{"label":"399.2.a","level":399,"weight":2,"dims":{"new":19,"cusp":49,"eisenstein":7,"modsym":105},"old":[[19,1,4],[21,1,2],[57,3,2],[133,9,2]],"T":[[2,1],[5,3],[11,5],[13,7],[17,9]],"status":"proven","checks":["dim M^+ at levels [1, 3, 7, 19, 21, 57, 133, 399]: [0, 1, 1, 2, 4, 8, 14, 56] (certified at ell = 2147483647)","T = [(2, 1), (5, 3), (11, 5), (13, 7), (17, 9)]; h of degree 19 = 1 x 19 (phi(ord eps) x dim S_k^new); 5 primes, 0 rejected"],"newforms":[{"label":"399.2.a.a","letter":"a","dim":1,"charpoly":["47","1"],"traces":["1","-1","-1","-1","0","1","1","3","1","0","-2","1","0","-1","0","-1","-4","-1","1","0","-1","2","-6","-3","-5","0","-1","-1","-6","0","0","-5","2","4","0","-1","-2","-1","0","0","-10","1","8","2","0","6","4","1","1","5","4","0","-6","1","0","3","-1","6","-4","0","-2","0","1","7","0","-2","-10","4","6","0","4","3","10","2","5","-1","-2","0","-6","0","1","10","0","1","0","-8","6","-6","-2","0","0","6","0","-4","0","5","-8","-1","-2","5","8","-4","16","0","0","6","4","1","-2","0","2","-1","2","1","0","6","0","4","-4","0","-7","2","10","0","0","-1","-10","3","-8","0","4","-2","1","10","0","-12","6","-6","20","0","-4","-4","0","-1","0","-10","-1","2","-22","-5","-22","3","-4","2","0","0","-14","6","6","0","-6","-1","16","10","0","0","-8","-3","-13","0","1","-8","18","-6","-5","2","4","2","12","0","12","0","2","-18","0","0","8","-4","-1","0","-22","-7","-14","8","0","-1","18","2","0","-15","10","-8","-6","-4","0","-16","-6","0","-2","0","-18","6","-4","-4","0","-3","0","2","-10","0","0","-2","20","-5","-5","-2","20","1","-18","0","2","-18","6","0","0","4","6","4","10","0","-12","7","-1","2","0","-10","0","0","0","0","-12","-1","12","10","0","-17","-30","8","-2","0","-6","-4","22","6","0","-1","2","10","-6","0","8","4","0","-6","10","-6","22","-20","0","0","-6","4","28","-4","0","0","-10","-5","-1","0","8","-10","18","1","0","-6","2","22","0","-5","8","22","-8","-1","0","4","16","2","-16","0","16","0","10","14","0","6","-10","-6","12","0","-4","6","-4","-1","0","-16","2","-30","4","0","10","0","-2","8","0","1","-10","13","-2","0","0","-1","1","24","0","-18","18","-6","10","5","0","10","12","-4","0","2","4","-12","-18","0","1","-12","7","0","0","-2","16","6","-10","0","-6","0","-6","-8","0","12","0","1","2","0","10","22","-24","-3","0","14","8","8","22","0","24","3","-4","-18","0","2","-6","0","-1","5","14","-10","0","-8","0","6","4","12","-16","0","-6","-16","-4","6","0","0","-20","2","-12","0","-6","18","4","-18","20","4","-2","-4","0","0","20","1","40","0","0","2","-6","10","-32","0","1","0","-10","-2","0","-20","22","7","2","5","20","-2","22","-20","0","-3","-42","18","4","0","0","-2","-16","6","0","-6","-24","0","-10","0","14","-12","-16","-6","-5","4","-6","-10","16","0","0","12","6","7","0","1","-18","-6","-16","0","-30","-10","24","0","0","0","4","0","0","0","8","12","-16","3","0","-12","13","10","-6","0","10","11","-1","30","0","8","-8","2","-18","0","-18","6","-24","-4","5","-22","0","-2","13","0","-4","-1","0","-2","0","-30","-12","6","-2","0","34","-8","-12","20","0","0","22","-6","-2","-10","-6","18","-6","-22","0","-20","2","0","0","0","-8","6","-4","4","0","-28","1","12","6","0","-20","0","22","10","30","7","-38","1","14","0","0","-8","12","30","0","-18","-40","1","0","0","-18","2","-24","-2","0","22","0","0","-36","15","-24","-8","-10","22","0","8","-28","-5","6","0","0","4","-10","-16","0","-6","-2","16","36","0","6","-16","-2","0","25","-10","2","14","8","0","28","-18","18","10","0","-6","0","-12","4","0","42","4","-36","6","0","4","8","3","8","0","0","-16","30","-2","0","10","10","-4","-28","0","-12","-10","0","0","0","2","36","8","-20","0","4","5","-34","10","5","13","-26","2","-8","0","-20","0","-8","-1","0","-1","18","-8","0","0","-28","-18","-2","-18","0","18","40","-10","-6","5","-2","0","-2","-14","0","-12","8","-4","-30","0","-6","-6","0","-4","0","-12","-10","18","0","0","16","-1","12","-12","30","-7","-8","0","1","0","-32","-2","-22","-16","0","30","20","10","52","0","0","6","-24","0","0","6","0","-8","4","0","38","-4","12","0","0","1","-10","-2","-12","0","-16","-10","-2","22","0","24","0","17","10","0","30","14","42","-8","0","-24","2","-22","-10","0","-8","-24","6","-1","0","4","-16","-18","-22","0","2","-6","0","6","0","0","42","1","-16","25","-2","-14","-20","-10","0","0","6","24","-46","0","0","6","-8","-4","0","-4","8","16","0","0","18","6","40","48","-10","4","12","6","-32","0","-22","0","-4","20","0","2","0","12","16","0","7","6","6","18","0","-4","-7","6","-28","-20","12","4","-26","2","0","12","-42","0","28","0","10","-20","-24","5","0","-40","1","0","12","0","0","-6","-8","6","0","10","38","32","-18","0","-28","-1","-8","0","0","10","48","6","-10","0","-2","-20","4","-22","0","3","0","-2","0","5","24","-20","-8","6","0","-22","-22","-20","8","0","12","1","0","42","0","18","4","-4","0","0","-16","0","0","-2","10","16","16","30","44","0","1","-6","-16","24","0","0","30","10","-10","0","-30","-14","60","4","0","16","-30","-6","0","5","10","-12","26","6","0","-10","-12","-16","6","0","-31","0","4","12","0","-6","4","-21","4","0","12","1","20","18","0","2","30","16","4","0","-2","30","40","30","0","-24","-4","0","-48","0","-30","0","-10","-4","0","0","-22","0","2","0"],"lmfdb":"agrees","curve":{"cremona":"399b1","lmfdb":"399.a","ainvs":[1,1,1,-13,-22],"rank":1,"torsion":2}},{"label":"399.2.a.b","letter":"b","dim":1,"charpoly":["-29","1"],"traces":["1","-1","1","-1","4","-1","-1","3","1","-4","-2","-1","4","1","4","-1","0","-1","-1","-4","-1","2","-6","3","11","-4","1","1","10","-4","0","-5","-2","0","-4","-1","6","1","4","12","-10","1","8","2","4","6","12","-1","1","-11","0","-4","-6","-1","-8","-3","-1","-10","-12","-4","-2","0","-1","7","16","2","-2","0","-6","4","-12","3","-6","-6","11","1","2","-4","2","-4","1","10","0","1","0","-8","10","-6","-2","-4","-4","6","0","-12","-4","-5","-12","-1","-2","-11","-4","0","-16","12","-4","6","4","-1","6","8","6","1","-14","1","-24","-10","4","12","0","12","-7","2","-10","0","24","1","-18","3","8","-16","4","2","1","2","4","0","-18","6","12","4","12","12","-8","-1","40","6","1","-6","-6","-11","2","-3","0","-2","0","-4","10","-2","-6","-20","6","-1","16","10","-8","0","16","-3","3","0","-1","-8","2","-10","-11","2","-12","2","-4","-4","-8","4","-2","-18","24","0","0","-12","-1","4","10","7","2","12","16","-1","-14","2","24","33","-2","4","-10","0","-40","16","-6","-4","2","4","22","6","-12","-4","32","3","0","-6","-6","8","0","-6","4","5","11","14","-12","1","14","24","2","30","-18","-4","48","12","2","0","-6","-4","8","7","1","2","4","10","-4","0","0","-24","4","1","12","18","0","-17","-22","-8","-6","-16","10","-4","-26","-6","-24","-1","-2","2","-6","-4","-8","0","-4","18","-22","6","22","-12","0","-12","26","-12","4","12","-4","8","10","-5","-17","-40","-12","6","2","-1","-48","18","-2","6","-24","-11","-8","-2","-4","1","-8","0","-8","-2","-16","0","-24","12","-22","-10","-4","-2","6","6","-20","28","4","-6","0","-1","44","-16","6","-30","-12","8","2","0","6","-16","-8","1","-2","-3","-14","0","0","1","-1","24","-24","-2","2","-10","34","11","4","10","16","12","-48","2","0","4","14","12","1","8","-7","4","-24","2","0","6","-10","-24","6","0","26","0","24","36","40","1","-6","4","-18","-10","-24","3","8","-2","8","12","30","-16","0","3","4","14","8","2","-30","-24","1","-11","-18","2","0","4","4","10","-12","0","-4","40","-18","16","12","6","0","-20","12","-2","36","4","-22","-22","12","-18","0","12","2","-4","-8","-32","-12","-1","4","0","40","-6","6","6","0","-24","1","0","6","-6","-8","-4","-6","-7","18","-11","20","14","2","12","-16","-3","22","-14","0","24","20","-2","-32","-10","0","18","24","-4","2","-48","10","-36","-16","-2","-11","0","-6","6","8","-20","24","-8","6","7","-48","-1","-26","-6","16","-4","2","10","0","4","-8","0","12","0","16","-24","16","-4","-24","-3","-16","-12","3","18","26","0","6","11","-1","22","-64","-8","-24","6","2","48","30","-10","16","-4","-11","26","0","2","13","24","-12","-1","-40","2","16","-6","-4","6","-2","-4","2","8","-8","0","24","4","-2","18","-2","22","-10","-18","-2","-22","24","-12","34","0","32","4","0","-26","4","-12","-56","-4","-1","-36","22","4","44","8","10","-10","-66","7","10","17","2","-40","0","12","12","-18","16","-2","-8","-1","0","48","-14","-6","36","2","0","6","24","24","12","33","-12","8","-2","-2","-28","4","20","5","-10","8","48","0","-26","8","-40","6","6","16","4","0","-6","24","2","-4","41","22","2","-10","0","4","44","6","22","-6","-72","6","4","20","-12","12","-6","-4","44","-6","32","0","-16","3","24","-44","0","-16","-42","-6","16","10","-6","12","-12","8","-32","-2","0","0","4","-6","-60","-16","4","8","4","5","22","2","11","-3","-18","14","12","0","-12","0","-24","1","-72","1","14","-8","-24","24","-4","-2","2","-2","48","30","0","-34","-18","11","6","-4","-6","-14","48","-16","4","12","-30","48","2","-6","0","0","-32","4","-6","-14","-24","-4","16","-1","8","8","110","7","8","-12","1","24","0","2","-30","0","4","30","4","10","-12","-24","-4","-6","-24","0","-24","-26","0","0","-4","-24","-50","-12","4","-40","8","1","38","6","12","-12","-36","18","-6","-10","0","24","-48","-17","26","-8","-22","-2","26","-8","0","-36","-6","-30","10","-16","24","0","10","-1","40","-4","40","14","-26","-8","14","-6","-8","30","-24","-24","-38","-1","0","-55","-2","18","12","2","24","0","-6","-12","18","-4","8","10","-8","12","64","0","-8","4","-4","40","50","18","-24","-48","-22","-12","-36","6","-28","0","22","28","0","-12","64","-2","0","-36","40","-12","71","22","26","-22","12","-12","7","6","4","0","-36","12","-10","-2","-4","12","22","8","-4","-32","10","12","24","-5","8","-4","-17","0","-4","-40","-8","18","-12","-6","-24","6","-50","0","2","8","-24","-1","56","0","-48","-6","32","18","18","8","-2","-4","-12","6","-16","-3","-24","-18","0","-11","0","-20","-8","-42","-32","-2","2","12","-4","16","12","1","0","-22","-8","-14","-4","0","-16","-72","-8","-20","-48","-2","66","32","-16","-50","32","0","-1","18","-24","-24","0","12","54","-2","-22","-48","50","-10","60","12","-4","16","-46","-2","-24","11","6","0","-22","6","40","6","-20","-8","18","28","-31","-24","4","-8","8","-6","-44","-21","0","48","-36","-1","-12","26","44","2","30","-16","4","-4","6","-2","0","-30","-56","0","-12","4","-48","8","26","0","2","-12","96","0","-14","-16","6","72"],"lmfdb":"agrees","curve":{"cremona":"399c1","lmfdb":"399.b","ainvs":[1,0,0,-431,3408],"rank":0,"torsion":2}},{"label":"399.2.a.c","letter":"c","dim":1,"charpoly":["73","1"],"traces":["1","1","-1","-1","0","-1","-1","-3","1","0","-2","1","-4","-1","0","-1","-4","1","-1","0","1","-2","2","3","-5","-4","-1","1","-2","0","0","5","2","-4","0","-1","6","-1","4","0","-6","1","8","2","0","2","0","1","1","-5","4","4","-2","-1","0","3","1","-2","4","0","-10","0","-1","7","0","2","14","4","-2","0","-12","-3","10","6","5","1","2","4","10","0","1","-6","-12","-1","0","8","2","6","-6","0","4","-2","0","0","0","-5","-4","1","-2","5","-16","4","-8","12","0","-2","12","1","-2","0","-6","1","-10","1","0","2","-4","4","4","0","-7","-10","6","0","0","-1","-2","-3","-8","0","-8","-2","1","14","0","12","-18","-2","-4","0","0","-12","8","-1","0","10","-1","-6","18","5","-6","3","-4","2","0","-4","18","10","2","0","-2","1","0","6","0","-12","-8","-3","3","0","-1","-8","6","2","5","2","-4","-6","-12","0","16","4","10","-6","0","0","8","0","1","0","-6","-7","-14","-4","0","-1","-14","-2","0","15","-14","-16","2","-4","0","-8","2","4","2","0","6","2","12","12","0","3","0","-2","-10","0","16","-6","12","-5","-5","-10","-12","-1","-26","0","-2","6","6","-4","0","-4","-10","4","-6","0","-16","-7","-1","10","0","6","4","0","12","0","16","1","-4","-2","0","-17","22","-8","-6","0","-2","-8","14","-6","0","1","6","-14","22","0","0","4","-4","-18","10","2","-26","-4","0","0","-26","0","-4","12","0","8","6","5","-1","0","4","-10","14","-1","0","-18","2","18","-8","-5","-8","-6","16","1","0","-4","0","-2","8","0","-12","-12","-14","18","0","-10","2","2","4","0","-12","-2","4","-1","20","0","2","18","0","0","26","12","6","-8","0","-1","22","3","10","0","0","-1","-1","-24","0","6","-22","-2","-30","5","4","-10","28","-4","0","6","-4","-12","22","0","1","16","7","-4","0","10","-8","-2","-6","0","2","0","10","8","0","0","8","1","34","0","2","-6","32","3","0","-14","8","4","6","0","-8","-3","8","-14","0","2","34","0","-1","5","-30","-14","0","16","0","2","-12","-12","4","0","18","8","-4","2","0","-20","4","2","40","0","2","6","0","6","20","12","10","-12","-8","0","20","1","-12","0","0","2","-2","-10","8","0","1","16","-26","6","0","12","-18","-7","30","-5","12","10","6","-12","0","-3","22","-26","4","0","-24","-2","-16","2","0","6","-20","4","-14","0","-18","-12","-16","-10","5","-4","-2","-6","-4","0","-24","-16","2","7","0","-1","38","30","0","0","-6","-6","8","4","0","0","12","12","-16","0","8","16","-20","3","0","-4","-3","2","30","0","-10","-11","1","22","0","8","0","-6","-6","0","-30","-2","32","8","-5","14","0","-2","-19","0","4","-1","24","6","0","-42","12","22","-2","0","-30","0","-16","-20","0","-4","22","18","-10","10","2","6","-10","-26","0","4","-38","0","-32","0","-8","-26","-36","0","0","-4","-1","36","-30","0","-36","-8","6","6","-10","7","-30","-1","14","0","12","4","4","-30","0","14","-20","1","0","0","14","-6","0","2","0","-18","0","-8","-36","-15","-12","-8","14","6","0","16","20","-5","-2","0","0","4","6","0","0","-6","6","8","-44","0","-2","-12","6","-4","25","-14","-2","-18","-24","0","12","-30","-6","2","0","-2","-4","4","-12","0","-18","-12","20","2","0","4","12","-3","-8","20","0","0","6","2","0","6","10","0","-20","0","0","26","-16","36","0","6","-4","8","-12","0","20","5","6","22","5","-3","34","10","4","0","12","0","-48","1","0","-1","26","-8","8","0","20","-6","2","-22","0","-6","24","-30","-6","-5","38","4","-6","-14","0","28","16","4","18","0","10","18","0","-4","0","12","6","22","-12","0","8","1","16","-16","10","7","-32","-12","1","0","-32","-10","34","-8","0","10","-28","-6","4","0","-4","2","-8","0","0","10","-12","-8","-12","0","-42","0","-16","8","0","-1","22","34","4","0","0","2","2","6","0","32","-16","17","-46","0","-22","14","14","8","0","12","6","6","6","0","24","-8","2","-1","0","8","-8","14","-14","0","10","6","40","34","0","0","-26","-1","0","-25","-6","-30","-20","14","0","0","-22","48","2","0","16","-2","0","-12","0","-4","-8","4","4","0","42","18","-8","24","-10","-4","36","-2","-20","0","26","-28","-4","4","0","-2","0","40","24","0","-25","2","26","-6","0","0","7","2","4","20","12","-12","-26","10","0","-36","34","-8","12","0","-6","20","-8","-5","0","-12","1","0","-20","0","-56","6","-4","-2","0","10","-18","8","-14","0","20","1","-40","-16","0","-26","0","18","2","0","-2","-12","0","-18","0","3","8","30","0","5","8","12","8","30","0","6","34","12","-16","0","12","-1","24","22","0","26","8","4","32","0","0","-24","48","2","-30","-16","-8","-10","4","0","-1","-6","12","-20","0","12","-42","-14","14","0","6","-18","-12","-4","0","-16","26","10","-40","5","-2","-12","22","-2","0","6","-4","-4","18","0","-31","-24","12","16","0","2","4","21","-4","0","12","1","4","38","-20","10","-30","0","12","0","-2","-6","-8","-18","0","8","0","-4","16","0","26","0","-26","12","0","-12","10","-16","-6","0"],"lmfdb":"agrees","curve":{"cremona":"399a1","lmfdb":"399.c","ainvs":[1,1,0,-210,-441],"rank":1,"torsion":2}},{"label":"399.2.a.d","letter":"d","dim":3,"charpoly":["-2129","1993","-127","1"],"traces":["3","1","-3","1","4","-1","-3","3","3","6","0","-1","6","-1","-4","-3","8","1","3","12","3","4","-4","-3","1","6","-3","-1","20","-6","8","-3","0","-2","-4","1","-10","1","-6","10","14","1","-8","-12","4","-32","6","3","3","23","-8","-10","4","-1","-12","-3","-3","-2","12","-12","14","8","-3","-11","-4","-4","-4","-8","4","-6","2","3","-10","-30","-1","1","0","-6","-16","-16","3","-18","-14","1","0","-8","-20","-16","14","6","-6","-8","-8","-8","4","3","10","1","0","31","-8","2","8","-10","4","2","10","-1","6","-4","10","3","16","-1","-12","8","6","4","-8","-10","-1","-22","-14","36","12","-1","-24","-33","8","8","30","12","-3","16","-4","2","22","32","4","-12","-6","4","32","-3","28","6","-3","-22","-2","-23","12","3","8","-4","44","10","6","-40","-4","-30","4","1","-64","-26","12","40","4","3","5","-4","3","-36","10","2","-1","32","-12","-18","6","12","54","-6","-14","20","-32","-8","12","-42","3","6","4","11","18","-42","4","1","-22","4","-28","9","4","10","-20","8","-12","48","-4","26","0","6","8","24","-2","52","-44","-3","-8","38","10","-4","28","30","24","3","1","50","8","-1","-2","-76","0","30","-14","6","-36","4","16","2","-8","16","10","-19","-3","-14","4","18","6","36","14","48","-30","-1","-48","-60","0","13","26","8","10","20","20","-16","40","16","28","-1","-14","-4","-2","-6","12","4","6","18","-16","8","-34","-24","8","-10","4","8","-24","-34","-4","0","-14","-3","-19","24","-10","18","-46","-1","16","-2","0","54","-56","-31","8","48","8","-3","0","-2","-4","12","-8","60","-14","10","-14","18","-4","0","-28","-2","-20","-32","-10","32","8","1","-14","-8","-6","6","-6","4","8","34","-10","-32","-8","-3","-14","-1","-16","12","-56","1","-3","-36","12","34","-28","-8","2","-23","-6","20","12","-4","-32","-26","8","-28","-12","10","3","10","1","10","8","22","-20","-44","14","-92","-4","-36","-14","20","-12","-28","20","1","-8","12","24","40","-20","33","12","22","-8","-58","6","-8","-4","3","-30","-50","-16","-12","-6","-8","3","-17","0","-16","-40","-16","4","2","-16","-2","42","-48","-22","64","-12","-32","20","14","-4","4","22","12","2","48","6","26","-28","-4","-14","30","-32","-60","62","3","-38","-8","-28","42","-4","-6","24","-12","3","16","-36","22","-12","48","2","11","0","23","16","44","-12","-4","4","-3","26","-90","-8","-84","-16","4","-16","-40","-44","-30","-18","-10","4","-52","-6","12","56","40","1","8","4","0","82","30","-36","-42","-4","-43","-48","-1","-20","22","64","6","36","26","52","6","-12","-64","-2","-40","36","20","-4","-20","34","-3","-24","56","-5","0","-34","4","10","61","-3","22","72","36","68","30","-10","8","10","-2","-92","14","1","8","-12","-32","107","32","12","-1","44","18","40","-24","-6","-14","0","-12","-22","84","-54","18","48","6","-28","74","14","-44","20","-20","16","30","32","28","-18","8","40","16","-12","-18","96","42","60","-52","-3","-36","-4","-6","-20","-56","-4","18","-76","-11","-30","-21","-18","64","14","42","-44","2","-4","-38","10","-1","8","24","22","-6","16","-4","0","82","28","-8","50","-9","26","8","-4","20","-44","-10","-32","-3","20","-44","80","-8","-34","-52","12","16","-26","-48","20","76","4","68","-14","-26","27","30","0","-46","-8","-6","-20","24","-8","6","-24","-24","6","44","2","-50","20","-52","-8","8","44","-2","46","3","0","2","8","-12","18","-38","44","2","-10","8","2","4","-50","108","-28","-20","-4","-30","28","52","-24","24","-16","-3","10","-6","-1","-89","-18","-50","-10","16","-8","0","-74","1","96","-1","2","64","-36","76","-24","10","0","-60","32","-30","68","-42","14","-31","34","-6","-10","-36","36","2","8","-4","-90","-24","-16","6","24","-2","-24","18","8","56","6","-16","-8","1","-10","42","-8","19","-52","10","3","20","12","14","-38","-104","-4","48","40","-18","-24","-112","-6","-2","-26","-36","80","-42","-14","-44","-10","-48","-12","62","30","40","32","1","-54","-12","48","10","16","60","-6","-16","0","-32","24","-13","-6","4","-26","-42","-102","-8","80","-6","-10","30","14","-20","76","-52","-20","-3","-40","16","44","22","-40","-96","-16","-16","12","54","-28","36","-46","1","60","-85","14","-18","-24","4","12","16","2","-34","94","6","-100","-8","-12","40","-76","-4","-8","90","-6","-20","-82","-18","-20","24","16","-4","14","-8","14","100","34","-58","8","24","56","-12","-8","-108","-8","10","65","2","-4","64","-84","-8","1","-48","24","14","136","34","-6","22","4","-12","-58","0","-60","-76","14","-56","10","3","20","22","19","-36","-80","-24","32","10","10","-32","-12","-18","-70","-8","46","12","-84","1","12","-60","-16","-44","4","2","24","-48","0","36","6","-54","24","33","56","-82","76","31","-12","64","-8","10","96","-48","-24","72","-8","-8","-66","3","12","-46","0","-78","-30","2","104","-20","4","10","80","-12","-94","-56","8","-14","8","-60","3","22","14","32","-32","-10","70","-16","14","-40","-50","-18","56","-12","4","0","16","0","-44","23","28","-2","0","2","-12","-60","20","0","-22","32","51","-20","10","-58","-24","-32","-28","-25","-8","-132","52","-1","-4","-44","14","-30","-32","8","16","12","6","36","32","-6","0","-32","6","-10","-24","-4","-100","-80","-8","-4","8","-34","-74","-68","10","-16"],"lmfdb":"agrees"},{"label":"399.2.a.e","letter":"e","dim":3,"charpoly":["-81441","6333","-143","1"],"traces":["3","1","3","9","0","1","-3","-9","3","10","4","9","2","-1","0","13","12","1","-3","-16","-3","-8","-8","-9","1","10","3","-9","-8","10","-8","-27","4","-6","0","9","-2","-1","2","14","22","-1","16","0","0","-12","-2","13","3","-9","12","18","0","1","12","9","-3","-42","12","-16","14","-32","-3","29","-12","-8","-8","52","-8","-10","-26","-9","6","18","1","-9","-4","10","12","-52","3","-2","2","-9","-16","-24","-8","-52","-2","10","-2","-36","-8","-40","0","-27","22","1","4","-9","-4","-6","16","34","0","58","-42","9","14","44","-2","-13","4","-1","12","12","2","-36","-12","14","15","-14","22","-4","12","-1","28","-53","16","-24","6","0","3","36","0","-50","14","-12","12","16","-2","20","-40","13","-36","-18","3","18","-10","-9","-16","9","12","8","-20","18","-18","-36","0","62","8","1","-8","54","12","0","-4","9","5","44","-3","68","10","-42","-1","12","12","30","-6","-16","34","-10","14","-16","-24","-32","4","30","-3","-10","-8","29","10","66","-12","9","10","-8","-4","-43","-8","-10","8","52","12","24","-8","14","-4","-10","-4","-12","-26","-4","-20","-9","8","6","6","-28","20","18","0","27","1","-38","-8","-9","-34","4","-4","-58","18","10","-36","100","12","6","-12","-52","-2","45","3","18","0","-2","-2","-44","2","-16","18","-9","32","48","-16","29","-14","-24","2","-4","-8","80","-44","-52","12","1","-2","-32","14","10","-4","104","-2","-54","44","-36","-2","24","-8","-14","56","-40","32","-70","0","-72","-22","-27","13","16","22","50","58","1","-64","86","4","-82","-48","-9","-16","52","-4","-13","24","-6","4","0","16","12","26","34","-14","34","0","100","-40","58","-4","-52","-42","12","-12","9","-42","8","14","-106","2","44","4","34","-2","40","8","-13","34","79","4","-100","8","-1","-3","-116","12","34","-64","12","-38","9","2","-40","24","-36","-8","-82","-12","28","8","14","3","70","15","-18","-32","-14","28","-40","22","-68","0","-4","-38","-76","12","-76","-12","-1","-44","16","28","28","-4","-53","-12","-74","16","26","-18","-24","-44","-9","6","102","-64","0","-14","-80","3","-1","12","36","-24","-52","0","42","-88","-50","-18","104","14","72","-12","-12","-28","-14","12","8","-26","16","-6","20","-2","162","-8","20","-14","-142","-40","92","2","13","54","32","-36","-14","8","-18","-40","20","3","64","-8","18","76","48","-10","-29","60","-9","72","48","-16","-100","12","9","-70","-90","12","36","-12","8","-48","116","-20","-54","-34","18","8","36","-18","-92","40","-36","-1","-52","0","-12","-62","62","84","58","8","-19","40","1","8","-122","-8","10","-64","54","4","-10","12","64","26","0","12","68","-4","4","-6","9","40","88","5","76","-58","44","-6","-99","-3","62","-24","68","4","-18","10","8","26","-42","28","-26","-1","-44","-12","12","-5","-104","12","9","-28","30","16","132","-6","-62","4","-16","26","-20","34","-170","56","-10","-16","82","14","64","8","-16","-12","-50","-24","4","-2","-32","-8","52","4","38","-32","30","-36","68","-3","172","-32","-10","60","-80","-8","2","40","29","18","-85","10","-72","-2","66","-92","-46","-12","10","34","9","8","56","10","2","36","-8","16","42","-4","-112","-18","-43","54","24","-8","-32","64","-10","80","27","8","108","-8","52","94","12","12","52","-18","24","-12","-36","-8","68","2","14","-37","-122","-4","-118","16","-10","-76","-92","-4","-34","8","-12","2","-44","-26","154","-32","-4","24","36","-20","6","30","-9","-32","-82","8","-68","-38","6","44","90","6","40","54","-28","-14","40","20","20","0","18","28","-132","0","-96","104","27","58","50","1","-1","-26","-38","-22","144","-8","0","-62","-9","-40","-1","-34","168","92","4","-64","-46","-4","-32","32","-58","76","-34","18","9","74","10","2","168","-36","-42","4","100","6","-152","12","22","40","6","-40","-66","-12","-44","62","-52","-16","1","-2","62","4","45","44","-34","3","28","84","18","-14","-88","0","68","-72","-2","72","24","-2","-58","-62","-44","-72","-130","2","28","42","-16","16","142","18","-40","-16","-9","-86","-32","32","-14","-12","48","-14","-100","-16","16","56","29","42","-44","-14","46","-6","-24","16","70","2","14","-22","-4","-108","-52","-8","13","64","80","-28","-74","-44","56","-4","-52","-76","-2","12","60","10","1","28","-13","-2","22","-16","-32","-12","-64","14","-54","54","10","-36","-12","-4","-128","44","104","-16","-74","-2","-124","-18","-54","12","32","44","36","10","-36","-110","-20","-2","-110","12","24","120","0","-8","108","48","-14","49","-198","56","-100","16","-40","-15","-140","32","-70","-80","-70","-54","14","0","140","6","-72","-44","-164","-22","8","-82","-27","76","18","13","4","-32","16","56","-94","22","12","-12","50","26","-160","58","-156","24","1","52","76","-64","24","-4","86","-28","8","4","4","2","-82","48","53","-48","-58","100","-9","-12","8","-16","-94","40","52","36","24","-4","24","-38","-13","-52","-14","24","-30","-6","-6","40","-36","4","-90","56","0","-86","-56","16","-118","-4","12","-3","150","26","8","-16","34","-34","-36","-14","-104","6","34","-16","260","0","-64","4","100","28","9","-40","50","60","58","76","-104","-4","56","-14","-52","-13","164","-42","-46","-16","12","44","11","-12","-4","-52","9","-12","-112","-42","50","44","8","88","-16","14","-32","80","-106","104","-184","2","-18","-24","44","-80","-56","4","-20","-72","34","-50","180","-2","-64"],"lmfdb":"agrees"},{"label":"399.2.a.f","letter":"f","dim":5,"charpoly":["79229023","12451365","80226","-7244","-23","1"],"traces":["5","1","5","7","-2","1","5","3","5","0","-2","7","8","1","-2","3","-2","1","5","-2","5","2","2","3","11","-32","5","7","0","0","8","-3","-2","-8","-2","7","2","1","8","-36","2","1","20","6","-2","-2","-26","3","5","-1","-2","4","4","1","-4","3","5","-2","-4","-2","10","4","5","-21","-4","2","10","-58","2","0","10","3","10","-6","11","7","-2","-32","14","-6","5","-26","-34","7","-36","8","0","6","10","0","8","-6","8","-8","-2","-3","-16","1","-2","5","6","-8","-8","-28","-2","-62","10","7","2","-76","2","3","-8","1","4","-8","8","4","-2","-36","13","10","2","20","-60","1","2","-5","20","12","-34","6","5","30","-2","28","14","-2","-20","-2","-26","40","-8","3","40","62","5","-50","38","-1","18","3","-2","2","-8","4","22","38","4","-4","2","1","12","50","-4","-64","-52","3","15","68","5","72","-2","-2","11","66","-4","-26","-10","-2","28","-32","10","-6","68","4","-12","-46","5","0","2","-21","6","16","-4","7","10","2","-20","69","10","4","0","-58","0","80","2","0","-2","0","-2","36","10","28","-72","3","8","6","10","-76","12","-6","-52","-3","11","54","0","7","10","76","-2","-42","26","-32","-20","12","14","-8","22","-6","28","65","5","70","-2","-26","8","12","-34","68","-18","7","-68","-42","-36","-37","66","8","2","68","0","-12","2","6","-32","1","10","-26","-14","0","-28","-14","8","-74","-62","-6","-6","-64","8","-36","72","-8","0","66","-2","0","2","-3","63","80","-16","-26","-42","1","-8","-74","-2","2","8","5","20","102","6","3","68","-8","16","6","-8","-76","-38","-28","14","78","-2","34","-12","-62","-72","-58","10","-2","-2","7","24","64","2","-26","-26","-76","-54","2","2","56","-80","3","34","-117","-8","-8","64","1","5","80","4","-22","-18","-8","-54","-1","8","66","-42","4","-32","58","-2","-52","-74","-36","5","-36","13","4","-4","10","-76","-66","2","80","4","20","2","60","-60","12","4","1","10","-2","2","-66","-52","-5","-4","-10","20","-96","-38","12","12","3","-34","-142","-80","6","-6","-8","5","-51","64","30","8","46","-2","-2","-28","28","0","-60","14","112","-4","-2","44","24","-20","2","-94","-2","-62","-18","-26","-30","82","40","10","-6","-8","-4","2","3","16","4","40","22","2","62","8","-4","5","108","-102","-50","-144","-24","38","-21","44","-1","12","-96","18","-20","-4","3","26","54","-2","76","-18","2","48","-72","-8","126","-22","4","10","72","22","12","-48","38","11","-58","4","78","-26","-4","16","44","2","15","20","1","-18","-58","12","0","-18","50","-24","-32","-4","72","10","-64","-32","4","-52","80","-78","3","44","-76","15","-66","-6","68","10","45","5","-14","8","72","-52","-6","-2","-52","-2","-2","48","-94","11","18","-16","66","-47","24","-4","7","56","-26","-24","110","-10","10","-2","-2","10","44","28","-4","60","-32","66","-86","10","78","0","-6","14","74","68","12","-82","4","24","-6","-12","18","24","-46","32","4","5","72","92","0","20","-8","2","-26","62","-21","-2","-125","6","116","-34","16","-56","66","-4","18","-70","7","8","-152","10","-26","38","2","-36","34","-20","0","38","69","32","8","10","38","6","4","36","-3","0","-64","-36","-58","-6","140","0","6","-34","80","-20","-80","2","56","10","0","33","-10","-2","98","36","0","-8","118","-2","-134","72","36","8","-152","10","112","116","28","80","-6","-72","-8","-70","3","136","-56","8","-16","46","6","-28","14","10","-8","78","-76","92","-98","12","-108","-2","-6","72","-60","-52","-24","4","-3","-62","-42","11","101","-10","54","-16","-4","0","80","66","7","-20","1","10","-28","132","76","16","62","-2","-130","8","-42","-96","-62","26","5","62","-32","2","-58","-20","92","6","12","-2","-12","14","118","-64","-8","144","-138","22","-22","14","-6","-8","1","28","-28","-8","65","-76","-28","5","48","-32","70","-14","-16","-2","-66","60","-26","-64","108","8","-62","46","12","-76","82","-34","-52","10","68","54","-78","-18","12","0","7","70","-106","-68","-36","94","-42","2","-6","-36","56","-16","-37","38","-76","66","-62","-2","8","-40","-4","2","-50","2","68","-44","-60","0","3","-76","-12","8","-106","2","-96","-8","6","0","-62","-32","-44","-34","1","60","-61","10","86","-12","-26","4","-64","-14","-40","58","0","88","-8","-28","-164","-80","-14","20","-112","8","40","86","-74","44","72","-62","4","2","-6","-16","-120","-6","-20","-2","-64","-48","6","8","-104","-56","-36","-33","38","72","74","-6","-8","13","-52","0","-204","28","66","-130","10","-2","52","34","0","52","-40","2","-4","90","-3","-8","-96","63","20","76","80","-40","-54","-16","-2","-60","-26","-50","-52","-42","-20","46","1","96","-140","-8","-30","-92","-74","2","-76","-2","-176","-26","2","40","-5","8","-62","-72","5","-32","12","20","22","132","102","10","-128","6","12","46","3","84","-126","68","-82","-34","-8","0","4","16","-44","-60","6","-106","24","-8","-70","38","-76","5","-42","-38","16","216","-28","-58","30","14","48","-70","78","-12","132","-2","96","-30","34","-104","-1","-12","28","-20","-62","-148","126","-72","52","14","-58","-75","80","10","36","76","-2","24","59","-2","288","52","7","-20","182","24","14","96","64","28","-2","2","14","24","-26","-20","8","-26","4","48","-76","18","60","-54","40","88","2","-18","-160","2","-20"],"lmfdb":"agrees"},{"label":"399.2.a.g","letter":"g","dim":5,"charpoly":["1325417","6853","-45454","4136","-121","1"],"traces":["5","3","-5","7","4","-3","5","9","5","-6","8","-7","-6","3","-4","19","12","3","-5","8","-5","-12","12","-9","15","6","-5","7","4","6","-8","31","-8","2","4","7","2","-3","6","-18","10","-3","-16","-4","4","16","-2","-19","5","-39","-12","-22","0","-3","-12","9","5","2","-4","-8","-14","-36","5","11","32","12","-20","8","-12","-6","-6","9","10","-2","-15","-7","8","-6","0","-20","5","-38","6","-7","8","-36","-4","-40","26","-6","-6","-48","8","24","-4","-31","-18","3","8","-47","52","-2","-16","-54","-4","14","22","-7","2","-28","-2","19","24","3","-12","68","-6","-28","12","18","73","22","-10","-84","24","3","-8","65","16","40","10","4","-5","-48","-4","46","-6","-16","12","8","2","-20","-24","19","-12","-6","-5","14","34","39","-12","-9","12","-12","-48","22","2","64","0","38","12","3","8","-14","12","24","-20","-9","51","-16","-5","-4","-10","-2","15","-104","4","42","-6","8","-22","6","14","-20","40","36","-44","10","-5","6","20","-11","-18","-30","-32","7","14","-12","4","-77","20","70","4","-8","60","24","12","-98","-8","6","-48","-56","6","-36","24","-9","-8","-70","-10","124","-56","2","-24","31","15","14","0","7","-22","68","-8","74","22","6","-20","44","0","2","0","20","22","71","-5","-18","4","38","6","-68","-6","-16","18","7","16","4","-8","123","-18","36","2","-96","4","64","-32","40","-20","-3","-26","4","-22","6","4","140","6","118","32","48","-6","-48","-8","-18","24","-24","-64","-86","4","144","10","31","19","-68","18","70","-26","-3","0","-46","-8","-22","32","47","-16","-88","-52","-19","-120","2","-76","-4","16","20","-10","54","22","30","4","32","-12","-14","28","-56","-22","16","-12","7","-26","20","-2","-38","-2","28","-24","-70","2","24","-16","-19","-26","29","-24","-4","32","-3","5","-36","12","30","20","-68","-10","-39","6","-180","-36","28","-8","194","-12","-36","-12","-18","5","54","-73","-22","-24","-22","28","20","10","-20","0","84","-42","-172","-24","76","-88","-3","-32","-8","8","144","-84","-65","-12","-6","-16","2","-22","-40","36","9","-10","-86","-72","-4","-26","-48","5","-39","-28","48","-72","112","4","2","48","-46","38","-72","6","8","-4","16","-92","-154","-12","12","38","-8","78","24","-2","-66","92","20","-14","-26","24","-52","82","-19","-42","-36","12","-58","-12","6","-8","12","5","-80","20","-14","12","28","-34","11","-76","-39","-32","96","12","-44","32","9","62","66","-12","-52","-20","12","32","76","48","-10","58","-22","-20","40","-2","-20","-48","-64","-15","8","0","-80","26","-38","76","74","-12","115","-88","-3","-4","26","-8","-6","-12","14","4","-6","-12","-56","-6","-24","76","32","20","20","38","9","80","104","-51","-56","82","16","10","151","5","50","24","4","-100","-2","10","24","54","2","-4","6","-15","-80","40","104","61","84","-4","-7","-36","-42","-24","0","6","46","8","-8","22","84","22","230","32","-6","12","78","-14","-108","-4","20","0","-18","-40","-100","-30","-36","-16","-20","44","34","-24","-10","4","-36","5","-132","96","-6","-28","248","-20","-38","76","11","30","85","18","96","6","30","60","6","32","-74","-6","-7","8","-96","-14","-122","-8","12","8","102","-4","40","-66","77","-34","-36","-20","-44","-12","-70","32","-31","-4","76","-20","8","-38","-48","-60","-40","34","-24","-28","72","-12","92","26","98","53","26","8","-58","-72","-6","28","160","48","26","64","56","-6","-124","-6","-54","-60","36","-32","-48","-24","-2","6","9","112","114","8","100","6","70","28","22","10","24","66","-124","-30","36","56","44","-4","-2","-116","-60","24","-80","96","-31","86","-42","-15","-31","-54","-14","-18","-80","0","-16","-54","-7","-72","3","22","-56","88","-68","64","-66","8","-68","-32","-74","108","90","-22","-47","6","-6","-2","-356","20","14","52","-44","98","52","0","186","64","-2","0","-70","0","0","-46","-20","-16","3","-22","-10","-60","-71","-20","-54","5","-92","0","18","-34","8","-4","-104","-40","-38","48","8","-6","14","-6","68","104","-14","6","-212","22","16","-20","162","-18","-56","136","-7","-42","132","-16","18","-40","-4","2","152","8","-136","-56","-123","54","-28","18","26","-74","-36","120","54","-2","66","-10","96","84","-28","-4","19","-40","-64","-108","-14","32","96","24","-40","-52","-198","20","-20","-2","3","60","-3","26","-158","216","-4","-12","16","22","178","-102","-6","60","68","-4","120","-64","-140","16","50","-6","44","-126","-118","60","80","-32","-28","94","-48","-70","112","6","-174","12","48","-16","4","8","-20","-104","18","-1","-2","-24","-104","-76","24","73","-120","64","-46","-24","86","-18","22","-4","4","106","-144","-44","24","-10","-24","86","-31","-100","-38","-19","-84","-112","68","-120","-58","-18","-16","24","-70","70","-44","26","-124","12","3","52","-200","0","108","4","46","-8","-136","8","-68","2","22","-120","65","-32","-126","-48","-47","-68","-224","16","110","-128","88","-96","-48","52","40","102","19","-20","34","120","110","10","-2","8","-36","76","38","76","4","-18","-24","-16","190","28","-20","-5","58","10","-96","-120","-54","42","-48","-22","-96","58","-30","-8","-124","-4","-128","-24","-32","-68","39","12","46","20","14","44","4","-28","-80","-6","56","85","132","22","74","-120","-16","20","133","12","-44","-36","-7","12","-60","26","-42","-60","-20","96","8","2","-4","0","38","192","52","2","22","-128","-28","76","-172","24","-20","40","70","10","68","-2","-8"],"lmfdb":"agrees"}],"seconds":0.241,"computed":"atlas","estimate":{"seconds":0.358,"low":0.218,"high":0.619,"bytes":2028853}}