Offset effect in FFT magnitude
Since your offset is 3/5ths (plus some integer), the truncation fractions will be different, resulting in a different sum of quantization noise.  You can get rid of this difference by using an integer offset (including/after scaling) before truncation or rounding.  (e.g. not (2^N)/5)

Also, if your signal is not exactly periodic in your FFT aperture, then the result magnitude of very low frequencies will have a small dependence on phase, relative to the window (edge or center), and thus not exactly match the input amplitude.