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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3403.1.b.a	$3403$	$1$	3403.b	3403.b	$2$	$1$	$1$	$1.698$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-83}) \), \(\Q(\sqrt{-3403}) \)	\(\Q(\sqrt{41}) \)	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}+q^{9}+q^{16}-2q^{23}+q^{25}+\cdots\)
3403.1.b.c	$3403$	$1$	3403.b	3403.b	$2$	$2$	$2$	$1.698$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-3403}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{4}+q^{9}-\beta q^{13}+q^{16}+\beta q^{19}+\cdots\)