Apex domains cannot have CNAME records.
Question and response
Question
dig alpha-mail.jp. NS
Answer
alpha-mail.jp. 5 NS tsukuba.aics.ne.jp.
alpha-mail.jp. 5 NS kotetsu.alpha-lt.net.
alpha-mail.jp. 5 NS amdns03.alpha-mail.jp.
Authority
The response has no authority records.
Additional
amdns03.alpha-mail.jp. 5 A 216.230.254.112
kotetsu.alpha-lt.net. 5 A 157.205.252.6
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0