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N-1, N-3, and N-7 are pyridine-like nitrogens. Their lone pairs are localized in $$sp^2$$ orbitals and do not participate in aromaticity, so they are available for donation. N-9 is pyrrole-like (NH). Its lone pair participates in the aromatic $$π$$ electron system of the ring to maintain aromaticity.
The lone pair on N-9 is the only one involved in the aromatic sextet of the five-membered ring. Therefore, it is the least available for donation, making N-9 the least basic nitrogen in the compound.
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