Character coordinates and annihilators of cyclotomic numbers

The object of this paper is a representation theoretical approach to the problem of determining allQ-linear relations between conjugate numbers in a cyclotomic field. We apply our method to relations between the numbers cot^(m)(k/n), tan^(m)(k/n), cosec^(m)(2k/n), sec^(m)(2k/n), respectively, where m is0 and (k,n)=1. Thereby we complete previous work of Chowla, Hasse, Jager-Lenstra, and others.