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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3479.1.d.a	$3479$	$1$	3479.d	71.b	$2$	$1$	$1$	$1.736$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-71}) \)	\(\Q(\sqrt{497}) \)	✓	$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+2q^{2}+3q^{4}+4q^{8}-q^{9}+5q^{16}+\cdots\)
3479.1.g.a	$3479$	$1$	3479.g	497.g	$6$	$2$	$1$	$1.736$	\(\Q(\sqrt{-3}) \)	$D_{2}$	\(\Q(\sqrt{-7}) \), \(\Q(\sqrt{-71}) \)	\(\Q(\sqrt{497}) \)		$8$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{6}^{2}q^{2}-3\zeta_{6}q^{4}-2q^{8}-\zeta_{6}^{2}q^{9}+\cdots\)