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For a fixed prime $p$, the maximum coefficient (in absolute value) $M(p)$ ofthe cyclotomic polynomial $\Phi_{pqr}(x)$, where $r$ and $q$ are free primessatisfying $r>q>p$ exists. Sister Beiter conjectured in 1968 that$M(p)\le(p+1)/2$. In 2009 Gallot and Moree showed that $M(p)\ge2p(1-\epsilon)/3$ for every $p$ sufficiently large. In this article Kloostermansums (`cloister man sums') and other tools from the distribution of modularinverses are applied to quantify the abundancy of counter-examples to SisterBeiter's conjecture and sharpen the above lower bound for $M(p)$.

Sister Beiter and Kloosterman: a tale of cyclotomic coefficients and modular inverses