  We consider the calculation of ground-state expectation values for the
non-Hermitian Z(N) spin chain described by free parafermions. For N=2 the model
reduces to the quantum Ising chain in a transverse field with open boundary
conditions. Use is made of the Hellmann-Feynman theorem to obtain exact results
for particular single site and nearest-neighbour ground-state expectation
values for general N which are valid for sites deep inside the chain. These
results are tested numerically for N=3, along with how they change as a
function of distance from the boundary.
