Apex domains cannot have CNAME records.
Question and response
Question
dig nic.me. NS
Answer
nic.me. 5 NS a2.nic.me.
nic.me. 5 NS a0.nic.me.
nic.me. 5 NS b0.nic.me.
nic.me. 5 NS b2.nic.me.
nic.me. 5 NS c0.nic.me.
Authority
The response has no authority records.
Additional
a0.nic.me. 137738 A 199.253.59.1
a2.nic.me. 172332 A 199.249.119.1
b0.nic.me. 152379 A 199.253.60.1
b2.nic.me. 141866 A 199.249.127.1
c0.nic.me. 168158 A 199.253.61.1
a0.nic.me. 137738 AAAA 2001:500:53:0:0:0:0:1
a2.nic.me. 172332 AAAA 2001:500:47:0:0:0:0:1
b0.nic.me. 152379 AAAA 2001:500:54:0:0:0:0:1
b2.nic.me. 141866 AAAA 2001:500:4f:0:0:0:0:1
c0.nic.me. 168158 AAAA 2001:500:55:0:0:0:0:1
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0