POWEV: A subroutine package to evaluate eigenvalues and eigenvectors of large sparse matrices. We present here a FORTRAN subroutine package capable of evaluating the extreme (either largest or smallest) eigenvalues of a real symmetric matrix and its corresponding eigenvectors. The procedure employed is the well-known power method, in a new implementation which includes Chebyshev iterations to obtain faster convergence speed in certain cases, together with an auxiliary algorithm to automatically set the parameters of the Chebyshev iterations when there is no previous knowledge about the eigenvalue spectrum. The code was designed to be used in present day computers, possessing the capacity of storing large arrays in high speed memory; and we find it particularly adequate to be applied to very large sparse matrices, especially in those situations where the traditional algorithms cannot be applied due to computer memory limitations. This work includes a comparative performance analysis of our routines and to those of standard library ones. (Source: http://cpc.cs.qub.ac.uk/summaries/)