A Nullstellensatz for the field of complex Laurent series

Let $T$ be the theory of the valued field of complex Laurent series $\mathbb{C}(\!(t)\!)$ in the language of rings expanded by a constant for $t$ and by predicates for $n$-th powers. We introduce a $t$-adic analogue of Kochen's operator, namely $γ(x)=x/(1+tx^{2})$, and the associated Kochen ring $Λ_