Roots on a Circle

Number Theory Level 5

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

Details and assumptions

A root on the unit circle is a complex root at the distance exactly $1$ from the origin.