  Let function $f$ be analytic in the unit disk ${\mathbb D}$ and be normalized
so that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we give sharp bounds of
the modulus of its second, third and fourth coefficient, if $f$ satisfies \[
\left|\arg \left[\left(\frac{z}{f(z)}\right)^{1+\alpha}f'(z) \right]
\right|<\gamma\frac{\pi}{2} \quad\quad (z\in {\mathbb D}),\] for $0<\alpha<1$
and $0<\gamma\leq1$.
