  Curious spectral properties of an ensemble of random unitary matrices
appearing in the quantization of a map p -> p+alpha, q -> q+f(p+alpha) in
[Giraud et al. nlin.CD/0403033] are investigated. When alpha=m/n with integer
co-prime m,n and matrix dimension N -> infinity is such that mN = 1 or -1 mod
n, local spectral statistics of this ensemble tends to the semi-Poisson
distribution [Bogomolny et al. Eur. Phys. J. B 19, 121 (2001)] with arbitrary
integer or half-integer level repulsion at small distances: R(s)-> s^{beta}
when s -> 0 and beta=n-1 or n/2-1 depending on time-reversal symmetry of the
map.
