  We describe an algorithm computing the monodromy and the pole order
filtration on the top Milnor fiber cohomology of hypersurfaces in
$\mathbb{P}^n$ whose pole order spectral sequence degenerates at the second
page. In the case of hyperplane arrangements and free, locally
quasi-homogeneous hypersurfaces, and assuming a key conjecture, this algorithm
is much faster than for a hypersurface as above. Our conjecture is supported by
the results due to L. Narv\' ez Macarro and M. Saito on the roots of
Bernstein-Sato polynomials of such hypersurfaces, by all the examples computed
so far, and by one partial result. For hyperplane arrangements coming from
reflection groups, a surprising symmetry of their pole order spectra on top
cohomology is displayed in our examples. We also improve our previous results
in the case of plane curves.
