How to add a new column to an existing DataFrame?

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I have the following indexed DataFrame with named columns and rows not- continuous numbers:

          a         b         c         d
2  0.671399  0.101208 -0.181532  0.241273
3  0.446172 -0.243316  0.051767  1.577318
5  0.614758  0.075793 -0.451460 -0.012493

I would like to add a new column, 'e', to the existing data frame and do not want to change anything in the data frame (i.e., the new column always has the same length as the DataFrame). 

0   -0.335485
1   -1.166658
2   -0.385571
dtype: float64

How can I add column e to the above example?

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