  In this work, we explore the rogue wave patterns in the coupled Fokas-Lenells
equation by using the Darboux transformation. We demonstrate that when one of
the internal parameters is large enough, the general high-order rogue wave
solutions generated at a branch point of multiplicity three can be decomposed
into some first-order outer rogue waves and a lower-order inner rogue wave.
Remarkably, the positions and the orders of these outer and inner rogue waves
are intimately related to Okamoto polynomial hierarchies.
