{"label":"689.2.a.f","letter":"f","dim":18,"charpoly":["-261538730199","-948764433015","1018606803678","356793961763","-337180309360","-61393728369","46765949293","5943203460","-3441005218","-336976478","145234150","11028396","-3576555","-196399","50080","1681","-362","-5","1"],"traces":["18","2","1","26","1","5","19","0","19","-7","9","-9","18","-1","27","38","-1","17","24","-19","-8","-7","0","-9","27","2","-8","41","13","9","38","2","-13","31","-30","33","18","-10","1","-43","1","22","0","33","-31","-6","17","-77","35","-25","9","26","-18","24","23","31","6","1","28","93","0","-22","28","54","1","-81","48","17","-4","6","22","-13","23","-64","-39","12","0","5","53","-29","58","-19","2","-94","-9","34","-52","-47","-22","-1","19","-60","-22","19","6","-67","16","-39","23","5","-54","-103","33","0","-37","-2","-4","-88","27","-89","40","101","-1","-78","52","15","19","-76","12","25","23","-32","36","38","6","-106","7","-36","18","-7","-26","-23","-16","-16","39","61","-47","-12","-12","-202","-72","-22","9","-99","-8","11","-34","46","-2","-79","128","-146","-101","-114","32","-9","-14","9","-1","-91","-38","-64","63","39","28","28","-52","-42","18","-155","6","-116","-70","70","56","23","-6","-78","1","-285","40","-1","10","-34","42","56","65","-17","-27","-22","37","-117","-71","-52","27","89","-52","65","34","65","40","20","31","-85","-66","-71","20","38","-82","43","28","-26","-46","-2","26","98","10","77","-6","-11","-1","-90","91","83","-41","49","45","38","10","-92","-37","-67","18","17","-18","56","-28","80","66","205","56","105","-88","36","-104","106","24","-98","-26","-176","-29","178","48","-3","80","94","-52","-178","42","-19","48","6","5","-37","-1","118","8","92","41","3","123","185","-8","69","5","60","24","-106","158","68","-22","-78","-109","-86","32","-7","7","125","75","156","24","85","10","46","56","32","-93","30","0","-197","-36","84","-46","156","72","119","84","-108","-68","-126","14","-9","-74","100","-115","255","-26","-5","118","-47","62","60","6","254","27","-165","118","-147","-87","218","136","146","-28","-90","52","-332","4","2","-115","-71","24","198","62","98","-26","74","10","-72","-58","276","-8","-43","-91","120","-12","18","91","31","-28","-57","2","62","-25","41","-94","-12","-32","-144","-74","-24","-19","114","22","67","21","99","13","43","4","78","-136","45","78","-265","-9","75","-18","-52","10","9","-36","-79","4","78","20","69","11","216","194","201","-110","152","38","-50","-134","-259","78","-175","32","12","33","-81","-84","-96","68","2","-180","-130","-21","269","65","84","-60","0","-51","240","96","-40","-13","122","104","-80","-27","68","15","117","-8","-74","190","-133","70","31","-127","88","-94","5","-6","237","-12","143","-40","25","-200","45","-30","-14","-94","60","-55","212","-48","-137","130","-61","-70","-140","24","33","-104","2","4","-80","-22","-100","38","234","-19","-66","-40","289","18","30","46","-19","-170","274","167","-236","39","-282","-11","182","-62","-10","-176","-30","18","-112","62","16","158","45","-25","34","-6","64","1","105","-61","260","29","122","16","38","-30","118","-68","-166","292","-43","-4","-112","-106","58","-229","291","-130","53","-30","7","-66","76","1","-110","124","24","-87","-19","54","55","16","-29","-60","-41","-22","22","-20","-279","-90","-9","-94","136","99","10","-54","24","-86","-24","0","-438","-172","-66","-139","58","21","41","46","-374","-60","-46","-21","33","-160","51","104","-127","-56","-173","-45","-22","96","274","-9","155","-31","186","37","-58","72","22","62","110","-98","-225","-51","-130","36","-6","-40","-459","-102","34","20","136","19","22","88","-114","-133","166","17","-143","-127","-92","-151","148","-117","-346","41","72","-184","68","-44","-77","-48","-54","-100","-154","-200","-73","262","101","-14","106","-92","9","35","170","234","-283","-44","380","59","-474","-64","-142","-38","-300","-96","-25","-86","243","-49","-154","-128","-5","-76","-183","-121","196","-104","232","9","120","-156","182","-108","48","-257","36","-80","-214","-155","-20","-19","26","-126","-169","114","-87","-194","-142","-33","-298","-39","88","222","-296","-18","-196","-24","58","-215","138","120","280","-86","-20","-124","-170","130","24","-48","209","-9","-13","-182","26","50","190","144","-130","20","-139","23","243","72","-186","-141","-229","29","-98","-76","-204","-98","-115","-58","31","-89","-150","-66","78","-80","-136","-101","-2","76","262","116","78","6","1","36","144","20","58","102","131","110","167","132","135","139","1","-102","-105","3","-22","-122","-238","-27","152","-101","219","-58","28","28","-145","27","99","-60","-3","35","-122","38","-176","-200","-102","64","93","72","136","-211","229","-80","172","74","-208","53","-268","-16","273","0","-15","-27","-94","84","120","144","427","204","-64","-148","56","-108","-22","-4","-104","60","360","9","3","41","-152","97","-193","136","30","28","6","-89","441","82","1","-48","42","-28","-60","-116","-230","128","54","40","384","-14","102","-122","-53","-67","309","-125","61","12","140","1","338","-6","-38","-13","357","-24","-158","-31","66","140","-238","5","-81","-64","290","63","228","85","-72","118","-183","-175","-130","-28","-89","48","137","16","76","-149","156","-16","-148","-82","-223","-152","148","-131","17","108","-97","-59","-178","-97","312","118","387","100","-184","-31","-9","-4","-70","104","117","1","134","242","39","0","154","62","91","-114","6","82","-2","56","104","-164","154","178","-343","49","16","78","-234","22","-167","212","290","-36","-115","172","-312","10","298","-28","-96","-66","-13","35","-228","88","54","0","-304","82","16","300","86","-72","4","23","82","170","80","-133","-17","-38","42","43","-210","190","441","158","-64","58","-108","-21","384","-9","39","50","156","22","-132","70","-57","-39","312","111","185","-66","-30","-60","203","63","90","-166","-76","-63","12","88","66","316","-26","54","-432","-138","-114","77","316","354","-576"],"lmfdb":"agrees","space":"689.2.a","level":689,"weight":2,"T":[[2,1],[3,3]],"status":"proven","derived":{"al":[[13,-1],[53,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0},"url":"https://sagebrush.space/atlas/mf/689.2.a.f"}