Apex domains cannot have CNAME records.
Question and response
Question
dig ilmprovider.net. NS
Answer
ilmprovider.net. 5 NS ns04.ilmserver.de.
ilmprovider.net. 5 NS ns02.ilmserver.de.
ilmprovider.net. 5 NS ns01.ilmserver.de.
ilmprovider.net. 5 NS ns03.ilmserver.de.
Authority
The response has no authority records.
Additional
ns01.ilmserver.de. 5 A 62.116.159.4
ns02.ilmserver.de. 5 A 217.160.113.37
ns03.ilmserver.de. 5 A 89.146.248.4
ns04.ilmserver.de. 5 A 74.208.254.4
ns01.ilmserver.de. 5 AAAA 2001:4178:3:a357:62:116:159:4
ns02.ilmserver.de. 5 AAAA 2001:8d8:580:401:217:160:113:37
ns03.ilmserver.de. 5 AAAA 2a01:130:2000:118:89:146:248:4
ns04.ilmserver.de. 5 AAAA 2607:f1c0:1800:8091:74:208:254:4
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0