What was found
ON CLIMBOUT NR 1 PROP RPM DECREASED WITH NO PROP LEVER INPUT. PLACED PROP TO FULL RPM POSITION & RPM DECREASE. TRIED TO MATCH RPM ON BOTH ENG, STOPPED WHEN NR 2 GOOD ENG WAS 1300 RPM. ENG HAD OUT OF SYNC PROP BEAT, ACFT YAWING. TORQUE ON NR 1 ENG ROSE, RPM'S DROPPED. OIL PRESSURE AT BOTTOM OF GREEN ARC/TOP OF YELLOW ARC. NR 1 PROP 200 RPM, WINDMILLING WITHOUT ANY FORWARD POWER. CREW SHUT DOWN NR 1 ENG, FOLLOWED CHECKLISTS & PROCEDURES. DIVERTED TO LIT, EMERGENCY VEHICLES AND EQUIPMENT STANDING BY. APPROACH TO LIT WAS UNEVENTFUL AND CREW SHUTDOWN AIRCRAFT AT TAXIWAY. MX LINED GCU PARAMS, REMOVED & REPLACED P-3 LINES, ADJUSTED BETA VALVE ACCOMPLISHING ENG RIGGING.