Distribution of the Error in Estimated Numbers of Fixed Points of the Discrete Logarithm

Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The author and Pieter Moree, building on work of Zhang, Cobeli, and Zaharescu, gave heuristics for estimating the number of such pairs and proved bounds on the error in the estimates. These bounds are not descriptive of the true situation, however, and this paper is a first attempt to collect and analyze some data on the distribution of the actual error in the estimates.