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Fast Fourier Transform : fft

fft takes as argument a list (or a sequence) $ \tt [a_0,..a_{N-1}]$ where N is a power of two.
fft returns the list $ \tt [b_0,..b_{N-1}]$ such that, for k=0..N-1

$\displaystyle \tt

where $ \omega_{N}^{}$ is a primitive N-th root of the unity.
Input :
Output :
[2.0, -1-i, 0.0, -1+i]

giac documentation written by Renée De Graeve and Bernard Parisse