Gamma-ray Bursts (GRBs) are highly energetic explosions in the universe and are currently being exploited as probes of first-generation stars and gravitational wave transients. Although the energetics of GRBs are fundamental physical parameters that reveal their progenitor systems, the total energies have been estimated so far without considering non-energized, cool electrons at the relativistic collisionless shock that do not emit observable radiation, while the existence of such cool electrons is well studied for supernova remnants and solar winds. As the first coincident multi-frequency polarimetry between radio with ALMA and optical with VLT was successfully managed, linear polarizations in radio band are essential for discovering these non-energized electrons, because the Faraday depolarization caused by the non-energized electrons suppress the linear polarization degree at a frequency of 100-1000 GHz. Further coordinated multi-wavelength polarimetric campaigns would improve our understanding of the total jet energies and magnetic field configurations in the emission regions of various types of GRBs, which are required to comprehend the mass scales of their progenitor systems and the physics of collisionless shocks.