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1: Speak with the NG Manager on the left side as you enter the Arcology Air Terminals from Arcology 108. If you decide to support the Queequeg promotion, you'll pay the manager 500 credits and receive weapon mods. If you choose Peequod's, pay 500 and get a BIOMOD CANISTER. I'd recommend Peequod's. After securing the deal, head back downstairs to Peequod's to get your reward, which I put into upgrading Biotox Attack Drone. If you chose Queequeg's, wait until a little later when you go back down to Medina.
2: Come back to Arcology Air and take the ramp down to the receptionist's desk, where she's getting grilled by a WTO Tax Auditor. Talk with the Auditor to learn the templars' shipment figures aren't computing properly, and to get an assignment to find out why, in Hangar 24. Now tell the receptionist you have a "friend in common" (from the Omar quest) and she'll give you the keycode to Hangar Bay 24. Take the hallway behind the receptionist to a Templar Only restricted area, and take the first right to some stacked crates and a vent. Take the vent to a ladder, climb it, and head left to some lockers. Open the left locker and read the datacube for the storage room safe code you're going to want later (though multitools work as well). The right locker holds a Refire Rate Weapon Mod. Backtrack down the ladder and through the vent, then continue to the Hangar Bay 24 door.
3: There are two hostile Templar Paladins roaming about on the ground, and one giant military bot. I'd suggest sending in your Spy Drone to deal with them from afar. However, they can be easily subdued by almost any other method, including the Mag Rail. When they're taken care of, notice the control booth on the top right side of the room. Climb halfway up the ladder on the right side of the booth, then Cloak and go the rest of the way up. Quickly get around the corner into the room (as there is a turret at the top) and deal with the only other Templar in Hangar 24. I'd suggest switching your Biotox Attack Drone while cloaked.
4: When it's clear up in the control booth, view the holocomm to get the storage room keycode and a message from Lin-May Chen to assassinate Leila Nassif when you find her. Descend the ladder and look for the chest along the back wall of the Hangar near the machine. Inside it is the datacube with the armor plans that the Omar Trader wants. Head to the storage room door in this same room. Open but do not enter, it's radioactive. If you happen to have the hazard drone, activate it, but otherwise, descend the ramp and head straight for the safe on the back wall. Open it using the code you got from the locker through the vent, take the items and read the datacube for the codes to the Nanoformer Station, to release counter nanites to purify the air.
5: Quickly make your way back out of the radioactive room, and back to the vent behind the crates. For an extra energy cell, head right and move some crates. Before the lockers where you got the safe code, take a right overlooking Hangar Bay 23 and go into the Chairman's office. When you open up conversation, you can bribe him for 750 credits using your first dialogue choice. Return toward the receptionist's area downstairs and for a quick repair bot, head left into Hangar 23. There are a few items here, but nothing of consequence: free multitool and other lesser items in a chest in a storage room.
6: Return to the Tax Auditor and tell her about their transport of Powered Armor. Exit Arcology Air, take a left after the elevator and proceed to the ApostleCorp Corporate Suites, currently being marauded by Templars... so beware.