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Every response — including 401 and 403 — carries these headers:

When you’re over the limit

A 429 response adds a Retry-After header (seconds to wait) and the standard error body:

Backing off

Reading X-RateLimit-Remaining on every response and slowing down before you hit 0 is friendlier than waiting for a 429 — and every response gives you that number for free.
Repeated authentication failures from the same address can also trigger 429, independently of your per-key quota.