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We present a new approach to calculating the higher Frobenius-Schurindicators for the simple modules over the Drinfeld double of a finite group.In contrast to the formula by Kashina-Sommerh{\"a}user-Zhu that involves a sumover all group elements satisfying a certain condition, our formula operates onthe level of conjugacy classes and character tables. It can be implemented inthe computer algebra system GAP, efficiently enough to deal, on a laptop, withsymmetric groups up to $S_{18}$ (providing further evidence that indicators arenon-negative in this case) or simple groups of order up to $2 \cdot 10^8$. Theapproach also allows us to test whether all indicators over the double of agiven group are rational , without computing them. Among simple groups of orderup to about $5 \cdot 10^{11}$ an inspection yields exactly one example (oforder about $5 \cdot 10^9$) where irrational indicators occur.

Higher frobenius-schur indicators for drinfeld doubles of finite groups through characters of centralizers