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    32.000004     0.000000
   2     -32.000000     0.000000    32.000000     0.000000
   3     -32.000004     0.000000     0.000000     0.000000
   4     -32.000000     0.000000   -32.000000     0.000000
   5       0.000000     0.000000   -32.000004     0.000000
   6      32.000000     0.000000   -32.000000     0.000000
   7      32.000004     0.000000     0.000000     0.000000
   8      32.000000     0.000000    32.000000     0.000000
   9       0.000000     0.000000    32.000004     0.000000
  10     -32.000000     0.000000    32.000000     0.000000
  11     -32.000004     0.000000     0.000000     0.000000
  12     -32.000000     0.000000   -32.000000     0.000000
  13       0.000000     0.000000   -32.000004     0.000000
  14      32.000000     0.000000   -32.000000     0.000000
  15      32.000004     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      32.000004     0.000000     0.000000     0.000000
   2      32.000000     0.000000   -32.000000     0.000000
   3       0.000000     0.000000   -32.000004     0.000000
   4     -32.000000     0.000000   -32.000000     0.000000
   5     -32.000004     0.000000     0.000000     0.000000
   6     -32.000000     0.000000    32.000000     0.000000
   7       0.000000     0.000000    32.000004     0.000000
   8      32.000000     0.000000    32.000000     0.000000
   9      32.000004     0.000000     0.000000     0.000000
  10      32.000000     0.000000   -32.000000     0.000000
  11       0.000000     0.000000   -32.000004     0.000000
  12     -32.000000     0.000000   -32.000000     0.000000
  13     -32.000004     0.000000     0.000000     0.000000
  14     -32.000000     0.000000    32.000000     0.000000
  15       0.000000     0.000000    32.000004     0.000000
  16      32.000000     0.000000    32.000000     0.000000
 press return to continue ...