Help me identifying this Vintage Omega!

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My wife brought this watch from her grandparent's. I want to identify the ref.number of this watch before getting it serviced. However it says nothing on the dial except for the logo and "automatic". And also nothing on the back.

The size is 34mm. Anyone have any clue?
 
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The reference number is inside the case-back. I don't think there's any particular need to identify the reference before having it serviced, especially since it is a family piece with sentimental value.