  We compute the spectral distortions of the Cosmic Microwave Background (CMB)
arising during the epoch of cosmological hydrogen recombination within the
standard cosmological (concordance) model for frequencies in the range 1
GHz-3500 GHz. We follow the evolution of the populations of the hydrogen levels
including states up to principle quantum number $n=30$ in the redshift range
$500\leq z\leq 3500$. All angular momentum sub-states are treated individually,
resulting in a total number of 465 hydrogen levels. The evolution of the matter
temperature and the fraction of electrons coming from HeII are also included.
We present a detailed discussion of the distortions arising from the main
dipolar transitions, e.g. Lyman and Balmer series, as well as the emission due
to the two-photon decay of the hydrogen 2s level. Furthermore, we investigate
the robusteness of the results against changes in the number of shells
considered. The resulting spectral distortions have a characteristic
oscillatory behaviour, which might allow experimentalists to separate them from
other backgrounds. The relative distortion of the spectrum exceeds a value of
$10^{-7}$ at wavelengths longer than 21cm. Our results also show the importance
of detailed follow-up of the angular momentum sub-states, and their effect on
the amplitude of the lines. The effect on the residual electron fraction is
only moderate, and mainly occurs at low redshifts. The CMB angular power
spectrum is changed by less than 1%. Finally, our computations show that if the
primordial radiation field is described by a pure blackbody, then there is no
significant emission from any hydrogen transition at redshifts greater than $z
\sim 2000$. This is in contrast to some earlier works, where the existence of a
`pre-recombination' peak was claimed.
