Fourier transform of first function:
      n     Real(n)    Imag.(n)   Real(N-n)   Imag.(N-n)
      0    0.000000    0.000000    0.000000    0.000000
      1    0.000000    0.000000    0.000000   -0.000000
      2    0.000000    0.000000    0.000000   -0.000000
      3    0.000000    0.000000    0.000000   -0.000000
      4   13.656855  -13.656855   13.656855   13.656855
      5    0.000000    0.000000    0.000000   -0.000000
      6    0.000000    0.000000    0.000000   -0.000000
      7    0.000000    0.000000    0.000000   -0.000000
      8    0.000000    0.000000    0.000000   -0.000000
      9    0.000000    0.000000    0.000000   -0.000000
     10    0.000000    0.000000    0.000000   -0.000000
     11    0.000000    0.000000    0.000000   -0.000000
     12    2.343146    2.343146    2.343146   -2.343146
     13    0.000000    0.000000    0.000000   -0.000000
     14    0.000000    0.000000    0.000000   -0.000000
     15    0.000000    0.000000    0.000000   -0.000000
     16    0.000000   -0.000000    0.000000   -0.000000

  press RETURN to continue ...
 Fourier transform of second function:
      n     Real(n)    Imag.(n)   Real(N-n)   Imag.(N-n)
      0    0.000000    0.000000    0.000000    0.000000
      1    0.000000    0.000000    0.000000   -0.000000
      2    0.000000    0.000000    0.000000   -0.000000
      3    0.000000    0.000000    0.000000   -0.000000
      4   13.656855   13.656855   13.656855  -13.656855
      5    0.000000    0.000000    0.000000   -0.000000
      6    0.000000    0.000000    0.000000   -0.000000
      7    0.000000    0.000000    0.000000   -0.000000
      8    0.000000    0.000000    0.000000   -0.000000
      9    0.000000    0.000000    0.000000   -0.000000
     10    0.000000    0.000000    0.000000   -0.000000
     11    0.000000    0.000000    0.000000   -0.000000
     12    2.343146   -2.343146    2.343146    2.343146
     13    0.000000    0.000000    0.000000   -0.000000
     14    0.000000    0.000000    0.000000   -0.000000
     15    0.000000    0.000000    0.000000   -0.000000
     16    0.000000   -0.000000    0.000000   -0.000000

  press RETURN to continue ...
 Inverted transform = first function:
      n     Real(n)    Imag.(n)   Real(N-n)   Imag.(N-n)
      0   32.000000    0.000000   32.000000    0.000000
      1    0.000000    0.000000   32.000000    0.000000
      2  -32.000000    0.000000   32.000000    0.000000
      3  -32.000000    0.000000    0.000000    0.000000
      4  -32.000000    0.000000  -32.000000    0.000000
      5    0.000000    0.000000  -32.000000    0.000000
      6   32.000000    0.000000  -32.000000    0.000000
      7   32.000000    0.000000    0.000000    0.000000
      8   32.000000    0.000000   32.000000    0.000000
      9    0.000000    0.000000   32.000000    0.000000
     10  -32.000000    0.000000   32.000000    0.000000
     11  -32.000000    0.000000    0.000000    0.000000
     12  -32.000000    0.000000  -32.000000    0.000000
     13    0.000000    0.000000  -32.000000    0.000000
     14   32.000000    0.000000  -32.000000    0.000000
     15   32.000000    0.000000    0.000000    0.000000
     16   32.000000    0.000000   32.000000    0.000000

  press RETURN to continue ...
 Inverted transform = second function:
      n     Real(n)    Imag.(n)   Real(N-n)   Imag.(N-n)
      0   32.000000    0.000000   32.000000    0.000000
      1   32.000000    0.000000    0.000000    0.000000
      2   32.000000    0.000000  -32.000000    0.000000
      3    0.000000    0.000000  -32.000000    0.000000
      4  -32.000000    0.000000  -32.000000    0.000000
      5  -32.000000    0.000000    0.000000    0.000000
      6  -32.000000    0.000000   32.000000    0.000000
      7    0.000000    0.000000   32.000000    0.000000
      8   32.000000    0.000000   32.000000    0.000000
      9   32.000000    0.000000    0.000000    0.000000
     10   32.000000    0.000000  -32.000000    0.000000
     11    0.000000    0.000000  -32.000000    0.000000
     12  -32.000000    0.000000  -32.000000    0.000000
     13  -32.000000    0.000000    0.000000    0.000000
     14  -32.000000    0.000000   32.000000    0.000000
     15    0.000000    0.000000   32.000000    0.000000
     16   32.000000    0.000000   32.000000    0.000000

  press RETURN to continue ...