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In this work we investigated spectrum of $H(x, - ih\frac{d}{{dx}}) = - h^2 \frac{{d^2 }}{{dx^2 }} + i(\cos x + \cos 2x)$ operator at $h \to 0$ (semi-classical limit) using Stokes lines technique. Computer-aided calculations were an important part of the work. We obtained equations for points of the spectrum and spectral graph. Points of the spectrum of the operator considered are in the $O(h^2)$ neighborhood of the spectral graph.
