  The computation of the gravitational radiation emitted by a particle falling
into a Schwarzschild black hole is a classic problem studied already in the
1970s. Here we present a detailed numerical analysis of the case of radial
infall starting at infinity with no initial velocity. We compute the radiated
waveforms, spectra and energies for multipoles up to l = 6, improving
significantly on the numerical accuracy of existing results. This is done by
integrating the Zerilli equation in the frequency domain using the Green's
function method. The resulting wave exhibits a "ring-down" phase whose dominant
contribution is a superposition of the quasi-normal modes of the black hole.
The numerical accuracy allows us to recover the frequencies of these modes
through a fit of that part of the wave. Comparing with direct computations of
the quasi-normal modes we reach a \sim 10^{-4} to \sim 10^{-2} accuracy for the
first two overtones of each multipole. Our numerical accuracy also allows us to
display the power-law tail that the wave develops after the ring-down has been
exponentially cut-off. The amplitude of this contribution is \sim 10^2 to \sim
10^3 times smaller than the typical scale of the wave.
