We experimentally study the equilibrium properties of a spin 1 Bose-Einstein condensate of sodium. The antiferromagnetic spin dependent interactions present in the system tend to minimize the transverse spin of the atoms which is connected to a locking of the relative phase between the different Zeeman components of the atoms. Resonant Rabi rotations allow us to reveal this effect, originating from the nematic order in the system, and infer the phase by analyzing shot to shot fluctuations of the resulting Zeeman populations. A maximum likelihood approach furthermore allows us to quantitatively measure the relative phase.