  This article describes a method for constructing approximations to periodic
solutions of dynamic Lorenz system with classical values of the system
parameters. The author obtained a system of nonlinear algebraic equations in
general form concerning of the cyclic frequency, constant terms and amplitudes
of harmonics that make up harmonic approximations to the desired solutions. The
initial approximation for the Newton method is selected, which converges to a
solution describing a periodic solution different from the equilibrium
position. The results of a computational experiment are presented. The results
are verified using high-precision calculations.
