Newton or Vieta?

Algebra Level 4

Let r1r_1, r2r_2, r3r_3, ..., and r20r_{20} be the roots of the equation z2019z+2=0z^{20}-19z+2=0.

Find

r120+r220+r320++r2020r_1^{20}+r_2^{20}+r_3^{20}+\dots+r_{20}^{20}

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