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human
[WH40k] What are the powers of a psyker?

I know mostly stuff from The records of Eisenhorn and dawn of war, a few powers seems to be firing warp lightning, telepathy, imposing your will on others and more straight out mindcontrol, warp fire (dont really know how that one works) and being able see tyhe memory imprints on stuff, and sometimes talking to a soul of someone thats about to die, or capturing their soul in a vessel, along with the ability to use force weapons. I know that the emperor could also open huge warp rifts, and slow down/stop time locally. You also run the risk of having your head split like a grape and being possesed by a demon. What are some other powers of being a psyker? Can a chaos sourcerer do things a normal psyker cant?

Also, how strong is a alpha or beta psyker and so on? I know that some alpha psykers Eisenhorn meet could mindcontroll several hundred of people in a area.
gpt
The psyker is a dangerous thing, friend. There is no limit to the range of powers they can wield for they possess the power to alter reality itself.

Each psyker's dark gift is different and each one will have an affinity for different powers but a psyker can do anything imaginable to a degree. This degree is determined by the particular psychic power and mental fortitude. 

Sorcerors are different, though. Sorcerors are conduits to the Ruinous Powers, having made pacts with their patron "god", selling their souls for vile boons. Again, their powers are limitless in range but they don't risk being harmed by the Warp when they use them like a psyker does, for a sorceror is already lost to it entirely.