# Problem #1792

 1792 Let $G$ be the set of polynomials of the form $$P(z)=z^n+c_{n-1}z^{n-1}+\cdots+c_2z^2+c_1z+50,$$ where $c_1,c_2,\cdots, c_{n-1}$ are integers and $P(z)$ has distinct roots of the form $a+ib$ with $a$ and $b$ integers. How many polynomials are in $G$? $\textbf{(A)}\ 288\qquad\textbf{(B)}\ 528\qquad\textbf{(C)}\ 576\qquad\textbf{(D)}\ 992\qquad\textbf{(E)}\ 1056$ This problem is copyrighted by the American Mathematics Competitions.
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