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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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Results (4 matches)

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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
1383.1.d.a	$1383$	$1$	1383.d	1383.d	$2$	$1$	$1$	$0.690$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1383}) \)	None	✓	$2$	$0$	\(-1\)	\(1\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{3}-q^{6}+q^{8}+q^{9}-q^{11}+\cdots\)
1383.1.d.b	$1383$	$1$	1383.d	1383.d	$2$	$1$	$1$	$0.690$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-1383}) \)	None	✓	$2$	$0$	\(1\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+q^{2}-q^{3}-q^{6}-q^{8}+q^{9}+q^{11}+\cdots\)
1383.1.d.c	$1383$	$1$	1383.d	1383.d	$2$	$3$	$3$	$0.690$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-1383}) \)	None	✓	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$		\(q+\beta _{1}q^{2}-q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)
1383.1.d.d	$1383$	$1$	1383.d	1383.d	$2$	$3$	$3$	$0.690$	\(\Q(\zeta_{18})^+\)	$D_{9}$	\(\Q(\sqrt{-1383}) \)	None	✓	$2$	$0$	\(0\)	\(3\)	\(0\)	\(0\)	$1$		\(q-\beta _{1}q^{2}+q^{3}+(1+\beta _{2})q^{4}-\beta _{1}q^{6}+\cdots\)

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