AMC 12 2012b Problem 23

Consider all polynomials of a complex variable, $P(z)=4z^4+az^3+bz^2+cz+d$, where $a,b,c,$ and $d$ are integers, $0\le d\le c\le b\le a\le 4$, and the polynomial has a zero $z_0$ with $|z_0|=1.$ What is the sum of all values $P(1)$ over all the polynomials with these properties?

\textbf{(A)}\ 84 \textbf{(B)}\ 92 \textbf{(C)}\ 100 \textbf{(D)}\ 108 \textbf{(E)}\ 120