Let K = Q(ζ3) for a primitive cube root of unity ζ3 ∈ C Determine the splitting behaviour in K (remains prime, splits or ramifies) of the following primes: 2, 3, 5, 7, 11, 13.

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Let K = Q(ζ3) for a primitive cube root of unity ζ3 ∈ C

Determine the splitting behaviour in K (remains prime, splits or ramifies) of the following
primes: 2, 3, 5, 7, 11, 13.

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