We introduce mod 3 triple Milnor invariants and triple cubic residue symbols for certain primes of the Eisenstein number field $mathbb{Q}(sqrt{-3})$, following the analogies between knots and primes. Our triple symbol generalizes both the cubic residue symbol and R{e}deis triple symbol, and describes the decomposition law of a prime in a mod 3 Heisenberg extension of degree 27 over $mathbb{Q}(sqrt{-3})$ with restricted ramification, which we construct concretely in the form similar to R{e}deis dihedral extension over $mathbb{Q}$. We also give a cohomological interpretation of our symbols by triple Massey products in Galois cohomology.
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