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In Python or Sage, how do I test if an eisenstein integer is a primitive root modulo a complex prime over the ring?

For instance, if I suspect (11 + 3√-3) is a primitive root modulo the complex prime, (167 + 77√-3) whose norm = 20959 (a prime that splits -3) then how would I test it?

Should I just find the norm and check if it is a primitive root modulo the norm of the complex prime?

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