Sampling Frequency and Spectral Regrowth

Sampling a cosine wave of 10 Hz at Fs = 64 and number of samples Ns = 256 I setup my time vector for the cosine wave as n=(0:Ns-1)*(1/Fs)

If I change the sampling frequency from 64 to 64.0005 I get imaginary spectrum coming up from the quantization noise and actually having significant amplitudes. I also get this at 65, 66, 67, etc but not at powers of 2, ie Fs=128,256...

I thought it was because the signal was truncated, but I substantially increased the number of samples (Ns) and this had little to no effect in removing the imaginary components of the cosine.