Let $n>3$ a natural number and let $a_{0},\,a_{1},\,\ldots,\,a_{n}$ be complex numbers such that $a_{0}+a_{1}+\ldots+a_{n}=0$. Is it possible to evaluate the following determinant: $$\left|\begin{array}{ccccc} a_{0} & a_{1} & a_{2} & \ldots & a_{n-1}\\ a_{1} & a_{2} & a_{3} & \ldots & a_{n}\\ a_{2} & a_{3} & a_{4} & \ldots & a_{0}\\ \vdots & \vdots & \vdots & \vdots & \vdots\\ a_{n-2} & a_{n-1} & a_{n} & \ldots & a_{n-4}\\ a_{n-1} & a_{n} & a_{0} & \ldots & a_{n-3} \end{array}\right|$$
(on every row and on every column is missing one element)?