Study of J/Psi -> gamma (piplus-piminus-piplus-piminus)

BES II data for the channel J/Psi -> gamma (piplus-piminus-piplus-piminus) are analysed from a sample of 58M J/Psi hadronic interactions. They reveal further detail in the J^{PC} = 0^{-+} sector for the 4pi channel. A broad 0^{-+} -> rho-rho component extending from 1500 to 2400 MeV is fitted. A narrower structure reveals a new J^P = 0^- contribution requiring a resonance of mass 1970 +- 25(stat) +- 60(syst) MeV and width Gamma = 210 +- 25(stat) +- 60(syst) MeV. There is also tentative evidence for a 0^- resonance with mass 1560 +- (25) +- 60(syst) MeV and width ~280 MeV. In the 0^{+} sector, there are clear contributions from f0(1500) and f0(1790). The observed f0(1790) is visibly distinct from f0(1710) and confirms the existence of f0(1790); its mass 1800 +- 25(stat) +- 20(syst) MeV and width 230 +- 30(stat) +- 25(syst) MeV are better determined here than elsewhere.