Simple finite solutions to the N. Kowalewski equations

Earlier we have found all 24 families of power-logarithmic expansions in $p$ of solutions to the N. Kowalewski system of equations, describing motions of a rigid body with a fixed point in the case $B\ne C$, $x_0\ne0$, $y_0=z_0=0$. Among them, 10 families have $p\to0$ (tails) and 14 families have $p\to\infty$ (heads). To find all finite expansions we check each pair a tail and a head: can it give a finite expansion or it cannot By this approach we find all finite solutions to the N. Kowalewski equations, in particular, all 7 known and 5 new. All new solutions are complex. We also prove the absente of other solution which is the finite sum of rational powers of $p$.