Faber polynomials with common zero

We describe the set of meromorphic univalent functions in the class Σ, for which the sequence of the Faber polynomials {Fj}∞j=1 have the roots with following properties |Fn(z0)|>0=∑j=1j≠n|Fj(z0)|. For such functions we found an explicit form of the Faber polynomials as well as we discussed some properties.