What is code po300,po306,p1316,p1314,p1313,po420

You need to get your vehicle to a good mechanic as this could be almost anything! One of the cylinders isn't firing correctly. This could be a fuel, an air or a spark issue. It will need further investigation. It also suggests there might be a problem with one of the O2 sensors on the exhaust system. I was unable to find a listing for P1317.
P0306 = Cylinder 6 - misfire detected.
P1000 = OBD Systems Readiness Test Not Complete.
P1314 = Misfire Rate Catalyst Damage Fault - Bank 2.
P1316 = Misfire Rate Exceeds Emissions.
P1317 = (no code found).
P1647 = Linear O2 Sensor Control Chip (Bank 2).

the engine managment system on this car treats each bank as 2 seperate engines bank 1 and bank 2 the fault codes you have got are emission related. diagnosis is not easy because the ecu will use the other bank to compensate and alter its fueling etc to reduce emissions. the only way to sort it out is to put it on suitable diagnostic equipment and monitor live data ie. lambda sensors/ catalyst efficiency hope this helps

PO300 and P1399 are random cylinder misfire detected.
PO301 cylinder 1 misfire
PO302 cylinder 2 misfire
PO304 cylinder 4 misfire
PO306 cylinder 6 misfire
I would say that you have damage to the ignition wiring harness or you ECM is failing.

the fault codes you have are all misfire codes p1313 and p1314 are manufactuer codes only. but they all point to same issue check the engine wiring harness under the air box for chaffing also the on plug coils are very unreliable the spark plug internal resistance is critical use only genuine plugs we had to change all 6 because pattern plugs had been fitted and check for water ingress in to the ecm/connector that may be the problem

Odd one this to have P1111 as well.

According to my data P1111 is all dtc checks compleated, http://www.bluejag.co.uk however some websites show it as a Intake Air Temperature (IAT) Sensor Circuit Intermittent High Voltage, I'm fairly sure that the latter is incorrect.

check the basics first plugs, leads, corroded ground connections etc then its a bit of a guessing game


As for the other codes

P0301 = Misfire detected - cylinder 1
P1313 = Misfire rate catalyst damage - bank 1
P1316 = Misfire excess emission


Possible causes (as per JTIS):

Cylinder compression low
Worn camshaft / broken valve spring(s)
Fuel delivery pressure (low / high)
Fuel injector(s) restricted / leaking
Fuel injector(s) continuously open
Fuel contamination
Fuel injector circuit fault(s)
(Injector DTCs also flagged)
Spark plug failure / fouled / incorrect gap
ECM to ignition coil primary circuit fault
(Cylinder misfire detected DTC also
flagged)
Ignition coil failure

hope this helps

CODE P1313 MISFIRE CATALYST DAMAGE BANK 1 CODE P1314 MISFIRE CATALYST DAMAGE BANK 2 COULD BE MANY THINGS THAT CAUSE THAT PROBLEM.FAULTY EGR VALVE FAULTY MASS AIR FLOW SENSOR OR BAD COOLANT SENSOR BAD O2 SENSORS.LEAKING INTAKE MANIFOLD LEAKING EXHAUST PIPE OR EXHAUST MANIFOLD.

THE P0302 is misfire cyclinder 2,4,and 5
The P1313 P1316 is Cyclinder compressor low, Worn camshaft/ broken valve springs. Fuel injector contamination, Spark plug failure/ incorrect gap. Iginition coil failure.
P0778 is 2/4 Brake prssure solenoid failure

HOPE THIS CAN HELP.

P1193 is the heated O2 sensor, P0300 is a random missfire, P1313 P1314 are Catalist damage banks A and B, the rest of the 'P' codes are all to do with the same area, have you changed one at a time? or both at once? as the conectors can be crossed and this will throw the ECU out, generating the fault codes given.
You will need a Jag garage to re set the sensors.

Well, the P in the code means powertrain.  As far as the code specifics, 
P1313 Misfire Rate Catalyst Damage Fault - Bank 1
P1316 Misfire Rate Exceeds Emissions

I would say check your spark plugs and wires.