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We find accurate quasinormal frequencies of a quantum corrected black hole constructed in the renormalization group theory via the coordinate-independent iterative procedure, leading to the Dymnikova regular black hole. We show that while the fundamental mode is only slightly affected by the quantum correction, the overtones change at a much stronger rate. This outburst of overtones occurs because of the deformation of the geometry of the Schwarzschild black hole solely near the event horizon. For finding accurate values of overtones we developed a general procedure allowing one to use the Leaver method to metrics which, initially, are not expressed in terms of rational functions.