  A Bethe Ansatz study of a self dual Z_N spin model is undertaken for even
spin system. One has to solve a coupled system of Bethe Ansatz Equations (BAE)
involving zeroes of two families of transfer matrices. A numerical study on
finite size lattices is done for identification of elementary excitations over
the Ferromagnetic and Antiferromagnetic ground states. The free energies for
both Ferromagnetic and Antiferromagnetic ground states and dispersion relation
for elementary excitations are found.
