Solution (source code)

= Solution

A <modulus of a number field> is a formal product
$$
\mathfrak m=\mathfrak m_0\mathfrak m_\infty,
$$
where $\mathfrak m_0=\prod_{\mathfrak p}\mathfrak p^{n_\mathfrak p}$ is a nonzero integral ideal and $\mathfrak m_\infty$ is a product of distinct real embeddings of $K$. Only finitely many $n_\mathfrak p$ are nonzero; complex places do not occur.