Sol[n_, a_] := 
      Module[{D = {{0, 0}}, s = {0, 1}}, 
        Do[s = {{1, 1/n}, {-1/n, 1}} . s // N; 
D = 
            Append[D, {N[k/n], s[[1]]}], 
{k, 1, a*n}]; 
        D]

Sol[10, Pi]

ListPlot[Sol[10, 2*Pi], PlotJoined -> True]