Another class of simple graded Lie conformal algebras that cannot be embedded into general Lie conformal algebras

In a previous paper by the authors, we obtain first example of finitely freely generated simple Z-graded Lie conformal algebra linear growth that cannot be embedded into any general algebra. this paper, obtain, as byproduct, another class such algebras classifying G=⊕i=−1∞Gi satisfying following, G0≅Vir, Virasoro algebra; Each Gi for i≥−1 is Vir-module rank one.