Witten's 3D quantum gravity

I have a simple question regarding Witten's application of the
irreducible 196883 to entropy of the BZT black hole. If one is to
recover 4pi or 8pi from quantum corrections, I do not understand how
this can be the case. Does one consider that 196883 is the smallest
irreducible dimension of the character of the Monster and that the
prime reduction 71*59*47 = 196883 does not apply? If the prime
reduction does count then how can pi be recovered involving quantum
corrections. Here is the example: Ln196883 = 12.19... but
Ln71+ Ln59 + Ln47 = 12.19...
Wouldn't pi need to be recovered as a whole as from a geometry and not
from some fractionation of a prime number? I could understand a
multiple of 2 being corrected but not pi.