Bethe's equation is incomplete for the XXZ model at roots of unity

We demonstrate for the six vertex and XXZ model parameterized by Delta = - (q + q(-1))/2 not equal +/- 1 that when q(2N) = I for integer N greater than or equal to 2 the Bethe's ansatz equations determine only the eigenvectors which are the highest weights of the infinite dimensional sl(2) loop algebra symmetry group of the model. Therefore in this case the Bethe's ansatz equations are incomplete and further conditions need to be imposed in order to completely specify the wave function. We discuss how the evaluation parameters of the finite dimensional representations of the sl(2) loop algebra can be used to complete this specification.