Does a new E.I. have to be calculated for each developer

I'm am trying to apply some zone system technique to my 35mm b&w work. I have figured out my exposure indexes for Tmax100 and Tmax400 in D76, by exposing for Zone 1 at different ISO speeds and choosing the speed that gives me the correct density for zone 1, than assigning that speed. I'm aware that shadow density changes very little with different development times, do I just use the same EI for developers other then D76, and just concern myself with changing development times for highlights and contrast?

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