We study the minimum value for the truncation in the photon number which allows the numerical convergence for the ground state energy and for a significative part of the energy spectra, as function of the atom-field coupling for different values of the atom number in the Dicke model. We employ two different basis, corresponding to the exact eigenstates in the two integrable limits of the model. The most interesting result is that the calculations done in the basis associated to the null atomic excitation energy limit always converges within a smaller space than the other, even along the phase transition region and for small values of the interaction.

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