A variation of the Division Algorithm states that for any integers $a$ and $b$ with $b \neq 0$, there exist unique integers $q$ and $r$ such that $a = qb + r$ and $-\frac{|b|}{2} < r \le \frac{|b|}{2}$. If we apply this variation to $a = -5000$ and $b = 83$, what is the value of the quotient $q$?