Here you find some GAP-files I use to compute Poincaré series of Coxeter groups, as well as a file containing the definitions of all the exceptional hyperbolic cocompact and hyperbolic Coxeter systems. The main file to be executed is run.gap
The programs need CHEVIE and VkCurve, thus they are compatible with GAP version 3.4.4 as available, e.g. on J. Michel's web page.
The output is a text file, which can be copied and pasted in a Mathematica notebook: once run, a LaTeX table containing the convergence radii is printed.
A second implementation in Magma is much more efficient.
Definitions are contained in the file PSDEFSforweb.magma, and the main file to be run is RUNforweb.magma. If you do not have access to Magma, I provide a copy of the file output.magma containing the results of the computations for the minimal non-affine, non-spherical Coxeter systems. It was obtained (in about 2 minutes) running the main file.