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Lowest zero Conductor Analytic conductor Central character Analytic rank
Degree Bad \(p\) Root analytic conductor Motivic weight Spectral label
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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

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  displayed columns for results
$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\) \(F_{ 11 }(T)\) \(F_{ 13 }(T)\) \(F_{ 17 }(T)\) \(F_{ 19 }(T)\) \(F_{ 23 }(T)\) \(F_{ 29 }(T)\) \(F_{ 31 }(T)\) \(F_{ 37 }(T)\) \(F_{ 41 }(T)\) \(F_{ 43 }(T)\) \(F_{ 47 }(T)\)
6-2268e3-1.1-c1e3-0-3 Modular form 2268.2.a.h $1$ $1$ $1 + T + 11 T^{2} + 9 T^{3} + 55 T^{4} + 25 T^{5} + 125 T^{6}$ $( 1 + T )^{3}$ $1 + 2 T + 8 T^{2} - 15 T^{3} + 88 T^{4} + 242 T^{5} + 1331 T^{6}$ $1 - 3 T + 6 T^{2} - 51 T^{3} + 78 T^{4} - 507 T^{5} + 2197 T^{6}$ $1 + 2 T + 32 T^{2} + 21 T^{3} + 544 T^{4} + 578 T^{5} + 4913 T^{6}$ $1 - 3 T + 33 T^{2} - 35 T^{3} + 627 T^{4} - 1083 T^{5} + 6859 T^{6}$ $1 + 14 T + 122 T^{2} + 675 T^{3} + 2806 T^{4} + 7406 T^{5} + 12167 T^{6}$ $1 + T + 47 T^{2} - 51 T^{3} + 1363 T^{4} + 841 T^{5} + 24389 T^{6}$ $1 + 3 T + 57 T^{2} + 159 T^{3} + 1767 T^{4} + 2883 T^{5} + 29791 T^{6}$ $1 + 3 T + 81 T^{2} + 199 T^{3} + 2997 T^{4} + 4107 T^{5} + 50653 T^{6}$ $1 + 90 T^{2} - 9 T^{3} + 3690 T^{4} + 68921 T^{6}$ $1 - 3 T + 33 T^{2} - 539 T^{3} + 1419 T^{4} - 5547 T^{5} + 79507 T^{6}$ $1 + 21 T + 261 T^{2} + 2181 T^{3} + 12267 T^{4} + 46389 T^{5} + 103823 T^{6}$
6-9072e3-1.1-c1e3-0-4 Modular form 9072.2.a.bv $1$ $1$ $1 + T + 11 T^{2} + 9 T^{3} + 55 T^{4} + 25 T^{5} + 125 T^{6}$ $( 1 - T )^{3}$ $1 - 2 T + 8 T^{2} + 15 T^{3} + 88 T^{4} - 242 T^{5} + 1331 T^{6}$ $1 - 3 T + 6 T^{2} - 51 T^{3} + 78 T^{4} - 507 T^{5} + 2197 T^{6}$ $1 + 2 T + 32 T^{2} + 21 T^{3} + 544 T^{4} + 578 T^{5} + 4913 T^{6}$ $1 + 3 T + 33 T^{2} + 35 T^{3} + 627 T^{4} + 1083 T^{5} + 6859 T^{6}$ $1 - 14 T + 122 T^{2} - 675 T^{3} + 2806 T^{4} - 7406 T^{5} + 12167 T^{6}$ $1 + T + 47 T^{2} - 51 T^{3} + 1363 T^{4} + 841 T^{5} + 24389 T^{6}$ $1 - 3 T + 57 T^{2} - 159 T^{3} + 1767 T^{4} - 2883 T^{5} + 29791 T^{6}$ $1 + 3 T + 81 T^{2} + 199 T^{3} + 2997 T^{4} + 4107 T^{5} + 50653 T^{6}$ $1 + 90 T^{2} - 9 T^{3} + 3690 T^{4} + 68921 T^{6}$ $1 + 3 T + 33 T^{2} + 539 T^{3} + 1419 T^{4} + 5547 T^{5} + 79507 T^{6}$ $1 - 21 T + 261 T^{2} - 2181 T^{3} + 12267 T^{4} - 46389 T^{5} + 103823 T^{6}$