a = 10;
data = Table[N[Sin[2*Pi*n/a]],  {n, 256}];

ListPlot[ data,  PlotJoined  ->  True ]

spec = Abs[Fourier[data]];
ListPlot[spec[[Range[1, 128]]],  PlotJoined  ->  True,  
      PlotRange  ->  All ]