  A new algorithm to calculate Coulomb wave functions with all of its arguments
complex is proposed. For that purpose, standard methods such as continued
fractions and power/asymptotic series are combined with direct integrations of
the Schrodinger equation in order to provide very stable calculations, even for
large values of |eta| or |Im(l)|. Moreover, a simple analytic continuation for
Re(z) < 0 is introduced, so that this zone of the complex z-plane does not pose
any problem. This code is particularly well suited for low-energy calculations
and the calculation of resonances with extremely small widths. Numerical
instabilities appear, however, when both |eta| and |Im(l)| are large and
|Re(l)| comparable or smaller than |Im(l)|.
