t define the eigenvalues of the pencil
          aS - bH.
          Together, the quantities alpha = (ALPHAR(j),ALPHAI(j)) and
          beta = BETA(j) represent the j-th eigenvalue of the pencil
          aS - bH, in the form lambda = alpha/beta. Since lambda may
          overflow, the ratios should not, in general, be computed.
          Due to the skew-Hamiltonian/Hamiltonian structure of the
          pencil, for every eigenvalue lambda, -lambda is also an
          eigenvalue, and thus it has only to 