{"label":"117.4.a","level":117,"weight":4,"dims":{"new":15,"cusp":38,"eisenstein":8,"modsym":84},"old":[[9,1,2],[13,3,3],[39,6,2]],"T":[[2,1],[5,3]],"status":"proven","checks":["dim M^+ at levels [1, 3, 9, 13, 39, 117]: [1, 2, 4, 5, 16, 44] (certified at ell = 2147483629)","T = [(2, 1), (5, 3)]; h of degree 15 = 1 x 15 (phi(ord eps) x dim S_k^new); 4 primes, 0 rejected"],"newforms":[{"label":"117.4.a.a","letter":"a","dim":1,"charpoly":["-36","1"],"traces":["1","0","0","-8","12","0","2","0","0","0","36","0","13","0","0","64","78","0","74","-96","0","0","96","0","19","0","0","-16","-18","0","-214","0","0","0","24","0","-286","0","0","0","384","0","524","-288","0","0","-300","0","-339","0","0","-104","-558","0","432","0","0","0","-576","0","74","0","0","-512","156","0","38","-624","0","0","456","0","-682","0","0","-592","72","0","704","768","0","0","888","0","936","0","0","0","1020","0","26","-768","0","0","888","0","110","0","0","-152","990","0","1208","0","0","0","-996","0","-1402","0","0","128","-1926","0","1152","144","0","0","156","0","-35","0","0","1712","-1272","0","-988","0","0","0","2100","0","148","0","0","0","2496","0","-2464","-192","0","0","468","0","-216","0","0","2288","-216","0","-898","0","0","0","-2568","0","-1510","0","0","0","192","0","-394","-3072","0","0","-84","0","169","0","0","-4192","-1194","0","38","2304","0","0","-3156","0","-1078","0","0","0","-3432","0","2808","2400","0","0","-3192","0","722","0","0","2712","-2796","0","-340","0","0","0","-36","0","4608","0","0","832","2664","0","-1924","4464","0","0","6288","0","-428","0","0","-3456","1014","0","5042","0","0","0","2676","0","-2410","0","0","0","-3726","0","-3600","4608","0","0","-1248","0","-4210","0","0","-592","-4068","0","962","0","0","0","7692","0","3456","0","0","4096","-1326","0","-572","-1248","0","0","6048","0","-6696","0","0","-304","-6474","0","5978","4992","0","0","684","0","8750","0","0","0","-8976","0","-592","-3648","0","0","768","0","1171","0","0","5456","4608","0","-6912","0","0","0","1248","0","1048","0","0","4736","888","0","-3166","-576","0","0","-2472","0","-3094","0","0","-5632","-2316","0","-648","-6144","0","0","5772","0","247","0","0","0","-600","0","-4426","-7104","0","0","456","0","866","0","0","-7488","-7704","0","-1364","0","0","0","2556","0","-11014","0","0","0","9720","0","5472","-8160","0","0","2988","0","-1383","0","0","-208","-8184","0","-2068","6144","0","0","-1116","0","902","0","0","0","-234","0","12818","-7104","0","0","1332","0","864","0","0","-880","-3054","0","7488","0","0","0","8448","0","11162","0","0","1216","14820","0","-2782","-7920","0","0","-10296","0","-9682","0","0","-9664","-1152","0","10656","0","0","0","348","0","2486","0","0","0","1482","0","148","7968","0","0","1812","0","-6226","0","0","11216","7104","0","-12544","0","0","0","8556","0","12240","0","0","-1024","-4116","0","13824","15408","0","0","312","0","-6514","0","0","-9216","-10500","0","-5542","-1152","0","0","5220","0","76","0","0","0","18864","0","1406","-1248","0","0","-11592","0","-3718","0","0","280","1320","0","12170","0","0","0","-1812","0","-1404","0","0","-13696","912","0","-1330","10176","0","0","2688","0","11880","0","0","7904","-5124","0","-1364","0","0","0","14496","0","-10800","0","0","0","882","0","-2320","-16800","0","0","-16692","0","-2951","0","0","-1184","4992","0","-11952","0","0","0","-12204","0","21422","0","0","0","-16824","0","7040","-19968","0","0","-1332","0","1408","0","0","19712","8400","0","6812","1536","0","0","-19044","0","-23112","0","0","0","4698","0","-8728","-3744","0","0","1824","0","2018","0","0","1728","1776","0","-20088","0","0","0","-11376","0","-15836","0","0","-18304","25596","0","1872","1728","0","0","-3480","0","10010","0","0","7184","-420","0","3764","0","0","0","-3900","0","13610","0","0","0","-6408","0","-6694","20544","0","0","2040","0","-17639","0","0","12080","-22308","0","-27250","0","0","0","-11856","0","-4407","0","0","0","12630","0","14798","-1536","0","0","-26232","0","-20736","0","0","3152","30390","0","25200","24576","0","0","28740","0","-9214","0","0","0","1776","0","-1728","672","0","0","2664","0","16598","0","0","-1352","8610","0","220","0","0","0","-804","0","29952","0","0","33536","-7254","0","2270","9552","0","0","-29568","0","29952","0","0","-304","-1782","0","-21164","-18432","0","0","1980","0","-10690","0","0","0","-20544","0","5616","25248","0","0","-11568","0","2416","0","0","8624","-342","0","-11644","0","0","0","40872","0","-15010","0","0","0","1368","0","33410","27456","0","0","6504","0","-2592","0","0","-22464","-1992","0","-13912","-19200","0","0","-10776","0","-23974","0","0","0","288","0","-2804","25536","0","0","-7488","0","1514","0","0","-5776","-15816","0","-4066","0","0","0","28416","0","16416","0","0","-21696","-18120","0","10154","22368","0","0","-3852","0","962","0","0","2720","17442","0","-23400","0","0","0","-24552","0","2304","0","0","0","8778","0","-430","288","0","0","-4728","0","38776","0","0","-36864","32976","0","-1168","0","0","0","17172","0","27146","0","0","-6656","-26442","0","-1008","-21312","0","0","-30696","0","-24065","0","0","15392","2028","0","-70","-35712","0","0","-27456","0","24842","0","0","0","-11406","0","20540","-50304","0","0","-9108","0","-14328","0","0","3424","25344","0","494","0","0","0","-2544","0","-24046","0","0","27648","-7998","0","24032","-8112","0","0","15648","0","-1976","0","0","-40336","-22200","0","-37872","0","0","0","3852","0","-43524","0","0","0","-12936","0","-808","-21408","0","0","-39144","0","31968","0","0","19280","4200","0","-38248","0","0","0","5928","0","-5434","0","0","0","54264","0","-25086","29808","0","0","33696","0","12206","0","0","28800","-17664","0","36864","-36864","0","0","51984","0","-8866","0","0","0","-13782","0","-38304","9984","0","0","4992","0","16005","0","0","33680","8664","0","14618","0","0","0","18708","0","-4928","0","0","4736","48804","0","36720","32544","0","0","44736","0","-33552","0","0","-7696","50304","0","-21004","0","0","0","-4080","0","9038","0","0","0"],"derived":{"al":[[3,null],[13,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"117.4.a.b","letter":"b","dim":1,"charpoly":["-26","1"],"traces":["1","5","0","17","7","0","-13","45","0","35","26","0","13","-65","0","89","-77","0","-126","119","0","130","96","0","-76","65","0","-221","82","0","196","85","0","-385","-91","0","-131","-630","0","315","-336","0","-201","442","0","480","105","0","-174","-380","0","221","432","0","182","-585","0","410","294","0","-56","980","0","-287","91","0","478","-1309","0","-455","-9","0","98","-655","0","-2142","-338","0","1304","623","0","-1680","308","0","-539","-1005","0","1170","1190","0","-169","1632","0","525","-882","0","70","-870","0","-1292","-420","0","588","585","0","2160","684","0","373","910","0","-1157","1734","0","672","1394","0","1470","1001","0","-655","-280","0","3332","-1407","0","1892","-2115","0","455","-1435","0","1638","2390","0","-3465","1776","0","-1869","-1547","0","-45","338","0","574","490","0","-2227","-2466","0","-3323","-5670","0","-1690","1372","0","-2730","6520","0","595","-1248","0","-544","-5712","0","1540","-1624","0","169","-2695","0","-3417","336","0","988","2314","0","5950","3029","0","-28","-845","0","4320","-917","0","-2002","1785","0","-4410","-422","0","492","350","0","-2958","-2991","0","-70","-3420","0","-2100","-1066","0","-2352","2940","0","1157","-3276","0","2851","7344","0","3420","-1407","0","-2548","1865","0","3094","-1001","0","217","-1105","0","8670","2576","0","455","3360","0","3690","-3061","0","735","4998","0","5005","3477","0","-1610","-3275","0","-952","-1218","0","-1638","8820","0","-7035","-1008","0","2496","9460","0","-8279","-6041","0","1703","1547","0","-7175","3708","0","3024","8190","0","8126","-8344","0","-1617","-6853","0","8880","-1976","0","-3820","-9345","0","-4095","6214","0","-5292","-153","0","1690","4368","0","1016","2870","0","1666","903","0","2058","-5895","0","-12330","1248","0","2613","-16615","0","-11214","-392","0","2114","-5746","0","6860","-3402","0","-10689","-13650","0","22168","7054","0","2132","-2009","0","-6240","9702","0","-988","-2720","0","-15120","-1365","0","9704","5236","0","-8120","3346","0","-10449","845","0","-9163","5096","0","6721","-9045","0","1680","621","0","12481","4940","0","2210","1400","0","-63","20230","0","15145","4968","0","9017","-140","0","-2873","686","0","8722","8544","0","-4585","-5616","0","10012","-10010","0","4725","1066","0","-3372","-14994","0","-2110","847","0","-2366","2460","0","1190","-11314","0","-7392","-7830","0","-14955","9128","0","1862","-350","0","-6764","-6820","0","2548","-7140","0","-5330","-3406","0","-12992","-11760","0","9996","-3822","0","2156","1105","0","-16380","7343","0","-5059","14255","0","19440","5852","0","728","11628","0","-7035","-3243","0","11599","-12740","0","6341","-12096","0","-17374","8190","0","-5005","-989","0","8330","1085","0","3731","14474","0","-8736","29478","0","12880","-1183","0","-1594","2275","0","11424","5915","0","-11072","7298","0","-15305","-1260","0","-6214","3675","0","13230","-5226","0","9576","17017","0","17385","12033","0","-1703","-8050","0","-11135","490","0","-2280","-2520","0","-6090","-16767","0","-6314","-8190","0","17444","117","0","12840","-23919","0","-5040","2198","0","-2940","12480","0","32164","17066","0","-1274","-24475","0","-30205","4116","0","2730","8515","0","4095","-2583","0","18620","-24395","0","18540","-15092","0","-2951","15120","0","27846","-4368","0","4788","21510","0","-41720","-4524","0","-16833","-8085","0","-6545","2611","0","-8615","30192","0","-9880","-10332","0","-16952","-19100","0","-31773","-8535","0","-2613","-8099","0","31070","4641","0","12138","-26460","0","-405","4793","0","-5563","5746","0","21840","-7296","0","24038","5080","0","9758","-4004","0","11232","4410","0","4515","21224","0","-24696","10290","0","-11659","-4354","0","7007","-41922","0","6240","-7310","0","-7595","13065","0","-56491","-4585","0","-826","-10710","0","-1960","1365","0","14590","10570","0","-15210","-4888","0","-11004","23324","0","-17010","-15470","0","-349","-53445","0","-46410","10087","0","-4975","58680","0","35270","13244","0","-2262","10660","0","-14805","-3950","0","-3682","-21216","0","48510","-10402","0","7644","-4940","0","-9248","31680","0","-10045","-29904","0","-6825","-21940","0","-31374","48520","0","13860","11466","0","7872","-27608","0","16730","-1456","0","18013","-52245","0","2873","10640","0","-910","-24255","0","25480","9336","0","12432","33605","0","-17889","5616","0","4200","5712","0","3105","-13083","0","25872","62405","0","16796","-9872","0","16506","-7462","0","7000","5460","0","28450","-315","0","53550","18816","0","2366","51493","0","24840","-32718","0","-7644","45085","0","-476","-6232","0","-22834","-7605","0","3430","15477","0","7875","43610","0","8160","12428","0","-2140","-15589","0","-28080","-31971","0","-17262","50060","0","-34034","-8892","0","-7432","9345","0","5330","-23261","0","20176","-16860","0","-39690","9478","0","-4849","-7174","0","4235","3822","0","-12096","-11830","0","8364","-17941","0","-14896","3150","0","-56570","42336","0","-234","-36960","0","-15486","-19110","0","6664","-50847","0","45640","-22542","0","-728","9310","0","-1190","1442","0","-8085","-6460","0","-34100","2548","0","-8736","12740","0","-18900","-30207","0","21140","-18122","0","-17030","-3808","0","25326","-64960","0","-39984","-569","0","-8538","26460","0","-19110","32702","0","-21154","10780","0","-3731","13398","0","-11368","-55692","0","36715","2184","0","-17665","-25295","0","48467","1183","0","8515","38448","0","29260","-12576","0","36687","3640","0","30780","-36806","0","4900","-23919","0","-16215","13697","0","2352","57995","0","-43316","33904","0","6214","16785","0","-60480","18291","0","6239","-86870","0","16198","-133","0","-26003","-17017","0","-4945","31248","0","-24596","41650","0","3689","-13230","0","21203","27495","0","72370","16072","0","-33264","-43680","0","78030","-196","0","-38253","43792","0","-5915","-36374","0","8008","-7970","0","7735","18655","0","-27648","30240","0","29575","-117","0","9956","-55360","0","6970","-756","0","21924","-52037","0","-6300","-14014","0","20846","-31070","0","12495","41321","0","-32256","26166","0","-26130","-54966","0","1274","47880","0","45045","44553","0","-2954","59109","0","60165","-23088","0","8625","-8515","0","-27370","3444","0","-27907","-29475","0","2450","16443","0","24297","-11400","0","-4984","45414","0","30940","-20706","0","-83835","8981","0","-20937","-31570","0","-27846","-19296","0","-17414","16660","0","585","-490","0","-23702","64200","0","-63315"],"derived":{"al":[[3,null],[13,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"117.4.a.c","letter":"c","dim":2,"charpoly":["1019","74","1"],"traces":["2","-2","0","14","-24","0","0","-54","0","-32","44","0","-26","56","0","-30","-164","0","48","-56","0","-380","-8","0","150","26","0","-112","-404","0","40","126","0","276","-112","0","-100","-104","0","592","-200","0","-616","980","0","1352","324","0","-574","1194","0","-182","164","0","144","56","0","-268","-140","0","628","688","0","-194","312","0","-472","-1372","0","-560","-428","0","-900","-684","0","448","-672","0","-432","1032","0","2832","1388","0","1744","-840","0","-1524","-960","0","0","-2744","0","572","-464","0","-532","574","0","-1638","364","0","-560","702","0","-3524","-1968","0","-60","2656","0","-672","-1404","0","-2592","-1484","0","1260","224","0","2338","-4436","0","-1176","-1488","0","48","3946","0","416","1472","0","-112","5232","0","4540","-328","0","920","560","0","-1924","-572","0","6192","-1228","0","868","2160","0","-840","-1352","0","1904","-1936","0","-644","2896","0","-896","2688","0","-3952","-6664","0","404","-620","0","338","1504","0","-1400","5724","0","2688","3372","0","-4360","-3144","0","2572","-728","0","1560","2768","0","-4952","476","0","-208","-3472","0","1908","6692","0","-4018","8504","0","5360","-2706","0","420","-1344","0","-2864","-11648","0","390","1728","0","-7704","7868","0","3088","10304","0","1456","-7780","0","-4592","2132","0","8872","-616","0","7900","612","0","-1372","-13312","0","10236","-6236","0","-5680","-3220","0","-4816","-3884","0","5532","-17122","0","12012","6888","0","-624","-352","0","-11840","-10512","0","-16304","9472","0","-7406","-1820","0","-1568","728","0","-5504","-5256","0","4752","1456","0","-12824","7212","0","1712","1116","0","5648","-12828","0","-2548","200","0","2352","5976","0","8472","1708","0","4940","5264","0","4070","13184","0","-2044","10032","0","-560","1916","0","5960","104","0","-2912","-2352","0","-48","80","0","632","-7168","0","-7920","-4968","0","-2580","15428","0","-7952","9384","0","-824","-7192","0","-2912","-4160","0","-1950","-2712","0","8032","1792","0","13080","6132","0","-2516","-3856","0","10364","-338","0","5712","-7856","0","0","15176","0","1556","-10648","0","764","1512","0","6468","-10504","0","9840","3920","0","17032","4980","0","-12454","5492","0","1456","15056","0","528","-16008","0","9440","-6720","0","356","34968","0","-7852","5252","0","8480","-1904","0","-2352","-14900","0","5600","9068","0","-16044","-15980","0","6032","15498","0","-5648","256","0","-19460","-2560","0","-18378","5088","0","-520","980","0","-9968","7208","0","2508","-23120","0","20496","2240","0","-20240","-1638","0","-11024","2624","0","-16700","6360","0","-7788","-6924","0","-7616","-16016","0","24416","12940","0","11980","-336","0","15260","-2880","0","-8064","-1088","0","-3588","-14528","0","22160","-13744","0","9520","-13968","0","-35984","-22820","0","-17972","1456","0","-10228","-16324","0","13664","-5384","0","-11360","14124","0","-12244","1280","0","9520","-14144","0","4900","3920","0","912","10752","0","28412","5260","0","1300","-30508","0","45934","-5936","0","-24600","-20764","0","9184","-11936","0","30440","1352","0","-9336","-4704","0","-23784","16240","0","19248","680","0","-5936","47216","0","-18704","10040","0","-4256","-1986","0","-14196","31136","0","-3624","-1232","0","-7696","-22796","0","-10040","18368","0","-18264","-368","0","40210","30976","0","-3472","2600","0","21376","17504","0","-18636","-12628","0","-4156","36872","0","-11564","16400","0","-18072","-12936","0","17196","-8352","0","4928","6580","0","4200","12960","0","8008","9744","0","-14096","-11560","0","3856","-24264","0","9204","-1180","0","19304","-12740","0","-10864","63912","0","11044","-22438","0","4592","3584","0","43928","22172","0","-35288","2556","0","-496","-8960","0","10908","-33840","0","6496","-1120","0","-17576","4776","0","2252","-14336","0","504","1512","0","-21392","3640","0","28032","-4212","0","-25524","-28240","0","19376","-20632","0","38504","6160","0","30056","-10640","0","25762","-20268","0","-34076","5064","0","20808","14128","0","-19968","-19616","0","7462","53912","0","-37328","13948","0","-7256","19264","0","11440","11808","0","-16520","-15522","0","-14336","1772","0","-9600","-28584","0","7280","23496","0","60","-20192","0","-35684","-1344","0","-30640","1932","0","-40048","59512","0","-24492","-42396","0","2366","3700","0","12320","-43840","0","17152","-9716","0","-6704","-35280","0","26712","-2132","0","26168","25508","0","56568","-13280","0","26928","29588","0","10416","18932","0","-832","-61388","0","-3440","1568","0","-45036","30368","0","20600","34784","0","-1872","-49784","0","-58740","-4504","0","-24416","9766","0","1876","-62556","0","-29072","-728","0","35680","44688","0","17588","66672","0","-15288","-67504","0","-1832","-5040","0","11312","22996","0","-42160","-33956","0","-94696","2240","0","34112","-15612","0","3484","16464","0","7188","-58040","0","11856","15672","0","-15680","-12656","0","34388","1820","0","-12300","-1568","0","-8596","-47024","0","37944","20524","0","4220","-10064","0","18808","-116688","0","8610","-21840","0","42040","53816","0","-17728","12992","0","-8164","36596","0","31920","17700","0","-22984","-5334","0","40888","5736","0","-31808","-8944","0","-9044","18228","0","40144","13216","0","-7656","60752","0","-11872","7236","0","31920","53248","0","29824","2912","0","-6160","62588","0","31044","-40128","0","2522","47068","0","13712","30688","0","12608","-39508","0","48958","65308","0","-51240","-4056","0","-29568","37860","0","-94884","-37232","0","-29284","25200","0","54256","-21020","0","-15384","2688","0","43732","-2324","0","-83248","-33708","0","7952","-39072","0","6136","-6220","0","35360","-26656","0","-2084","59472","0","-35760","-17132","0","-26520","17836","0","-68128","2480","0","19040","68560","0","71848","5984","0","9952","-10024","0","-37496","-25552","0","-26888","127488","0","44404","-46992","0","-7864","39004","0","7280","-52208","0","9032","-18780","0","25788","-8064","0","20288","54080","0","51024","5564","0","-45132","-2248","0","-18060","7544","0","-13776","-6692","0","-63776","-608","0","-42836","-22736","0","-112","-19856","0","127136","-11340","0","67536","-45532","0","11700","27144","0","-10640","22868","0","53312","-76244","0","45700","10640","0","-39854","8892","0","88676","-44848","0","40280","-77910","0","-53088","-24536","0","2240","70576","0","36276","48992","0","42720","16072","0","27840","10444","0","-107760","2040","0","-5824","-67424","0","-65728","-5488","0","-7280","-69920","0","3708","16672","0","26848"],"derived":{"al":[[3,null],[13,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"117.4.a.d","letter":"d","dim":2,"charpoly":["-52","-8","1"],"traces":["2","-1","0","-7","3","0","-9","3","0","7","-80","0","-26","-89","0","-39","-19","0","-84","-19","0","142","-196","0","-237","13","0","125","44","0","-86","123","0","-135","-107","0","209","314","0","-89","230","0","287","178","0","-4","-435","0","383","144","0","91","118","0","-18","1015","0","794","368","0","-1058","332","0","769","-39","0","68","211","0","-125","131","0","456","-147","0","22","-762","0","-1008","69","0","72","-1958","0","-173","-1359","0","-1242","720","0","117","788","0","-811","146","0","-928","650","0","804","-1258","0","-608","-39","0","196","-2292","0","1521","-178","0","-1227","-2256","0","-396","-970","0","870","1675","0","1762","2144","0","12","-705","0","312","-2125","0","-91","-1775","0","-2614","1938","0","1561","4450","0","-505","553","0","-2029","1040","0","882","-2438","0","-689","4512","0","-3771","-3118","0","3662","160","0","2680","164","0","703","2004","0","4790","-992","0","-568","2534","0","338","-211","0","211","4398","0","786","3090","0","-3658","189","0","-158","1157","0","828","271","0","-974","2551","0","-22","-4958","0","1794","-3854","0","-2182","3217","0","2030","-636","0","1836","-9174","0","532","2888","0","507","6624","0","2031","-668","0","-44","-785","0","-2792","-395","0","250","247","0","-4691","-6257","0","-878","-2406","0","839","-788","0","-8910","-2047","0","-1681","-2342","0","701","3005","0","396","-9041","0","2088","1416","0","1092","-3308","0","-1679","5940","0","6616","2768","0","-5591","-1939","0","-473","247","0","5707","-8472","0","432","4010","0","-2210","-3858","0","-2941","-1797","0","-508","9786","0","2258","-6947","0","1803","-5064","0","-9576","1505","0","-1846","-3092","0","-7189","970","0","614","4851","0","1606","781","0","-4330","2548","0","12079","-1863","0","5718","28","0","-7408","-614","0","-12","-4026","0","6213","6514","0","3868","1824","0","8032","397","0","8620","-3826","0","3081","1260","0","-1712","13271","0","-8766","8400","0","6400","2074","0","-1531","-169","0","903","6908","0","-7893","13801","0","-11668","-12911","0","13445","10572","0","1302","11482","0","-1767","778","0","-341","5286","0","-1486","-4664","0","-1625","-1526","0","9618","2292","0","689","-3336","0","-2482","5298","0","10661","-572","0","-5290","-562","0","-4950","-10453","0","2138","-2648","0","7566","932","0","3596","-8682","0","10249","-1852","0","-17348","-6710","0","5004","-6354","0","1118","3196","0","-1142","-8870","0","3846","992","0","-456","-13250","0","-4484","-1599","0","-18476","1195","0","6385","3549","0","-2628","1818","0","-13004","9212","0","-211","-15547","0","-24287","4116","0","-5689","4968","0","3042","2030","0","1755","-19945","0","-2218","-12419","0","4861","6384","0","-6956","9902","0","9856","1391","0","18380","439","0","2372","-17137","0","20122","11382","0","-4255","-21800","0","-21998","-2551","0","-11042","-26066","0","10770","-7401","0","-9943","20429","0","-2717","21358","0","1993","-5710","0","-15186","-19352","0","2182","-4423","0","-14290","-4082","0","6012","21009","0","4446","4499","0","6312","16018","0","-680","-9224","0","-4016","1564","0","22258","17067","0","2253","1672","0","5058","-9343","0","1157","23363","0","-13556","1393","0","8316","-4096","0","-3902","668","0","6446","-2990","0","-4628","-21590","0","20544","-5222","0","11423","11611","0","-9983","2647","0","15645","-17292","0","-18000","24264","0","8276","27788","0","8967","-2271","0","-3731","-591","0","6646","-1463","0","-5390","-4188","0","21795","-14609","0","-259","-2314","0","-10048","22920","0","-5780","6340","0","-4498","25828","0","-1660","24994","0","-15065","4422","0","12860","2342","0","-4713","38604","0","4051","-13718","0","52","-2034","0","12827","-13987","0","16947","-5517","0","18010","11426","0","-2088","5655","0","-8700","18562","0","-37234","-25106","0","20918","-628","0","26306","33038","0","26536","-31539","0","-17234","-1263","0","-42567","2228","0","-22842","3392","0","-4979","-34412","0","-3689","-43204","0","-17732","-16636","0","5398","3294","0","-2072","-1872","0","-20420","11518","0","2157","-1680","0","18329","4308","0","14232","5420","0","14080","-1218","0","-14104","-16536","0","2210","61700","0","-2469","-14883","0","-1183","-12970","0","51674","3013","0","-19400","-40822","0","8392","14325","0","-23829","-1534","0","-19402","-5924","0","-8445","-7957","0","-5364","-10199","0","-13716","-26174","0","-10138","-39838","0","8284","-7616","0","-19152","-1505","0","37358","4960","0","234","-415","0","-2184","-12458","0","-25688","-22105","0","5296","-2766","0","43258","-13195","0","-614","17937","0","11051","-12102","0","-18276","20944","0","20950","-1773","0","-4996","35285","0","4694","-15844","0","-1402","23404","0","-44008","-6945","0","-10322","-9405","0","-17070","-568","0","-342","-24456","0","-10865","24782","0","28355","-4784","0","-12246","614","0","-4528","-25081","0","11058","46106","0","-37798","-3676","0","-28802","13332","0","5154","11874","0","31498","-23117","0","-3868","32218","0","13754","14590","0","-1410","-18312","0","21617","-13020","0","-1328","-44760","0","12628","-4316","0","-15164","5427","0","31882","37838","0","16794","10840","0","-50950","46068","0","-3120","-21349","0","-9818","-29336","0","-15322","11752","0","-12672","-8400","0","-9997","-17944","0","11468","-8020","0","57041","34654","0","30526","48989","0","-11673","507","0","81831","1524","0","15972","-19972","0","13775","48696","0","9652","-19048","0","-1260","3351","0","-4271","22481","0","-2872","-4083","0","7052","36240","0","-884","-1739","0","-24856","25519","0","-42521","17094","0","-2454","-9655","0","-18411","-2743","0","9029","64204","0","-33568","-778","0","31183","-14642","0","37","15079","0","7654","25852","0","-5456","7728","0","18682","-4980","0","-41029","-232","0","1625","68378","0","59756","-28026","0","-3795","-45027","0","21764","10252","0","22755","-1703","0","-24894","-24800","0","52482","-101366","0","10842","12443","0","2332","3350","0","-20960","-1054","0","9275","36065","0","-24784","8634","0","76290","-44360","0","-5928","-38688","0","-14411","8887","0","-14866","-2077","0","-28379","-38912","0","-46058","1911","0","-22942","940","0","-63679","92403","0","-7566","-68953","0","81467","16688","0","44856","-30980","0","-68376","-7846","0","-51585","32777","0","16683","-3786","0","-286","-13540","0","-18754","12340","0","-7793","-2650","0","-20388","-3736","0","21289"],"derived":{"al":[[3,null],[13,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"117.4.a.e","letter":"e","dim":2,"charpoly":["-847","0","1"],"traces":["2","0","0","-2","0","0","-44","0","0","-56","0","0","26","0","0","-110","0","0","-252","0","0","-28","0","0","-26","0","0","44","0","0","-364","0","0","616","0","0","-172","0","0","504","0","0","192","0","0","168","0","0","282","0","0","-26","0","0","112","0","0","280","0","0","1148","0","0","1118","0","0","-1060","0","0","1232","0","0","-308","0","0","252","0","0","-920","0","0","-2352","0","0","-2464","0","0","252","0","0","-572","0","0","1932","0","0","140","0","0","26","0","0","-2856","0","0","-1008","0","0","-676","0","0","2420","0","0","-672","0","0","-3108","0","0","-2606","0","0","364","0","0","-752","0","0","-728","0","0","5544","0","0","-5544","0","0","4200","0","0","4284","0","0","-1120","0","0","172","0","0","7052","0","0","616","0","0","6132","0","0","-952","0","0","-6884","0","0","-1708","0","0","338","0","0","-192","0","0","572","0","0","7616","0","0","6748","0","0","-1512","0","0","-1232","0","0","7056","0","0","-3084","0","0","-282","0","0","-1904","0","0","-7728","0","0","9408","0","0","-1430","0","0","-3280","0","0","-8568","0","0","8008","0","0","-112","0","0","-9772","0","0","-8904","0","0","11116","0","0","-2520","0","0","-7728","0","0","-13552","0","0","-1204","0","0","-1148","0","0","-3276","0","0","7728","0","0","-336","0","0","-3022","0","0","3784","0","0","-3640","0","0","4032","0","0","1060","0","0","-5628","0","0","7392","0","0","-6380","0","0","-11088","0","0","-9576","0","0","-364","0","0","17278","0","0","308","0","0","12432","0","0","-10584","0","0","-4224","0","0","13860","0","0","-812","0","0","10192","0","0","-11172","0","0","920","0","0","-560","0","0","-3696","0","0","-338","0","0","21168","0","0","-8852","0","0","14252","0","0","16740","0","0","2464","0","0","8888","0","0","18480","0","0","8708","0","0","-476","0","0","-17136","0","0","896","0","0","18034","0","0","572","0","0","-15568","0","0","4816","0","0","-17020","0","0","-17388","0","0","3300","0","0","-6272","0","0","-2464","0","0","-140","0","0","7392","0","0","11256","0","0","-2828","0","0","1430","0","0","-4732","0","0","-6160","0","0","11564","0","0","2856","0","0","6832","0","0","3528","0","0","-28388","0","0","9072","0","0","-25256","0","0","-5376","0","0","-1372","0","0","676","0","0","-2744","0","0","8008","0","0","-30464","0","0","-24596","0","0","4704","0","0","9884","0","0","-35732","0","0","672","0","0","-27436","0","0","-18928","0","0","23320","0","0","27972","0","0","3276","0","0","-15540","0","0","-2236","0","0","2606","0","0","9012","0","0","-7896","0","0","12320","0","0","20020","0","0","-1572","0","0","-18648","0","0","30912","0","0","752","0","0","6776","0","0","15568","0","0","-3864","0","0","6552","0","0","-35336","0","0","4536","0","0","-22318","0","0","-5544","0","0","34272","0","0","1736","0","0","-3300","0","0","10472","0","0","7592","0","0","364","0","0","20240","0","0","-4200","0","0","2496","0","0","32368","0","0","35616","0","0","-38556","0","0","-39224","0","0","51744","0","0","31444","0","0","1120","0","0","2016","0","0","-35448","0","0","45864","0","0","9460","0","0","54208","0","0","2184","0","0","11900","0","0","-7052","0","0","28336","0","0","-32144","0","0","-12652","0","0","-5544","0","0","-48972","0","0","43848","0","0","-27662","0","0","-6132","0","0","44860","0","0","-44408","0","0","3666","0","0","-23688","0","0","32956","0","0","-77616","0","0","6216","0","0","6884","0","0","14560","0","0","-42504","0","0","-28476","0","0","15372","0","0","3360","0","0","29680","0","0","-9748","0","0","-338","0","0","-3080","0","0","5096","0","0","-29568","0","0","-10560","0","0","588","0","0","32256","0","0","-103488","0","0","-572","0","0","21672","0","0","18032","0","0","-13444","0","0","-68544","0","0","1456","0","0","-41076","0","0","62832","0","0","-6748","0","0","25648","0","0","8624","0","0","-59220","0","0","2856","0","0","-31244","0","0","22176","0","0","42336","0","0","1232","0","0","58936","0","0","3640","0","0","-70060","0","0","-63504","0","0","14872","0","0","-45836","0","0","-54684","0","0","3084","0","0","4732","0","0","12824","0","0","-8568","0","0","-15510","0","0","45332","0","0","25760","0","0","14924","0","0","1904","0","0","85008","0","0","-27664","0","0","14784","0","0","69552","0","0","-18956","0","0","2408","0","0","-24192","0","0","-9408","0","0","80952","0","0","68376","0","0","54964","0","0","14534","0","0","-57008","0","0","-60760","0","0","-43178","0","0","3280","0","0","57332","0","0","-8008","0","0","63924","0","0","77112","0","0","23408","0","0","27636","0","0","-73920","0","0","-8008","0","0","-13780","0","0","-21168","0","0","-2012","0","0","-6160","0","0","248","0","0","12376","0","0","16544","0","0","9772","0","0","-3584","0","0","91280","0","0","-44352","0","0","80136","0","0","-85992","0","0","16016","0","0","3416","0","0","-11116","0","0","16488","0","0","11144","0","0","2236","0","0","4760","0","0","-35532","0","0","21672","0","0","-36428","0","0","7728","0","0","-28224","0","0","-2688","0","0","-4004","0","0","121968","0","0","25088","0","0","46116","0","0","6666","0","0","1204","0","0","19156","0","0","-3920","0","0","-92400","0","0","-63140","0","0","-15232","0","0","-114408","0","0","-45024","0","0","3276","0","0","-13696","0","0","-94248","0","0","-11620","0","0","-69552"],"derived":{"al":[[3,null],[13,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"117.4.a.f","letter":"f","dim":3,"charpoly":["27696","-2247","14","1"],"traces":["3","-2","0","10","-4","0","30","6","0","-4","16","0","39","176","0","-110","146","0","94","244","0","-56","48","0","145","-26","0","80","2","0","302","-154","0","164","-80","0","374","-312","0","-516","-480","0","-260","-712","0","-1104","24","0","447","-814","0","130","678","0","-1552","-96","0","-628","1788","0","230","-1952","0","-750","-52","0","74","460","0","1216","948","0","-222","-1724","0","2392","-112","0","-24","-1100","0","564","796","0","-248","-1800","0","1608","-1436","0","390","1296","0","-1920","4032","0","3242","5070","0","-2010","-774","0","-2096","78","0","3036","2172","0","386","2768","0","-2176","-1290","0","2208","-956","0","-3864","3028","0","775","724","0","672","-4680","0","-1164","3078","0","-52","-1052","0","-556","1576","0","84","-3168","0","-488","128","0","3792","208","0","-1928","-7732","0","-2196","-2160","0","3962","-3720","0","-4288","-1072","0","1126","1664","0","5692","-5952","0","930","-5988","0","-1544","1072","0","507","1480","0","-152","5202","0","-2854","3512","0","-2732","-1196","0","-4890","2288","0","-1104","-7384","0","416","5664","0","-9936","-3664","0","-5018","-3716","0","5562","10452","0","2124","5994","0","11196","-3740","0","-8136","3888","0","-1430","-11472","0","1292","3444","0","8616","1776","0","-7484","9364","0","3376","1898","0","2486","-11936","0","-6492","2344","0","-8478","-11040","0","2556","2086","0","11136","5976","0","12064","-180","0","14570","-4474","0","-2916","7548","0","1222","3024","0","5976","8196","0","-4416","4064","0","3858","2534","0","-5108","3172","0","7480","-3672","0","1464","14496","0","-9672","-8630","0","1126","-6788","0","-6156","17168","0","-6678","18744","0","-2112","-7840","0","2872","912","0","-728","-3336","0","-5543","88","0","1604","-2904","0","-2352","9108","0","6876","624","0","-14440","-10352","0","-12344","-7672","0","10542","-3008","0","-9568","-3096","0","10414","-17004","0","-3328","-5308","0","7040","-12364","0","-5376","2580","0","1885","7592","0","7572","-11184","0","3306","4040","0","-9008","-19936","0","-9434","-338","0","8792","7120","0","26388","24","0","-2772","348","0","-4930","-16496","0","-13816","-6344","0","-5760","-8260","0","-12968","-13776","0","17123","-12796","0","1040","4984","0","-13444","-1008","0","4424","27708","0","-11326","-7696","0","-9216","26","0","4966","6480","0","5408","3872","0","-5120","60","0","10452","7390","0","-6240","-12618","0","-12804","-6464","0","-450","-6544","0","11454","5116","0","3926","12756","0","-14432","25600","0","-4438","19656","0","2512","1848","0","1712","-2002","0","23520","14284","0","-13230","6856","0","-4500","1318","0","7564","1080","0","-14352","34752","0","22898","-8800","0","-7908","26112","0","4920","-21936","0","2132","26684","0","-5032","8608","0","576","-20012","0","23280","-12276","0","16600","-1040","0","3066","-2044","0","14496","-15764","0","21110","8500","0","17908","24684","0","10492","-33792","0","6216","-1728","0","-31046","14816","0","35136","-22020","0","4862","-5924","0","-25758","-5032","0","-10994","6948","0","15324","-2844","0","-4916","-4056","0","1104","36024","0","-6350","-5112","0","-6744","-4088","0","31704","29760","0","5024","-884","0","-49500","-7322","0","-43132","21792","0","-29568","-19360","0","-6708","-22338","0","18552","-23704","0","2736","692","0","7659","15288","0","-3808","-6240","0","-15216","18360","0","-10196","-32784","0","18250","30144","0","-21356","-18904","0","-24856","-28452","0","-14728","-11580","0","9648","7076","0","-18392","15672","0","-3380","-6016","0","25172","-8268","0","-14232","-22824","0","1968","-39266","0","3216","-9256","0","-51072","5328","0","21318","31706","0","9608","1880","0","-10464","2748","0","1596","4468","0","14612","-18480","0","12348","26068","0","5408","4308","0","-14352","-31984","0","26846","-38592","0","16560","-57716","0","-3276","49464","0","19688","312","0","42686","-2296","0","9408","-53192","0","14566","46240","0","-21456","-36496","0","9091","-8724","0","27484","6404","0","-16806","4800","0","8012","19360","0","5811","1616","0","-9732","-18886","0","-40590","-41472","0","8304","-29672","0","14784","-10582","0","-34696","23706","0","-38992","38076","0","8256","-6956","0","-8714","62840","0","-168","-3168","0","12384","34448","0","49328","21568","0","-58822","47964","0","1690","13702","0","23092","-21048","0","22528","216","0","-31560","65440","0","17800","8814","0","2578","-14556","0","15720","-32880","0","-21408","72244","0","-31248","-7834","0","-34516","33400","0","-22652","56340","0","58730","34272","0","7764","58176","0","-20176","-41080","0","41808","-17472","0","-6016","-96490","0","29996","34390","0","84","-1248","0","-56360","-28440","0","-54086","-8576","0","74928","56656","0","-2322","55000","0","95712","-38988","0","25896","2212","0","-29168","82104","0","-49776","-17376","0","-8164","1424","0","3110","-31656","0","29232","-27328","0","61588","-10976","0","-33568","23244","0","-13970","-15488","0","19540","-29168","0","63306","8748","0","316","-86712","0","9696","-46176","0","-68958","45960","0","-31018","38772","0","22912","-57012","0","2990","-41644","0","69200","-41522","0","-14064","-20726","0","40612","512","0","-35328","-25376","0","-42900","89430","0","-6474","-28192","0","-14864","-76832","0","15128","57196","0","-33192","-42136","0","-5912","-25680","0","67584","16672","0","36390","-12688","0","-9750","64698","0","60320","-7008","0","-91592","-5124","0","-52931","10628","0","38424","-676","0","-15994","-51708","0","-50756","25632","0","-42626","3680","0","6600","-5194","0","50444","1104","0","-17664","-20984","0","-70728","-18692","0","-66144","16064","0","962","9540","0","-140352","-29664","0","11910","-22576","0","3760","-26858","0","8552","5980","0","-39160","-48168","0","8088","-6328","0","-33312","101520","0","-72592","30240","0","13252","37892","0","60900","-39312","0","20724","99112","0","39424","-56920","0","15808","-55744","0","-2048","26636","0","-2836","30152","0","21136","-288","0","-19796","12324","0","122322","-7424","0","12604","-43704","0","46950","-43780","0","10680","-61664","0","-68190","-32416","0","13632","-49448","0","-50592","-49608","0","47520","24156","0","-2886","17976","0","-17472","-10242","0","7360","13536","0","-31776","-81288","0","36903","-22412","0","23028","79224","0","28254","62190","0","-12232","-50796","0","105632","20208","0","4716","28092","0","20560","-36204","0","-91512","-102476","0","-6072","-41432","0","31096","64704","0","-6652","67088","0","104064","121408","0","-5782","48072","0","-33192"],"derived":{"al":[[3,null],[13,-1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}},{"label":"117.4.a.g","letter":"g","dim":4,"charpoly":["5273968","0","-5253","0","1"],"traces":["4","0","0","58","0","0","36","0","0","-4","0","0","-52","0","0","354","0","0","84","0","0","176","0","0","660","0","0","988","0","0","-604","0","0","-720","0","0","184","0","0","-2356","0","0","880","0","0","-2888","0","0","-116","0","0","-754","0","0","1152","0","0","-1760","0","0","656","0","0","3482","0","0","3052","0","0","-4696","0","0","-312","0","0","-2044","0","0","-720","0","0","396","0","0","32","0","0","-720","0","0","-468","0","0","4840","0","0","-344","0","0","6774","0","0","3392","0","0","-4648","0","0","3384","0","0","12972","0","0","2448","0","0","4080","0","0","-3820","0","0","-8292","0","0","4440","0","0","52","0","0","-5768","0","0","-6544","0","0","-344","0","0","-8936","0","0","-11520","0","0","10124","0","0","2700","0","0","-2144","0","0","2912","0","0","-30436","0","0","3244","0","0","160","0","0","676","0","0","14624","0","0","348","0","0","18388","0","0","-10288","0","0","-30888","0","0","-1408","0","0","32536","0","0","-7608","0","0","6706","0","0","-3176","0","0","-8064","0","0","-10456","0","0","-4602","0","0","3216","0","0","-6136","0","0","-4504","0","0","9248","0","0","-4252","0","0","19160","0","0","-3272","0","0","7200","0","0","5584","0","0","-10208","0","0","-1656","0","0","19764","0","0","-1092","0","0","27800","0","0","-3328","0","0","37490","0","0","16568","0","0","16184","0","0","-9072","0","0","36332","0","0","-860","0","0","-17540","0","0","-9848","0","0","-51960","0","0","16344","0","0","-2288","0","0","-13892","0","0","-36212","0","0","17216","0","0","30292","0","0","11648","0","0","-61068","0","0","-12044","0","0","-4056","0","0","-30072","0","0","15656","0","0","-15040","0","0","-50224","0","0","-8580","0","0","24476","0","0","34812","0","0","-19528","0","0","12472","0","0","19104","0","0","3384","0","0","-3392","0","0","-14744","0","0","-17808","0","0","34032","0","0","1496","0","0","19996","0","0","-12844","0","0","13080","0","0","-74744","0","0","8824","0","0","32392","0","0","-9068","0","0","-15912","0","0","-4544","0","0","-29220","0","0","23104","0","0","-38596","0","0","-26200","0","0","-306","0","0","7852","0","0","21440","0","0","15864","0","0","28680","0","0","5792","0","0","29792","0","0","-18712","0","0","-23688","0","0","26408","0","0","-19520","0","0","23552","0","0","28564","0","0","16560","0","0","9360","0","0","-8936","0","0","106364","0","0","-9664","0","0","-83104","0","0","-1400","0","0","104464","0","0","16484","0","0","102856","0","0","11624","0","0","2288","0","0","53004","0","0","-248","0","0","-2392","0","0","-66574","0","0","-2508","0","0","-83764","0","0","14080","0","0","-43668","0","0","27324","0","0","23280","0","0","-62272","0","0","42944","0","0","-66184","0","0","17592","0","0","15264","0","0","30628","0","0","-39064","0","0","-76752","0","0","48644","0","0","-103208","0","0","-99472","0","0","4944","0","0","-35960","0","0","-50512","0","0","40344","0","0","51408","0","0","45712","0","0","-48792","0","0","-11440","0","0","10988","0","0","80336","0","0","-148488","0","0","-21272","0","0","47368","0","0","31496","0","0","-92480","0","0","-18368","0","0","83108","0","0","-19208","0","0","172860","0","0","37568","0","0","37544","0","0","-54968","0","0","18180","0","0","-16792","0","0","-103176","0","0","-40152","0","0","-10208","0","0","-45644","0","0","77272","0","0","-2548","0","0","61796","0","0","-85908","0","0","-112788","0","0","1508","0","0","-135124","0","0","58604","0","0","10976","0","0","25376","0","0","72668","0","0","-100464","0","0","45424","0","0","1320","0","0","-10144","0","0","33280","0","0","76168","0","0","17040","0","0","9802","0","0","-51560","0","0","-30304","0","0","-28216","0","0","117024","0","0","19372","0","0","87312","0","0","-3168","0","0","56772","0","0","-100520","0","0","187388","0","0","-1368","0","0","183364","0","0","-14976","0","0","116376","0","0","-10480","0","0","-107236","0","0","40040","0","0","317192","0","0","74392","0","0","-262920","0","0","11588","0","0","-28784","0","0","-16424","0","0","-5504","0","0","38992","0","0","22880","0","0","-42384","0","0","165816","0","0","-10552","0","0","-96632","0","0","26376","0","0","-192332","0","0","-105252","0","0","-102344","0","0","16160","0","0","165882","0","0","-1516","0","0","-260240","0","0","-8528","0","0","21984","0","0","-38720","0","0","-63532","0","0","159968","0","0","51968","0","0","-97372","0","0","-51552","0","0","-7616","0","0","-135768","0","0","7184","0","0","-11744","0","0","31968","0","0","-45266","0","0","-25808","0","0","-111368","0","0","52844","0","0","-26064","0","0","-56748","0","0","-96432","0","0","6040","0","0","143720","0","0","23328","0","0","18440","0","0","44224","0","0","-131480","0","0","-39676","0","0","108976","0","0","139112","0","0","-54624","0","0","115080","0","0","125464","0","0","-2912","0","0","-124564","0","0","-120688","0","0","-223084","0","0","37184","0","0","11768","0","0","112072","0","0","61048","0","0","6112","0","0","-94044","0","0","41584","0","0","-183396","0","0","-59112","0","0","178080","0","0","-119868","0","0","60320","0","0","58160","0","0","-58832","0","0","-33584","0","0","23808","0","0","4056","0","0","-167008","0","0","125968","0","0","-215032","0","0","-27028","0","0","22588","0","0","-34748","0","0","242664","0","0","-90704","0","0","273348","0","0","27840","0","0","-131088","0","0","128136","0","0","26572","0","0","-108536","0","0","-261232","0","0","77016","0","0","90296"],"derived":{"al":[[3,null],[13,1]],"fricke":null,"sign":null,"cm":null,"cmInert":0,"cmExact":0}}],"seconds":0.118,"computed":"atlas","estimate":{"seconds":0.342,"low":0.209,"high":0.591,"bytes":1975373},"url":"https://sagebrush.space/atlas/mf/117.4.a"}