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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
3383.1.d.a	$3383$	$1$	3383.d	3383.d	$2$	$11$	$11$	$1.688$	\(\Q(\zeta_{46})^+\)	$D_{23}$	\(\Q(\sqrt{-3383}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-\beta _{9}q^{2}-\beta _{3}q^{3}+(1-\beta _{5})q^{4}+(-1+\cdots)q^{6}+\cdots\)
3383.1.d.b	$3383$	$1$	3383.d	3383.d	$2$	$11$	$11$	$1.688$	\(\Q(\zeta_{46})^+\)	$D_{23}$	\(\Q(\sqrt{-3383}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\beta _{9}q^{2}+\beta _{3}q^{3}+(1-\beta _{5})q^{4}+(1-\beta _{1}+\cdots)q^{6}+\cdots\)

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