{"label":"231.2.a","level":231,"weight":2,"dims":{"new":11,"cusp":29,"eisenstein":7,"modsym":65},"old":[[11,1,4],[21,1,2],[33,1,2],[77,5,2]],"T":[[2,1],[5,3],[17,5],[19,7],[23,9]],"status":"proven","checks":["dim M^+ at levels [1, 3, 7, 11, 21, 33, 77, 231]: [0, 1, 1, 2, 4, 6, 10, 36] (certified at ell = 2147482951)","T = [(2, 1), (5, 3), (17, 5), (19, 7), (23, 9)]; h of degree 11 = 1 x 11 (phi(ord eps) x dim S_k^new); 3 primes, 0 rejected"],"newforms":[{"label":"231.2.a.a","letter":"a","dim":1,"charpoly":["-31","1"],"traces":["1","-1","-1","-1","-2","1","1","3","1","2","-1","1","6","-1","2","-1","2","-1","4","2","-1","1","0","-3","-1","-6","-1","-1","-2","-2","8","-5","1","-2","-2","-1","6","-4","-6","-6","10","1","-4","1","-2","0","-8","1","1","1","-2","-6","6","1","2","3","-4","2","4","-2","-10","-8","1","7","-12","-1","-12","-2","0","2","0","3","2","-6","1","-4","-1","6","16","2","1","-10","4","1","-4","4","2","-3","18","2","6","0","-8","8","-8","5","2","-1","-1","1","6","2","0","18","2","-6","-12","1","-2","-2","-6","-1","18","4","0","2","6","-4","2","6","1","10","-10","-8","12","-1","-16","3","4","12","4","-1","4","12","2","6","-6","0","-20","2","8","0","-6","-1","4","-2","-1","-6","-10","-1","8","12","2","1","-16","6","-2","-16","-6","10","0","-1","-12","-10","-2","-4","-8","-3","23","4","4","4","14","-2","-1","1","-4","-18","12","2","-10","-6","10","0","-12","8","-2","8","-1","8","-24","-7","2","-2","12","-1","-26","1","16","-3","12","-6","-2","2","-20","0","0","-6","-4","-2","-12","-6","0","12","8","-3","8","2","-2","-2","12","6","-24","-5","-1","-18","-12","4","-26","0","1","-6","26","-6","16","-4","-16","-2","-24","-2","26","-1","-1","10","-2","10","24","24","-4","-12","-12","-1","0","16","4","-17","-6","-4","6","12","-2","-4","0","3","-12","-4","-18","12","-10","-2","16","-2","-6","6","1","0","22","20","8","-6","10","-8","-4","0","8","6","10","-5","-13","-4","-2","-2","-10","1","-8","18","1","10","0","-1","-4","-8","-6","-4","20","-2","20","1","0","16","32","-18","-6","2","-2","-16","-18","6","2","-14","12","0","8","-1","-6","12","2","30","-8","2","28","-4","6","8","24","1","2","-23","-18","4","-8","-4","1","-12","0","-14","4","-2","-10","1","-6","5","-22","4","0","-18","-2","-12","0","-6","-3","10","-1","-6","-4","-10","-8","0","10","12","6","8","22","2","-12","-24","-12","1","28","8","16","24","8","-3","2","-2","-4","-2","6","-12","0","3","-4","26","-32","1","14","-16","-4","1","34","-12","48","-6","-2","2","-6","-6","-14","20","6","0","4","0","-8","-30","20","4","12","-2","6","12","-8","18","-2","0","-10","12","6","-8","-24","1","-30","-8","-4","2","0","2","8","6","1","-12","-12","6","-36","24","10","7","34","1","-10","-18","-8","12","-12","-12","-22","26","-2","0","-34","-1","-32","2","16","-26","12","-6","-12","-16","2","12","4","16","-4","-2","6","24","0","-10","36","-26","0","-1","-4","1","8","-30","12","2","20","10","-4","-24","2","-8","0","4","20","-12","8","12","-24","3","-12","0","-23","16","6","-4","2","11","-4","6","0","-4","8","-6","-14","-36","2","2","-4","-4","1","0","16","-1","-23","12","4","-4","60","18","24","-36","-12","10","-1","-2","-34","-16","10","-10","4","6","-12","6","-10","-1","-8","0","16","-22","12","20","-18","-8","-24","2","2","-10","-12","-8","-36","4","1","0","-22","-8","-20","6","24","-10","0","7","-14","13","-2","-4","4","2","-6","6","-12","10","36","1","32","8","26","-6","-14","-1","-4","10","-16","0","16","3","-14","4","-12","-8","-2","6","0","-20","2","-20","-48","-2","-10","-20","20","-3","-6","0","20","16","0","-32","18","6","-19","6","4","2","12","2","-8","48","12","18","32","6","6","-2","0","-6","18","-12","28","0","-8","-8","32","3","-4","6","-8","12","-18","-2","-8","-10","2","8","12","2","-10","-28","-12","12","-8","-6","0","8","24","-24","10","5","18","-2","1","-23","6","18","2","-12","12","8","36","-4","12","-1","26","4","36","0","-20","-14","-1","-4","40","6","20","10","-26","1","30","6","24","-7","-16","22","6","4","38","0","16","54","0","2","12","-12","24","0","-40","2","0","3","-26","10","2","1","32","18","1","4","-8","-10","6","8","2","0","12","-10","-44","12","-24","-6","-48","-24","20","-22","4","2","-12","12","-16","8","12","12","-16","1","-10","-28","0","-24","10","-16","-2","24","-4","-8","24","17","-22","-2","6","-2","30","4","-8","6","-6","-6","40","-12","0","0","2","-1","4","4","-12","26","0","32","18","-3","-60","-14","12","-16","6","4","-16","5","18","-34","-2","-12","0","-48","10","18","-38","2","-4","2","-16","6","24","2","-16","14","6","20","-42","-6","-40","0","-1","-4","-44","0","-50","8","-22","42","2","-20","16","4","-8","-12","0","6","-25","-6","-10","12","-46","8","1","-6","4","2","0","0","-34","10","-8","-36","10","-6","52","-8","-10","24","-40","5","-28","30","13","-8","-16","4","-72","-6","2","0","12","2","-34","-8","10","-2","42","-1","36","-12","8","12","-8","-18","-16","36","-1","24","-32","-10","-24","3","0","-34","-16","1","12","10","4","54","20","8","-20","12","6","12","40","4","-4","22","-20","26","4","2","24","0","-20","34","0","-1","-6","32","0","10","-54","-16","4","-26","-32","-12","4","18","50","12","6","-16","14","-2","0","-4","2","-4","-36","16","12","4","18","6","-22","-6","48","24","-2","0","-6","14","33","-36","-12","-26","-4","0","8","3","-8","4","-12","1","-20","-8","6","10","-30","-12","-18","2","-2","-20","-16","-30","52","4","8","-24","0","-2","-32","-40","-28","0","-32","4","46","-20","-6","36"],"lmfdb":"agrees","curve":{"cremona":"231a1","lmfdb":"231.a","ainvs":[1,1,1,-34,62],"rank":0,"torsion":4},"derived":{"al":[[3,1],[7,-1],[11,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"231.2.a.b","letter":"b","dim":2,"charpoly":["-2315","-1","1"],"traces":["2","-1","-2","7","6","1","2","-12","2","-3","-2","-7","2","-1","-6","13","6","-1","-4","21","-2","1","-2","12","8","-1","-2","7","2","3","-2","-35","2","18","6","7","2","-19","-2","-36","-4","1","-6","-7","6","-20","12","-13","2","-4","-6","7","-10","1","-6","-12","4","-43","0","-21","20","22","2","44","6","-1","8","0","2","-3","4","-12","14","-1","-8","7","-2","1","-4","39","2","-40","-14","-7","18","24","-2","12","0","-3","2","14","2","-27","-12","35","-14","-1","-2","28","14","-18","16","-12","-6","-16","-16","-7","-2","3","-2","13","0","19","-6","49","2","21","6","36","2","-10","4","-28","-6","-1","-14","-57","6","-3","-32","7","-4","17","-6","6","-14","20","4","21","-12","40","-2","13","6","-7","-2","7","-6","4","-2","-18","6","1","-6","-7","20","44","10","-105","-2","-1","8","28","6","-14","18","12","-24","54","-4","-42","4","43","8","-13","0","42","-8","21","-2","-1","-20","-30","6","-22","-6","63","-2","-57","14","-44","-14","28","-6","7","-8","1","-10","-48","-8","14","2","0","-12","-50","-2","13","4","3","-8","-14","-4","-13","-18","12","-2","22","-14","-21","6","1","12","-35","8","42","-44","-7","-26","-60","2","-96","-28","-1","36","-21","4","18","24","-39","-2","-1","-2","70","6","40","-4","54","14","3","24","7","2","-14","-18","119","38","-24","2","21","2","16","0","-12","-30","-19","0","7","20","3","20","-66","-2","-14","-8","-14","-20","40","-2","-36","-18","27","28","-28","12","1","-4","-35","26","-129","14","49","0","1","0","-12","2","45","-2","-28","-6","22","-14","79","60","18","0","-7","-16","66","-8","12","30","32","6","-56","-54","16","-2","132","16","-20","-54","7","8","17","2","-60","12","-3","12","-28","2","-72","24","-13","26","12","0","0","2","-19","2","78","6","-44","16","-49","-30","-4","-2","35","30","-21","12","-42","-6","88","-36","-36","12","-20","-2","7","42","10","44","92","-4","-3","-10","28","-42","-18","6","-114","2","1","-16","21","14","14","-16","57","-6","28","-6","-70","-16","3","-48","-12","32","46","-12","-7","-54","-16","4","52","18","-17","-2","28","6","-43","-2","-6","-20","-120","14","98","0","-20","-42","-35","-4","19","-4","-21","6","-38","12","18","24","-40","20","-35","2","72","8","-13","-4","22","-6","-28","46","7","44","36","2","18","-28","-7","0","-6","6","44","0","-4","4","-42","2","22","6","18","6","76","-6","42","0","-1","8","223","6","14","-68","7","8","-81","-20","42","6","-44","-16","0","-10","9","-22","105","2","-41","2","7","-42","1","-16","-120","-8","-3","0","-28","-78","-19","-6","-118","4","14","56","-21","-18","-33","26","-12","42","20","24","-28","12","-54","14","-124","4","-19","48","42","-12","-1","-4","-36","50","-43","40","-112","-8","-105","36","13","-2","-48","0","7","-4","-42","-48","-6","8","-10","-2","-21","0","-31","2","0","-6","1","16","-28","20","4","80","30","-4","-32","-6","-28","-18","22","-6","39","6","-75","-66","-63","0","49","2","60","20","57","76","-7","-14","-40","-8","44","2","113","14","147","-14","-28","10","-84","6","0","48","-7","-38","63","8","13","32","-1","18","-63","10","-20","-4","48","-6","24","8","-28","6","-14","-16","-35","-2","-30","12","0","-26","0","12","12","24","50","6","-84","2","88","0","-13","-58","6","-4","28","6","-3","28","108","8","48","-42","14","2","43","4","-171","78","13","-6","14","18","-78","24","-12","0","-4","2","7","-24","-22","-96","184","14","-27","-48","21","-14","-48","-6","42","-12","-1","82","126","-12","51","-20","35","50","8","-8","-84","-72","-42","-14","18","44","-22","-2","7","-42","-1","26","-144","-10","60","20","56","-2","76","12","96","-96","15","28","28","20","1","-4","-44","-36","27","14","21","-18","120","-4","84","-40","-18","-6","-112","-24","60","36","39","16","78","2","14","8","1","14","-12","2","-21","24","-70","-68","-22","-6","-70","-8","-40","-18","21","4","-16","-24","-54","-18","-42","-14","0","-16","-3","28","183","-24","-43","-6","-7","18","-13","-2","-54","48","14","-2","28","18","92","0","-119","-42","3","-38","-70","-6","24","-8","126","-2","-76","92","-21","-4","-60","-2","13","60","-16","68","-70","0","132","0","12","20","6","30","-14","-50","19","-6","-140","0","96","-14","-7","-6","22","-20","-42","-18","-3","-32","49","-20","1","24","66","-30","94","2","84","-94","14","-52","-180","8","21","-28","14","-80","-42","20","44","6","-40","54","-7","2","23","60","36","112","-171","18","14","-72","-27","2","40","-28","72","-2","28","16","-10","-12","54","-52","-1","24","-126","4","59","38","35","12","-40","-26","-28","4","129","8","54","-14","40","-6","-49","-36","-43","0","-39","-2","-1","-84","0","0","-28","50","12","-14","126","-2","42","18","-45","-24","-57","2","-84","-86","28","-72","40","6","84","-6","-22","48","-154","14","-3","48","-79","14","-108","-60","-154","-32","-18","-62","-90","0","84","4","7","8","17","16","-245","-6","-66","-4","-98","8","13","-18","-12","20","17","-30","189","52","-32","88","-105","-6","-24","72","56","14","-76","54","6","-38","-16","42","63","2","-10","-14","-132","-18","-1","-16","35","-42","20","-8","-12","54","84","-16","-7","4","92","-8","130","74","-17","0","21","-2","-105","-28","60","-24","-66","-12","7","-36","3","-68","140","-12","40","-30","28","-52","35","-2","36"],"lmfdb":"agrees","derived":{"al":[[3,1],[7,-1],[11,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"231.2.a.c","letter":"c","dim":2,"charpoly":["-461","-19","1"],"traces":["2","1","2","-1","2","1","2","0","2","1","2","-1","-2","1","2","-3","6","1","0","-1","2","1","-2","0","-8","-11","2","-1","10","1","-6","-9","2","-2","2","-1","-14","15","-2","0","4","1","-2","-1","2","-16","-4","-3","2","-4","6","-9","-2","1","2","0","0","5","0","-1","4","2","2","4","-2","1","-24","-8","-2","1","4","0","18","-7","-8","15","2","-11","-20","-3","2","12","18","-1","6","-16","10","0","0","1","-2","-14","-6","-7","0","-9","6","1","2","4","14","-2","8","20","2","24","-4","-1","10","1","-14","-3","8","15","-2","-5","-2","25","6","0","2","2","4","8","-18","1","6","25","-2","-11","-16","-1","0","-17","2","10","26","-16","20","-1","-4","12","-2","-3","10","19","2","7","10","-4","-6","-30","6","1","-6","-9","-4","0","-2","-9","-2","1","-32","8","2","14","-14","0","16","-2","0","-14","-12","5","-8","-3","0","10","0","-1","-6","-11","4","30","-14","2","6","-3","2","15","-26","4","-2","-12","-2","-1","-24","1","-30","0","-24","-18","10","-8","4","-26","-2","33","0","1","-16","26","4","3","-2","0","-6","10","18","-1","14","-7","-12","-9","-8","14","-4","15","10","-16","2","0","-12","-11","-4","25","-20","-2","-20","-3","34","1","2","-2","2","12","-60","-10","18","-9","-16","-1","-2","38","6","7","-14","-16","-14","-9","10","-28","-12","0","-2","15","0","7","20","1","24","6","-2","-2","-8","-14","-4","0","-6","0","14","-7","-32","8","0","-11","4","-9","-6","5","6","1","-32","1","0","0","2","5","62","4","-2","22","14","-45","4","-2","-24","-1","8","2","-16","20","18","28","2","20","26","24","10","4","-4","-16","-30","-1","8","-1","10","-20","-4","1","4","-4","-14","28","-24","-3","6","28","8","-8","-6","15","2","30","-2","-16","56","-5","30","-4","-2","-9","58","25","4","10","6","-20","20","0","52","-8","2","-9","18","2","-4","48","4","-7","-2","8","-22","-2","-18","10","-10","1","-40","15","6","-18","48","25","2","-36","-2","-18","40","-11","24","0","-16","-2","-20","-1","6","-40","0","12","-46","-17","-14","-32","2","5","-14","10","60","12","26","-34","0","-16","18","-1","20","15","20","-1","-26","-38","-4","-50","-24","12","4","7","-2","-16","4","-3","-12","2","10","0","-90","19","0","0","2","-18","28","7","0","-6","10","4","40","-4","4","6","-6","-2","-2","-30","26","0","6","-14","-56","1","-32","-15","-6","14","36","-9","-24","-7","-4","-50","-2","0","0","-8","-2","-55","10","-9","14","-3","-2","-1","6","1","16","0","-32","1","4","8","30","-45","2","-6","4","14","0","9","-14","-53","18","0","14","-16","16","32","-60","-2","18","-24","0","-7","8","-14","-4","-7","-12","20","14","5","-12","-12","-8","39","-28","-3","46","24","0","15","-44","10","-4","10","0","30","2","-1","-56","27","-6","-32","10","-11","-24","-28","4","-4","0","30","-20","8","-14","-20","-34","2","62","-3","6","-3","38","-3","8","-21","2","-20","60","15","44","-9","-26","12","8","4","46","-33","-2","-5","18","-12","-2","-20","-2","-16","16","-1","30","25","-24","21","8","1","6","-5","-30","56","-60","0","54","-16","-24","28","2","-18","36","15","10","2","24","-8","-22","8","4","0","56","-26","-30","8","-2","-48","0","33","22","-26","0","32","-42","1","44","-20","-16","-12","6","26","-2","5","4","25","-26","3","-2","-14","-2","30","56","0","0","44","-6","31","-72","10","-16","-36","18","-7","-20","-1","14","32","14","-10","0","-7","-10","42","-12","-17","4","-9","-42","28","-8","12","-24","14","6","10","-4","2","-2","15","26","1","10","48","-98","-16","4","-4","2","28","20","0","-8","45","-12","4","44","-11","0","4","-4","39","14","25","-10","12","-20","-20","-24","-2","-2","-20","-20","-20","20","-3","8","26","34","-2","-40","1","26","20","2","19","24","-2","-52","38","2","-6","-24","12","10","7","-60","24","28","-10","10","-46","18","-8","-4","-9","84","21","-16","-55","-6","-1","-14","5","-2","-30","-16","38","10","8","6","4","-100","7","10","1","-14","-34","-2","-16","24","30","-14","40","60","-9","4","-28","10","-3","-4","-28","-24","22","-12","0","8","0","-4","-42","-2","-10","-14","15","-2","36","0","-8","18","7","-2","18","20","50","-50","1","44","-5","24","-7","-32","6","-90","50","-2","8","-6","-2","-12","60","-8","25","56","-14","0","14","-4","-24","6","0","-14","15","-6","35","20","0","-8","-13","14","-22","16","-7","2","-72","-32","8","14","8","-32","2","0","-10","36","-11","-80","-14","4","-13","-82","-9","-12","4","-6","8","-20","5","44","-10","6","-60","-18","1","36","-25","-32","-3","74","1","-52","-32","0","4","26","0","6","10","2","6","-30","5","0","25","62","20","-30","4","-56","12","-2","-20","-6","22","56","2","14","-11","-56","-45","18","8","4","-10","-16","-2","30","30","-24","-28","-44","-1","56","-41","8","-45","-10","2","0","26","-16","-7","6","20","-44","-17","18","-3","-76","28","-64","-75","2","-16","16","20","-58","-60","26","10","18","24","-26","-35","10","-10","26","4","-34","77","-4","-37","-2","-16","-24","0","-30","-12","24","-1","20","-12","8","-6","-14","-1","0","-1","10","47","28","-20","-24","-10","-4","15","92","1","-36","32","4","12","-30","-4","36","5","-14","0"],"lmfdb":"agrees","derived":{"al":[[3,-1],[7,-1],[11,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"231.2.a.d","letter":"d","dim":3,"charpoly":["341991","-7596","-30","1"],"traces":["3","0","-3","6","0","0","-3","3","3","9","3","-6","0","0","0","12","0","0","12","-21","3","0","-6","-3","15","9","-3","-6","12","-9","-6","6","-3","-24","0","6","0","-15","0","18","6","0","6","6","0","-24","-24","-12","3","-39","0","-21","0","0","0","-3","-12","-9","-24","21","18","6","-3","-21","30","0","12","-6","6","-9","12","3","24","39","-15","-3","-3","-9","12","9","3","30","-18","6","-18","-24","-12","3","18","9","0","-18","6","15","12","-6","24","0","3","-3","-12","24","0","18","0","-6","-12","-6","-12","9","0","-12","-6","15","-18","45","0","3","0","-18","3","0","-6","36","-6","0","18","12","-6","-39","12","-6","-12","15","0","-48","0","24","24","21","24","-48","0","12","-30","-9","-3","33","36","39","-18","-18","0","0","-42","21","-30","48","0","-21","6","0","-12","66","0","6","-6","3","-9","42","12","6","-30","9","-15","12","24","12","-36","-21","24","-9","-18","-54","6","-6","0","-21","3","39","-6","21","12","6","-30","6","6","0","-6","-63","-12","-60","-12","6","-24","30","-6","9","12","9","12","-48","-12","15","-18","-3","6","12","-24","-21","-18","-39","-12","-6","15","-48","-24","3","0","24","3","-6","30","9","-12","-117","-12","24","24","-9","0","0","-3","36","0","-30","12","6","18","45","0","-6","-6","-54","18","-42","-12","24","0","27","12","-60","-24","-3","42","15","-18","51","-30","-9","0","-24","0","36","15","18","-30","84","-6","-18","-12","-15","12","12","-12","9","-6","6","-3","75","-24","69","30","0","72","78","-3","-9","-18","3","-6","-42","12","33","0","-24","12","-6","0","18","24","-18","-12","-66","0","36","12","6","12","18","12","24","30","6","-6","-81","12","66","24","-9","24","12","0","36","-12","12","12","-39","6","-72","-6","-15","-3","-42","18","-30","12","-45","-24","39","0","6","-12","-3","-36","132","0","0","12","18","33","-42","-3","21","-30","0","-12","-48","6","-45","0","-36","36","-24","6","6","-30","0","12","-129","-18","42","0","-12","0","18","6","96","30","39","48","3","-12","-48","36","6","12","12","12","21","48","-15","-42","54","0","9","0","48","-18","12","0","54","24","-24","-42","-21","-24","-15","-12","-21","-60","30","-24","-12","78","48","-18","3","0","60","-24","-12","30","-6","30","-114","6","9","0","18","3","42","0","-33","-84","-114","-36","21","18","-39","6","-24","18","18","-30","18","0","-6","0","-30","6","0","0","39","42","-60","-60","-21","-12","-75","30","-18","6","-48","132","6","0","81","42","21","6","21","-6","6","-42","0","72","18","12","9","60","-66","18","39","0","-18","-12","-6","-12","-117","6","-63","-6","-3","-138","-24","9","-24","-54","-42","-24","-45","-12","69","-24","-6","-24","-39","30","-48","24","-9","24","-84","15","15","-12","-12","-9","-36","-24","3","-24","-12","-12","42","36","-36","3","21","6","-15","-24","-6","102","9","60","102","18","-39","36","54","-12","30","-6","-24","-24","6","-18","-9","0","75","-6","21","-36","21","-3","-84","-42","-39","0","-21","6","-30","48","-21","0","12","-12","-111","18","-6","0","6","30","42","-24","-6","-78","-147","-6","39","-6","0","18","93","6","24","12","63","-12","24","12","0","0","60","12","-3","12","54","-12","-6","-36","60","24","-3","66","-30","54","60","6","-96","-18","-9","75","-72","-12","-30","-78","-9","12","108","-12","138","6","48","0","-9","12","-63","36","-15","-30","18","18","-42","-12","3","-24","90","-6","-21","54","-12","48","54","24","-15","12","21","12","84","18","-6","-12","39","-6","90","12","33","18","6","-60","-102","-15","-51","54","48","-24","66","24","6","-42","-3","-66","0","0","0","42","-24","-48","-114","-3","24","156","6","-60","-87","-30","3","-30","-9","-72","-21","12","-81","12","117","-12","120","12","42","0","-24","30","-72","-24","12","0","9","0","-63","0","84","66","0","-54","-18","3","111","48","-36","-54","18","0","-18","12","30","90","117","-12","6","-48","-6","-30","-24","-18","-6","12","-45","-60","-81","0","75","-78","6","-24","21","6","90","42","54","12","-48","-18","-36","72","42","48","-9","12","168","-108","-24","-96","36","0","-114","-60","-27","12","60","-12","12","-96","60","108","0","24","-48","6","3","0","-84","-42","-102","0","-15","-30","-3","18","42","24","-51","18","18","30","-132","-12","9","72","-45","0","39","-84","24","54","156","0","48","36","-36","84","60","-15","-3","48","-18","-18","-18","30","18","0","-84","-66","-3","6","-87","-24","18","-9","-39","12","78","-6","15","-3","-6","-12","-54","-78","-12","-42","0","12","18","-66","-9","12","-114","6","51","-30","-6","24","66","3","-36","12","-75","-12","12","24","-12","6","-69","-102","-51","-30","9","36","0","0","-72","-72","-84","90","-78","-18","126","3","-6","-138","9","0","-12","18","150","18","-3","12","30","6","-102","-78","42","60","-90","-12","39","-24","-33","-18","6","0","-48","-12","24","-78","30","-12","114","-36","6","-150","147","0","45","48","-18","12","-48","-24","75","-18","18","30","-15","12","213","-78","66","-72","-93","0","-24","12","-36","-30","-120","-12","48","-48","-6","78","45","-12","-18","0","-18","15","-45","-12","75","-126","-24","24","3","-30","108","24","-6","-24","-60","6","72","48","81","18","-21","-12","51","36","-66","-36","-138","-24","-129","36","9","-12","36","-24","48","102","-12","18","21","0","84"],"lmfdb":"agrees","derived":{"al":[[3,1],[7,1],[11,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"231.2.a.e","letter":"e","dim":3,"charpoly":["32609","344","-88","1"],"traces":["3","2","3","6","4","2","-3","3","3","-11","-3","6","-4","-2","4","-4","8","2","-8","-3","-3","-2","10","3","15","-1","3","-6","-4","-11","-2","8","-3","-4","-4","6","0","-13","-4","-18","14","-2","-14","-6","4","28","0","-4","3","-19","8","-29","0","2","-4","-3","-8","-1","0","-3","-6","-38","-3","-5","14","-2","-4","42","10","11","-12","3","-20","29","15","-11","3","-1","12","-41","3","-6","6","-6","-6","24","-4","-3","26","-11","4","26","-2","35","-8","8","-4","2","-3","29","-4","-4","-16","-46","-4","-6","24","6","24","11","0","4","2","-13","-14","-29","-4","23","-8","-18","3","-4","14","0","30","-2","-18","-10","-14","81","12","-6","8","-7","4","60","0","28","-24","3","0","4","4","-4","14","-15","3","1","-4","-19","-14","2","8","2","30","-29","-6","-4","0","27","-10","2","-4","38","-4","-14","-46","-3","31","-126","-8","10","2","-1","-15","4","0","60","-4","-3","20","1","-6","22","-30","-38","-8","17","-3","-1","2","-5","-32","46","14","6","-10","-2","14","13","-4","-36","4","42","24","-26","10","-35","8","11","-28","-16","-12","39","-90","3","2","80","-20","3","-98","29","-44","-8","15","20","-16","-11","20","-12","3","-46","14","-1","-52","-15","12","4","-12","-41","4","2","3","-12","4","-6","-12","6","6","-55","16","-6","-10","-18","-6","-10","8","24","0","41","-4","8","36","-3","22","13","26","-45","42","-11","-68","32","4","-64","-15","26","18","-4","-2","18","28","35","-8","8","-8","1","-14","8","93","81","-4","-19","-2","2","-8","2","-3","23","-10","29","14","-58","-4","13","-8","-4","-28","6","-16","-78","24","-46","40","66","-4","-8","4","-6","4","10","24","-28","14","6","-46","-7","24","34","0","11","48","-36","0","-40","36","4","0","77","2","-32","2","-13","-3","62","-14","102","-4","-29","20","19","-4","-8","-56","23","-60","64","-8","52","-20","-18","-23","50","3","29","-46","-4","12","20","14","55","0","0","16","4","30","34","70","-2","36","21","-18","-78","-40","-10","4","-70","-14","20","22","81","8","3","12","-104","60","-6","-24","-12","8","-51","8","-7","-46","-46","4","1","0","60","38","-112","0","-22","0","28","74","-35","-24","13","4","3","20","-34","0","-32","94","4","6","33","4","4","-20","-4","-10","38","14","66","-42","-15","28","18","3","-114","32","1","-20","-26","-4","5","-22","-19","-14","-48","-14","-38","-14","2","28","-42","8","-86","-2","2","72","-35","30","-52","-12","-29","4","19","-6","-30","14","-4","-12","-42","0","-55","-30","27","26","-69","-10","6","-82","2","40","-6","-4","-11","88","38","-98","-7","-4","-26","12","-14","-36","89","-46","-67","74","-3","66","-28","31","-52","-6","-126","20","-93","-8","-39","-16","10","0","-29","2","40","12","-1","-20","24","-15","71","84","4","7","36","0","11","-64","60","24","-78","-4","52","-3","-3","14","-53","20","66","-50","1","20","-18","-6","19","-12","22","-12","-10","-30","-16","16","-38","-62","41","-8","-53","26","17","36","-129","-3","52","30","-1","48","29","2","6","-8","-5","-20","74","-32","41","-6","46","0","22","14","2","16","6","46","91","-10","31","-62","-2","6","35","14","-76","60","13","80","-24","-4","-56","4","-36","-24","-1","4","22","-16","42","24","36","24","3","-46","-26","26","104","10","16","-26","-35","11","48","8","22","-54","11","108","-52","-28","94","-2","-16","-4","1","-12","61","-12","39","-34","-26","-90","10","28","3","0","58","2","-45","-58","80","16","-14","-20","-35","48","3","-56","20","-98","-90","8","29","-10","-66","-44","117","6","-8","64","-18","15","85","-58","20","4","-46","-16","38","22","-11","82","-2","20","128","42","-12","24","18","3","-64","-76","-46","108","-9","14","-29","-86","-1","-28","5","-52","19","4","-15","-84","-28","12","50","-80","4","-14","36","-12","36","24","-41","16","17","4","36","-46","2","-34","46","3","7","48","-12","2","-26","4","-10","4","-6","-66","-89","-12","6","-36","6","-74","-4","6","-42","-24","-55","28","69","16","103","58","-6","-88","59","-10","66","26","-18","-24","-4","-6","28","68","-10","-44","-11","8","-92","-32","24","104","52","0","18","-12","41","12","108","-4","-4","-112","8","24","-76","36","28","-2","-3","8","-44","22","22","-20","13","-2","97","26","42","20","-45","14","54","42","-80","92","-11","-52","29","-68","-29","36","32","42","32","4","12","4","-64","-20","4","-15","-23","92","26","-50","86","18","94","8","-4","-78","11","-2","53","-24","18","-17","155","28","-46","-38","35","-3","-38","-8","-142","58","8","-66","4","-8","-6","-26","1","-36","-162","-14","-45","42","8","-112","-138","93","0","-12","81","112","60","-4","-80","-30","-19","2","127","-2","41","88","2","-16","-224","-8","-28","10","2","18","-46","-3","-130","-18","23","-104","10","-10","6","-46","29","-52","6","14","-102","-6","-58","-44","-54","-4","-81","-72","13","-6","122","-8","96","-12","-4","-10","-130","-28","26","-68","6","-86","-11","-16","-35","52","-78","-8","68","24","-89","6","-46","6","7","40","-139","34","66","16","-7","-4","-24","-68","-8","-38","-8","4","-60","0","-6","90","-73","4","126","0","10","63","-63","24","-5","34","-28","56","3","14","28","8","6","24","-52","-46","8","-80","-7","-26","-3","24","51","-124","34","140","-114","0","55","20","11","100","72","48","-4","46","-36","-14","59","0","88"],"lmfdb":"agrees","derived":{"al":[[3,-1],[7,1],[11,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.116,"computed":"atlas","estimate":{"seconds":0.272,"low":0.166,"high":0.47,"bytes":1925365},"url":"https://sagebrush.space/atlas/mf/231.2.a"}