Updated solver to make good choices for ambiguities in the solutions.
There is a parity choice, and there are degenerate solutions.
We use initial guesses to fix the parity of the best solution.  We demand
the second best solution be in the x-y plane if it is allowed, and to point
in the x direction if allowed.  The direction of the third solution
is fixed by orthogonality.  We must still fix the parity of the last two
solutions to guarantee a right-handed system, and we must fix the case
when there is spherical symmetry.