  It is shown that the normalized fluctuations of Riemann's zeta zeros around
their predicted locations follow the Gaussian law. It is also shown that
fluctuations of two zeros, $\gamma _{k}$ and $\gamma _{k+x},$ with $x\sim(\log
k)^{\beta}$, $\beta >0$, for large $k$ follow the two-variate Gaussian
distribution with correlation $(1-\beta)_{+}$.
