{"label":"871.2.a","level":871,"weight":2,"dims":{"new":67,"cusp":77,"eisenstein":3,"modsym":157},"old":[[67,5,2]],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 13, 67, 871]: [0, 1, 6, 80] (certified at ell = 2147483053)","T = [(2, 1), (3, 1)]; h of degree 67 = 1 x 67 (phi(ord eps) x dim S_k^new); 7 primes, 0 rejected"],"newforms":[{"label":"871.2.a.a","letter":"a","dim":1,"charpoly":["-4","1"],"traces":["1","2","2","2","2","4","2","0","1","4","0","4","-1","4","4","-4","-5","2","-5","4","4","0","1","0","-1","-2","-4","4","3","8","-2","-8","0","-10","4","2","11","-10","-2","0","-12","8","10","0","2","2","11","-8","-3","-2","-10","-2","14","-8","0","0","-10","6","-3","8","10","-4","2","-8","-2","0","1","-10","2","8","-8","0","-11","22","-2","-10","0","-4","-4","-8","-11","-24","12","8","-10","20","6","0","11","4","-2","2","-4","22","-10","-16","-8","-6","0","-2","10","-20","8","0","8","28","17","-8","6","0","22","-8","-16","-20","2","6","-1","-6","-10","0","-11","20","-24","-4","-12","4","-1","0","20","-4","-20","0","-10","2","-8","0","16","4","10","8","22","-16","0","-4","6","-22","-6","22","-7","-4","-17","0","-5","0","-4","-4","-7","-8","28","-16","2","-22","-1","-24","0","24","8","0","1","-20","-5","20","-21","12","-2","0","-6","22","-12","4","-1","-4","20","0","22","-8","0","22","-8","-20","-14","-16","21","-16","-4","-6","18","0","7","0","2","20","6","-20","-24","16","1","4","0","16","4","28","-16","34","20","0","-4","12","-22","0","5","44","7","-16","-1","-32","-17","-20","16","4","0","0","14","-2","22","-6","-8","-20","-8","-16","-15","-22","-10","20","-6","-48","5","0","24","-24","18","4","0","-2","-20","16","-1","40","22","-4","3","-40","-24","0","28","-20","22","2","18","-16","-8","20","-4","32","0","4","-2","20","-2","0","-30","44","-11","-16","-20","0","-24","-8","8","12","-16","-22","-6","-12","-6","0","0","-14","-1","-4","20","-34","20","20","20","-10","-5","0","16","-8","-18","0","12","-14","4","-8","30","56","0","-16","34","4","25","-22","1","-2","12","0","22","0","-10","24","11","16","2","-16","-34","2","-32","-20","0","-10","-20","0","4","-42","18","12","-26","-4","4","0","8","-12","-16","22","-20","-24","15","0","6","-2","-22","-4","-22","40","-24","-4","-12","44","28","-8","12","0","-24","0","-3","-16","10","-20","-2","-28","16","0","0","42","10","-16","6","-8","-5","0","-40","36","-8","0","13","14","-20","4","24","4","2","20","-22","12","0","0","-32","-48","32","16","-6","2","24","8","20","0","-9","16","15","8","11","0","5","-32","20","34","0","40","35","16","26","-8","12","12","-5","-44","-1","0","-3","10","2","44","22","14","-14","-16","11","-2","0","-32","-34","-34","-4","0","1","32","20","4","9","0","12","-12","-8","28","-28","-2","2","44","-14","0","0","-16","5","-20","14","-16","39","-32","-11","-30","4","-22","-16","-20","34","0","-2","-12","-33","-48","-15","10","0","8","-16","48","-24","-24","16","36","-18","0","20","0","2","-2","-3","-40","-22","32","20","-2","16","40","0","44","-42","0","-8","6","13","-40","-4","-48","10","0","-22","56","-3","-20","12","44","34","0","-24","36","0","-16","-10","-16","-2","40","12","-8","-2","32","10","0","-15","0","-8","-4","44","20","46","-4","-10","-16","0","-60","16","44","-32","-22","-22","0","17","-40","-39","0","-28","-48","-1","-8","-20","16","42","12","24","-32","0","0","-2","-12","8","-12","10","-12","36","-44","-2","0","-20","-14","14","-2","4","0","-5","40","1","-34","-22","40","0","40","12","40","-11","-10","19","-10","-48","0","27","32","-4","-8","-4","-36","22","8","-19","24","0","-14","-55","8","-34","0","8","60","-2","56","3","0","-8","0","-12","68","4","4","40","50","-2","0","0","2","-8","-2","-2","24","-40","48","-11","44","23","0","-6","-20","10","0","-20","22","3","16","14","4","0","-32","14","-68","4","2","44","-64","-16","0","-34","0","30","-10","32","-40","32","-40","-14","8","11","-42","0","36","20","0","60","-52","28","-4","-4","8","-55","0","44","16","20","-12","-2","-32","-4","0","-2","-40","0","-24","-16","30","-15","-8","16","12","-30","-2","-3","-44","-18","0","13","-44","-50","40","32","-48","-12","-8","0","-24","-52","44","10","56","-40","0","-14","24","12","0","34","-48","-5","-44","36","-6","-34","-16","36","20","0","0","3","-4","12","-28","-10","32","3","32","34","0","-2","42","-3","20","2","0","44","12","60","-8","0","-10","-12","12","-14","-80","-32","36","-48","-16","-32","0","-10","26","56","14","10","-40","-55","8","11","48","0","4","4","4","36","0","18","-44","-54","12","-16","0","-2","40","-50","-64","-2","-48","-29","64","-37","0","0","-12","-51","2","17","48","-4","8","15","40","16","0","8","-18","21","0","-20","30","-60","8","2","22","-22","-56","-22","10","11","-32","-7","40","-10","0","-18","0","-40","40","-48","70","21","32","-42","52","16","-8","0","24","-1","0","-8","-10","-24","-44","-27","-2","-12","0","-33","-6","24","10","-12","4","-39","0","-2","44","0","14","-55","-28","-24","0","-2","22","-6","-2","-70","0","40","0","-2","-68","-19","-34","10","-8","-55","40","0","2","40","32","-40","40","-36","0","-10","18","8","0","-11","24","8","-24","34","-16","15","28","-36","-56","0","0","-26","4","24","44","-12","-28","-12","12","-16","0","5","-16","11","10","60","0","57","28","-28","-16","0","78","32","-32","-27","-22","17","-30","42","8","-32","0","50","-32","-15","-20","20","68","2","-40","-33","-4","0","-12","6","-66","-32","0","36","-30","44","10","10","0","-28","16","-20","-32","14","48","14","-48","-44","0"],"lmfdb":"agrees","curve":{"cremona":"871a1","lmfdb":"871.a","ainvs":[0,-1,1,-42,139],"rank":0,"torsion":1},"derived":{"al":[[13,1],[67,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"871.2.a.b","letter":"b","dim":3,"charpoly":["2","-6","0","1"],"traces":["3","0","0","-6","0","0","0","0","3","0","-6","0","3","0","0","12","-3","0","3","0","-6","0","-9","0","-15","0","-6","0","-15","0","-6","0","-18","0","0","-6","-3","0","0","0","-6","0","6","12","0","0","-3","0","3","0","-18","-6","0","0","0","0","6","0","-15","0","-6","0","-18","-24","0","0","3","6","0","0","18","0","3","0","0","-6","-12","0","-12","0","-9","0","12","12","0","0","18","0","-21","0","0","18","-12","0","0","0","6","0","24","30","-6","0","-12","0","0","0","15","12","-18","0","36","0","0","0","0","30","3","0","30","0","27","0","-18","12","0","0","21","0","-36","0","0","36","-24","0","0","0","-24","0","30","0","0","0","-6","12","0","0","30","6","39","0","-21","0","-15","0","0","0","-21","0","-36","0","0","0","9","12","0","0","-24","0","3","0","21","-12","-3","0","0","-24","54","0","-30","0","33","0","24","0","0","0","12","6","0","0","24","0","-33","0","0","-6","-6","0","33","0","0","0","-30","36","0","0","-9","12","6","0","-12","0","-18","0","0","0","48","0","-12","0","-3","0","15","0","-15","0","-45","-12","24","0","18","0","-12","0","0","30","36","0","-30","0","-3","0","12","12","0","0","3","0","36","0","-30","36","18","0","0","48","-15","0","-18","0","-3","0","-12","0","0","0","18","-6","-42","0","6","-12","-6","0","30","0","6","0","-42","0","-78","0","15","-36","0","0","-12","0","0","0","72","-6","30","0","0","0","12","0","-9","0","18","0","36","12","0","0","21","24","-18","0","-54","0","-36","0","0","24","30","0","24","0","54","0","-33","18","-15","0","-6","0","-42","0","18","-24","-21","0","0","-24","-6","0","-36","0","-12","0","6","0","0","0","0","-36","-12","0","-6","0","-18","0","0","42","54","0","9","0","-30","0","6","0","0","0","24","-36","24","0","18","24","-12","0","0","0","-15","0","72","0","24","0","6","0","0","0","24","-12","-42","0","9","0","-54","0","0","-48","39","0","-36","-60","-30","0","-6","12","0","0","-48","0","-36","0","18","24","-48","0","0","0","-48","0","-27","0","3","0","39","0","15","0","30","-30","-18","0","21","-24","-36","0","0","36","-9","0","-27","0","-33","0","-48","-72","0","0","0","0","-27","0","60","0","-18","0","0","0","-21","0","6","0","-33","0","6","-60","0","0","12","-6","0","0","-72","0","42","0","-15","-60","18","0","-9","0","-3","0","18","-54","0","0","42","0","12","0","-3","36","-33","0","0","-24","-54","0","-24","0","0","0","0","0","0","0","0","-42","-3","0","-78","0","-6","0","0","72","48","0","-18","0","18","0","-57","0","30","0","66","-72","-42","0","-21","48","-6","0","0","0","0","0","-72","0","78","0","-18","0","0","0","12","48","-60","0","15","0","-18","0","0","-60","-24","0","6","0","30","0","-42","0","0","0","66","0","-33","0","51","12","36","0","45","-24","24","0","60","0","24","0","54","0","0","0","72","-60","-54","0","18","-12","12","0","0","-78","-18","0","24","0","-27","0","3","42","0","0","36","0","-18","0","-3","30","27","0","0","0","-33","0","42","0","18","0","12","0","75","0","-36","42","-51","0","24","0","18","0","0","72","3","0","90","0","-72","0","-48","0","0","0","36","0","-30","0","72","-18","-36","0","0","-24","93","0","45","0","12","0","-18","0","0","0","45","48","54","0","-66","0","-24","0","30","-6","-30","0","-36","0","-18","0","42","-42","0","0","-18","24","0","0","-21","6","84","0","0","0","12","0","36","0","-48","0","15","48","0","0","24","-108","6","0","-30","0","18","0","0","60","18","0","51","0","-54","0","90","-66","75","0","42","0","-69","0","48","-48","42","0","0","0","-6","0","-18","0","6","0","0","0","0","0","-48","-24","-6","0","-87","-12","72","0","0","0","24","0","54","0","-87","0","24","-48","0","0","-15","0","60","0","36","66","-45","0","30","0","-48","0","6","0","54","0","30","12","0","0","42","12","18","0","18","0","-6","0","0","-66","-90","0","-39","0","-51","0","96","0","0","0","-54","0","78","0","60","60","36","0","0","-72","-12","0","-18","0","-9","0","-3","0","90","0","57","18","3","0","36","-24","-27","0","0","-12","12","0","-9","0","36","0","-18","24","0","0","102","0","-36","0","9","36","-57","0","0","0","-36","0","-12","0","18","0","63","0","0","0","96","-96","-30","0","3","0","-30","0","0","24","105","0","0","0","81","0","-48","6","0","0","27","0","-96","0","-36","-30","39","0","0","0","0","0","-30","30","54","0","42","0","0","0","-69","90","-66","0","-45","24","-120","0","0","-48","90","0","30","0","-48","0","18","-36","15","0","60","0","48","0","-3","24","-36","0","0","0","36","0","-96","0","-18","0","18","-60","0","0","-3","-72","3","0","-36","0","-33","0","0","60","78","0","96","0","15","0","-33","6","0","0","24","0","-72","0","-9","-24","66","0","0","-24","99","0","-6","0","-36","0","36","0","0","0","-36","-6","-18","0","102","0","-42","0","0","-72","-102","0","6","0"],"lmfdb":"agrees","derived":{"al":[[13,-1],[67,-1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"871.2.a.c","letter":"c","dim":8,"charpoly":["9","69","142","9","-133","-56","10","8","1"],"traces":["8","-4","-4","12","-8","-1","0","-6","-6","-3","-3","-1","8","-11","2","-12","-16","2","-5","-15","-3","6","-8","-2","4","-4","-1","17","-13","-1","1","-21","4","6","-2","-19","6","-8","-4","-4","-18","-15","-17","-6","-1","6","9","3","-2","4","0","12","-33","2","-13","-32","0","-16","7","6","1","-9","2","20","-8","11","8","-23","-1","37","-40","34","3","3","16","-30","-16","-1","2","22","-16","13","-8","-36","6","-2","-17","-8","-20","20","0","-55","10","-50","-9","47","-16","-9","-1","-7","-33","27","5","-6","-18","63","-37","-3","8","22","-10","55","-39","14","-12","-14","-6","6","-29","-14","-59","61","36","24","-21","68","9","-25","18","-3","-18","3","-2","-4","28","10","6","54","-20","-22","-38","91","-3","-21","57","-13","-3","48","-78","13","19","94","24","-13","-2","-1","17","56","20","50","-28","31","43","-17","19","8","-20","63","8","10","27","-45","16","23","-24","8","-1","79","1","29","-15","-11","-16","78","-92","-3","30","14","29","7","-41","-60","15","23","2","49","-15","-35","-33","81","-4","68","69","7","45","41","9","-12","-24","73","11","-13","51","9","77","-27","-19","-65","-6","0","-16","63","58","-66","0","34","46","26","4","48","27","-25","-51","2","22","33","-50","40","21","14","11","30","48","-52","-40","-26","-5","25","-15","12","6","-16","20","-38","51","36","-19","-60","-36","-15","7","53","4","3","-3","28","44","12","27","-2","-51","36","-3","-115","7","22","18","70","0","60","-8","109","-6","-80","-43","6","1","23","-58","31","-55","63","-75","22","6","-53","-19","36","-8","40","-25","10","25","-66","4","-38","55","-8","-23","-85","-25","-2","54","-33","11","-92","-31","-57","-43","-4","-30","-28","-8","1","4","-133","31","-60","-26","-47","-24","-10","6","75","-8","-50","-58","-4","21","42","-27","-19","45","11","-40","-51","41","-55","1","-46","-1","12","11","-65","17","-68","34","-32","-32","-29","-29","-26","4","17","-67","22","5","-52","-38","23","18","31","-18","-31","-63","-46","-13","-21","-23","-3","2","95","21","35","32","10","22","-95","-68","-1","21","-87","-62","23","60","-3","24","-81","56","-91","-49","-1","1","-83","18","-34","77","-30","-30","10","15","-32","3","-95","-29","-21","46","6","19","26","-4","-20","4","30","-8","-31","-126","-37","4","12","35","72","-48","21","-43","9","80","27","66","-44","-5","6","25","-24","-15","21","91","85","-79","-72","24","-52","-61","-20","-2","-57","34","1","-6","-12","31","-1","45","117","-5","-103","-89","-19","0","55","28","-63","2","-41","103","-49","32","-111","-25","-33","6","-12","107","-128","52","31","16","28","-36","40","35","10","-26","-8","-1","-6","-12","-3","-12","4","32","-18","60","29","-79","17","-4","107","-30","-100","69","69","-10","16","51","46","21","-101","-24","-4","-56","89","81","-25","71","-157","4","-17","-22","-123","6","-89","-18","-53","26","-6","63","2","24","-16","-21","56","88","32","-55","-15","23","1","5","0","26","-55","-88","-83","107","-50","55","14","-17","-53","-54","43","58","-18","163","9","-40","41","-144","52","6","-6","65","-24","88","-16","-50","5","27","12","-43","-60","-19","-94","-1","52","-58","-59","50","-19","7","90","-127","3","80","-54","-36","6","-109","-28","-59","189","-6","-51","110","-71","110","59","-41","-60","9","19","51","-37","-35","-3","83","-105","48","-8","13","-42","-54","3","-36","39","18","-35","97","-151","-17","113","-76","-171","123","-18","-2","22","-34","105","-77","169","54","-72","41","59","-4","-93","8","4","-29","67","-36","-96","-46","64","-8","-44","74","-24","-133","-16","0","-18","28","-78","18","-71","26","-3","73","111","-50","99","-80","12","-5","16","1","-35","-23","11","-33","46","34","-42","26","-45","-33","6","99","37","-11","138","-35","46","17","80","133","-121","-127","2","-55","15","89","-51","70","-10","92","-65","73","68","-47","25","-13","-29","57","23","-52","36","-71","6","45","-79","-92","32","-93","-32","15","65","35","38","6","34","30","63","-3","9","20","-97","0","67","-6","-31","29","140","60","11","5","16","192","127","-94","-16","35","143","-49","-12","-19","-28","-14","-16","13","-143","-34","226","7","-6","73","-8","10","163","71","30","61","208","46","-105","-86","6","24","28","137","155","1","56","66","-119","115","-61","19","40","1","-42","-17","-18","108","-76","57","27","-18","176","23","-1","78","-9","-81","91","-8","-47","-48","178","-26","-78","-11","25","-55","-59","2","56","15","92","-21","169","-23","87","96","57","13","71","-91","20","28","-77","-110","30","-42","100","133","-108","-1","-96","16","132","-8","-15","-8","12","79","45","3","13","170","119","8","-15","-57","11","-38","185","-30","-131","37","-142","-47","-37","19","-100","-2","107","8","83","148","-133","94","-78","53","-134","169","38","-71","44","29","-23","79","-42","61","24","-7","-48","57","14","-32","-6","75","-98","-1","14","-41","-15","42","25","-3","-136","-46","51","37","147","55","37","-112","40","76","47","109","72","5","-19","48","-47","-76","-95","-40","24","83","123","78","-86","-71","-44","-48","-108","-32","-106","12","34","147","-11","139","24","39","59","-24","-3","6","3","46","31","3","-56","-22","2","-145","21","-15","131","81","-154","110","16","-109","3","14","16","-43","-51","-2","105","-24","-42","-104","21","-18","-141","16","-134","18","-36","42","-78","66","64","-55","70","61","75","65","-30","-66","29","-87","-11","-24","-48","-137","-4","19","47","-46","-86"],"lmfdb":"agrees","derived":{"al":[[13,-1],[67,-1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"871.2.a.d","letter":"d","dim":12,"charpoly":["18","24","-266","-324","719","411","-766","-27","235","-20","-26","2","1"],"traces":["12","-4","2","8","-8","-3","-4","-12","-6","1","-9","-3","-12","-11","-16","4","-4","-20","-7","-15","-7","-2","-12","-10","-4","4","5","1","-17","13","-5","-3","-16","-8","-22","13","-16","-10","-2","8","-40","23","7","-50","3","4","-11","5","-18","-2","-6","-8","3","-6","15","-28","-6","28","-39","0","7","19","4","4","8","15","-12","5","-17","15","-34","-8","-13","-15","-8","40","8","3","14","-8","-24","41","-20","0","-24","-8","-17","56","-62","16","4","-7","-40","34","1","-41","10","35","-27","5","-17","33","13","12","-18","-57","3","21","-28","0","-20","35","-71","22","60","2","6","64","-25","54","9","-45","10","2","-3","-8","13","11","-2","-1","22","3","18","4","2","30","-36","16","-20","18","26","27","9","51","-19","23","25","-36","-30","21","-17","-44","12","69","-2","3","17","-20","48","22","-32","57","-21","-3","49","28","20","3","12","54","-47","105","32","-27","56","-14","9","11","-29","21","21","11","20","32","38","45","-8","30","9","27","-13","128","1","27","16","-27","-3","101","23","-23","-2","-34","-33","-25","5","55","49","-4","-56","3","55","45","11","67","-25","45","-7","91","54","48","4","103","-30","-6","-20","46","-8","14","14","-108","7","123","-17","20","0","-125","70","-84","-19","-68","-41","28","-8","90","20","-42","7","13","-49","80","-18","52","-14","22","63","-76","-43","66","68","15","-13","19","36","51","-41","-6","-50","-8","-73","66","65","-8","7","-19","19","-2","30","-24","26","60","-72","-63","30","-26","65","2","57","-69","6","-5","-61","-51","-13","12","22","11","-13","10","12","-34","-1","-38","9","-46","-102","66","-17","-64","-37","89","19","10","-12","-71","63","-12","-45","-35","11","6","-4","64","12","-91","4","23","33","-12","-38","-111","14","56","-6","-117","8","64","-14","-4","53","-78","-19","35","-59","-75","-28","-37","9","-13","33","6","-5","104","-139","43","65","-168","-60","-62","-56","-21","-37","92","56","-1","-29","-60","37","-20","-32","-43","-30","-115","-30","-27","109","-30","17","-95","-35","-65","-62","-59","17","-63","-74","-54","22","-3","12","-13","-39","39","4","-109","-46","-41","2","69","-8","-47","-91","3","5","25","-12","22","-27","-32","-10","-60","-25","-108","-3","-25","123","3","10","-44","47","-52","-8","-42","-26","-114","-36","5","36","-49","16","-66","-69","38","50","-143","105","-105","-56","-61","-34","20","-45","8","107","-106","69","1","-1","-37","-209","26","-60","78","159","-72","22","-49","-8","-115","30","92","-79","15","-19","-87","19","133","99","-13","4","-85","44","35","-170","-37","37","61","-22","45","-23","91","16","82","-27","-4","-56","27","48","-40","-38","-100","-101","130","58","10","47","-18","4","-183","56","28","-20","118","-18","-7","135","-43","2","-153","-8","-42","51","-45","-40","-84","-41","-162","29","59","10","-8","-82","75","57","-133","41","-85","86","-105","-30","203","90","57","40","63","-48","12","-5","-28","92","-96","-57","40","-6","4","29","-23","1","-133","39","-4","10","91","-20","-87","-17","124","49","-2","-7","39","-74","75","102","42","-31","-53","36","-163","-84","-74","62","50","-127","24","-100","20","46","93","13","-104","-59","-6","43","60","-3","-32","50","-49","-56","-89","137","-82","3","29","96","-86","98","-4","51","54","41","-67","6","-37","-90","95","-110","19","39","84","11","-77","25","91","39","-3","-101","129","-12","-64","-17","72","86","-5","-92","-47","62","129","-43","-27","-23","13","-70","-47","57","142","18","-194","52","37","-103","-41","90","14","-7","-75","70","109","34","2","7","-11","-8","2","26","70","20","-60","-86","152","69","44","6","2","-16","34","70","31","12","-1","55","-91","0","-65","52","8","61","-212","117","13","57","9","-23","58","134","150","138","-95","-3","72","-51","13","-43","-170","57","32","-43","-164","-127","11","91","6","117","-107","37","9","-40","36","-62","91","67","296","-59","-83","-15","-57","-41","79","8","-42","71","28","63","-147","32","-28","125","28","15","-45","-13","46","86","26","106","-39","9","1","22","169","6","7","-20","119","-39","-44","52","89","-97","-194","-112","109","-30","-28","113","7","125","-48","-5","74","12","182","-3","193","42","-170","39","6","-141","24","8","33","-43","-104","109","-76","-30","-65","162","0","-56","154","77","-121","-93","180","-34","155","123","41","17","48","-7","172","93","-14","76","-4","-13","133","48","184","33","3","98","-19","141","-203","-142","-11","72","-102","92","8","103","-27","121","-11","-4","-12","-3","68","7","107","39","37","-38","-35","45","13","181","-4","16","-175","120","44","184","-70","-81","36","-81","118","-38","84","-8","-27","120","-6","-33","-229","31","105","-12","1","62","147","91","-15","106","29","130","41","27","-38","-99","149","9","44","-80","-117","12","71","-68","143","-6","-76","13","84","-185","-6","17","98","113","-5","-65","-106","-31","240","-49","-36","55","12","-12","18","47","130","17","24","45","-59","124","-5","-73","-18","-130","-281","-23","-81","79","-15","156","106","26","-75","31","106","-23","-137","18","-75","4","71","34","-96","11","-45","-82","-18","29","-38","-18","-74","24","-62","60","8","-27","11","-69","30","5","-69","-4","27","74","-27","-46","-37","13","-36","-38","154","-17","105","83","-81","-19","-36","-30","-134","-49","15","-34","-82","175","53","-4","-151","2","34","24","-113","-22","-49","8","78","-172","-52","120","118","-8","62","-27","-216","-211","-71","33","-40","54","-89","-55","121","152","-100","-19","184","171","83","-26","-22"],"lmfdb":"agrees","derived":{"al":[[13,1],[67,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"871.2.a.e","letter":"e","dim":20,"charpoly":["22834","233658","144695","-2346028","-223248","5928735","-527544","-6350364","1068970","3308844","-626997","-900727","170877","130056","-24739","-9839","1900","361","-71","-5","1"],"traces":["20","5","0","23","10","3","0","21","38","-1","19","-7","-20","13","4","41","0","11","9","20","5","6","-2","-12","38","-5","9","15","11","-41","23","52","26","-6","-6","8","-16","4","0","14","66","-63","-11","34","43","-23","3","13","28","33","44","-23","7","42","-29","-12","60","0","47","-80","3","-25","-4","77","-10","43","20","-49","-19","35","42","59","1","5","-44","-50","-28","-3","6","88","68","-25","-14","-92","10","2","-31","-48","60","-14","0","17","22","-60","5","-19","-4","63","21","82","-35","-95","-31","-21","-26","-53","-47","-111","-6","-58","-18","-27","79","-2","-34","76","-38","38","41","-214","75","-45","-50","32","99","72","-21","60","-30","1","26","67","-32","5","-54","-132","100","-80","-14","-26","16","-9","-19","44","19","-33","-3","-56","66","-19","33","-32","-72","-100","26","7","-63","20","-80","-84","146","-50","-7","79","113","-86","-38","-181","20","34","-45","-99","-40","-23","-124","19","73","-33","85","-150","1","-13","-120","-32","46","-149","-64","-30","59","-213","125","-62","-7","-135","-4","-16","35","-167","-15","120","0","-106","-19","115","1","-49","-101","-41","22","-133","-65","19","27","-91","-39","-195","29","-100","-64","-161","0","-113","-24","33","110","156","-14","192","26","-7","-33","-6","17","-11","-92","31","-82","-37","75","-270","65","-5","52","-152","56","104","-9","-70","51","-4","-18","160","-2","72","93","133","-15","-118","-72","-20","-21","123","-48","175","43","28","-6","23","21","-110","11","-226","-5","78","33","-120","-24","116","-50","9","240","125","80","60","-63","-6","-39","314","22","70","1","3","69","-28","108","-43","-21","38","2","-38","55","10","-19","-36","80","84","-21","115","-41","-22","-15","12","2","-33","-125","-40","11","31","95","-6","-10","8","6","-92","-38","109","-11","-17","78","215","32","-18","36","47","10","-284","-40","5","-79","164","-27","-9","-87","151","56","-49","15","-89","25","-5","-9","-56","83","91","71","206","-74","112","-6","381","33","108","-46","-15","-81","74","-67","8","68","-175","10","-119","48","-48","-147","-134","-11","97","43","-91","-110","23","89","21","-102","172","-24","-25","34","41","-113","80","158","41","-20","-153","4","-13","220","311","145","3","-23","-159","360","-166","39","74","52","-55","-55","32","-39","-28","-133","-52","70","298","69","-184","-24","73","42","26","-16","-147","-96","-118","-26","48","47","-178","2","191","71","-105","8","303","-28","-200","-91","6","77","240","-3","-69","-93","-62","143","3","28","52","39","80","6","199","26","-76","126","160","51","-9","75","255","67","-75","-89","-8","0","-155","-216","249","32","141","-23","-7","-4","37","-107","-195","16","-28","41","83","76","201","-128","-100","142","307","-3","-36","-40","-4","-109","98","40","-67","-56","285","-50","-22","-6","-31","-135","-43","0","51","200","44","-27","194","58","-76","73","-98","-55","-85","-44","-14","132","-7","-121","176","-177","107","100","435","58","-393","-124","-37","-66","107","-38","21","-29","168","96","-194","-89","148","30","-309","-79","63","-125","117","-23","-108","0","-163","14","-135","-9","-52","-1","94","11","44","288","5","96","142","59","42","32","197","180","154","-20","-34","-55","198","-62","149","36","191","15","152","15","-108","-157","-140","-43","20","116","-93","6","1","-59","-214","97","431","32","40","-144","23","109","-48","37","-89","38","23","58","-17","-102","-243","-153","16","-3","-19","33","271","-15","-9","89","-121","10","284","-43","104","-124","-13","-80","51","-358","143","169","269","-19","-213","-204","101","-95","206","-28","-171","164","-289","49","-195","-52","-54","-5","-187","6","-102","-120","-33","-107","137","-28","332","-182","124","-124","-28","24","156","17","-104","-44","40","178","-112","0","89","-42","-1","-19","-169","20","-13","-406","23","-261","68","-159","172","-43","-66","35","-234","46","-178","-84","201","-7","278","-87","-281","-379","-16","-111","58","-39","36","-107","-122","95","-42","123","-311","-95","-57","-178","582","-112","171","21","-126","79","97","29","97","-105","-107","-6","200","53","-103","55","562","16","-410","-89","12","191","151","27","-130","-84","212","120","-135","19","-49","-206","-71","-60","53","4","-121","-185","122","-76","-104","47","238","-78","59","10","0","-255","29","-25","112","-437","-316","64","146","-131","181","-200","-30","-47","250","95","-73","-228","-165","-3","6","87","-306","-58","107","-38","80","-78","-244","-247","-92","107","60","-66","61","61","-169","-59","-276","-3","40","-153","110","-170","264","43","50","312","166","-115","-7","-118","25","-185","-259","120","151","-58","-55","48","204","-53","-381","-149","110","4","108","149","-498","17","190","135","-339","-104","-131","57","-231","-131","-77","-92","271","-200","196","110","-192","-59","-116","-65","-190","-178","-84","10","93","-92","230","55","172","-111","-373","-88","155","24","-311","-17","-43","-46","-359","18","111","-61","-152","-47","-239","-105","171","312","-295","-20","-341","-50","-3","-262","146","-45","122","-193","-240","281","-80","29","49","-233","220","-81","80","-169","-6","75","-140","-118","-126","-131","124","19","198","-117","-58","-178","22","-335","504","130","39","67","3","-131","-35","-10","26","-50","-85","-315","-188","77","-213","94","-36","-126","129","-42","270","83","-97","-54","150","291","-8","4","-104","136","260","-8","-59","5","13","19","-176","149","-315","14","113","36","-325","-226","419","-1","-514","-62","-80","23","115","-93","22","15","156","-34","-684","-251","-5","-56","-96","5","3","-144","113","148","-158","18","-341","-146","-88","44","-36","148","92","104","325","-4","-196","83","54","-7","-39","-79","50","-102","-283","23","-137","-74","112","197","180","-39","-177","4","374"],"lmfdb":"agrees","derived":{"al":[[13,1],[67,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"871.2.a.f","letter":"f","dim":23,"charpoly":["733790","1021734","-5854232","-7667302","18672541","22332731","-31246998","-32465613","30528661","25407834","-18487636","-10914842","7118905","2502496","-1699634","-267843","235093","6158","-17331","919","610","-60","-8","1"],"traces":["23","4","4","26","6","-3","-2","12","49","-7","7","7","23","9","2","24","28","-4","-1","4","7","-6","20","0","27","4","1","-21","55","29","-11","23","0","16","26","107","10","0","4","-52","28","23","-3","6","-1","19","9","-37","55","32","-26","26","47","-78","7","48","-18","-32","17","54","-1","23","-54","-20","6","-73","-23","49","47","-55","42","-30","5","-17","14","20","40","-3","-6","-32","147","33","-18","-4","-46","64","-47","12","68","-108","-2","-15","-28","-30","-11","-71","6","-48","-13","-49","67","47","-3","12","-18","-43","23","13","-12","-16","-30","-39","53","-38","8","86","49","-86","1","62","22","-25","22","-58","-27","-112","9","1","54","-7","10","-153","-14","-4","44","70","24","-62","-62","-34","30","-5","7","39","-39","63","-59","-74","34","-215","-39","-2","56","12","22","7","21","-64","4","-94","48","-5","-21","19","-109","-42","-38","-65","23","-18","-49","-49","108","-169","-6","-29","-13","-117","53","-50","-15","9","0","-38","82","15","-38","-50","-77","51","-13","-182","-21","67","2","-53","-59","-75","-73","-65","-4","-90","-29","-269","-19","29","53","24","168","-255","55","-13","-111","-23","-33","-147","-99","-18","62","-41","28","-69","-32","21","75","-134","-24","-292","-34","-143","-47","-78","103","-4","-12","73","18","51","5","156","-33","64","-98","120","16","-8","-1","110","41","-12","-10","-308","2","78","-91","-108","185","100","-8","4","139","-71","76","-145","-55","42","-88","-26","35","198","-75","80","7","60","-1","236","-6","-94","60","-9","130","-115","-26","178","-7","-6","77","7","81","2","-33","75","-95","122","-130","43","93","-4","20","-64","-87","4","21","-32","90","16","-15","-53","-53","166","49","0","-6","-39","171","16","-17","193","-83","62","-4","-56","88","391","27","-41","-167","253","34","-49","-34","-40","-78","-125","-6","242","106","4","229","-144","49","15","11","105","52","69","-55","73","49","91","1","-24","33","59","-73","-28","-42","74","4","-401","58","-130","30","-21","11","-180","45","-40","136","155","-60","191","-6","228","145","-50","55","95","-19","-141","24","-27","-37","31","-36","-64","-114","109","192","29","-3","-97","14","11","-34","41","-78","55","-164","132","235","3","-11","207","-250","174","-9","-124","34","125","-101","-228","29","238","27","23","-18","28","23","130","114","-171","-92","72","80","105","-32","210","0","2","-7","-36","-12","-121","-5","63","-104","-93","-86","-64","344","16","61","90","35","-39","-43","90","273","106","-76","188","-121","90","26","-193","-76","162","-196","-140","-67","123","1","-27","-141","99","39","107","2","197","98","11","102","9","-61","-65","116","129","-33","89","10","22","-55","42","140","-227","-4","38","22","-27","99","96","74","0","-149","-350","22","425","200","-109","46","-130","-86","261","135","153","4","143","-4","374","-93","-39","-82","76","-31","-74","-15","-77","54","-52","138","-205","-7","-16","31","163","-86","-29","15","209","206","-167","28","-221","38","-12","23","156","-144","470","-27","-108","-48","203","261","23","-5","125","83","60","-110","-257","56","331","-217","-122","-11","162","-3","0","-134","79","-94","-2","-3","-140","-400","29","92","652","38","6","17","-174","120","-76","-58","-136","-73","84","23","346","59","296","-1","-198","-160","349","-12","-365","-67","56","-117","-415","-204","62","-26","19","89","-494","-111","-173","-49","-31","-18","-99","-78","173","201","-92","9","91","-155","-27","-133","-77","7","61","-172","-212","-39","82","-34","-37","135","-53","42","5","-59","-239","1","39","108","227","-55","-162","55","173","12","149","205","-13","36","216","-69","-127","-30","317","92","32","-263","87","28","-114","-86","-120","-86","320","62","76","-41","-92","-26","-116","10","76","-174","-105","124","7","29","-267","-122","133","44","26","29","56","161","-56","205","-18","-79","54","-162","238","-86","179","47","-348","-149","17","105","28","-95","8","-79","-70","-71","100","39","-78","-159","79","-143","-71","-116","60","24","-153","-191","-248","-21","221","7","153","-209","23","-28","-264","-195","204","-179","64","80","202","-203","48","262","-19","-39","-418","-56","-128","-528","131","-7","565","22","83","-18","65","-114","113","97","-120","-284","28","93","-148","-116","-119","86","-32","53","-339","-77","-92","163","54","22","-168","9","217","-226","150","17","-130","61","-177","-64","11","-101","528","-309","24","-266","153","76","54","-108","92","-9","-65","167","-20","-176","-91","-125","69","-35","40","-1","-114","-375","34","80","136","-63","27","70","-252","-41","-7","-22","23","-289","-7","136","-423","-120","-89","50","-26","-177","-193","-75","92","-54","-308","-75","198","-109","-194","-109","11","-26","25","-107","19","-243","-20","44","413","-94","174","-264","108","-123","-260","126","-164","62","-72","6","-401","-268","-2","141","388","199","-249","-74","-163","-572","-33","39","-73","-46","45","-388","-235","11","-132","-173","-139","-255","83","96","-63","-23","-47","-146","-17","110","-28","9","-142","-51","-156","-7","-369","-63","49","19","140","1","72","23","-186","-335","-202","176","6","5","-224","47","-56","-35","623","144","-418","133","-60","232","271","-123","-1","55","-55","88","-388","-88","-155","211","40","-97","357","-146","-152","268","-113","42","146","-141","-97","46","-4","-53","54","-184","-84","-160","192","-80","-30","19","-9","-21","-86","-109","81","-32","123","120","125","-38","-17","5","216","-118","152","163","-99","37","152","-143","-44","-14","362","272","-17","-98","12","-123","255","162","-68","-144","-54","56","341","-56","224","14","-46","292","152","-68","-459","-82","64","-73","-64","-119","-11","97","20","78","115","-43","-261","124","324","-275","-32","27","71","214","-326"],"lmfdb":"agrees","derived":{"al":[[13,-1],[67,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.248,"computed":"atlas","estimate":{"seconds":0.647,"low":0.395,"high":1.119,"bytes":2421520},"url":"https://sagebrush.space/atlas/mf/871.2.a"}