  We present efficient numerical techniques for calculation of eigenvalue
distributions of random matrices in the beta-ensembles. We compute histograms
using direct simulations on very large matrices, by using tridiagonal matrices
with appropriate simplifications. The distributions are also obtained by
numerical solution of the Painleve II and V equations with high accuracy. For
the spacings we show a technique based on the Prolate matrix and Richardson
extrapolation, and we compare the distributions with the zeros of the Riemann
zeta function.
