Apex domains cannot have CNAME records.
Question and response
Question
dig swamp-cooler.com. NS
Answer
swamp-cooler.com. 5 NS ns-539.awsdns-03.net.
swamp-cooler.com. 5 NS ns-1117.awsdns-11.org.
swamp-cooler.com. 5 NS ns-604.awsdns-11.net.
swamp-cooler.com. 5 NS ns-1166.awsdns-17.org.
Authority
The response has no authority records.
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0