# Wow!

**Algebra**Level pending

Define a Geber rotation to be the swapping of coefficient \(k\) with \(n+1-k\) in an \(n^\text{th}\) degree polynomial. Find the number of integer rooted \(2016^\text{th}\) degree polynomials such that roots are not changed when coefficients are changed in a Geber rotation and let this be \(k\). Find the remainder of \(k\) when divided by 1000.