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coefficients of Moonshine (McKayThompson) series
Posted:
Aug 1, 2007 1:30 PM


Hi,
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 McKayThompson series).
The first dozenorso 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 qseries of monstrous moonshine & the decomposition of the head characters* (Comm. Algebra 18 (1990), 253278). But Google seems to indicate that no further data are easily found. So I thought it might be nice to have a clean, computerusable, 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, gzipcompressed down from 21MB to 8MB; each one of the 550400=3200*172 lines in the file gives one coefficient as a tabseparated 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.
Furthermore, the (Python) program used to compute the coefficients can be found at <URL: ftp://quatramaran.ens.fr/pub/madore/moonshine/moonshine.py >. It is very inefficient at the task but, even then, computing several thousand coefficients takes a matter of minutes on a modern computer.
Enjoy.
 David A. Madore (david.madore@ens.fr, http://www.dma.ens.fr/~madore/ )



