Chart 3 may be the correct spectrum. The sinsum function may only have two frequencies of sine wave but you have a windowing function which has a spectrum also which will show up in the output. If chart 2 is the input, the large DC level makes the windowing energy very strong and may be dominating the signal. Try doing a reverse FFT on the computed spectrum ansd see if you get the original function back. Be sure to use all 64 complex numbers as the input to the inverse FFT, without taking the magntiude.