Newton's Sum is too slow!

Algebra Level 5

$\Large{x^3 + 2x^2 + 3x + 1 = 0}$

Let $p,q,r$ be three distinct complex numbers that satisfies the above cubic equation. Evaluate the last three digits of:

$\large{p^{81} + q^{81} + r^{81} } .$

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