sage: zeta84 in Q1092

True

sage: zeta12 in Q84

True

sage: zeta12 in Q1092

False

sage: Q12.embeddings(Q1092)

[

Ring morphism:

  From: Cyclotomic Field of order 12 and degree 4

  To:   Cyclotomic Field of order 1092 and degree 288

  Defn: zeta12 |--> zeta1092^91,

Ring morphism:

  From: Cyclotomic Field of order 12 and degree 4

  To:   Cyclotomic Field of order 1092 and degree 288

  Defn: zeta12 |--> -zeta1092^91,

Ring morphism:

  From: Cyclotomic Field of order 12 and degree 4

  To:   Cyclotomic Field of order 1092 and degree 288

  Defn: zeta12 |--> zeta1092^273 - zeta1092^91,

Ring morphism:

  From: Cyclotomic Field of order 12 and degree 4

  To:   Cyclotomic Field of order 1092 and degree 288

  Defn: zeta12 |--> -zeta1092^273 + zeta1092^91

]

Perhaps Sage now wants you to choose an embedding.

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