The concept of metastability has caused a lot of interest in recent years. The spectral decomposition of the generator matrix of a stochastic network exposes all of the transition processes in the system while it evolves toward the equilibrium. I discuss an efficient way to compute the asymptotics for eigenvalues and eigenvectors starting from the low lying group for networks representing energy landscapes. I apply this algorithm to Wales's Lennard-Jones-38 stochastic network with 71887 states and 119853 edges whose underlying potential energy landscape has a double-funnel structure. The result turns out to be surprising at the first glance. The concept of metastability should be applied with care to this system.