We prove that a modied version of Beliaev-Smirnov, which corresponds to the classical Loewner whole-plane process, together with m-fold symmetric versions, have a lot of exact solutions. We deduce results about the multifractal spectrum of this version of SLE and surprising results related to coefficient estimates, namely that E(janj2) is equal to 1 resp. n if P anzn is f0 for this whole-plane SLE with = 6 resp. 2. This is a joint work with B.Duplantier, Nguyen Thi Thuy Nga and Nguyen Thi Phuong Chi.
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