Is there independent scientific studies as to rather liberals or conservatives are more likely to believe in conspiracy theories?

Question

I'm asking in relation to a recent question Why does it seem like US conspiracy theorists are overwhelmingly Republican-oriented?

This question takes the presumption that conservative CT (conspiracy theories) are more common than democratic ones. Many answers and comments debated this presumption. Thus I wanted to ask two, closely related, questions which came up as a result of that question but that I feel have not been adequately addressed in any of it's answers.

1. Are conservative conspiracy theories more common then liberal conspiracy theories? This is by it's nature harder to define, as what makes a theory 'conservative' or 'liberal' is very subjective. Thus I'll add a potentially easier to answer, but closely related, question

2. Are Conservatives more, or less, likely to believe in CTs then liberals?

In both cases I'm looking for scientific evidence, not random cherry picked examples. I'd like an independent study, or studies, that attempts to objectively define and measure these values across a large sample group.

For the propose of this question I'd define a CT fitting under at least one of two below categories:

1. A belief in a theory that the overwhelming majority of scientific evidence has proven to be false or implausible.
2. A belief in actions being due to a hidden conspiracy of individuals. specifically when that conspiracy would have to be unusually wide reaching and require a(n implausibly) massive number of individuals collaborating in the conspiracy to keep it secret and functional.

Answer 1

An investigation involving 5000+ adults has been conducted, this is their summary.

Results reveal that conservatives in the United States were not only more likely than liberals to endorse specific conspiracy theories, but they were also more likely to espouse conspiratorial worldviews in general (r = .27, 95% CI: .24, .30). Importantly, extreme conservatives were significantly more likely to engage in conspiratorial thinking than extreme liberals (Hedges' g = .77, SE = .07, p < .001). The relationship between ideology and conspiratorial thinking was mediated by a strong distrust of officialdom and paranoid ideation, both of which were higher among conservatives, consistent with Hofstadter's account of the paranoid style in American politics.

https://onlinelibrary.wiley.com/doi/full/10.1111/pops.12681