Effective solution of the problem of the optimal stability polynomial

An effective method for finding the polynomial approximating the exponential function with order 3 at the origin and deviating from 0 by at most 1 on the longest interval of the real axis is put forward. This problem is reduced to the solution of four equations on a 4-dimensional moduli space of algebraic curves. A numerical realization of this method using summation of linear Poincare series is described.