Let $$ \eta^{(d)}(z) = \sum_{n=1}^\infty \dfrac {(-1)^d(-1)^{n-1}\ln(n)^d} {n^z} $$ be the derivative of Dirichlet Eta function of order $d$.

Does it exist any known or not known zero of $\eta^{(d)}(z)$ such that $d \geq 1$ and $\frac{1}{2}<\Re(z)<1$

Thanks