Challenge problem

Find $\displaystyle \mod (\det A)$ being $\displaystyle A\in\textrm{Mat}_{n\times n}(\mathbb{C})$ defined by

$\displaystyle A=\begin{bmatrix} 1 & 1 & 1 & \ldots & 1\\ 1 & \epsilon & \epsilon^2 & \ldots & \epsilon^{n-1} \\ 1 & \epsilon^2 & \epsilon^4 & \ldots & \epsilon^{2n-2}\\ \vdots&&&&\vdots \\ 1 & \epsilon^{n-1} & \epsilon^{2(n-1)}&\ldots & \epsilon^{(n-1)^2}\end{bmatrix}\quad (\epsilon=\cos(2\pi/n)+i\sin (2\pi/n))$