  Attention has been brought to the possibility that statistical fluctuation
properties of several complex spectra, or, well-known number sequences may
display strong signatures that the Hamiltonian yielding them as eigenvalues is
PT-symmetric (Pseudo-Hermitian). We find that the random matrix theory of
pseudo-Hermitian Hamiltonians gives rise to new universalities of level-spacing
distributions other than those of GOE, GUE and GSE of Wigner and Dyson. We call
the new proposals as Gaussian Pseudo-Orthogonal Ensemble and Gaussian
Pseudo-Unitary Ensemble. We are also led to speculate that the enigmatic
Riemann-zeros (${1 \over 2}\pm i t_n)$ would rather correspond to some
PT-symmetric (pseudo-Hermitian) Hamiltonian.
