how to find out all non-constant entire functions?

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Find all non-constant entire functions $f(z)$ with real integer Taylor coefficients at $z = 0$ such that $f(1/n)=-f(-1/n)$ and $|f(z)|\le 3|z|$ for all $z$ such that $|z|>10$.

. have no idea how to state this problem. Any help will be appreciated.