When someone submits their email on your landing page, their email goes to the Sign Ups panel inside of the Loop screen. To find this, follow the steps below.
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Step 1: Click on "Loop" in the left navigation panel.

Step 2: Once you are viewing the Loop canvas, scroll down until you see your "Landing Page". Click anywhere on the landing page block.
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Step 3: Once clicked, the right panel should open up to the list of people that have signed up.