TOMS384 is a FORTRAN77 library which implements ACM TOMS algorithm 384, for computing the eigenvalues and eigenvectors of a symmetric matrix.
The text of many ACM TOMS algorithms is available online through ACM: http://www.acm.org/pubs/calgo or NETLIB: http://www.netlib.org/toms/index.html.
TOMS384 is available in a FORTRAN77 version.
EISPACK, a FORTRAN90 library which can compute eigenvalues and eigenvectors of a variety of matrix types.
LAPACK_EXAMPLES, a FORTRAN90 program which demonstrates the use of the LAPACK linear algebra library.
TEST_MAT, a FORTRAN90 library which defines matrices with various properties for testing linear algebra software.
You can go up one level to the FORTRAN77 source codes.