The given expression is a convex quadratic, so the extremum is a minimum. It is known that if $f$ is a quadratic and $f(a) = f(b)$, then the extremum value of $f(x)$ is achieved on $x = \dfrac{a+b}{2}$. Let $f$ be the given expression. Note that $f(0) = f(-20)$, thus the minimum of $f$ is $f(-10) = \dfrac{\sum_{k=-20}^{20} k^2}{4} = \boxed{1435}$.