Just a century

Algebra Level 5

\[ \large \displaystyle \sum^{100}_{a=0} \sum^{100}_{b=1}x_{b}^{a} \]

Let \(x_{1},x_{2},x_{3},\ldots,x_{100}\) be the roots of the equation \(x^{100}+x+1=0\). Evaluate the summation above.

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