  We present the improved Mathematica code which computes quasinormal
frequencies with the help of the Bernstein spectral method for a general class
of black holes, allowing for asymptotically flat, de Sitter or anti-de Sitter
asymptotic. The method is especially efficient when searching for purely
imaginary and unstable modes and here it is used for detecting the instability
region of a charged scalar field in the background of the charged
asymptotically de Sitter dilatonic black hole. We show that the instability has
superradiant nature and the dilaton field essentially influences the region of
instability.
