Class of the language of Turing machines that loop on at least one input $L = \{ \langle M \rangle \mid \text{there is at least one input string on which the \(M\) does not halt} \}$

Here, for a Turing machine $M$, the notation $\langle M \rangle$ denotes an encoding, over some alphabet, of the code of the Turing machine. To which of the following language classes does $L$ belong?


Regular.
Context-free but not Regular.
Recursive but not Context-free.
Recursively enumerable but not recursive.
Not recursively enumerable.
The language $L$ consists of (descriptions of) Turing machines $M$ such that $M$ does not halt on all inputs. In other words, $\langle M \rangle \notin L$ if $M$ halts on all inputs. Can you think of any connection to the halting problem?