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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
643.1.b.a	$643$	$1$	643.b	643.b	$2$	$1$	$1$	$0.321$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-643}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+q^{4}-q^{7}+q^{9}+q^{16}-q^{23}+q^{25}+\cdots\)
2572.1.b.a	$2572$	$1$	2572.b	643.b	$2$	$3$	$3$	$1.284$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-643}) \)	None	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{7}+q^{9}+\beta _{2}q^{23}+q^{25}+(\beta _{1}+\cdots)q^{29}+\cdots\)

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