{"label":"427.2.a","level":427,"weight":2,"dims":{"new":31,"cusp":39,"eisenstein":3,"modsym":81},"old":[[61,4,2]],"T":[[2,1],[3,3]],"status":"proven","checks":["dim M^+ at levels [1, 7, 61, 427]: [0, 1, 5, 42] (certified at ell = 2147482921)","T = [(2, 1), (3, 3)]; h of degree 31 = 1 x 31 (phi(ord eps) x dim S_k^new); 5 primes, 0 rejected"],"newforms":[{"label":"427.2.a.a","letter":"a","dim":1,"charpoly":["-2","1"],"traces":["1","-1","1","-1","0","-1","-1","3","-2","0","-5","-1","4","1","0","-1","-5","2","-7","0","-1","5","9","3","-5","-4","-5","1","-6","0","0","-5","-5","5","0","2","2","7","4","0","-10","1","1","5","0","-9","7","-1","1","5","-5","-4","-6","5","0","-3","-7","6","-6","0","-1","0","2","7","0","5","5","5","9","0","1","-6","10","-2","-5","7","5","-4","-3","0","1","10","1","1","0","-1","-6","-15","-13","0","-4","-9","0","-7","0","-5","10","-1","10","5","6","5","4","12","0","6","-2","5","13","0","2","1","13","7","0","6","-8","6","5","0","14","1","-10","0","0","-2","12","3","1","0","17","5","7","-5","0","-15","-21","-9","4","0","7","-1","-20","2","0","-10","1","-2","-14","5","8","-21","10","-5","0","-4","17","3","-6","0","-9","-1","-12","10","0","-1","-9","-3","3","0","14","-1","-26","6","5","5","-6","13","-12","0","-10","4","-1","27","0","0","25","-7","5","0","-24","7","-26","-10","0","-1","-15","-10","-3","-15","5","-6","6","5","0","-4","-18","-4","35","0","-23","6","1","2","0","-15","0","-13","10","0","-20","-2","14","5","10","-13","18","7","0","0","5","-18","-20","8","0","6","-3","-5","-4","0","-24","-14","16","1","0","10","-28","0","1","0","12","-2","-45","-12","0","-17","2","-1","-2","0","12","-17","26","-15","0","-7","-13","-5","0","0","8","5","-4","21","25","-9","28","-4","0","0","0","-7","0","-1","0","20","10","10","8","0","10","-10","6","-1","0","6","25","14","36","5","-1","-8","6","7","0","-10","-4","-5","4","0","-6","12","-21","-17","0","3","-6","6","30","0","-2","9","35","-1","-20","12","13","-30","-7","0","-8","-1","-4","9","0","1","-2","-3","13","0","0","-14","-1","3","0","26","-16","6","-33","-5","-20","25","28","6","0","13","5","12","-21","0","30","10","14","4","0","1","23","-9","20","0","6","0","-28","-25","0","21","-24","-5","-8","0","12","24","2","3","0","26","-2","-10","10","0","-45","3","17","15","0","-10","-13","3","7","5","-2","-5","0","-6","0","-6","-10","-15","6","0","-21","-4","6","18","0","-20","4","-35","22","0","8","23","-14","-18","25","-1","1","2","-20","0","6","5","-29","0","0","-13","-63","-10","33","0","-2","20","6","-2","0","-14","-14","-7","13","-10","50","-13","8","-18","0","-21","-14","0","25","0","30","-5","20","6","0","20","-28","8","-5","0","17","-18","-5","3","35","-5","12","4","-4","0","8","24","-9","-14","0","-16","-18","-3","-12","0","-34","10","30","28","0","0","-1","-1","-11","0","-9","-12","-11","6","0","45","3","-12","31","0","-10","11","35","-2","0","-1","-35","2","-26","0","-14","-12","0","-17","5","-26","0","5","58","0","12","-7","-40","13","0","15","-12","0","-5","0","-14","-8","-10","25","0","4","28","21","2","-25","42","27","3","-28","0","-4","14","0","4","0","25","0","-19","-7","0","0","-1","3","3","0","-22","20","-24","-10","-45","-14","-17","-8","-26","0","-1","-10","30","30","0","-6","8","-1","0","0","-15","-2","-9","-25","0","14","-3","-36","4","-15","-40","1","-10","-8","0","-6","7","35","6","0","28","-10","-9","4","0","15","16","-4","-4","0","-45","6","13","-4","25","21","35","-17","-10","0","37","-9","-23","6","0","6","4","-30","-2","0","-32","2","-16","9","0","-35","24","3","30","20","0","12","16","-13","0","10","-20","7","-34","0","-35","8","-20","3","0","4","-54","9","14","0","5","5","50","2","25","-3","-5","-13","-10","0","18","0","14","-14","0","1","0","-1","-24","0","43","26","-10","16","0","-18","50","33","-20","-5","-30","20","-14","-35","0","-28","-6","6","-40","0","6","-39","0","-5","0","12","-4","21","35","0","-4","-30","-24","10","30","-14","23","-12","13","0","-5","1","16","-23","0","-45","-25","-20","-45","0","-28","-6","0","0","0","28","-2","-25","2","0","38","-7","12","24","0","-5","-42","8","-45","0","-17","-12","-13","24","0","-2","-24","-17","-25","0","2","26","-10","2","0","30","-2","-10","70","0","-5","45","30","-1","0","-17","-12","15","26","0","-13","30","-4","13","0","3","46","-7","-35","25","26","2","-50","-5","0","0","0","18","-15","0","-38","-6","8","10","0","5","-7","-6","8","0","6","21","12","12","25","-6","-22","18","0","0","28","28","-5","-4","0","-35","0","-22","-27","0","7","-8","0","23","0","14","-14","6","0","-25","18","-1","2","-1","0","-6","52","20","-15","0","10","-6","16","25","0","29","8","0","15","0","20","39","-20","63","0","-10","-18","-33","6","0","-2","2","51","20","0","-6","34","6","-12","0","-5","-14","-49","14","0","-3","36","-13","0","-10","30","-50","-1","39","0","-8","15","-18","-12","0","-28","7","-5","14","0","0","-17","-25","10","0","-4","-30","4","-5","-10","-20","-8","30","-30","0","-7","20","-6","28","0","-24","-12","5","-21","0","39","-17","-90","6","0","5","-56","3","40","-35","-6","15","-46","-12","0","4","30","4","21","0","-31","-8","4","24","0","9","8","42","35","0","27","-16","-4","18","-20","1","-3","12","65","0","-26","34","-30","-30","0","-30","-7","28","9","0","30","0","-8","1","0","-1","34","11","-10","0"],"lmfdb":"agrees","curve":{"cremona":"427c1","lmfdb":"427.a","ainvs":[1,0,0,-28,-59],"rank":1,"torsion":1}},{"label":"427.2.a.b","letter":"b","dim":1,"charpoly":["-6","1"],"traces":["1","0","2","-2","4","0","1","0","1","0","-2","-4","2","0","8","4","5","0","-8","-8","2","0","-6","0","11","0","-4","-2","2","0","1","0","-4","0","4","-2","4","0","4","0","0","0","8","4","4","0","-8","8","1","0","10","-4","-12","0","-8","0","-16","0","1","-16","-1","0","1","-8","8","0","6","-10","-12","0","6","0","-10","0","22","16","-2","0","-14","16","-11","0","-2","-4","20","0","4","0","10","0","2","12","2","0","-32","0","-2","0","-2","-22","-5","0","-16","0","8","0","-9","8","-13","0","8","4","-3","0","-24","-4","2","0","5","0","-7","0","0","-2","24","0","19","0","16","0","22","8","-8","0","-16","0","3","0","-3","-8","-16","0","-4","4","8","0","2","-8","13","0","10","0","5","0","4","-8","-7","0","-24","0","-6","0","-11","0","-16","0","-8","0","-9","0","-8","-16","6","0","11","-8","2","0","15","-8","25","0","-2","0","16","0","-10","16","-4","0","24","-16","4","0","16","-2","3","0","4","0","12","0","2","-20","0","0","-6","8","16","0","-18","24","12","0","32","0","1","0","-20","16","10","0","11","0","11","0","3","32","-10","0","-4","0","6","0","-32","-2","-28","0","15","32","22","0","-10","2","4","0","-16","0","-4","0","20","-2","12","0","40","16","-14","0","4","-16","2","0","31","0","-48","0","20","-12","-26","0","10","20","4","0","-22","24","2","0","1","0","0","0","-8","-12","-64","0","0","0","8","0","-4","20","30","0","4","0","8","0","-12","-44","8","0","-10","-32","-4","0","20","4","-32","0","-15","0","-6","0","4","28","-7","0","-4","-32","-18","0","-40","22","22","0","-26","0","-8","0","-18","4","4","0","24","8","32","0","-6","-40","-2","0","1","0","-48","0","-11","-8","7","0","-8","0","-14","0","24","-20","10","0","14","0","45","0","-14","-4","-40","0","-32","-24","0","0","-12","-4","28","0","48","0","4","0","-9","64","38","0","-21","0","-8","0","8","4","26","0","-30","0","44","0","-56","4","-25","0","-16","44","-14","0","2","10","-44","0","-8","0","5","0","6","32","1","0","-8","0","-6","0","-24","-16","-30","0","-8","0","55","0","-1","18","-8","0","8","-16","13","0","16","26","48","0","10","0","1","0","-12","-16","40","0","26","-8","5","0","0","6","20","0","8","0","-32","0","-20","48","-24","0","28","8","8","0","29","-4","6","0","-14","0","-16","0","-88","-10","-12","0","12","0","8","0","-12","14","-8","0","-3","0","-22","0","12","0","10","0","-8","4","6","0","-14","-48","-16","0","-12","0","-20","0","-18","-38","18","0","-10","0","32","0","-64","-32","16","0","12","0","-17","0","7","-44","22","0","5","-16","13","0","1","16","0","0","-36","0","30","0","-2","32","-16","0","50","0","-52","0","-32","-6","-1","0","-16","0","-14","0","32","6","30","0","16","16","-20","0","34","32","-12","0","-11","0","-13","0","-20","8","48","0","-66","-8","42","0","8","-16","-2","0","24","0","8","0","44","-4","-8","0","6","16","1","0","20","-26","8","0","-32","0","-14","0","6","-20","-28","0","38","0","4","0","-16","-10","-19","0","0","0","12","0","-36","-8","24","0","10","16","41","0","32","14","20","0","-12","0","-36","0","76","48","2","0","6","0","-50","0","27","12","64","0","-7","0","-2","0","2","22","34","0","88","0","-10","0","7","32","38","0","20","0","-32","0","-12","16","22","0","2","0","4","0","-44","18","-25","0","-2","0","6","0","8","16","12","0","-20","32","-24","0","10","-12","-2","0","-12","0","0","0","12","-22","22","0","-32","16","-64","0","-5","-4","-20","0","-14","0","-6","0","-16","-30","30","0","34","16","-16","0","44","-50","22","0","-52","0","13","0","40","4","-36","0","8","0","-12","0","-34","-32","-32","0","-24","0","52","0","-2","20","-9","0","-8","-32","40","0","40","8","-5","0","24","0","34","0","-13","-48","20","0","2","32","-35","0","-28","-8","44","0","11","0","8","0","0","-32","-12","0","-8","4","-28","0","-5","-6","62","0","-3","0","-2","0","-96","-8","16","0","-40","0","10","0","20","-24","-24","0","-52","0","49","0","-4","-4","20","0","-44","40","-64","0","2","0","24","0","38","0","-44","0","12","12","0","0","4","-16","5","0","-32","-32","-4","0","36","0","-25","0","0","36","-36","0","-7","-48","-16","0","-24","-24","-2","0","-32","0","-10","0","10","-64","0","0","5","0","24","0","16","-2","28","0","12","0","-2","0","24","40","-4","0","60","-32","-12","0","-18","-20","8","0","9","0","19","0","22","-22","64","0","60","0","-24","0","2","-22","-60","0","16","0","100","0","2","-6","-5","0","8","-64","4","0","-8","20","22","0","11","0","40","0","12","8","44","0","-16","0","-50","0","-8","-12","-30","0","-40","0","2","0","-12","64","27","0","0","4","-16","0","-36","56","-20","0","-14","0","-56","0","96","-30","-8","0","3","-64","-30","0","-9","-44","16","0","-7","0","-80","0","12","20","-3","0","44","-4","-23","0","-20","-8","-13","0","-16","0","12","0","-16","32","-48","0","-49","0","-36","0","16","8","22","0","-16","0"],"lmfdb":"agrees","curve":{"cremona":"427a1","lmfdb":"427.b","ainvs":[0,-1,1,-1,-1],"rank":0,"torsion":1}},{"label":"427.2.a.c","letter":"c","dim":1,"charpoly":["-4","1"],"traces":["1","1","1","-1","-4","1","1","-3","-2","-4","-3","-1","-4","1","-4","-1","5","-2","1","4","1","-3","7","-3","11","-4","-5","-1","-10","-4","-8","5","-3","5","-4","2","10","1","-4","12","-6","1","-1","3","8","7","-9","-1","1","11","5","4","-2","-5","12","-3","1","-10","-6","4","1","-8","-2","7","16","-3","3","-5","7","-4","-1","6","-2","10","11","-1","-3","-4","-5","4","1","-6","-15","-1","-20","-1","-10","9","5","8","-4","-7","-8","-9","-4","5","14","1","6","-11","-6","5","4","12","-4","-2","6","5","-11","12","10","-1","5","1","-28","10","8","-6","5","12","-2","1","-6","8","-24","-2","16","-3","-1","16","-7","3","1","3","20","-15","3","7","0","4","-9","-1","12","2","40","-2","1","-10","-6","11","-24","-3","-10","-3","32","4","7","-5","-2","-20","7","1","16","6","12","-15","-17","-3","3","-20","-2","1","-14","-10","11","3","-6","5","12","-8","-22","-4","1","-21","-40","-8","-15","9","-5","-4","0","7","26","14","16","-1","1","6","5","-33","3","-6","-10","-5","24","4","-14","4","-3","-4","-9","2","-1","6","4","15","-8","-11","-2","-12","-20","10","2","5","-22","5","14","-1","-8","-28","-3","30","-24","8","36","6","-5","5","-8","4","4","-2","16","-1","-4","-6","-4","24","-15","-24","8","2","-21","16","-20","-17","-2","-1","10","-16","20","-7","30","9","8","1","5","-3","24","20","8","-5","-4","3","-33","-7","-8","0","16","12","-24","-9","16","1","-4","12","-6","-10","8","40","14","2","-26","1","24","-30","15","-6","-28","-11","-1","-24","-6","-1","-4","-10","-16","3","4","32","-18","12","-19","7","8","5","10","-2","30","-28","6","7","5","-1","-44","16","-11","18","-9","12","-8","15","-20","-17","-12","-1","-14","3","5","20","24","-2","1","3","-28","-14","24","10","17","11","20","-15","-16","-6","4","-5","5","12","21","-24","-18","-22","-2","4","8","1","7","-7","12","-40","-2","8","16","-15","-24","27","40","-5","-20","4","16","0","-30","-3","12","26","2","-14","-10","16","35","-3","-7","1","20","-6","21","5","1","-11","22","3","32","6","-4","-10","-30","-15","26","24","3","-4","-6","-14","60","-20","0","-3","-18","4","0","-9","18","6","55","-1","1","-6","12","4","-2","5","5","-8","40","11","7","-2","1","-36","-2","-20","-6","-10","-20","2","-6","7","-35","-22","18","-5","-24","14","16","-3","10","-8","-25","28","38","-3","-20","10","32","-24","36","-8","3","36","7","18","3","-5","11","-5","4","-8","-4","-20","-40","4","7","2","-56","16","18","-3","16","-4","30","6","-50","-4","-24","8","-1","-15","-13","24","-17","8","5","6","24","-21","3","-16","-15","-20","-2","-11","-5","-2","-16","1","27","10","-14","-48","30","20","32","7","11","30","-40","3","26","8","12","-1","24","5","-24","-9","12","24","-3","-20","-22","8","-22","25","44","-4","4","-3","-2","-33","-10","-21","-5","-8","-40","0","-42","16","4","4","-15","-24","21","9","-20","16","1","3","3","-4","-26","-12","0","-6","77","-14","-7","8","26","-40","-15","14","6","6","-32","-26","32","-1","-8","24","1","-10","-7","15","-20","6","5","-28","-4","-33","8","-1","-6","24","8","-6","-17","5","-10","-4","36","10","7","-16","24","9","28","4","12","-32","-35","-18","5","4","41","-19","-3","-7","50","8","-21","15","-9","10","-64","2","-4","30","2","12","36","6","-36","-7","4","5","-16","-3","18","-44","-8","-16","-36","-11","28","6","4","-9","6","-12","-29","-8","-20","45","-4","-20","-70","17","2","-12","-3","5","-26","-14","-55","-3","-27","5","14","60","14","24","-34","2","-12","1","-8","1","8","-28","-21","14","6","24","0","30","-30","17","-24","-11","-6","20","10","-21","36","-16","-6","6","20","4","10","-15","-56","5","-48","-12","-8","21","-21","-8","4","-18","4","22","-110","-2","-17","12","13","8","-5","-1","0","7","-4","35","-9","12","5","40","-4","-2","8","24","24","16","30","15","6","-24","34","9","8","40","96","5","-10","-20","-21","12","-7","16","-11","0","40","-30","24","-17","-23","12","-2","-26","-6","2","-88","-42","10","-10","-6","-16","3","35","50","-1","-28","-7","-4","-1","30","20","5","-18","-4","21","8","-5","6","1","-45","55","-10","22","6","-3","-28","32","24","18","-55","-4","10","10","8","-30","-64","-5","-1","26","8","-24","6","3","-44","-12","-33","-6","-14","14","12","60","-8","-28","5","0","68","3","40","-18","-19","12","71","0","-24","9","-12","18","-2","2","16","55","70","1","-38","1","8","-18","-24","12","25","-4","-6","-2","16","-25","56","5","8","8","15","40","-12","33","-28","7","-24","2","38","1","-26","-12","18","-2","-3","20","24","-6","10","-30","16","-20","-3","-2","-9","-6","-48","-3","-28","-35","80","22","-10","18","-1","-15","88","-24","-23","-14","12","16","40","-1","45","10","-4","8","-7","-25","-50","84","-16","38","4","3","110","-20","-8","-50","18","32","1","24","-18","36","60","-24","-8","3","-19","-36","33","7","-42","6","20","3","56","5","8","11","10","-15","14","4","0","8","30","-4","3","-28","33","-40","-12","-4","-104","7","8","6","5","-56","-61","-16","0","18","-44","-1","-51","16","-15","4","22","30","-18","18","-4","-50","-9","4","-7","-24","-26","-40","-8","-1","-20","15","-2","-13","-50","72"],"lmfdb":"agrees","curve":{"cremona":"427b1","lmfdb":"427.c","ainvs":[1,0,1,-8,7],"rank":1,"torsion":1}},{"label":"427.2.a.d","letter":"d","dim":6,"charpoly":["-4527","-5841","-480","914","281","29","1"],"traces":["6","-5","-8","9","-9","1","6","-9","10","13","0","-12","-5","-5","10","11","-17","-3","-10","-36","-8","-16","-10","18","9","-1","-23","9","-2","-8","6","-23","-2","-15","-9","14","-15","-3","25","30","-23","1","1","-11","-20","25","-1","-43","6","-28","8","16","-26","38","-15","-9","17","-9","-25","78","6","13","10","13","-11","47","0","19","-27","13","11","-7","-26","36","-10","-26","0","-17","19","-34","18","59","-19","-12","19","42","-8","13","-3","15","-5","13","-28","25","35","101","-2","-5","35","72","-22","71","13","-23","10","23","-1","-25","-12","71","24","11","-6","19","2","32","-55","13","-17","-111","20","-5","34","26","-42","-3","-2","-44","7","20","7","-3","-10","-25","40","-44","-47","23","9","-36","-40","-35","-18","55","-17","8","-8","-96","-21","56","18","10","6","-16","15","-34","-18","5","72","103","-10","-41","-17","-23","-23","-34","18","18","-27","15","-27","-43","-28","44","9","18","7","-57","49","-112","22","-1","-8","-23","39","-56","-3","-40","-23","-12","12","-69","-1","-22","7","9","-53","-104","-7","-90","10","24","-2","-34","7","15","55","0","1","-8","24","-64","3","25","-11","-25","6","70","59","-32","1","-45","35","-23","29","-70","-95","70","21","-47","-2","-61","42","45","2","-15","-10","-15","48","167","-6","-26","8","9","-9","-95","-5","35","31","102","-19","14","-23","-13","47","35","-38","-133","-15","-11","12","-15","-18","54","79","-3","75","-11","-2","-58","-41","83","25","47","69","-101","-7","-21","52","30","28","35","-15","28","-52","18","-23","-193","71","51","-23","9","-78","1","32","132","-85","10","-10","-219","1","20","51","-4","-9","-72","1","-11","-16","-149","-26","80","32","-10","-20","12","-102","-47","2","-110","47","25","51","-46","50","-26","26","52","-1","-94","16","34","-12","30","36","-43","-51","19","22","4","-98","-16","6","167","114","115","17","-100","5","-28","91","-56","0","95","29","-72","8","4","-41","179","-66","73","17","16","-59","1","1","61","-64","-75","-26","42","-17","122","75","35","17","38","124","97","-74","19","34","106","-15","47","27","-83","9","-17","73","-9","42","24","-23","23","-67","-54","17","127","38","80","-51","39","51","-9","63","50","39","-115","44","91","-25","-46","-40","35","-26","98","24","78","-82","-93","94","17","-19","62","6","29","83","-144","39","-10","-2","13","79","-19","-13","10","-46","73","10","16","-11","153","42","-125","60","13","81","-108","-51","34","30","50","-11","-62","72","-20","-1","-62","15","47","27","94","41","-191","-58","68","0","-8","-16","-90","14","-20","-68","19","-169","-19","12","-325","-21","-5","-27","47","100","-23","-98","-9","-23","13","-5","-28","51","15","26","-72","11","96","-44","-111","-26","98","-65","-7","8","-44","-49","1","14","-226","-26","12","25","-9","-41","113","69","36","103","7","14","-62","-65","0","-10","112","69","-161","4","-67","-29","-26","69","-18","-46","-104","-51","-60","0","98","-8","170","-69","-81","57","-17","47","-129","10","-194","-6","52","19","52","-144","134","-93","134","-25","-34","-147","-32","-25","-29","-3","-66","18","-155","33","-29","-22","34","56","59","19","165","15","41","7","-115","-19","94","-70","-6","-19","-5","11","-12","-4","55","16","-156","-56","92","19","-110","35","20","-19","375","71","42","-70","-148","-49","-122","-119","91","-8","13","-54","-5","-104","6","13","13","-17","-88","-27","77","32","64","-3","-30","72","-47","-68","24","-78","15","14","-84","64","108","34","146","-5","-17","-92","211","16","-115","-19","13","-92","45","93","80","8","-59","-28","30","-32","-167","-74","-111","-64","25","66","72","60","-48","-41","-44","35","12","49","-22","44","104","0","101","-5","-69","-16","-172","-76","116","-2","214","146","117","43","-113","127","-5","47","-257","70","-97","54","-36","35","-73","-114","161","-29","57","33","72","-68","-68","18","220","29","-14","-22","-107","115","100","-58","162","65","71","-42","64","-23","-84","-90","-266","13","132","-14","-128","71","-94","-54","-23","19","116","-120","-12","-41","55","10","-178","-10","138","-80","228","-1","23","-14","-261","36","127","2","11","-1","-249","-36","24","45","-15","54","-25","-41","-93","-16","-59","91","187","-12","5","-21","-229","40","-90","-27","71","86","49","-74","169","-165","49","24","-48","-29","11","-80","-156","26","11","21","-46","50","-85","28","77","-6","-94","-5","30","-132","-14","-87","19","-43","-268","-63","-12","103","3","2","45","10","63","49","-26","35","32","-72","-69","79","-88","-54","62","-55","112","78","40","96","-68","50","13","-7","162","-38","143","-45","-12","-17","12","54","-2","-116","-150","44","-111","-126","145","31","140","126","-132","20","-67","-42","12","-33","-26","64","-5","84","-16","-76","-81","-50","191","34","118","-10","169","32","41","37","26","-35","-199","24","41","59","-65","-42","-151","-46","220","81","-111","-42","-3","71","-3","79","-54","-33","-219","-2","15","79","83","-22","-59","-86","-44","-36","9","-26","379","14","-54","7","-41","-23","-133","-33","-105","-69","20","74","73","106","38","10","-37","7","-45","-71","181","-97","150","38","-3","-51","68","-21","-133","44","235","-10","229","134","28","66","-172","6","-25","-123","-43","58","152","83","173","40","-125","67","-88","116","105","159","-44","-17","112","-27","91","-28","5","-47","261","170","36","-125","54","-100","23","-108","56","-32","-37","4","291","9","222","-115","11","18","90","108","-36","-113","53","104","-46","76","-66","-40","-2","-20","169","26","-13","-26","-35","128","-116","-41","25","18","264"],"lmfdb":"agrees"},{"label":"427.2.a.e","letter":"e","dim":6,"charpoly":["-4075","2445","1392","-246","-79","5","1"],"traces":["6","-5","0","9","-5","-3","-6","-21","2","1","-6","4","-13","5","-14","19","-11","-21","10","-2","0","8","-18","-8","1","15","15","-9","-14","30","6","-27","-20","31","5","22","-15","-25","-27","0","9","3","3","-13","-24","-3","-11","27","6","-14","-2","-20","-42","-30","19","21","-15","39","15","-54","-6","19","-2","53","1","39","-18","-53","-3","-1","-17","1","22","-12","36","22","6","67","-7","30","10","-11","3","-4","17","2","24","29","-3","93","13","-1","2","31","-5","-21","-14","-5","-17","48","-12","-9","-9","75","14","55","-17","77","-8","-31","20","-19","-30","69","20","-68","-13","-31","11","93","-40","5","26","-4","-12","21","-14","-52","-5","-48","11","-53","-10","39","-20","62","9","-17","9","2","12","25","40","-5","-11","4","0","42","-13","-80","14","-4","-22","-8","-45","-70","-24","1","24","-53","18","-21","3","-33","53","4","4","8","61","11","-1","-43","-16","14","-1","-46","5","9","-27","-146","-28","-15","0","45","41","-44","13","-10","-15","-52","-16","-49","-11","28","95","9","-41","60","13","-70","-12","6","14","-4","-49","-51","49","-142","5","-30","-18","-98","-59","5","43","-135","-6","0","-9","56","-19","-1","-21","27","37","-4","-19","-98","-31","73","20","87","12","41","-6","57","-22","-31","20","-125","72","8","10","-9","-5","-79","51","-5","-9","42","27","-22","21","37","33","99","-40","33","15","37","-72","-29","-26","70","27","25","17","-83","16","76","9","-87","27","-35","-37","59","-27","31","20","0","-62","-59","45","-2","34","-82","-9","61","-21","-81","9","37","-120","-3","4","-76","-31","-36","14","137","-3","-36","55","38","5","54","-29","13","40","47","68","44","26","10","24","-122","-30","-5","-10","116","-11","3","-81","90","-12","14","18","84","11","-126","6","-30","-56","-62","-2","-27","69","-31","24","-12","-8","20","-6","35","-2","-103","13","-76","63","14","-73","48","18","-33","71","-12","2","76","67","193","34","-33","55","20","-67","3","-3","-49","124","-105","42","98","-25","-22","-25","-15","39","30","16","101","56","-25","108","122","-19","-53","-35","-121","-29","-185","41","-21","26","38","1","-111","29","52","15","75","-46","18","35","7","-57","-39","-5","54","29","221","46","19","-15","-14","80","141","-6","-44","58","54","-14","127","-20","161","-41","78","6","65","79","-22","39","120","18","-19","67","-79","-75","-76","48","-93","2","-96","5","-37","0","103","-30","-53","29","-120","-35","18","-62","32","-1","40","-106","-14","-29","-92","-81","-39","-85","-52","-31","-23","72","-116","18","6","18","-106","2","106","-36","53","-53","-51","-60","123","-13","-3","3","-33","-48","-45","110","21","-89","1","51","148","19","-5","86","-134","17","70","-44","-117","90","-110","-33","-1","8","20","53","5","-14","-114","-22","-196","-71","101","59","-107","-1","12","-1","1","8","126","-3","152","-36","2","1","-79","8","-29","25","-22","-87","-66","-14","156","23","-160","-6","-138","-36","-10","85","153","-37","-67","-41","95","-2","94","34","-68","7","-72","2","-34","-77","-156","-101","-30","57","136","3","91","53","-146","-10","-7","-3","-61","38","90","86","11","5","-167","5","-11","-45","93","-3","58","18","-72","177","87","-65","4","-52","27","-108","234","20","114","-17","42","59","-62","11","-167","3","-2","10","106","-17","-206","-13","-97","-24","-1","6","-45","92","140","-99","-29","-25","30","-61","-165","42","4","3","-70","-16","47","-14","4","-20","-93","-144","284","48","46","-94","-36","-13","-53","-70","-267","32","3","5","1","32","61","-91","-166","-20","203","-2","26","-90","45","-26","-137","68","-31","82","206","12","0","131","-28","5","192","-103","56","-40","48","6","21","27","-1","100","8","8","22","14","14","-120","25","11","-87","-151","5","-21","65","42","19","-18","174","17","-55","8","99","37","-67","-111","-48","-14","152","-6","-4","-17","-190","12","53","-27","-112","70","-2","-3","9","-96","-100","31","48","86","-298","9","-38","118","94","5","-90","-70","-75","-13","112","58","-4","-31","51","-14","126","30","-258","-30","196","-121","-55","-84","-121","74","39","-120","57","17","123","-36","-50","-33","33","116","-77","39","37","8","-131","17","-123","8","27","89","-179","-80","-188","35","31","-66","17","-44","141","65","267","-20","12","-37","303","76","-2","-168","19","71","-54","4","-53","-176","107","30","158","13","-8","92","-8","-3","-69","51","-112","23","-52","-13","-13","-20","17","-50","-53","-3","46","21","68","8","13","167","-54","14","84","13","-328","-50","-100","-52","-8","-76","31","-19","84","-2","-155","-9","-140","-11","84","-66","76","78","-168","72","-93","110","169","-63","-110","-76","-16","40","-113","114","16","-9","-100","50","-5","44","-64","18","-153","-36","137","-26","58","-6","-137","40","19","-55","4","29","-163","62","201","37","33","12","189","-200","74","-47","95","34","-21","-45","163","-79","226","7","115","14","75","-65","-165","-130","25","-14","52","40","153","-40","203","106","90","5","-15","3","23","-5","-39","87","48","-50","5","6","190","14","-1","-11","167","133","65","53","86","86","53","69","66","-17","15","-46","91","10","37","-52","20","-50","166","-120","-39","-173","-75","-80","-44","75","147","20","-35","69","-156","20","147","-35","-62","67","192","-51","95","90","159","-9","-79","-30","174","-13","34","12","17","12","132","158","63","114","-13","-9","-70","-99","-19","-54","128","-14","-2","51","-129","-36","-268","84","-232","-12","54","-24","-259","-58","183","80","-25","-4","-212","65","101","-16","222"],"lmfdb":"agrees"},{"label":"427.2.a.f","letter":"f","dim":7,"charpoly":["87878","-5905","-20597","2742","746","-105","-7","1"],"traces":["7","4","1","8","7","2","7","6","4","5","1","-3","5","4","-10","-6","12","-11","9","18","1","-7","9","13","-8","-5","4","8","10","2","2","-4","-1","16","7","-12","3","16","-19","-6","13","2","-14","-26","14","-24","18","-2","7","-5","-17","-2","16","-39","-7","6","26","-11","11","-22","-7","7","4","-12","-11","10","-29","22","4","5","-6","-23","8","-30","-37","-5","1","5","-8","-18","-9","-23","-2","-3","13","-3","-8","-46","10","3","5","-28","-20","-2","7","-18","-8","4","17","5","38","-44","-7","-23","-10","25","-7","-16","5","-23","-18","-6","35","-38","-2","-2","7","73","12","13","-22","-4","-20","-30","-12","-11","-6","3","16","-56","26","0","9","-6","0","37","4","-10","9","18","43","-40","44","-67","7","44","1","30","-15","-3","-36","27","8","-7","21","6","57","-20","6","33","9","14","-29","45","-1","-49","45","13","32","39","25","-16","50","0","-8","-45","-21","-46","-11","-20","-6","-5","-1","-16","47","-36","-26","93","4","74","-54","42","5","-8","-59","8","24","66","-44","-31","-15","24","10","3","-9","5","35","-44","-16","2","31","40","80","-27","-43","20","2","41","-19","-50","33","-29","-29","-4","-1","51","1","9","-21","-21","-1","29","12","39","22","35","1","16","-56","43","18","62","8","-8","7","73","-65","-23","4","-22","39","-12","36","51","-63","-30","14","102","3","-51","-18","-10","-8","-21","37","16","-42","30","76","-30","-29","8","-19","12","-8","-22","39","-1","4","-6","28","92","-23","-47","30","94","13","-3","-25","15","-65","-29","12","2","-12","42","-12","62","22","-28","-14","-88","33","5","-7","-26","-43","-26","-24","91","-6","54","25","-3","14","13","-12","-17","-16","6","-59","-24","18","-3","-2","28","-29","64","18","-2","-34","-43","32","13","-22","-2","-51","168","-61","42","6","-32","7","-30","-10","9","37","-18","-60","-5","-17","-27","-6","-27","-107","33","-17","-32","-70","-67","-40","61","9","-2","1","-2","-48","-34","-76","13","16","-14","11","-59","3","98","-33","-39","-32","21","-22","-25","88","-73","-7","-71","-83","-29","-19","-47","-2","6","-37","-71","-23","89","-2","41","26","-4","-10","33","-71","87","-53","-11","-83","95","-5","-103","103","-63","11","16","16","-59","84","-37","0","-22","-20","-78","-34","11","6","23","-7","-69","-33","-76","-15","3","-35","7","1","68","16","52","-99","-109","4","40","-49","-77","6","21","-18","-12","-74","58","-29","125","-36","-22","-11","15","18","-74","8","4","97","10","-41","46","5","9","36","70","-29","-66","-77","38","45","-43","-37","22","43","63","6","-15","-93","-99","4","57","32","53","60","-6","-105","5","-95","-14","19","-81","76","22","-6","81","-13","-59","65","22","32","-23","36","63","6","-19","29","-108","8","-95","16","1","3","40","-84","-30","-87","-123","64","-30","79","55","-37","138","9","-6","-82","39","-59","-5","65","71","-18","59","-13","10","1","50","-44","-114","61","-42","41","5","45","-4","-4","-19","28","31","-8","-20","-54","94","157","80","13","-18","-66","120","30","-24","47","-90","-9","44","-24","-45","-32","172","-20","-23","-24","123","24","69","115","91","-2","88","-16","-52","105","131","-5","-3","66","79","75","24","-9","-19","13","-32","-36","10","-1","-8","-49","-3","-100","-14","21","216","2","-28","-8","-5","-66","-47","47","-76","-31","-46","49","94","43","61","67","-20","10","82","-59","-122","7","57","36","3","3","-9","117","4","56","-12","5","-79","0","47","4","-63","-51","-28","102","-6","-31","129","-4","-51","-20","-62","14","-4","94","73","-84","-2","-60","-20","81","-8","-19","-103","7","-84","43","-75","144","-28","-1","-18","3","-91","-11","221","183","153","-8","18","-6","-39","-23","-53","-53","4","75","40","0","31","21","10","17","159","-12","3","27","-16","97","5","-4","-92","28","27","31","178","38","85","33","-150","78","-61","29","-44","78","24","123","-163","-35","-94","-7","-76","66","8","-5","6","-65","-23","-80","88","-119","3","27","-42","-10","-7","-95","-112","79","154","-49","25","-52","-45","-20","95","30","-94","-7","-25","-30","43","11","-151","36","-16","-7","-55","-13","45","-36","-57","5","-213","43","241","96","-87","-10","-23","-16","-99","44","27","37","-95","-18","150","-87","-79","51","-67","70","-6","69","-35","16","-58","8","-113","35","48","-5","-167","-50","-47","23","-38","-28","59","37","42","67","16","-2","-171","58","13","-110","66","-49","-2","72","-157","-45","89","-71","68","7","104","2","-9","58","-214","-19","73","-81","84","114","-81","127","-120","12","56","-2","-121","16","104","27","13","-107","73","-25","43","28","-236","-22","-51","-38","51","9","67","-14","-4","-16","-8","-70","-37","7","-71","-20","22","82","44","106","12","-51","-30","16","49","-68","-14","-87","-24","-12","43","84","-87","167","-131","-104","-11","-74","-51","-41","-92","41","81","-6","-217","-94","33","-3","-173","24","3","-68","-104","72","29","46","-106","16","66","-85","137","-62","-131","-95","-56","-170","-84","83","-28","10","-207","26","-54","51","-77","-135","20","112","0","59","40","21","33","-16","-59","9","-99","16","-72","-58","36","-114","-6","74","125","17","-29","17","39","0","62","5","3","-32","80","31","37","87","-32","-51","-29","-20","23","4","57","-33","-288","-37","62","-40","-10","8","110","-37","19","79","115","9","-60","-43","6","11","-194","75","18","21","-35","-72","28","-42","4","43","-198","-23","137","40","21","-142","-40","-120","-65","97","-152","122","28"],"lmfdb":"agrees"},{"label":"427.2.a.g","letter":"g","dim":9,"charpoly":["-1134608","924662","129957","-175428","-7005","9052","201","-168","-2","1"],"traces":["9","5","-1","13","9","-4","-9","15","10","3","3","5","13","-5","2","21","9","14","1","2","1","-3","1","-27","10","9","-10","-13","18","-16","-7","45","7","-16","-9","13","13","-28","-3","6","3","4","10","6","0","4","16","-64","9","-4","-11","8","38","-25","-9","-15","2","-17","-34","-6","9","1","-10","19","37","-18","5","8","2","-3","-6","20","4","8","-17","-65","-3","-67","-14","-8","-3","-7","14","-5","-13","-7","-28","-2","-4","-41","-13","-36","16","-54","19","-70","8","5","-53","-16","3","-20","-13","9","-2","-45","28","-22","2","23","6","-21","26","34","-36","36","45","-63","-9","-87","-12","5","48","14","54","-14","-19","88","-50","0","-24","-20","-1","46","32","25","49","118","-32","-2","-25","-4","22","72","37","-34","-1","-58","76","15","18","-49","33","3","-19","-38","-22","88","10","-53","-1","7","12","-43","39","75","11","27","-26","-21","-13","46","42","-54","-10","21","63","30","-20","44","13","-9","-1","-60","-31","80","-8","31","10","-58","-2","-146","17","4","53","13","45","-30","28","-12","-47","-24","-18","-65","35","-13","-41","64","2","16","-47","-24","-40","61","-5","-60","7","15","25","6","3","115","-8","-45","-59","113","18","73","-5","3","-7","-13","94","9","18","-19","47","16","55","-93","-60","-49","4","13","9","57","7","85","-8","50","-35","-13","4","-75","-1","145","12","-24","-13","97","54","54","35","59","9","28","-2","0","-38","48","-17","58","3","-30","-30","192","-49","-1","-61","-6","24","-120","-19","1","-28","2","-3","158","-50","27","-33","-35","90","-4","-92","-80","-52","154","-74","84","-10","48","-29","-45","9","134","-13","-6","-16","-81","-41","-142","5","-37","0","57","75","69","-64","-34","41","-4","32","-46","0","12","-39","-102","-16","-62","-6","105","-26","15","-116","64","-53","-63","-105","-66","-18","-40","-9","66","-14","77","-70","90","39","4","-45","57","80","17","19","-31","11","52","30","49","-58","-47","21","-8","45","-4","-28","-122","18","63","-38","18","-55","-61","-113","42","9","25","-13","-107","14","-37","63","-159","9","75","-37","123","-1","-51","-56","15","-49","-49","-31","3","-29","93","-2","-107","18","35","-91","-133","-39","17","53","-165","-30","25","-161","-91","34","-80","4","117","-154","13","-70","6","-48","10","-32","-27","-87","63","-9","133","11","34","-15","-175","52","-1","21","-28","12","50","-51","-51","10","68","51","61","-88","-111","22","-19","89","-193","-17","-39","64","-60","-37","83","-66","78","14","-102","63","18","-29","-90","-143","75","-27","144","-5","8","5","-162","-7","111","27","-8","49","-77","-14","37","-17","-75","-2","-230","104","95","-83","15","-29","3","65","46","-23","-57","-80","84","6","-59","55","55","29","-6","20","-20","4","29","26","-33","35","8","-4","118","16","65","-9","26","72","-8","9","55","-23","-56","-74","-17","17","-64","34","110","0","-167","-14","65","33","31","58","-5","-97","-24","3","2","118","94","-39","194","43","67","9","-12","10","105","-60","399","14","-90","36","-92","25","-2","-59","8","6","-42","96","-136","55","-50","3","80","57","71","40","-84","90","7","54","274","-56","-10","-117","147","-14","-128","-24","-176","-47","109","11","5","58","-125","61","-88","58","-37","13","312","180","-52","9","68","-1","7","98","144","87","-4","26","-146","28","3","42","133","102","-26","57","2","-5","-40","-95","-241","-29","96","4","-286","51","2","87","179","38","41","35","63","-57","72","-100","290","13","9","60","139","-12","19","-106","36","-74","10","-36","-108","6","-19","-16","-68","32","50","-174","-163","88","54","71","-86","-41","-228","-3","247","-19","90","31","111","-54","72","3","70","-35","-145","73","-20","88","-127","-8","50","-26","29","21","-51","69","-5","123","32","-4","87","-21","54","53","-103","-58","-15","13","22","-7","16","-38","20","60","-119","13","60","-3","269","-67","54","-112","-23","27","20","100","-150","-57","-31","-53","16","13","-19","62","118","169","142","55","-9","-158","12","-17","5","127","-100","2","-271","-3","10","1","-118","79","45","58","55","-62","-155","130","-20","-28","115","-10","77","-131","-3","2","22","-54","-89","-1","17","24","97","-2","-11","137","155","-66","-293","35","-23","24","51","96","-45","-12","121","-6","-108","45","13","-205","-195","20","21","-97","87","83","178","-22","85","-26","8","13","-79","-10","263","177","-34","124","-318","-77","-92","-145","-70","36","-55","2","-121","-39","204","53","-36","20","-55","147","-267","-49","-232","-45","28","32","-159","-36","-158","137","63","155","-394","-120","-215","7","102","9","-132","-46","-49","38","62","-137","87","55","-117","137","-81","-36","68","12","-43","54","-223","133","-217","44","-5","40","280","-44","-37","59","-5","-48","-2","19","-236","-74","-140","-35","-14","68","-59","-26","-34","-65","70","-54","267","72","29","-21","7","-134","14","30","39","169","112","-92","195","19","-77","114","-233","41","-29","224","-88","-40","-12","-128","-204","98","-62","50","0","-175","-159","30","-7","80","0","-18","200","-71","-26","2","11","24","-42","-26","-109","-77","-114","-120","20","-71","-190","213","7","-142","1","1","103","-40","0","-98","124","-28","-46","154","1","20","-257","-23","-279","-32","54","-21","25","-16","-96","-113","-25","-39","-22","101","-219","30","-115","-49","-191","-22","90","182","-212","4","-118","137","-147","23","135","-55","-9","32","-4","73","21","62","72","181","2","-46","7","32","-6","34","-162","25","-142","85","-91","11","-7","-8","4","80","7","-81","64","-16","94"],"lmfdb":"agrees"}],"seconds":0.199,"computed":"atlas","estimate":{"seconds":0.319,"low":0.195,"high":0.552,"bytes":2070988}}