  The plasma dispersion function $Z(s)$ is a fundamental complex special
integral function widely used in the field of plasma physics. The simplest and
most rapid, yet accurate, approach to calculating it is through rational or
equivalent multi-pole expansions. In this work, we summarize the numerical
coefficients that are practically useful to the community. Besides the Pade
approximation to obtain coefficients, which are accurate for both small and
large arguments, we also employ optimization methods to enhance the accuracy of
the approximation for the intermediate range. The best coefficients provided
here for calculating $Z(s)$ can deliver twelve significant decimal digits. This
work serves as a foundational database for the community for further
applications.
