We study complex functions of two variables through topological studies of their amoebas and coamoebas. The number of holes in the coamoeba to certain polynomials are carefully investigated. Using winding numbers it is proven that a maximum number of holes in the coamoeba cannot be found to every maximally sparse function. The properties of the lopsided and the ordinary coamoeba are compared. In most studied cases the number of holes in the lopsided coamoeba is equal to the number of holes in the ordinary coamoeba. Moreover we numerically nd a set of coecients to the polynomial for which the amoeba is solid. In the study we study the location of the discriminant loci of the polynomial. In all studied cases the discriminant loci are connected to the topological structure of the amoeba.