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We study the densities of the semigroup generated by the operator $-X^2+\left|Y\right|$ on the 3-dimensional Heisenberg group. We show that the 7th derivatives of the densities have a jump discontinuity. Outside the plane x=0 the densities are $C^{\infty }$. We give explicit spectral decomposition of images of $-X^2+\left|Y\right|$ in representations.