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According to the documentation:

Int32Parameter (object) Nullable Filters accounts by last activity level (where the account was updated)

But I'm not sure how to use an integer to specify a date or cycle. I'm trying to get a list of delegators who have been active in the last month.

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lastActivity parameter is used to compare the level of the blockchain.

To get the list of active delegators within the last month, first, you'll need to get the block level that was applied just a month from now. You can use Get Level By Timestamp query to get the level at any particular time. So, one month from the time of writing this answer is 2023-06-30T15:50:00Z GMT. So, the query https://api.tzkt.io/v1/blocks/2023-06-30T15:50:00Z/level returns 3797616.

Now, we can use lastActivity.gt to filter only those items which were active sometime later than the given timestamp. Hence, you can add lastActivity.gt=3797616 to the query.

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