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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 (9 matches)

  displayed columns for results
$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
12-248e6-1.1-c1e6-0-1 Modular form 248.2.b.a $1 - T^{3} + 8 T^{6}$ $( 1 - 3 T^{2} )^{6}$ $( 1 - 2 T^{3} + 125 T^{6} )( 1 + 2 T^{3} + 125 T^{6} )$ $( 1 - 16 T^{3} + 343 T^{6} )( 1 + 16 T^{3} + 343 T^{6} )$
12-620e6-1.1-c1e6-0-0 Modular form 620.2.e.a $1 + T^{3} + 8 T^{6}$ $( 1 - 3 T^{2} )^{6}$ $1 - 2 T^{3} + 125 T^{6}$ $( 1 - 16 T^{3} + 343 T^{6} )^{2}$
12-620e6-1.1-c1e6-0-2 Modular form 620.2.e.b $1 - T^{3} + 8 T^{6}$ $( 1 - 3 T^{2} )^{6}$ $1 - 2 T^{3} + 125 T^{6}$ $( 1 + 16 T^{3} + 343 T^{6} )^{2}$
12-992e6-1.1-c1e6-0-2 Modular form 992.2.b.a $1$ $( 1 - 3 T^{2} )^{6}$ $( 1 - 2 T^{3} + 125 T^{6} )( 1 + 2 T^{3} + 125 T^{6} )$ $( 1 - 16 T^{3} + 343 T^{6} )( 1 + 16 T^{3} + 343 T^{6} )$
12-1105e6-1.1-c1e6-0-4 Modular form 1105.2.c.a $1 - T^{2} - T^{4} + 9 T^{6} - 4 T^{8} - 16 T^{10} + 64 T^{12}$ $( 1 - 3 T^{2} )^{6}$ $( 1 + T )^{6}$ $( 1 - 6 T + 23 T^{2} - 62 T^{3} + 161 T^{4} - 294 T^{5} + 343 T^{6} )^{2}$
12-1105e6-1.1-c1e6-0-5 Modular form 1105.2.c.b $1 - T^{2} - T^{4} + 9 T^{6} - 4 T^{8} - 16 T^{10} + 64 T^{12}$ $( 1 - 3 T^{2} )^{6}$ $( 1 - T )^{6}$ $( 1 + 6 T + 23 T^{2} + 62 T^{3} + 161 T^{4} + 294 T^{5} + 343 T^{6} )^{2}$
12-2014e6-1.1-c1e6-0-0 Modular form 2014.2.b.b $( 1 + T^{2} )^{3}$ $( 1 - 3 T^{2} )^{6}$ $( 1 - 9 T^{2} + 25 T^{4} )^{3}$ $( 1 - 4 T + 20 T^{2} - 51 T^{3} + 140 T^{4} - 196 T^{5} + 343 T^{6} )^{2}$
12-2140e6-1.1-c1e6-0-0 Modular form 2140.2.c.a $1$ $( 1 - 3 T^{2} )^{6}$ $( 1 - 4 T + 5 T^{2} )^{3}$ $1 - 21 T^{2} + 189 T^{4} - 1273 T^{6} + 9261 T^{8} - 50421 T^{10} + 117649 T^{12}$
12-2890e6-1.1-c1e6-0-3 Modular form 2890.2.b.n $( 1 - T )^{6}$ $( 1 - 3 T^{2} )^{6}$ $( 1 + T^{2} )^{3}$ $1 - 397 T^{6} + 117649 T^{12}$