We used the MACH2 supercomputer to study coefficients in the $q$-series expansion of $(1-q)(1-q^2)\dots(1-q^n)$, for all $n\leq 75000$. As a result, we were able to conjecture some periodic properties associated with the before unknown location of the maximum coefficient of these polynomials with odd $n$. Remarkably the observed period is 62,624.