B737 FO ATTEMPTS TO MANUALLY CREATE THE MOUNTAIN 1 DEP OUT OF SEA AFTER FINDING IT IS NOT INCLUDED IN THE FMC STORED COMPANY RTE.

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AFTER RECEIVING OUR CLEARANCE; I PROCEEDED TO PROGRAM THE FMC FOR OUR NEXT LEG. AFTER PUTTING IN THE STANDARD COMPANY ROUTE (FMC STORED); I NOTICED THAT THE MOUNTAIN DEPARTURE WAS NOT PROGRAMMED; SO I PROCEEDED TO INPUT THE WAYPOINT MANUALLY. THE ACTIVE RUNWAY FOR DEPARTURE WAS 34L. I ALSO INPUT A 070 COURSE (INCORRECTLY) OUT OF THE WAYPOINT WHEN THE DEPARTURE SHOWS A 070 HEADING. THIS WAS MY FIRST MISTAKE; INCORRECTLY PROGRAMMING THE FMC. MY NEXT MISTAKE OCCURRED ON DEPARTURE. THE CAPTAIN WAS FLYING AND HE SELECTED LNAV AS WE BOTH THOUGHT THE FMC WAS PROGRAMMED CORRECTLY. BECAUSE I HAD INCORRECTLY PROGRAMMED THE 070 COURSE OUT OF THE WAYPOINT; THE AIRCRAFT USED A LEAD POINT TO INTERCEPT THE COURSE AND TURNED A COUPLE MILES EARLY INSTEAD OF FLYING ALL THE WAY OUT TO SEA 8 DME. AS THE PILOT MONITORING; I DIDN'T NOTICE THE AIRCRAFT HAD STARTED TO TURN EARLY UNTIL SEA DEPARTURE SAID SOMETHING WHEN WE WERE IN OUR TURN. THE CONTROLLER DIDN'T SEEM TOO CONCERNED; HE SIMPLY INFORMED US THAT WE HAD TURNED EARLY AND; 'FOR FUTURE REFERENCE; WE NEEDED TO GO ALL THE WAY TO 8 DME BEFORE TURNING.' CREW ACTIONS TO HELP PREVENT THIS FROM HAPPENING AGAIN WOULD BE TO MONITOR THE 'SYSTEM' MORE CLOSELY. I SHOULD HAVE REALIZED SOONER THAT THE AIRCRAFT WAS TURNING BEFORE WE HAD REACHED 8 DME. ALSO; HOW ABOUT SIMPLY FLYING THE BASICS -- INTERCEPT THE RADIAL INSTEAD OF FLYING LNAV FOR SUCH A SIMPLE DEPARTURE. ACTIONS BY OTHER GROUPS: HAD THE MOUNTAIN DEPARTURE ALREADY BEEN PROGRAMMED INTO THE COMPANY ROUTE; I NEVER WOULD HAVE MADE THE MISTAKE THAT I DID TRYING TO MANUALLY PROGRAM THE DEPARTURE.