A sequence of complex numbers $z_0,z_1,z_2,\dots$ is defined by the rule

$z_{n+1}=\frac{i{z}_n}{\overline{z_n}}$,

where $\overline{z_n}$ is the complex conjugate of $z_n$ and $i^2=-1$. Suppose that $|z_0|=1$ and $z_{1000}=1$. How many possible values are there for $z_0$?