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Further on we asked the Queen if she has a sigil, she said it's the Quadriform posted in the OP.
I have never earlier had any interest in these well known "classic" demons. Their sigils seem mostly void of energy on the surface and their descriptions aren't very attractive. Most people said to be working with them also do it for retarded reasons, like above mentioned fame.
After the experience with Adremelech however, my view changed a little bit. His hall isn't clean in the least but it's large and he's very powerful. They just don't care an awful lot about the finer details down at his place. He can get things done and his energy is still a strong red along with some very persistent virtue, despite what the general descriptions say.
At a later session, the Queen recommended we contact Beelzebub. Some quick research revealed that he's the same as Baal ze bub, lord of the flies or simply lord of the flying, another possible mistranslation. When people talk of Baal, they refer to him as well. He has been very cooperative since.