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Using (10087±44)×106 J/ψ events collected with the BESIII detector, we present a study of resonant structures in the J/ψ→ΛΛ¯γ and Λς¯0γ processes, reporting the first observation of the electromagnetic radiative decays of the Λ(1520) and Λ(1690) to γς0, with a statistical significance of 16.6σ and 23.2σ, respectively. The ratio of the branching fractions {B[Λ(1520)→γΛ]/B[Λ(1520)→γς0]} is determined to be 3.19±0.34(stat)±0.19(syst), which is in agreement with flavor SU(3) symmetry within two standard deviations. The branching fraction of Λ(1520)→γς0 is measured to be B[Λ(1520)→γς0]=[2.66±0.28(stat)±0.50(syst)]×10-3, corresponding to a partial width of Γ[Λ(1520)→γς0]=[46.8±6.6(stat)±9.3(syst)] keV, which is inconsistent with predictions from the relativized constituent quark model and the Algebraic model. Additionally, we observe a clear resonant structure in the γς0 mass spectrum near 1.7 GeV/c2, attributed to the Λ(1690). The product branching fraction B[J/ψ→Λ¯Λ(1690)+c.c.]×B[Λ(1690)→γς0] is measured for the first time as [6.05±0.42(stat)±0.39(syst)]×10-6. However, no corresponding structure is seen in the γΛ mass spectrum, so an upper limit on the product branching fraction B[J/ψ→Λ¯Λ(1690)+c.c.]×B[Λ(1690)→γΛ] is determined to be 5.08×10-7 at the 90% confidence level.