The modulus of Gamma function $\left| \Gamma(x+iy) \right|$ is strictly decreasing when $x \in (0,\frac{1}{2})$ for a fixed $y \in \mathbb{R_+}$

Question

Let $\Gamma(s)$ be the Gamma function, extension of the factorial function to complex numbers.

My question is:

Fixed $y \in \mathbb{R_+}$ is it true that $\left| \Gamma(x+iy) \right|$, the modulus of gamma function, is strictly decreasing when $x \in (0,\frac{1}{2})$

Answer 1

False for $y=1$. Here is the graph of $|\Gamma(x+i)|$ for $0 < x < 1/2$.