AN FA20 EXPERIENCED A FLAMEOUT AT FL270. AT FL190 A SUCCESSFUL ENG RELIGHT WAS ACCOMPLISHED BUT WITH ENG VIBRATION. THE FLT DIVERTED TO A NEARBY ARPT.

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WE HAD LEVELED OFF AT FL270. AFTER ABOUT 10 MINS AT CRUISE; WE EXPERIENCED 2 PWR SURGES FOLLOWED BY THE FAILURE OF THE #1 ENG. WE ADVISED ATC OF OUR SITUATION AND REQUESTED LOWER. ATC DECLARED AN EMER ON OUR BEHALF. WE DSNDED TO FL230 AND THEN WERE CLRED TO FL190. WE LOST COM WITH ATC DURING A FREQ CHANGE. COM WAS RE-ESTABLISHED ON FREQ 121.5 ABOUT 1 MIN LATER. AFTER DSNDING THROUGH FL200; WE ACCOMPLISHED A SUCCESSFUL RELIGHT. ALL ENG INDICATIONS WERE NORMAL. I SET THE PWR AT A REDUCED SETTING OF 80% N1. MOMENTS LATER; WE EXPERIENCED A VIBRATION FROM THE #1 ENG. I REDUCED THE PWR TO IDLE AND DIVERTED TO ZZZ. ATC HAD CANCELLED OUR EMER STATUS. I HAD THE FO FLY THE ACFT WHILE I REFED THE EMER CHKLIST. WHEN WE ARRIVED AT THE INITIAL TRANSITION; I NOTICED THE FO HAD TURNED THE WRONG WAY. I BROUGHT THE MISTAKE TO HIS ATTN AND HE IMMEDIATELY CORRECTED. AT THIS TIME ATC QUERIED OUR TURN AS WE WERE CORRECTING. I TOOK OVER CTL OF THE ACFT AND COMPLETED THE APCH AND ARR WITHOUT INCIDENT. THE LNDG WAS ACCOMPLISHED FLAPS 25 DEGS AND THE #1 ENG AT IDLE THRUST. THE COURSE DEV COULD HAVE BEEN PREVENTED WITH BETTER SUPERVISION OF THE FO.