G = {{-3.11018, 0.0004195}, {-3.04734, 0.000451273}, {-2.98451, 0.000486051},
{-2.92168, 0.000524223}, {-2.85885, 0.000566223}, {-2.79602, 0.000612542},
{-2.73319, 0.000663741}, {-2.67035, 0.000720457}, ...};

interG = Interpolation[G];

p = PadeApproximant[interG[x], {x, 0, {l-1, l}}];