Well, notice that the input impedance of your circuit is given by:
\begin{equation}
\begin{split}
\underline{\text{Z}}_{\space\text{i}}\left(\omega\right)&=\underline{\text{Z}}_{\space\text{L}}+\underline{\text{Z}}_{\space\text{C}\space\text{||}\space\text{R}}\\
\\
&=\text{j}\omega\text{L}+\left(\frac{1}{\text{j}\omega\text{C}}\space\text{||}\space\text{R}\right)\\
\\
&=\text{j}\omega\text{L}+\frac{\displaystyle\frac{1}{\text{j}\omega\text{C}}\cdot\text{R}}{\displaystyle\frac{1}{\text{j}\omega\text{C}}+\text{R}}\\
\\
&=\text{j}\omega\text{L}+\frac{\displaystyle\frac{\text{j}\omega\text{C}}{\text{j}\omega\text{C}}\cdot\text{R}}{\displaystyle\frac{\text{j}\omega\text{C}}{\text{j}\omega\text{C}}+\text{j}\omega\text{C}\text{R}}\\
\\
&=\text{L}\omega\text{j}+\frac{\displaystyle\text{R}}{\displaystyle1+\text{CR}\omega\text{j}}\\
\\
&=\text{L}\omega\text{j}+\frac{\displaystyle\text{R}}{\displaystyle1+\text{CR}\omega\text{j}}\cdot\frac{\displaystyle1-\text{CR}\omega\text{j}}{\displaystyle1-\text{CR}\omega\text{j}}\\
\\
&=\text{L}\omega\text{j}+\frac{\displaystyle\text{R}\left(1-\text{CR}\omega\text{j}\right)}{\displaystyle1^2+\left(\text{CR}\omega\right)^2}\\
\\
&=\text{L}\omega\text{j}+\frac{\displaystyle\text{R}-\text{CR}^2\omega\text{j}}{\displaystyle1+\left(\text{CR}\omega\right)^2}\\
\\
&=\text{L}\omega\text{j}+\frac{\displaystyle\text{R}}{\displaystyle1+\left(\text{CR}\omega\right)^2}-\frac{\displaystyle\text{CR}^2\omega}{\displaystyle1+\left(\text{CR}\omega\right)^2}\cdot\text{j}\\
\\
&=\frac{\displaystyle\text{R}}{\displaystyle1+\left(\text{CR}\omega\right)^2}+\left(\text{L}\omega-\frac{\displaystyle\text{CR}^2\omega}{\displaystyle1+\left(\text{CR}\omega\right)^2}\right)\text{j}\\
\\
&=\frac{\displaystyle\text{R}}{\displaystyle1+\left(\text{CR}\omega\right)^2}+\omega\left(\text{L}-\frac{\displaystyle\text{CR}^2}{\displaystyle1+\left(\text{CR}\omega\right)^2}\right)\text{j}
\end{split}\tag1
\end{equation}
Where \$\alpha\space\text{||}\space\beta:=\frac{\displaystyle\alpha\beta}{\displaystyle\alpha+\beta}\$.
So, we can see that the amplitude of the input impedance is given by:
\begin{equation}
\begin{split}
\left|\underline{\text{Z}}_{\space\text{i}}\left(\omega\right)\right|&=\left|\frac{\displaystyle\text{R}}{\displaystyle1+\left(\text{CR}\omega\right)^2}+\omega\left(\text{L}-\frac{\displaystyle\text{CR}^2}{\displaystyle1+\left(\text{CR}\omega\right)^2}\right)\text{j}\right|\\
\\
&=\sqrt{\left(\frac{\displaystyle\text{R}}{\displaystyle1+\left(\text{CR}\omega\right)^2}\right)^2+\left(\omega\left(\text{L}-\frac{\displaystyle\text{CR}^2}{\displaystyle1+\left(\text{CR}\omega\right)^2}\right)\right)^2}
\end{split}\tag2
\end{equation}
Solving:
$$\frac{\displaystyle\partial\left|\underline{\text{Z}}_{\space\text{i}}\left(\omega\right)\right|}{\displaystyle\partial\omega}=0\space\Longrightarrow\space\omega_0=\dots\tag3$$
Gives:
$$\omega_0=\frac{\displaystyle1}{\displaystyle\text{C}^2\text{R}}\cdot\sqrt{\frac{\text{R}}{\text{L}}\cdot\sqrt{\text{C}^5\left(2\text{L}+\text{CR}^2\right)}-\text{C}^2}\tag4$$
Using your values, we find:
$$\omega_0=\sqrt{2\sqrt{30}-1}\approx3.15507\space\text{rad/sec}\tag5$$
And:
$$\left|\underline{\text{Z}}_{\space\text{i}}\left(\omega_0\right)\right|=\frac{\sqrt{4\sqrt{30}-21}}{10}\approx0.0953364\space\Omega\tag6$$