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I'm making my own Inquisitor Coteaz and I'm unsure what base sizes to use.
Going by what bases are listed in the battle force box it states seven 40mm bases.
I'm guessing five for the Terminators and the last two for Coteaz and his eagle?
Does anyone know for sure? Thanks.

As I think you already identified:

This set comprises 332 plastic components, and is supplied with 1x Citadel 32mm Round Slotta Base, 7x Citadel 40mm Round Bases, 3x Citadel 32mm Round Bases, and 12x Citadel 25mm Round Bases.

I have the priest model (formerly 'Pious Vorne') and her base is 32mm with a slot in it. I also have the henchmen kit. A single kit contains one 32mm base (for the servitor) and six 24mm bases (for five dudes plus a tome skull). There are two such kits so you have double that. The chimera obviously doesn't have a base.

This accounts for everything except the seven 40 mm bases and a single 32mm base. The Culexus assassin kit on the GW Webstore says that it comes with a 32mm base and the Grey Knight terminator squad says that it comes with five 40mm bases. This leaves two 40mm bases, which must be used for Coteaz and his eagle. All of this seems to match with the image for the Ordo Malleus set.

So I don't know for sure, but based on my deduction I don't see how it can be any other way. Both Coteaz and the eagle have 40mm bases

Thanks. I used process of elimination too.
I'm pretty sure it is 40mm. If not, it's not the end of the world to re-base them.

Definitely 40mm Bases:
https://www.reddit.com/r/WarhammerInstructions/comments/1eqg8ee/coteaz_instructions/#lightbox

Thanks for that conformation.

The eagle doesn't really matter its a token so there's no advantage/disadvantage if you wish to model differently

OK, I did wonder how the Eagle was actually used.
I thought that it might be able to fly out to the terrain in was to uncover or whether it counted as a retinue and might give an extra wound to Coteaz.

He sends the eagle to flap around an enemy squad. They are so busy trying to shoo it away that they forget that they can hide behind rocks to stop bullets. The token is just there to remind you which squad is affected.