{"label":"815.2.a","level":815,"weight":2,"dims":{"new":55,"cusp":81,"eisenstein":3,"modsym":165},"old":[[163,13,2]],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 5, 163, 815]: [0, 1, 14, 84] (certified at ell = 2147482693)","T = [(2, 1), (3, 1)]; h of degree 55 = 1 x 55 (phi(ord eps) x dim S_k^new); 6 primes, 0 rejected"],"newforms":[{"label":"815.2.a.a","letter":"a","dim":1,"charpoly":["2","1"],"traces":["1","0","-2","-2","1","0","2","0","1","0","0","4","-4","0","-2","4","6","0","2","-2","-4","0","-6","0","1","0","4","-4","-6","0","-4","0","0","0","2","-2","-10","0","8","0","-9","0","5","0","1","0","-9","-8","-3","0","-12","8","9","0","0","0","-4","0","-12","4","-1","0","2","-8","-4","0","-4","-12","12","0","3","0","-16","0","-2","-4","0","0","2","4","-11","0","15","8","6","0","12","0","-12","0","-8","12","8","0","2","0","11","0","0","-2","-12","0","2","0","-4","0","18","-8","20","0","20","8","-9","0","-6","12","-4","0","12","0","-11","0","18","8","1","0","2","0","-10","0","3","0","4","0","4","0","-12","0","-10","-4","18","0","0","4","-6","0","6","20","0","0","-13","0","6","0","-4","-16","8","0","-18","0","-12","0","1","18","0","0","24","0","3","0","2","-10","21","0","2","0","24","0","-12","-2","2","0","2","0","-10","0","0","18","8","0","6","16","-16","0","8","6","-3","0","-16","0","8","0","-12","24","-9","0","-6","-16","0","0","-22","-18","-6","0","5","0","-8","0","32","0","-24","0","-19","0","1","0","-12","8","2","0","0","0","0","0","-9","24","-4","0","6","-8","-10","0","10","2","-3","0","-8","0","-30","0","9","-4","0","0","-12","16","-24","0","-20","8","-6","0","12","0","9","0","24","8","-24","0","14","24","16","0","0","-24","-4","0","-4","0","15","0","14","-6","-4","0","-18","0","19","0","-22","32","18","0","-12","0","0","0","24","4","10","0","24","8","-1","0","20","0","-4","0","24","0","-19","0","2","-4","-30","0","0","-8","-36","0","12","22","-4","0","-40","0","-18","0","14","-30","-10","0","-4","-16","-22","0","18","-12","0","0","-20","0","12","0","15","-24","-10","0","-16","0","24","0","3","24","-24","0","24","0","-15","0","22","16","-16","0","17","-24","-9","0","18","-16","-13","0","-2","0","24","0","11","-4","-4","0","15","0","0","0","5","-22","18","0","-36","0","-6","0","2","0","29","0","-8","4","18","0","16","24","-11","0","0","0","-31","0","24","-4","-24","0","15","0","20","0","0","8","-31","0","-9","0","6","0","-2","-36","0","0","18","16","14","0","12","-40","-12","0","5","0","-3","0","-30","-40","-12","0","0","-16","24","0","0","18","26","0","-8","0","-19","0","24","12","27","0","-34","-24","8","0","6","8","-8","0","-16","0","0","0","2","-24","9","0","24","0","40","0","24","22","11","0","-16","0","-2","0","6","-36","-36","0","0","-16","6","0","-37","-2","-48","0","3","0","-12","0","-6","-4","0","0","-32","0","8","0","2","20","0","0","-42","0","18","0","-31","-6","-4","0","-24","0","13","0","-12","-8","36","0","18","0","24","0","0","-8","14","0","-4","0","20","0","-13","24","-1","0","-12","0","4","0","20","20","6","0","-20","8","0","0","-12","-36","-9","0","-22","0","-24","0","32","0","-12","0","-6","-8","-25","0","32","12","30","0","0","0","-4","0","6","-12","-8","0","6","-40","15","0","12","0","32","0","-30","0","-10","0","-4","26","-11","0","29","0","24","0","36","-12","32","0","18","0","18","0","-4","8","-24","0","-24","32","1","0","0","-16","-60","0","38","0","44","0","2","36","12","0","3","0","-33","0","14","24","-10","0","24","0","0","0","16","-2","-6","0","3","-36","-16","0","6","0","-34","0","48","0","4","0","36","-48","38","0","0","0","-25","0","4","-6","42","0","22","0","24","0","-48","-4","-12","0","-4","20","-36","0","17","-42","0","0","-10","0","-54","0","0","-4","18","0","-20","0","18","0","-24","-48","17","0","2","0","24","0","0","24","-12","0","-12","4","4","0","20","-4","-6","0","14","0","13","0","30","-4","50","0","6","0","0","0","-16","20","16","0","33","0","0","0","15","0","36","0","20","-36","-18","0","-13","-16","2","0","0","0","-12","0","40","-12","6","0","48","-32","50","0","48","32","18","0","-4","0","40","0","-18","-16","0","0","-24","-12","8","0","-7","6","-24","0","-18","0","4","0","-18","32","3","0","-54","0","-12","0","0","-16","-12","0","48","0","-24","0","-10","24","-28","0","1","-48","10","0","-8","18","18","0","14","0","0","0","12","12","5","0","8","32","-18","0","24","0","-16","0","-36","0","7","0","-30","44","3","0","-22","36","-28","0","60","12","53","0","2","0","-36","0","-40","-10","36","0","12","0","21","0","-38","16","0","0","16","0","11","0","2","-64","-10","0","-36","0","30","0","-40","48","24","0","0","0","4","0","0","38","-18","0","-12","0","-48","0","24","-2","54","0","-20","0","2","0","-28","24","-12","0","15","-16","0","0","2","-4","6","0","-55","0","-40","0","-12","0","-10","0","2","0","-6","0","-6","0","-48","0","0","0","20","0","38","18","-18","0","54","-48","8","0","-36","8","64","0","60","0","36","0","6","-12","0","0","-24","16","-15","0","18","20","-16","0","17","0","-24","0","-21","-20","-20","0","8","-4","18","0","0","6","20","0","-48","0","-3","0","36","16","-30","0","-4","0","-28","0","-16","60","-46","0","-40","0"],"lmfdb":"agrees","curve":{"cremona":"815a1","lmfdb":"815.a","ainvs":[0,1,1,15,-69],"rank":1,"torsion":3}},{"label":"815.2.a.b","letter":"b","dim":5,"charpoly":["1","6","-3","-6","2","1"],"traces":["5","-2","0","2","5","-3","-5","-3","-5","-2","-7","0","-7","-2","0","-12","-11","-3","-13","2","-8","7","6","4","5","0","3","5","-13","-3","-6","7","-1","6","-5","-7","-3","11","-5","-3","-16","5","-7","-2","-5","-12","8","12","-12","-2","-4","-12","-4","14","-7","-6","-11","5","7","0","-22","3","2","7","-7","-4","19","4","-7","-2","-6","18","-14","18","0","-13","13","9","-14","-12","-15","12","-8","13","-11","-19","-20","-10","-10","-3","15","0","7","5","-13","-16","-15","16","2","2","-26","19","4","16","-8","-38","9","-10","-39","7","1","7","16","32","6","6","19","-28","5","4","-36","17","28","-6","5","17","-17","26","25","0","9","10","5","21","3","5","38","30","28","5","-22","16","10","20","-13","20","26","-6","0","-3","3","23","1","2","-6","-9","5","19","35","7","-16","35","5","-16","-1","-13","10","-20","-26","6","15","40","19","25","-5","20","1","-33","5","-7","-15","27","7","35","-3","16","7","16","14","11","-4","-25","-18","6","-5","-30","13","5","34","-3","6","67","36","0","-16","6","6","24","5","5","-6","34","4","22","-7","-8","-21","23","-10","-2","-9","11","71","36","-5","-61","18","-21","2","-12","18","-6","-25","10","8","6","18","-24","-28","12","-63","4","-16","-15","-12","-33","20","26","17","-2","25","8","-35","89","-4","-10","37","-21","-25","-12","2","-40","-1","1","-4","-4","-27","-61","-32","14","9","4","-5","41","-7","-29","-2","8","9","-6","-8","-4","-11","-16","-11","10","-3","-18","-24","5","24","30","2","-5","7","0","-2","-2","-4","0","4","8","10","9","-22","-5","-47","-13","-23","3","-46","8","15","-14","2","-35","7","-32","21","7","9","-5","51","12","-7","-2","-26","-1","27","-4","-46","7","-9","-6","19","-5","-81","47","-25","4","-11","-17","-4","-17","-7","-50","43","14","-39","-2","20","3","37","3","-6","20","40","-16","-32","18","-18","7","-5","0","-14","3","-32","-36","20","18","8","-23","-68","-23","0","-47","19","-7","-44","-13","-9","-14","25","54","13","18","-14","-17","-31","9","16","35","10","-37","-14","10","-11","6","22","-12","-11","-26","-12","-73","-15","-14","-6","-38","1","12","5","-44","9","-11","-8","-3","25","-11","4","13","28","-14","-29","7","-11","-54","10","-28","2","-19","44","-39","-22","-11","-20","-24","35","-30","5","-10","26","-40","49","-15","-10","0","-25","-26","-51","-3","37","56","-40","35","15","-19","-64","-114","-3","0","-22","-18","69","3","7","5","-20","24","-45","5","69","26","10","-1","-13","-25","8","-80","-48","-16","-31","-57","-17","-21","-15","-45","4","8","0","16","50","5","45","-55","2","5","42","30","24","2","51","-14","8","-27","-26","37","4","-57","-49","19","58","-55","33","8","4","43","10","-33","-11","16","-43","11","15","30","-8","35","46","-29","-21","-38","15","-22","17","55","9","20","5","-56","3","-10","-4","-44","42","-19","-39","-3","-55","-27","20","7","48","-24","-26","-38","1","25","-35","-17","-57","7","27","-1","39","34","16","45","12","-50","17","32","19","7","78","29","6","-3","35","48","-20","6","-35","-44","5","-90","19","21","68","-39","48","-28","43","-14","54","15","5","23","17","-39","-35","4","-22","-39","21","63","-36","-11","-72","-42","63","17","-10","11","-24","29","28","11","28","-7","23","-6","27","90","52","5","5","53","30","62","51","17","53","33","-72","4","-17","35","5","-9","6","26","-31","26","0","11","25","-21","-34","-57","-18","0","-4","2","55","38","9","85","-36","-24","-102","10","124","-35","21","53","5","-42","-4","-39","74","21","34","41","-75","-6","3","14","-30","-38","20","5","-55","-13","29","37","38","33","9","21","-22","30","116","-60","-2","-51","28","-50","-2","100","43","5","-35","-43","44","-11","-22","21","-24","-5","-3","16","30","41","44","-15","10","41","-37","52","84","20","39","-66","62","55","-13","49","36","-35","58","20","57","-3","32","-73","26","-14","-18","13","-73","-6","32","9","22","-10","0","16","14","-8","-84","-3","-87","-41","-61","-2","3","-31","22","44","37","23","-14","-36","69","0","1","28","25","-46","-35","2","5","-27","-39","48","-6","-9","11","35","-10","-9","62","32","41","55","5","-17","47","-7","-4","19","117","-17","23","19","35","-52","27","-3","-18","7","23","-19","68","-60","-16","-57","-49","5","8","35","-25","-44","84","-34","5","-20","-29","-106","-42","-16","41","-46","-49","8","-1","33","-47","1","-51","-13","-2","22","26","-62","10","2","-21","50","33","-20","-60","29","47","-31","-26","0","29","48","-21","6","26","40","41","8","15","41","-26","-12","52","40","-16","-102","83","27","19","127","4","4","11","25","56","13","26","-32","-5","84","21","-88","23","20","0","-29","-102","22","1","73","-66","-2","-1","-33","40","18","-33","44","5","-68","11","7","-2","-7","2","-52","50","-58","-15","54","-25","0","32","27","73","6","-31","-82","7","28","19","-68","-60","35","-14","126","58","-26","-3","-18","34","39","1","16","44","-104","0","92","7","-45","-97","81","-132","16","63","-77","-91","-2","14","-34","-36","-38","-22","11","35","74","-55","81","-4","105","51","-9","-81","-25","-85","-93","-3","-5","-18","28","-54","61","17","6","35","67","-52","-103","-5","61","-132","-3","-8","-30","40","49","-65","49","13","-39","43","71","-34","5","82","-66","-18","56","34","-32","18","25","0","-3"],"lmfdb":"agrees"},{"label":"815.2.a.c","letter":"c","dim":6,"charpoly":["4","-40","49","57","-21","-3","1"],"traces":["6","-5","8","7","6","1","0","-9","12","-5","-10","0","12","0","8","13","4","-1","4","7","24","38","-20","2","6","-18","26","-28","-6","1","12","-28","2","2","0","8","-10","0","20","-9","28","-48","-10","-38","12","-7","20","-19","26","-5","-28","37","-40","-21","-10","44","26","-32","2","0","36","30","32","9","12","32","-10","-25","-14","0","6","-32","36","15","8","36","0","-33","-28","13","22","-18","0","16","4","-16","-42","54","6","-1","-4","4","34","-34","4","28","-12","-45","-2","7","16","41","40","-31","24","44","2","9","8","38","-8","-56","4","-8","-20","12","22","12","-12","2","10","-87","50","-24","6","-28","22","-5","-40","-18","18","8","12","-56","26","63","0","-104","48","-28","30","41","-36","23","-6","-38","0","-66","-50","1","-10","-34","-98","-56","12","83","10","0","-50","-28","36","8","-6","37","2","42","26","-60","-16","2","46","22","-28","-74","0","-92","-12","10","-44","8","64","-28","10","34","-10","8","4","-42","12","0","-36","-93","-10","4","20","47","-40","64","-4","-9","-80","-50","-52","-43","28","-13","-46","10","0","-48","-14","-100","8","-44","-10","-95","-20","68","52","-38","-18","-12","20","124","12","38","-22","50","-26","-7","-96","-16","-12","-65","20","-30","-24","-12","-2","-19","20","-61","26","26","26","-11","34","62","-14","-5","22","-40","-14","-8","-28","17","-28","58","64","37","-74","-9","-40","-38","-40","-48","-48","23","64","-21","50","-42","12","34","-10","153","-30","4","18","44","-6","-52","-36","-64","26","122","-28","38","72","-32","-54","65","-2","65","2","100","-42","86","28","0","-20","24","62","-22","36","105","-10","88","10","30","2","-55","-24","19","32","-22","-32","-30","-64","9","-32","-88","-58","-134","12","5","56","-71","84","32","-38","-62","-40","-80","-10","152","42","-42","52","-25","60","-32","24","-82","-14","8","14","100","62","0","8","70","50","72","6","52","-20","28","-80","-32","-30","-34","-24","4","36","-64","0","-95","106","15","28","132","72","-34","8","30","40","108","66","36","32","-38","-52","72","0","121","-10","68","-84","-33","-44","-65","60","92","-28","-68","-16","-35","-8","13","36","-1","42","140","22","80","30","123","96","-18","-12","96","-44","-134","0","-36","8","88","16","16","-84","-42","52","144","4","-4","8","137","-66","-16","-22","187","70","-120","-42","-34","30","-29","-22","54","-8","99","-106","-47","6","44","-28","-92","48","-1","-36","50","-12","40","-4","-26","18","70","-140","4","68","128","-42","70","34","30","60","167","8","-34","0","-20","-32","-162","4","-4","-104","40","116","28","-56","0","-96","183","-12","17","8","-90","-8","-45","-44","55","0","-40","-2","-116","32","108","34","7","18","88","-42","-60","16","-72","54","-11","96","41","-4","63","-12","-46","40","-202","-68","-72","-102","-31","14","-130","-12","4","24","26","38","64","88","44","24","-40","74","114","2","-35","-94","-120","-90","9","-6","26","74","-96","8","-132","22","26","48","38","-92","-123","8","9","-8","78","-46","28","-68","-56","82","18","-16","-96","4","39","140","212","72","-8","-40","-134","-148","24","-20","-151","8","-134","44","12","-52","114","88","-67","22","-57","94","-208","-8","12","-46","-95","74","122","-12","-100","4","-101","52","2","72","180","-138","-124","10","-120","12","0","-48","-87","-8","-23","-122","20","50","-224","48","104","-84","-24","-186","-72","-120","-41","6","120","-16","-38","80","-28","-96","74","-46","-58","22","28","-4","0","-138","-5","-12","45","2","256","-40","88","-14","38","24","-18","-112","-7","-30","82","18","92","70","4","-30","8","82","78","-98","50","12","58","106","78","62","-56","-174","-68","146","-15","26","93","-54","-56","-60","63","24","0","-60","66","0","88","64","156","-92","-104","42","54","-56","2","48","-94","-74","-98","-16","-28","-2","-110","-38","-122","30","5","68","-140","-68","41","-72","-14","-42","-44","-36","3","0","77","52","23","-148","67","-14","88","-6","13","34","40","108","-38","-32","-107","18","6","0","192","-112","-63","20","-66","112","-68","-62","-156","-50","-70","-16","134","-56","1","-152","68","130","-150","-10","-212","172","-108","-208","-34","66","37","-20","176","-98","-12","-58","-24","142","-56","-24","-146","24","46","12","-68","16","-22","10","83","82","133","-22","133","10","-12","-142","-78","10","0","-44","78","50","74","-50","-128","-18","-112","44","-28","-140","-96","-76","-183","36","34","22","-102","28","8","-36","160","78","-172","-6","-171","-8","-99","-16","37","22","174","-94","-94","2","128","62","237","-8","42","-164","-34","124","206","26","-68","-4","3","88","-60","170","94","-84","82","-16","-16","-112","-162","-2","2","20","195","8","180","46","-169","-48","246","-92","22","80","26","6","-54","-28","-11","126","168","0","-74","-48","50","-96","-120","0","83","-28","136","-64","-92","76","103","20","-204","-12","0","42","27","56","10","16","32","-68","42","-44","44","150","6","32","8","40","186","100","32","64","76","-10","-140","70","-28","-22","-46","84","38","10","-72","-16","110","-14","34","-66","-18","38","-312","-10","72","-22","14","54","8","28","-117","-90","-32","4","-139","154","164","20","-42","88","-16","-98","104","12","4","-94","290","110","0","-88","136","-10","26","-36","-52","-148","-100","-132","-93","50","93","-34","30","-10","124","-68","-237","-24","4","42","-237","-184","128","20","277","-30","-1","20","47","88","58","-76","-117","-40","134","252","134","-56","64","-54","12","-70","-300","-4","-112","100","-95","-88","-9"],"lmfdb":"agrees"},{"label":"815.2.a.d","letter":"d","dim":7,"charpoly":["-20","-60","103","68","-45","-14","4","1"],"traces":["7","-2","-2","2","-7","5","-3","-3","-3","2","3","-10","-13","-2","2","-4","-5","-3","-5","-2","4","-23","-6","-4","7","8","-5","1","9","-5","2","-3","-9","-18","3","-7","-17","1","-13","3","2","-21","-23","0","3","8","-8","2","-26","-2","-4","-8","-8","2","-3","18","-15","-7","1","10","-4","-7","-14","-17","13","30","-17","12","-11","2","0","4","-26","10","-2","1","-7","1","-16","4","-13","-6","-4","17","5","17","-8","2","4","3","-9","8","-3","-23","5","32","-33","-6","0","2","44","9","-14","12","-4","34","-7","36","-7","23","21","-15","-34","4","6","44","11","14","9","4","-18","-1","6","2","-7","29","-17","34","-5","-8","27","2","-5","-3","5","1","-26","-12","-12","-1","-2","16","16","28","-9","40","12","-14","4","5","-31","9","7","10","-2","35","-13","43","21","3","4","5","-7","4","9","69","6","4","-20","18","13","-14","17","-7","-3","24","-29","57","1","7","19","25","21","7","17","48","17","20","2","-1","60","17","-56","30","13","10","-45","7","10","-3","26","-21","14","-28","-2","14","16","12","9","21","2","-2","-12","-34","23","-12","-41","11","38","0","-5","-17","-21","4","-3","31","10","43","-12","-8","32","-22","-59","-30","8","52","-4","34","-6","-2","-1","30","38","-55","26","11","36","-40","-33","2","15","-8","-27","17","4","-10","-55","9","7","8","-2","-16","-37","21","8","-4","-9","1","20","-2","31","36","5","-43","3","35","-44","10","65","-18","6","38","15","-48","15","36","-5","-12","-62","7","42","-70","20","-9","-1","0","-20","20","12","-10","-26","-48","-8","-21","4","23","19","-37","5","7","14","-2","-11","-70","14","-35","19","0","-43","17","29","-9","-25","-20","-13","2","54","-15","-15","-30","-24","-9","-9","-18","17","7","-69","-23","1","-12","-11","-21","36","-7","11","-46","-13","-26","-1","-2","16","13","-17","-5","0","-52","22","56","32","-4","-84","19","-25","-28","26","-21","-8","-36","-18","-10","-34","-75","-40","-17","2","-33","-67","59","38","-1","-25","-58","-19","-78","7","-66","62","7","5","-1","-24","-7","-44","-53","16","34","-39","-70","14","-4","17","-44","-26","11","13","-20","-8","58","-81","6","-31","-62","-9","-15","4","-63","-39","27","48","-17","-30","-18","3","-53","-5","-10","22","2","22","-17","-30","-1","-94","75","8","6","39","6","-1","-2","-4","14","-1","-31","-4","54","19","-14","-1","-3","23","-4","52","-21","9","-27","-30","12","37","-8","-4","-36","-53","-65","3","29","16","38","47","23","1","-32","-28","-21","-5","-41","-34","-10","82","-32","25","19","3","31","33","-73","-8","56","2","6","-64","63","-7","3","0","77","-6","-58","62","-2","-1","-14","-16","-31","-44","13","104","41","121","-9","-46","-3","-7","36","14","-7","48","37","15","-12","13","13","-27","90","4","11","38","-59","-103","-34","-13","8","1","-85","7","20","65","62","5","-36","-40","-104","46","17","7","33","-13","-35","6","-23","4","-30","-22","-46","-21","-15","3","-37","57","15","-25","83","-51","-54","34","-87","62","54","41","-4","-21","-37","-26","-83","-6","5","-77","52","32","-44","-11","-62","-11","-14","-11","-31","24","39","-32","-14","-69","62","-16","-79","-9","-97","17","1","169","-4","-42","77","-9","-25","18","-7","30","-18","15","1","20","27","-18","31","-6","31","56","35","31","-2","11","42","28","-31","7","-65","4","154","55","-29","-27","17","20","-68","17","-27","33","-67","88","-34","-25","30","66","31","5","7","6","59","-30","8","10","-2","11","-110","-27","-75","60","54","98","-2","4","57","9","31","5","18","54","47","-12","3","12","-7","-97","42","-5","-26","96","-8","32","-1","23","-37","59","-17","26","-7","69","69","52","12","-18","-62","-18","97","12","16","-76","102","131","1","-59","-27","-52","13","2","17","28","-89","35","-16","-80","89","-14","-11","-16","-55","55","78","50","-28","-49","34","-46","-59","9","-47","84","-35","-24","-40","29","145","28","87","-12","-6","-42","7","27","14","44","3","-34","14","-4","-130","44","60","4","-5","25","55","73","78","31","-55","-20","48","21","-9","96","76","99","56","-7","-100","25","82","-41","-10","13","59","-11","-48","2","-17","-31","23","72","-35","-54","22","31","-13","13","43","-27","17","52","-43","-23","-5","-3","-7","-21","72","3","5","60","-3","-25","53","-36","72","-4","-59","151","25","26","-5","29","34","-46","28","7","0","5","-18","54","-4","53","28","31","8","-9","93","11","-49","51","-69","22","86","12","-102","-6","-18","29","4","117","-4","-38","-19","149","-7","20","6","17","-8","-45","-18","-54","28","111","-124","-13","-27","20","-22","146","14","0","166","41","-49","-17","51","28","-56","71","7","-40","39","-16","-22","3","32","-29","22","-53","-24","-14","33","74","-6","29","25","14","60","-93","-57","28","-78","-19","76","-1","-72","21","5","14","-7","-44","82","-12","-20","-19","-2","69","-96","2","-25","-69","-44","-125","58","-21","8","-27","-22","78","-7","10","-124","-10","42","-17","-78","94","73","37","-48","34","-68","-112","-116","-17","39","-49","-91","26","-20","67","39","55","-2","-2","38","-12","58","58","1","-37","-4","-137","-47","-60","-11","1","-39","15","-17","-15","-71","43","97","56","16","18","11","13","-30","-95","1","92","135","-13","-47","-76","-5","-60","-10","-56","-65","33","-51","45","-27","25","-41","16","-7","-26","38","8","44","-10","70","28","-61","40","3"],"lmfdb":"agrees"},{"label":"815.2.a.e","letter":"e","dim":16,"charpoly":["35095","-6300","-394535","-157591","639873","211350","-413878","-91398","126883","17880","-20106","-1693","1665","72","-67","-1","1"],"traces":["16","7","-6","21","16","4","3","12","26","7","19","0","-1","6","-6","19","-1","-6","9","21","4","-29","14","2","16","14","-27","15","47","4","-6","21","-3","0","3","7","19","-31","-13","12","14","0","33","36","26","47","-50","9","25","7","36","-4","36","-5","19","-18","-27","59","1","0","24","-69","-48","6","-1","-6","29","9","27","6","-10","-25","10","-25","-6","15","-9","24","40","19","48","0","-34","-59","-1","19","-16","30","20","-6","31","-62","-35","-9","9","-16","-3","37","-48","21","52","-93","-28","-49","4","28","-17","-13","29","-29","1","-3","-10","-108","14","82","-45","-18","-23","2","79","-56","-32","-54","16","69","-3","-21","39","14","-3","-120","29","-35","-27","-50","6","32","-54","15","16","-4","-38","-167","47","26","-124","68","82","4","51","-135","75","-106","-6","-32","-27","-69","-61","21","-20","-135","-16","-77","-3","-31","-82","-84","59","0","-39","-48","-7","-121","3","70","-9","65","-11","7","-41","-123","-27","-27","19","-56","-11","-90","22","-31","12","-1","80","-142","-13","9","-43","-37","-14","12","70","15","-18","-102","14","60","-2","6","29","0","36","2","-84","-42","33","60","165","-103","-30","36","25","-93","31","-121","26","-25","-52","-101","96","47","6","52","35","-70","-50","68","-4","70","0","9","91","17","-32","-17","25","93","24","-120","63","7","-15","31","11","-3","36","53","7","37","-13","-4","194","3","-21","-95","36","88","3","116","34","-5","-17","-124","-21","-5","19","113","108","2","43","-18","40","84","13","-44","-27","-6","-25","50","69","59","-10","45","-54","-135","1","8","10","82","-20","0","56","42","-42","-7","24","-10","-19","-93","-9","-69","-56","121","13","54","-48","49","-65","136","81","6","85","-92","97","92","-1","-7","-8","92","-27","-6","28","33","-49","-24","29","-48","75","5","-29","9","13","-45","-6","85","27","100","-47","4","-67","6","-112","69","-47","-99","-10","36","-82","110","68","-25","117","1","-115","-108","10","111","20","18","56","-25","-72","-145","-44","-59","-6","5","-35","74","84","15","-65","44","-45","-42","-9","34","110","17","105","24","-84","66","104","-165","40","90","-41","-16","34","19","-9","186","34","15","48","-80","18","-15","55","0","-103","-2","-127","276","-34","65","135","-109","-48","-59","90","-12","-121","-21","-1","50","6","-62","20","19","78","-142","0","107","-16","116","-89","161","105","30","47","107","19","-37","20","-162","-119","-32","115","-6","-35","-6","-80","-115","31","33","120","58","205","-62","28","46","-33","87","-35","143","-6","2","79","-9","-95","12","-134","-43","9","20","196","52","-42","-16","9","93","33","-18","-3","262","-36","-254","6","37","-18","79","15","51","-48","-51","-42","114","60","21","-103","10","-36","45","52","115","-104","60","-19","-93","-102","10","-23","-26","-28","245","-8","154","245","-49","-11","99","21","142","4","-77","-98","217","-30","28","-297","286","-105","-149","-17","-177","53","128","79","-13","40","28","-68","-11","29","156","93","83","158","-29","-72","103","4","25","1","147","-53","-91","79","-3","-127","73","-129","50","-10","78","-84","-134","87","-108","-9","-129","-46","-15","14","-220","71","147","-104","82","-71","228","-11","202","-45","-142","-94","85","80","-18","-127","142","-138","-85","-23","53","-67","-22","-3","2","80","43","65","143","79","67","-82","-202","-27","-56","-126","264","28","165","-32","-33","-86","201","49","-54","-35","14","-108","273","16","31","44","124","115","69","-47","-29","-6","-142","-3","-151","35","231","22","-21","-145","-81","-172","-189","39","13","-174","-106","182","14","-276","-21","-95","46","-3","-151","-42","-26","78","-120","-46","91","-297","-157","29","-81","106","-227","-124","-35","-66","-159","73","209","-27","-101","-130","94","122","-50","-103","5","-131","19","6","-175","99","-131","32","32","-188","176","-84","-149","-54","54","64","-16","-77","15","-13","152","42","183","16","64","-220","149","-49","-4","-106","147","-68","117","-38","-138","-73","115","-12","-167","143","113","-152","-141","47","-60","38","-16","101","26","-113","46","-56","113","-124","-50","76","134","-73","68","-294","61","56","-124","82","12","-180","-306","-116","4","-99","105","-57","-138","51","-64","-16","98","139","-135","-136","13","-43","84","75","72","11","66","-77","-106","-179","-19","-273","-290","-6","-309","-149","245","-162","-32","98","-89","-159","-190","-27","-161","149","83","44","-69","-13","197","119","47","-61","-240","-81","199","-258","21","195","179","-64","-110","-20","-365","-9","325","38","-135","-271","-12","-212","-178","-16","-75","-35","116","110","-77","-17","-171","25","120","-3","-409","-23","2","71","-31","-114","118","-194","-218","-82","-14","-139","-93","-103","-84","61","-127","-11","-117","59","-62","55","-84","61","0","-138","-169","49","173","-39","-6","-72","208","30","-48","-168","-40","-113","-209","-7","-118","188","244","159","-121","64","169","116","-142","3","49","-9","10","31","70","72","264","70","26","-9","41","-32","-99","-33","65","-242","60","-47","-438","-11","-114","-9","-35","66","7","46","-288","-84","-56","-41","343","19","102","52","-123","-103","70","61","-92","-27","-42","-157","197","168","-27","152","76","-136","-18","19","218","4","103","-23","-56","-72","371","100","-80","-11","-300","27","-13","-98","-90","87","157","219","340","22","-170","-46","136","-248","-31","75","161","233","-5","12","-19","93","127","135","-1","78","350","-195","113","80","-96","178","56","-257","-142","-141","120","166","-23","-13","-448","-76","-4","-100","9","80","1","-53","104","-43","-157","97","51","46","-37","-4","-80","152","-92","-14","128","-284","40","188","12"],"lmfdb":"agrees"},{"label":"815.2.a.f","letter":"f","dim":20,"charpoly":["-5066","179029","215190","-1263704","-1066497","3066091","2162424","-3363255","-2072493","1846111","942588","-559503","-201949","101916","19592","-10671","-575","557","-20","-11","1"],"traces":["20","5","6","27","-20","1","11","18","32","-5","-5","14","23","-10","-6","45","21","32","11","-27","-4","15","12","-16","20","2","27","43","-9","-1","10","46","39","-4","-11","58","43","19","7","-18","-19","-8","36","-24","-32","12","9","4","61","5","-20","37","19","-14","5","-62","43","-7","-23","-14","-5","-5","-14","80","-23","-80","23","-2","-19","10","-15","94","60","4","6","-27","31","-77","40","-45","40","-6","9","17","-21","-57","2","-44","-26","-32","-13","18","-3","21","-11","-136","44","-55","-4","27","-60","-56","8","-6","4","-78","23","-66","27","-15","-39","7","29","32","-12","-62","83","-8","-19","16","103","25","10","26","-20","-187","97","41","27","-2","-28","-20","-5","1","-27","-85","36","-102","36","-43","-68","-17","-4","153","9","-78","84","32","-42","1","22","9","63","70","-10","-193","59","-29","29","-46","-40","42","20","-72","-39","-47","12","-184","121","4","-57","118","38","-35","11","-166","-15","-157","-3","-58","1","-37","-57","59","-43","-64","-33","-42","-74","-19","-2","-166","98","-44","-7","-49","-14","-255","-2","18","-14","-89","-52","-93","19","-161","-32","18","-31","8","84","10","-22","22","-36","-183","109","-5","-10","24","-89","31","0","-29","32","-73","-2","-11","-40","-12","16","-14","35","119","-9","-52","-10","-4","-58","-4","-11","93","-18","41","-61","-10","42","-60","13","-5","6","-19","9","61","20","87","5","5","-25","-37","-48","-10","23","-25","-19","-64","-55","-119","-72","14","65","136","29","131","-5","-206","62","76","-95","62","25","-42","33","86","-43","-126","-9","269","75","7","48","32","50","146","23","2","190","-128","-104","14","4","138","-22","53","5","29","33","163","-55","5","-26","-104","118","95","14","143","55","34","-23","-80","173","142","-45","197","23","5","-140","-11","-15","80","-10","185","103","24","-23","-68","209","114","-137","2","-103","167","-74","129","19","6","-14","-216","53","-10","140","-79","75","349","15","-206","48","-18","28","-94","141","161","131","148","-60","7","-75","197","-115","-4","-100","319","169","157","-6","-71","47","-186","-109","27","-101","-38","-6","-114","-31","169","-47","53","-75","77","36","-30","136","97","-40","-158","-6","79","-46","45","-25","33","-54","-107","-40","138","-118","-320","112","6","1","-68","83","210","-9","95","139","-47","-64","-17","83","-6","-78","-151","21","-78","-48","163","-18","57","-52","-165","78","13","-2","-110","73","88","-114","44","157","56","-19","116","26","64","5","-84","-17","32","107","-84","-2","53","13","247","91","68","-135","-18","-109","-112","61","-17","3","-257","-76","127","43","-21","-3","106","52","-25","11","248","-71","30","-104","136","133","-69","-83","388","-44","-177","-60","98","6","55","-18","-82","39","33","4","169","164","150","-105","-27","-33","-94","5","-243","60","95","-112","243","-139","56","-10","180","177","62","-8","233","86","-38","-173","6","35","333","-92","-172","-4","129","-48","-77","96","78","-25","-260","89","-39","-23","128","119","-116","-185","66","-30","-106","-154","51","-27","28","-132","131","53","15","-100","-202","200","-72","39","-39","31","-239","-155","-7","307","-27","-19","-234","-29","53","-228","50","45","-32","119","-159","34","129","12","170","-36","-4","-208","62","3","144","-131","37","-83","27","-138","283","-32","8","53","-105","91","-93","19","-17","109","85","-81","-16","160","-217","-71","149","-103","71","1","-2","-75","-25","80","-37","234","39","-10","163","46","-409","-75","-26","-53","46","12","-172","20","19","-342","-88","-225","187","59","-99","124","-18","-97","319","121","185","-131","-41","138","-144","-18","-65","-27","-123","40","389","-126","2","134","27","-29","316","28","-85","146","132","-94","20","-28","-179","-15","-61","5","267","-94","-7","-74","-1","-26","-79","222","-68","27","65","62","-148","-80","85","55","-171","-13","107","-36","-79","-165","113","-94","102","-7","320","0","85","-36","-194","-10","186","35","43","-75","-284","-108","-515","68","179","-236","-67","0","17","-114","-421","-36","285","4","21","-29","-70","-162","-153","95","15","-206","155","-9","85","-142","-146","35","78","85","-341","-50","-341","-84","166","40","-333","67","-32","-214","-249","-73","192","42","58","-199","-176","-208","-1","33","-87","-79","96","-22","44","-50","-86","-309","-9","-42","-114","51","128","-63","-280","-207","-346","7","-70","-11","419","91","-116","10","-123","-3","45","-124","193","8","-90","-163","8","-59","87","-234","-315","-426","29","49","-777","63","-39","-29","36","-34","-249","-10","46","-111","225","-260","271","40","183","-311","-343","22","-42","5","-318","-108","204","-20","-234","-7","-107","-354","72","-75","607","-51","-358","39","-89","33","-167","40","47","90","-134","-16","524","-12","58","-185","92","-95","184","161","-283","73","169","-121","432","-215","204","79","-4","30","-6","90","5","57","-79","48","-260","48","-118","-100","-102","219","-243","-38","61","-180","-84","-125","35","-136","47","-137","-24","-11","248","97","-24","103","166","-106","-164","-90","-258","15","133","-62","90","-17","157","-46","-154","-35","316","3","102","59","-205","-126","58","-50","12","-226","172","-1","-29","-13","-98","-178","37","16","70","-109","-84","57","-124","-97","-185","-231","-59","-10","-106","110","674","43","254","104","-291","-101","64","184","0","-118","172","33","507","-33","63","82","42","-221","-71","-15","-344","74","170","-4","202","162","19","87","-51","91","87","2","-47","-61","-339","115","166","106","385","319","-17","-98","120","-77","-16","171","44","118","-231","22","67","7","91","250","1","-100","49","-54","-251","13","487","14","225","-165","169","-18","255","126","-24","-296","132","2","334","194","147","-44","-18"],"lmfdb":"agrees"}],"seconds":0.339,"computed":"atlas","estimate":{"seconds":0.571,"low":0.348,"high":0.987,"bytes":2355331}}