Solution
= Solution
Use the printed unnormalized inverse <discrete Fourier transform>, with positive exponent: $x_\ell=\sum_j\omega_n^{j\ell}y_j$. Its natural domain and codomain are $\mathbb C^n$; the printed real-to-real designation is not literal, as the first example below has complex output. There is no factor $1/n$ in the convention of this question.