Let G be the set of polynomials of the form
P(z)=z^{n}+c_{n-1} z^{n-1}+\cdots+c_{2} z^{2}+c_{1} z+50
where c_{1}, c_{2}, \ldots, c_{n-1} are integers and P(z) has n distinct roots of the form a+i b with a and b integers. How many polynomials are in G ?
Answer Choices
A. 288
B. 528
C. 576
D. 992
E. 1056