Constructing the ${\mathbf{2}}^{{\mathbf{2}}^{\mathbf{5}}}+\mathbf{1}={\mathbf{F}}_{\mathbf{5}}$-gon, the first step: the 641-gon

In an article S. Adlaj showed the construction of the $F_4=65537$-gon ($F_4$ a Fermat prime). Extending the authors method to cases, where the multiplicative group is not of order $2^n$, but has an additional prime factor, here the $641$-gon ist constructed. $641$ is the smaller prime factor of the composite Fermat number $F_5=2^{2^5}+1$.