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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	\(F_{ 2 }(T)\)	\(F_{ 3 }(T)\)	\(F_{ 5 }(T)\)	\(F_{ 7 }(T)\)	\(F_{ 83 }(T)\)
4-2828e2-1.1-c1e2-0-0	Modular form 2828.2.a.c	$1$	$( 1 - 3 T + 3 T^{2} )^{2}$	$1 - T - T^{2} - 5 T^{3} + 25 T^{4}$	$( 1 + T )^{2}$	$1 - 31 T + 405 T^{2} - 2573 T^{3} + 6889 T^{4}$
4-3610e2-1.1-c1e2-0-1	Modular form 3610.2.a.n	$( 1 + T )^{2}$	$1 - 3 T + 7 T^{2} - 9 T^{3} + 9 T^{4}$	$( 1 + T )^{2}$	$1 + 2 T + 10 T^{2} + 14 T^{3} + 49 T^{4}$	$1 - 31 T + 405 T^{2} - 2573 T^{3} + 6889 T^{4}$
4-3610e2-1.1-c1e2-0-9	Modular form 3610.2.a.p	$( 1 - T )^{2}$	$1 + 3 T + 7 T^{2} + 9 T^{3} + 9 T^{4}$	$( 1 + T )^{2}$	$1 + 2 T + 10 T^{2} + 14 T^{3} + 49 T^{4}$	$1 - 31 T + 405 T^{2} - 2573 T^{3} + 6889 T^{4}$
4-9315e2-1.1-c1e2-0-1	Modular form 9315.2.a.v	$1 - 3 T + 5 T^{2} - 6 T^{3} + 4 T^{4}$	$1$	$( 1 - T )^{2}$	$1 - 7 T + 25 T^{2} - 49 T^{3} + 49 T^{4}$	$1 - 31 T + 405 T^{2} - 2573 T^{3} + 6889 T^{4}$