ei diphthong (/ei̯/)

According to Wiktionary, Classical Latin had a diphthong for the ei letter combination. However, the only words in which I've found e directly in front of i are names, such as Anneius (probably not a diphthong), and a few starting with the silent h, such as heiluátio. Did the ei diphthong exist? If so, what are some examples of its use?
 
Thanks. Would a mod please rename this topic Diphthong Discussion and merge the bottom of this post into the first post?

Currently, I'm using Wikipedia's list of diphthongs (ae, au, eu, oe, and ui) in a wiki article about the Salákian alphabet and pronunciation, having removed ei from the list. Should eu ("eh-oo") and ui ("oo-ee") be removed on grounds of them being disyllabic by nature, like ei?
 
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