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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 (7 matches)

  displayed columns for results
$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\) \(F_{ 83 }(T)\)
4-4162e2-1.1-c1e2-0-0 Modular form 4162.2.a.c $( 1 + T )^{2}$ $1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4}$ $( 1 + 5 T^{2} )^{2}$ $( 1 - 2 T + 7 T^{2} )^{2}$ $1 - 30 T + 386 T^{2} - 2490 T^{3} + 6889 T^{4}$
4-76e4-1.1-c1e2-0-2 Modular form 5776.2.a.bf $1$ $1 - 2 T + 2 T^{2} - 6 T^{3} + 9 T^{4}$ $1 - 5 T + 15 T^{2} - 25 T^{3} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )^{2}$ $1 - 30 T + 386 T^{2} - 2490 T^{3} + 6889 T^{4}$
4-76e4-1.1-c1e2-0-6 Modular form 5776.2.a.u $1$ $1 + 2 T + 2 T^{2} + 6 T^{3} + 9 T^{4}$ $1 - 5 T + 15 T^{2} - 25 T^{3} + 25 T^{4}$ $( 1 - 2 T + 7 T^{2} )^{2}$ $1 - 30 T + 386 T^{2} - 2490 T^{3} + 6889 T^{4}$
4-7017e2-1.1-c1e2-0-0 Modular form 7017.2.a.c $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $( 1 + T )^{2}$ $1 - 2 T + 6 T^{2} - 10 T^{3} + 25 T^{4}$ $1 + T + 13 T^{2} + 7 T^{3} + 49 T^{4}$ $1 - 30 T + 386 T^{2} - 2490 T^{3} + 6889 T^{4}$
4-7664e2-1.1-c1e2-0-1 Modular form 7664.2.a.a $1$ $1 - T + 5 T^{2} - 3 T^{3} + 9 T^{4}$ $1 + T + 9 T^{2} + 5 T^{3} + 25 T^{4}$ $1 + T + 13 T^{2} + 7 T^{3} + 49 T^{4}$ $1 - 30 T + 386 T^{2} - 2490 T^{3} + 6889 T^{4}$
4-8544e2-1.1-c1e2-0-1 Modular form 8544.2.a.e $1$ $( 1 + T )^{2}$ $1 + T - T^{2} + 5 T^{3} + 25 T^{4}$ $1 - 2 T + 10 T^{2} - 14 T^{3} + 49 T^{4}$ $1 - 30 T + 386 T^{2} - 2490 T^{3} + 6889 T^{4}$
4-9401e2-1.1-c1e2-0-1 Modular form 9401.2.a.a $1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4}$ $1 + T + 5 T^{2} + 3 T^{3} + 9 T^{4}$ $1 - 3 T + 11 T^{2} - 15 T^{3} + 25 T^{4}$ $( 1 - T )^{2}$ $1 - 30 T + 386 T^{2} - 2490 T^{3} + 6889 T^{4}$