  We report on a precise measurement of the electron-antineutrino angular
correlation ($a$ coefficient) in free neutron beta-decay from the $a$SPECT
experiment. The $a$ coefficient is inferred from the recoil energy spectrum of
the protons which are detected in 4$\pi$ by the $a$SPECT spectrometer using
magnetic adiabatic collimation with an electrostatic filter. Data are presented
from a 100 days run at the Institut Laue Langevin in 2013. The sources of
systematic errors are considered and included in the final result. We obtain $a
= -0.10430(84)$ which is the most precise measurement of the neutron $a$
coefficient to date. From this, the ratio of axial-vector to vector coupling
constants is derived giving $|\lambda| = 1.2677(28)$.
