# parallel algorithms for the determinant of the Hessenberg matrix

I am interested in highly parallel algorithms for computing the determinant of matrices of a special form (over finite fields).

It is known that computing determinant of general matrices over finite fields is in NC2. I've been wondering whether something better is known (hopefully NC1) for the (say, lower) Hessenberg matrix.

If it helps, it is further restricted so that its subdiagonal is all 1's, and all I care about is whether the determinant is 0 or not.