  We obtained the spectrum of the Sinai billiard as the zeroes of a secular
equation, which is based on the scattering matrix of a related scattering
problem. We show that this quantization method provides an efficient numerical
scheme, and its implementation for the present case gives a few thousands of
levels without encountering any serious difficulty. We use the numerical data
to check some approximations which are essential for the derivation of a
semiclassical quantization method based also on this scattering approach.
