  Aims: To investigate the extension of the very-high-energy spectral tail of
the Crab pulsar at energies above 400 GeV. Methods: We analyzed $\sim$320 hours
of good quality data of Crab with the MAGIC telescope, obtained from February
2007 until April 2014. Results: We report the most energetic pulsed emission
ever detected from the Crab pulsar reaching up to 1.5 TeV. The pulse profile
shows two narrow peaks synchronized with the ones measured in the GeV energy
range. The spectra of the two peaks follow two different power-law functions
from 70 GeV up to 1.5 TeV and connect smoothly with the spectra measured above
10 GeV by the Large Area Telescope (LAT) on board of the Fermi satellite. When
making a joint fit of the LAT and MAGIC data, above 10 GeV, the photon indices
of the spectra differ by 0.5$\pm$0.1. Conclusions: We measured with the MAGIC
telescopes the most energetic pulsed photons from a pulsar to date. Such TeV
pulsed photons require a parent population of electrons with a Lorentz factor
of at least $5\times 10^6$. These results strongly suggest IC scattering off
low energy photons as the emission mechanism and a gamma-ray production region
in the vicinity of the light cylinder.
