### Exact Kronecker constants of Hadamard sets

A set S of integers is called ε-Kronecker if every function on S of modulus one can be approximated uniformly to within ε by a character. The least such ε is called the ε-Kronecker constant, κ(S). The angular Kronecker constant is the unique real number α(S) ∈ [0,1/2] such that κ(S) = |exp(2πiα(S)) - 1|. We show that for integers m > 1 and d ≥ 1, $\alpha 1,m,...,{m}^{d-1}=({m}^{d-1}-1)/\left(2({m}^{d}-1)\right)$ and α1,m,m²,... = 1/(2m).