The comment I'll post here is applicable to the other stories I looked at this morning (namely T1602 and T1604).

Your description of the story (as... I can... in order to...) tends to be a bit too focused on the GUI still.
It shows in your usage of "looking" almost everywhere, it tends to in fact duplicate in some way the given part of your scenario. You should try to avoid that in my opinion. I would try to describe the user himself, not through a state of the application (what he sees). For instance in Zanshin depending which US we're looking at we're using "As a leader", "As someone collecting tasks", "As an organized person", etc. Depends what we want to convey from our user. If you got personas you can refer to it's even better (if you don't understand that last sentence feel free to ignore it), I think Thomas and Heiko provided some but I'm unsure.
Your "in order" part tends to be tautological still. You motivate the search by the search itself ("I can write a query in order to search" is equivalent to "I can search in order to search" in my opinion). This part should be more about the added value to the user, why does he conduct the action? What is his motive? No one searches for the sake of it, they have a real motive behind the act. Why is it important that the search is in natural language? Is the motive different depending on the criteria of the search? I probably have a different motive if I search by sender or if I search by date or if I accumulate criteria (yes, I also suspect it could be more than one story that one).

On top of that there's something odd about T1601 and T1604, their scenarios both end up with the results appearing. One is a special case of the other? They should be merged? One is badly worded?

Kevin is right: This is a common mistake that I see very often in user stories (even in industry projects): People are told to write a story from a user's perspective, so they just start with "As a user" but then still write their story purely from an application/feature perspective.

See the stories that Heiko and I originally wrote: They all use an actual persona (taken from https://techbase.kde.org/Projects/Usability/Principles/KDE4_Personas ) with actual motives.

The reason why stories should be really written from a user's perspective is that you might notice during design or development that your original ideas don't work out, but if you know why the user wants something, you might come up with an alternative with which the user could still reach their real-world goal.