2020 AMC 10A Problem 11

What is the median of the following list of 4040 numbers? 1, 2, 3, \ldots, 2020, 1^2, 2^2, 3^2, \ldots, 2020^2 \textbf{(A)}\ 1974.5\qquad\textbf{(B)}\ 1975.5\qquad\textbf{(C)}\ 1976.5\qquad\textbf{(D)}\ 1977.5\qquad\textbf{(E)}\ 1978.5

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.