Let $H(\mathbb{C})$ be the space of holomorphic functions on the complex plane.  Then it is well-known that for $a\neq 0$, the translation operator
$$
t_a(f)\triangleq f(x)\mapsto f(x+a),
$$
is topologically transitive on $H(\mathbb{C})$.  Are there known, sufficient conditions for $f$ to by a cyclic vector of this map; i.e. for 
$$
\mathrm{Orb}(f,t_a)\triangleq \left\{
t_a^n(f):n \in \mathbb{N}
\right\}$$
to be dense in $H(\mathbb{C})$?