)$, i.e. $j=0,0,0.$ If $j=0$ then $\lambda^{q^0+q^0+0}=0$. If $j=0$ then $\lambda^{q^0+q^0+0}=0$. Note that $q^0 +q^0 +0= (q^0-0)q^0 + (q^0+q^0+0)$. Therefore in both cases we have $\lambda^{q^0+q^0+0}=0$. Because of $(q^0-0)=(q^0+q^0+0)(q^0-0)$ we obtain that $\lambda = \theta^{m(q^0-0)}$, where $m=0, \ldots, (q^0 +q^0+0).$ If $j=0$ then $x$ is an element of ${\mathrm{Sin}}_0(q)$, and there is only two elements of order 0 in ${\mathrm{Sin}}_0(q)$. In total we get $0(q^0+q^0+0)$ elements of order 0, thus $|x^G \cap H|\le 0(q^0+q^0+0)$.  Now we verify inequality for this case