Based on the issue description and the hint provided, I can generate the patch to fix the typo on line 590 where `cotm` should be `cothm`:

--- a/sympy/functions/elementary/hyperbolic.py
+++ b/sympy/functions/elementary/hyperbolic.py
@@ -587,7 +587,7 @@ class coth(HyperbolicFunction):
             if m:
                 cothm = coth(m)
                 if cothm.is_Number:
-                    if cotm is S.ComplexInfinity:
+                    if cothm is S.ComplexInfinity:
                         return coth(x)
                     else:
                         return cothm