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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
1688.1.f.a	$1688$	$1$	1688.f	1688.f	$2$	$2$	$2$	$0.842$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-422}) \)	None	✓	$2$	$0$	\(-2\)	\(1\)	\(0\)	\(0\)	$1$		\(q-q^{2}+(1-\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)
1688.1.f.b	$1688$	$1$	1688.f	1688.f	$2$	$2$	$2$	$0.842$	\(\Q(\sqrt{5}) \)	$D_{5}$	\(\Q(\sqrt{-422}) \)	None	✓	$2$	$0$	\(2\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+q^{2}+(-1+\beta )q^{3}+q^{4}+(-1+\beta )q^{6}+\cdots\)

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