Solutions of the Bethe ansatz equations for XXX antiferromagnet of arbitrary spin in the case of a finite number of sites

For the exactly integrable isotropic Heisenberg model of the chain of $N$ spins $s$, numerical solutions of the Bethe-ansatz equations are obtained which correspond to the antiferromagnetic vacuum (for $sN\leq 128$) and the simplest excitations. At $s=1$, the complete set of states is presented for $N=6$ and the vacuum solution is estimated analytically for finite $N$. Deviations from the “string” picture for large $N$ are discussed.