What is the most efficient algorithm to compute polynomial coefficients from its roots?

Question

Given $n$ roots, $x_1, x_2, \dotsc, x_n$, the corresponding monic polynomial is $y = (x-x_1)(x-x_2)\dotsm(x-x_n) = \prod_{i}^n (x - x_i)$. To get the coefficients (i.e. $y = \sum_{i}^n a_i x^i$), a straightforward expansion requires $O(n^2)$ steps.

Alternatively, if $x_1, x_2, \dotsc, x_n$ are distinct with each other. The problem is equivalent to polynomial interpolation with $n$ points: $(x_1, 0), (x_2, 0), \dotsc, (x_n, 0)$. The fast polynomial interpolation algorithm can be run in $O(n\log^2(n))$ time.

I want to ask whether there is any more efficient algorithm better than $O(n^2)$? Even if there are duplicated values among $\{x_i\}$? If it helps, we can assume that the polynomial is over some prime finite field, i.e. $x_i \in \mathbf{F}_q$.