Eulerex

Eulerex is a Fallen. He leads the "moderate faction".

Appearance
He has the appearance of a giant owl. He can take on a humanoid form with an owl head.

Personality
Eulerex is a very cold fallen who cares nothing for others, wishing only to fight the races. He is a strategic thinker who's always composed, examining any situation calmly.

He is willing to kill anyone who gets in his way or disrupt your plans, including fallen and Demon kings, as he did not hesitate to attack Krebskulm and Edelgard, when he learned that he did not want war.

He is willing to sacrifice fallen, how many required, if that is what it takes to achieve the objective. He is quite selfish, as his desire to annihilate the races is above all for him.

when someone is threatening his position in charge of the Demon King Army, he will quickly plot his destruction, as he let members of the Vahl faction be sacrificed for Modinalam's 《Ruination Flame》, or when he sent Ryoka alone against the hero of Faltra City, with the intention that she dies and arouses the blood thirst of Modinalam.

While the fallen see the Demon King as a being to be worshiped, he sees them as another weapon for the destruction of races.

Volume 3
He went to meet Krebskulm to feast on the revival and to ask him to increase the number of demonic beasts, when Krebskulm refuses for the sake of the biscuits, he decides that Krebskulm should be put to revive again.

Volume 9
He leads an army of 1,000 fallen to Faltra City, and sacrifices the Vahl faction for considering them a problem difficult to control.

Abilities
He was a Brawling Sorcerer/《Punching/Hitting Magician》, he easily dominated Edelgard, even though she had received the power of Krebskulm. He was quick to notice the Magic Reflection from Diablo. Edelgard praised him as fallen but strong, and his faction as the strongest.

He is also an excellent commander, as he leads the strongest faction of the fallen, but he had the flaw of being overconfident, as he had an invincible army, the barrier of Faltra City had been eliminated, and victory was guaranteed.

Martial Arts

Unknown bare-fist《Martial Art》: It’s a powerful and large 《Martial Art》. Gathering strength in the fist. The SP was emitting a phosphorescence. Then being clad in Purple lightning, rush and punch at the target. Blowing them away and causing Purple lightning to course through the target.

Spells
《Quartz Lance》: a Earth Type spell;  a translucent crystal turned into a sharp lance and sprung forth towards the opponent.

Krebskulm
He had hoped for her to lead the Demonic Beings to destroy the races but when she refused because of wanting biscuits he doesn't mind to kill her so she can "properly resurrect".

Edelgard
He sees her as a foolish child, by choosing to stand beside a useless Demon King.

Ryoka
He saw her as a threat to his position, given his talent and the fact that fallen from the extinct faction Edelgard, was at her side.

Quotes

 * (to Krebskulm)I am the Demonic Being Eulerex. An old Demonic Being that serves the many generations of Demon King-samas.
 * (to Edelgard)What is the meaning of this? This is the first time a Demon King-sama has not wanted to kill the Races. Bestowing Demonic Beings power, increasing Demonic Beasts, and giving the order to eradicate the Races should be the correct Demon King-sama……Are you really telling me that this is the Demon King-sama?
 * (to Edelgard)Thou art young. Therefore, you are unable to understand the importance of this. The Demon King must be the king of the fallen, and the fallen are things that kill the Races. They are creatures that destroy. They are creatures that pollute the land. And so, Demon King-sama’s soul is confined--As long as this Krebskrem-sama exists, it means that the proper Krebskrem-sama will not be revived.

Triva

 * The anime version of his larger form (especially the face) looks nothing like an anthropomorphized owl.