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The Omega sector was a remote spatial region in the Beta Quadrant. This sector was named after the Omega system. This was the home system for the Omega IV natives. (TOS: "The Omega Glory"; VOY: "The Gift"; PIC: "Maps and Legends")

During the late 2340s, a remote outpost in the Omega sector became the last recorded location of the Hansen family, who refused to file a flight plan aboard the exploration vessel, the USS Raven. The Hansens, who had dedicated their careers to studying the Borg, set a course for the Delta Quadrant, and were not heard from again.

In 2374, Kathryn Janeway managed to locate this piece of information in the records of Deep Space 4, while researching the background of the Hansens' young daughter, Annika, who had been assimilated by the Borg and transformed into the USS Voyager's newest crewmember, Seven of Nine. (VOY: "The Gift")

The Star Trek Encyclopedia, 4th ed., vol. 2, p. 104 located this sector in the Alpha Quadrant.
In the okudagram Janeway was referencing, this event occurred in 2354, however, it was later revealed in PIC: "Penance" that Annika was assimilated four years earlier (in 2350).

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