FFT sample ordering with odd N
Since your input is discrete the spectrum is periodic with the DFT length. $X_0$ is your DC term, but so is $X_{512}$, $X_{1024}$, $X_{-512}$, etc.
It really doesn't matter which exact period you pick: [0 511], [-255 256], [-256 255], etc. Any choice will work and you always get the same amount of data. Note that $X_{-256} = X_{256}$.