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 \(2014\)?

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