How many photos do I need to take to make a panorama?

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How many photos do I need to cover a full circle around the tripod, and all the sky as well?

I've calculated my angle of view (AOV) from their spec sheet, with my Sony RX10 IV Camera as

$\alpha_{horizon} = 3.4388°$

$\alpha_{vertical} = 2.3150°$

$\alpha_{diagonal} = 4.1446°$

Any help would be appreciated.

Thanks in advance!