Functions

Let the function $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined by

\(f(x)=\frac{\sin x}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+3\right)}+\frac{2}{e^{\pi x}} \frac{\left(x^{2023}+2024 x+2025\right)}{\left(x^2-x+3\right)} .\)

Then the number of solutions of $f(x)=0$ in $\mathbb{R}$ is _________.