I'm just comparing two transfer function for a simple T-CLC low pass with load and inner resistance of the voltage source taken care of.

One transfer function is obtained numerically via LT-Spice and looks like I expect (blue RIN=50Ω, black RIN->0Ω):

However if I calculate the transfer function analytically I seem to mess up. It looks qualitatively fine, but neither maximal amplitude nor cut-off frequency fit (blue RIN=50Ω, black RIN->0Ω):

I tried to obtain the transfer function via input and output impedance as

\[ |\mathcal{H}(i \omega)| = | \frac{Z_a}{Z_e}| \\ Z_a =\frac{R_1 (R_{in}+i L \omega )}{R_1+(R_{in}+i L \omega )} \\ Z_e =\frac{2}{i C \omega }+R_{in}+Z_a \]

both capacities shall be identical.

Where is my mistake?