  The aim of this article is to study the fields generated by the Fourier
coefficients of Hilbert newforms at arbitrary cusps. Precisely, given a
cuspidal Hilbert newform $f$ and a matrix $\sigma$ in (a suitable conjugate of)
the Hilbert modular group, we give a cyclotomic extension of the field
generated by the Fourier coefficients at infinity which contains all the
Fourier coefficients of $f||_k\sigma$.
