Cassini state locations for Kepler-62 f, using our mass set ﹩{ \mathcal A }﹩. The left panel corresponds to the fourth eigenvalue in inclination (see Table 3) and the right to the fifth eigenvalue. The fourth eigenvalue has the highest amplitude (see Table 5) and thus is the strongest forcing term on planet f’s inclination and obliquity. At a critical value of ﹩| \alpha /{s}_{i}| ﹩, states 1 and 4 merge and then vanish, leaving only states 2 and 3 (not shown); see Ward & Hamilton (2004). This occurs for ﹩{P}_{\mathrm{rot}}\approx 1.2﹩ days for s₄ and ﹩{P}_{\mathrm{rot}}\approx 0.35﹩ days for s₅.