Newton's Sum is too slow!

Algebra Level 5

x3+2x2+3x+1=0\Large{x^3 + 2x^2 + 3x + 1 = 0}

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

p81+q81+r81.\large{p^{81} + q^{81} + r^{81} } .

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