Just in case this is of any value to anyone, I have computed the 3200 first coefficients of each of the Monstrous Moonshine functions (aka McKay-Thompson series).
The first dozen-or-so coefficients can seemingly be found on Sloane's encyclopedia of integer sequences (albeit with incoherent conventions as to the constant coefficient and skipping of zero values), e.g., A007240/A014708, A007241/A101558, A007191/A007246, A007243/A030197, A007244/A030182, A007245 (omitting zeroes), etc. Fifty coefficients of each function were tabulated in J. McKay & H. Strauss, *The q-series of monstrous moonshine & the decomposition of the head characters* (Comm. Algebra 18 (1990), 253-278). But Google seems to indicate that no further data are easily found. So I thought it might be nice to have a clean, computer-usable, source for higher coefficients.
I am making them available here: <URL: ftp://quatramaran.ens.fr/pub/madore/moonshine/moonshine.dat.gz >. This is a flat text file, gzip-compressed down from 21MB to 8MB; each one of the 550400=3200*172 lines in the file gives one coefficient as a tab-separated list, the first column being the class (labeled as in the ATLAS), the second being the index and the third being the coefficient's value.