Apex domains cannot have CNAME records.
Question and response
Question
dig conwayfreethinkers.org. NS
Answer
conwayfreethinkers.org. 5 NS ns-1715.awsdns-22.co.uk.
conwayfreethinkers.org. 5 NS ns-1275.awsdns-31.org.
conwayfreethinkers.org. 5 NS ns-477.awsdns-59.com.
conwayfreethinkers.org. 5 NS ns-1182.awsdns-19.org.
Authority
The response has no authority records.
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0