{"label":"538.2.a","level":538,"weight":2,"dims":{"new":22,"cusp":66,"eisenstein":3,"modsym":135},"old":[[269,22,2]],"T":[[3,1],[5,3]],"status":"proven","checks":["dim M^+ at levels [1, 2, 269, 538]: [0, 1, 23, 69] (certified at ell = 2147482661)","T = [(3, 1), (5, 3)]; h of degree 22 = 1 x 22 (phi(ord eps) x dim S_k^new); 4 primes, 0 rejected"],"newforms":[{"label":"538.2.a.a","letter":"a","dim":2,"charpoly":["59","16","1"],"traces":["2","2","-1","2","-5","-1","-4","2","-3","-5","-4","-1","-2","-4","0","2","-4","-3","4","-5","-3","-4","-12","-1","5","-2","2","-4","-5","0","6","2","7","-4","15","-3","-4","4","1","-5","2","-3","0","-4","10","-12","-7","-1","4","5","7","-2","0","2","5","-4","-2","-5","7","0","-2","6","11","2","5","7","8","-4","1","15","6","-3","-8","-4","10","4","-2","1","-3","-5","-2","2","-6","-3","5","0","10","-4","5","10","4","-12","7","-7","-10","-1","-6","4","1","5","1","7","15","-2","10","0","-20","2","4","5","-13","-4","-33","-2","35","-5","3","7","-2","0","-4","-2","14","6","0","11","17","2","5","5","10","7","-8","8","5","-4","-29","1","1","15","-4","6","4","-3","5","-8","18","-4","-15","10","-2","4","1","-2","-25","1","14","-3","0","-5","34","-2","19","2","-10","-6","5","-3","-24","5","-6","0","-6","10","-35","-4","-26","5","24","10","12","4","-9","-12","25","7","18","-7","16","-10","-28","-1","-12","-6","0","4","-47","1","-13","5","-9","1","-5","7","-20","15","23","-2","-8","10","-5","0","12","-20","-5","2","-32","4","-11","5","4","-13","5","-4","-20","-33","-19","-2","-8","35","1","-5","4","3","25","7","-26","-2","-5","0","4","-4","10","-2","-30","14","-4","6","-2","0","37","11","14","17","-10","2","-2","5","38","5","0","10","13","7","0","-8","-30","8","2","5","8","-4","3","-29","15","1","-45","1","-19","15","-36","-4","16","6","0","4","-34","-3","-16","5","38","-8","24","18","5","-4","-24","-15","12","10","-10","-2","-13","4","15","1","24","-2","0","-25","-30","1","33","14","-40","-3","-56","0","25","-5","5","34","-8","-2","-5","19","-17","2","29","-10","24","-6","21","5","-15","-3","-9","-24","19","5","8","-6","-20","0","10","-6","-18","10","9","-35","-2","-4","-13","-26","-30","5","1","24","-16","10","-30","12","-18","4","35","-9","-43","-12","-18","25","0","7","-4","18","-25","-7","5","16","19","-10","19","-28","-37","-1","5","-12","-5","-6","40","0","14","4","-10","-47","35","1","-35","-13","-6","5","25","-9","-6","1","-10","-5","-22","7","8","-20","12","15","31","23","20","-2","22","-8","-55","10","14","-5","18","0","15","12","24","-20","-7","-5","-22","2","49","-32","-15","4","-24","-11","45","5","-26","4","40","-13","15","5","25","-4","17","-20","26","-33","-19","-19","-15","-2","29","-8","-24","35","2","1","-29","-5","-20","4","-40","3","-6","25","28","7","10","-26","10","-2","0","-5","-24","0","4","4","23","-4","-20","10","24","-2","8","-30","18","14","25","-4","0","6","-42","-2","6","0","0","37","24","11","10","14","12","17","69","-10","46","2","4","-2","-45","5","-1","38","-7","5","34","0","53","10","-20","13","8","7","36","0","12","-8","-2","-30","55","8","3","2","32","5","32","8","24","-4","5","3","31","-29","13","15","-10","1","61","-45","30","1","70","-19","0","15","-29","-36","28","-4","80","16","-26","6","-23","0","20","4","34","-34","-55","-3","6","-16","1","5","22","38","0","-8","-10","24","-37","18","12","5","26","-4","-28","-24","5","-15","9","12","18","10","9","-10","-7","-2","30","-13","-1","4","0","15","7","1","-62","24","-30","-2","3","0","-28","-25","8","-30","45","1","0","33","14","14","-22","-40","35","-3","10","-56","-70","0","-4","25","-24","-5","-16","5","-15","34","-10","-8","-28","-2","-59","-5","-19","19","12","-17","-20","2","27","29","-47","-10","-35","24","-7","-6","30","21","15","5","-20","-15","-16","-3","8","-9","-45","-24","-55","19","-58","5","-23","8","-38","-6","75","-20","-11","0","0","10","10","-6","3","-18","-25","10","26","9","3","-35","25","-2","-8","-4","15","-13","23","-26","-58","-30","32","5","-56","1","-5","24","-35","-16","62","10","-45","-30","-17","12","25","-18","-76","4","21","35","10","-9","-22","-43","-40","-12","-26","-18","41","25","2","0","-43","7","20","-4","14","18","50","-25","-3","-7","-6","5","25","16","-60","19","-27","-10","24","19","22","-28","0","-37","-7","-1","-51","5","-9","-12","46","-5","65","-6","21","40","4","0","18","14","-35","4","-70","-10","-36","-47","31","35","61","1","2","-35","0","-13","51","-6","-1","5","20","25","-14","-9","-125","-6","-1","1","40","-10","-46","-5","41","-22","-65","7","0","8","-11","-20","32","12","-66","15","-20","31","-33","23","63","20","25","-2","32","22","-15","-8","-34","-55","-27","10","-23","14","-7","-5","60","18","48","0","-13","15","54","12","3","24","20","-20","-26","-7","17","-5","-18","-22","19","2","25","49","-12","-32","-49","-15","-8","4","-26","-24","50","-11","-11","45","-22","5","-51","-26","-2","4","45","40","26","-13","-89","15","34","5","-14","25","-75","-4","-1","17","15","-20","0","26","-5","-33","-60","-19","12","-19","11","-15","3","-2","2","29","20","-8","-10","-24","-42","35","33","2","-6","1","-85","-29","-30","-5","58","-20","8","4","10","-40","-25","3","-55","-6","-24","25","-47","28","-42","7","-55","10","-49","-26","8","10","23","-2","-12","0","50","-5","-40","-24","63","0","-4","4","35","4","35","23","-3","-4","14","-20","30","10","-47","24","-10","-2","69","8","-65","-30","9","18","-83","14","115","25","18","-4","-10","0","-35","6","-37","-42","30","-2","-62","6","56","0"],"lmfdb":"agrees"},{"label":"538.2.a.b","letter":"b","dim":2,"charpoly":["-9","-4","1"],"traces":["2","2","1","2","1","1","-2","2","1","1","6","1","10","-2","-6","2","-4","1","4","1","-1","6","2","1","-3","10","4","-2","13","-6","-12","2","3","-4","-1","1","0","4","5","1","-10","-1","-10","6","-6","2","-9","1","-12","-3","-15","10","0","4","3","-2","2","13","-5","-6","-2","-12","-1","2","5","3","18","-4","27","-1","-6","1","0","0","-8","4","-6","5","-9","1","-14","-10","10","-1","11","-10","0","6","-11","-6","-10","2","-19","-9","2","1","2","-12","3","-3","3","-15","-3","10","6","0","-10","4","16","3","-13","-2","-9","2","-25","13","5","-5","4","-6","-4","-2","-18","-12","0","-1","-3","2","-31","5","34","3","-4","18","15","-4","27","27","-27","-1","-24","-6","30","1","13","0","-6","0","19","-8","-24","4","-15","-6","7","5","14","-9","0","1","-2","-14","-21","-10","-18","10","-1","-1","24","11","2","-10","-14","0","3","6","30","-11","-6","-6","12","-10","-1","2","13","-19","-12","-9","-4","2","16","1","8","2","-30","-12","39","3","-17","-3","35","3","-13","-15","8","-3","27","10","12","6","23","0","36","-10","21","4","12","16","-13","3","-20","-13","-17","-2","-8","-9","15","2","-24","-25","-3","13","12","5","15","-5","2","4","-9","-6","0","-4","-32","-2","-6","-18","20","-12","18","0","9","-1","6","-3","12","2","-6","-31","0","5","0","34","25","3","0","-4","-12","18","-2","15","22","-4","-5","27","-9","27","-7","-27","-19","-1","0","-24","-26","-6","-12","30","10","1","0","13","14","0","12","-6","-35","0","12","19","10","-8","10","-24","21","4","-1","-15","2","-6","44","7","6","5","-31","14","6","-9","56","0","39","1","21","-2","-8","-14","-15","-21","47","-10","9","-18","-2","10","-13","-1","-17","-1","7","24","15","11","-36","2","26","-10","-6","-14","36","0","-13","3","20","6","-17","30","-42","-11","15","-6","0","-6","-30","12","-2","-10","13","-1","-35","2","-18","13","0","-19","56","-12","39","-9","65","-4","-23","2","5","16","-25","1","-3","8","-31","2","-20","-30","-56","-12","30","39","-11","3","-13","-17","-2","-3","53","35","-60","3","6","-13","0","-15","-48","8","-6","-3","5","27","-8","10","-46","12","45","6","14","23","-24","0","19","36","2","-10","15","21","-40","4","37","12","-39","16","4","-13","3","3","-6","-20","4","-13","1","-17","3","-2","21","-8","-30","-9","-25","15","-5","2","-11","-24","18","-25","-10","-3","61","13","36","12","-20","5","-18","15","20","-5","-30","2","-6","4","0","-9","34","-6","0","0","-27","-4","-12","-32","-48","-2","-4","-6","-54","-18","-13","20","-18","-12","6","18","20","0","-72","9","-24","-1","-18","6","12","-3","11","12","0","2","8","-6","-47","-31","-27","0","45","5","-30","0","-43","34","8","25","50","3","60","0","30","-4","-50","-12","-31","18","-81","-2","-36","15","-12","22","32","-4","-31","-5","33","27","-1","-9","26","27","9","-7","0","-27","26","-19","-50","-1","-45","0","42","-24","-24","-26","14","-6","-51","-12","-4","30","-18","10","-29","1","-38","0","-61","13","-10","14","0","0","-30","12","35","-6","-24","-35","0","0","12","12","-11","19","11","10","-18","-8","29","10","35","-24","-2","21","13","4","0","-1","-45","-15","-58","2","30","-6","11","44","24","7","-48","6","11","5","-24","-31","6","14","26","6","-9","-9","-34","56","-8","0","-60","39","36","1","16","21","-5","-2","30","-8","30","-14","-15","-15","19","-21","20","47","4","-10","-13","9","-11","-18","19","-2","-75","10","-2","-13","-13","-1","-28","-17","-6","-1","28","7","7","24","35","15","-2","11","-51","-36","14","2","33","26","53","-10","0","-6","-2","-14","-3","36","19","0","46","-13","45","3","-21","20","0","6","27","-17","-3","30","22","-42","2","-11","-64","15","15","-6","15","0","42","-6","3","-30","65","12","-13","-2","18","-10","13","13","72","-1","10","-35","36","2","54","-18","-43","13","10","0","9","-19","16","56","18","-12","10","39","7","-9","-54","65","1","-4","44","-23","81","2","-60","5","-16","16","12","-25","-25","1","-15","-3","-3","8","-18","-31","31","2","13","-20","-20","-30","-18","-56","39","-12","-6","30","50","39","45","-11","9","3","-10","-13","0","-17","45","-2","57","-3","-12","53","0","35","25","-60","-1","3","-4","6","-38","-13","11","0","-17","-15","-20","-48","-5","8","-12","-6","-4","-3","-24","5","-15","27","5","-8","-49","10","24","-46","71","12","2","45","-21","6","33","14","39","23","12","-24","4","0","-13","19","-52","36","-27","2","-12","-10","42","15","-19","21","18","-40","-7","4","-59","37","52","12","-27","-39","90","16","14","4","0","-13","-5","3","6","3","-11","-6","32","-20","15","4","48","-13","3","1","-42","-17","-18","3","75","-2","135","21","-65","-8","0","-30","31","-9","-20","-25","6","15","21","-5","-9","2","30","-11","6","-24","-34","18","46","-25","53","-10","-30","-3","13","61","44","13","26","36","-24","12","42","-20","33","5","-51","-18","-22","15","-21","20","-62","-5","-15","-30","73","2","0","-6","15","4","16","0","34","-9","0","34","-27","-6","36","0","21","0","69","-27","45","-4","-30","-12","-42","-32","27","-48","-40","-2","-3","-4","-33","-6","47","-54","23","-18","39","-13","24","20","-114","-18","19","-12","-1","6","-28","18","-66","20","26","0"],"lmfdb":"agrees"},{"label":"538.2.a.c","letter":"c","dim":4,"charpoly":["-16","256","45","-18","1"],"traces":["4","-4","3","4","5","-3","-1","-4","3","-5","7","3","4","1","8","4","4","-3","2","5","-5","-7","16","-3","-1","-4","6","-1","0","-8","-1","-4","1","-4","3","3","-2","-2","3","-5","-1","5","9","7","8","-16","13","3","-15","1","3","4","28","-6","13","1","10","0","19","8","-20","1","12","4","5","-1","15","4","-5","-3","15","-3","-7","2","12","2","-6","-3","-17","5","4","1","6","-5","-29","-9","-34","-7","20","-8","-18","16","-5","-13","-6","-3","3","15","-16","-1","-12","-3","-3","-4","-2","-28","8","6","-23","-13","-27","-1","-3","-10","3","0","-31","-19","-18","-8","-19","20","12","-1","12","-12","-15","-4","-23","-5","-15","1","-26","-15","-1","-4","-13","5","7","3","-20","-15","24","3","-17","7","-24","-2","-1","-12","14","-2","3","6","-31","3","-35","17","4","-5","-4","-4","15","-1","14","-6","18","5","-14","29","-24","9","-10","34","-4","7","10","-20","24","8","-19","18","-15","-16","-11","5","-10","13","24","6","22","3","2","-3","8","-15","-24","16","-13","1","7","12","17","3","-14","3","-5","4","12","2","-18","28","24","-8","41","-6","-4","23","33","13","4","27","34","1","-22","3","17","10","-19","-3","-13","0","45","31","29","19","-34","18","-9","8","-58","19","36","-20","-40","-12","36","1","30","-12","1","12","28","15","-26","4","46","23","26","5","-17","15","-9","-1","52","26","-2","15","4","1","4","4","-5","13","28","-5","-7","-7","12","-3","-44","20","51","15","4","-24","-21","-3","38","17","-2","-7","8","24","11","2","-32","1","16","12","19","-14","25","2","-25","-3","-15","-6","-32","31","-27","-3","18","35","-2","-17","59","-4","0","5","-11","4","36","4","33","-15","-47","1","1","-14","47","6","7","-18","23","-5","-13","14","87","-29","-23","24","-2","-9","-2","10","23","-34","-1","4","-62","-7","-26","-10","74","20","-5","-24","-15","-8","-24","19","-10","-18","-47","15","-5","16","-5","11","10","-5","-25","10","9","-13","-17","-24","5","-6","-75","-22","2","-3","1","-2","-40","3","-46","-8","50","15","-24","24","-17","-16","-13","13","6","-1","-23","-7","-18","-12","-12","-17","-12","-3","28","14","-48","-3","25","5","-52","-4","-50","-12","28","-2","22","18","-54","-28","-103","-24","22","8","35","-41","-6","6","26","4","-51","-23","8","-33","3","-13","-41","-4","38","-27","-9","-34","-5","-1","0","22","-6","-3","19","-17","3","-10","4","19","40","3","-75","13","12","0","-36","-45","26","-31","9","-29","-56","-19","54","34","8","-18","4","9","-85","-8","-36","58","-37","-19","8","-36","12","20","92","40","-5","12","17","-36","-20","-1","26","-30","84","12","-12","-1","27","-12","36","-28","-2","-15","44","26","-45","-4","-48","-46","-25","-23","61","-26","-101","-5","-32","17","19","-15","14","9","84","1","6","-52","78","-26","16","2","-7","-15","103","-4","-22","-1","-23","-4","-10","-4","-67","5","35","-13","19","-28","-34","5","-17","7","-38","7","90","-12","26","3","-33","44","4","-20","60","-51","-35","-15","83","-4","-42","24","-26","21","-55","3","28","-38","-7","-17","-10","2","66","7","-26","-8","-89","-24","8","-11","16","-2","11","32","37","-1","71","-16","-22","-12","7","-19","24","14","6","-25","17","-2","-34","25","47","3","39","15","-2","6","56","32","88","-31","24","27","-39","3","54","-18","26","-35","-2","2","-45","17","46","-59","-6","4","2","0","41","-5","-5","11","136","-4","18","-36","-33","-4","-5","-33","-3","15","18","47","-74","-1","16","-1","-7","14","-21","-47","-31","-6","10","-7","51","18","0","-23","-52","5","40","13","-95","-14","10","-87","80","29","85","23","-68","-24","-63","2","-27","9","28","2","28","-10","21","-23","-55","34","50","1","21","-4","-40","62","-52","7","9","26","20","10","-1","-74","-102","-20","30","5","47","24","-45","15","18","8","-29","24","-69","-19","-68","10","28","18","15","47","-110","-15","39","5","-64","-16","22","5","-11","-11","10","-10","23","5","88","25","98","-10","-36","-9","29","13","22","17","9","24","23","-5","-13","6","42","75","27","22","76","-2","-49","3","12","-1","43","2","2","40","-106","-3","-23","46","42","8","39","-50","17","-15","-82","24","-13","-24","57","17","-29","16","-54","13","56","-13","22","-6","-55","1","-53","23","-42","7","29","18","3","12","22","12","15","17","37","12","-11","3","-38","-28","29","-14","32","48","-58","3","72","-25","47","-5","-20","52","-103","4","36","50","-37","12","58","-28","-38","2","-14","-22","1","-18","-26","54","-8","28","153","103","26","24","-88","-22","4","-8","-140","-35","-34","41","14","6","15","-6","-123","-26","54","-4","17","51","-2","23","151","-8","-54","33","135","-3","-62","13","67","41","20","4","21","-38","2","27","25","9","-27","34","-2","5","115","1","29","0","34","-22","-40","6","-41","3","6","-19","-41","17","42","-3","-22","10","-66","-4","-40","-19","-43","-40","-75","-3","27","75","-2","-13","-59","-12","-100","0","58","36","18","45","52","-26","-123","31","-43","-9","22","29","-2","56","-4","19","13","-54","-69","-34","10","-8","57","18","14","-4","2","-9","-34","85","-35","8","-43","36","-79","-58","45","37","-94","19","10","-8","29","36","11","-12","46","-20","50","-92","52","-40","4","5","-103","-12","-13","-17","-46","36","36","20","-21","1","31","-26","22","30","30","-84","48","-12"],"lmfdb":"agrees"},{"label":"538.2.a.d","letter":"d","dim":7,"charpoly":["189675","202484","14023","-11679","-1842","48","22","1"],"traces":["7","-7","-4","7","-6","4","-3","-7","7","6","-12","-4","3","3","-6","7","-8","-7","-7","-6","-5","12","-22","4","9","-3","-22","-3","-7","6","-3","-7","-19","8","-25","7","-13","7","1","6","-11","5","-14","-12","-17","22","-23","-4","6","-9","-21","3","-21","22","15","3","-14","7","-20","-6","13","3","-12","7","-29","19","-30","-8","13","25","-23","-7","9","13","3","-7","8","-1","11","-6","43","11","-3","-5","21","14","28","12","16","17","-10","-22","-13","23","0","4","21","-6","-9","9","29","21","-1","-3","74","21","-23","-22","24","-15","53","-3","-33","14","33","-7","44","20","14","6","57","-13","8","-3","18","12","25","-7","53","29","-4","-19","22","30","34","8","-17","-13","-9","-25","68","23","0","7","19","-9","-10","-13","-2","-3","44","7","49","-8","19","1","12","-11","19","6","20","-43","-64","-11","42","3","-36","5","20","-21","35","-14","-49","-28","-17","-12","-2","-16","-21","-17","4","10","-23","22","-1","13","-48","-23","-20","0","24","-4","4","-21","-23","6","-13","9","-7","-9","27","-29","-51","-21","22","1","-51","3","38","-74","-39","-21","50","23","11","22","28","-24","-36","15","-14","-53","4","3","29","33","-10","-14","-58","-33","69","7","-31","-44","-37","-20","-28","-14","-21","-6","22","-57","-75","13","13","-8","-85","3","38","-18","-54","-12","34","-25","52","7","-12","-53","-68","-29","8","4","7","19","-58","-22","4","-30","-7","-34","47","-8","-62","17","-65","13","5","9","-49","25","36","-68","-12","-23","47","0","8","-7","3","-19","-20","9","-61","10","5","13","56","2","-64","3","42","-44","-37","-7","-10","-49","-16","8","-10","-19","111","-1","16","-12","-9","11","-70","-19","-51","-6","5","-20","18","43","66","64","-19","11","-11","-42","12","-3","-21","36","107","-5","-1","-20","57","21","2","-35","18","14","-42","49","46","28","-8","17","42","12","14","2","-51","16","-7","21","1","17","20","-4","75","-10","-15","23","12","-22","-100","1","44","-13","-34","48","-15","23","-7","20","-30","0","49","-24","-32","4","1","-4","-117","21","-3","23","28","-6","8","13","51","-9","-81","7","29","9","-83","-27","-32","29","-57","51","82","21","-128","-22","78","-1","2","51","-6","-3","90","-38","-13","74","93","39","12","21","23","-50","-56","-23","-125","-11","21","-22","-4","-28","1","24","66","36","-15","-15","19","14","-41","53","-89","-4","-12","-3","18","-29","88","-33","55","10","71","14","-14","58","-96","33","88","-69","8","-7","153","31","25","44","12","37","-86","20","-126","28","-83","14","113","21","-3","6","-2","-22","133","57","-6","75","28","-13","16","-13","60","8","23","85","184","-3","78","-38","-148","18","40","54","39","12","82","-34","155","25","-19","-52","32","-7","-144","12","47","53","-39","68","25","29","48","-8","-28","-4","-39","-7","36","-19","33","58","59","22","50","-4","97","30","-17","7","-46","34","28","-47","116","8","33","62","-31","-17","154","65","-8","-13","-79","-5","-123","-9","-52","49","-76","-25","135","-36","8","68","-46","12","117","23","-15","-47","-103","0","-180","-8","-47","7","8","-3","-97","19","-32","20","-80","-9","-96","61","-21","-10","-34","-5","4","-13","46","-56","-49","-2","-29","64","-24","-3","21","-42","-209","44","-93","37","-72","7","-100","10","57","49","36","16","11","-8","-60","10","70","19","90","-111","91","1","-141","-16","120","12","-136","9","-33","-11","-70","70","44","19","-21","51","-87","6","13","-5","3","20","2","-18","21","-43","13","-66","-81","-64","-79","19","32","-11","-28","11","17","42","79","-12","15","3","-14","21","-91","-36","-171","-107","-22","5","28","1","9","20","155","-57","-103","-21","81","-2","-47","35","-67","-18","77","-14","62","42","-21","-49","-33","-46","-71","-28","-60","8","-7","-17","-77","-42","64","-12","-103","-14","-47","-2","-64","51","46","-16","-94","7","69","-21","3","-1","65","-17","-45","-20","27","4","5","-75","-8","10","43","15","76","-23","18","-12","-94","22","2","100","-66","-1","-92","-44","-17","13","-46","34","-16","-48","-28","15","57","-23","33","7","31","-20","150","30","35","0","6","-49","2","24","-148","32","-29","-4","26","-1","17","4","57","117","-22","-21","17","3","-114","-23","46","-28","-25","6","26","-8","-74","-13","-39","-51","157","9","-24","81","82","-7","3","-29","-5","-9","35","83","136","27","-13","32","4","-29","-22","57","-128","-51","-79","-82","123","-21","-22","128","-34","22","1","-78","-24","1","-92","-2","-19","-51","-43","6","31","3","42","-90","15","38","-4","13","148","-74","20","-93","133","-39","-174","-12","-53","-21","39","-23","18","50","-59","56","62","23","66","125","-35","11","50","-21","65","22","-21","4","-33","28","-47","-1","-66","-24","89","-66","130","-36","-8","15","28","15","37","-19","27","-14","163","41","34","-53","-111","89","-132","4","12","12","-40","3","-7","-18","101","29","126","-88","-39","33","-14","-55","-142","-10","-9","-71","36","-14","-20","14","-58","-58","-32","96","-17","-33","-91","-88","26","69","-68","-8","16","7","72","-153","17","-31","-124","-25","15","-44","59","-12","-260","-37","-5","86","12","-20","128","126","-66","-28","-40","83","107","-14","-84","-113","26","-21","52","3","59","-6","22","2","-58","22","3","-133","28","-57","-92","6","168","-75","-21","-28","119","13","-96","-16","-175","13","-155","-60","1","-8","-103","-23","-84","-85","98","-184","60","3","9","-78","70","38","29","148","102","-18"],"lmfdb":"agrees"},{"label":"538.2.a.e","letter":"e","dim":7,"charpoly":["-398928","175952","37221","-28680","4150","-55","-22","1"],"traces":["7","7","1","7","7","1","6","7","12","7","-3","1","-9","6","8","7","8","12","-11","7","-6","-3","12","1","22","-9","-14","6","-5","8","14","7","-4","8","-4","12","13","-11","-18","7","12","-6","-11","-3","3","12","2","1","15","22","-26","-9","19","-14","-40","6","-12","-5","-9","8","-3","14","-26","7","-10","-4","-33","8","-64","-4","28","12","-14","13","-45","-11","10","-18","2","7","15","12","-7","-6","-16","-11","16","-3","18","3","-26","12","6","2","-34","1","-4","15","-37","22","-1","-26","-8","-9","-40","19","33","-14","3","-40","-4","6","38","-12","-2","-5","-19","-9","-26","8","-2","-3","-48","14","30","-26","4","7","8","-10","-71","-4","-24","-33","-33","8","8","-64","-24","-4","52","28","-10","12","-44","-14","46","13","-3","-45","0","-11","30","10","46","-18","47","2","17","7","24","15","7","12","60","-7","42","-6","-26","-16","1","-11","37","16","-11","-3","28","18","15","3","-17","-26","-20","12","30","6","0","2","24","-34","10","1","14","-4","21","15","29","-37","14","22","-40","-1","36","-26","-20","-8","46","-9","22","-40","-51","19","-38","33","-60","-14","-28","3","35","-40","54","-4","-10","6","27","38","25","-12","37","-2","-6","-5","38","-19","-84","-9","86","-26","-12","8","-4","-2","-11","-3","133","-48","25","14","20","30","-1","-26","2","4","4","7","34","8","-20","-10","25","-71","-16","-4","34","-24","48","-33","-7","-33","-65","8","-17","8","-11","-64","-6","-24","91","-4","84","52","-31","28","-49","-10","69","12","57","-44","-34","-14","-1","46","94","13","36","-3","18","-45","3","0","-12","-11","-9","30","15","10","6","46","24","-18","-16","47","-91","2","19","17","-1","7","8","24","90","15","19","7","-28","12","8","60","-83","-7","34","42","30","-6","60","-26","-54","-16","-7","1","-42","-11","-32","37","39","16","27","-11","-62","-3","90","28","25","18","0","15","62","3","-24","-17","-45","-26","-18","-20","-13","12","67","30","-58","6","-53","0","72","2","-42","24","-47","-34","14","10","16","1","-48","14","119","-4","63","21","68","15","-12","29","14","-37","-66","14","41","22","-4","-40","-80","-1","51","36","36","-26","120","-20","-24","-8","-33","46","-46","-9","48","22","-83","-40","-45","-51","-4","19","-30","-38","0","33","-6","-60","51","-14","-80","-28","32","3","2","35","-4","-40","-142","54","19","-4","-86","-10","149","6","28","27","-78","38","-106","25","-30","-12","36","37","-186","-2","67","-6","-16","-5","-107","38","-19","-19","-17","-84","6","-9","-76","86","-137","-26","125","-12","-18","8","-50","-4","4","-2","26","-11","64","-3","-120","133","-61","-48","-128","25","-94","14","68","20","-2","30","12","-1","2","-26","-86","2","115","4","-73","4","-105","7","-68","34","66","8","66","-20","-46","-10","-32","25","-73","-71","-165","-16","26","-4","-9","34","-135","-24","34","48","-18","-33","4","-7","32","-33","-29","-65","-94","8","12","-17","-96","8","-43","-11","-66","-64","-126","-6","23","-24","22","91","-16","-4","40","84","-50","52","2","-31","110","28","-54","-49","-95","-10","-6","69","134","12","-52","57","8","-44","-102","-34","-2","-14","-10","-1","-24","46","50","94","-6","13","-119","36","-182","-3","146","18","-14","-45","-98","3","7","0","-67","-12","15","-11","74","-9","-34","30","-63","15","-53","10","126","6","-106","46","-130","24","40","-18","129","-16","62","47","-10","-91","24","2","-40","19","-104","17","-39","-1","98","7","-24","8","47","24","-124","90","86","15","-54","19","-16","7","-37","-28","-6","12","-42","8","8","60","6","-83","114","-7","-136","34","-42","42","21","30","-24","-6","52","60","-80","-26","-33","-54","143","-16","112","-7","111","1","70","-42","172","-11","-78","-32","-59","37","-24","39","76","16","30","27","6","-11","-23","-62","-12","-3","144","90","69","28","65","25","74","18","16","0","18","15","-6","62","-11","3","-32","-24","-14","-17","-45","-45","-30","-26","-72","-18","4","-20","3","-13","106","12","-60","67","-5","30","58","-58","16","6","102","-53","74","0","68","72","66","2","35","-42","-10","24","19","-47","84","-34","-88","14","63","10","172","16","82","1","96","-48","56","14","27","119","-32","-4","-80","63","-52","21","-45","68","188","15","80","-12","-69","29","46","14","50","-37","90","-66","30","14","35","41","-4","22","30","-4","24","-40","72","-80","-1","-1","-4","51","63","36","18","36","2","-26","64","120","29","-20","1","-24","-8","-8","20","-33","112","46","-25","-46","124","-9","-134","48","46","22","-66","-83","122","-40","4","-45","14","-51","-84","-4","73","19","106","-30","34","-38","99","0","170","33","134","-6","1","-60","112","51","144","-14","-22","-80","-5","-28","-2","32","14","3","-140","2","70","35","55","-4","78","-40","-58","-142","-25","54","-32","19","-106","-4","-40","-86","-35","-10","22","149","157","6","56","28","-83","27","-14","-78","190","38","-216","-106","-97","25","-145","-30","20","-12","90","36","180","37","-13","-186","168","-2","-286","67","-52","-6","113","-16","50","-5","-182","-107","-155","38","-64","-19","-100","-19","42","-17","184","-84","-149","6","120","-9","123","-76","179","86","78","-137","-22","-26","-190","125","-32","-12","-134","-18","32","8","75","-50","-27","-4","-88","4","4","-2","2","26","1","-11","-174","64","65","-3","48","-120","11","133","47","-61","14","-48","30","-128","52","25","-38","-94","-67","14","62","68","-2","20","23","-2","-24","30"],"lmfdb":"agrees"}],"seconds":0.205,"computed":"atlas","estimate":{"seconds":0.359,"low":0.219,"high":0.621,"bytes":2084076}}