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I thought about it but since it's always the same position I assumed that it's the chainring.
@PhilDAS I tightened the chain just before we started the ride because I had a fair amount of chain slack again. And since the chain is quite new and might still lengthen itself I just pulled the wheel back without checking the (un)trueness of the chainring/cog/chain. Might have been a dumb move.
Who says it isn't your chain or even the cog? My chain has a different tension at different crank orientations. I wouldn't worry about it, and I wouldn't worry about the Zen chainring especially.