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 $|lambda| = 1.2677(28)$.
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