Divisible by this year??? (Part 10: Let's make some magic!)

A magic square is a square that is divided into smaller squares, each containing a number, such that the figures in each vertical, horizontal, and diagonal row add up to the same value and this value is called the Magic Sum.

In an $(2n + 1)$ by $(2n + 1)$ magic square, let $a$ be the middlemost integer (the intersection of the $(n + 1)^{th}$ row and the $(n + 1)^{th}$ column) where $a$ is the smallest positive integer that will make the magic sum divisible by $2014$ . For how many values of $n$ where $n \leq 1000$ is $a$ not equal to $2014$ ?