2012 AMC 12B 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\qquad\textbf{(B)}\ 92\qquad\textbf{(C)}\ 100\qquad\textbf{(D)}\ 108\qquad\textbf{(E)}\ 120

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.