In the OEIS index, see
"McKay-Thompson sequences or series for Monster simple group, sequences related to"
These may come with tables of coefficients, and with programs to compute coefficients. [If you understand how "replicable" series work, you can program your own.]
When was working on related things, when I computed long lists of the coefficients, I added them to the OEIS database. Others do the same, so it is improving all the time.