Cyclotomic explosion

\[ P_{n}(x) = \Phi_1 (x) \Phi_2 (x) \Phi_3 (x) \cdots \Phi_{n-2} (x) \Phi_{n-1}(x) \Phi_{n}(x),\]

Let there be a polynomial \(P_{n} (x) \), which is defined as above.

where \( \Phi_{n} (x) \) is the \( n^\text{th} \) cyclotomic polynomial.

How many distinct roots does \(P_{2017} (x) \) have?

You may use a calculator for the final step of your calculation.

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