Logistic Regression Coefficients transformation?

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I have 5 columns of data. Column of lists_1, Total_1 which is a constant, column of lists_2 and Total_2 as a constant.

Like this:

Lists_1            Total_1 Lists_2         Total_2 Gender
[23, 11, 43, 53]     500   [99, 35, 1, 0]  5       0
[73, 111, 47, 13]    500   [72, 1,44,19]   5       0
[33, 19, 23, 86]     500   [87, 9, 0, 0]   5       1

I perform a formula: L = ((Lists_1 / Total_1) / (Lists_2 / Total_2))

This new calculated field will be attached to the Gender.

Now I will run a logistic regression on the calculated field L against Gender.

I have got 4 coefficients + intercept explaining Gender.

What transformation should I perform to go back and multiply the Lists_1, and Lists_2 members to explain Gender?

Please advise.