AMC 12 2009b Problem 19

For each positive integer $n$, let $f(n) = n^4 - 360n^2 + 400$. What is the sum of all values of $f(n)$ that are prime numbers?

\textbf{(A)}\ 794 \textbf{(B)}\ 796 \textbf{(C)}\ 798 \textbf{(D)}\ 800 \textbf{(E)}\ 802