{"label":"713.2.a","level":713,"weight":2,"dims":{"new":55,"cusp":63,"eisenstein":3,"modsym":129},"old":[[23,2,2],[31,2,2]],"T":[[2,1],[3,3]],"status":"proven","checks":["dim M^+ at levels [1, 23, 31, 713]: [0, 3, 3, 66] (certified at ell = 2147482921)","T = [(2, 1), (3, 3)]; h of degree 55 = 1 x 55 (phi(ord eps) x dim S_k^new); 8 primes, 0 rejected"],"newforms":[{"label":"713.2.a.a","letter":"a","dim":1,"charpoly":["-4","1"],"traces":["1","1","1","-1","0","1","-3","-3","-2","0","-4","-1","2","-3","0","-1","3","-2","-4","0","-3","-4","1","-3","-5","2","-5","3","-6","0","1","5","-4","3","0","2","6","-4","2","0","-1","-3","4","4","0","1","6","-1","2","-5","3","-2","13","-5","0","9","-4","-6","-14","0","5","1","6","7","0","-4","-13","-3","1","0","-14","6","0","6","-5","4","12","2","-8","0","1","-1","4","3","0","4","-6","12","-2","0","-6","-1","1","6","0","5","-6","2","8","5","-13","3","-9","-6","0","13","11","5","4","0","6","3","0","-4","0","6","-4","-14","-9","0","5","5","-1","-1","0","6","13","-3","4","0","0","4","12","-13","0","-9","18","1","13","0","6","-14","-8","2","0","0","2","-6","-22","-5","8","12","-6","12","0","-2","-8","-8","13","0","-3","1","12","1","0","4","-17","9","-9","0","8","-4","-13","-6","15","4","-14","-2","15","0","5","-6","5","-3","0","1","-12","-6","15","0","8","7","7","-6","0","-2","-12","8","-20","15","-13","-13","18","-3","0","-9","-2","-2","16","0","-26","-13","-14","11","0","15","-3","4","0","0","6","6","-1","-15","10","0","4","4","-13","0","12","18","9","-4","0","14","-8","-9","-27","0","22","5","16","-5","0","-1","-8","-3","4","0","6","-6","-4","13","0","-17","-3","4","-18","0","12","0","6","12","0","12","-2","13","28","0","-29","-3","-6","18","20","-1","-24","13","-2","0","24","6","-13","14","0","-8","3","-10","-8","0","-6","0","6","2","0","-18","20","-22","2","5","-12","8","-13","4","0","-6","-26","-12","-9","0","20","-6","-7","-8","0","8","9","13","24","0","11","-3","-12","-1","-10","12","4","3","-18","0","4","-4","-12","-17","0","3","9","-9","0","0","-4","8","15","-12","0","-13","13","6","-31","15","-10","-20","-20","-14","0","2","-9","15","8","0","-3","5","5","6","0","5","-30","-1","2","0","-39","-1","4","-12","0","-18","-12","15","-32","0","13","8","10","-3","0","7","-8","6","-9","0","3","-6","0","-12","0","-8","26","-20","12","5","-7","-13","2","13","0","18","-24","-9","16","0","18","9","42","-2","0","10","13","16","-35","0","-6","-26","-12","-39","-15","-14","-15","-11","-8","0","-7","5","18","-3","0","-4","-4","0","-24","0","-4","6","14","-6","0","-1","-22","-21","14","10","4","0","8","4","0","12","3","-13","-15","0","40","12","19","6","0","9","35","4","39","0","-8","42","-16","-8","20","9","-26","-27","25","0","12","22","-3","-5","0","16","-29","-15","12","0","-28","1","-18","-8","0","-1","42","4","13","0","-17","6","29","-18","0","-4","-9","-13","-16","0","0","-11","20","-3","0","-4","-24","-18","-13","0","22","12","14","0","15","6","3","4","1","0","28","-12","-2","-2","0","39","15","28","-8","0","-33","-29","5","15","0","-6","-40","-18","-10","20","24","-3","24","-24","0","-13","27","-2","8","0","-12","24","-5","-6","0","-13","-3","42","-31","0","4","8","8","3","-5","-14","-2","-8","7","0","-12","-6","-52","0","0","6","-27","-2","-4","0","-12","-6","7","20","0","22","-20","2","-12","15","-14","-12","26","-8","0","-13","10","-20","18","0","12","6","9","-26","0","-36","12","-9","4","0","-5","20","6","-2","25","-7","16","8","18","0","-30","24","-26","9","0","-13","4","24","28","0","-21","11","26","3","0","-12","-16","-3","56","-10","-3","-12","39","4","0","1","0","-18","15","0","8","4","6","-12","0","-12","-6","17","-1","0","-20","-15","28","9","25","9","30","0","18","0","4","-4","32","-8","0","15","-13","-4","26","0","-26","13","-24","13","0","18","-3","-31","9","-15","-16","-10","-24","-28","0","-20","39","14","19","0","16","6","1","-9","0","-15","-27","8","31","0","27","-3","22","-5","30","5","4","18","13","0","12","-5","-6","-30","0","5","52","2","-7","0","-8","-39","24","-3","0","4","-8","12","-33","0","13","-6","6","-12","0","-15","-35","-32","-4","0","2","13","-12","-8","0","10","-28","-17","0","0","-3","-7","21","-8","-5","18","-18","-9","4","0","56","3","30","-2","0","0","-44","12","6","0","0","-24","10","26","0","20","-22","12","18","-25","4","-7","0","13","0","2","28","39","6","0","-38","-18","-29","-24","0","-3","-16","16","12","0","6","18","11","27","20","42","12","2","44","0","-24","14","6","13","0","-16","-5","-35","-21","0","7","-6","24","26","0","-12","-15","-13","-13","-15","6","14","-1","-15","0","-33","34","-8","52","0","3","-7","-40","-25","0","18","-8","3","32","0","-26","-12","12","-4","0","0","-3","-24","6","0","51","-4","31","-6","0","14","-6","-18","-39","0","-4","1","-24","-22","0","9","2","14","-6","-10","39","4","-12","0","0","8","52","-4","26","0","18","4","-16","3","0","13","0","-15","-57","0","-26","40","-28","-12","-30","19","18","-30","6","0","-8","-9","20","35","0","12","14","39","-7","0","-42","-8","-1","14","0","-16","-20","8","0","20","9","27","-34","-26","0","27","24","25","-54","0","1","12","-22","-22","0","-3","-37","-15","-12","0","33","-16","-39","-29","-10","-5","-20","12","8","0","-8","-28","-50","3","0","-18","-18","8","4","0","45","5","4","42","0","-4","-25","13","-30","0"],"lmfdb":"agrees","curve":{"cremona":"713a1","lmfdb":"713.a","ainvs":[1,0,1,-1,1],"rank":1,"torsion":1}},{"label":"713.2.a.b","letter":"b","dim":2,"charpoly":["-55","5","1"],"traces":["2","1","-2","-1","-4","4","-2","0","6","-7","-4","6","0","-1","-6","-3","8","-7","2","-3","2","-2","-2","-10","8","0","-20","1","10","-8","-2","-9","4","4","4","-13","0","-9","0","10","-6","-4","-6","2","8","-1","-16","-12","-12","24","-8","0","2","0","8","0","-22","10","8","-2","2","-1","-6","4","0","-8","-16","-4","2","7","0","20","-2","-10","32","-11","4","0","-12","21","22","7","22","-6","-16","2","0","0","-10","9","0","1","2","-8","16","14","-16","-6","-12","16","10","16","-10","0","6","-4","-6","20","12","14","-20","3","8","4","4","0","0","29","-8","10","-14","-24","26","1","-36","7","-12","25","16","0","12","-12","-2","-8","20","0","-22","-4","6","3","16","-15","0","21","-30","14","12","-10","16","16","-20","20","24","2","4","0","-28","-26","-12","13","2","-19","-16","13","12","6","-18","10","-26","-28","46","8","-4","20","-8","6","42","-30","-30","1","4","0","-52","0","20","-4","-16","8","20","23","-10","6","14","-3","0","6","22","14","-18","-40","16","25","-10","24","-8","5","-6","0","-4","8","12","-6","-30","27","2","-20","2","-9","32","6","0","0","-4","9","-56","9","20","26","-2","7","-4","-10","-10","0","32","21","-28","-4","-16","24","14","-7","-22","-26","24","-12","0","0","-32","-53","30","13","4","-6","-24","7","34","-12","0","0","10","-4","26","20","6","9","-40","8","0","40","-18","-12","0","-16","-16","-6","-4","-2","-6","-10","-8","-32","28","-15","14","0","6","-37","-2","-50","26","16","16","-24","-66","20","40","18","0","-16","6","-30","30","27","46","-28","-48","-2","30","7","12","0","-42","-9","-8","-14","-42","4","-20","-18","66","1","8","-41","0","27","-42","-20","16","16","28","-16","40","16","32","12","4","-13","2","-12","4","-17","26","-10","6","-22","-16","20","12","-24","0","18","-6","16","30","-20","8","-20","-42","-10","4","52","14","0","-26","4","34","3","-58","30","-2","-6","-24","-8","-34","0","0","0","-16","7","12","-5","-12","-20","-8","37","-38","13","-44","0","-8","0","-32","-4","64","26","-46","-14","22","-72","34","-32","0","15","16","-10","0","-40","24","-9","12","15","-8","7","-34","0","-16","18","30","2","-12","41","-48","10","32","0","-2","33","0","6","-72","0","2","1","-40","-21","-2","-4","56","-20","-36","0","-56","20","70","-12","4","-4","-34","-8","12","1","-20","-20","0","-30","-8","54","-80","3","10","8","18","-30","6","5","22","0","16","56","38","-50","12","-24","-72","4","26","22","6","22","0","22","-2","7","22","44","-62","50","86","42","36","-38","40","0","-16","3","0","44","-58","-17","68","10","78","-20","-60","2","26","6","-28","-32","2","-24","-60","37","0","-28","32","10","-36","0","24","-30","48","-16","-32","28","-8","24","2","8","-76","11","0","-20","-48","0","20","-40","24","20","10","-14","96","-36","6","0","-44","6","106","-48","-10","10","12","18","20","-8","-66","7","0","-21","16","-39","6","-48","-26","-16","-22","30","28","32","-14","0","10","-7","-8","-8","0","-1","46","-20","-22","-32","-4","-30","0","-2","4","-36","-2","-103","-52","30","-18","0","16","2","8","0","-4","0","54","-2","-48","-10","28","20","-56","-19","0","68","0","-52","-4","-29","-2","0","8","-20","6","3","20","-39","10","0","102","-36","44","19","0","-9","-24","40","58","-31","24","16","0","-20","60","-55","-22","-12","22","-1","8","-36","6","60","-16","0","-2","43","68","24","-4","-21","-66","8","-6","4","48","14","0","10","-16","-10","-10","34","-16","56","-4","-14","28","62","0","13","86","16","16","40","-80","2","52","-63","54","13","112","-6","0","8","8","-18","12","12","-2","-40","-24","26","30","-16","20","0","40","-8","48","32","-10","-26","-28","45","44","50","2","-16","0","10","76","-11","22","-27","10","-18","16","48","80","-28","-54","0","66","-38","-24","56","32","2","36","9","32","31","6","10","0","4","4","10","-52","3","86","8","6","-72","-66","24","-40","0","80","-20","-52","-48","-4","-30","14","-24","-12","5","32","-26","0","38","68","-14","6","23","30","26","-8","-10","20","-32","-46","0","0","-4","-80","18","46","24","40","-26","4","102","-8","-40","0","-3","4","4","-84","-4","-64","-16","70","-18","4","-48","-4","0","-80","-40","68","13","8","0","8","20","-38","-48","-26","-28","0","-1","-30","-44","-100","-20","-64","-29","16","13","-66","-62","44","0","-48","12","-14","22","20","5","12","-10","2","29","-62","29","52","56","14","12","-88","96","0","30","-8","24","-12","-60","16","0","-6","4","-26","-36","22","100","48","26","2","-1","24","-60","0","30","-68","9","36","-36","46","13","-36","-42","-84","42","52","0","-74","-13","16","-20","12","110","-44","-8","-16","32","70","-25","0","-62","-10","48","8","-14","-16","-10","-108","-40","18","-40","-50","0","24","-12","-44","-24","44","56","-12","0","88","-10","38","-10","0","12","-80","-26","-70","-40","-22","8","-12","15","-102","-39","32","0","-12","8","12","24","-14","-56","6","-87","-20","-4","14","4","0","-56","22","0","-28","-12","20","38","0","43","22","-22","2","0","-138","8","-88","4","-6","0","-88","41","4","66","-6","-36","0","72","-36","-32","20","18","96","-12","18","50","-14","40","-16","0","6","-18","36","9","-28","15","46","76","-58","-14","-40","70"],"lmfdb":"agrees"},{"label":"713.2.a.c","letter":"c","dim":5,"charpoly":["2521","1363","-477","-119","4","1"],"traces":["5","-4","0","4","-6","10","-12","-9","5","2","11","-19","-3","0","-3","6","-6","-4","-8","6","-8","-10","-5","8","-5","0","21","-3","1","-14","-5","-2","-23","-11","27","-10","0","23","-22","-5","1","-30","-31","30","-29","4","16","7","33","-5","-8","-7","-16","-11","0","26","19","-23","-19","30","4","4","-51","-9","-9","30","4","-5","0","-22","19","-2","4","-7","-3","-15","-17","2","-37","8","49","-44","-32","64","-8","41","-38","-38","-14","27","18","-4","0","3","2","-5","14","16","-54","0","3","3","-18","39","9","39","-19","-22","-16","1","20","11","-16","-17","6","47","-38","31","24","4","26","22","-43","-4","21","55","-33","41","-14","46","6","-13","-31","17","-34","35","-6","-10","8","20","-20","8","20","25","-10","51","37","5","8","9","-53","-4","31","-16","6","37","-15","27","64","-25","12","24","-37","89","48","-1","-1","-3","12","36","38","-7","0","57","-5","-16","8","-1","27","-7","22","38","10","9","30","-10","-44","-23","-66","-7","-47","12","10","-38","78","-18","10","-31","-15","13","18","-26","-30","-7","26","-9","-5","-53","-30","85","-19","-91","31","-32","43","-30","12","-28","22","-12","28","-25","-42","-53","48","2","46","11","9","-2","83","-34","2","-41","-55","-15","45","77","17","-55","63","39","93","3","-93","63","-35","9","-39","21","37","35","-11","-10","27","-36","-22","-50","44","-76","28","-1","-43","40","2","-19","13","-77","15","-38","-108","9","125","-9","-38","19","14","-44","-5","-54","10","32","-33","1","-28","16","5","69","-15","56","-82","-42","33","75","38","-23","-79","21","3","-22","32","67","-19","-29","-7","-1","13","-71","4","-2","-22","-7","79","-38","149","-53","28","-93","25","43","-21","0","-24","-112","4","4","-67","-92","-50","-29","-5","2","-13","6","-57","-75","-67","-32","3","-37","-11","-30","-135","18","3","16","-52","-60","-40","67","-127","-19","97","-53","7","19","49","16","-26","59","-5","-90","35","-109","-33","10","-35","-6","10","-80","44","19","8","-59","33","47","21","-24","-7","-19","-60","26","21","-63","8","32","-71","108","31","-65","6","-50","-11","42","16","81","-2","14","-58","0","-60","-20","3","-18","-103","117","-24","6","-5","-11","-43","26","36","4","49","11","-16","80","-12","-183","-22","132","-24","95","44","-6","-74","11","66","-10","-17","127","2","0","100","25","8","-9","-61","-25","173","-46","20","3","40","17","18","60","75","-25","29","-15","-19","-42","-40","-38","-14","-9","5","-6","15","-79","12","-17","3","-52","35","177","-12","98","-45","10","-2","-69","17","-43","45","3","50","45","-70","-66","8","4","-14","24","70","-42","-4","83","39","-83","28","-10","68","-6","-35","-47","72","-73","73","-68","-24","16","-82","10","45","-36","-43","-51","-106","18","13","47","80","138","71","-71","-27","37","-30","-91","20","-24","29","20","6","-84","5","-36","-56","49","-48","-21","-2","115","6","-22","30","154","-2","115","-79","23","15","-69","-8","73","15","-32","12","-8","39","-128","-97","59","16","4","25","19","-33","36","74","-5","64","14","-186","-60","1","4","11","-107","-23","93","5","-145","5","114","10","-103","135","122","-128","7","114","-20","-32","-175","8","-46","103","91","-23","-77","3","15","29","0","-42","5","-33","-32","34","7","-11","64","40","60","175","-4","122","52","57","58","58","92","-13","-54","-79","-6","-21","-35","31","-22","-55","-112","5","39","-14","-106","52","71","76","-78","-16","81","-42","-75","-29","-30","83","13","-17","3","71","-34","134","-5","-11","-38","8","2","-119","10","-73","72","10","40","67","-37","72","6","-33","68","34","121","-1","-101","-67","88","37","57","-37","44","16","-12","60","-79","-86","19","-2","10","56","-59","57","31","103","-108","-26","14","3","-26","184","129","-31","70","13","77","-72","-30","50","57","-26","48","102","-45","-57","102","-4","-83","139","-36","5","-46","-120","-48","45","135","-115","-94","122","-3","-20","138","47","15","-21","37","92","36","-35","-14","-40","-27","-35","2","-39","-9","31","139","-45","-79","-27","-8","61","-67","-99","-22","59","7","-34","-104","52","-34","128","220","62","-40","23","71","96","-20","103","-30","-31","135","-13","98","-80","-65","7","-76","-75","-56","5","-110","-137","62","-7","11","56","11","-80","-67","29","49","28","-120","-68","-3","151","71","-32","-40","-139","-77","55","15","5","53","28","123","45","25","-27","0","-102","78","-41","-48","-86","-148","10","-55","30","44","112","-25","149","-5","-92","16","-54","-29","-45","-77","-38","10","16","5","-6","15","-69","90","-77","-32","-21","113","-43","42","-2","-16","106","-137","-13","-116","-143","13","-51","16","0","-23","44","-44","-56","50","112","13","-68","-98","143","-23","-71","-14","-73","-54","3","3","-205","-155","104","61","-20","-23","-89","29","15","102","45","110","46","-188","-54","66","-12","-92","-70","12","120","-65","-122","69","-54","-46","-69","-73","22","-132","-1","20","36","-175","130","41","29","-121","-26","44","164","-81","-78","51","-35","-61","-5","-71","-85","74","-60","5","72","-86","-76","-41","-28","65","-77","91","71","14","122","13","75","12","-8","-82","-86","36","-98","-124","-50","10","-1","-39","200","157","-16","38","22","-45","1","-64","-76","103","-41","-27","-38","20","29","-33","5","142","92","25","-29","30","-150","-108","-8","82","-20","-155","-76","11","-58","-53","103","-28","-58","-87","-88","-115","-16","133","-43","-31","126","134","31","120","-16","2","-6","-150","31","139","120","-85","123","71"],"lmfdb":"agrees"},{"label":"713.2.a.d","letter":"d","dim":5,"charpoly":["32","176","0","-28","0","1"],"traces":["5","0","0","4","5","-14","-9","0","-1","2","-14","0","-3","-2","-2","-10","-13","0","-12","-1","2","-2","-5","2","-4","7","0","-17","5","-9","-5","5","2","9","-20","14","-15","-9","-7","-16","7","35","2","-21","-6","0","-11","-5","2","13","-9","21","7","30","-25","11","9","-1","1","12","-14","0","-8","-20","-1","49","-7","-24","0","-1","-6","5","3","19","-13","-28","46","-15","16","-9","-27","8","5","-7","-2","-40","1","11","38","-14","-20","-4","0","-11","-30","40","-24","-6","-7","-12","-7","50","-7","-2","1","-16","-10","-5","-7","-3","-19","33","-6","52","-5","10","24","-11","26","11","5","16","-8","-4","9","9","3","-11","40","-44","3","-7","58","-4","20","-11","4","14","1","-17","11","8","-17","-14","36","55","6","46","-1","20","-3","18","-11","-4","-5","-12","-11","73","16","15","9","5","-16","23","3","44","-9","1","12","44","-16","-33","18","-20","-22","43","11","-21","22","10","34","32","-16","0","-37","14","39","37","-15","27","45","1","-63","-17","44","26","22","9","15","-38","4","-26","-46","-7","-22","1","1","9","70","57","-13","13","-8","-6","22","-20","9","58","-55","-16","-35","-16","-52","-14","-8","-81","-40","0","6","-2","4","-31","41","5","-65","49","-73","-51","13","17","-14","-2","-5","-31","49","-37","-70","0","-44","46","0","-20","14","-41","-44","38","-14","29","-9","19","5","-74","3","-1","6","-27","21","-33","38","29","55","13","-32","8","-18","0","-17","-34","1","47","-49","-15","-42","32","-27","25","-1","-6","-2","37","17","-11","-83","-30","-36","22","-15","14","3","12","11","-12","26","20","9","-2","-14","71","-1","-2","6","-51","4","-6","3","-13","11","-27","-51","4","6","2","63","-82","-13","74","-58","29","28","66","-21","41","61","44","54","-8","6","-48","81","-9","14","9","-12","-20","2","29","-60","33","21","-44","16","-19","-41","-51","21","39","51","-102","-40","7","29","-17","2","-58","-14","59","-73","10","16","-78","-19","0","-113","-60","-46","54","-2","-69","75","-25","41","-68","-22","2","104","-26","-35","-23","-53","-17","13","-47","74","-37","16","-34","0","-11","27","-19","-6","47","3","-23","-11","-4","6","35","-20","-75","-8","-91","-13","0","-5","-22","34","-18","-2","-45","-11","-79","48","1","68","-20","22","-25","-25","12","95","11","-44","2","-37","-30","12","5","4","63","24","-4","35","-60","41","-36","-14","38","46","-25","-8","-43","12","-62","9","36","-36","94","29","1","-64","-163","-91","-58","2","1","-79","18","-21","-38","6","37","9","-19","-13","96","6","68","-29","14","136","-65","-2","48","-6","46","-94","-23","-74","-5","45","-45","22","78","9","10","-53","-51","95","22","-44","-54","-49","-11","27","2","48","-6","115","13","25","-22","-36","-24","87","100","39","18","-29","27","81","-32","-36","-42","44","-14","13","-3","5","-71","48","109","70","-115","-65","-61","102","113","-77","-15","33","30","17","-29","-39","98","-29","-73","-17","-57","-44","-2","-3","-46","78","18","8","0","-67","87","60","106","49","-32","-6","-68","93","-27","-30","85","13","-79","68","30","4","-22","-4","-40","26","37","-36","71","-26","17","20","-20","103","59","12","-87","37","5","76","-99","6","7","11","-7","-45","43","104","88","-26","-27","74","37","-108","-3","4","28","21","-63","-15","41","75","-58","-29","105","82","1","0","-68","-80","26","23","34","18","11","-33","46","-32","0","79","39","-51","31","70","-3","38","78","-37","45","-49","17","-12","-58","-17","-16","-14","-87","-2","-40","74","44","15","37","-14","6","-49","-57","-71","29","4","10","98","41","-5","-34","36","97","36","-104","85","-159","64","37","-23","55","29","-5","62","2","-82","-56","-29","78","-94","14","60","9","11","6","25","112","-7","38","-96","89","-1","42","94","-21","-69","58","38","53","-4","-15","-23","41","-29","-3","5","-148","10","47","-68","61","-4","-9","4","-87","65","95","99","-58","-76","-29","35","-49","6","-9","-71","-123","5","-5","-14","37","-96","20","-78","102","-56","-2","-82","89","36","120","90","-40","63","-47","54","-83","-18","14","86","-92","-2","43","-74","0","69","56","-7","-116","87","44","55","10","24","-75","-8","-60","4","-18","-18","-47","-62","61","-47","-9","29","-53","-25","36","-68","4","14","41","49","-16","-6","54","71","82","54","-225","-5","-5","1","9","22","69","20","-7","-113","-34","20","17","110","-19","-30","-1","14","51","41","69","-38","-21","57","65","-34","-94","57","72","-17","-14","79","53","46","-107","-11","-20","-60","137","0","-60","81","-53","-30","5","-106","-24","-64","43","-122","29","68","46","15","11","49","-37","5","55","-73","113","87","25","-30","49","37","-70","-26","-30","40","17","-19","-109","-66","32","1","9","-25","-127","-132","119","20","96","13","-53","13","-124","87","113","21","-97","57","-32","120","15","66","-5","32","-54","7","1","-5","-47","-92","22","-88","0","10","33","-46","54","-16","113","-31","-33","-41","-223","-28","-109","27","-65","-54","16","-41","-61","32","66","-46","42","-84","39","6","9","-123","-23","68","89","8","4","84","-28","-34","5","100","11","-7","-22","-49","128","-31","-146","73","5","-39","20","38","-15","-20","94","3","-34","102","-108","5","14","-15","-32","-80","-35","-70","-69","58","19","19","21","-11","-11","87","50","-69","72","-118","77","-23","15","-60","-83","34","112","-6","-150","-2","60","-89","-5","-29","-30","51","-98","-15","46","16","6"],"lmfdb":"agrees"},{"label":"713.2.a.e","letter":"e","dim":9,"charpoly":["-12048","-52616","2932","55218","10963","-4255","-941","53","20","1"],"traces":["9","-5","-5","9","1","1","-12","-6","2","-14","1","-2","-18","9","-15","13","-10","-22","0","-5","9","-8","9","-19","8","-1","-2","-35","-8","33","9","-22","7","-7","-17","18","-25","22","-19","-1","-11","24","-45","-9","23","-5","-29","27","9","-15","6","-40","-10","28","-29","24","-24","0","24","-30","-1","-5","-37","-4","24","-39","-24","48","-5","25","-25","-47","-63","46","-35","43","-27","37","-9","11","-15","41","-15","-38","-30","31","-3","-27","12","-15","20","9","-5","18","-20","-28","8","4","39","-21","53","-22","-40","11","60","-42","2","8","17","84","27","-103","36","21","1","31","38","-66","1","93","18","17","-26","9","66","78","-99","-7","46","36","-43","140","-5","42","-52","17","-20","1","-30","63","37","62","37","77","14","2","-1","-89","-13","80","-26","38","-14","66","1","27","46","12","-37","14","-12","20","-29","-29","-9","21","31","87","21","32","-14","-58","15","27","-36","81","27","42","20","61","-35","-4","27","-6","31","1","-9","-48","18","-64","14","82","-20","37","-48","98","-48","-6","14","20","27","-23","76","7","-42","71","2","-38","-56","-120","6","53","49","-59","-63","63","-12","22","-1","-68","5","-29","-43","118","54","-17","-8","-121","4","-14","-33","-17","-22","56","52","68","14","-87","-47","-120","-29","-100","-6","-61","6","67","-89","-6","117","-11","-17","-65","1","30","59","-13","23","-45","7","35","-63","149","-34","-189","6","-66","-28","-33","-33","47","4","-13","77","11","-26","-2","-19","101","2","-3","33","-25","24","-201","87","61","13","-35","15","-53","55","-67","-28","-143","-34","153","14","13","-18","-101","61","-93","-22","-57","28","45","13","-46","32","-14","8","80","-10","-16","-72","-6","-34","107","-132","-69","24","9","25","-1","1","-106","53","90","62","-79","-44","-45","-68","-97","-7","-56","-46","73","-20","-14","1","-107","-90","56","-15","18","49","-93","8","32","-5","-104","-2","42","-66","-122","-55","41","40","-76","63","-14","-14","225","1","-70","32","13","20","18","72","-2","25","-15","-15","-65","-9","-114","-20","40","68","26","-7","-106","-4","127","-22","-65","39","-52","-10","-83","21","-25","24","-27","0","-1","-3","28","-67","84","-18","-46","64","-13","-54","-70","25","-30","-63","-64","-27","-22","-108","111","-19","-20","33","68","107","-213","-28","-117","-93","54","-17","67","-115","148","109","-95","-6","9","49","129","0","88","47","64","77","-40","-91","-31","-51","14","-110","9","-39","-80","9","242","-3","20","-95","82","-37","-54","75","-5","33","174","-122","-153","-15","-4","43","-93","48","6","125","-179","67","-2","36","-122","65","-20","-36","-1","-30","-107","9","45","8","-26","-75","88","28","14","-44","-169","38","-96","-17","13","176","-114","-26","105","-6","48","4","183","15","-8","8","-39","54","-14","91","-1","63","-2","-13","78","-62","-167","67","-36","1","23","-16","-106","130","-28","-10","159","9","-25","104","-162","36","0","-7","-17","41","-5","113","-115","32","130","-55","47","0","-179","31","4","-66","107","56","-19","46","56","137","-38","139","-22","118","18","69","-188","-76","47","62","63","78","139","-40","95","10","-128","-143","-196","8","-5","-65","98","-7","84","113","-125","-22","108","84","64","-44","228","0","-19","96","-46","90","-92","175","8","50","-1","-11","165","-73","-134","24","-66","65","-92","-118","-53","-63","44","25","-53","-41","21","-1","202","34","-124","47","-5","-2","101","33","-190","-93","55","59","-16","-21","52","-136","-171","-7","44","-25","-79","20","150","-103","200","59","-81","20","-35","95","142","3","46","67","39","9","-34","36","-232","-142","-56","26","166","93","134","139","-115","113","-70","96","174","-8","252","234","-107","-7","154","-92","-92","-101","-56","-3","-100","-71","-88","82","-8","10","89","40","-2","-2","-36","46","33","116","59","-85","-26","-44","186","62","21","46","67","26","-114","45","164","22","-126","-24","-39","78","90","30","63","9","147","202","-58","180","70","120","43","-5","89","11","20","-60","-28","5","-64","-58","101","143","100","105","-262","-108","-22","-89","2","-138","-133","235","200","-103","-19","107","146","-105","22","-78","-17","-44","-45","-60","-25","60","9","-37","132","7","-194","26","-37","-176","-24","-60","7","-102","125","31","-169","54","36","-28","212","8","164","35","-16","53","134","-1","-7","47","258","-120","-53","4","-210","184","-36","-204","35","4","-208","-32","83","-37","-44","-162","-7","-3","-43","3","-285","-17","-1","-47","109","-85","-119","-10","77","-35","56","-24","66","-111","-172","-83","116","43","153","-77","-58","-48","261","9","18","117","138","4","-68","66","41","67","-65","-2","50","-37","-221","25","-1","156","105","101","15","-110","-91","-122","143","-25","-110","-58","-100","29","-178","-103","98","-109","-31","158","-143","16","-9","17","40","-3","-35","-12","60","-30","-77","-103","22","-94","-82","74","-179","-39","-60","-96","-137","-96","-118","-147","15","-79","87","140","93","-214","-97","6","197","-121","102","-19","-55","-8","147","-23","65","-54","-211","71","-36","-102","74","-118","-60","-1","-58","24","-81","55","41","118","-44","-151","-1","-229","87","-4","-507","80","108","19","124","21","33","-35","167","-129","-64","20","176","-82","-47","73","-1","0","-241","-11","209","117","-31","-45","36","47","-200","-37","43","-148","-178","71","-58","119","-85","65","149","9","-54","111","135","-69","24","-81","-86","-66","37","138","-220","38","51","-45","4","18","134","156","-274","-29","150","76","131","93","-167","-106","-52","-45","152","-42","-22","29","-122","-82","119","-10","188","-11","-93"],"lmfdb":"agrees"},{"label":"713.2.a.f","letter":"f","dim":15,"charpoly":["27053777664","7382578560","-13042354112","-2824262304","2394440880","337235440","-226250688","-13937952","11431542","-30449","-284982","11778","3242","-207","-13","1"],"traces":["15","1","4","19","1","2","23","0","13","0","7","1","18","-10","15","23","5","-23","18","-1","16","22","-15","6","22","-17","13","22","-8","1","15","16","-13","-14","7","15","19","-16","-9","13","-30","37","29","43","3","-1","13","-26","4","-1","-9","36","17","-37","27","-13","0","32","-6","-20","16","1","17","-34","18","-17","21","15","-4","-7","17","-32","19","-10","16","21","5","-1","19","-77","-9","-2","11","-9","-6","15","15","59","-12","-15","42","-19","4","-28","-64","-47","18","-25","-3","-75","-26","1","-21","-13","-4","19","21","1","23","-88","25","20","-6","23","-1","-65","32","-36","16","-41","32","-34","-15","19","-24","-164","82","19","-14","-14","-39","-40","-1","3","6","-20","10","-2","11","-9","-85","-40","31","2","44","-72","-43","5","-21","-37","50","-38","20","-18","1","-107","16","-38","-20","12","-23","-90","31","-90","-77","41","14","56","-17","8","12","-76","-52","-35","27","43","33","-48","-21","35","4","-60","60","0","-77","2","-53","-110","-3","0","46","-131","-23","-11","-52","-9","14","-46","34","-38","0","-6","-18","-136","-32","-28","-13","34","-16","-20","16","82","-21","60","25","-6","23","-78","-9","20","15","93","68","-25","-61","45","-22","45","15","0","3","103","-27","-158","10","34","24","-104","58","-88","31","94","58","26","-24","82","63","0","11","-117","29","141","-7","-5","55","-99","-50","59","113","45","-45","9","58","-49","-70","-58","-2","74","33","107","75","132","-9","39","32","-1","63","-26","13","-131","-3","149","79","33","-109","-109","-38","16","-22","125","13","51","-30","131","138","-141","-76","121","-18","80","49","-1","77","75","8","-41","51","118","-77","0","-80","22","65","120","40","16","-67","40","-4","55","21","10","61","57","-63","-54","59","-53","60","-119","28","37","-32","70","17","9","51","51","-2","6","7","-39","85","32","-15","55","-22","17","-113","115","-43","234","-20","112","-78","-74","-80","-36","126","94","-35","147","31","161","-37","107","102","-23","-84","102","-151","1","-7","-51","111","-59","-41","-163","-4","8","-71","58","21","31","16","-32","146","-37","-88","-24","-5","-132","25","69","-84","109","8","67","-51","-54","-32","-181","18","-83","-34","55","-2","171","-13","12","-165","21","-59","23","140","59","-26","-68","66","-72","-9","85","-32","6","-12","-144","84","214","-45","104","20","66","94","-10","-113","-69","-18","80","71","-164","-18","14","-53","157","41","93","40","-128","-115","189","-77","50","13","24","121","76","54","65","20","1","-105","170","149","-77","15","-157","10","25","-29","24","-145","-41","-77","150","-42","39","25","-3","41","-53","-54","-25","-16","215","32","-70","92","13","4","66","72","208","-180","-6","-173","23","-38","-216","115","95","-19","104","59","-167","-67","-22","23","268","-24","-98","65","9","41","-223","-21","-298","-28","119","82","84","-23","113","60","-14","113","-136","5","-141","15","-61","-4","106","-262","186","-43","-28","-76","169","-11","-39","-67","29","56","-40","-44","195","3","94","30","-13","-56","-6","86","134","-151","-191","64","-23","96","-174","-183","92","-53","-335","-62","36","91","29","23","3","50","-72","-269","93","-22","-96","-21","-159","84","166","-59","-11","138","-22","-146","-144","-19","-142","18","55","-76","38","-77","138","-113","-18","-106","17","17","144","-57","-174","14","78","9","-285","-72","-21","37","-120","41","25","64","151","15","-158","-60","111","-119","-1","-13","-7","95","4","-51","-80","59","88","-99","8","-16","-13","-49","-97","-23","2","-2","74","157","2","-46","102","32","-22","83","62","-85","-204","7","-21","16","-226","21","-212","-40","-109","-228","-94","-124","14","-91","229","-33","6","-222","-138","8","-103","-135","29","-91","127","-2","-51","-148","14","-11","-100","-193","84","-78","22","-170","55","-152","5","81","42","-16","-1","-30","54","7","-53","116","-448","-21","-44","-149","-174","-46","-28","73","124","-4","24","-71","-145","21","-34","42","-133","-15","170","-14","-109","-135","12","-81","129","-162","115","15","75","-84","-99","83","-196","-44","7","23","289","83","314","28","-16","-101","190","-53","-269","71","-15","-53","6","-133","-214","-39","86","69","-105","97","85","-84","115","50","-130","18","-138","13","66","2","76","4","124","164","-103","78","132","-9","-97","-193","47","59","22","22","-40","13","95","-7","64","-157","14","153","15","-136","127","154","92","126","-208","-32","-135","-84","192","-36","-133","131","4","130","75","25","20","-197","342","-7","-17","89","-206","-253","159","16","-391","-20","224","84","-151","-31","42","199","-152","-65","167","130","47","224","-27","-5","-15","91","302","-96","-68","54","-6","29","-233","13","-185","-140","43","35","325","-170","-113","-83","91","21","98","-55","-120","-19","236","23","-131","-19","183","25","-46","3","265","-103","14","28","66","-103","112","-171","22","16","122","94","-9","-31","16","18","170","-23","-235","195","-68","91","-344","7","294","-101","-311","103","95","85","233","-198","252","44","-153","-125","121","9","61","-8","-270","-64","59","-58","183","-145","88","-162","-92","42","64","65","62","-136","212","63","-110","-14","213","138","-13","89","133","-116","41","24","63","-33","8","-79","1","-191","36","-45","73","36","-162","-64","92","4","33","114","49","30","-21","-103","-39","15","50","-1","-22","4","-86","160","328","-89","-111","5","-176","127","29","15","-152","-37","91","69","-37","162","412","-118","-11","-45","352","183","-138","161","-171","14","-114","-136","46","201","-34","180","126","73","303","-262","60","-29","200","11","16","-179","-192","90","147","11","-187","37","-85"],"lmfdb":"agrees"},{"label":"713.2.a.g","letter":"g","dim":18,"charpoly":["-331599840512","-182408157696","454883377792","190476212576","-183601428336","-64249268704","30472997400","9277641200","-2402253608","-633932929","102548464","21796294","-2609631","-387049","39329","3351","-315","-11","1"],"traces":["18","5","2","25","1","4","23","15","20","1","3","-5","2","5","15","35","-9","29","12","-8","-6","-12","18","-40","33","7","5","55","12","-7","-18","10","15","14","-13","13","21","15","35","-7","10","-39","43","-41","-25","5","25","6","57","0","-15","6","-27","23","31","11","2","2","-6","22","-10","-5","59","65","-32","-43","55","-33","2","-8","-27","59","9","-2","-84","12","5","-45","43","6","26","-1","1","-79","26","-53","11","-65","-14","-104","-30","25","-2","-28","48","-67","-20","-24","-19","98","18","-23","69","-83","-32","-15","-15","-115","-7","32","-43","47","-6","-135","1","45","-26","25","-6","-9","31","-44","51","-25","0","87","110","11","-6","-64","-35","8","25","-89","28","-50","-38","4","7","-138","39","97","-31","-42","-78","12","15","11","-33","-103","64","-70","-70","-90","-1","21","-10","-12","8","-121","23","30","71","-11","-61","-123","-20","-216","24","-176","6","154","-26","-151","129","-121","-39","-58","-1","-244","-44","-16","30","15","-3","-4","107","110","-89","-101","-48","91","73","30","82","60","-18","-20","22","-25","-60","-51","10","42","42","-9","20","-40","-44","50","28","-40","-15","-103","-5","-34","-23","87","79","-86","-67","-17","62","6","102","-94","64","-149","-1","1","-37","13","53","196","14","-37","-106","54","-22","146","-9","-94","-18","-4","-112","46","183","-15","-25","116","-17","40","3","151","27","67","26","11","-33","-7","-49","1","60","115","30","119","-58","160","-87","27","69","8","25","-17","30","-5","-15","16","-20","119","-77","73","-35","70","51","103","152","2","43","-123","-59","63","-44","49","-88","125","84","-71","2","-182","17","157","101","6","16","3","99","-138","53","-1","40","10","-67","45","-136","-70","17","-100","118","151","-39","5","7","159","19","37","63","57","6","173","2","-47","50","-54","-27","-165","-35","19","-36","22","-3","342","163","-44","15","-69","-8","65","117","-69","37","-118","-58","-84","30","58","-20","134","82","-244","50","-37","-9","23","-47","-71","58","35","-48","8","63","5","1","113","-77","-43","-45","147","40","83","-63","89","-15","-25","-36","91","-28","34","22","22","-9","107","-85","77","68","-195","-36","69","-5","47","-100","127","-2","110","-238","-75","-6","-85","67","-25","13","114","-103","29","66","-231","-2","112","-28","290","-5","206","120","142","-110","6","-58","-75","-85","36","76","-218","-124","-5","137","102","12","-168","-57","254","75","-14","-37","-115","-137","-71","180","258","39","258","-69","25","-91","64","-151","-342","-4","-131","-122","-8","-11","-82","183","463","-15","62","-14","183","59","-166","133","201","11","100","126","-223","-99","65","-37","221","-62","281","-6","-59","-138","-142","46","-141","-52","-146","-36","138","122","-6","313","-35","-8","72","-15","-254","-123","50","-17","137","-65","-12","-125","4","-12","422","35","0","-81","208","-1","182","-12","21","32","-268","-161","87","-2","30","-327","-76","9","21","18","109","-184","65","98","92","41","-24","36","-137","-31","243","117","-5","44","-42","38","-267","-41","-84","-240","-89","-98","-40","-80","-76","145","-75","-34","-29","0","93","-141","81","77","203","24","-232","161","55","-201","141","-118","242","-11","18","33","-89","-95","89","-2","-172","-91","-143","182","-2","16","-26","-21","4","-12","154","64","-22","-17","-174","113","-126","164","7","-11","-520","-99","26","-36","162","-223","261","160","-282","-91","140","-117","3","56","-162","-117","-234","46","123","55","8","5","82","-135","0","-12","-136","-117","-121","-75","-497","30","153","-163","-18","-229","-114","16","-230","-107","-243","-238","-118","-18","55","-233","-180","51","207","-157","183","6","341","-1","294","240","-40","22","24","56","-194","1","33","-157","60","18","-126","12","-89","-15","-167","61","-217","-60","125","-176","-284","-125","256","163","-178","-152","12","50","316","-66","-94","25","166","-118","-7","-78","-326","-223","193","-144","-32","-119","-16","33","482","-78","76","-43","-294","-106","-336","-57","-75","-169","-9","-58","-81","-18","-90","-110","217","101","-77","127","-150","48","88","123","-141","-26","65","67","-234","-73","-105","-201","79","23","198","-234","10","-77","-349","69","125","-139","-45","143","40","-21","31","-79","-18","-105","335","-41","137","-60","-161","24","-222","88","130","15","-440","20","128","-32","-117","-74","-159","-14","-48","-7","283","137","224","-149","56","-33","-2","-35","13","-155","-66","109","14","-47","-40","126","89","-230","142","-66","128","-68","293","84","-21","-260","5","21","-418","54","-172","-159","54","95","176","-13","-7","45","44","35","-162","-52","323","-40","140","-34","-71","-89","-116","-95","213","75","85","72","-13","-48","-20","-73","13","-83","0","112","-40","-16","150","-113","175","-5","330","88","331","92","32","208","28","33","151","59","-190","33","20","21","6","77","127","-15","-345","23","6","-67","219","199","-118","184","-124","65","-278","-15","-55","188","482","-64","-51","-117","15","-158","-202","113","-30","17","-276","-171","613","23","280","195","152","-85","213","101","-91","-182","-80","-146","197","61","254","35","-117","-12","259","28","-69","130","-229","223","-164","38","156","230","-196","-77","-166","24","316","-245","-114","-90","-391","-36","-7","-99","-237","40","125","-210","-31","-61","174","111","7","151","65","89","-284","-56","182","172","-164","22","63","-30","-37","10","260","127","-239","187","70","-109","578","-56","0","-162","86","55","9","87","-27","77","269","18","30","69","-143","269","-39","406","83","66","42","7","36","-205","148","253","-27","-36","-104","56","-630","133","-40","68","196","-71","169","98","192","43","-94","-37","-10","237","107","-124","97","83","51","-15","23"],"lmfdb":"agrees"}],"seconds":0.239,"computed":"atlas","estimate":{"seconds":0.498,"low":0.304,"high":0.861,"bytes":2293585}}