[math] \newcommand{\mathds}{\mathbb}[/math]

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Prove that the set [math]E_N[/math] formed by the [math]N\times N[/math] complex Hadamard matrices modulo the equivalence relation is given by

[[math]] E_N=Z_N\Big/(S_{N-1}\times S_{N-1}) [[/math]]

and compute this set at [math]N=2,3,4,5[/math].