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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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
647.1.b.a	$647$	$1$	647.b	647.b	$2$	$11$	$11$	$0.323$	\(\Q(\zeta_{46})^+\)	$D_{23}$	\(\Q(\sqrt{-647}) \)	None	✓	$2$	$0$	\(-1\)	\(-1\)	\(0\)	\(-1\)	$1$		\(q-\beta _{3}q^{2}-\beta _{5}q^{3}+(1+\beta _{6})q^{4}+(\beta _{2}+\cdots)q^{6}+\cdots\)