  Let $A$ be a subset of $\mathbb{Z} / N\mathbb{Z}$ and let $\mathcal{R}$ be
the set of large Fourier coefficients of $A$. Properties of $\mathcal{R}$ have
been studied in works of M.-- C. Chang, B. Green and the author. In the paper
we obtain some new results on sets of large exponential sums.
