Evolution of various parameters during the time interval (–500, 500) kyr for three Neptune L₄ Trojans: 2001 QR₃₂₂, 2004 UP₁₀, and 2005 TN₅₃. The distance to the objects from Neptune is given in panel A); the value of the Hill sphere radius of Neptune, 0.769 AU, is displayed. The resonant angle, λ_r, is displayed in panel B) for the nominal orbit (source: JPL Small-Body Database and AstDyS-2). The orbital elements are depicted in panel C), a with the current value of Neptune’s semi-major axis, panel D), e, and panel E), i. 2005 TN₅₃ appears to be the most stable of Neptune’s Trojans and 2001 QR₃₂₂ the one with the largest libration amplitude.