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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3347.1.b.a	$3347$	$1$	3347.b	3347.b	$2$	$5$	$5$	$1.670$	\(\Q(\zeta_{22})^+\)	$D_{11}$	\(\Q(\sqrt{-3347}) \)	None	✓	$2$	$0$	\(0\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+\beta _{4}q^{3}+q^{4}+(1-\beta _{3})q^{9}+\beta _{4}q^{12}+\cdots\)