Apex domains cannot have CNAME records.
Question and response
Question
dig coopinfa.coop. NS
Answer
coopinfa.coop. 1 NS ed.ns.cloudflare.com.
coopinfa.coop. 1 NS elle.ns.cloudflare.com.
Authority
The response has no authority records.
Additional
ed.ns.cloudflare.com. 4 A 108.162.193.111
ed.ns.cloudflare.com. 4 A 172.64.33.111
ed.ns.cloudflare.com. 4 A 173.245.59.111
elle.ns.cloudflare.com. 4 A 108.162.192.110
elle.ns.cloudflare.com. 4 A 172.64.32.110
elle.ns.cloudflare.com. 4 A 173.245.58.110
ed.ns.cloudflare.com. 4 AAAA 2606:4700:58:0:0:0:adf5:3b6f
ed.ns.cloudflare.com. 4 AAAA 2803:f800:50:0:0:0:6ca2:c16f
ed.ns.cloudflare.com. 4 AAAA 2a06:98c1:50:0:0:0:ac40:216f
elle.ns.cloudflare.com. 4 AAAA 2606:4700:50:0:0:0:adf5:3a6e
elle.ns.cloudflare.com. 4 AAAA 2803:f800:50:0:0:0:6ca2:c06e
elle.ns.cloudflare.com. 4 AAAA 2a06:98c1:50:0:0:0:ac40:206e
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0