Which symptoms signal a pulmonary embolism?

A pulmonary embolism and a deep vein clot are named in the same breath, yet readers ask about them separately. This page takes the symptom question for the pulmonary embolism and keeps its neighbor in view.
The answer, with its source beside it
The publisher medlineplus.gov lists the following. Symptoms of PE include: Shortness of breath Rapid breathing Chest pain or discomfort, which usually gets worse when you cough or take a deep breath Increased heart rate Coughing up blood Very low blood pressure, lightheadedness, or fainting Sometimes people with PE don't have any symptoms until they have serious complications, such as pulmonary hypertension (high blood pressure in the arteries to your lungs).
Where this question splits from its look-alike
Deep vein thrombosis is the look-alike here, and its symptom list belongs to its own publisher page. The pulmonary embolism list above should not be merged with it.
Pages to read alongside this one
The Cleveland Clinic overview of deep vein thrombosis sits on the neighboring condition. The Cleveland Clinic page on venous disease gives the wider venous background.
The follow-up question
The source notes that some people have no symptoms until complications arrive, so the follow-up is: how else is a pulmonary embolism recognized?