To also obtain the angle of these roots, a multitude of methods has been proposed, the most simple one being to successively compute the square root of a (possibly complex) root of q^m(y), m ranging from k to 1, and testing which of the two sign variants is a root of q^{m-1}(x). Before continuing to the roots of q^{m-2}(x), it might be necessary to numerically improve the accuracy of the root approximations for q^{m-1}(x), for instance by Newton's method.
