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I have done a cointegration test in my study, but the max-eigenvalue test results were confusing, see the following out puts please:

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No. of CE(s)~ eigenvalue~~~max-eivalue statistic ~~~ 5%critical value ~~ p value
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0 ~~~~~~~ 0.225 ~~~~~~~~~57.349 ~~~~~~~~~~~~~~~~~40.078~~~~~~~0.000*
1~~~~~~~~0.130 ~~~~~~~~~31.381~~~~~~~~~~~~~~~~~33.877~~~~~~~~0.097
2~~~~~~~~0.124 ~~~~~~~~~29.707 ~~~~~~~~~~~~~~~~27.584~~~~~~~~ 0.026
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Note: Max-eigenvalue test indicates there is only one cointegration vector in the system.

I was confused with the results, the first p-value reject the null at 1%, but the third p-value also reject the null,(the second can not), why Eviews software indicates one cointegration vector only? How can I interpret this in my study?
I am really appreciate any one who can help me fix this. Thank you in advance.

Hope to here from you experts...