  It has been conjectured that the statistical properties of zeros of the
Riemann zeta function near $z = 1/2 + \ui E$ tend, as $E \to \infty$, to the
distribution of eigenvalues of large random matrices from the Unitary Ensemble.
At finite $E$ numerical results show that the nearest-neighbour spacing
distribution presents deviations with respect to the conjectured asymptotic
form. We give here arguments indicating that to leading order these deviations
are the same as those of unitary random matrices of finite dimension $N_{\rm
eff}=\log(E/2\pi)/\sqrt{12 \Lambda}$, where $\Lambda=1.57314 ...$ is a well
defined constant.
