{"label":"539.2.a.k","letter":"k","dim":4,"charpoly":["634912","21608","-4471","-2","1"],"traces":["4","2","0","10","0","0","0","18","2","0","-4","0","0","0","-10","6","0","18","0","0","0","-2","-14","0","26","0","0","0","8","-56","0","18","0","0","0","22","26","0","32","0","0","0","-8","-10","0","-24","0","0","0","30","4","0","-8","0","0","0","-28","4","0","-76","0","0","0","14","16","0","6","0","0","0","-26","26","0","-4","0","0","0","16","36","0","-24","0","0","0","36","-72","0","-18","0","0","0","-52","6","0","20","0","0","0","-2","82","0","-32","0","0","0","-4","12","0","28","0","0","0","-18","-48","0","20","0","0","0","-96","4","0","4","0","0","0","-36","-46","0","-128","0","0","0","-48","-26","0","-26","0","0","0","4","72","0","54","0","0","0","48","24","0","20","0","0","0","-82","80","0","-16","0","0","0","-46","-32","0","10","0","0","0","60","-16","0","-88","0","0","0","-6","70","0","-22","0","0","0","44","-80","0","88","0","0","0","112","-6","0","-40","0","0","0","16","-18","0","134","0","0","0","-24","36","0","-24","0","0","0","36","-20","0","40","0","0","0","116","12","0","48","0","0","0","30","76","0","-104","0","0","0","36","16","0","36","0","0","0","8","-168","0","2","0","0","0","-32","-64","0","-8","0","0","0","14","16","0","-34","0","0","0","-96","4","0","44","0","0","0","-102","-36","0","72","0","0","0","4","-26","0","12","0","0","0","36","-32","0","20","0","0","0","26","-28","0","94","0","0","0","-50","100","0","12","0","0","0","112","-40","0","-148","0","0","0","60","-24","0","144","0","0","0","56","-34","0","-8","0","0","0","-8","-94","0","120","0","0","0","56","-10","0","-4","0","0","0","56","-106","0","56","0","0","0","-104","86","0","12","0","0","0","-80","-18","0","120","0","0","0","-96","8","0","-20","0","0","0","108","192","0","-72","0","0","0","100","-20","0","-66","0","0","0","90","152","0","-88","0","0","0","-156","-72","0","-54","0","0","0","-20","76","0","-22","0","0","0","90","8","0","-64","0","0","0","-26","-16","0","-16","0","0","0","-80","-72","0","-28","0","0","0","48","120","0","-36","0","0","0","64","-32","0","-16","0","0","0","-20","172","0","-96","0","0","0","-112","-70","0","34","0","0","0","-18","134","0","40","0","0","0","-160","36","0","-44","0","0","0","30","12","0","76","0","0","0","-16","-46","0","8","0","0","0","-4","-64","0","-96","0","0","0","10","-106","0","50","0","0","0","-28","-24","0","-32","0","0","0","64","-48","0","4","0","0","0","-88","24","0","-56","0","0","0","-78","36","0","-4","0","0","0","-80","-64","0","36","0","0","0","-80","-76","0","-26","0","0","0","48","-136","0","-24","0","0","0","20","148","0","-74","0","0","0","40","-48","0","-30","0","0","0","-164","-14","0","0","0","0","0","-4","188","0","-24","0","0","0","-32","96","0","72","0","0","0","-108","-10","0","-82","0","0","0","200","8","0","-128","0","0","0","-12","-280","0","-12","0","0","0","60","-108","0","-128","0","0","0","-48","152","0","48","0","0","0","-176","48","0","84","0","0","0","-48","64","0","-188","0","0","0","48","-44","0","28","0","0","0","38","128","0","68","0","0","0","-4","72","0","26","0","0","0","224","64","0","-142","0","0","0","56","-66","0","92","0","0","0","-28","76","0","80","0","0","0","100","-28","0","-46","0","0","0","-20","28","0","14","0","0","0","128","-112","0","-16","0","0","0","-38","-216","0","264","0","0","0","40","20","0","40","0","0","0","92","96","0","-14","0","0","0","260","78","0","-16","0","0","0","-16","-140","0","-64","0","0","0","58","8","0","52","0","0","0","8","-48","0","280","0","0","0","-80","-6","0","28","0","0","0","152","112","0","92","0","0","0","-152","6","0","-142","0","0","0","40","96","0","192","0","0","0","-100","-16","0","160","0","0","0","-96","-236","0","-104","0","0","0","-180","-8","0","26","0","0","0","-6","-112","0","108","0","0","0","-26","-16","0","20","0","0","0","40","134","0","-132","0","0","0","240","88","0","-152","0","0","0","-64","4","0","-96","0","0","0","56","-16","0","46","0","0","0","-8","-128","0","32","0","0","0","-48","-236","0","70","0","0","0","-100","92","0","192","0","0","0","-12","112","0","-74","0","0","0","112","88","0","-16","0","0","0","-144","56","0","96","0","0","0","-36","-112","0","228","0","0","0","-72","56","0","116","0","0","0","-128","-16","0","16","0","0","0","408","24","0","-8","0","0","0","-112","-196","0","194","0","0","0","4","14","0","56","0","0","0","-80","-144","0","-220","0","0","0","80","-184","0","-56","0","0","0","152","-104","0","36","0","0","0","108","132","0","-36","0","0","0","62","56","0","-40","0","0","0","72","82","0","144","0","0","0","60","-36","0","-48","0","0","0","16","34","0","40","0","0","0","-36","18","0","-376","0","0","0","8","208","0","-14","0","0","0","116","88","0","-16","0","0","0","-160","96","0","-48","0","0","0","116","48","0","-24","0","0"],"lmfdb":"agrees","space":"539.2.a","level":539,"weight":2,"T":[[2,1],[3,3],[5,5],[13,7]],"status":"proven","derived":{"al":[[7,null],[11,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0},"url":"https://sagebrush.space/atlas/mf/539.2.a.k"}