## [Numerical] Computing a contour of an integral function

Suppose I want to compute all complex points z such that,

$$\int_{z^*}^z F(t) dt = 0$$

Here $$z^*$$ is a given constant. In general, the points z which satisfy that relation form a continuous curve beginning from the initial point.

What is the best way to tackle this numerically? I'm sure it's a fairly standard numerical problem. Unfortunately, I'm just not sure where to look (in the literature).
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