  Let $K$ be a number field. The $K$-arithmetic type of a rational prime $\ell$
is the tuple $A_{K}(\ell)=(f^{K}_{1},...,f^{K}_{g_{\ell}})$ of the residue
degrees of $\ell$ in $K$, written in ascending order. A well known result of
Perlis from the 70's states that two number fields have the same Dedekind zeta
function if and only if for almost all primes $\ell$ the arithmetic types of
$\ell$ in both fields coincide. By the end of the 90's Perlis and Stuart asked
if having the same zeta function implies that for ramified primes the sum of
the ramification degrees coincide. Here we study and answer their question for
septic number fields.
