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.