This elaborates my question perfectly. I'm sorry for the vague language in my last post. I am curious about automorphic and Dirichlet L-functions, and became very lost after the first few replies here. I stumbled upon these fairly plain implementations on github...
First off, very neat paper. As for (58), if they are reabsorbing the matrix of phases (U) into the definition of α, then anything having to do with α is dependent on what U is set to (in this case = 1). I think this is informed by (51) and the instructions for (60). You are correct in saying...
Your post has a section labeled "relevant equations", but it has been left blank. Did you mean to fill that section out before posting?
To comment on the statement "in other literature it is reported that the low Q value should be of the order of the 0110 laser lower auxiliar level lifetime"...
You might take this SageMath code for geodesics in a Schwarzschild metric and rewrite the code to fit your simpler 2D metric. I highly recommend learning/using SageMath for anything Euler-Lagrange related.
Not many code examples exist for how one would go about writing an L-function. Can anyone give me a step-by-step run down of how to do this and/or link me to relevant resources?