Periods of t-modules as special values

In this article we show that all periods of uniformizable $t$-modules (resp. their coordinates) can be obtained via specializing a rigid analytic trivialization related dual $t$-motive at $t=\theta$. The proof is even constructive. central object in the construction subset $H$ Tate algebra points $E$ which turns out to isomorphic period lattice kind generating series one direction and residues other. This isomorphism holds for arbitrary $E$, non-abelian ones.