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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
1047.1.d.a	$1047$	$1$	1047.d	1047.d	$2$	$1$	$1$	$0.523$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-1047}) \)	\(\Q(\sqrt{349}) \)	✓	$4$	$0$	\(0\)	\(1\)	\(0\)	\(0\)	$1$		\(q+q^{3}-q^{4}+q^{9}-q^{12}+q^{16}+2q^{19}+\cdots\)
1745.1.h.a	$1745$	$1$	1745.h	1745.h	$4$	$2$	$1$	$0.871$	\(\Q(\sqrt{-1}) \)	$D_{4}$	None	\(\Q(\sqrt{349}) \)		$4$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q+(1+i)q^{3}-iq^{4}-iq^{5}+iq^{9}+(1+\cdots)q^{12}+\cdots\)

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