# Elegance Comes Only Periodically

**Calculus**Level 5

When \(x \in \mathbb{Z}\) and \(P(x) \neq 0\) , the value of \(P\left( x \right)\) can be expressed in the form \(\frac { \alpha }{ { \pi }^{ \beta } }\), where \({ \alpha }\) is a perfect square and \({ \beta }\) is a prime number. Find \({ \alpha }^{ \beta }\).

This problem is original. The picture of the graph was produced by Wolfram.