received call at 3:36 in the morning.  Left no message on answering machine.  Dead number when called back.  Supremely annoying.  Somehow someone is spoofing a dead number to harass me?

Good bet the calls are coming from overseas, where 336 AM is about 4PM in the Middle East. Expect most numbers that appear on your ID to be dummies to protect the callers' locations and certainly do not return their calls. Try shutting down your answering machine, an answer there still confirms your number is open for business. Ignore it completely, they give up after a while.