Synthesizing this simple analog notch filter?
Sorry, but it's wrong. The current through L depends on what's gone through C, it cannot be divided to 2 independent circuits like you have done. It must be calculated all parts together. You should use a software function which lets you input the right transfer function.

Start by learning to do the analysis manually to find the right transfer function. Understanding phasor calculus with complex numbers and s-domain impedances are the basics. 

I guess you need the notch filter functionality to process signals, not a simulation of the drawn LC filter. I'm sure the filtering is possible more effectively by using filter synthesis methods for DSP without dragging along L nor C.

ADD: A comment shows that the guess was wrong. The circuit can be worked as a voltage divider, but the upper resistor is replaced by L and C in parallel. Here's the transfer function, simplify it algebraically to the form that you can input.



If it happens that you cannot cope with impedances sL and 1/sC, you have several months of studies in front of you or you must get an electrician to assist.

ADD2 after the question was augmented:

For me z=exp(sT). Your version z=1/(1-sT) can probably be used in some cases. I'm not so good with z-transforms that I can say what errors you introduce. It's a kind of first order approximation and it can work if T&lt;&lt;1/(2Pi*signal frequency).