For the partial theta function θ(q,x), real zeros lie left of a vertical line Re x = -a (a≥5) while complex zeros lie right of it, with no real zeros ≥-6 for q>0 and similar bounds for q<0.
Kostov, On the double zeros of a partial theta function, Bull
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Some analytic properties of the partial theta function
For the partial theta function θ(q,x), real zeros lie left of a vertical line Re x = -a (a≥5) while complex zeros lie right of it, with no real zeros ≥-6 for q>0 and similar bounds for q<0.