1200 followers problem!

Consider a 1200 digit number \(N_a=\underbrace{aaaa\dots aaa}_{\text{1200 } a\text{'s} }\).

Define \(\varphi_a\) as the number of zeroes in the decimal representation of the quotient obtained when \(N_a\) is divided by 37.

Compute \(\displaystyle\sum_{a=1}^9 \varphi_a\).


Bonus: Generalize this.

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