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Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1735.1.d.a	$1735$	$1$	1735.d	1735.d	$2$	$6$	$6$	$0.866$	\(\Q(\zeta_{26})^+\)	$D_{13}$	\(\Q(\sqrt{-1735}) \)	None	✓	✓			1735.1.d.a	$2$	$0$	\(-1\)	\(0\)	\(6\)	\(-1\)	$1$		\(q-\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
1735.1.d.b	$1735$	$1$	1735.d	1735.d	$2$	$6$	$6$	$0.866$	\(\Q(\zeta_{26})^+\)	$D_{13}$	\(\Q(\sqrt{-1735}) \)	None	✓	✓			1735.1.d.a	$2$	$0$	\(1\)	\(0\)	\(-6\)	\(1\)	$1$		\(q+\beta _{3}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)