Eigenvalues with positive real parts obtained with a QZ algorithm for various finite-difference schemes. The labelling of the eigenvalues is based on a visual inspection of the corresponding eigenmodes. The shaded grey area corresponds to solutions which are not fully resolved – we required approximately 8 points per oscillation period of the genuine solutions (in the sixth panel, this area is larger simply because we used a non-uniform grid). In all cases, the resolution is N = 51.