diff --git a/jedi/parser/tokenize.py b/jedi/parser/tokenize.py
index f26a6719..48d0da51 100644
--- a/jedi/parser/tokenize.py
+++ b/jedi/parser/tokenize.py
@@ -303,8 +303,14 @@ def generate_tokens(readline, use_exact_op_types=False):
                 elif token in ')]}':
                     paren_level -= 1
 
+                try:
+                    # This check is needed in any case to check if it's a valid
+                    # operator or just some random unicode character.
+                    exact_type = opmap[token]
+                except KeyError:
+                    exact_type = typ = ERRORTOKEN
                 if use_exact_op_types:
-                    typ = opmap[token]
+                    typ = exact_type
                 else:
                     typ = OP
                 yield TokenInfo(typ, token, spos, prefix)
diff --git a/test/completion/basic.py b/test/completion/basic.py
index 8337b8dd..b3b07ee9 100644
--- a/test/completion/basic.py
+++ b/test/completion/basic.py
@@ -215,6 +215,9 @@ if 1:
     #? str()
     xyz
 
+#?
+¹.
+
 # -----------------
 # exceptions
 # -----------------