inverse Jacobi Elliptic Function with Complex arguments

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I need to find the inverse of Jacobi Elliptic function that has a complex argument. I know how to calculate the Jacobi Elliptic function with complex input but I have not seen any formula or MATLAB/python functions that can calculate the inverse Jacobi Elliptic function that has complex arguments.

If anyone knows how to calculate this, please give me some suggestions.

Thank you. Khalid