Let $f(z)$ be an entire function that is not a polynomial of degree 1 or degree 0 , where $z$ is a complex number.
Let $f(z,1) = f(z)$ and let $f(z,n) = f(f(z,n-1))$.
Let $g(f,1)$ be the amount of distinct complex fixpoints of $f(z,1)$.
More general let $g(f,n)$ be the amount of distinct complex fixpoints of $f(z,n)$.
Let $G(f,n)$ = $g(f,1)$ + $g(f,2)$ $+ ... +$ $g(f,n)$
What is an example $f(z)$ such that $G(f,30)$ = 0 ?