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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 (19 matches)

  displayed columns for results
$L(s) = \prod_p F_p(p^{-s})^{-1}$
Label Origin \(F_{ 2 }(T)\) \(F_{ 3 }(T)\) \(F_{ 5 }(T)\) \(F_{ 7 }(T)\)
6-1012e3-1.1-c1e3-0-1 Modular form 1012.2.a.f $1$ $1 - T + 3 T^{2} - 9 T^{3} + 9 T^{4} - 9 T^{5} + 27 T^{6}$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 + T + 15 T^{2} + 17 T^{3} + 105 T^{4} + 49 T^{5} + 343 T^{6}$
6-1208e3-1.1-c1e3-0-0 Modular form 1208.2.a.b $1$ $1 + T + 3 T^{2} + 9 T^{3} + 9 T^{4} + 9 T^{5} + 27 T^{6}$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $( 1 + T + 7 T^{2} )^{3}$
6-2052e3-1.1-c1e3-0-2 Modular form 2052.2.a.e $1$ $1$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 + T + 17 T^{2} + 13 T^{3} + 119 T^{4} + 49 T^{5} + 343 T^{6}$
6-2268e3-1.1-c1e3-0-2 Modular form 2268.2.a.g $1$ $1$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $( 1 - T )^{3}$
6-2416e3-1.1-c1e3-0-4 Modular form 2416.2.a.i $1$ $1 - T + 3 T^{2} - 9 T^{3} + 9 T^{4} - 9 T^{5} + 27 T^{6}$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $( 1 - T + 7 T^{2} )^{3}$
6-2527e3-1.1-c1e3-0-0 Modular form 2527.2.a.h $1 - 2 T + 3 T^{2} - 5 T^{3} + 6 T^{4} - 8 T^{5} + 8 T^{6}$ $1 - T + 5 T^{2} - 5 T^{3} + 15 T^{4} - 9 T^{5} + 27 T^{6}$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $( 1 - T )^{3}$
6-2527e3-1.1-c1e3-0-2 Modular form 2527.2.a.g $1 + 2 T + 3 T^{2} + 5 T^{3} + 6 T^{4} + 8 T^{5} + 8 T^{6}$ $1 + T + 5 T^{2} + 5 T^{3} + 15 T^{4} + 9 T^{5} + 27 T^{6}$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $( 1 - T )^{3}$
6-2862e3-1.1-c1e3-0-3 Modular form 2862.2.a.m $( 1 + T )^{3}$ $1$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 + T + 17 T^{2} + 13 T^{3} + 119 T^{4} + 49 T^{5} + 343 T^{6}$
6-4048e3-1.1-c1e3-0-2 Modular form 4048.2.a.q $1$ $1 + T + 3 T^{2} + 9 T^{3} + 9 T^{4} + 9 T^{5} + 27 T^{6}$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 - T + 15 T^{2} - 17 T^{3} + 105 T^{4} - 49 T^{5} + 343 T^{6}$
6-4114e3-1.1-c1e3-0-2 Modular form 4114.2.a.o $( 1 + T )^{3}$ $1 + T + 5 T^{2} + 5 T^{3} + 15 T^{4} + 9 T^{5} + 27 T^{6}$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 + T + 15 T^{2} + 17 T^{3} + 105 T^{4} + 49 T^{5} + 343 T^{6}$
6-4114e3-1.1-c1e3-0-5 Modular form 4114.2.a.r $( 1 - T )^{3}$ $1 + T + 5 T^{2} + 5 T^{3} + 15 T^{4} + 9 T^{5} + 27 T^{6}$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 - T + 15 T^{2} - 17 T^{3} + 105 T^{4} - 49 T^{5} + 343 T^{6}$
6-6642e3-1.1-c1e3-0-1 Modular form 6642.2.a.bg $( 1 - T )^{3}$ $1$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 + 5 T + 23 T^{2} + 59 T^{3} + 161 T^{4} + 245 T^{5} + 343 T^{6}$
6-7057e3-1.1-c1e3-0-0 Modular form 7057.2.a.e $1 - 2 T + T^{2} + T^{3} + 2 T^{4} - 8 T^{5} + 8 T^{6}$ $1 - 2 T + 6 T^{2} - 9 T^{3} + 18 T^{4} - 18 T^{5} + 27 T^{6}$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 - 6 T + 24 T^{2} - 75 T^{3} + 168 T^{4} - 294 T^{5} + 343 T^{6}$
6-7266e3-1.1-c1e3-0-1 Modular form 7266.2.a.q $( 1 + T )^{3}$ $( 1 + T )^{3}$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $( 1 - T )^{3}$
6-7436e3-1.1-c1e3-0-2 Modular form 7436.2.a.m $1$ $1 - T + 5 T^{2} - 5 T^{3} + 15 T^{4} - 9 T^{5} + 27 T^{6}$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 + 5 T + 17 T^{2} + 41 T^{3} + 119 T^{4} + 245 T^{5} + 343 T^{6}$
6-8208e3-1.1-c1e3-0-7 Modular form 8208.2.a.bg $1$ $1$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 - T + 17 T^{2} - 13 T^{3} + 119 T^{4} - 49 T^{5} + 343 T^{6}$
6-9072e3-1.1-c1e3-0-3 Modular form 9072.2.a.bt $1$ $1$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $( 1 + T )^{3}$
6-9234e3-1.1-c1e3-0-13 Modular form 9234.2.a.s $( 1 - T )^{3}$ $1$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 - 4 T + 20 T^{2} - 55 T^{3} + 140 T^{4} - 196 T^{5} + 343 T^{6}$
6-9234e3-1.1-c1e3-0-8 Modular form 9234.2.a.j $( 1 + T )^{3}$ $1$ $1 + 3 T + 9 T^{2} + 21 T^{3} + 45 T^{4} + 75 T^{5} + 125 T^{6}$ $1 + 4 T + 20 T^{2} + 55 T^{3} + 140 T^{4} + 196 T^{5} + 343 T^{6}$