  We consider the whole-plane SLE conformal map f from the unit disk to the
slit plane, and show that its mixed moments, involving a power p of the
derivative modulus |f'| and a power q of the map |f| itself, have closed forms
along some integrability curves in the (p,q) moment plane, which depend
continuously on the SLE parameter kappa. The generalization of this
integrability property to the m-fold transform of f is also given. We define a
generalized integral means spectrum corresponding to the singular behavior of
the mixed moments above. By inversion, it allows for a unified description of
the unbounded interior and bounded exterior versions of whole-plane SLE, and of
their m-fold generalizations. The average generalized spectrum of whole-plane
SLE takes four possible forms, separated by five phase transition lines in the
moment plane, whereas the average generalized spectrum of the m-fold
whole-plane SLE is directly obtained from a linear map acting in that plane. We
also conjecture the form of the universal generalized integral means spectrum.
