  We study the spectral rigidity of the non-Hermitian analog of the Anderson
model suggested by Tzortzakakis, Makris and Economou (TME). This is a $L\times
L \times L$ tightly bound cubic lattice, where both real and imaginary parts of
on-site energies are independent random variables uniformly distributed between
$-W/2$ and $W/2$. The TME model may be used to describe a random laser. In a
recent paper we proved that this model has the Anderson transition at $W= W_c
\simeq 6$ in three dimension. Here we numerically diagonalize TME $L \times L
\times L$ cubic lattice matrices and calculate the number variance of
eigenvalues in a disk of their complex plane. We show that on the metallic side
$W < 6$ of the Anderson transition, complex eigenvalues repel each other as
strongly as in the complex Ginibre ensemble only in a disk containing
$N_c(L,W)$ eigenvalues. We find that $N_c(L,W)$ is proportional to $L$ and
grows with decreasing $W$ similarly to the number of energy levels $N_c$ in the
Thouless energy band of the Anderson model.
