  In this letter we continue the investigation of finite XXZ spin chains with
periodic boundary conditions and odd number of sites, initiated in paper
\cite{S}. As it turned out, for a special value of the asymmetry parameter
$\Delta=-1/2$ the Hamiltonian of the system has an eigenvalue, which is exactly
proportional to the number of sites $E=-3N/2$. Using {\sc Mathematica} we have
found explicitly the corresponding eigenvectors for $N \le 17$. The obtained
results support the conjecture of paper \cite{S} that this special eigenvalue
corresponds to the ground state vector. We make a lot of conjectures concerning
the correlations of the model. Many remarkable relations between the wave
function components are noticed. It is turned out, for example, that the ratio
of the largest component to the least one is equal to the number of the
alternating sing matrices.
