I am reading a book (am a programmer so I suck at math) and it states that for a number of $k$-values that are symmetric around 0 (for example $k = -3, -2, -1, 0, 1, 2, 3$), we need to calculate
$$\sum_{j = 0}^{N - 1} x_j e^{-2\pi i kj/N}$$
and the book claims this can be done with FFT.
I know nothing about FFT but Wikipedia tells me that FFT can calculate above sum for $k = 0, ..., N - 1$ in $O(N\log N )$-time.
How does the book then intend to apply FFT to get the values for the $k$ we are interested in here? We want the sum for $k = -3, -2, -1, 0, 1, 2, 3$, but the FFT will calculate them for $k = 0, 1, 2, 3, 4, ..., N - 1$.