LGT FLC TUNES WRONG VOR FREQ MISSES XING RESTRICTION.

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I WAS FLYING THE ACFT. ZDC ADVISED 'CROSS KERNO INTXN AT FL260.' I WAS USING THE NANCI4 STAR ARR PLATE. I WROTE DOWN THE DME FOR THE XING RESTRICTION ON MY NOTE PAD; AS I ALWAYS DO IN LARGE LETTERS; TO PREEMPT THE POSSIBILITY OF MISREADING THE SMALL PRINT ON THE CHART. I WROTE 'KERNO DIRECT 49'; WHICH WAS CORRECT DME N OF NOTTINGHAM VOR. THE COPLT SAID 'I'LL TUNE IN DUPONT.' I THEN MENTALLY TRANSFERRED MY ATTN TO HIS DME INFO INSTEAD OF MINE. HE HAD INCORRECTLY DIALED FREQ 114.4 INSTEAD OF 114.0 FOR DUPONT. I HAD LOOKED DOWN AND SEEN; WHAT I THOUGHT; WAS 114.0 DIALED IN. THE DME READ ABOUT 130 MI AND I THOUGHT IT RATHER ODD TO GIVE US SUCH ADVANCE ROOM FOR A XING GOING INTO LGA. NOT 5 MINS BEFORE I HAD BRIEFED THE BRAND NEW COPLT THAT GOING INTO NY; ALWAYS START DOWN IMMEDIATELY ON RECEIPT OF A XING RESTRICTION BECAUSE INVARIABLY THERE IS NO TIME TO WASTE. NEXT SECTOR QUERIED US AS I WAS IN A LEISURELY DSCNT IF THE PREVIOUS SECTOR HAD GIVEN US A XING RESTRICTION AT KERNO. COPLT REPLIED 'AFFIRMATIVE.' CTLR SAID; 'DO YOU KNOW WHERE KERNO IS?' BIG SILENCE; FOLLOWED BY (EXPLETIVE DELETED) IN COCKPIT. NO LOSS OF SEPARATION WITH OTHER TFC. WE MADE THE XING ABOUT 10 MI LATE. CLASSIC HUMAN FACTORS ABORTION: I RETURNED FROM 3 WKS VACATION. THIS MY FIRST DAY FLYING. MY BODY RHYTHM ONLY 3 DAYS BACK FROM BEING ON ENGLAND CIRCADIAN RHYTHM (+5 HRS). JUST MOVED HOUSE FULL OF FURNITURE AND BELONGINGS TO MY NEW HOUSE 2 DAYS BEFORE. COMMUTED TO BASE DAY BEFORE; AFTER FURTHER TASKS IN NEW HOUSE. POOR SLEEP LAST 4 DAYS. NEW COPLT WHOM I TRUSTED TOO MUCH. HE DID A GOOD JOB THROUGHOUT EARLIER IN THE DAY SO I ASSUMED HE WOULD NOT MAKE MISTAKES. I HAVE FLOWN INTO NY MANY TIMES BEFORE AND KNOW MY WAY AROUND. I NEVER WOULD HAVE MISSED THE ABSURDITY OF THE DME READINGS WHICH DID NOT TOTAL TO A REASONABLE DISTANCE FOR A TYPICAL LGA ARR. OBVIOUSLY; MY ALERTNESS WAS QUITE SUBOPTIMUM AND I WAS TOO DULLED TO EVEN KNOW IT. PRETTY BAD. COPLT OBVIOUSLY DID NOT IDENT HIS NAVAID. COPLT DID NOT CATCH A BASIC ERROR IN THE DME'S OR PAY SUITABLE ATTN TO HIS CHART. WE HAD 2 OMEGA NAV UNITS RIGHT IN FRONT OF US (NOT BEING DIRECTLY UTILIZED) WHICH DISPLAY APPROX DISTANCE TO FIX. DID NOT REGISTER WITH MY AWARENESS. IF I HAD KEPT MY ENRTE CHART OUT; IT WOULD HAVE MORE CLRLY GIVEN A CHANCE TO CATCH THE OBVIOUS. TERRIBLE SHOW ON MY PART; TERRIBLE SHOW BY THE COPLT. WE GOT A CHEAP LESSON HERE.