You can see list of supported key names in the documentation. There are only:
<f0> - <f63>
functional keys.
<c-f1>,...,<c-f12>
functional keys with Control key pressed.
<a-f1>,...,<a-f12>
functional keys with Alt key pressed.
<s-f1>,...,<s-f12>
functional keys with Shift key pressed.
You can try using <f39> if it gets resolved to <c-s-f3> by the terminal.