  In the solution of the superintegrable chiral Potts model special polynomials
related to the representation theory of the Onsager algebra play a central
role. We derive approximate analytic formulae for the zeros of particular
polynomials which determine sets of low-lying energy eigenvalues of the chiral
Potts quantum chain. These formulae allow the analytic calculation of the
leading finite-size corrections to the energy eigenvalues without resorting to
a numerical determination of the zeros.
