Problem 1623 (difficulty: 3/10)

An entire function \(\displaystyle f(z)\) satisfies \(\displaystyle |f(1/n)|=1/n^2\) for \(\displaystyle n=1,2,\ldots\), and \(\displaystyle |f(i)|=2\). What are the possible values of \(\displaystyle |f(-i)|\)?

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