For integers $a$ and $b$ consider the complex number
 $\frac{\sqrt{ab+2016}}{ab+100}-\left({\frac{\sqrt{|a+b|}}{ab+100}}\right)i$
  Find the number of ordered pairs of integers $(a,b)$ such that this complex number is a real number.

Let's think step by step and output the final answer within \boxed{}.
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