A 2015 degrees! what is it, mercury???

Algebra Level 3

If the roots of the polynomial:

\[ P(x) =x^{1007}+x^{1006}+x^{1005}\dots\dots+x^2+ x+1\]

are \(a_1,a_2,a_3,a_4\dots\dots a_{1007},\) what is the value of \(\displaystyle{\sum_{i=1}^{1007} F(a_i)}\) when

\[F(x)=x^{2015}+x^{2014}+x^{2013}+x^{2012}+\dots\dots+x^2+x+1?\]

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