I‘m not sure about your conjugation (ie your second output). Using the conjugation by John Carlos Baez (npub1nf4…nqe4) you should have all 𝑋ᵢ↦−𝑋ᵢ* and only 𝑋₀↦𝑋₀* . In your code, however, 𝑋₃,𝑋₅ and 𝑋₆ behave akin to 𝑋₀.
What is your convention though, do you have 𝑒₁𝑒₂=𝑒₄ or 𝑒₃ ? In the latter case it seems that your code does not take into account that (𝑎𝑏)*=𝑏*𝑎* .