  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.
