  The Keiper-Li criterion gives a necessary and sufficient condition for the
Riemann hypothesis. It requires that a set of quantities $\lambda_n$ be
positive, and involves auxiliary constants $a_n$, known to be positive. A
recently derived expression for the $a_n$ is used to provide accurate numerical
values for the first four thousand $a_n$'s, and asymptotic expressions together
with bounds for them are investigated.
