A problem for a friend II

Algebra Level 3

The roots of \(x^{2016}-x^{2015}+x^{2013}-x^{2010}+x^{2006}-\ldots-1 = 0\) are \(r_{1}, r_{2}, \ldots, r_{2016}\).

Find

\[\sum_{1 \leq i < j \leq 2016} r_{i}r_{j}\]

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