As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
EXPERIENCED PITCH OSCILLATIONS IN CLIMB WITH KP/FD COUPLED TO AUTO PILOT. VIS FLUCTUATED FROM 500FPM TO +5000 FPM. GOT RED X ON VSI AND ALT AND A/S YELLOW FLAGS. APPEARS TO BE NR 1 ADC. REPLACED NR 1 ADC WITH REPAIR UNIT CERTIFIED TO AN ALTITUED OF 59,500 FT. PERFORMED PILOT PITOT/STATIC SYSTEM LEAK CHECK IAW CESSNA 560XL MM 34-11-09, FAR 91.411 AND FAR 91.413. NR 1 ADC GROUND CHECKS OPERATIONAL AND NR 1 PITOT/STATIC SYSTEM LEAK CHECK WII=THIN LIMITS.