  The standard $\Lambda$CDM paradigm is complemented with a magnetized
contribution whose effects on the anisotropies of the Cosmic Microwave
Background (CMB) are assessed by means of a dedicated numerical approach. The
accuracy on the temperature and polarization correlations stems from the
inclusion of the large-scale magnetic fields both at the level of the initial
conditions and at the level of the Einstein-Boltzmann hierarchy which is
consistently embedded in a generalized magnetohydrodynamical framework.
Examples of the calculations of the temperature and polarization angular power
spectra are illustrated and discussed. The reported results and the described
numerical tools set the ground for a consistent inclusion of a magnetized
contribution in current strategies of cosmological parameter estimation.
