The initial question was: what is the minimum needed to gain practical control over the zeta function across the full complex plane, for s ∈ ℂ (including Re(s) < 1 and Re(s) < 0)? This project is one possible answer. It provides two JavaScript functions, vanilla_zeta() and vanilla_gamma(), aimed at computing the complex zeta and gamma functions with a very simple JS implementation. You can try both functions directly in the browser via the linked calculator at: www.zeta-calculator.com