{"label":"697.2.a","level":697,"weight":2,"dims":{"new":53,"cusp":61,"eisenstein":3,"modsym":125},"old":[[17,1,2],[41,3,2]],"T":[[2,1],[3,1]],"status":"proven","checks":["dim M^+ at levels [1, 17, 41, 697]: [0, 2, 4, 64] (certified at ell = 2147482801)","T = [(2, 1), (3, 1)]; h of degree 53 = 1 x 53 (phi(ord eps) x dim S_k^new); 6 primes, 0 rejected"],"newforms":[{"label":"697.2.a.a","letter":"a","dim":3,"charpoly":["-7","3","5","1"],"traces":["3","-3","-2","-3","0","2","-4","9","3","0","4","2","-8","4","6","-3","3","-3","2","0","-8","-4","0","-6","1","8","-2","4","0","-6","-16","-15","-4","-3","-6","-3","-4","-2","-4","0","3","8","-4","-4","-16","0","-14","2","-5","-1","-2","8","-22","2","-26","-12","-18","0","20","-6","14","16","2","21","20","4","-8","-3","6","6","-30","9","-4","4","-22","-2","-4","4","10","0","-17","-3","-16","8","0","4","0","12","-24","16","20","0","26","14","-22","10","20","5","30","-1","8","2","20","-24","4","22","-32","2","2","26","-46","4","16","18","16","0","-28","-20","-4","18","23","-14","-2","16","-12","-2","-16","9","12","-20","-12","4","14","8","20","9","4","-6","-4","6","26","30","-60","-3","0","4","40","4","22","22","-18","6","3","4","-4","4","6","-10","36","0","-6","17","-12","-3","60","16","-4","-24","41","0","24","4","6","0","20","-4","-4","24","8","16","18","-20","-12","0","-40","-26","4","14","12","22","12","-14","4","-20","-56","5","-30","-30","12","3","-2","-8","0","2","0","-20","-16","8","30","-4","12","22","40","32","-20","-6","6","-2","-34","26","-8","46","-20","20","13","-16","-18","18","20","-16","-34","0","36","28","22","-20","-60","4","6","-6","-18","-23","2","-14","8","2","-16","-48","32","12","-40","-2","-26","16","6","-51","12","-12","54","-20","0","12","-6","-12","12","-14","16","8","26","-20","-28","-3","60","-4","4","-6","-36","4","-12","-18","-42","-26","-12","30","48","60","-4","-15","3","0","8","4","-6","-40","-20","-12","-52","-22","20","22","-4","18","40","-2","-52","-3","20","4","-32","4","-40","-12","-42","-6","-6","-10","34","-36","0","0","-6","6","2","17","16","12","44","9","2","-60","4","16","36","4","-42","8","12","-41","26","0","2","-24","-2","-12","-32","-6","-46","0","-2","-20","64","-20","-46","4","-14","24","-8","-8","-20","-48","-17","-18","-64","-20","-8","12","16","0","3","40","8","-26","-38","-4","-4","-42","0","-12","-44","22","-8","-12","8","-6","-8","-4","16","-20","-66","56","0","-15","78","30","-30","-30","-8","-12","6","-1","8","2","4","-8","4","0","26","-6","34","0","16","-20","-36","16","12","40","-10","-30","28","-4","60","-12","-36","-66","1","-40","-16","32","52","20","0","2","-50","-6","0","-2","-22","34","8","-78","-13","8","-8","46","0","20","-60","-28","42","-13","4","-16","26","18","16","-54","40","-20","-2","-16","-54","34","-62","0","-24","-36","-48","28","18","-22","84","60","44","60","34","4","-34","-6","0","-30","28","18","4","-23","12","-2","-40","42","54","-8","4","2","0","16","-50","16","20","-32","22","12","16","40","-14","6","76","26","34","16","38","-6","42","33","-12","-12","40","-12","-46","-54","8","60","40","0","-12","12","28","6","-16","4","-53","-12","40","-14","-8","-16","-28","-24","30","-26","14","-20","76","28","-64","-15","76","-60","10","-4","66","-4","0","18","40","36","72","4","16","12","-48","6","-4","42","20","-26","8","12","38","-90","2","-48","28","60","54","4","-12","21","52","-3","68","0","0","-8","-32","-12","44","6","20","-40","-22","20","-68","4","-54","52","-6","-22","8","-20","20","-66","4","4","34","18","-40","-40","72","-10","0","52","48","-3","14","-20","6","-12","-26","32","24","4","20","40","32","4","-37","42","-102","-6","-4","6","-8","30","-80","-34","40","-36","-44","0","-16","0","-54","6","-40","6","32","-2","-36","-51","76","-16","8","12","14","-44","52","-3","4","-2","-38","-60","-42","-4","-4","-48","-4","-36","0","4","120","42","120","40","6","-12","18","-41","12","-26","-48","0","32","-2","-26","-24","-40","2","-84","4","40","32","2","-6","4","46","56","0","3","2","16","-20","42","-64","86","28","-72","46","-56","4","44","14","40","-72","-4","8","32","-8","70","20","10","16","-8","17","-64","-18","0","64","10","60","3","8","-4","12","2","-16","-26","0","66","-3","-36","40","108","-8","-32","78","-76","38","-28","-4","70","4","32","14","88","0","-30","-12","-28","44","60","-66","-10","8","-48","-12","-16","-8","-112","34","-34","8","4","-4","-20","-16","-36","60","68","66","2","56","8","0","0","5","100","-78","8","30","-10","30","-58","90","-136","8","-68","-12","-86","-6","-14","-5","-24","-8","-26","2","0","-4","4","24","18","-4","-12","0","-12","-26","-12","2","8","-34","4","0","28","-16","102","60","-80","36","-60","16","-38","-12","18","-56","-5","10","58","-30","-28","-28","-36","12","-87","-60","4","-12","-16","36","18","22","-14","-1","-40","-40","2","16","-66","-96","36","-52","-52","20","-8","0","4","10","32","50","-2","-6","20","0","-48","6","8","22","28","34","10","-8","-60","26","42","13","-102","8","80","8","-76","-138","40","0","-46","20","-48","60","-18","-12","-56","-42","0","-13","-22","-4","-28","48","-4","-26","24","18","-68","-16","-20","18","-24","-40","132","-20","-54","2","0","48","-160","54","12","34","96","62","-20","0","-20","24","-48","-36","-24","48","-26","-84","-26","-18","52","-22","138","-84","0","-20","4","-44","-52","60","68","-34","-20","-12","22","34","98","-6","0","0","-24","42","27","-28","-4","18","-36","-4","16","69","-18","-12","6","-2","18","40","108","-14","-30","-54","-32","-8","-74","-4","-32","-6","-100","0","26","16","-20","50","10","80","42","-20","110","-32","10","-22","20","-36"],"lmfdb":"agrees","derived":{"al":[[17,-1],[41,-1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"697.2.a.b","letter":"b","dim":3,"charpoly":["5","-1","-3","1"],"traces":["3","1","2","5","-2","-4","4","9","-1","10","0","-10","-6","18","-6","13","-3","1","0","6","0","-14","6","-12","-3","-2","2","12","10","-2","2","29","20","-1","14","-19","26","-26","-4","14","3","-8","-16","-40","2","-10","24","-10","15","-13","-2","-10","-6","22","-14","34","16","-18","-8","-10","-6","34","10","13","4","20","-10","-5","0","2","2","-19","-22","-2","-6","-32","-8","8","-18","34","-5","1","8","-44","2","-12","16","-54","14","-22","-8","18","-4","10","-26","-12","-6","25","26","3","42","4","16","-18","-8","-30","-2","22","-14","-26","22","84","-14","16","-16","-2","2","40","-4","-18","27","-14","2","14","0","-32","-12","17","20","-20","-2","8","-36","-44","20","-9","-14","-12","14","58","-8","24","0","1","-28","-18","-8","34","-18","0","-36","-58","1","-60","32","20","10","-4","36","10","-20","-15","10","5","0","-24","56","-52","-27","-10","6","-88","-10","-4","-32","-56","-24","-10","2","2","46","-36","-8","14","-28","-8","0","88","36","-6","-2","-50","-38","-38","12","61","26","28","4","-13","-12","14","-20","10","-2","-44","-22","-26","48","-36","-28","-90","-32","30","4","46","64","2","-10","-42","6","-30","8","66","-19","6","38","36","-2","40","66","-10","46","-2","-14","24","-36","-18","8","-26","18","77","-22","-2","10","-4","0","50","-20","-40","0","-42","-12","36","6","61","-14","52","18","-12","-6","18","12","48","-24","-48","-12","-6","-62","4","12","-13","0","50","-12","8","-18","-26","22","74","6","-56","-10","70","0","28","4","-43","3","36","-16","-46","46","-38","48","58","-28","-10","-12","38","-4","26","28","-104","-8","-1","44","-156","60","-16","-4","24","2","-22","-42","18","-26","48","28","62","-24","48","0","17","6","34","-40","9","12","28","-2","64","-10","14","-34","-32","54","-9","-14","-6","-16","52","14","-116","-12","58","62","0","2","-6","-4","-94","-18","-8","22","66","0","0","20","-18","11","6","16","-24","4","4","18","-22","-1","88","-24","-68","46","14","36","122","-20","40","10","-78","-44","-64","26","-52","-52","-46","60","14","-34","4","-6","101","-28","-46","14","14","-26","-18","38","-61","22","8","-4","70","-10","32","14","12","2","10","-24","-72","56","26","-32","-58","32","100","6","-24","-50","50","-54","-126","3","-36","-36","42","-40","-108","50","94","-54","28","-20","38","20","34","-8","-82","-21","2","-36","-70","-24","0","36","100","-30","23","0","-14","-36","-44","-28","68","14","42","-2","-24","-18","82","64","-42","-4","22","72","38","-100","126","64","56","92","0","20","-12","54","62","56","-58","-52","18","-28","49","-32","-72","30","-22","-16","66","-52","-10","-10","52","2","142","16","-36","-26","-72","44","60","-18","-64","-28","-16","-18","52","-6","2","-46","5","-52","58","-60","36","-72","142","-52","-28","46","46","0","50","-28","-58","-2","140","-25","-72","8","-184","-6","-40","32","-60","-40","-14","-54","68","-2","-28","44","-29","16","16","-6","6","-18","26","52","-4","-44","-46","-52","-22","2","-66","32","50","-20","-54","-10","-60","20","30","-46","96","54","52","48","80","68","18","26","-51","-14","1","-20","-44","-68","-4","120","-86","-4","6","70","-72","-72","-32","32","70","-14","-80","-14","-126","-12","20","28","32","34","-188","-48","-36","50","-56","34","-90","16","0","-48","19","-30","40","-6","-224","-74","28","-18","104","-20","30","-32","20","-25","-58","-14","-98","-26","10","-72","-4","-40","-130","48","36","-30","24","-44","70","58","-20","4","-4","32","26","-68","-3","-56","26","12","62","82","-12","20","13","6","216","68","80","14","56","4","48","-12","30","44","80","-12","18","-12","-96","-26","-54","-26","-45","-38","14","-92","-14","64","-92","-46","26","64","18","-20","-96","12","20","70","74","88","52","-40","12","-3","-86","0","-40","-70","-44","26","-176","-48","-2","56","-40","34","50","-40","70","-52","8","28","86","-16","-36","66","-82","-28","61","16","50","14","-38","-16","-68","-13","-72","16","48","26","46","-30","62","-16","1","-52","20","-32","-156","78","-80","8","106","-80","40","36","36","-56","112","20","36","62","140","6","-14","-12","-110","-2","-20","-36","-142","-2","-44","16","14","18","-112","28","-74","46","8","-58","-30","8","-6","0","20","-100","10","-36","145","-32","-24","-34","14","12","-14","-2","68","12","-70","12","36","-14","110","-24","-25","-62","-70","14","120","68","-68","-72","126","62","22","22","-92","-52","-86","24","10","44","-110","-20","6","-62","4","-50","-100","-72","8","24","-26","2","104","-50","-26","-15","4","-42","172","68","26","-24","-68","-11","-38","84","-4","18","4","170","-138","-12","13","64","-20","-18","-24","46","70","-10","-40","-40","-52","0","-2","12","78","68","62","2","168","-72","36","20","26","-58","-72","-44","90","34","6","44","-146","-74","-35","84","10","16","-72","-4","-78","28","104","-38","48","-28","72","-2","122","0","26","-60","31","6","-14","116","-22","-40","36","-106","-14","-14","-4","-34","112","-76","78","12","34","8","-22","-50","0","-28","6","-4","70","-14","-2","44","38","-42","-68","-58","138","16","24","14","38","-42","-44","64","54","-34","44","6","136","4","180","-22","80","44","6","8","-34","-42","54","-62","56","40","54","76","-26","31","4","-14","22","-8","12","-38","153","-16","40","-96","-10","-20","-78","12","-74","2","-36","-64","90","-50","-44","66","-12","-72","18","-94","64","-80","38","98","74","-40","112","-22","52","-6","-80","-4","-112"],"lmfdb":"agrees","derived":{"al":[[17,1],[41,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"697.2.a.c","letter":"c","dim":7,"charpoly":["-109","-7","178","21","-73","-15","5","1"],"traces":["7","-3","-2","9","-5","2","-7","-21","7","1","-6","-5","5","-9","-26","9","7","-6","-13","-4","4","8","-26","7","-4","-23","-14","3","10","13","-2","0","-11","-3","3","-9","1","-13","-1","14","7","-5","-12","-34","13","37","-18","-21","-8","1","-2","31","-6","37","17","-7","-8","1","-55","-13","6","-15","-8","-5","-4","-24","-13","9","29","14","16","-36","-6","-12","38","9","-25","-35","-12","12","23","-3","-41","24","-5","21","-16","67","6","-37","-3","-41","-35","28","21","35","-3","25","-6","-28","-52","2","-52","-4","25","7","-17","-24","-2","16","27","36","-26","76","-3","45","-41","23","-7","92","13","-6","-2","12","-9","-11","-35","11","53","58","19","62","18","12","-30","-21","15","-8","48","-27","-43","0","31","90","6","40","24","35","-6","11","4","7","7","63","37","58","31","3","-12","-35","2","26","28","9","35","68","-30","-14","-18","1","-8","-53","-55","-7","7","-65","7","-2","-20","48","28","20","-11","81","-28","58","-6","-15","-25","-63","-54","8","16","-20","27","0","19","82","-4","-1","24","18","-22","-5","-5","60","-16","-13","-16","43","12","-61","-26","10","-41","61","-31","64","46","-28","5","37","-77","-18","60","-8","-18","-139","-6","-29","3","-54","-2","44","61","-85","44","-9","-27","-96","4","-99","-9","72","-16","2","-24","32","54","-17","89","58","-19","48","-26","-35","27","-26","19","-89","58","-51","-40","-13","18","82","7","8","43","-45","-71","9","35","26","-22","-20","7","-71","-42","21","-42","-26","-4","22","55","-26","-7","-6","7","6","-86","-91","4","-64","48","-47","-23","69","-70","2","47","75","23","19","5","-6","-27","-73","34","-43","-21","-24","0","-83","21","-76","7","11","-62","-3","-43","-58","-13","-54","-48","-3","-53","-21","64","-82","31","-106","-25","62","-11","21","34","-72","65","-4","75","-81","7","31","65","26","-73","-25","23","-12","-48","94","-31","-115","10","22","4","-2","-32","-46","4","-91","-19","-16","-40","60","47","-55","7","-25","11","-109","72","8","44","28","-26","-19","45","130","-43","71","-40","11","22","-18","-43","15","61","60","-26","71","-48","61","-32","-143","23","-84","-50","39","30","67","48","-67","28","-175","-80","7","-1","1","-14","-73","122","6","-13","22","56","7","-39","-91","23","82","-48","26","-4","-51","43","-49","-3","5","30","-118","7","151","-72","-112","19","63","87","-54","-80","-23","32","-99","-13","-19","-23","51","2","73","-6","64","81","-2","-32","162","-27","-23","-14","61","19","69","27","81","83","-20","37","-52","-41","-2","73","154","-27","-7","-11","3","99","-76","-101","-29","-22","4","-39","95","89","-131","-52","-97","11","39","-73","-5","10","76","62","-61","23","-25","116","46","-74","-84","-115","54","29","-10","100","-83","5","13","-49","97","46","-4","18","64","-34","-18","20","28","11","-80","-34","-26","-75","-104","-2","9","51","-18","-60","-55","5","101","60","37","43","-77","29","105","-38","-62","-68","0","55","2","32","50","-60","26","-78","-99","-69","43","-5","57","-7","-41","-37","-57","-11","-5","-13","49","-39","-221","-53","-82","15","44","16","3","88","-9","68","14","-44","-3","56","-20","-26","117","44","65","92","-132","-28","47","116","92","13","29","-71","-113","3","-22","143","138","-65","-123","56","35","-21","-82","6","-135","-50","-32","66","-54","-31","-9","26","145","-26","72","-15","-53","126","97","160","-56","-73","42","-15","76","194","114","1","45","-74","131","96","-52","78","55","27","192","94","-22","48","80","61","-6","26","-13","-3","14","43","-3","-20","-41","96","137","29","9","37","-48","59","183","-28","51","-1","193","32","-63","78","-149","-45","-79","-146","-80","69","109","33","16","46","-203","32","14","13","-150","11","254","-1","-5","135","-49","-41","-109","-3","-26","47","70","-104","26","7","140","4","103","71","58","60","-107","145","73","72","270","86","51","0","-7","-92","-5","-28","28","-43","-78","-90","91","76","-67","-64","161","16","11","-71","-70","-101","-103","-12","-168","37","-92","80","-59","-24","-6","-24","64","11","44","12","224","29","-78","-90","-34","69","-152","70","1","-35","56","-85","-91","63","23","22","-169","66","-131","-8","-88","13","-180","-8","-74","-99","-132","21","100","-90","75","-110","-34","-44","45","-13","-99","-65","37","0","-122","-104","-71","50","-136","-66","4","47","97","-37","23","-69","162","18","24","-18","64","11","-14","39","-188","37","-19","12","200","51","-6","-89","61","96","68","-39","-21","11","-44","98","-4","40","-132","3","177","-93","13","-45","13","-76","-43","25","-97","-8","-65","104","32","-1","46","28","-19","67","116","-71","-31","-82","-135","38","49","103","1","33","115","-88","-67","-14","-3","-53","90","-18","-11","4","46","-98","-8","35","-90","-2","-194","166","84","-49","-11","37","3","53","-102","-123","107","-121","56","43","55","56","31","218","-114","-122","5","49","-99","115","-66","17","-182","-23","46","-75","-118","-152","-69","-6","8","-67","75","40","-179","-28","11","-167","-22","47","-167","70","59","53","-69","21","37","11","18","6","-85","-23","-148","28","109","-246","-199","34","28","-54","-76","-192","-55","17","92","-47","0","63","-34","-105","97","-26","-23","102","-67","132","42","-86","84","42","-7","66","67","-34","32","-38","198","15","-7","53","0","82","6","-72","18","45","-90","-8","-97","-56","161","-5","-141","-102","55","19","10","-1","-47","214","-14","47","7","-32","1","110","-137","47","103","-64","48","-201","-188","-139","4","-181","-77","78","54"],"lmfdb":"agrees","derived":{"al":[[17,-1],[41,-1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"697.2.a.d","letter":"d","dim":10,"charpoly":["-439","-2348","1616","3853","-799","-1491","228","174","-27","-6","1"],"traces":["10","4","2","6","11","10","3","6","14","3","6","27","7","-15","-2","-10","-10","1","-3","8","-4","0","20","-5","13","15","14","-9","-4","5","10","-9","5","-4","25","24","-13","5","21","14","10","-13","24","10","7","21","26","-15","-13","6","-2","5","10","-11","5","-23","-38","-21","21","15","12","-17","34","-16","-14","-28","-3","-6","-23","-38","24","-13","16","34","-20","3","-5","-3","12","0","26","4","11","8","-11","17","12","7","14","-63","9","9","-49","44","53","-7","1","-8","-12","-33","-30","-10","-4","-38","-43","-33","29","26","22","-22","-41","-52","6","-12","41","-17","-29","3","-3","-32","-52","0","2","-66","-9","-55","-7","14","-47","-20","37","22","40","-70","-46","-6","-3","-18","-12","-71","-23","22","49","-85","-2","10","-30","-31","78","43","-30","-19","-14","-25","-7","8","-37","7","-14","15","20","9","10","6","-13","0","48","-62","-9","-3","26","-5","63","-51","-13","21","-29","-60","-16","-38","-56","60","81","15","-56","10","-6","3","-25","59","8","-112","36","22","7","-3","21","-30","-2","68","84","16","10","-27","11","-8","54","-39","-56","7","-8","37","-2","-32","65","-27","-27","42","-94","-28","-7","3","35","8","-63","-62","72","-47","-64","7","35","-80","-8","56","39","-25","36","15","31","12","-56","0","-1","56","24","10","-64","18","-16","7","45","28","31","-28","2","10","-7","112","-73","-71","-24","-9","36","55","54","-8","7","-16","39","-31","21","10","79","-144","20","74","-11","93","-18","-35","-12","102","94","46","-13","36","3","-51","10","16","-10","7","-2","-30","-4","-45","1","9","-6","14","-11","55","79","-57","81","-1","33","-5","-86","-55","-31","70","-4","-35","75","100","11","53","-18","27","-29","-66","3","7","-28","101","95","6","-8","-106","-55","-34","-9","-36","89","-19","22","61","-85","-8","29","-57","9","79","-73","22","-13","-69","-11","-28","42","38","107","65","-66","-30","4","96","-8","2","23","-33","55","52","-28","100","63","29","14","47","97","-19","-94","0","-42","20","42","1","-19","52","23","27","56","-9","-36","76","61","111","-137","-156","-20","42","-30","95","90","49","-5","-76","-82","138","4","5","-8","57","104","81","-30","5","5","3","-70","-21","-72","-96","127","4","-36","-37","41","53","-67","32","-4","56","-13","233","-61","75","39","-49","72","-86","-47","19","136","68","39","27","67","20","-57","-15","64","-77","-5","93","75","59","-36","-74","6","-10","-9","54","4","-28","-149","-65","-14","17","57","-65","-77","-101","-51","-42","17","120","107","-10","-113","2","39","-127","-81","9","27","-92","-19","89","-16","4","-63","-28","-87","77","-6","135","35","65","-49","27","4","-52","-144","65","23","-99","94","-66","-38","112","69","138","-97","70","2","5","-47","-5","-5","-100","-118","-30","40","36","56","58","24","-132","-97","82","2","-2","-91","-90","-10","41","-46","14","4","-91","7","-151","-16","-83","-25","97","-47","29","-22","10","-4","9","83","-40","-84","-74","38","48","42","29","-17","-131","43","7","-35","95","-31","-79","-5","-27","41","15","-99","-1","45","102","-87","216","-68","15","42","-15","84","-45","-158","4","44","-18","46","-83","-80","75","-244","70","-42","-31","-98","84","-5","9","109","-109","-25","66","-25","98","51","-55","-42","-89","-23","74","-32","253","10","54","130","10","93","-24","96","-143","-2","-48","-135","-3","-84","-115","-126","78","125","-12","-44","-4","-118","-90","13","-69","-38","61","68","32","-110","19","-87","-136","40","18","10","-108","51","-90","-174","-5","189","25","-73","21","-42","141","-50","-23","-91","-10","-63","8","-187","-53","-26","-115","-21","-35","-8","233","-142","25","-51","-61","32","120","-139","151","-105","-13","-8","-19","-112","-14","45","32","-7","-214","-21","81","93","19","-73","23","-93","4","11","52","-52","6","-10","26","-108","-87","29","-54","52","-81","-107","95","-14","-34","-76","-51","28","-85","16","13","36","-124","-115","-34","60","-89","-8","72","-92","43","-154","3","5","-74","-178","41","-24","110","-65","42","-34","-19","-20","1","-8","28","-91","-40","114","-6","171","-132","98","-10","-125","60","6","-29","-81","-114","-87","165","-111","-53","82","91","-40","147","64","182","-7","-80","-70","112","-85","-30","-51","-62","102","159","142","66","-4","-9","-3","-183","-61","-21","156","87","-164","1","-30","80","2","58","-15","-51","-103","-51","-77","-94","-28","112","-26","-103","267","66","-5","-72","87","5","8","38","-1","52","53","145","70","30","181","15","7","86","-202","8","-6","-90","35","45","75","7","-101","-61","-14","53","-41","-41","13","-13","-4","-42","11","42","94","-193","-16","-36","-149","-57","18","199","-24","-105","3","-6","-11","95","110","-203","170","97","41","162","-2","-143","-4","-66","38","0","-37","-100","2","60","114","10","75","-51","83","19","-27","-14","3","49","87","140","41","-282","50","-5","140","58","146","145","-25","-349","-19","50","-11","56","-95","102","153","66","-12","-58","-10","0","-211","-5","-48","-43","224","49","25","210","-39","111","-18","-173","29","27","101","11","1","126","-42","-183","25","8","-80","-55","70","99","-10","4","96","-122","28","-27","-5","-4","155","114","15","-132","-109","-129","20","-55","-12","99","-2","102","-4","-30","30","23","172","-229","76","38","-186","142","65","-71","-56","-62","-24","-92","2","20","25","-59","38","-29","-32","7","-127","-113","152","127","-35","204","165","131","258","206","63","-5","104","21","-98","-97","71","-155","80","-86","125","16","-89","46","-117","203","-8","72"],"lmfdb":"agrees","derived":{"al":[[17,1],[41,-1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"697.2.a.e","letter":"e","dim":15,"charpoly":["5","41","-140","-997","985","5673","-905","-8439","515","3791","228","-689","-125","39","13","1"],"traces":["15","-5","-8","17","-9","-8","-19","-15","15","3","-14","-13","-11","7","-2","17","-15","-24","1","-40","4","-10","-30","-19","24","-7","-14","-49","-20","-5","-14","-30","-7","5","-17","55","-5","-5","-11","24","-15","23","4","0","-21","-5","-62","7","40","-29","8","-41","6","-33","-11","43","8","5","-7","37","-8","-43","-86","27","-34","88","7","-17","-35","34","-36","-2","-6","30","-30","37","7","81","-28","-92","23","5","-33","0","9","-11","-60","-53","12","77","7","-13","5","58","-53","-17","-35","-77","-22","108","36","8","-16","22","35","47","19","62","28","16","1","-32","0","0","17","-7","45","71","19","-18","37","-2","8","32","-21","127","33","-79","-29","70","-57","-66","-4","14","28","15","-51","122","-12","37","93","60","-79","122","14","36","2","21","16","113","-4","-19","-15","35","33","44","3","105","-2","215","62","8","-20","-17","-9","-4","-142","210","74","-3","12","107","1","181","-45","41","21","10","16","-48","4","2","-11","25","56","44","14","-143","91","13","-28","32","-44","74","63","52","-39","2","-42","-95","14","22","-38","13","9","-40","-48","-11","2","-51","4","25","54","-16","-113","-263","-17","-96","34","18","11","-89","39","82","-40","-54","-84","61","22","-49","25","56","-68","-124","-65","-13","52","-7","-99","174","-10","79","-45","-86","58","8","-8","-36","-20","27","-47","-274","45","-28","2","69","-57","-24","1","-11","0","7","-84","123","-30","-46","-65","-88","-49","57","41","-17","-11","12","48","16","49","-13","12","-67","74","56","36","-10","-49","-106","19","-172","15","-30","74","-13","-74","-6","-10","89","65","-229","30","-260","-27","-23","-31","35","81","24","-47","-41","84","85","-91","88","60","55","55","-224","1","-49","66","-153","93","54","-1","90","28","-5","-105","15","80","2","9","-138","-41","-82","-113","-279","-2","154","-15","40","-39","-83","-149","-65","93","-20","17","-317","3","60","-82","-12","-3","-7","80","-30","-4","10","16","46","-24","99","-9","188","116","-180","7","-179","-15","-305","-89","65","32","10","-84","150","2","137","31","-76","47","-119","-106","27","36","-54","129","-123","25","-160","30","-127","-68","9","28","17","-85","-28","0","23","40","87","2","73","-96","21","-54","19","23","-3","26","59","4","-54","73","-84","58","-13","39","99","-59","34","-106","52","-24","-303","9","45","119","163","-74","196","-1","-23","240","152","-83","-301","-55","238","248","7","-116","53","109","1","53","-177","-18","-109","14","-48","-1","62","-24","-184","7","-111","14","45","-37","-233","-1","109","37","-50","-3","-312","73","-8","-91","-2","-37","169","29","49","41","86","-141","-153","-44","-24","165","91","33","41","-4","159","79","-47","55","13","20","12","-26","-125","-21","33","26","-60","158","-68","-203","136","-93","36","-176","81","29","5","29","-109","16","4","-6","-152","84","32","102","-38","33","102","106","-106","233","64","14","-199","103","-44","-144","-49","11","143","16","-129","-75","33","27","-97","-78","154","-4","30","-55","-236","18","68","218","-470","18","143","19","-53","105","-113","-87","-25","115","211","7","177","-1","-107","157","201","-199","-2","99","80","-18","-5","70","-7","-82","306","28","-5","-132","-172","220","-31","-6","209","24","-174","-44","287","68","10","69","-33","93","-181","17","86","47","12","91","577","-82","19","-29","-136","86","-327","-2","-150","278","134","121","-55","-26","-3","2","-12","79","-89","6","9","2","-28","-143","8","197","-82","158","28","5","-211","18","191","4","56","-204","-263","119","-188","98","240","60","-36","-47","268","210","5","-239","148","97","191","100","-57","126","69","57","-17","41","-244","127","99","152","-25","11","173","100","165","38","37","59","251","-162","232","13","67","177","-184","-84","109","20","-24","181","226","-19","58","5","289","153","311","63","-117","77","8","175","94","-56","170","15","-228","0","-131","-65","398","-130","151","137","-219","40","-158","8","-99","-250","-247","68","-23","60","134","91","-114","-30","-323","-126","-17","154","161","22","15","-39","-2","171","69","-4","204","45","-20","-144","203","72","24","8","120","-141","-28","-86","114","15","10","-74","0","-183","-158","-108","-11","-21","-116","73","-263","-23","51","0","-1","-78","-137","112","142","21","-132","-114","62","17","254","79","38","152","-45","2","-156","-194","-75","-1","57","31","5","-260","126","-22","175","-50","-60","12","-298","-39","41","49","71","107","-220","102","162","62","-354","7","-88","-177","154","65","11","36","-82","-49","-134","-15","157","-2","56","137","-7","3","32","34","40","-92","-34","-161","-19","-77","-405","9","-411","44","137","33","35","-40","19","120","-42","-101","56","-78","-283","127","76","27","57","80","213","-134","-9","43","29","53","407","36","67","40","-113","9","-156","18","-417","-4","44","-138","-212","-185","58","-8","84","-78","-212","131","-117","-125","-93","-159","-204","-87","-143","157","-136","-3","-399","64","41","-164","-30","-216","-321","-97","127","-105","-114","-19","202","63","300","-75","290","-20","-137","-6","10","-11","-49","-232","179","36","-103","253","-314","31","263","-130","33","-77","-37","37","33","41","-6","8","123","-257","198","-200","-19","106","-3","-12","-382","88","58","132","265","11","-22","17","-52","-13","90","5","-145","30","-251","-166","-187","-32","126","-282","260","-118","-43","18","123","-26","-134","-70","-34","13","87","21","90","-34","-174","-36","-440","-91","-36","-8","143","80","37","107","281","20","-141","55","96","229","187","68","-98","-167","19","-104","-5","-162","7","-45","-113","-76","-22","-169","172","193","-44","43","-9","66","228"],"lmfdb":"agrees","derived":{"al":[[17,1],[41,1]],"fricke":1,"sign":-1,"cm":null,"cmInert":0,"cmExact":0}},{"label":"697.2.a.f","letter":"f","dim":15,"charpoly":["-833","6149","9996","-54763","-11393","113303","-10249","-66683","18405","12021","-4990","-447","389","-21","-9","1"],"traces":["15","5","4","17","7","6","7","15","19","-7","6","-1","7","7","10","17","15","-2","13","8","4","0","18","23","8","-17","10","3","6","-33","-8","40","-15","5","21","7","-23","33","15","-20","-15","15","0","8","-3","-19","68","21","4","5","4","13","-4","-13","37","-11","-4","7","29","-59","-4","13","20","-21","4","-4","3","17","-17","-6","24","24","12","-40","8","33","23","-51","-36","-48","-45","-5","79","-60","7","-43","32","-23","-12","7","-25","-1","33","-26","15","-9","-31","-19","-48","-24","26","6","4","20","3","37","3","-48","-38","42","33","-64","4","-102","-27","3","1","-29","7","-98","17","-22","-4","24","27","-15","9","15","-9","-48","-1","-126","-56","52","-4","15","-1","34","-6","13","-13","-76","91","30","-34","-22","44","-101","-30","-73","44","47","19","-37","-7","-106","17","23","-24","-83","42","-90","-52","-17","-93","-92","92","-2","10","-7","-64","3","-7","-35","51","-93","-7","-8","-6","-46","-14","-98","-27","-83","36","30","6","69","-53","-77","28","128","-28","24","7","-36","-11","-56","-28","-85","-120","28","-10","-1","-7","100","56","59","36","-15","24","37","46","-36","97","49","-123","32","66","86","7","-23","35","-122","-36","104","42","143","20","-93","-87","-26","-2","-84","-43","7","44","7","45","-14","-4","-15","59","-20","50","-6","0","80","22","59","49","-32","13","12","10","37","61","-66","17","79","50","127","82","-141","-86","66","-21","-58","-19","151","37","17","-99","58","26","-44","7","-27","26","101","2","-14","28","66","-69","-8","-7","82","15","-60","38","-91","42","130","-50","-1","9","69","42","28","-45","-67","21","85","-43","-2","49","203","-36","-19","59","-106","-30","17","65","32","11","61","2","-123","125","52","13","-246","-56","9","39","-15","34","34","33","66","-45","114","55","-15","-138","64","27","8","-47","145","89","-109","55","-30","25","175","-13","70","56","-102","-27","-163","32","98","4","-64","88","-106","32","79","-151","-36","-24","52","-55","-13","-19","107","-115","169","12","0","-22","66","82","41","-75","82","-59","9","184","105","-6","68","-87","-51","73","132","18","3","60","-51","-78","145","-29","82","-32","-77","-66","-69","66","-99","-80","-35","144","23","-121","7","62","211","106","-58","-27","110","-72","101","-23","-181","11","-54","256","188","8","169","77","-89","-131","153","38","-4","31","-153","-84","-122","-13","191","-23","76","24","-17","-68","-61","-75","29","55","-193","-22","89","-6","18","47","-52","-16","-56","41","39","10","49","-61","129","77","63","3","-12","-3","72","-41","-64","-1","14","-87","125","93","3","-209","58","-3","81","-22","54","45","-121","57","-145","-48","-39","-71","-97","123","1","6","-40","116","151","-89","255","-124","136","-50","-216","189","-122","5","-38","-158","85","-29","-33","41","125","-52","86","40","-96","-148","8","-50","-10","-19","-96","6","-4","-7","154","-8","-183","-97","-160","-4","45","-7","23","64","-9","-53","1","-13","-61","-70","90","-80","40","-87","126","-6","104","-74","122","38","-95","-125","49","-191","59","-35","-35","-23","25","-15","-7","115","21","-103","247","-37","136","-85","-248","-82","-5","-50","-7","-52","78","98","5","-96","218","28","109","-130","-165","84","-46","156","-3","4","-158","-1","-301","43","131","21","-24","-141","-92","-121","-53","-96","207","43","-226","-84","-35","-4","12","-290","-98","-131","7","-66","53","-10","112","109","85","-18","-47","-28","-60","43","-170","-131","20","114","166","-23","-33","-18","27","-128","38","-8","345","-135","-116","20","16","-108","-170","-113","174","90","33","41","-78","-35","-165","-222","-161","18","-171","17","-17","109","130","71","75","-152","-75","15","-83","-164","-155","22","167","-167","113","212","-232","-21","-311","-77","68","-146","245","0","-20","-251","-154","127","96","-47","-21","-93","-77","-41","87","-73","-36","-57","-126","100","298","-15","-20","-104","-57","-13","94","2","-119","-51","33","10","-106","-62","-149","-82","-65","-88","15","-224","-88","233","322","-140","5","-14","-175","30","-99","112","89","-37","-46","7","-111","0","-166","5","-164","-38","13","-62","2","-84","-52","41","-76","42","206","-247","98","10","8","-71","-62","88","85","-75","-290","-81","-7","-29","185","-24","-65","34","-15","-84","-222","-3","288","200","56","77","-84","63","104","-20","-109","-152","28","14","9","-13","217","39","-19","-36","-26","-42","45","-12","-26","-26","132","171","-53","71","-31","59","-28","6","-90","68","-104","-157","188","3","32","-177","39","184","-116","17","36","9","-35","96","-22","73","21","-149","140","-70","-8","58","44","131","17","27","69","9","17","64","-163","87","79","4","21","136","-158","-17","38","20","175","43","-4","117","-53","-216","3","132","299","65","5","-135","7","160","-41","-160","-3","27","144","-22","219","-4","6","-34","-80","79","34","4","-112","-30","-10","-77","141","-155","101","-3","28","-31","29","-135","-56","65","19","16","13","214","250","76","87","-91","-115","-7","46","69","12","59","-254","-143","-40","140","-73","-4","0","197","15","8","209","-234","155","-39","18","-1","-165","162","-155","-81","31","99","-13","45","-2","76","67","111","42","-68","-103","54","71","-40","194","-64","-164","-8","145","37","170","-83","-196","-225","-16","159","441","-18","-43","128","271","108","54","96","-130","90","-11","-138","189","116","126","-34","240","-1","-125","-71","-156","142","362","-138","458","99","-194","-4","163","-34","83","67","139","186","-111","95","-308","-121","-287","-42","22","107","-23","176","7","-22","55","-53","117","-40","202","7","-308","63","110","201","-127","156","150"],"lmfdb":"agrees","derived":{"al":[[17,-1],[41,1]],"fricke":-1,"sign":1,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.225,"computed":"atlas","estimate":{"seconds":0.485,"low":0.296,"high":0.838,"bytes":2274879},"url":"https://sagebrush.space/atlas/mf/697.2.a"}