  Using a data sample of $\psi(3770)$ events collected with the BESIII detector
at BEPCII corresponding to an integrated luminosity of 2.9 fb$^{-1}$, we report
a measurement of $\Lambda$ spin polarization in
$e^+e^-\rightarrow\Lambda\bar\Lambda$ at $\sqrt{s} = 3.773$ GeV. The
significance of polarization is found to be 2$\sigma$ including the systematic
uncertainty, which implies a zero phase between the transition amplitudes of
the $\Lambda\bar{\Lambda}$ helicity states. This phase can be interpreted in
terms of psionic form factors, and is determined to be $\Delta\Phi^{\Psi}$ =
$\Phi^{\Psi}_{E} - \Phi^{\Psi}_{M}$ = $(71^{+66}_{-46}$ $\pm$ 5)$^{\circ}$.
Similarly, the ratio between the form factors is found to be $R^{\psi}$ =
$|G^{\Psi}_{E}/G^{\Psi}_{M}|$ = $0.48^{+0.12}_{-0.07}$ $\pm$ 0.04. The first
uncertainties are statistical and the second systematic.
