AMC 12A 2013 Problem 25

Let f: \mathbb{C} \rightarrow \mathbb{C} be defined by f(z)=z^{2}+i z+1. How many complex numbers z are there such that \operatorname{Im}(z)>0 and both the real and the imaginary parts of f(z) are integers with absolute value at most 10 ?

Answer Choices
A. 399
B. 401
C. 413
D. 431
E. 441