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Lowest zero	Conductor	Analytic conductor	Central character	Analytic rank

Degree	Bad \(p\)	Root analytic conductor	Motivic weight	Spectral label

Root number	Primitive	Origin	Exclude origin

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Columns to display		Euler factor constraints
	e.g. 3,7,19		e.g. F3=1-T,F5=1+T+5T^2

Results (4 matches)

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		$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label	Origin	\(F_{ 2 }(T)\)	\(F_{ 3 }(T)\)	\(F_{ 5 }(T)\)	\(F_{ 7 }(T)\)	\(F_{ 97 }(T)\)
4-5750e2-1.1-c1e2-0-0	Modular form 5750.2.a.a	$( 1 + T )^{2}$	$( 1 + T + 3 T^{2} )^{2}$	$1$	$1 + 9 T^{2} + 49 T^{4}$	$1 - 32 T + 445 T^{2} - 3104 T^{3} + 9409 T^{4}$
4-6038e2-1.1-c1e2-0-0	Modular form 6038.2.a.a	$( 1 - T )^{2}$	$1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4}$	$1 + 5 T + 15 T^{2} + 25 T^{3} + 25 T^{4}$	$( 1 + 3 T + 7 T^{2} )^{2}$	$1 - 32 T + 445 T^{2} - 3104 T^{3} + 9409 T^{4}$
4-8326e2-1.1-c1e2-0-0	Modular form 8326.2.a.c	$( 1 + T )^{2}$	$1 + T + 5 T^{2} + 3 T^{3} + 9 T^{4}$	$1 - 2 T + 6 T^{2} - 10 T^{3} + 25 T^{4}$	$1 - 3 T + 15 T^{2} - 21 T^{3} + 49 T^{4}$	$1 - 32 T + 445 T^{2} - 3104 T^{3} + 9409 T^{4}$
4-9383e2-1.1-c1e2-0-0	Modular form 9383.2.a.b	$1 + 3 T + 5 T^{2} + 6 T^{3} + 4 T^{4}$	$( 1 + T + 3 T^{2} )^{2}$	$1 - T + 9 T^{2} - 5 T^{3} + 25 T^{4}$	$( 1 - T + 7 T^{2} )^{2}$	$1 - 32 T + 445 T^{2} - 3104 T^{3} + 9409 T^{4}$