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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
583.1.d.a	$583$	$1$	583.d	583.d	$2$	$1$	$1$	$0.291$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-583}) \)	\(\Q(\sqrt{53}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{4}+q^{9}+q^{11}+q^{16}+q^{25}-q^{36}+\cdots\)
583.1.d.b	$583$	$1$	583.d	583.d	$2$	$2$	$2$	$0.291$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-583}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}+q^{4}+q^{9}-q^{11}-q^{16}-\beta q^{18}+\cdots\)

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