  It follows from generalities of quadratic forms that the spinor class of the
integral trace of a number field determines the signature and the discriminant
of the field. In this paper we define a family of number fields, that contains
among others all odd degree Galois tame number fields, for which the converse
is true. In other words, for a number field $K$ in such family we prove that
the spinor class of the integral trace carries no more information about $K$
than the determinant and the signature do.
