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Adverb: coincidentally  kow,in-si'den-t(u-)lee
  1. By chance or coincidence; happening at the same time or place without planning
    "Coincidentally, we were both at the same restaurant that night"; "I was just thinking of you and, coincidentally, here you are"
     
  2. Happening at the same time; concurrently
    "The actions one does are coincidentally just or unjust";
    - coincidently

See also: at the same time, concurrently