The manga I am trying to remember I believe is sci-fi or supernatural and focused on battle. The main character goes to a school where everyone has these spirit-animal type familiars they can call out and do battle with. I think they are supposed to be the result of gathering data from an alien artifact or something. The MC has never battles in his time at the school and we don't know what his familiar it is at the start. He is at the bottom of his class as a result of not participating in battles/tests. I remember he ends up being forced to battle the class rep; she has two wolves as her familiars and is ranked at 101 in the school. When the main character summons his familiar it is a humanoid wearing a tiger suit sort of like a sporting mascot character. Needless to say main character is victorious and he gains a lot of attention from having a rare humanoid type making him the target of others at the school.
That's basically the gist of what I remember. Additionally later in the story the MC fights a guy who had a spider familiar with mind control powers who manipulates his "sister"/"friend"; I cant remember which.
Any help would be appreciated. Thank you.