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Using (10 087±44)×106 J/ψ events collected with the BESIII detector, a full angular analysis is carried out on the process J/ψ→ΛΛ¯→nπ0p¯π++c.c. The decay parameters α0 for Λ→nπ0 and α¯0 for Λ¯→n¯π0 are measured to be 0.668±0.007±0.002 and -0.677±0.007±0.003, respectively, yielding the most precise test for CP symmetry of neutral decays of Λ, ACP0=(α0+α¯0)/(α0-α¯0), to be -0.006±0.007±0.002. The ratios α0/α- and α¯0/α+ are determined to be 0.884±0.013±0.006 and 0.885±0.013±0.004, where α- and α+ are the decay parameters of Λ→pπ- and Λ¯→p¯π+, respectively. The ratios, found to be smaller than unity by more than 5σ, confirm the presence of the ΔI=3/2 transition in the Λ and Λ¯ decays, which is expected to improve the theoretical calculations for isospin amplitudes, and ACP, in hyperon decays. In all results, the first and second uncertainties are statistical and systematic, respectively.