The 
Eigenburst is a Pearlescent 
Tediore Shotgun.
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How to Unlock the Pearlescent Eigenburst Tediore Shotgun
Weapons
Legendary Loot
Overview
How to Get
Unlock Location + Farm Method:
The Eigenburst is available from the Ordonite Processor event scattered around Kairos introduced in Bounty Pack 2, The Legend of the Stone Demon.
To complete this event:
- Kill enemies until a cannister spawns
- Inserted the cannister into a drill at the center to progress the event
- Eventually, Ordonite empowered enemies spawn that can drop this weapon.
Notes
- This, alongside the Conflux Sniper Rifle and the Hand Cannon Pistol were the first Pearlescent weapons introduced to Borderlands 4.
- You do not need to own The Legend of the Stone Demon to get access to the events that drop this weapon.