  In this paper we continue the study of the three-layer Zamolodchikov model
started in our previous works. We analyse numerically the solutions to the
Bethe ansatz equations. We consider two regimes I and II which differ by the
signs of the spherical sides (a1,a2,a3)->(-a1,-a2,-a3). We accept the two-line
hypothesis for the regime I and the one-line hypothesis for the regime II. In
the thermodynamic limit we derive integral equations for distribution densities
and solve them exactly. We calculate the partition function for the three-layer
Zamolodchikov model and check a compatibility of this result with the
functional relations. We also do some numerical checkings of our results.
