$\mathfrak{S}_n$ is amazing (part 2)

See part 1 for the definition of $\mathfrak{S}_n$ and standard representation.

Let $\mathbf{E}_n$ denote the expected value of the number of cycles in the standard representation of permutation $w \in \mathfrak{S}_n$ . What is the value of $\lfloor \mathbf{E}_{1000} \rfloor$ ?