formal languages ​​- $ L = {a ^ i ;: ; ( exists x in Lang (M_i)) ;[ xx notin Lang(M_i) ] } $ not recursively listable

Paper question of the past year:

To let $ M_i $ identify the Turing machine with code $ i $ with the alphabet $ Sigma = {a, b } $,

Show that the following language can not be recursively enumerated:

$ L = {a ^ i ;: ; ( exists x in Lang (M_i)) ;[ xx notin Lang(M_i) ] } $

I tried to show that we can reduce $ L_e $, the set of Turing machines that accept no conditions to $ L $, For that, I have to find a transformation $ f $ That's how it is $ Long (M) $ is empty, then the machine is represented by $ f (M) $ has a string $ x $ but not $ xx $, and if $ Long (M) $ is not empty, then the machine is represented by $ f (M) $ contains $ xx $ if it contains $ x $,

But I am not sure how to find such a transformation.