# Stored data for newform 8.13.d.b, downloaded from the LMFDB on 25 April 2024.
{"label": "8.13.d.b", "space_label": "8.13.d", "level": 8, "weight": 13, "hecke_orbit": 2, "hecke_orbit_code": 4503806003904520, "dim": 10, "is_polredabs": true, "trace_hash": 1436933726632557686, "analytic_rank": 0, "is_twist_minimal": true, "hecke_cutters": [[3, [-7437355394400, 326191796496, -685590480, -1697352, 330, 1]]], "qexp_display": "q+(-11-\\beta _{1})q^{2}+(-66+3\\beta _{1}-\\beta _{2}+\\cdots)q^{3}+\\cdots", "char_order": 2, "char_parity": -1, "char_degree": 1, "char_conductor": 8, "char_orbit_label": "d", "char_is_real": true, "Nk2": 1352, "analytic_conductor": 7.311950538210285, "hecke_ring_index": 21849495067164672, "level_radical": 2, "field_poly_is_cyclotomic": false, "field_poly_root_of_unity": 0, "field_poly_is_real_cyclotomic": false, "hecke_ring_index_proved": true, "self_twist_type": 0, "is_self_dual": false, "is_self_twist": false, "is_cm": false, "is_rm": false, "trace_zratio": {"__RealLiteral__": 0, "data": "0.506", "prec": 17}, "analytic_rank_proved": true, "char_values": [8, 2, [7, 5], [1, 1]], "hecke_ring_generator_nbound": 5, "inner_twist_count": 2, "level_primes": [2], "conrey_indexes": [3], "field_disc": -102678058031731657831671391733279615898545210484375, "field_disc_factorization": [[-1, 1], [3, 6], [5, 6], [7, 3], [11, 1], [67, 1], [1783643, 2], [3347929531469, 2]], "field_poly": [824967906703360, 41051831642368, 1335549648384, 28213427840, 143571008, 29155008, 710096, 1496, 468, -5, 1], "hecke_ring_index_factorization": [[2, 45], [3, 3], [23, 1]], "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "8.596", "prec": 17}, {"__RealLiteral__": 0, "data": "1.829", "prec": 17}, {"__RealLiteral__": 0, "data": "395.361", "prec": 24}, {"__RealLiteral__": 0, "data": "226.092", "prec": 24}, {"__RealLiteral__": 0, "data": "26665.800", "prec": 30}], "related_objects": [], "self_twist_discs": [], "cm_discs": [], "rm_discs": [], "relative_dim": 10, "sato_tate_group": "12.2.3.c2", "trace_display": [-110, -660, 0, 0], "traces": [0, 10, -110, -660, -2444, 0, -130788, 0, 27160, 1692798, 1873200, -4591444, -5427720, 0, 12728736, 0, -38294000, 42876500, 8229270, 36062828, 17615520, 0, -227004580, 0, 169102992, -706946390, 151295184, 1382414040, -132075840, 0, 456064800, 0, -2651204000, -478018200, 4454663012, -2838470400, -4074739428, 0, 1644178460, 0, 8180322240, -12339248044, 14692585920, 25081495340, -27950589832, 0, -16813594656, 0, 13310114400, -39532486838, 24888425650, 36757299288, -36172521120, 0, -74007907272, 0, 154450364544, 80408630760, 193270394640, -109448026708, -347360715840, 0, -299237961600, 0, 276213192256, 96485235840, 486280823688, -49860896020, -296812951960, 0, -799057954560, 0, 1077572984520, -58835592940, 742739480496, -251792743380, -699737494024, 0, -1795838526240, 0, 1981932232320, 259515975474, 1654109754980, -146236977940, -3144240693120, 0, -2261898070564, 0, 2170357811600, 913341514388, 3983485096080, 361546645248, -2649411172800, 0, -2517413216064, 0, 2836588548672, -1474226441260, 2377890492370, -717160631484, -4855448648780, 0, -1871291056200, 0, 3108899797056, -620289108480, 2274256483824, 5263000688300, -1786270928400, 0, -3193494432480, 0, 1812185445120, -9101664804460, 4859802672648, 6172076071680, 906183756000, 0, 2955018152540, 0, -8463454611840, 2033377011006, -7130839889520, -18142410101160, 12794799179520, 0, 19665672440544, 0, -24022511258240, 21139266042984, -23444975295360, 5605253785580, 19073605185360, 0, 16372383228572, 0, -5518035847888, 2385506510420, -34542428203200, -4254692437972, 38102036405760, 0, 22680001963680, 0, -56206165113552, -20996627306880, -47644285483228, 371081281260, 52053290651040, 0, 49791966226140, 0, -8887538850160, 19613068341180, -68010212432448, -12696293698560, 71997240175680, 0, 64040476887360, 0, -73898981157120, 27092357872128, -57884734799910, 1429746582380, 10425138718568, 0, 60811670560412, 0, -54896530832640, -23918362573718, 3987520564320, -57078607669116, 21629183747960, 0, 16881891777120, 0, -13918109823904, -56556027977880, 123431763457700, 146267724283628, -90405200409120, 0, -76894677653760, 0, 35014423115136, -47359471962240, 74537126019840, -45945662091560, -33574026003840, 0, -110737225978080, 0, 197182119177600, 9218088296660, -13590429931804, 365597580829440, -264874817033996, 0, -253284046677420, 0, 198379352745880, -152699214244632, 305745345455280, -481070672098560, -147450792471312, 0, -288061655376096, 0, 244424902988160, 284179088904040, 566235915548160, 286015981720556, -534197987508960, 0, -175188782227108, 0, 635451118111008, 110441453721600, 434240374574160, -702371726749992, -518569360879680, 0, -681709347594720, 0, 322253624111616, -61761946637730, -68688349865308, 512108647757420, 27869775370320, 0, -339648246570240, 0, 486714694067520, 370642433917460, -60605747458704, -912192683450880, -150108052433800, 0, 23548647616320, 0, 140094590764800, -271488291236524, 314626752934230, 1402512664127940, 375622681398240, 0, -351021913436232, 0, -258515764876800, -174724215921432, 34180023972960, -1315137528041044, 80913969115200, 0, 429926378835456, 0, -754965406703360, -173243132355820, -699640829042040, 2334678352173312, 476216790163200, 0, 1017049836134300, 0, -1758146457278112, 177642767671680, -981148739522112, -3200164419875880, 168784533852920, 0, 1904622755780160, 0, -633357436534240, 1005993095784960, -813980747752348, 3672489290369900, 2504123931073920, 0, 2258813799631580, 0, -2700313788779520, -1343661264378220, -2159610846276480, -4013638433174740, 2165953168647360, 0, 2061908446734048, 0, -2123410709510880, -2905982389226082, -2253249964978560, 6422357053896024, 1609512396737000, 0, 1839893406898332, 0, -983618252283456, 735490695859920, -1572272332970640, -6288409377946368, 1677727625929080, 0, 22684245780960, 0, 176723550874208, 774857225185920, -2033524287063060, 9764587437946220, 195997955725440, 0, 1427954212008960, 0, -1913596816533120, 2076371580288980, -1276665481381104, -13289233273171200, 1149707912319360, 0, 1894110483710880, 0, 1710878446471680, 3271834895720808, 599042427148800, 3825666688922200, 494469228543300, 0, -3945534527595748, 0, -2652362885548240, 1650320140280832, 2398291998463680, -6648075575242324, -1252466945077000, 0, -2570304538274784, 0, 3294092317463040, -3660300363857260, 3320416512061810, 11594887370272728, -3130590880870080, 0, -4852567197703020, 0, 9715261275952016, 1493472398922240, 4097269773731664, -11041243174752340, -9477620997478080, 0, -9021445911911520, 0, 5235054332509760, 3447148136966420, 8503353067252104, 17732398654613760, -3121020970074904, 0, -3919198054982500, 0, 10110206572004160, -11103983347574274, 8047067485221360, -23602137417462780, -9335429914172928, 0, -10054411663378080, 0, 6082554199507200, -1172705184779844, 3379703344590720, 21773447682041088, -4280339181811200, 0, -4715263841655752, 0, 4570504624045824, -1277995313854080, 9636649149559680, -14554482008843092, -10997814406317120, 0, 2484424252266240, 0, -710850857488128, 5304199016117760, 15190486521722852, 26960277940934340, -15717015454873240, 0, -4000817638790400, 0, 6279145121449240, 4352967719510760, 7251024786398256, -28560803151859200, 1170919954126824, 0, -4444268056714080, 0, -5755624005724400, -6151816001079724, -17935760718649080, 21462390459264000, -13426654394625120, 0, 4970376249250560, 0, 7597058979513120, -5695472049076012, 869142992277600, -10287020599713192, 23047911141366720, 0, 679276877701536, 0, 2844558527203584, -4212364040574360, 1967602872332680, 10208418457343468, 23418227620377600, 0, -8139639835292260, 0, -24857655235723584, 11926054211975060, -38359658119602240, -11694529014693120, 20482721950546040, 0, 28743788884273440, 0, -23218046325875520, 3154503228444500, -10587314756413440, 9336195636084480, 19116686676171360, 0, 37345129611050040, 0, -18637764909920640, -2010642351366594, -27291327700998240, -19112256916748500, 35527955538824640, 0, 6069802319639424, 0, -33577795173995520, 16506496673174228, -34280441299708170, -26932045497574184, -6070736651140120, 0, 26829346625924636, 0, -15477950542211232, 10209205919664980, 255605125909680, -4633103878006608, 31725352898112000, 0, 43207970467390080, 0, 11755435495743360, 6725427365591040, -27197160823813084, -13984772494229140, 52000049602836000, 0, -917000395706880, 0, -41759366810961520, 7506185196834280, -38636593322678400, 51752912105815340, -4343326227077760, 0, 21235203333474240, 0, -54865557570393600, -30271168422471552, -13694332534591900, -26301892572595200, 22626250984847004, 0, 23129076158468820, 0, 29530915887839040, -20386909818021912, -20921356988060880, 69130600473071660, -9452821498621200, 0, -29850357386949408, 0, -25466796696437760, -4381969397137920, 4158267891096840, 4708931168000492, -53094649845309120, 0, 36900691838996060, 0, 16889338154054016, -46023293683843200, 76207524357780288, 50260716483535020, -9899331632593920, 0, 3899581068724800, 0, 87115182769047040, -26227930706645040, 17271181639293476, -85242463123587840, -14583917719713456, 0, -139419547088244480, 0, 31539266372098560, 71082727255649876, 69055788308785200, 74488408193106860, -112007498010586888, 0, -33334656527470176, 0, -8965632309543360, 4195546002927562, 175127946452023680, -180782122018102716, -35604527848767360, 0, 6308520439766328, 0, 80763144260799632, 48073771416946920, -11138666715017520, 146107425940118060, -88458952363620480, 0, -147521760240461760, 0, 68222594064650432, -67222074861590400, 27522819956820480, -175384468031513620, -92251806963980440, 0, -65363087113733860, 0, 34957182985171200, -10601956896752640, 139736852679836016, 272927821063230720, 14412172263793016, 0, -66064263130281600, 0, 245017810913310720, 70606198288849872, -13472157486472540, -174408447229074580, 8803673272323840, 0, -130359515925932068, 0, 41213861981965440, -163633896091090732, 27400428665860800, 164322534513505580, -210536392672774080, 0, 1580268064548672, 0, 40815654364024512, 179403327211403540, 56849715817821750, -365794029910140072, 52017616349326080, 0, -81259073502951240, 0, 82222437996844592, 93888896554823040, -37910137610584656, 273175485817750700, 42669402652951800, 0, -203505907694127840, 0, -23271407268443520, -22774908621402220, -29529948837624048, -327399478901890560, -191053148473375200, 0, 162238952120352000, 0, -221961498489479280, 71427779587606676, 178988269692173760, 373907385206590980, 209473751881704000, 0, 275121093181447200, 0, 214471564050920000, 15222474335285760, -241935886247587200, -265127252370365952, 143604839822583480, 0, 27986935398410012, 0, -306803215040163072, -8850148699891180, -344062559535754560, 156348523081266092, -131848850545551360, 0, 241258436798367840, 0, -381245328851347200, -209361915189867830, 261652126033065956, -227739923908424400, 315044840531562720, 0, 355466982417488640, 0, 142441172113639680, -293073558701834520, -295042163970578544, 306102627342397440, 382935811187194560, 0, -146195543537857440, 0, -337686847197004800, 147369555278581460, -293511292794439800, -74142178250704660, -141206848675550208, 0, 3812916902417848, 0, -191034064212556680, 200818466132803816, 148695072664447440, 349910876230717440, 295797422615868920, 0, 460011934010296800, 0, -75041394369348064, -325048117820681220, -421338345934494720, -114148017163695892, 563476746320062080, 0, 30827932639592540, 0, -306135117311321968, -105195498497026560, -386813909557676016, 229105761360595200, -273156773555027520, 0, 425220076593019680, 0, -563318165956531200, 191320363474192340, 269561982613295012, -98943166780914600, 298295596306766644, 0, 260350850657346360, 0, 322929231035598720, -21990151075517976, -336217980146822400, -54339087514358740, 204299164812746856, 0, -212702383791375552, 0, -219653428487550880, -4218983664144768, -405780839293079040, -673660924045071124, -498861662824098720, 0, 540901657443932252, 0, -358542351392929920, 217075199434640680, 539274205054337040, 362370290562075864, 234632020332968640, 0, 6720690146927040, 0, 528328710442087808, 368986070109066240, -97672302417187804, -164573262781413120, 254987680861054800, 0, -1003070889761898240, 0, 95732360137183280, 410314395695155200, -38593217174828160, -119706955821108480, -441575751651673864, 0, -117263242345532640, 0, 298153752575218560, -46725106610514432, 447638399392156950, 305460023296082520, -176758019597933280, 0, 1770796619054100, 0, 1166022263777725440, -836926118428287834, -262849594780217760, -483045621905007656, 112392491980741440, 0, -1180647633693248064, 0, 72131017201534464, -429867469349446040, 414482461767046380, 504656726996301932, -1195653006770538240, 0, 118877043206872320, 0, 95083968259537920, 694642667207863680, 1206226118346622704, -623265873431501820, 277669290611350000, 0, 31338768637508160, 0, 977872493340817920, 173597778972710760, -39120885692964480, 853775532849703680, -428219904437395200, 0, -1018144202568859300, 0, -13063802595404160, -418098118803791404, 110461411601372160, -1389462675436919040, -1285714701672168960, 0, -106813322657266176, 0, -22735964175505920, -124083450738821932, 1744316519615239680, 1177719870833691864, 63702529194775400, 0, -561232781265312300, 0, 1224357404895964976, 1341060744634836480, 196344493411521840, -215039418788732840, -172640433623262720, 0, -1103948712797428800, 0, -298438593448280048, -390631296585824640, -267950558416795896, 1085617332300014060, -1739701670273151840, 0, -74941548925263360, 0, -210689581564579920, -1081483843391928960, 1723680635385126096, -2226681908974391040, 425040377736480960, 0, 338541826238474880, 0, 1017098810294201440, 233663161152665724, -225635041209201820, 1575000861568603480, -457246249591265712, 0, -974136664072811520, 0, -267992008806365760, 485469814120076372, -271430287976682000, -526768676968086100, -1010854234991900160, 0, 614510923080401952, 0, -196098699547797312, -899898519951276440, 559064583502349540, 2252028508945304832, 1273465954133616960, 0, 2045278313333885880, 0, 860391576267970176, -2053010450665921560, -1366758039697054272, -950776608018837460, 887598945562910400, 0, -701445581859368160, 0, -1108092387110914560, 1127930573016696020, -1157001121289525112, 2543404524845794560, 500508209248345936, 0, 228800954010923420, 0, -2112095587316582400, 917743031189760490, -341974026356055120, -3753535499654466600, 495112591358968568, 0, 870902467253388864, 0, 517158855546468480, 32486398075347048, -725906913985207900, 1146150132091699968, 2155414699818714240, 0, -517234051763631360, 0, -769167427353847408, -1425757036073317420, -1218156310120263360, -1746155197424731732, -1182992184268200000, 0, 1969490094161668800, 0, -1143933055993441152, 1160329979419697280, -341546810108776348, 861452179837695300, 1547414544634368000, 0, 2689610143323252480, 0, 563912622288866880, 3812020403502151740, -1187778457011603648, -2524461652036247040, 2168873952099480048, 0, -713584433924814240, 0, -2386247327754512640, -326458010455670380, -1896091841342153130, 1038735597797783660, 515337783300884160, 0, 1822823521051670492, 0, -1971062065841765760, -3061945647893864448, 206366192980345440, -1537034560611011748, 1561126976925692160, 0, 2825134602173112480, 0, 172330828688001024, 745532153738227200, -1785540706526049820, 2365026181700705280, 1782091394251443420, 0, -2097205473773956040, 0, -2591644171522648528, 2718016397312065920, -3314516115507453120, -1348799688397941460, -531902920458647560, 0, 1629915513011312640, 0, -576003469314379200, -856389240944218520, 774543884239559012, 3676636222009808640, 2002833802230752160, 0, -764387608829377680, 0, 661666352281205760, -3246870024976201752, -1112915900228900400, -3658569784628578560, 2220171910858556160, 0, -1379388938398347456, 0, -595811180091974400, 1103002217741456852, -1010043383618979840, 2991685359308007404, -157757266793245720, 0, 2636320322258499356, 0, -648240914117618496, 3147176020810321940, 2213159160888400320, -1199561520223439016, -932437715568491520, 0, -655061967790726560, 0, 2065948262552554592, -3578983244187816960, 1123420882087947784, 152531381762730860, -1991454465550206720, 0, -272744002710552100, 0, 206113227674108160, -1684740166762125100, 860138285310637776, -749763044178585600, -2076614847322416000, 0, -320513267460708480, 0, 2029182687040896000, 1507735399473619210, 1804879926651461760, 1376949586735482180, -3502644687858226072, 0, -1465780234320061440, 0, 1682715120024667080, 1749650850828422352, 2736622343535059040, -920776263378809044, -857616751667156760, 0, -813119089946959584, 0, 236727679422614400, -3204959775544927660, 2188502844673549320, 1239592199184548440, -3122239871658180960, 0, -928294699102599460, 0, -1038821401083056352, -6874287445053617280, 2095640612878332960, 2277965169202206720, -2500906317038777280, 0, -3594711851375721120, 0, 2920451371601356800, 7778479709026552680, 1036633686220070400, -2014744039951230720, -549739188050703792, 0, -803830082508687460, 0, 2641371857743505280], "weight_parity": -1, "has_non_self_twist": 1, "level_is_prime": false, "level_is_prime_power": true, "level_is_square": false, "level_is_squarefree": false, "inner_twists": [[1, 1, 1, 1, 1, 1, 1], [1, 1, 8, 4, -1, 2, 0]], "char_orbit_index": 4, "prim_orbit_index": 4, "minimal_twist": "8.13.d.b", "char_is_minimal": true, "conrey_index": 3, "id": null, "nf_label": null, "fricke_eigenval": null, "atkin_lehner_string": null, "projective_image": null, "projective_image_type": null, "artin_degree": null, "artin_image": null, "artin_field_label": null, "projective_field_label": null, "atkin_lehner_eigenvals": null, "projective_field": null, "artin_field": null, "embedded_related_objects": null, "qexp": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-11, -1, 0, 0, 0, 0, 0, 0, 0, 0], [-66, 3, -1, 0, 0, 0, 0, 0, 0, 0], [-244, 12, 1, -1, 0, 0, 0, 0, 0, 0], [0, 48, 1, 0, 0, -1, 0, 0, 0, 0], [-13081, 113, 12, 5, -1, 0, 0, 0, 0, -1], [0, 323, 7, 0, 1, 0, 0, 0, 1, 1], [2710, 241, -20, 14, -4, 2, -2, -1, -1, 2], [169275, -763, -189, 11, 6, 0, -1, -4, 0, 4], [187302, -548, -92, 44, 9, 20, 6, -6, 6, -2], [-459250, 7249, 297, 242, -44, 0, -22, 0, 0, 0], [-542836, 15674, 1218, 166, -38, -92, -8, 6, 14, 36], [64, 3760, 79, -216, 32, 17, 8, -16, 8, -104], [1272852, -4480, -2456, 104, 6, -280, 84, -28, -20, -60], [896, 10231, -53, -2256, 61, -32, -144, 32, -19, 205], [-3829556, 7178, -1472, 540, -220, 660, 84, 70, -10, 52], [4287290, -127881, -8607, 825, 706, 0, -75, 20, 0, -20], [822855, -167931, 18304, 568, -440, 1184, 416, 48, -80, -184], [3604718, -56143, -13399, 3586, 372, 0, -326, 128, 0, -128], [1761384, -173228, 49216, 1184, -20, -1432, 736, 28, -244, -216], [7616, 361568, 5508, -19560, 1632, -100, -1096, 144, -200, 808], [-22702361, 511313, -60852, 5797, -2849, -704, 704, 352, 352, 671], [6528, -436207, -10659, -18192, -741, 864, -464, -352, 139, -2325], [16908372, 440942, -158152, 6084, 3760, -2020, 2068, -814, 370, -420], [-70709183, -395986, 41026, 33330, 516, 0, -3030, 104, 0, -104], [15122586, 103012, 275804, 17748, -10217, -7700, -710, -122, 250, 2626], [138237804, 1408380, -160512, 8250, -4572, 0, -750, -1920, 0, 1920], [-13215568, -1056360, 462848, 18496, 11880, 14768, 832, -1144, 1704, -1744], [-7680, 4916368, 107051, 19776, 16768, 85, 1088, -128, 2240, 1344], [45609796, -500736, -777528, -11320, -20562, 20296, -2940, -1708, -2500, -972], [-21376, -7559524, -156340, 59088, -30668, -10720, 1680, 992, -380, 6564], [-265117592, 4521676, -311712, -14072, 26600, -21096, -8904, 3668, -3148, -3112], [-47726580, -12099879, 215567, -172425, 58014, 0, 15675, -660, 0, 660], [445516274, -5646074, 108672, -131096, -24168, -8480, 480, 1040, 1680, -12648], [-283796064, 21135412, 549468, -116820, -104712, 0, 10620, 11392, 0, -11392], [-407402940, 499540, 745939, -182035, 97456, -17440, -22464, 7504, -5360, 23008], [-153664, 19079120, 447305, 395736, 62944, 1623, 21752, -2544, -14600, -32408], [164449943, -4575199, -864756, -91723, -64241, -49344, -1856, 4192, 8288, -15153], [-134144, -45421239, -931691, 360576, -157565, 80640, 13952, 2816, -765, 18947], [818121872, -3801480, 1117632, -227824, 225008, 98032, -18576, -4536, 11144, 45424], [-1233871822, -37314966, 2102502, -121418, 149068, 0, 11038, -1096, 0, 1096], [1469134648, -5944336, -4292912, 283376, -236972, 136848, -37448, -11384, -16392, 16920], [2508180734, 48826271, -2469645, -71500, -193848, 0, 6500, -29440, 0, 29440], [-2795254132, 30459770, -1913758, 444422, 200090, -141020, 16632, -15290, 1870, -103004], [126912, 100901936, 2113987, -311592, 349792, -6307, -23048, 7184, 59512, 109800], [-1681345892, 7445760, 5560568, -36360, -434206, -148360, -42148, -8948, -6940, 81452], [166272, -63919238, -1393774, -495888, -271106, -408224, -976, -19808, 7790, -130866], [1330597000, -15229156, 11378240, 1010920, 159864, 61240, 83960, -18620, -4636, -204296], [-3953924639, -48476552, -493496, 1549064, 199824, 0, -140824, 10144, 0, -10144], [2489173909, 62694079, -6641920, -716976, -430160, -128576, 86976, 47648, 50976, 52144], [3675394188, 34437752, -6036364, 769406, -94836, 0, -69946, 512, 0, -512], [-3616909672, -11368404, -10933312, -609440, 520340, 263320, 162080, -33180, 39284, 241624], [1286208, 55817808, 811829, -3327192, 282016, -4181, -177144, 16368, -146040, -31464], [-7401626754, -117756654, 6653208, 2273082, -278130, 559680, 208320, 27360, -34080, -112050], [1255936, -83577945, -2094565, -3258816, 18381, 1457280, -169664, 12672, -13299, 75405], [15445917408, -27044592, 5950080, -1802272, 160032, -829920, 110368, 68976, -94480, 416032], [8041262796, -144294263, 1871071, -916025, 675390, 0, 83275, 4780, 0, -4780], [19325448418, -53664268, -5206900, 4106084, 259459, -702628, 210178, -45826, -24830, -142422], [-10945426594, -39068077, 9074319, 1429824, 23680, 0, -129984, 194176, 0, -194176], [-34737076240, 58717240, 17283072, 2324288, -1543224, 791792, -164288, 209000, -107768, -362896], [-851392, -179649552, -3498413, 1982568, -628320, 72845, 190536, -84112, 148680, -440104], [-29920635504, 74842752, -7489248, -7896544, 1417464, 568608, 181392, -18864, 74992, -258736], [-224640, 500967737, 10518565, 969360, 1030867, -3725920, -98480, 126560, -39197, 846723], [27619504880, 185724936, -28503616, 3863472, -1903440, 431120, -362416, -41032, 274680, -304240], [9649843728, 540701266, -45840066, -3025330, -1832196, 0, 275030, -96104, 0, 96104], [48632714636, -68918476, 49619328, -12110824, 2287208, 702240, -438240, -245520, -266640, -204952], [-4985168722, -392498463, 15407865, -2110350, 1680084, 0, 191850, -456960, 0, 456960], [-29679598024, -370192408, 17127874, -4511618, -1285488, -1439584, -414016, -226448, 28336, 545440], [-5304256, -868818784, -17018580, 13852968, -3436128, -90700, 686600, -23568, 286600, 121624], [-79913865248, 491135072, -65864960, 19069792, 2994720, -3123328, -1433472, -261056, 103488, 1022112], [-6964608, 583061179, 14647167, 17548176, 2971177, 6729120, 1115216, -244640, 174905, -1537575], [107759549538, 61065283, -121024380, -6204854, -2335500, 2649318, -559718, -120179, -627, 84710], [-5884699894, 1282756125, 134716907, 2613875, -8017578, 0, -237625, 12060, 0, -12060], [74265226230, -153033668, 95973380, 21403852, 4843585, 2586100, -784298, 746218, 691350, 712334], [-25173117378, -1170803881, 43343771, -14109700, 5237016, 0, 1282700, 209024, 0, -209024], [-69972883380, 27169946, 3174658, -2863130, -2387782, -4021660, 78456, -624858, 321710, -606492], [2033856, -1729492512, -37979260, -3822984, -6300448, -403172, -759528, 505296, -1329768, 2207304], [-179565812164, 483456896, 20717368, -44813000, 5964562, -989000, 168700, 751020, -312892, -825012], [-4264448, 1635638870, 36048414, 10254528, 4457458, -7926400, 846272, -313216, -35150, -2227662], [198198530400, -1429761968, -73352832, -11852064, -3659808, -993120, 1048864, 147760, -1322576, -736352], [25957437165, 1234872201, -304495137, -13382457, -1203138, 0, 1216587, 625836, 0, -625836], [165428141818, 814746830, 49554688, -42564880, 2902544, 686400, -248000, -167840, -202912, 1162768], [-14624160514, -1492621005, -2810673, 1060400, 7060192, 0, -96400, 913280, 0, -913280], [-314427300064, -630488560, 17017088, 8690816, -8889616, 6170400, 230784, 1819824, -493200, -1546720], [7265600, 90335168, 537746, -19913400, 864160, 1087054, -627800, -280400, 2102440, 139640], [-226214802313, -1883859935, 96593356, 65040373, -740657, 9157760, 2618240, 131520, -810560, -1074097], [24343168, 389503101, 660505, -60258672, 2560063, 3440544, -4256944, 1214048, -901041, 7597295], [217018007316, 2448941198, 303182264, 43645316, -6224592, -3631012, 1030612, -294734, 1884498, -1460580], [91323136010, -3152696603, 416293731, 25243691, 8394310, 0, -2294881, -298116, 0, 298116], [398319828498, -1240312556, -386274772, 74360772, -1271797, -13615748, 4988978, -2015474, -1693582, -4340070], [36126681696, 1813309132, -112186204, 64127316, -8461560, 0, -5829756, -2293376, 0, 2293376], [-264938071920, 2310023688, -307742720, -1515840, 6585848, 13796240, 2944960, -529320, 273592, 7108112], [6214144, 1884616448, 39951248, -21648576, 8861696, 1085552, 1002048, -1778816, -1134272, -13585984], [-251725774760, 856940672, 369088304, -39059920, -12279500, -7120, 1170904, -2841544, 2753320, 2867448], [29283840, -2857925673, -68089461, -77313600, -6702115, 10187136, -3512640, -147840, 1204125, 169245], [283668065392, -1949460792, 466679104, -18072016, 14632176, -13347440, -1716144, 1455608, 1834040, 13719312], [-147448328326, 322170951, -951621615, 58859625, 10569762, 0, -5350875, -2957100, 0, 2957100], [237815190229, 3283451935, -243477504, -62522048, -23368000, -7590144, 3532544, 2172032, 2496640, -1079616], [-71728800198, 6632125049, 74905677, 29189072, -33005280, 0, -2653552, 3014528, 0, -3014528], [-485571685620, -1293588372, -225404591, 59672367, 16571424, -19880128, -945792, -3780640, -695712, -9782464]]}