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Level	Weight	Analytic conductor	\(Nk^2\)	Dim.

Bad \(p\)	Char.	Primitive character	Character order	Coefficient field

Self-twists	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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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$	Coefficient ring index	Sato-Tate	$q$-expansion
1643.1.c.a	$1643$	$1$	1643.c	1643.c	$2$	$2$	$2$	$0.820$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-1643}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{7}+\cdots\)
1643.1.c.b	$1643$	$1$	1643.c	1643.c	$2$	$2$	$2$	$0.820$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-1643}) \)	None	✓	$2$	$0$	\(0\)	\(1\)	\(0\)	\(-1\)	$1$		\(q+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{7}+(1+\cdots)q^{9}+\cdots\)

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