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We propose a conjectural formula for $DR_g(a,-a) \lambda_g$ and check all itsexpected properties. Our formula refines the one point case of a similarconjecture made by the first named author in collaboration with Gu\'er\'e andRossi, and we prove that the two conjectures are in fact equivalent, though ina quite non-trivial way.

A conjectural formula for $DR_g(a,-a) \lambda_g$