  To treat the spectral statistics of quantum maps and flows that are fully
chaotic classically, we use the rigorous Riemann-Siegel lookalike available for
the spectral determinant of unitary time evolution operators $F$. Concentrating
on dynamics without time reversal invariance we get the exact two-point
correlator of the spectral density for finite dimension $N$ of the matrix
representative of $F$, as phenomenologically given by random matrix theory. In
the limit $N\to\infty$ the correlator of the Gaussian unitary ensemble is
recovered. Previously conjectured cancellations of contributions of
pseudo-orbits with periods beyond half the Heisenberg time are shown to be
implied by the Riemann-Siegel lookalike.
