I have read up on a few upgrades for the carburetor and airbox and thought I would combine everything I have read into this thread.
I wish I was more analytical and had the patience to change one thing and then try it out and so on. Also I live in town and have to drive about an hour to test the Eiger so I am just going to change it all and I will see how it goes.
The machine is a totally stock 400 automatic Eiger.
At the airbox I replaced the stock air filter with a Uni one. I also opened up the air intake opening at the top of the box. I did this mod on my wifes Polaris which also has a very restrictive opening. I did this with a dremel and a grinding stone. I basically just melted the plastic.
I changed the main jet from the stock 122 to a 130 and changed the pilot jet from a 38 to a 40. I am very interested to see what difference the pilot jet makes. I did this mod on my 400EX and it made a ton of difference. It turned it from a hard starting machine to a jump on it and hit the button and go machine.
I cut an inch off the spring from 3 1/2 to 2 1/2 that goes to the needle valve. While I was in there I also drilled out the vacuum port to 1/8 inch. The Eiger has alot of lag on acceleration and I think these 2 things will help that out alot.
I am now waiting on a new float bowl gasket to put it all back together and see what I have. It will take some tuning I am sure to get it dialed in and since it is pretty cold I won't exactly know how much good the pilot jet did me and will probably have to adjust things some after it warms up.

 

Here are some pics of the air intake after I opened it up with a dremel. I am an idiot and didn't think to take pics before. If anybody has any stock pics and would like to help me out by posting I would appreciate it. If anybody does post them you will see it is definitely the bottleneck in the air system.

 

I got the carb reinstalled and it starts up alot better with the new pilot jet. In this cold weather (around 30 degrees today) the ATV almost started without the choke. It started for a second and then died. So I turned the choke on started it up and after a few seconds turned the choke off. The 130 main jet is not going to work. As soon as you give it gas it stumbles and hesitates. I ordered 2 more main jets a 125 and 127.

 

After a little homework I put a 4mm flat washer to raise the needle out of the jet a little since a stock needle does not have the adjustments that a dynojet kit would have. It made a heck of a difference. I then drilled 7 three quarter inch holes into the airbox as aksafari did in another thread. I then put the 135 jet in and took it out. It really runs well. It is slightly hard to tell how much better since the ground was covered with snow so all the atvs were spinning their wheels. It seems to be pretty dialed in. I will check the plug again when the temperature warms up outside.