{"label":"843.2.a","level":843,"weight":2,"dims":{"new":47,"cusp":93,"eisenstein":3,"modsym":189},"old":[[281,23,2]],"T":[[2,1],[5,1]],"status":"proven","checks":["dim M^+ at levels [1, 3, 281, 843]: [0, 1, 24, 96] (certified at ell = 2147482681)","T = [(2, 1), (5, 1)]; h of degree 47 = 1 x 47 (phi(ord eps) x dim S_k^new); 5 primes, 0 rejected"],"newforms":[{"label":"843.2.a.a","letter":"a","dim":1,"charpoly":["-1","1"],"traces":["1","1","-1","-1","0","-1","3","-3","1","0","-5","1","-4","3","0","-1","6","1","-4","0","-3","-5","3","3","-5","-4","-1","-3","-8","0","-9","5","5","6","0","-1","-10","-4","4","0","-3","-3","13","5","0","3","-7","1","2","-5","-6","4","4","-1","0","-9","4","-8","6","0","-12","-9","3","7","0","5","4","-6","-3","0","-8","-3","4","-10","5","4","-15","4","-5","0","1","-3","3","3","0","13","8","15","6","0","-12","-3","9","-7","0","-5","-8","2","-5","5","14","-6","14","12","0","4","8","1","-15","0","10","-3","11","4","0","8","-4","6","18","0","14","-12","3","9","0","3","12","-3","-13","0","-12","-5","-12","4","0","-18","8","-3","4","0","7","-8","20","-1","0","4","-2","10","24","5","-22","12","6","-15","0","-4","-13","-5","-4","0","9","1","-1","3","0","3","14","9","3","0","-4","-13","-15","8","-15","5","-6","6","-9","0","7","-12","12","-9","0","9","-30","7","-3","0","0","-7","6","-8","0","-2","6","-5","24","15","-4","14","-24","6","0","14","3","4","20","0","4","-4","8","8","0","3","-27","-15","-4","0","-24","10","16","15","-5","11","-11","-4","-14","0","15","24","-21","-4","0","-6","5","18","0","0","-18","14","-1","12","0","3","16","27","-3","0","-13","-3","-15","12","0","-17","3","-13","-30","0","-8","-12","-20","-15","0","-12","-6","-4","-25","0","-15","-6","12","8","25","3","-21","4","-9","0","-1","7","-12","8","0","20","-9","5","19","0","8","-4","14","-2","0","30","5","24","-12","-5","39","-22","-14","4","0","6","8","15","-14","0","33","-12","-19","-13","0","5","-10","-4","40","0","-8","9","-24","-1","20","-1","15","9","-21","0","1","-3","-10","14","0","3","-9","3","-11","0","45","-4","-15","-39","0","-15","32","-8","-31","-15","4","-25","-4","-6","0","-6","-18","-9","-10","0","-3","7","-14","12","0","12","24","-3","-3","0","12","-9","-14","-30","0","21","32","-3","-23","0","-12","0","1","3","0","6","13","8","-22","0","18","-6","12","6","0","5","7","24","12","5","-30","-4","36","-14","0","-24","50","18","19","0","-8","-14","18","3","0","-20","-4","20","30","0","-26","4","-7","-12","-30","8","-36","-8","-20","0","-35","1","4","-27","0","15","-12","-4","11","0","2","-24","16","-10","0","16","-24","21","21","-5","15","-11","22","-11","0","-12","-18","-14","-6","0","34","15","8","8","0","-21","28","4","12","0","13","-18","-65","5","20","-18","4","0","9","0","40","-18","-9","-14","0","-1","2","36","1","0","-9","-3","-48","16","0","9","-24","-3","13","0","-14","-13","16","-9","0","-15","-3","-12","-24","0","12","-11","4","3","0","13","35","-30","15","0","39","-8","41","12","15","-20","-54","-5","-14","0","6","12","12","-6","0","-12","9","-25","-10","0","-32","-15","-7","30","0","12","28","-8","-12","25","32","9","-15","-21","0","-4","22","-9","-52","0","30","-1","-2","-7","0","-12","3","24","-20","0","3","-20","0","-9","-15","7","-20","19","-6","0","9","8","-20","-12","0","14","-32","2","36","0","-6","10","20","5","0","-24","-24","-12","-9","-15","-7","39","4","22","0","-14","-37","-20","24","0","28","-6","30","8","0","45","-22","-14","1","0","-3","33","18","-4","25","-19","-20","13","-60","0","-16","15","-4","-10","0","4","-8","40","-8","0","-34","-8","-41","-9","0","-24","14","-3","-30","20","27","1","-31","15","0","3","4","-21","21","0","-20","1","24","-9","0","-10","-24","-14","-16","0","60","-15","30","-9","5","-3","3","-11","-24","0","11","45","-30","4","0","-15","14","-13","-16","0","-8","15","-15","32","0","-24","-18","-31","21","15","-34","4","40","-35","0","-4","42","6","52","0","-5","-18","-27","-18","0","9","0","-10","48","0","42","-3","18","-7","40","-14","-7","36","1","0","78","-12","38","24","0","15","-20","-3","-14","0","-16","12","-20","-27","0","-14","3","30","24","0","22","7","13","32","0","3","41","-23","15","0","-15","-12","-45","0","0","1","-24","17","4","0","-3","-6","-40","13","45","24","30","-22","12","0","40","18","8","-2","0","12","-1","-6","20","0","33","15","48","7","0","-24","-3","12","-42","-25","6","-30","-20","4","0","36","25","-42","16","0","52","24","15","50","0","6","-52","19","-12","0","-39","-8","-13","-42","-25","18","-34","-3","27","0","21","-28","12","-4","0","-20","9","30","10","0","35","-26","1","-4","0","-7","42","-4","12","-30","-30","-8","11","-36","0","-24","-26","-20","4","0","9","-35","14","-5","0","4","-19","27","25","0","-16","45","-8","-12","0","4","13","11","-14","0","15","2","9","24","0","16","-24","-30","36","0","-5","-16","28","-24","0","-9","12","21","72","5","24","15","-39","-33","0","22","28","11","14","0","-36","-4","-15","-18","0","14","-36","-6","-40","0","-8","34","32","-15","50","8","14","-40","16","0","-8","21","-33","28","0","12","-14","12","19","0","-8","13","-9","-6","0","-65","-23","-5","-16","20","10","-54","21","4","0","0","-40","9","24","0","50","40","8","18","0","-9","-32","-42","24","0","-42","1","12","2","-20","12","-9","1","-30","0","-15","-9","10","-9","0","-48","21","-16","39","0","-2","-45","-1","-24","0","3","-34","13","10","0"],"lmfdb":"agrees","curve":{"cremona":"843a1","lmfdb":"843.a","ainvs":[1,1,0,5,4],"rank":1,"torsion":1},"derived":{"al":[[3,1],[281,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"843.2.a.b","letter":"b","dim":3,"charpoly":["1","8","6","1"],"traces":["3","-2","3","6","-4","-2","-4","-3","3","-5","-6","6","-9","-14","-4","-4","0","-2","2","-13","-4","7","-3","-3","3","9","3","11","-8","-5","-5","-8","-6","29","3","6","-19","-3","-9","14","5","-14","-4","-20","-4","-4","13","-4","39","27","0","-26","-19","-2","13","-34","2","13","-37","-13","10","17","-4","-5","17","7","15","-1","-3","59","-20","-3","0","8","3","-17","-11","9","7","3","3","-46","-11","11","-28","50","-8","22","-18","-5","-7","10","-5","-1","20","-8","-30","-29","-6","5","-34","29","3","25","3","-10","4","6","13","-4","-19","60","-15","-3","-6","-11","-9","14","-31","14","-13","-28","5","-21","-12","-14","-14","10","-4","1","23","-20","-43","5","-4","2","23","-4","6","-4","13","-14","26","-4","-2","-12","39","-51","-2","27","28","40","0","62","4","-26","11","9","-19","31","42","-2","-14","22","13","21","-41","-34","-4","-59","2","-7","-23","13","-35","-11","-37","47","27","-13","43","76","10","-29","43","17","1","31","-4","-21","-34","-5","13","49","17","86","3","7","25","-1","15","38","13","-1","24","41","-3","-7","17","59","6","-3","-20","-41","-43","-3","-29","-30","0","39","1","8","13","25","3","39","38","-17","34","33","-11","-2","-19","9","-30","-71","7","-53","18","3","26","-14","3","26","-57","-46","15","27","-11","-39","-13","11","-10","0","-28","-10","7","50","4","52","-8","15","-38","22","13","99","-18","-10","69","-5","47","-31","-7","-55","-5","10","16","-103","-5","17","3","-1","60","-18","20","-43","60","-8","35","3","-30","32","-2","-29","57","45","-6","-8","-7","5","-40","18","-34","-43","2","29","-56","-66","3","-30","12","25","-38","-44","3","3","-56","-10","11","42","4","-54","-26","6","-8","15","13","-29","-15","-4","23","-33","-19","21","5","60","-4","-26","-15","-27","21","-3","-5","2","-6","47","-30","-11","-17","-67","-9","18","-53","14","32","-53","-31","-111","12","14","9","-27","-13","-77","-20","-28","4","42","5","28","118","-21","-36","-60","-12","-23","19","-14","19","35","-14","67","-23","10","4","-56","-4","-61","5","1","-2","-55","23","18","-12","-20","-23","11","-43","-35","-10","5","26","-58","-4","-3","51","2","-30","89","23","44","66","-4","12","26","6","-34","-14","-4","-3","-56","13","-51","86","-14","20","-17","26","-87","-41","-4","-46","51","-2","32","-44","-12","35","-39","39","-89","50","-51","6","44","-2","-36","22","27","-22","-31","28","46","1","40","-26","9","0","-13","23","62","-56","13","4","12","-47","-26","-115","-32","11","31","7","9","-24","-120","-19","17","-34","31","70","-26","42","9","12","-2","-8","-22","-14","-51","12","22","28","-31","13","-29","98","21","19","25","-41","-11","64","-34","20","37","-4","-54","-3","-59","76","93","2","-33","-85","-7","-31","163","-23","-53","-44","13","73","16","-35","-19","30","-11","-34","112","-37","-70","-27","47","58","65","27","-52","-86","-13","-97","-5","43","-57","-2","76","-59","50","10","-53","-28","-29","-45","-82","43","47","-27","17","11","-85","1","-2","-3","31","-8","-29","-4","-24","-47","-21","24","95","-34","2","-5","-5","-7","91","13","17","-21","49","3","-64","17","-119","-30","86","16","86","3","4","25","7","173","-30","25","41","-16","-1","-35","-81","15","60","5","38","61","19","13","32","-44","-1","-14","57","24","99","6","41","85","30","-3","18","-45","-7","-1","117","17","18","-27","59","22","15","6","-7","54","-3","-125","-24","-20","-61","23","-41","-1","77","-43","-5","-53","-3","71","-80","-29","-94","-39","-30","-31","60","0","-101","63","39","95","83","1","33","-29","8","18","-116","13","-95","-26","25","-2","-106","3","43","6","39","9","-30","38","-61","52","-17","5","-118","34","-40","22","33","-77","-105","-11","-103","56","-2","-116","124","-19","-109","13","9","31","36","-30","58","50","-71","-53","110","7","52","-17","-53","-52","73","18","44","-13","3","29","-69","26","107","20","-14","-19","133","3","56","143","26","33","29","-57","4","10","-46","68","113","15","-41","-60","27","38","7","-11","33","-17","-39","41","-15","-13","-37","-78","11","-13","-97","-10","-10","23","0","16","-59","-28","162","108","-10","-3","-135","7","25","-48","50","25","32","4","132","10","52","18","-25","-8","-33","26","15","-15","29","-38","-50","-11","22","-36","23","13","78","-68","99","28","-65","-18","10","-32","-10","-23","-78","69","14","66","-5","39","-40","47","-61","79","-31","-53","-53","-7","-3","46","-55","-66","-79","-5","179","57","10","-19","-20","16","41","-1","-103","95","69","-5","-6","-24","17","-53","39","3","-2","-17","-1","110","118","60","86","-7","-18","62","-34","20","46","8","-43","95","-32","60","-18","-25","-8","58","28","35","-117","-3","3","-5","-25","-30","83","161","32","-5","-72","-2","4","-33","-29","-13","34","57","-35","-12","45","-24","-57","-6","-89","-14","-8","38","122","-7","36","16","5","-33","121","-40","17","-80","18","46","13","-34","-194","-48","-43","33","-21","2","9","-121","29","22","8","-56","54","38","-66","-46","21","3","1","-53","-30","5","-138","12","-93","27","25","50","100","-38","-74","-122","-44","19","66","3","-102","34","3","-32","-8","-56","147","35","-10","-8","35","11","47","17","42","-60","-69","4","126","31","-54","32","-57","-26","-9","-93","6","161","-62","-8","20","-3","15","53","-182","13","-23","-40","-29","-47","-57","-15","86","6","-4","-22","-3","23","38","-89","-33","32","-6","-19","-86"],"lmfdb":"agrees","derived":{"al":[[3,-1],[281,-1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"843.2.a.c","letter":"c","dim":6,"charpoly":["-59","-182","-19","138","77","15","1"],"traces":["6","-4","6","2","-11","-4","-2","-12","6","11","-5","2","-3","5","-11","18","-10","-4","-3","-8","-2","-2","-19","-12","5","-15","6","-18","-12","11","-1","-23","-5","-13","-8","2","-17","-5","-3","14","-14","5","3","9","-11","11","-40","18","-16","-10","-10","33","-13","-4","0","42","-3","13","9","-8","-11","-7","-2","50","-7","-2","-16","19","-19","-11","-22","-12","5","37","5","38","-7","-15","10","-19","6","27","6","-18","14","-12","-12","-13","-5","11","4","-12","-1","51","-7","-23","10","9","-5","-7","12","-13","-15","-7","-8","-4","-12","2","-31","14","-17","-48","16","-5","57","8","-3","-22","-5","14","31","52","-14","-41","-6","5","23","-71","3","21","-25","9","-11","14","-11","27","-26","11","1","50","-40","50","-58","18","58","2","-16","-43","6","-10","-3","-62","-10","-6","-12","33","-23","31","-13","50","-11","-4","-11","-9","0","-20","15","42","23","31","-3","55","22","13","48","47","9","35","-17","-8","24","39","-11","56","49","-7","10","-47","-2","1","15","50","-49","30","-7","1","-37","-2","19","54","-16","49","-29","19","17","26","-19","-22","17","-11","60","51","-22","14","-21","-12","45","33","5","16","40","37","15","44","5","-24","-23","38","-46","-29","-7","-55","18","-15","80","38","10","4","-31","-19","37","-1","6","-81","35","27","31","120","6","-15","7","-18","-31","-65","14","106","31","-12","12","-60","-12","33","23","-13","43","44","-5","-47","-76","11","1","-26","4","19","52","-12","-39","28","-1","-71","6","51","-17","-31","-7","36","5","-23","-28","-52","10","-4","-4","9","-20","52","-5","-91","31","-7","-12","29","12","48","47","-13","39","-19","-15","31","-36","-7","18","35","-8","-80","-8","-4","13","-103","-12","-24","-5","2","2","33","-31","-20","41","14","43","61","-17","-54","46","-48","-28","-2","16","-35","17","-5","-1","-109","57","-67","48","8","-35","-22","-3","-93","6","-22","18","-69","-5","-31","-30","14","-43","-43","31","-40","0","52","36","-90","-14","-95","-75","-41","-52","57","-6","109","-41","5","-23","-45","23","-20","36","-71","-42","64","3","-102","-21","21","63","1","-25","-22","-24","9","-40","-41","-11","-64","31","14","-25","-92","-11","22","-43","27","-64","-66","-26","-88","-46","11","60","1","1","-49","-30","50","-93","-45","-40","-58","4","50","-8","-32","-58","8","52","18","26","-59","58","-45","-29","2","-26","-37","-16","-44","19","-43","-72","-2","6","-123","-26","-10","78","101","-3","48","67","-62","-26","-8","-10","-11","-29","-6","41","113","-12","42","21","33","32","-147","-23","-38","21","31","12","7","-13","-3","56","50","-2","-15","-11","-96","19","-4","-16","90","-11","-16","12","-9","-19","1","0","-69","48","-20","-8","121","15","13","-32","42","-23","87","23","110","-41","31","-13","-236","-3","-97","92","55","-86","-39","22","71","62","13","-55","4","48","-12","42","47","-3","19","9","-60","-60","35","9","142","-17","9","97","-8","55","-52","24","22","86","39","26","-83","-11","-33","9","56","13","-72","49","-35","-53","-7","27","74","10","-4","21","-47","-59","88","-2","13","31","1","23","24","15","-11","-98","50","23","91","-49","-35","-76","30","21","-67","-7","81","24","1","-90","76","-37","-112","21","-2","40","126","19","-21","10","54","-51","74","-16","-106","-47","49","62","-99","-29","-92","74","19","-98","-101","17","109","-49","26","-14","89","-19","33","91","-22","36","-1","17","-43","-23","-11","2","135","60","-62","-4","51","-65","-48","-22","99","95","14","-2","108","-21","-19","-37","-12","28","32","45","-6","-106","33","155","4","5","-42","-26","16","-19","-37","40","-195","37","37","51","-61","15","-41","0","44","-70","-72","5","-51","22","-24","28","-47","-23","48","-76","38","-12","-52","-46","132","50","-29","160","25","-7","-49","5","-55","-47","97","18","-37","39","-15","-7","133","80","66","16","38","0","-141","10","138","12","4","142","116","-31","-72","-114","-19","20","32","37","93","-146","-1","12","-52","6","1","-33","-81","-9","74","35","175","-135","27","53","67","31","27","64","120","-76","-16","6","-55","59","-15","107","-216","7","68","45","-18","-140","-85","-31","131","58","-65","51","4","14","-4","26","106","-13","31","31","-60","-40","-12","99","114","12","-131","60","-60","-4","27","-12","28","20","33","84","10","23","-22","-23","-13","-72","-112","43","73","42","44","10","4","-5","70","158","-47","83","34","-76","68","33","11","90","-7","1","5","53","-26","92","63","4","66","-65","19","143","116","52","15","-50","-12","58","3","-39","13","24","28","-72","14","-1","61","-26","-71","-4","40","6","15","-19","51","84","-43","-17","-15","71","-31","-109","-104","-7","50","30","36","88","-66","5","-152","-27","-23","-48","-184","-28","30","-83","-52","93","63","10","24","-97","-4","-70","-56","-4","-146","-51","9","42","3","-20","111","80","52","-51","-45","-5","-6","19","-91","-77","275","31","-49","-72","-7","85","-108","-12","-180","-96","29","-3","-102","12","-66","61","48","24","82","47","19","-132","-13","164","-59","39","133","2","-19","-81","-64","-15","-138","127","31","10","-84","-36","-233","7","-7","27","-50","18","97","57","35","-42","-21","-8","-100","-45","-80","-177","47","-8","-34","-43","-4","37","13","13","-59","66","-103","23","79","-12","-9","81","-24","-61","139","-5","-55","92","2","-38","89","2","-222","-15","33","79","19","-31","24","-42","-20","79","81","41","-20","-76","14","-68","56","43","-12","16","61","-31","-100","-17","-224"],"lmfdb":"agrees","derived":{"al":[[3,-1],[281,-1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"843.2.a.d","letter":"d","dim":8,"charpoly":["-1","-5","2","29","4","-30","-1","6","1"],"traces":["8","-3","-8","5","-3","3","-9","0","8","-6","10","-5","-12","0","3","-9","-6","-3","-3","3","9","-10","-9","0","-11","14","-8","-12","-2","6","-5","-8","-10","-22","9","5","-38","-2","12","-16","4","0","-18","2","-3","-12","18","9","-19","-14","6","-49","-36","3","-19","3","3","-14","18","-3","-9","9","-9","-26","-8","10","-31","12","9","-16","20","0","-21","29","11","5","-37","-14","-6","26","8","20","12","12","-30","-15","2","-8","11","-6","7","-23","5","-7","-7","8","-30","34","10","5","-20","22","-26","18","-9","30","-22","-5","-35","44","38","19","-50","2","13","17","-12","30","-2","16","-16","18","-4","13","-6","0","-11","16","18","60","20","-2","-28","31","3","7","-15","12","11","12","-18","-20","18","-9","0","20","19","-18","-8","14","-3","40","-6","35","16","49","-7","-1","36","37","52","-3","-28","60","19","76","-10","-3","0","54","-3","41","-12","14","8","11","-18","52","19","3","-12","-3","9","48","8","-9","35","41","9","38","25","26","-56","19","8","13","-50","-10","-18","18","31","-27","42","-12","-9","33","-9","39","-8","16","-2","-82","-20","43","76","0","23","84","21","-15","-15","-29","-32","0","-11","10","50","-5","-14","-12","37","11","-14","14","-52","43","6","69","39","-26","-35","-55","-8","-31","-28","-20","-38","-64","-12","74","73","-12","-78","5","30","33","-27","15","22","-42","-2","-24","9","8","-8","-19","-11","-15","-50","6","-13","15","-7","-32","4","23","-42","-35","-5","34","-8","7","19","-37","7","29","22","-8","4","-41","30","34","-70","-34","-27","37","-10","25","20","-5","-39","-23","20","-57","-41","-22","3","-28","26","-51","29","-18","51","-22","9","22","-92","-30","-56","-29","22","-27","15","5","8","7","35","-46","-29","-44","1","-27","-38","25","25","-19","-19","-41","50","18","3","-2","-3","-104","-13","-5","-24","-17","47","72","12","22","25","-30","6","-38","2","43","102","-16","53","19","16","65","-40","-18","-48","-17","4","35","9","-13","-38","-125","6","-1","-64","0","3","-36","11","-129","26","-16","56","78","-18","-29","-108","-60","-11","12","-20","-40","0","2","-26","16","28","-48","27","-31","-11","-18","-3","95","-78","-7","-9","-101","15","-44","-74","-12","12","29","-11","-7","28","-12","-10","-37","18","55","58","20","10","-99","-18","-27","78","9","14","13","0","-28","-43","-20","46","-76","-19","23","-61","18","12","-26","8","44","17","-14","-47","-51","3","-91","-12","-40","54","51","6","54","-2","-35","-31","-86","-16","-57","24","-49","-23","11","7","-37","41","1","32","-45","-36","136","-13","-37","44","-85","-52","-5","-35","3","-26","32","28","85","13","-60","-23","-44","-19","89","-74","-76","-14","-34","10","139","24","3","9","119","0","82","12","-54","-9","56","3","-13","-67","-41","48","-134","12","16","77","-14","37","-40","-8","73","20","-11","49","123","18","-64","-145","-52","-19","-19","-19","126","35","-3","-22","-134","12","-21","0","3","-81","111","-9","-51","65","-48","111","-93","-8","42","-8","9","2","-77","-35","3","-50","-41","81","-53","-9","55","60","-38","32","-83","-25","-26","30","-26","-26","-55","56","-22","12","-19","-4","-15","-8","-48","12","-13","-118","-8","50","24","50","10","53","-14","18","-8","-7","-18","141","-46","-31","-18","-30","27","48","12","-42","62","-12","12","-34","30","9","-9","9","-33","-18","31","9","-150","54","-39","-38","-135","8","10","56","-16","76","-57","2","153","62","82","34","2","20","18","-6","-43","126","54","-76","46","154","0","65","-8","-23","-81","-8","-84","2","19","-21","72","-24","15","-8","-21","15","-1","116","29","17","-35","32","44","12","0","30","-45","11","79","-59","-10","33","-83","-50","-34","-56","5","-63","-71","14","121","116","12","65","65","-37","-92","105","-11","83","-74","14","19","98","-14","48","-16","52","68","14","-43","-35","85","-6","22","-70","-69","30","-32","-39","-26","107","26","7","-2","35","-133","92","55","32","-9","8","37","-2","31","-22","-117","28","18","1","20","-53","24","38","-18","20","64","58","101","12","144","48","-74","-4","-132","-73","29","61","12","30","59","78","37","70","-5","96","47","-30","-41","2","-33","-32","-94","27","-69","-44","-15","-57","74","-22","-51","-8","42","70","188","2","-59","-58","24","86","-119","-9","-120","163","-8","108","-60","8","-33","-43","19","24","82","11","114","10","15","-48","48","50","64","15","-6","-35","69","13","110","-56","-15","-29","181","7","43","-28","32","58","53","-4","-16","95","-23","-80","-97","42","98","39","35","3","39","5","9","202","-34","60","89","8","29","134","-7","-60","63","-19","17","156","37","22","114","-7","8","-36","-29","-57","80","-22","-75","112","8","176","60","-4","14","-75","41","72","-79","-30","23","28","-34","-68","-61","70","150","65","34","-84","23","27","116","120","-37","47","-102","10","-191","-91","-25","-81","54","-20","14","-54","5","12","-74","39","-48","46","23","-45","126","-20","-14","71","57","-72","67","41","-66","-15","22","64","37","-3","-95","44","28","5","229","-26","91","-16","51","145","-121","-29","-54","-70","18","33","-60","-51","-27","-1","22","-82","-119","-9","-1","-16","-22","7","-111","92","-29","-49","30","-3","82","56","103","-41","29","-71","-154","-22","11","-80","27","-89","10","-15","72","95","-5","-17","-207","-8","-148","-1","-7","-102","-81","-35","12","-28","46","70","124","29","162","-117","44","-166","-66","-1","-80","-53","27","-49","37","38","74"],"lmfdb":"agrees","derived":{"al":[[3,1],[281,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"843.2.a.e","letter":"e","dim":14,"charpoly":["7160","-75708","81776","147619","-282508","93244","83567","-65750","6223","7412","-2413","2","112","-19","1"],"traces":["14","6","14","16","13","6","0","15","14","2","13","16","8","1","13","16","8","6","-9","17","0","-3","18","15","19","6","14","-21","20","2","-8","11","13","-16","-1","16","28","-14","8","-20","13","1","-11","3","13","-35","33","16","8","7","8","-23","28","6","-31","-10","-9","-2","26","17","-17","-32","0","-13","-2","-3","-5","-10","18","-52","25","15","1","15","19","-53","5","6","-9","4","14","-29","17","-21","10","-6","20","-1","32","2","-49","38","-8","-16","3","11","-12","24","13","30","16","-16","-24","-8","-1","-58","-11","16","12","-8","28","-38","31","-14","-7","-3","8","0","40","-20","-17","-26","13","-44","60","1","-19","-7","-11","4","-7","3","20","-11","13","-83","17","-35","-47","-150","33","6","2","16","-16","-44","8","54","8","7","-25","-52","8","12","-14","-23","-14","-32","28","-43","8","6","-15","25","-31","-5","-22","-10","-10","-64","-9","-26","55","-2","-89","-44","26","28","10","17","5","-35","-17","-27","18","-32","-67","22","0","-50","21","-13","-16","-109","-2","-79","45","-3","-62","-17","-5","-5","-64","-10","3","-23","18","-35","-6","-52","-33","-60","25","-15","-24","15","-19","39","1","-73","19","15","-17","21","19","-75","3","-53","-50","-138","5","43","11","6","-50","71","-9","107","62","4","-14","7","14","-5","30","-29","-34","-93","17","46","-10","-21","76","81","10","-66","14","-6","-82","34","20","76","-17","-1","-40","13","32","65","49","2","-66","-69","-49","84","-59","38","15","49","-8","-74","-14","-16","-14","-17","3","-27","72","11","-6","47","-12","56","-12","24","33","29","13","-43","-2","30","-17","-27","16","-57","71","-16","-3","-5","-24","53","68","-8","-14","105","-1","17","82","-58","-34","-77","-11","62","35","16","18","-46","12","5","-48","-8","24","114","28","83","103","-38","70","-36","31","-14","59","-14","-93","65","-7","70","-18","-3","-6","-87","8","63","21","0","-36","-146","40","120","24","-20","-1","-50","-17","83","56","-26","17","82","13","79","-17","-44","80","-11","60","76","80","1","6","-116","-19","87","25","-7","68","42","-11","63","34","4","-33","32","-7","40","-42","3","103","-16","20","191","46","-11","-29","110","13","-57","46","-83","-76","-143","17","12","64","-35","20","-45","-47","125","-60","-150","39","17","33","7","-54","6","2","-57","2","113","79","16","48","52","-16","101","15","-44","27","-28","8","155","21","54","70","-74","8","131","88","7","-115","8","-25","30","30","-52","2","-27","8","-28","-12","12","15","22","-14","106","-19","-23","23","9","-14","137","26","-32","-146","83","28","122","38","-43","0","-33","8","111","85","6","92","-40","-15","233","-112","25","41","90","-31","-140","38","-5","-11","190","-22","42","-10","-10","125","-82","-10","74","22","-64","-119","-65","-9","170","-89","-26","150","-74","55","72","60","-2","-68","100","-89","49","-8","-44","-36","-21","26","88","49","28","-5","-119","10","93","22","17","32","67","5","-31","-4","-35","25","-7","-17","66","-43","-27","41","128","18","-90","52","-32","-94","-169","-67","-6","-100","22","115","75","0","185","-76","-50","-83","-107","21","141","-33","-13","48","0","-16","234","-87","-109","-34","71","-2","-30","-96","-79","36","-262","45","106","36","-3","37","76","-62","92","-48","-17","-60","-53","-5","46","-166","-5","-27","-200","-64","142","-120","-10","42","-30","3","30","54","-23","-79","23","18","59","-50","-35","28","-150","-6","193","-2","-52","-75","12","-33","119","-140","-60","36","-56","25","-70","-108","-15","-105","-79","-24","4","20","15","33","-100","-19","122","-25","39","-116","-28","1","-27","-53","-73","18","80","19","120","20","15","-37","-107","-17","166","32","21","-25","96","19","-172","18","-75","-157","-251","3","17","0","-53","-7","-230","-50","14","-38","-138","-149","82","5","208","-139","43","173","-185","11","-236","81","6","-116","51","-50","64","-94","71","-23","93","-9","58","-43","107","2","-9","62","-100","57","4","1","113","-14","14","34","7","-133","-51","14","125","-74","-5","-10","9","30","111","-85","-29","-75","174","-34","150","-122","-93","-54","-3","17","-176","-46","46","-116","115","-10","-13","-211","-21","217","-110","76","-39","-29","81","-104","293","10","12","-22","-66","-26","-84","14","25","42","-6","-34","-310","-82","137","-104","34","66","52","20","123","-50","76","-113","-103","-17","-96","-65","-1","-44","177","-40","-211","66","13","-86","85","32","-94","-168","65","-16","-62","49","-38","15","2","-122","-23","-66","24","-94","-69","1","-50","-49","107","-131","84","-37","-65","-59","-122","67","38","-19","59","15","-8","-233","49","-277","29","-8","35","-12","-74","-42","-3","-14","-21","-76","-16","-58","15","-14","-281","38","-17","31","-36","3","-120","-98","-27","-25","-178","72","186","14","11","-22","8","-6","69","-16","47","-260","190","-12","99","-188","56","167","-162","-12","-208","28","24","-45","107","33","-216","35","29","-71","340","13","91","-37","-43","-57","-23","-2","-35","42","30","72","-121","-17","-27","-118","-27","67","81","16","-76","-113","-57","-50","-29","71","-326","229","-16","-142","-139","-3","47","-84","-5","187","91","-24","-21","-18","53","-121","0","68","-66","-20","-8","-3","10","-14","87","9","105","-61","299","-1","-90","11","17","35","-329","82","121","74","-58","-71","36","-34","108","15","-77","-236","190","-11","-117","-154","62","24","0","35","-134","15","16","45","363","18","-200","212","-46","-84","345","12","-103","-46","5","-26","-140","-48","102","-25","-8","-46","-57","24","70","-191","114","157","128","28","46"],"lmfdb":"agrees","derived":{"al":[[3,-1],[281,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"843.2.a.f","letter":"f","dim":15,"charpoly":["-335624","-1396348","5655892","-3754271","-1680647","2137784","-68941","-424377","78441","37345","-10897","-1229","606","-11","-12","1"],"traces":["15","5","-15","19","7","-5","8","18","15","8","1","-19","18","5","-7","23","4","5","5","11","-8","13","-2","-18","26","-12","-15","27","12","-8","16","46","-1","6","-3","19","54","-4","-18","26","9","-5","29","5","7","21","-21","-23","25","8","-4","23","42","-5","9","0","-5","40","-22","-11","25","6","8","50","16","-13","37","8","2","28","-27","18","33","-1","-26","15","-3","12","11","-4","15","-7","-3","-27","22","-10","-12","5","-24","8","9","-30","-16","-32","-13","-46","40","-25","1","-29","-14","-6","-4","-58","3","0","-7","-19","26","-66","-54","14","49","4","7","-1","18","-64","-100","-26","32","-10","-9","-40","24","5","25","34","-29","-46","-39","-5","62","-59","-7","-37","19","-21","1","-8","21","-42","-4","23","4","-64","-25","-14","18","-8","-19","-50","4","-112","-42","-23","64","-2","-42","-21","4","5","17","-63","-9","-71","-24","0","29","-90","5","-2","35","-40","-13","-52","22","-66","-50","11","35","-57","-25","-87","14","-6","27","-98","-8","-76","-87","-50","48","-19","-16","-12","59","13","-4","-32","-37","-55","2","-8","25","-83","-2","-113","-44","-28","19","64","27","-33","-80","-18","9","-25","-33","-19","79","1","11","-1","26","-7","31","-15","28","-14","3","41","35","-12","12","-151","-11","-117","-28","4","-8","88","-15","17","66","7","66","59","3","-86","-28","27","88","-65","-22","109","38","10","54","-52","12","44","-41","-5","68","59","24","-45","-17","-8","-6","79","-9","46","95","30","157","-83","16","30","15","32","50","43","13","13","-2","46","77","79","-40","124","44","25","-7","-35","-1","35","-26","29","75","153","14","-15","-43","6","33","-121","4","1","-38","58","48","-67","-3","41","178","0","-10","17","7","34","-23","19","74","20","-26","-149","0","66","20","72","54","-29","-91","-14","52","63","-49","-50","-49","-4","31","33","-7","44","28","1","76","79","-18","7","35","64","-8","-38","100","-168","-26","26","-8","140","-32","-127","108","10","33","-82","9","-55","-35","40","-46","121","-24","-74","-74","-5","18","-6","-25","-89","-61","-34","-50","-4","29","59","-22","46","-43","171","39","28","-26","5","65","86","-62","-248","22","59","19","-122","7","-37","-18","37","70","177","-19","-142","0","21","-8","-37","-1","-283","-26","8","33","129","-21","73","18","42","-16","145","4","69","-105","-23","-20","-18","-4","-9","73","64","-77","-108","25","183","23","14","52","10","-18","-45","4","8","-51","150","19","-26","-58","50","-36","31","-4","-146","-28","112","-37","228","42","16","37","23","-113","103","-64","-211","-18","2","-18","-135","42","-100","-64","21","-12","139","-4","246","31","-5","64","-22","-17","11","-48","63","45","28","9","-32","2","71","61","142","24","42","-70","0","-43","194","-29","56","12","90","-67","202","-5","44","-39","2","-98","158","-35","-30","-24","40","-52","48","13","-59","-42","52","-3","35","-22","242","123","66","-135","-17","50","-141","-22","-11","58","119","-35","-117","12","57","13","35","25","-62","-123","87","65","314","-14","-28","8","6","-134","113","-27","5","22","98","-25","-65","8","-117","86","76","-107","175","87","27","-83","50","24","51","-48","-86","-73","19","46","149","16","-124","-42","12","-80","136","-59","102","-50","-13","-147","132","4","124","-6","32","-126","119","37","56","140","55","-3","-4","-2","36","-118","8","-36","-16","-25","-150","160","83","53","19","2","23","24","113","-71","106","44","-213","-104","28","-23","156","-19","69","40","-64","-66","150","-27","112","60","33","51","57","80","-90","-78","18","-119","-22","-9","-30","167","25","-58","-216","33","-165","-61","19","24","130","-79","164","-192","-1","-1","25","-11","-314","-290","1","-35","170","-26","-79","32","7","47","115","-31","109","-82","15","-147","-94","-28","-126","-14","14","-43","124","-3","-32","-15","-41","-123","27","-35","-24","65","12","68","-157","-12","18","40","151","77","-179","11","-258","-23","117","22","-221","28","4","-133","-4","-143","144","8","52","-54","-88","-37","-253","15","-35","-136","-17","-28","149","-66","-231","21","-7","-47","146","-66","46","-46","-59","-146","-221","-3","96","140","86","10","93","28","21","-145","-27","-169","-80","-88","-3","-181","65","8","-337","22","2","-54","-109","-60","18","-38","111","-24","-10","-66","-160","-54","-303","-66","52","-86","-148","-12","42","-2","-44","43","227","41","-264","-157","5","32","191","-68","-79","-12","-59","-46","-172","-24","-24","-156","45","-152","170","17","-192","-107","8","2","-59","6","-168","-170","-79","17","54","9","-9","-81","-46","-85","-147","-95","-82","137","-30","31","-97","-157","-94","-15","83","-137","-231","-16","7","-58","-30","-107","79","-15","259","4","-32","18","25","-50","133","-20","-43","69","152","-13","-76","80","-13","-57","92","2","34","16","-46","-56","-178","-77","-235","140","-79","156","-12","40","-13","64","-124","73","-44","-44","-308","-266","-25","7","273","7","76","-43","35","-37","-228","1","211","139","-35","-31","81","26","-173","-92","-29","4","-21","-75","373","36","-153","83","-217","-14","-122","61","15","-98","17","43","76","-49","-6","104","-319","-33","129","120","121","171","-105","-4","97","-82","-1","13","108","38","350","-172","-58","-135","-92","-48","9","111","67","31","-363","3","-98","23","-41","103","-11","-178","-299","-148","0","145","-126","10","-136","-45","-17","5","-290","-7","-55","102","-34","52","393","23","206","109","-19","77","103","-74","112","-106","-20","28","-247","26","255","38","149","-156","20","0","54","-67","-66","140","79","-20","196","-11","-72","-97","-132","-54","-6"],"lmfdb":"agrees","derived":{"al":[[3,1],[281,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.35,"computed":"atlas","estimate":{"seconds":0.57,"low":0.348,"high":0.986,"bytes":2349224},"url":"https://sagebrush.space/atlas/mf/843.2.a"}