{"label":"731.2.a","level":731,"weight":2,"dims":{"new":57,"cusp":65,"eisenstein":3,"modsym":133},"old":[[17,1,2],[43,3,2]],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 17, 43, 731]: [0, 2, 4, 68] (certified at ell = 2147480161)","T = [(2, 1), (3, 1)]; h of degree 57 = 1 x 57 (phi(ord eps) x dim S_k^new); 6 primes, 0 rejected"],"newforms":[{"label":"731.2.a.a","letter":"a","dim":1,"charpoly":["-2","1"],"traces":["1","1","1","-1","-1","1","0","-3","-2","-1","-6","-1","1","0","-1","-1","-1","-2","-2","1","0","-6","2","-3","-4","1","-5","0","6","-1","2","5","-6","-1","0","2","-3","-2","1","3","-4","0","-1","6","2","2","13","-1","-7","-4","-1","-1","1","-5","6","0","-2","6","-3","1","-7","2","0","7","-1","-6","-9","1","2","0","11","6","-7","-3","-4","2","0","1","-8","1","1","-4","-9","0","1","-1","6","18","2","2","0","-2","2","13","2","5","10","-7","12","4","6","-1","-11","-3","0","1","6","5","-2","6","-3","0","1","-2","-2","-6","-2","-3","0","3","25","-7","-4","-2","9","0","-5","-3","-1","-1","-1","6","0","-9","5","3","-18","2","4","0","13","11","-6","2","-6","-7","-7","3","6","-4","4","6","2","0","-2","-1","2","-8","1","-5","0","1","5","4","6","-9","-18","0","-12","1","4","1","-24","6","0","6","-3","2","-10","-2","-8","0","-7","-6","3","2","6","-13","0","2","26","7","6","10","-1","7","8","12","-25","12","-9","6","0","1","4","-11","-4","-1","12","0","23","-1","11","6","1","15","0","-2","-7","-6","-1","-3","-4","0","8","1","8","2","-27","-2","0","-18","6","-2","-13","3","-8","0","16","1","18","25","16","7","7","-4","-2","-6","-9","9","-5","0","-12","-5","1","-17","18","-1","0","1","-12","-1","-12","18","-1","0","2","9","-22","5","11","1","0","-18","24","-2","-11","4","-4","0","-23","13","-6","-11","2","-6","0","-10","1","-6","10","7","-14","-7","3","9","30","6","2","4","0","4","6","2","7","2","-28","0","-11","-2","24","-3","-5","2","0","8","12","1","-36","-7","6","0","2","-1","-4","5","-2","12","0","6","-20","9","6","-18","9","0","6","-12","1","-1","-12","4","0","3","-2","-24","-5","-6","8","0","-5","-30","-19","-3","-11","-2","0","-10","13","-6","-15","-8","25","0","7","-7","-2","-2","8","3","0","-2","-16","6","9","-39","6","0","20","-2","-5","26","-16","-3","0","6","2","-10","-30","-1","-2","21","-1","8","8","-12","0","-25","0","4","-10","-9","2","-6","-1","0","18","3","-12","4","-18","11","0","-4","9","5","4","12","-4","0","-10","23","-26","-3","4","11","0","-6","-6","1","-12","5","-24","0","-6","2","-4","-7","20","-18","14","-1","-37","3","-2","-4","6","0","-9","8","24","-1","4","8","0","6","-24","-27","5","2","39","0","16","-6","-2","6","36","2","0","-13","2","9","6","-8","8","0","-2","16","36","-5","-3","18","0","-25","-10","16","30","21","5","7","-30","4","-6","-2","-12","-2","0","-9","37","-9","-18","-5","33","0","-6","-12","-12","5","9","1","0","-11","10","18","11","1","-78","0","-24","3","38","-12","-18","1","0","-12","-2","6","-19","-1","6","0","-4","2","-6","27","-10","-22","42","-5","-8","11","-8","-5","2","0","-2","18","14","24","-12","-6","0","-11","3","-4","3","-4","-1","0","6","-23","-20","-13","-1","-6","0","-33","-35","2","28","6","26","0","-8","-14","10","1","6","6","0","10","-6","21","2","-14","26","7","-4","3","8","3","14","30","0","-6","-25","2","-19","12","-19","0","18","-4","-25","6","11","-10","0","7","13","-2","-6","-28","4","0","-42","-11","-6","2","-10","24","0","-1","11","-5","12","-2","3","0","-6","24","23","12","5","-1","-7","-36","-22","3","39","6","18","0","1","2","-6","-3","18","-4","0","-5","-14","-2","1","4","14","0","20","-6","25","-20","-1","27","0","6","12","18","-4","9","42","0","-7","6","20","12","-2","1","0","-3","8","-12","24","-4","18","0","-27","1","1","-2","-4","24","0","-5","-4","-18","4","8","6","0","-23","-5","6","-42","-13","-19","0","3","-10","-11","16","-6","4","0","6","10","16","13","26","-2","0","-15","18","8","-24","25","-8","0","13","7","1","7","38","-2","7","10","54","8","-34","-3","-2","0","15","-6","-6","-16","18","-6","0","9","33","-13","-5","6","-4","0","46","20","-12","-6","20","-5","0","-26","-2","-16","-3","-17","-15","0","18","-6","38","2","-8","-30","0","-30","8","1","-66","-2","-30","7","-2","-1","22","-8","-12","8","0","-36","-7","0","-1","25","15","0","-13","-20","-4","-10","42","9","0","2","-22","-18","-16","-1","28","0","11","18","-5","1","2","-12","0","-4","22","-18","26","33","24","0","-30","4","-40","9","-11","7","7","4","18","-12","-10","-4","23","0","7","-10","-23","-23","12","-26","0","-1","-6","4","-6","-11","22","0","-4","-18","32","-6","22","-1","0","-12","36","-25","24","-24","1","0","48","-6","-9","6","-20","-4","0","7","32","20","-14","-6","58","14","43","1","3","-37","-28","9","0","-2","-6","4","-26","6","10","0","2","-9","12","-8","-1","24","0","-3","8","4","-58","-8","-12","0","-13","2","54","-24","7","27","0","5","5","6","-28","39","11","0","12","16","22","30","-30","-2","14","-6","24","36","-6","6","8","0","-5","13","-24","2","-8","3","0","6","-54","8","-7","8","12","0","-44","-2","-26","-16","-36","36","0","-7","-27","-3","-12","-18","-6","0","16","-75","2","-10","-7","-16","0","30","-4","7","58","5","-12","-7","4","-30","-15","12","-8","-6","0","2","-2","-12","-61","10","-20","0","25","9","-38","37","15","-27"],"lmfdb":"agrees","curve":{"cremona":"731a1","lmfdb":"731.a","ainvs":[1,0,1,-539,4765],"rank":1,"torsion":1},"derived":{"al":[[17,1],[43,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"731.2.a.b","letter":"b","dim":2,"charpoly":["-4","1","1"],"traces":["2","-2","1","-2","-1","-1","0","6","3","1","-4","-1","-5","0","-9","-2","-2","-3","6","1","0","4","4","3","-1","5","7","0","-2","9","-12","-10","-2","2","0","-3","-7","-6","-11","-3","-2","0","-2","4","-10","-4","-15","-1","-14","1","-1","5","-9","-7","2","0","-14","2","-3","9","-11","12","0","14","11","2","7","2","2","0","7","9","-3","7","8","-6","0","11","-10","1","-14","2","11","0","1","2","-18","-12","16","10","0","-4","-6","15","14","-5","16","14","-6","1","-4","1","-31","-15","0","9","4","-7","8","-2","5","0","-3","14","-2","2","-16","3","0","-27","-14","11","16","12","-3","0","7","6","-1","-11","3","2","0","-7","5","-6","8","-2","-14","0","1","-7","10","-3","18","3","-7","7","0","-8","16","18","-3","0","6","11","-12","10","21","5","0","14","-39","2","18","-11","44","0","-5","-1","-8","2","-2","18","0","4","41","-16","26","10","-14","0","-31","12","-5","6","4","15","0","-14","14","7","4","-16","31","14","-6","6","23","-3","-5","4","0","1","-16","31","6","5","-12","0","-29","9","-5","-4","1","21","0","-8","41","-2","5","-5","-32","0","7","3","8","14","-9","2","0","-6","30","16","-1","3","12","0","-16","9","14","14","-28","11","7","-16","2","-36","-37","3","-17","0","-8","-7","9","-34","52","1","0","-11","-20","-3","-8","-6","-21","0","42","-7","0","-5","-9","2","0","-8","2","-2","33","14","-18","0","-13","-1","8","-7","-10","-10","0","-15","2","-18","-26","3","16","7","-41","-21","-14","0","-10","-8","0","-16","-2","-6","31","3","-12","0","-7","-6","6","-33","11","12","0","10","-14","-21","4","-7","2","0","-6","14","-6","39","38","-6","0","-18","24","-11","-2","-44","5","0","-24","5","41","-1","24","8","0","-6","-18","2","-41","18","-30","0","-9","20","7","-41","5","-16","0","-26","13","-30","14","14","-7","0","-41","31","4","-4","14","5","0","6","-50","-4","41","-45","22","0","-10","-14","-73","-14","0","3","0","-4","-3","-16","-28","-31","-4","-42","-41","6","-12","6","22","-23","0","1","-24","5","30","4","7","0","14","-3","-14","16","-30","31","0","-6","37","25","44","12","-40","0","-24","29","-14","-27","1","5","0","-4","22","-1","-18","-7","-2","0","26","-8","12","-41","6","6","-21","-5","-1","-5","-42","32","34","0","-65","-7","4","3","8","-8","0","-42","-34","9","-7","2","-15","0","-16","2","54","-30","-32","16","0","1","62","-9","4","-12","-20","0","12","16","38","45","9","-14","0","14","26","28","-20","-33","-11","-7","14","-16","2","-2","20","12","0","37","-3","3","22","17","17","0","2","8","40","-7","-29","-9","0","22","38","-52","7","1","30","0","16","33","-30","20","70","-3","0","8","12","2","-38","21","38","0","-12","-42","-2","21","30","0","28","-5","2","9","44","10","-38","0","36","-8","-42","-2","28","6","0","-33","23","14","-7","18","5","0","2","13","-20","-1","-41","-8","0","21","3","10","-44","-10","-10","0","-2","21","40","-2","2","-18","0","26","18","-9","42","-16","-30","7","-36","41","-88","7","8","14","0","0","71","10","37","24","9","0","2","-16","7","2","51","-30","0","-31","29","3","-36","12","-8","0","64","7","48","-6","14","-6","0","11","-36","-11","28","12","7","0","-42","-30","-57","14","73","-21","35","-4","2","-3","31","-2","72","0","9","6","2","-42","6","6","0","39","-14","-38","41","2","38","0","-76","-18","-85","-24","11","33","0","2","-4","-44","-16","-5","22","0","77","24","-12","5","-42","-41","0","3","-64","-24","62","8","30","0","-47","2","-3","18","32","2","0","41","-44","-54","2","30","-2","0","19","9","-38","-28","59","-7","0","-41","44","-5","2","48","-24","0","-22","-26","-8","-13","-12","10","0","-14","58","14","-16","7","-52","0","-6","41","2","31","0","-4","63","-20","-14","-14","-6","5","18","0","-1","-18","-34","50","-26","-4","0","-41","-23","15","-17","-22","-8","0","20","10","-4","42","2","73","0","-14","10","0","-35","-17","-21","0","26","-4","-12","3","6","48","0","28","-40","-31","-14","4","10","14","-62","41","-4","6","-72","12","0","-18","53","-22","15","-23","-3","0","15","5","58","24","6","5","0","-30","-34","-12","54","-7","-48","0","55","-14","11","1","-6","14","0","16","-16","30","52","-93","-16","0","-8","-6","74","-37","-43","-35","14","-44","-22","12","-42","40","19","0","-22","24","53","29","-40","14","0","9","-30","-1","-14","5","-44","0","4","12","66","-22","30","-1","0","18","8","-35","-16","2","1","0","20","-26","-9","24","-10","-12","0","-41","-34","-6","42","-2","-52","21","-9","-5","-29","1","60","15","0","42","28","32","-62","-34","-30","0","-22","65","12","-7","9","-4","0","-9","-44","-8","44","-8","-6","0","43","14","-22","34","75","9","0","7","-3","-6","28","15","-9","0","12","16","-38","10","6","-54","-42","-30","-48","32","-2","-48","-6","0","-37","1","82","-62","-4","3","0","-4","-16","-12","-35","20","44","0","-50","-12","10","16","36","-38","0","-63","10","-9","6","-14","-2","0","16","-42","14","-26","-11","28","0","20","-20","11","64","11","-32","-7","46","-14","-15","48","88","-2","0","-2","-4","-20","-17","60","12","0","-71","37","-10","3","-33","-9"],"lmfdb":"agrees","derived":{"al":[[17,1],[43,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"731.2.a.c","letter":"c","dim":6,"charpoly":["1","-1","-13","-16","-1","4","1"],"traces":["6","-1","-3","5","3","-7","-7","-9","-3","-4","4","11","-10","-7","1","-1","-6","1","-20","1","-8","2","-3","-9","-7","-3","-6","-11","-15","-6","12","1","-2","1","-9","-16","-14","27","5","-7","-2","19","-6","-12","-18","14","-11","-6","3","7","3","-5","3","25","6","22","11","-21","2","-1","-20","3","23","-39","-34","7","-2","-5","-17","-1","1","21","13","28","-5","-29","-11","0","-26","12","2","-9","10","-3","-3","1","12","-6","-15","15","8","-9","-11","-33","-21","25","-22","-3","-5","-53","-20","7","45","15","24","7","23","-13","-62","1","25","17","18","50","-19","21","47","-5","7","7","-48","20","9","21","30","25","5","50","3","15","-15","17","12","3","29","9","-27","-13","34","36","9","-9","-10","26","-25","62","15","37","-53","32","-25","29","3","-3","19","25","7","67","18","29","4","-5","57","-18","-6","-10","33","14","18","4","-18","-5","29","24","-4","13","-37","-10","-20","22","-53","75","-6","23","-21","-63","-4","-36","-14","-1","-12","16","18","-21","32","4","8","-17","6","19","45","20","72","-11","-83","-10","47","16","0","7","-60","12","33","41","-3","19","-47","2","-67","-25","10","15","35","9","-19","-83","18","-74","-11","25","-11","18","-9","-31","36","14","-39","7","-69","11","-70","24","19","-36","-7","33","4","-13","12","48","17","-49","-14","-16","-1","15","-34","7","2","27","4","37","6","-3","4","-54","24","-29","17","21","-10","1","-59","-51","34","-4","-12","-6","19","-6","10","24","-44","86","-17","-15","10","-34","6","-30","9","-31","0","-4","0","3","-6","86","54","-11","7","-47","-50","-46","-33","-1","30","8","-42","30","-37","-27","7","-26","-18","-43","-7","28","-39","-45","-41","26","20","-28","-53","-63","61","-5","25","-4","-52","80","-70","-67","32","-36","-12","-77","31","-1","-8","-38","16","9","22","29","32","-32","-1","1","-54","11","41","-18","-16","43","8","-72","35","4","42","51","19","-110","2","70","51","3","70","-38","-9","21","-39","-2","-52","13","8","-42","27","-16","6","-16","46","31","-30","29","3","-77","-72","10","3","-21","8","-19","-30","6","2","-53","53","60","-18","18","20","-4","7","-29","-40","9","-49","-13","97","48","71","-24","-28","-33","27","21","-47","-41","-77","-59","11","-24","7","-80","66","-109","2","4","64","-22","2","67","34","-48","-21","-13","-27","-6","-8","3","36","-141","28","-56","-23","8","74","-12","23","-5","18","30","26","56","11","-94","6","11","14","-10","-45","-24","-11","-34","-30","5","-100","23","58","33","-4","5","27","11","-72","-81","-43","-13","-51","33","-15","-67","89","-10","-81","46","-29","-3","12","107","15","32","-26","15","-53","-90","-47","-114","33","63","41","-8","19","-36","17","78","-37","6","2","30","32","37","42","-11","23","-127","21","36","24","68","-92","-149","56","-46","-12","-37","-61","-43","44","95","156","-72","39","-41","87","-24","17","-62","0","-36","-26","-1","-5","42","84","99","5","13","54","-4","25","-6","-32","67","74","-7","10","-77","2","62","-4","54","67","125","36","-35","95","20","-6","49","-45","76","-37","2","35","-1","10","103","-44","54","12","41","53","30","-13","33","-122","2","-35","-145","-76","-21","9","-127","-5","-88","60","50","47","7","-67","-12","-2","12","58","-34","7","-14","5","16","-70","66","83","33","65","-57","-33","-33","7","24","-37","-10","76","-30","18","-6","14","11","83","91","135","-49","-23","-43","29","6","-15","-33","22","107","64","-82","-1","-27","26","-5","-47","12","-2","-9","-29","51","21","21","34","95","40","10","-21","-31","-5","-32","81","18","-26","89","-56","13","-10","-16","-107","56","77","24","33","-23","24","7","-60","-50","-11","64","-17","89","126","1","-80","3","-23","88","57","-148","60","17","2","-75","6","135","-32","-2","162","5","-12","-28","128","-31","14","-7","66","6","73","-19","-63","120","46","92","57","-77","-5","-117","111","-33","-80","69","38","43","-21","31","6","-71","-60","-43","-5","-80","70","-91","44","46","-43","-105","9","-33","108","-6","26","12","-7","37","37","114","-35","178","47","91","-151","-56","8","59","59","-107","3","-97","18","71","-26","-115","49","13","44","70","-95","-1","-15","35","120","43","41","-61","-51","-14","-38","2","35","130","-88","-20","45","64","-43","22","-8","-66","-29","87","-42","-157","11","51","2","6","-10","41","-17","-155","15","90","-110","-39","44","69","8","12","48","6","20","-79","18","73","-8","-12","37","-48","-39","-54","29","8","-29","0","-42","65","-3","-32","1","52","40","93","-73","-3","27","65","20","46","144","25","36","-66","58","-7","-43","-22","-41","-101","108","-5","3","-13","-6","-1","-190","-7","-176","-36","-53","12","-3","-131","-48","15","2","63","-32","-82","-81","-79","-54","-114","-90","52","12","-36","11","5","42","11","87","62","-35","44","33","-8","-34","50","76","-48","-4","-60","-123","100","-3","38","8","-67","-73","34","0","-9","23","60","-82","5","-48","-273","19","128","-42","-25","-22","16","-24","225","61","-14","-91","2","-26","38","14","-12","2","26","95","-65","-6","-55","-29","87","-83","-58","-63","90","30","0","-41","-2","42","-140","-58","-118","21","-22","-94","7","-52","-31","15","56","-2","-23","12","118","-60","12","69","55","9","77","-11","45","114","40","-81","40","31","-38","-16","2","-49","-19","1","-18","22","-82","-29","21","-18","-40","3","-1","-51","-49","109","81","-78","20","-56","-32","68","-8"],"lmfdb":"agrees","derived":{"al":[[17,1],[43,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"731.2.a.d","letter":"d","dim":8,"charpoly":["46","-50","-215","69","131","-24","-21","2","1"],"traces":["8","1","-3","3","-7","-1","-5","-3","5","-12","-4","-13","-12","1","-9","-3","8","5","0","-5","-20","-14","-9","-1","-7","-17","-12","1","-27","10","-12","5","10","1","15","-4","-24","-1","3","-9","-8","-9","8","-16","10","-14","15","10","-7","21","-3","1","-23","-19","-14","-20","-13","-7","16","-3","-34","15","9","-25","10","15","0","3","-19","11","-3","-19","-3","-4","27","13","-3","4","-24","20","-8","33","-8","17","-7","1","48","16","23","11","-16","49","17","-11","3","37","-10","29","-15","23","0","-1","-21","45","-4","-11","-3","13","-68","33","3","-27","22","-42","27","9","-29","25","-5","39","-18","-18","-5","-25","-18","41","-21","4","-3","41","3","61","-16","21","23","-3","65","47","-28","28","-39","7","34","-22","-1","4","47","-67","11","22","-45","37","5","21","-7","47","-7","-43","-10","7","38","65","33","14","-12","44","-1","44","-30","-12","24","3","-43","18","2","-23","19","58","10","40","-11","-17","92","-37","37","57","-4","58","-50","31","-16","18","-36","99","38","-38","-2","-13","-22","-7","7","10","-48","-13","-3","22","-27","14","-4","-23","-12","-30","-73","-33","-7","45","17","-26","43","21","-12","65","-1","-11","-63","-17","-4","6","-25","-59","55","34","-13","-41","-22","20","45","1","35","29","-56","-4","-9","-62","11","-39","38","-51","50","-20","19","83","-38","10","-9","-3","-4","-1","-18","-21","-54","73","52","-47","20","4","-58","-23","23","-43","-8","-3","73","-55","28","-52","-68","-34","13","32","-68","32","8","-46","39","-17","48","-38","8","14","13","-5","-48","-50","-34","53","-4","-74","-14","11","-5","-43","6","-14","1","5","66","6","18","-50","-37","-21","-19","-26","-14","-23","-11","-94","13","-23","9","-30","0","2","-21","7","27","7","-29","-46","-8","-70","-38","71","8","16","-4","43","-31","-5","16","38","-52","-3","-24","45","6","12","-63","-47","76","-1","47","-16","90","-23","-20","48","5","12","-80","3","-27","-30","-32","60","13","-1","-76","34","61","-5","-39","-14","6","11","68","-118","-71","-46","42","-56","52","-105","-30","-11","5","17","12","34","-9","5","-74","-73","80","-18","-22","101","-35","-36","54","-26","-54","20","19","-67","46","-1","3","-33","7","-62","-61","-50","14","-15","-101","-79","77","-37","-75","65","51","8","-7","-18","18","-109","-72","-12","-10","116","-8","-9","26","2","-43","41","-3","62","92","-17","26","93","-80","-60","41","68","0","-84","-53","49","58","-98","6","22","67","-108","-12","53","-64","40","7","30","-43","126","72","-43","-44","-83","-80","13","-4","53","-65","1","76","89","-51","-65","81","-49","85","-9","-17","-122","53","-36","5","37","26","19","-27","0","-2","15","51","-128","49","-8","-21","-3","5","-6","-49","102","11","-48","25","10","34","-24","-6","-99","22","-13","17","-59","77","-60","-84","-92","86","129","120","46","-12","-103","-7","169","-4","-9","-18","-28","49","-31","41","16","-75","-16","-106","24","-38","5","119","82","-84","1","-119","43","16","80","-3","-104","86","-95","-4","-37","-12","11","10","-36","-24","-58","-39","59","114","-7","-39","56","4","3","-23","-32","65","30","17","1","-22","-29","8","-218","68","-99","-9","18","17","-77","-94","-70","139","139","54","59","15","125","-3","80","22","-66","-73","1","149","-94","14","-34","22","-38","65","72","7","-4","114","-88","37","29","15","83","3","89","67","-18","23","-88","50","-28","2","8","-24","-29","-19","-11","-11","19","45","113","-17","38","107","79","16","-1","-12","-54","-9","-1","178","-13","-53","-20","24","135","15","-5","-45","7","2","-33","72","-16","-39","77","3","-42","39","-138","28","-59","102","7","72","-30","-37","-24","9","-44","19","113","-20","-9","192","132","-11","-42","-77","-33","34","-3","42","69","93","-6","-45","132","106","-37","-8","9","66","-95","106","172","-22","115","-22","46","76","-75","-180","53","-102","6","49","-9","43","-2","18","-122","-81","-39","-9","27","-45","31","76","-17","92","23","29","-41","8","95","128","75","45","44","-42","-35","64","16","77","151","-47","-53","14","10","82","-16","-7","-111","-43","-32","63","100","45","-49","-7","-38","98","-95","53","35","83","115","10","-13","-28","71","19","-85","-146","-18","-3","5","119","47","146","-53","-29","-3","-69","-14","118","68","59","-142","124","-32","-131","80","57","88","16","-30","17","33","64","-29","15","11","120","104","24","-81","-21","-1","121","-26","-96","55","-122","-15","-160","60","-38","10","0","-99","-56","-105","-52","94","89","12","53","-68","121","66","-157","118","16","-9","-7","-132","7","-22","8","-45","-107","-15","-19","-19","-28","60","-20","-23","18","-124","-40","21","-51","-4","-61","15","10","17","-99","-77","-16","-5","116","9","34","-10","-45","44","-3","69","-48","17","-52","13","56","56","-85","-29","-36","-180","-168","58","-2","66","-63","1","4","1","-69","-144","-59","-88","-109","64","32","86","-6","140","52","214","23","-36","-23","-30","-20","-23","69","10","-116","-45","-65","-2","-20","49","-80","-121","-53","18","94","-19","-4","-36","32","-123","-11","-68","-47","62","-62","30","-40","-134","68","-112","-51","-69","-14","59","13","23","15","26","-203","-14","62","30","33","-14","66","-4","-100","-70","-105","-20","72","209","58","-167","-61","-138","12","-29","-26","124","56","48","17","67","-143","59","-13","13","-180","-16","145","-262","-115","14","-60","-180","79","-27","-159","-6","76","10","43","-7","-6","-16","-9","-45","57","-15","53","43","-48","-14","38","74","214","152"],"lmfdb":"agrees","derived":{"al":[[17,-1],[43,-1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"731.2.a.e","letter":"e","dim":19,"charpoly":["18664","97184","-438020","-872528","2310386","1968634","-3412797","-1383186","2172759","362811","-683939","-25108","113803","-4548","-10047","894","435","-53","-7","1"],"traces":["19","2","5","26","11","3","7","-6","28","-2","4","9","14","5","-7","32","19","12","12","23","16","36","-1","-13","30","-21","8","5","41","-26","-8","-20","-14","2","3","-5","50","-29","17","-15","6","-1","-19","16","24","38","-21","-2","46","-36","5","39","-9","53","10","-12","-5","-45","-4","-7","68","-25","61","-14","22","-17","0","26","-9","-37","23","-4","-1","-30","-25","47","-19","12","16","28","-21","-13","-32","-47","11","-2","-8","108","11","5","52","-23","-23","47","-25","-103","36","-100","-11","44","-4","3","-37","-47","32","61","-3","-33","50","-63","-9","13","24","2","-55","15","-33","-37","7","-53","69","-36","45","-13","48","-155","-29","-31","-5","-67","23","-179","36","-33","-11","-6","-17","-93","24","28","11","-29","-46","-59","27","2","-69","33","25","-194","87","-143","28","-7","-61","27","33","-65","-22","-175","-60","34","-7","-20","56","-50","-25","-134","15","-2","-102","-26","27","52","-26","-11","-97","-44","-20","14","95","-117","-38","-51","-69","13","4","-138","36","77","32","74","-6","-33","-92","125","52","-81","86","-132","-11","-66","-64","9","81","38","-15","104","30","-103","-2","-76","-51","-21","-11","85","21","-76","37","-5","14","3","71","33","0","93","-18","-98","73","89","-41","-116","29","-61","70","-136","41","5","1","5","48","39","-1","-2","-27","-119","60","193","-26","112","-73","41","-30","12","-7","-56","-76","-3","66","223","152","-55","-38","193","24","68","74","-19","137","-123","0","32","-115","35","-52","216","106","130","-123","-42","2","20","-68","72","3","-25","-46","-43","19","-46","61","49","44","234","-12","-125","-30","12","-70","-29","-7","1","30","6","-1","12","-60","4","188","198","7","7","-19","68","12","133","23","138","5","-19","11","-126","12","-95","129","-33","-43","59","-9","-60","-32","-62","64","3","22","-24","102","12","-37","23","-104","-82","38","6","88","71","-90","40","69","77","-60","267","21","-40","52","-27","16","124","-27","86","43","71","61","36","-18","174","-83","7","126","-14","41","-139","119","36","-260","41","0","362","5","150","112","48","-10","-73","-242","83","-28","15","-26","-202","-1","-282","4","-5","106","54","-12","105","-107","213","28","30","54","-54","-23","-77","-52","-13","-39","7","15","-10","97","176","-16","-235","-17","-59","-15","419","49","-151","-63","110","30","-96","-102","203","-18","2","74","-88","20","83","-50","52","57","139","37","-110","193","-21","-126","133","68","184","-103","190","26","113","-21","161","-78","130","-72","-60","9","-96","8","-173","-90","-40","75","226","-107","-36","-38","183","118","-183","-8","-115","-4","13","67","5","8","35","-87","23","107","85","-63","378","-15","34","-107","-30","59","-209","-80","-217","41","-140","-14","-77","-93","196","43","90","-63","-93","-27","-286","169","196","1","-40","103","-26","-190","-63","-150","107","-108","-9","41","201","93","-228","-110","74","20","-47","4","-70","-8","-201","100","49","-30","-17","126","88","-9","75","-103","86","-127","28","84","-68","10","-20","-89","-162","36","77","193","221","-140","-48","-11","262","-362","-19","-90","-241","-14","155","-14","-112","26","126","-145","59","140","129","19","288","-30","-165","253","-180","-3","-103","33","2","-190","-185","-18","102","-96","11","-81","-84","-185","-87","146","146","-99","13","-166","-233","3","55","-159","30","-110","-154","95","-5","43","256","68","10","32","82","13","86","29","-5","70","-198","-11","337","33","263","-73","-233","-85","-194","-165","390","17","-114","-194","-56","50","-141","83","-287","-53","53","87","-25","9","258","-35","-191","26","-345","-136","-22","7","-29","-82","-74","-89","38","-332","71","77","135","-37","105","-336","143","40","-420","-77","-135","17","-108","-175","84","-50","89","-30","-157","-130","-164","-51","-18","-133","-115","-13","241","20","-15","-156","-126","-67","68","-89","79","-130","-32","96","73","-191","-44","-179","72","-264","49","6","43","22","-345","76","60","42","-89","-46","158","-36","-5","138","161","-106","-240","-91","-1","-211","80","-74","188","-245","-1","-31","2","-201","317","186","-65","-174","-353","-74","-293","-19","-85","78","-47","1","68","-54","117","128","-84","-119","-125","5","7","170","-256","-14","16","-179","-127","31","-40","59","-88","-3","-221","75","208","-204","-55","-63","-125","135","127","24","-65","-4","77","-63","421","-114","-236","-121","-12","-73","13","220","-171","-127","269","333","38","-110","19","79","-78","32","482","45","-152","-79","94","-92","156","-67","-3","-166","95","-21","-432","80","-188","-86","-73","71","115","75","96","-130","65","88","-63","150","-28","176","-2","-12","19","144","457","98","126","-59","156","29","-32","17","210","-19","-350","152","-123","46","120","169","-180","-56","-185","109","-295","54","155","-118","-8","-122","-43","44","-2","218","-36","-119","-432","133","175","-198","-97","67","319","-10","-23","220","41","-72","118","-109","26","5","41","-4","-135","-2","-179","-66","140","13","351","2","470","150","-360","0","67","-31","39","-130","-181","157","78","87","104","-169","152","-106","232","-202","28","116","24","-287","-187","-9","-114","-16","291","-37","0","-40","-165","67","-40","142","-11","20","341","37","200","-62","53","0","288","-26","-125","-71","-216","189","-174","54","-176","-144","372","74","-104","-89","-17","10","139","-79","-1","333","126","39","42","-66","-198","-333","-36","58","376","242","-70","-11","-12","80","-39","-86","25","51","-226","72","551","97","240","-48","296","-43","-209","-177","128","-5","-163","40","-194","55","122","-43","-80","-212","338","-23","271","207","-18","148","-62","-37","-45","12","-232","1","315","175","219","-51","169","-94","178","54","-66","-26","152"],"lmfdb":"agrees","derived":{"al":[[17,-1],[43,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"731.2.a.f","letter":"f","dim":21,"charpoly":["8336","-232064","-1019600","1516088","11299712","11063844","-10981847","-17778836","2738738","10310917","444674","-3005123","-286856","502944","46482","-50238","-3306","2897","100","-86","-1","1"],"traces":["21","2","-1","32","-3","1","5","6","34","12","2","-5","26","-3","5","62","-21","-10","16","-27","36","-14","-1","15","40","-3","-16","25","15","38","18","14","14","-2","-5","73","12","19","-11","41","0","-45","21","-34","-18","28","-1","-36","40","24","1","23","39","-83","-2","-10","3","19","4","-35","50","5","-37","120","-8","-37","16","-32","33","-1","1","-54","15","52","11","-15","13","-100","56","-100","97","-11","0","61","3","2","-8","-56","5","-69","-4","-27","17","-47","-9","81","-28","18","-19","14","28","-1","19","-25","-76","-17","17","-105","140","-51","-25","-47","-12","-78","19","49","91","-27","-5","-69","55","-84","-93","-49","-66","69","63","-47","-1","3","-73","49","-8","-35","-7","-6","-13","-89","12","-180","45","-25","-38","55","3","-78","-3","-23","53","-16","-33","29","-34","-79","-11","-145","31","-65","-52","141","54","-186","7","-112","-50","20","-17","-168","85","-12","36","32","-97","-242","0","-165","-11","-16","-26","-290","85","-81","2","123","-13","-115","-2","10","88","-143","-76","-206","44","31","52","-5","-10","69","-24","8","-19","32","28","5","145","-102","-79","-40","-82","31","88","152","29","11","-3","-105","5","60","5","-7","-26","-19","-97","-27","46","-103","-48","174","57","-11","-3","130","-33","153","-78","44","17","3","41","-35","44","-59","-29","172","35","85","-58","-27","130","-28","3","37","118","42","-5","262","42","1","6","-87","96","101","76","-175","-2","-34","-120","109","-45","149","8","-62","61","187","68","-12","90","-60","17","-28","-10","-80","26","26","51","49","0","55","21","138","-135","-149","60","-108","-40","147","-60","52","22","241","5","97","-86","54","-93","10","72","50","42","-194","-63","-243","39","140","-168","143","-73","-24","33","91","-43","82","-16","207","105","81","-57","-65","109","438","12","10","82","-93","-136","132","-2","126","107","27","204","194","-38","6","-190","-77","-2","-48","71","-243","56","-219","-27","170","-72","119","-36","28","85","56","121","-161","-147","164","170","-84","97","-47","-136","-82","-45","223","115","14","88","-101","-60","-130","25","-52","34","-92","4","315","70","83","34","37","22","142","1","38","-4","-27","-92","-192","16","95","-11","-53","-36","134","-96","58","-43","77","-30","-15","77","51","-143","-122","1","260","12","95","-57","9","-31","-473","191","53","-23","138","-40","110","-14","361","148","12","-158","-152","-70","-113","86","238","-149","-47","67","162","-97","3","50","41","112","-80","-23","-198","-68","63","51","-173","54","-154","28","178","65","306","16","81","18","-6","-129","-58","1","54","-152","251","186","135","-62","-51","2","129","-201","-25","152","53","-65","-389","-63","-155","-59","56","83","-22","-43","-146","-101","309","50","35","-15","192","-270","-111","-69","358","-23","-14","135","33","-37","320","-147","-294","-157","180","11","-38","90","-47","120","87","-18","-5","-17","117","-67","68","8","-336","-2","-15","184","90","-18","597","-34","-171","-186","-105","-48","212","-95","-39","-69","146","-13","156","110","180","-230","-14","107","-18","-26","-133","87","-67","-22","-460","-47","82","30","9","46","263","26","-149","-14","-70","-62","300","55","19","-318","-15","-21","-312","144","-75","-97","112","-143","199","-141","2","-94","187","-90","-158","20","-51","-47","-108","-91","261","438","270","-117","-175","-4","-37","5","23","5","30","50","-118","27","-3","-45","-222","-172","64","-126","226","-197","-16","-167","-73","134","140","-129","-555","-61","-33","13","-59","51","-74","-145","-446","95","246","-178","82","-12","339","-99","-67","159","-131","-283","-67","177","42","-121","71","-24","63","22","510","5","-19","-6","-4","69","-194","-14","-67","-177","-153","-137","-557","86","-177","4","-10","191","-75","11","186","-177","342","-76","-33","-112","77","80","-466","79","194","-157","-21","-93","-287","-136","-41","-8","-28","-101","-318","103","-327","-204","62","-96","19","33","-138","135","288","-34","-405","0","151","-154","181","44","-446","-30","-309","-214","-204","-116","69","124","-131","-12","-176","-31","45","-137","74","-178","-210","-25","-421","-59","-304","39","-91","0","-319","-92","275","124","-89","-21","35","-10","121","-295","174","-150","109","-40","-200","-15","-261","83","3","-268","84","-186","34","77","613","1","36","-201","170","-157","199","51","-212","198","-381","59","257","-177","-221","18","107","-184","-495","61","271","8","-16","35","-10","-133","-167","-190","117","75","197","91","-28","102","221","-85","-150","-18","-122","41","-36","-91","-70","146","280","45","109","74","487","1","46","-98","166","-20","47","235","241","-91","0","-48","-263","-290","-131","96","-32","16","36","16","47","-94","263","26","164","171","60","-335","-242","111","-230","149","120","-96","85","-40","-156","-29","194","60","145","-215","341","68","15","220","268","12","137","-2","530","-140","-24","69","192","-87","-309","180","-225","-59","171","-44","-27","-6","-173","-114","432","63","-54","-1","-55","-8","367","-170","215","-174","-294","53","-125","156","38","-60","126","-34","-313","65","-23","130","113","-159","-40","-153","40","259","-252","56","-76","188","120","-208","-48","11","379","-39","102","36","-91","-39","-80","-74","-137","3","-110","-78","265","-164","245","91","-172","-14","83","56","-132","-82","-145","131","382","175","78","186","246","100","126","4","336","149","67","2","-179","-1","247","97","-520","107","-110","154","-42","-15","-14","-20","332","-30","466","-193","10","2","23","-92","9","-89","26","-62","-17","-9","-182","166","-170","181","67","35","64","-3","-131","-40","86","89","-50","59","328","96","364","25","19","439","-406","88","-166","23","-19","340","-40","-1","-209","217","7","45","-221","126","262","-86","160","-14","-232"],"lmfdb":"agrees","derived":{"al":[[17,1],[43,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.236,"computed":"atlas","estimate":{"seconds":0.515,"low":0.314,"high":0.891,"bytes":2313420},"url":"https://sagebrush.space/atlas/mf/731.2.a"}