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The ZEPLS routine  prepared by P. Lampariello and R. Sorrentino in the above paper calculates the zeros of analytic function f(z). Unfortunately, an additional difficulty is often introduced by the fact that the analytic function has polar singularities and that the poles are placed in the complex plane only by the zeros. In this case, the ZEPLS routine cannot be used successfully. On the other hand, the zeros and the poles create at that time the couples so that the regions with only one zero and one pole can be separated. The modification permits an adaptation the ZEPLS routine for such a case.