Roots on a Circle

Denote by NN the number of pairs of positive integers (n,m),(n,m), such that m<n100m<n\leq 100 and the polynomial xn+xm+1x^n+x^m+1 has a root on the unit circle. Find the last three digits of N.N.

Details and assumptions

A root on the unit circle is a complex root at the distance exactly 11 from the origin.

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