1\)		\(q-\zeta_{6}q^{3}+\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots\)
1344.1.z.b	\(2\)	\(0.671\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(1\)	\(0\)	\(1\)		\(q+\zeta_{6}q^{3}-\zeta_{6}^{2}q^{7}+\zeta_{6}^{2}q^{9}+(\zeta_{6}+\zeta_{6}^{2}+\cdots)q^{13}+\cdots\)
1344.1.ba.a	\(4\)	\(0.671\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+(-\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
1344.1.ba.b	\(4\)	\(0.671\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+(\zeta_{12}^{2}+\cdots)q^{13}+\cdots\)
1344.1.bm.a	\(4\)	\(0.671\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(-2\)	\(0\)	\(0\)		\(q-\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}-\zeta_{12}^{5}q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
1344.1.bm.b	\(4\)	\(0.671\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{12}^{5}q^{3}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}-q^{13}+\cdots\)
1344.1.bm.c	\(4\)	\(0.671\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(0\)	\(0\)	\(0\)		\(q-\zeta_{12}^{5}q^{3}-\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+q^{13}+\cdots\)
1344.1.bm.d	\(4\)	\(0.671\)	\(\Q(\zeta_{12})\)	\(\Q(\sqrt{-6}) \)	None	\(0\)	\(2\)	\(0\)	\(0\)		\(q+\zeta_{12}^{2}q^{3}-\zeta_{12}q^{5}+\zeta_{12}^{5}q^{7}+\zeta_{12}^{4}q^{9}+\cdots\)
1344.1.bn.a	\(2\)	\(0.671\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(-1\)	\(0\)	\(1\)		\(q+\zeta_{6}^{2}q^{3}+\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots\)
1344.1.bn.b	\(2\)	\(0.671\)	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)	None	\(0\)	\(1\)	\(0\)	\(-1\)		\(q-\zeta_{6}^{2}q^{3}-\zeta_{6}q^{7}-\zeta_{6}q^{9}+q^{13}+\cdots\)
1344.2.a.a	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(-4\)	\(1\)	\(+\)	\(q-q^{3}-4q^{5}+q^{7}+q^{9}+2q^{11}+6q^{13}+\cdots\)
1344.2.a.b	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(-2\)	\(-1\)	\(-\)	\(q-q^{3}-2q^{5}-q^{7}+q^{9}-6q^{13}+2q^{15}+\cdots\)
1344.2.a.c	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(-2\)	\(-1\)	\(+\)	\(q-q^{3}-2q^{5}-q^{7}+q^{9}+2q^{13}+2q^{15}+\cdots\)
1344.2.a.d	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(-2\)	\(1\)	\(+\)	\(q-q^{3}-2q^{5}+q^{7}+q^{9}-2q^{13}+2q^{15}+\cdots\)
1344.2.a.e	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(0\)	\(1\)	\(-\)	\(q-q^{3}+q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1344.2.a.f	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(0\)	\(1\)	\(-\)	\(q-q^{3}+q^{7}+q^{9}+6q^{11}-2q^{13}+\cdots\)
1344.2.a.g	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(2\)	\(-1\)	\(+\)	\(q-q^{3}+2q^{5}-q^{7}+q^{9}-4q^{11}+2q^{13}+\cdots\)
1344.2.a.h	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(2\)	\(-1\)	\(-\)	\(q-q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}+6q^{13}+\cdots\)
1344.2.a.i	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(2\)	\(1\)	\(+\)	\(q-q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}-6q^{13}+\cdots\)
1344.2.a.j	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(-1\)	\(4\)	\(1\)	\(-\)	\(q-q^{3}+4q^{5}+q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1344.2.a.k	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-4\)	\(-1\)	\(-\)	\(q+q^{3}-4q^{5}-q^{7}+q^{9}-2q^{11}+6q^{13}+\cdots\)
1344.2.a.l	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-2\)	\(-1\)	\(+\)	\(q+q^{3}-2q^{5}-q^{7}+q^{9}-2q^{13}-2q^{15}+\cdots\)
1344.2.a.m	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-2\)	\(1\)	\(+\)	\(q+q^{3}-2q^{5}+q^{7}+q^{9}-6q^{13}-2q^{15}+\cdots\)
1344.2.a.n	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(1\)	\(-2\)	\(1\)	\(-\)	\(q+q^{3}-2q^{5}+q^{7}+q^{9}+2q^{13}-2q^{15}+\cdots\)
1344.2.a.o	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(1\)	\(0\)	\(-1\)	\(+\)	\(q+q^{3}-q^{7}+q^{9}-6q^{11}-2q^{13}+\cdots\)
1344.2.a.p	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(1\)	\(0\)	\(-1\)	\(-\)	\(q+q^{3}-q^{7}+q^{9}+2q^{11}+2q^{13}+\cdots\)
1344.2.a.q	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(1\)	\(2\)	\(-1\)	\(-\)	\(q+q^{3}+2q^{5}-q^{7}+q^{9}+4q^{11}-6q^{13}+\cdots\)
1344.2.a.r	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(1\)	\(2\)	\(1\)	\(-\)	\(q+q^{3}+2q^{5}+q^{7}+q^{9}-4q^{11}+6q^{13}+\cdots\)
1344.2.a.s	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(1\)	\(2\)	\(1\)	\(-\)	\(q+q^{3}+2q^{5}+q^{7}+q^{9}+4q^{11}+2q^{13}+\cdots\)
1344.2.a.t	\(1\)	\(10.732\)	\(\Q\)	None	None	\(0\)	\(1\)	\(4\)	\(-1\)	\(-\)	\(q+q^{3}+4q^{5}-q^{7}+q^{9}-2q^{11}+2q^{13}+\cdots\)
1344.2.a.u	\(2\)	\(10.732\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(-2\)	\(0\)	\(-2\)	\(-\)	\(q-q^{3}+\beta q^{5}-q^{7}+q^{9}+(-2-\beta )q^{11}+\cdots\)
1344.2.a.v	\(2\)	\(10.732\)	\(\Q(\sqrt{3}) \)	None	None	\(0\)	\(2\)	\(0\)	\(2\)	\(-\)	\(q+q^{3}+\beta q^{5}+q^{7}+q^{9}+(2+\beta )q^{11}+\cdots\)
1344.2.b.a	\(2\)	\(10.732\)	\(\Q(\sqrt{-6}) \)	None	None	\(0\)	\(-2\)	\(0\)	\(-2\)		\(q-q^{3}+\beta q^{5}+(-1-\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
1344.2.b.b	\(2\)	\(10.732\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(-2\)	\(0\)	\(4\)		\(q-q^{3}+(2-\zeta_{6})q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots\)
1344.2.b.c	\(2\)	\(10.732\)	\(\Q(\sqrt{-3}) \)	None	None	\(0\)	\(2\)	\(0\)	\(-4\)		\(q+q^{3}+(-2+\zeta_{6})q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
1344.2.b.d	\(2\)	\(10.732\)	\(\Q(\sqrt{-6}) \)	None	None	\(0\)	\(2\)	\(0\)	\(2\)		\(q+q^{3}+\beta q^{5}+(1+\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
1344.2.b.e	\(4\)	\(10.732\)	4.0.2312.1	None	None	\(0\)	\(-4\)	\(0\)	\(-2\)		\(q-q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1344.2.b.f	\(4\)	\(10.732\)	4.0.2312.1	None	None	\(0\)	\(4\)	\(0\)	\(2\)		\(q+q^{3}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{5}+(1+\cdots)q^{7}+\cdots\)
1344.2.b.g	\(8\)	\(10.732\)	8.0.836829184.2	None	None	\(0\)	\(-8\)	\(0\)	\(4\)		\(q-q^{3}-\beta _{1}q^{5}-\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
1344.2.b.h	\(8\)	\(10.732\)	8.0.836829184.2	None	None	\(0\)	\(8\)	\(0\)	\(-4\)		\(q+q^{3}-\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(\beta _{2}+\beta _{4}+\cdots)q^{11}+\cdots\)
1344.2.c.a	\(2\)	\(10.732\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q+iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
1344.2.c.b	\(2\)	\(10.732\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(-2\)		\(q-iq^{3}+2iq^{5}-q^{7}-q^{9}-2iq^{11}+\cdots\)
1344.2.c.c	\(2\)	\(10.732\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(2\)		\(q+iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)
1344.2.c.d	\(2\)	\(10.732\)	\(\Q(\sqrt{-1}) \)	None	None	\(0\)	\(0\)	\(0\)	\(2\)		\(q-iq^{3}+2iq^{5}+q^{7}-q^{9}+2iq^{11}+\cdots\)

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L-functions

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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.