A191904 Logarithms Dirichlet series table roots of unity

(*start*)
Clear[n, k, nn];
nn = 10;
TableForm[
 Chop[N[Table[
    Table[ k/(2*Pi*I) (Log[(-E^(((2 I (n + 1) \[Pi])/k)))] -
        Log[(-E^(((2 I n \[Pi])/k)))]), {k, 1, nn}], {n, 1, nn}]]]]
(*end*)

{{0, 1, 1, 1, 1, 1, 1, 1, 1, 1},
{0, -1, 1, 1, 1, 1, 1, 1, 1, 1},
{0, 1, -2, 1, 1, 1, 1, 1, 1, 1},
{0, -1, 1, -3, 1, 1, 1, 1, 1, 1},
{0, 1, 1, 1, -4, 1, 1, 1, 1, 1},
{0, -1, -2, 1, 1, -5, 1, 1, 1, 1},
{0, 1, 1, 1, 1, 1, -6, 1, 1, 1},
{0, -1, 1, -3, 1, 1, 1, -7, 1, 1},
{0, 1, -2, 1, 1, 1, 1, 1, -8, 1},
{0, -1, 1, 1, -4, 1, 1, 1, 1, -9}}