Vieta's take too long

Algebra Level 5

$100 (a_1^2 + 1)(a_2^2 + 1)\cdots (a_{10}^2 + 1)$

Let $a_1, a_2, \ldots,a_{10}$ denote the roots to the equation $\displaystyle \sum_{m=1}^{10} m x^m = 0$ . Find the value of the expression above.