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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 (14 matches)

  displayed columns for results
$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
6-129e3-1.1-c1e3-0-0 Modular form 129.2.a.d $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $( 1 - T )^{3}$ $1 + 4 T + 14 T^{2} + 38 T^{3} + 70 T^{4} + 100 T^{5} + 125 T^{6}$ $1 - 4 T + 18 T^{2} - 46 T^{3} + 126 T^{4} - 196 T^{5} + 343 T^{6}$
6-485e3-1.1-c1e3-0-0 Modular form 485.2.a.e $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $( 1 - 2 T + 3 T^{2} )^{3}$ $( 1 - T )^{3}$ $1 - 5 T + 23 T^{2} - 60 T^{3} + 161 T^{4} - 245 T^{5} + 343 T^{6}$
6-825e3-1.1-c1e3-0-0 Modular form 825.2.a.i $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $( 1 + T )^{3}$ $1$ $1 - 3 T + 14 T^{2} - 25 T^{3} + 98 T^{4} - 147 T^{5} + 343 T^{6}$
6-847e3-1.1-c1e3-0-1 Modular form 847.2.a.i $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $1 + T + 3 T^{2} + 8 T^{3} + 9 T^{4} + 9 T^{5} + 27 T^{6}$ $1 - T + 7 T^{2} - 6 T^{3} + 35 T^{4} - 25 T^{5} + 125 T^{6}$ $( 1 + T )^{3}$
6-2475e3-1.1-c1e3-0-4 Modular form 2475.2.a.z $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $1$ $1$ $1 + 3 T + 14 T^{2} + 25 T^{3} + 98 T^{4} + 147 T^{5} + 343 T^{6}$
6-3157e3-1.1-c1e3-0-0 Modular form 3157.2.a.b $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $1 - T + T^{2} - 2 T^{3} + 3 T^{4} - 9 T^{5} + 27 T^{6}$ $1 + T + 7 T^{2} + 6 T^{3} + 35 T^{4} + 25 T^{5} + 125 T^{6}$ $( 1 + T )^{3}$
6-4335e3-1.1-c1e3-0-2 Modular form 4335.2.a.p $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $( 1 + T )^{3}$ $( 1 - T )^{3}$ $1 - 4 T + 18 T^{2} - 46 T^{3} + 126 T^{4} - 196 T^{5} + 343 T^{6}$
6-4335e3-1.1-c1e3-0-4 Modular form 4335.2.a.q $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $( 1 - T )^{3}$ $( 1 + T )^{3}$ $1 + 4 T + 18 T^{2} + 46 T^{3} + 126 T^{4} + 196 T^{5} + 343 T^{6}$
6-5025e3-1.1-c1e3-0-6 Modular form 5025.2.a.n $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $( 1 + T )^{3}$ $1$ $1 + 11 T^{2} - 8 T^{3} + 77 T^{4} + 343 T^{6}$
6-77e6-1.1-c1e3-0-2 Modular form 5929.2.a.t $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $1 - T + 3 T^{2} - 8 T^{3} + 9 T^{4} - 9 T^{5} + 27 T^{6}$ $1 + T + 7 T^{2} + 6 T^{3} + 35 T^{4} + 25 T^{5} + 125 T^{6}$ $1$
6-6321e3-1.1-c1e3-0-0 Modular form 6321.2.a.p $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $( 1 + T )^{3}$ $1 - 4 T + 14 T^{2} - 38 T^{3} + 70 T^{4} - 100 T^{5} + 125 T^{6}$ $1$
6-7623e3-1.1-c1e3-0-5 Modular form 7623.2.a.bz $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $1$ $1 + T + 7 T^{2} + 6 T^{3} + 35 T^{4} + 25 T^{5} + 125 T^{6}$ $( 1 - T )^{3}$
6-9075e3-1.1-c1e3-0-4 Modular form 9075.2.a.cd $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $( 1 - T )^{3}$ $1$ $1 - 3 T + 14 T^{2} - 25 T^{3} + 98 T^{4} - 147 T^{5} + 343 T^{6}$
6-9675e3-1.1-c1e3-0-3 Modular form 9675.2.a.bq $1 + 2 T + T^{2} + 2 T^{4} + 8 T^{5} + 8 T^{6}$ $1$ $1$ $1 + 4 T + 18 T^{2} + 46 T^{3} + 126 T^{4} + 196 T^{5} + 343 T^{6}$