  Based on data samples collected with the BESIII detector at the BEPCII
collider, the process $e^{+}e^{-} \to \Sigma^{+}\bar{\Sigma}^{-}$ is studied at
center-of-mass energies $\sqrt{s}$ = 2.3960, 2.6454, and 2.9000 GeV. Using a
fully differential angular description of the final state particles, both the
relative magnitude and phase information of the $\Sigma^{+}$ electromagnetic
form factors in the timelike region are extracted. The relative phase between
the electric and magnetic form factors is determined to be $\sin\Delta\Phi$ =
-0.67~$\pm$~0.29~(stat)~$\pm$~0.18~(syst) at $\sqrt{s}$ = 2.3960 GeV,
$\Delta\Phi$ = 55$^{\circ}$~$\pm$~19$^{\circ}$~(stat) $\pm$~14$^{\circ}$~(syst)
at $\sqrt{s}$ = 2.6454 GeV, and 78$^{\circ}$~$\pm$~22$^{\circ}$~(stat)
$\pm$~9$^{\circ}$~(syst) at $\sqrt{s}$ = 2.9000 GeV. For the first time, the
phase of the hyperon electromagnetic form factors is explored in a wide range
of four-momentum transfer. The evolution of the phase along with four-momentum
transfer is an important input for understanding its asymptotic behavior and
the dynamics of baryons.
