Fenchel-Nielsen coordinates for SL(3,C) representations

We define Fenchel-Nielsen coordinates for representations of surface groups to $\mathrm{S}\mathrm{L}(3,\mathbb{C})$. We also show how these coordinates relate to the classical Fenchel-Nielsen coordinates and to their generalisations by Kourouniotis, Tan, Goldman, Zhang and Parker-Platis.