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

Where do the maximum absolute $q$-series coefficients of $(1-q)(1-q^2)(1-q^3)\dots(1-q^{n-1})(1-q^n)$ occur?