How many integers $n\ge 2$ are there such that whenever $z_1,z_2,...,z_n$ are complex numbers such that $|z_1|=|z_2|=...=|z_n|=1$ and $z_1^2+z_2^2+...+z_n^2=0$, then the numbers $z_1,z_2,...,z_n$ are equally spaced on the unit circle in the complex plane?