Translation of entire functions along the real axis

Given a whole function $f(z)$, and also $0\neq a\in \mathbb R$. We specify the translation driver: $$T_{a}f(z)=f(z-a).$$ What buildings the new function $f(z-a)$ could have? It is whole function! What concerning the absolutely nos of $f(z-a)$?

I recognize it is an open inquiry, yet anything you recognize can aid me.