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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
1639.1.d.a	$1639$	$1$	1639.d	1639.d	$2$	$5$	$5$	$0.818$	\(\Q(\zeta_{22})^+\)	$D_{11}$	\(\Q(\sqrt{-1639}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+\beta _{4}q^{2}+(1-\beta _{3})q^{4}-\beta _{1}q^{5}+(-\beta _{1}+\cdots)q^{8}+\cdots\)
1639.1.d.b	$1639$	$1$	1639.d	1639.d	$2$	$5$	$5$	$0.818$	\(\Q(\zeta_{22})^+\)	$D_{11}$	\(\Q(\sqrt{-1639}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(-1\)	\(0\)	$1$		\(q+(1-\beta _{1}+\beta _{2}-\beta _{3}+\beta _{4})q^{2}+(1-\beta _{1}+\cdots)q^{4}+\cdots\)

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