# Stored data for newform 144.12.a.b, downloaded from the LMFDB on 15 December 2025.
{"Nk2": 20736, "analytic_conductor": 110.6414180005808, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [3, -1]], "atkin_lehner_string": "--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [144, 1, [127, 37, 65], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[5, [5766, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503599828697232, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "144.12.a.b", "level": 144, "level_is_powerful": true, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": true, "level_is_squarefree": false, "level_primes": [2, 3], "level_radical": 6, "minimal_twist": "6.12.a.a", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-5766q^{5}-72464q^{7}-408948q^{11}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "11.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "144.12.a", "trace_display": [0, 0, -5766, -72464], "trace_hash": 1409842965466939190, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.979", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.912", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.734", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "traces": [0, 1, 0, 0, 0, -5766, 0, -72464, 0, 0, 0, -408948, 0, 1367558, 0, 0, 0, -5422914, 0, -15166100, 0, 0, 0, -52194072, 0, -15581369, 0, 0, 0, -118581150, 0, 57652408, 0, 0, 0, 417827424, 0, -375985186, 0, 0, 0, -856316202, 0, 1245189172, 0, 0, 0, -1306762656, 0, 3273704553, 0, 0, 0, -409556358, 0, 2357994168, 0, 0, 0, -2882866260, 0, 5731767302, 0, 0, 0, -7885339428, 0, -3893272244, 0, 0, 0, -9075890088, 0, -15571822822, 0, 0, 0, 29634007872, 0, 30196762600, 0, 0, 0, 23135252628, 0, 31268522124, 0, 0, 0, 25614819990, 0, -99098722912, 0, 0, 0, 87447732600, 0, -61937553406, 0, 0, 0, 94964150058, 0, -54371908448, 0, 0, 0, 5713477884, 0, -49672374010, 0, 0, 0, -177802571058, 0, 300951019152, 0, 0, 0, 392966040096, 0, -118073203907, 0, 0, 0, 371385142404, 0, 473707536136, 0, 0, 0, 168573812532, 0, 1098996270400, 0, 0, 0, 801479261526, 0, -524839237820, 0, 0, 0, -559260108984, 0, 683738910900, 0, 0, 0, -1257020226870, 0, 492117459808, 0, 0, 0, -332423784528, 0, -997091613946, 0, 0, 0, 3782191233408, 0, 484141975612, 0, 0, 0, 2315373820584, 0, 78054489327, 0, 0, 0, -3371566157598, 0, 1129088323216, 0, 0, 0, 1645977026340, 0, 2742173271902, 0, 0, 0, 2167930582476, 0, 2217689834472, 0, 0, 0, 4084089808512, 0, -4472389991422, 0, 0, 0, 7370248975146, 0, -2693084564000, 0, 0, 0, 8592864453600, 0, 4937519220732, 0, 0, 0, 6202146262800, 0, -6634577708612, 0, 0, 0, -7179760765752, 0, -4177724093312, 0, 0, 0, -7416149424012, 0, 5995589013832, 0, 0, 0, -7749301902396, 0, 3758040333710, 0, 0, 0, -9026758358298, 0, 7534793474496, 0, 0, 0, -4022692975920, 0, -14999667337678, 0, 0, 0, -18876180452598, 0, -20740521383800, 0, 0, 0, -14681681636868, 0, 21344661356256, 0, 0, 0, 16447633968126, 0, 27245390518304, 0, 0, 0, -19681818745272, 0, 2361501960228, 0, 0, 0, 11617411525650, 0, -7467876506792, 0, 0, 0, 6371969689812, 0, 15956443695614, 0, 0, 0, -39611493918282, 0, -15000063411788, 0, 0, 0, 62052097261728, 0, -4863900056237, 0, 0, 0, -38825493139158, 0, 16622606855160, 0, 0, 0, -71378420716176, 0, -90231388159808, 0, 0, 0, -33049370263332, 0, -75819366414884, 0, 0, 0, -79990659222888, 0, -68561413056022, 0, 0, 0, -6378911616414, 0, 48493524130200, 0, 0, 0, 82244456015400, 0, -21308425826902, 0, 0, 0, 94693249104384, 0, -89020993584092, 0, 0, 0, 22448607758904, 0, 142600806741554, 0, 0, 0, -23576836946784, 0, -93940721623840, 0, 0, 0, -133725973385316, 0, -63047442118810, 0, 0, 0, 28974898162302, 0, 52331582247408, 0, 0, 0, 43310836423800, 0, 113520330311781, 0, 0, 0, 89787130391652, 0, 112470912775336, 0, 0, 0, 29678091926112, 0, 129947513379758, 0, 0, 0, -162166600331700, 0, 94538171865220, 0, 0, 0, 54511744524288, 0, -170869689389952, 0, 0, 0, 51137944162170, 0, 283043963765808, 0, 0, 0, -174114533151600, 0, -48723411062986, 0, 0, 0, -376407484129122, 0, 78843011779664, 0, 0, 0, 153758389844328, 0, 312467212549610, 0, 0, 0, 208904020664640, 0, -133397866653048, 0, 0, 0, 281729092206660, 0, -301063838733778, 0, 0, 0, 84496424089266, 0, -415346785772128, 0, 0, 0, 346694170280832, 0, 482345467463378, 0, 0, 0, 791580515359200, 0, -118934088249200, 0, 0, 0, -199914264990852, 0, -147695052062340, 0, 0, 0, 506701914104430, 0, 350188798175496, 0, 0, 0, 571403236310592, 0, -362768435523526, 0, 0, 0, -65646585500862, 0, 206748343519192, 0, 0, 0, -379400882843916, 0, 282122079889216, 0, 0, 0, -509217621511056, 0, 236308600390900, 0, 0, 0, 367939370639280, 0, -514181548995788, 0, 0, 0, 357131932938996, 0, -631644906594224, 0, 0, 0, 278183150638332, 0, 643055378471100, 0, 0, 0, 657675299336832, 0, -459050093742500, 0, 0, 0, -915702867160632, 0, -547563289234428, 0, 0, 0, -1085622825947550, 0, 1128396568973408, 0, 0, 0, 313508424111168, 0, 534397974645888, 0, 0, 0, 163924983100278, 0, -46912694264588, 0, 0, 0, -312644050476912, 0, 1771411394027257, 0, 0, 0, -1171062072574716, 0, -32943913479144, 0, 0, 0, -1338774929540244, 0, -1281958508682538, 0, 0, 0, 286410908541660, 0, -1105639461244004, 0, 0, 0, 1798413579015000, 0, -2188178205046400, 0, 0, 0, -2121608950717374, 0, 1702868413681976, 0, 0, 0, -2448882915166092, 0, 1025209624720428, 0, 0, 0, 738094760695590, 0, 21010268758708, 0, 0, 0, 813255095444568, 0, 1132487353279874, 0, 0, 0, -1676472946435392, 0, 167487253491384, 0, 0, 0, -2912545182972516, 0, -874362184968800, 0, 0, 0, -1529013546440658, 0, -2265842187193536, 0, 0, 0, 2715166624101000, 0, -2591038342922998, 0, 0, 0, 680810093727762, 0, -1687610876689304, 0, 0, 0, -1787073724314048, 0, -535763782489282, 0, 0, 0, 2843668860910086, 0, -814487455941980, 0, 0, 0, -1856152315755360, 0, -1380597697898339, 0, 0, 0, 2038935328952004, 0, 1458684356311168, 0, 0, 0, -2731397653360176, 0, 4476980851091574, 0, 0, 0, 1162971435762798, 0, -4734612318417668, 0, 0, 0, 5475272623688664, 0, 1178942391294480, 0, 0, 0, 887970661792482, 0, -971996603059512, 0, 0, 0, 3144543068000100, 0, 1329822392592302, 0, 0, 0, -6336812495126400, 0, 6189233080942800, 0, 0, 0, -2343994774618296, 0, -6844380693513502, 0, 0, 0, -888819607540614, 0, 4488242870012384, 0, 0, 0, 2224018428599628, 0, -4621329421958916, 0, 0, 0, -560092073833764, 0, -4597206126295892, 0, 0, 0, 3026223045270120, 0, 4643729120252628, 0, 0, 0, 2587014691966818, 0, 5702228929394600, 0, 0, 0, -6881482169802912, 0, 2520806909453870, 0, 0, 0, -3009113934125376, 0, 3224693788401744, 0, 0, 0, 3037163189811840, 0, 3940005973775872, 0, 0, 0, 1847656654594350, 0, -6520856018525024, 0, 0, 0, -6752553793487208, 0, -1482084159648202, 0, 0, 0, 1592145897639312, 0, -5393426983129460, 0, 0, 0, 8961919068060168, 0, 7247978628132420, 0, 0, 0, -414021461386176, 0, 7787200900914568, 0, 0, 0, -2837549273252928, 0, -2419224924478786, 0, 0, 0, 5025522575565318, 0, 3599458910260640, 0, 0, 0, -3942486816793080, 0, 12105571636854530, 0, 0, 0, 7456300773991722, 0, -898303442786552, 0, 0, 0, 12986977151152200, 0, 3711567099707424, 0, 0, 0, 5749230246012636, 0, 11257989560649676, 0, 0, 0, 12884285509146912, 0, 7838524227988516, 0, 0, 0, 10466895892615986, 0, 7086461501899584, 0, 0, 0, 6368065799411256, 0, -21808114651830528, 0, 0, 0, 12817970979489270, 0, -9792950640539852, 0, 0, 0, -2791562631378792, 0, -18884663501469200, 0, 0, 0, -7084100698669542, 0, -19856913386391008, 0, 0, 0, -20553656994225396, 0, -14592049502444170, 0, 0, 0, -17753018252327442, 0, -13350445449487344, 0, 0, 0, 6549633589083960, 0, 1860979369616671, 0, 0, 0, -450062185459482, 0, 8556056647916848, 0, 0, 0, 19624197869017392, 0, 19924415074625198, 0, 0, 0, -15914882431310394, 0, 1190195095374820, 0, 0, 0, -1733431366649952, 0, 19440450464710068, 0, 0, 0, -12348905671744800, 0, -5324275603460152, 0, 0, 0, -26912052959163456, 0, 11660223223786454, 0, 0, 0, 16609123048628718, 0, 12820490726271532, 0, 0, 0, -221358390467016, 0, -34326742898559104, 0, 0, 0, 19818493117161600, 0, -9490703533876440, 0, 0, 0, -6836488840909200, 0, 2220988907587212, 0, 0, 0, -15811371085786932, 0, 24836086882256116, 0, 0, 0, 8102951455624752, 0, -9461115291715344, 0, 0, 0, -12215532751318848, 0, 33381374096334400, 0, 0, 0, -12411806096965104, 0, 5858363921599634, 0, 0, 0, -35671257106709970, 0, -49649330621253300, 0, 0, 0, -12787199585565552, 0, 39624761192998394, 0, 0, 0, -5371931506709022, 0, 44694629501954544, 0, 0, 0, 22224103394043684, 0, -21295370874808676, 0, 0, 0, -7668673573745178, 0, -23548861835880192, 0, 0, 0, -58078393207220064, 0, -22084676748206367, 0, 0, 0, 25787800690539252, 0, -28047373147337984, 0, 0, 0, -24342728765789268, 0, 38031950529388480, 0, 0, 0, 21914442147874206, 0, -10475129405270520, 0, 0, 0, -7045855376252712, 0, -42496855590691836, 0, 0, 0, -64991493296988384, 0, -40487293131612392, 0, 0, 0, 15528325596024000, 0, 17960734932482174, 0, 0, 0, 40526224537416576, 0, 15633535801481640, 0, 0, 0, 6211372681063800, 0, -11702091187813390, 0, 0, 0, -20255731606089078, 0, -49546456439457600, 0, 0, 0, -17953019169671220, 0, -13325880316933018, 0, 0, 0, 13342578724040538, 0, 41295824267730800, 0, 0, 0, -16615423460382168, 0, -24898739350723942, 0, 0, 0, -31082881146758028, 0, 8688156920124040, 0, 0, 0, 91088713719907680, 0, -35761575351304800, 0, 0, 0, 36801180581909430, 0, 41225248580309428, 0, 0, 0, 38254975067856792, 0, -35660799607526912, 0, 0, 0, -10392717675269862, 0, -25876540988235488, 0, 0, 0, 25329238590276888, 0, 20542789971481910, 0, 0, 0, 44584755738843900, 0, -19401751963736468, 0, 0, 0, 31638799813442424, 0, 68205264154175232, 0, 0, 0, 24088757122036992, 0, 32571111393047416, 0, 0, 0, 70719001461061572, 0, -7709542602506002, 0, 0, 0, 3467432584492326, 0, 72253246712982944, 0, 0, 0, -43713598626699312, 0, 42761517578853192, 0, 0, 0, -23227844334941910, 0, -38835399237918984, 0, 0, 0, -34570566253755312, 0, 56574365174603894, 0, 0, 0, 43721837985786000, 0, 14352699322266412, 0, 0, 0, -170867971146009816, 0, 24649781792845850, 0, 0, 0, 22235283215992704, 0, 44682474769215336, 0, 0, 0, 21112880557799016, 0, -35082864120747968, 0, 0, 0, -21668860564171860, 0, -21676451345227888, 0, 0, 0, -3963592283528448, 0, 35143101344748098, 0, 0, 0, 35029751995884420, 0, -86928556078862200, 0, 0, 0, 88582120297047228, 0, 52048288693946268, 0, 0, 0, -167781248534798976, 0, 83223982371916348, 0, 0, 0, 20361151138556064, 0, -2336515353706032, 0, 0, 0, 137966990526431538, 0, -5656140514591728, 0, 0, 0, -134152095060825516, 0, 101542959996792300, 0, 0, 0, 3798867130950342, 0, 23194847699154720, 0, 0, 0, 20313418006641480, 0, -84050834285187118, 0, 0, 0, 86488081869051348, 0, 49217771420676432, 0, 0, 0, 244317170044181472, 0, -168310223389326442, 0, 0, 0, 40066904983228926, 0, 21376414037509776, 0, 0, 0, 124015727712314088, 0, -51008798637273057, 0, 0, 0, -2131291789073790, 0, -44984833738573352, 0, 0, 0, 119589846298990800, 0, 15844807169430974, 0, 0, 0, 84444655986943308, 0, 72712005829026984, 0, 0, 0, -147655963983307800, 0, 162741821329134050, 0, 0, 0, -119274079236701760, 0, 84654576318180888, 0, 0, 0, 8999311647631500, 0, -84703196660802548, 0, 0, 0, -123073317380172096, 0, -198708843975106528, 0, 0, 0, -49368691054714416, 0, 59045756179728400, 0, 0, 0, 202231843237520226, 0, -21705993438649400, 0, 0, 0, -148449678792021372, 0, -94837057460214516, 0, 0, 0, -196382200948376250, 0, -157352925535162892, 0, 0, 0, -157096921728540864, 0, 141375782023592114, 0, 0, 0, -33830751560047062, 0, -61678022712370448, 0, 0, 0, 100256533229719884, 0, -160702676165179008, 0, 0, 0, 129868983125018364, 0, 113485366885238352, 0, 0, 0, 108480794052093720, 0, -161002457425886278, 0, 0, 0, 6381448740294102, 0, -192277681510144184, 0, 0, 0, 164963437664387064, 0, 71788154181326176, 0, 0, 0, -295949483884013568, 0, -74356738373329984, 0, 0, 0, -163754446658216400, 0, -66985994856897900, 0, 0, 0, 137645856663616800, 0, 324087268338403808, 0, 0, 0, 43059775938162672, 0, 150468529140810720, 0, 0, 0, 99624957234174078, 0, 154957418525534400, 0, 0, 0, -128786130232745256, 0, -36552761688005817, 0, 0, 0, -181514757671739438, 0, -151877211215830992, 0, 0, 0, -534077721734979744, 0, -308612723936939218, 0, 0, 0, -92004854348910324, 0, 236163822100734200, 0, 0, 0, 7813512388087272, 0, 195151679845696000, 0, 0, 0, -193721749487744928, 0, -91117323486571760, 0, 0, 0, -299164275247833744, 0, 228399873932814012, 0, 0, 0, 337312640638704270, 0, -125460485369917992, 0, 0, 0, 86490365632369608, 0, -67929852456367580, 0, 0, 0, -388199650654975950, 0, -316411313659900328, 0, 0, 0, 74651090584915284, 0, 229791332488503470, 0, 0, 0, -97092978950700138, 0, -357792392811123648, 0, 0, 0, 219837678138606960, 0, -68937923487336336, 0, 0, 0, 28045247724262542, 0, 258063384035888896, 0, 0, 0, 118778880166104252, 0, -304382007240123322, 0, 0, 0, -75338013802875648, 0, 411431754219789580, 0, 0, 0, -449432326787539200, 0, 223867793440385028, 0, 0, 0, -243155328470936364, 0, -210271058520051032, 0, 0, 0, 44919002974709940, 0, 480768039076859968, 0, 0, 0, 130517470271183718, 0, 210123859962675892, 0, 0, 0, 63467017382750304, 0, -509623482831413230, 0, 0, 0, -312983174920463478, 0, 411567973849470816, 0, 0, 0, 201540458065605180, 0, -457967121267860000, 0, 0, 0, 520274184129452928, 0, -327763341042534648, 0, 0, 0, 114914735516093112, 0, -138906965931250860, 0, 0, 0, 321962206483783572, 0, 188736950561013624, 0, 0, 0, 261734398238477748, 0, -89308781354596438, 0, 0, 0, 214631956628013360, 0, -445474684490664332, 0, 0, 0, 437174466748221144, 0, 48565663921451700, 0, 0, 0, 203205731818937568, 0, -465425911169227088, 0, 0, 0, 537403851861605568, 0, 609340521265687190, 0, 0, 0, -116730399068772018, 0, 461226141079172208, 0, 0, 0, 35615779412746440, 0, -434464362298322048, 0, 0, 0, 395325107681022852, 0, 647055491047505656, 0, 0, 0, -414292261114696908, 0, -161471954588649106, 0, 0, 0, -350871554881510800, 0, -242960848146750140, 0, 0, 0, 416052631215682128, 0, 36780804380243124, 0, 0, 0, 561545413055223744, 0, -468172682439605992, 0, 0, 0, -279613660134733200, 0, 762616350786184694, 0, 0, 0, -307382736368212002, 0, -272322634741961440, 0, 0, 0, -686455847754551976, 0, 116268128190559130, 0, 0, 0, 475166098538839122, 0, -474221533384796400, 0, 0, 0, -582351703687607580, 0, 545986087871836862, 0, 0, 0, 507890722575729432, 0, 151278318826737556, 0, 0, 0, 654115017675706272, 0, 473707660717158336, 0, 0, 0, -664456031680881654, 0, 514055907738032760, 0, 0, 0, -23611910250410064, 0, -546001274335878144, 0, 0, 0, 335882025491145084, 0, 647822530703075888, 0, 0, 0, 513295049005874472, 0, -605806952504896726, 0, 0, 0, -201250450953561984, 0, 142957828772881672, 0, 0, 0, -704131521310867596, 0, -540575250102259570, 0, 0, 0, 291500423807066880, 0, 60662511451222036, 0, 0, 0, 812756841542711184, 0, 182948406091456363, 0, 0, 0, -822236251671800364, 0, 1086935893957498592, 0, 0, 0, -388476921450339000, 0, 744304489133340998, 0, 0, 0, -683108602342054674, 0, -456815868387114740, 0, 0, 0, 230534465918636856, 0, 135944041835156544, 0, 0, 0, 197074108939689090, 0, 341853596406999000, 0, 0, 0, 541662200883061440, 0, -514982418847629012, 0, 0, 0, 486076389539161398, 0, -410692476746993948, 0, 0, 0, 407758621339988808, 0, 1502941141555683200, 0, 0, 0, -666260695924218438, 0, 771063962539732056, 0, 0, 0, 491323400274014016, 0, 516828561732819062, 0, 0, 0, 363531551257058460, 0, -27003850416956324, 0, 0, 0, 294854183529377472, 0, -550261614478750582, 0, 0, 0, 1063893378134002752, 0, 355353872129372440, 0, 0, 0, -1066275662538564744, 0, -167069262803833332, 0, 0, 0, -679679558203557300, 0, -1546719540519734784, 0, 0, 0, 141414792464570472, 0, -1448984185105737646, 0, 0, 0, 1096069375933973508, 0, -462450276029168048, 0, 0, 0, -1485231550797244836, 0, -889233721608771130, 0, 0, 0, -197988892642576176, 0, -249730282819630800, 0, 0, 0, -1191861347866282464, 0, 1474490674340495642, 0, 0, 0, -654558224577729246, 0, -717748098394643560, 0, 0, 0, 720652006132000932, 0, -1230864415268751858, 0, 0, 0, -1576092001311307200, 0, -30983699205833976, 0, 0, 0, 953175477964555248, 0, 242630317392203318, 0, 0, 0, -166204181830954080, 0, -1712780347249156832, 0, 0, 0, -648507283062587376, 0, -946867493180185632, 0, 0, 0, 1426223313557390208, 0, 939351128710736600, 0, 0, 0, 1161609992732962344, 0, 621202334594822877, 0, 0, 0, 269369012432065140, 0, -171123878045961792, 0, 0, 0, -31920227301297996, 0, -1516543280423300578, 0, 0, 0, -749277362147684628, 0, -524982966143094764, 0, 0, 0, -1699374363573461328, 0, -675441855996783982, 0, 0, 0, -696897612011317974, 0, 86984061871675360, 0, 0, 0, -841844108794701600, 0, 935052617512582200, 0, 0, 0, 445633418223604350, 0, 330450187055963216, 0, 0, 0, -545107098974858520, 0, 541152203188175488, 0, 0, 0, 585195659798426178, 0, 1378795237017386904, 0, 0, 0, 1460216178589822884, 0, -1207523041404021216, 0, 0, 0, -1180794104421709578, 0, -314314718927044608, 0, 0, 0, -1440235796194633800, 0, 964208051826423012, 0, 0, 0, -461738411602536768, 0, 1119002034501352512, 0, 0, 0, -170857229953143108, 0, 2159935697066332118, 0, 0, 0, -1719048067417883460, 0, -1156267735958972896, 0, 0, 0, 461668699956600600, 0, -294861386039072220, 0, 0, 0, 1094877826772342610, 0, 752082053291587048, 0, 0, 0, -1632031495073648928, 0, 824609800713212800, 0, 0, 0, 153987123440112588, 0, 672999169100108864, 0, 0, 0, 2870407295294386848, 0, -673119012967690320, 0, 0, 0, 346053446017105722, 0, -470506900675999400, 0, 0, 0, 903910736492027100, 0, 1086964595071805632, 0, 0, 0, 280939188189177276, 0, 725740000885495516, 0, 0, 0, -1121406275197779096, 0, -1414650959108111782, 0, 0, 0, 969546271744134306, 0, -1829796233650709240, 0, 0, 0, -2409174599808446652, 0, 2170365553488517452, 0, 0, 0, -2803326249295067706, 0, 1224421008710763268, 0, 0, 0, -454608805921542624, 0, -807967937676947326, 0, 0, 0, -1627166709625160832, 0, 352457653675157968, 0, 0, 0, 7816708904514924, 0, -1888987041042515290, 0, 0, 0, -86651176936532400, 0, -886570875842395248, 0, 0, 0, -424558721405158680, 0, -1363580613384763868, 0, 0, 0, -1801685947561051260, 0, -1336941758825099280, 0, 0, 0, 2813450534835945312, 0, 556568780484739358, 0, 0, 0, 640300830492124998, 0, 1076229483908641200, 0, 0, 0, 116954162135604048, 0, -1204540583152314240, 0, 0, 0, -1542961933124293350, 0, 753336191473061000, 0, 0, 0, -360478908105087732, 0, -224456519866163552, 0, 0, 0, 3123230878284992718, 0, -218912053400294948, 0, 0, 0, 1973431257311506824, 0, 722815882527358010, 0, 0, 0, 5172365878776977664, 0, -1624449945663601560, 0, 0, 0, -250019222755824060, 0, -1670180359011365376, 0, 0, 0, 1735934094138963948, 0, 4076381461722700116, 0, 0, 0, -1949902172302828368, 0, 2838361504990670978, 0, 0, 0, 1846524657829005300, 0, 662092231883995496, 0, 0, 0, 1828974942212044056, 0, -2013989688134645256, 0, 0, 0, 2196443375737298670, 0, -1491945548375084612, 0, 0, 0, 2394889566762090048, 0, 1915155187039060874, 0, 0, 0, -3468363697973798622, 0, -328788443515463048, 0, 0, 0, 2696571572922733800, 0, 5494174567888154176, 0, 0, 0, 3817563235271321622, 0, -1999038585839277312, 0, 0, 0, -2568875229617420304, 0, 2887633181986219442, 0, 0, 0, -2781203965393837548, 0, -3014048577888006408, 0, 0, 0, 3166407991330213872, 0, 350709744987512316, 0, 0, 0, 5796443129927356032, 0, -1684143866545985540, 0, 0, 0, 1083915006979224360, 0, -4564253251561147200, 0, 0, 0, 1101331546278672000, 0, 4968234235691578208, 0, 0, 0, 685773952844887200, 0, -2344139242833398180, 0, 0, 0, -523246918316531904, 0, -1320458545753748348, 0, 0, 0, -3534934728088471776, 0, -764530575967837967, 0, 0, 0, -3820274549019263718, 0, 1152705651937252632, 0, 0, 0, 462241451371824096, 0, 3824911764772361222, 0, 0, 0, -399113962132766310, 0, -914161288013158248, 0, 0, 0, 3232773121976609232, 0, -3514034732570812800, 0, 0, 0, 3146096510497479666, 0, 3074360927157587560, 0, 0, 0, 1043856971846783508, 0, -2921643236726143380, 0, 0, 0, -4610812271352405684, 0, 4843393060882229188, 0, 0, 0, -2019188610279909936, 0, -2155059595151188172, 0, 0, 0, -5959762260699945600, 0, -897753082637655376, 0, 0, 0, -405411094614422916, 0, 1234733784699398150, 0, 0, 0, -1774632809611932738, 0, 1544093769120626528, 0, 0, 0, -509975142305355576, 0, 4890241339815743162, 0, 0, 0, 2091722799228650916, 0, -1758549236607793064, 0, 0, 0, -3580766835384990000, 0, 258122103627654158, 0, 0, 0, -3008809560594903834, 0, 1790710017773952700, 0, 0, 0, -4277954856637572768, 0, 378518211997970292, 0, 0, 0, -373936655270348790, 0, 1241674262332516768, 0, 0, 0, -1192110948731661072, 0, 6450817279077642688, 0, 0, 0, 2713197284781460176, 0, -4956565685546056176, 0, 0, 0, 2250969050187477720, 0, -4346353108039006764, 0, 0, 0, 349691909009575362, 0, 2187625490478019656, 0, 0, 0, 4283912663853865380, 0, -4986631895357370418, 0, 0, 0, -1626715912641219456, 0, 1002235388995789636, 0, 0, 0, 480398658022484832, 0, 3750080995375755316, 0, 0, 0, 6757705809471782106, 0, -10333424859719969056, 0, 0, 0, 2846158050523407480, 0, 2936148805632748896, 0, 0, 0, 2837891304312320256, 0, 5590007299270324828, 0, 0, 0, -5632464208213304400, 0, -102574883987692486, 0, 0, 0, -4401733416400065102, 0, -3217834503723390728, 0, 0, 0, 1708471912511755776, 0, 947179372841759150, 0, 0, 0, -7316222315124719178, 0, -2121538411106088480, 0, 0, 0, -2056217698603200000, 0, 334136890422180881, 0, 0, 0, 2964770811509713608, 0, -2743404862168762200, 0, 0, 0, -7501167586020432708, 0, -7184295863792189600, 0, 0, 0, -3865378124832479394, 0, 2468645086637144520, 0, 0, 0, -2706412624754532072, 0, 965071874576092814, 0, 0, 0, 9690318935393538624, 0, 3032819474650859376, 0, 0, 0, 3642064531422295584, 0, -4900487271833353666, 0, 0, 0, 1128641367126598278, 0, 4568669845697447840, 0, 0, 0, -6777810296717820336, 0, 1740916077694340800, 0, 0, 0, -2451884136028568736, 0, -1604004046580622312, 0, 0, 0, 3254021198034541500, 0, -298209676047903648, 0, 0, 0, -3707857312264362600, 0, -7970892224851495604, 0, 0, 0, -2099637020433052128, 0, -3112579213416359302, 0, 0, 0, -62748428347749774, 0, 1463812688808977384, 0, 0, 0, 5585229690349053696, 0, -3792155775976173312, 0, 0, 0, -2556607298241565200, 0, 535192954161766848, 0, 0, 0, 2646882840519255000, 0, 3169061514381039408, 0, 0, 0, -4908205206796427004, 0, -3220791829103839088, 0, 0, 0, 2592603465488868720, 0, -6116252711889087476, 0, 0, 0, -3138476450614243200, 0, 5279942732048204112, 0, 0, 0, -1536843078390037080, 0, -3943960525834823158, 0, 0, 0, -1479671463825069402, 0, -8226137215712898384, 0, 0, 0, 3031935763824096132, 0, 6816712586576499180, 0, 0, 0, -3589713851276136720, 0, 543329071284646420, 0, 0, 0, 903299859205708848, 0, 6259701214413573300, 0, 0, 0, 3359446848990512250, 0, -5383280789614316672, 0, 0, 0, -6506334616700670528, 0, 446905004045592854, 0, 0, 0, 10079242947952713468, 0, 3691474777109250504, 0, 0, 0, -2668710662437240512, 0, -8150092223351947904, 0, 0, 0, 1333803023692528224, 0, 847188768762505312, 0, 0, 0, -1239967050742857900, 0, -3037434811457188500, 0, 0, 0, -3081338721808190208, 0, -3682949340174712000, 0, 0, 0, 4751578074687943392, 0, 4591987389432664418, 0, 0, 0, -1340766513894697974, 0, 9280240195586368176, 0, 0, 0, -12155314628229468600, 0, -945191452556202948, 0, 0, 0, 3072301297424469630, 0, -9416516609550783712, 0, 0, 0, 270498595129614408, 0, 5432419431004609994, 0, 0, 0, -2096615537220283662, 0, 7137134580874053944, 0, 0, 0, 3412400222852236368, 0, 1645072247116532160, 0, 0, 0, -2824627523652547818, 0, 1802705595049874592, 0, 0, 0, 11751240526436308800, 0, 7959764364701902000, 0, 0, 0, -10213958097961163862, 0, 4602339699152000416, 0, 0, 0, 6134083958408742744, 0, -6850614086041302080, 0, 0, 0, 8402243779399192926, 0, 5739830186416149340, 0, 0, 0, -2994169485176660952, 0, 6752343910465812456, 0, 0, 0, 5407142072550358644, 0, 7285396657311662728, 0, 0, 0, -89023807183943196, 0, 1986334812778411934, 0, 0, 0, -3950139055208005632, 0, 6037276435562893012, 0, 0, 0, -12765138150408196656, 0, 4967533717401603650, 0, 0, 0, -10648918291590061158, 0, 7719376243729046904, 0, 0, 0, 8742477802174965180, 0, 5854774700088714892, 0, 0, 0, 7391772761063514108, 0, 588580654445318956, 0, 0, 0, -9793433203540936008, 0, -9384925383157116502, 0, 0, 0, 8481794738862242400, 0, -14307401610479114840, 0, 0, 0, -3705659985767486880, 0, 773963588555819690, 0, 0, 0, -5505684519959490090, 0, -6626536477982477612, 0, 0, 0, 6375117133532927064, 0, -20510497790325510912, 0, 0, 0, 4463254599962277738, 0, -9073169822034009496, 0, 0, 0, 3333872101334097288, 0, 9700274686151140550, 0, 0, 0, 1025610767721816462, 0, -10369652696600490000, 0, 0, 0, 1476756052910035920, 0, 6004044342033894864, 0, 0, 0, 12617035530297542400, 0, 7034632395355929016, 0, 0, 0, -2625460297533973368, 0, 3767221970810386560, 0, 0, 0, 10850271213634638726, 0, 3530693259268217504, 0, 0, 0, 6162721305992639304, 0, 12233197209836378484, 0, 0, 0, 1245618175429363050, 0, 9213042523036976368, 0, 0, 0, -9818739273290273616, 0, 12696347761702258694, 0, 0, 0, 13325804933030518398, 0, -1032001375537107188, 0, 0, 0, 27275991929932696608, 0, -9101299518993967433, 0, 0, 0, 7344626311069896900, 0, 14120258888847686472, 0, 0, 0, 12938785174065067140, 0, -5713280005601572096, 0, 0, 0, 2770407468803418402, 0, -6726227015997191448, 0, 0, 0, 19064094462733107000, 0, -12345235460607425422, 0, 0, 0, -508136083391917974, 0, -12556073106878461776, 0, 0, 0, -6431745152806050852, 0, -4255854390170771940, 0, 0, 0, -11141947961679384192, 0, 16571838082416077308, 0, 0, 0, -121145209662710328, 0, -2848427163485392006, 0, 0, 0, -6607910601811835982, 0, -22642624090194939040, 0, 0, 0, -7490059463135474112, 0, -7463502607194108800, 0, 0, 0, -423282782934238878, 0, -19384102862364629088, 0, 0, 0, 10222045903152800640, 0, -4847860441876941968, 0, 0, 0, -6529922079011753484, 0, 11518428124968809296, 0, 0, 0, -9437652401052081780, 0, 8048840412241493856, 0, 0, 0, 12546283762866351006, 0, 8199315720578062256, 0, 0, 0, 1522886092073707848, 0, 9666543009146470272, 0, 0, 0, -7806583354261934190, 0, 7771831729925605776, 0, 0, 0, -965731503631320144, 0, -12815825551443467746, 0, 0, 0, -24724725248024985792, 0, -11353535402758843600, 0, 0, 0, -13287618358368538416, 0, -11260958122650206700, 0, 0, 0, -20415216937663410240, 0, 16793735525019527256, 0, 0, 0, 1596973749288565020, 0, 18283713317964400572, 0, 0, 0, 5041572358530100800, 0, 21816290010004488992, 0, 0, 0, -10597619811036868968, 0, -22285563625386365542, 0, 0, 0, 7914425535182500626, 0, -4750917208591516200, 0, 0, 0, -19491558272647821132, 0, 8816292108776834028, 0, 0, 0, 6362335448985826710, 0, -3224420266210609052, 0, 0, 0, -6122948875204571424, 0, 5139338122687780180, 0, 0, 0, 3053973161699574816, 0, 15121991126266430600, 0, 0, 0, 6447483431458555200, 0, 18764112713293926006, 0, 0, 0, 13334404177151962044, 0, -15655650754566366000, 0, 0, 0, 17879340898072239240, 0], "weight": 12, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 0, 0, 0, -5766, 0, -72464, 0, 0, 0, -408948, 0, 1367558, 0, 0, 0, -5422914, 0, -15166100, 0, 0, 0, -52194072, 0, -15581369, 0, 0, 0, -118581150, 0, 57652408, 0, 0, 0, 417827424, 0, -375985186, 0, 0, 0, -856316202, 0, 1245189172, 0, 0, 0, -1306762656, 0, 3273704553, 0, 0, 0, -409556358, 0, 2357994168, 0, 0, 0, -2882866260, 0, 5731767302, 0, 0, 0, -7885339428, 0, -3893272244, 0, 0, 0, -9075890088, 0, -15571822822, 0, 0, 0, 29634007872, 0, 30196762600, 0, 0, 0, 23135252628, 0, 31268522124, 0, 0, 0, 25614819990, 0, -99098722912, 0, 0, 0, 87447732600, 0, -61937553406, 0, 0, 0, 94964150058, 0, -54371908448, 0, 0, 0, 5713477884, 0, -49672374010, 0, 0, 0, -177802571058, 0, 300951019152, 0, 0, 0, 392966040096, 0, -118073203907, 0, 0, 0, 371385142404, 0, 473707536136, 0, 0, 0, 168573812532, 0, 1098996270400, 0, 0, 0, 801479261526, 0, -524839237820, 0, 0, 0, -559260108984, 0, 683738910900, 0, 0, 0, -1257020226870, 0, 492117459808, 0, 0, 0, -332423784528, 0, -997091613946, 0, 0, 0, 3782191233408, 0, 484141975612, 0, 0, 0, 2315373820584, 0, 78054489327, 0, 0, 0, -3371566157598, 0, 1129088323216, 0, 0, 0, 1645977026340, 0, 2742173271902, 0, 0, 0, 2167930582476, 0, 2217689834472, 0, 0, 0, 4084089808512, 0, -4472389991422, 0, 0, 0, 7370248975146, 0, -2693084564000, 0, 0, 0, 8592864453600, 0, 4937519220732, 0, 0, 0, 6202146262800, 0, -6634577708612, 0, 0, 0, -7179760765752, 0, -4177724093312, 0, 0, 0, -7416149424012, 0, 5995589013832, 0, 0, 0, -7749301902396, 0, 3758040333710, 0, 0, 0, -9026758358298, 0, 7534793474496, 0, 0, 0, -4022692975920, 0, -14999667337678, 0, 0, 0, -18876180452598, 0, -20740521383800, 0, 0, 0, -14681681636868, 0, 21344661356256, 0, 0, 0, 16447633968126, 0, 27245390518304, 0, 0, 0, -19681818745272, 0, 2361501960228, 0, 0, 0, 11617411525650, 0, -7467876506792, 0, 0, 0, 6371969689812, 0, 15956443695614, 0, 0, 0, -39611493918282, 0, -15000063411788, 0, 0, 0, 62052097261728, 0, -4863900056237, 0, 0, 0, -38825493139158, 0, 16622606855160, 0, 0, 0, -71378420716176, 0, -90231388159808, 0, 0, 0, -33049370263332, 0, -75819366414884, 0, 0, 0, -79990659222888, 0, -68561413056022, 0, 0, 0, -6378911616414, 0, 48493524130200, 0, 0, 0, 82244456015400, 0, -21308425826902, 0, 0, 0, 94693249104384, 0, -89020993584092, 0, 0, 0, 22448607758904, 0, 142600806741554, 0, 0, 0, -23576836946784, 0, -93940721623840, 0, 0, 0, -133725973385316, 0, -63047442118810, 0, 0, 0, 28974898162302, 0, 52331582247408, 0, 0, 0, 43310836423800, 0, 113520330311781, 0, 0, 0, 89787130391652, 0, 112470912775336, 0, 0, 0, 29678091926112, 0, 129947513379758, 0, 0, 0, -162166600331700, 0, 94538171865220, 0, 0, 0, 54511744524288, 0, -170869689389952, 0, 0, 0, 51137944162170, 0, 283043963765808, 0, 0, 0, -174114533151600, 0, -48723411062986, 0, 0, 0, -376407484129122, 0, 78843011779664, 0, 0, 0, 153758389844328, 0, 312467212549610, 0, 0, 0, 208904020664640, 0, -133397866653048, 0, 0, 0, 281729092206660, 0, -301063838733778, 0, 0, 0, 84496424089266, 0, -415346785772128, 0, 0, 0, 346694170280832, 0, 482345467463378, 0, 0, 0, 791580515359200, 0, -118934088249200, 0, 0, 0, -199914264990852, 0, -147695052062340, 0, 0, 0, 506701914104430, 0, 350188798175496, 0, 0, 0, 571403236310592, 0, -362768435523526, 0, 0, 0, -65646585500862, 0, 206748343519192, 0, 0, 0, -379400882843916, 0, 282122079889216, 0, 0, 0, -509217621511056, 0, 236308600390900, 0, 0, 0, 367939370639280, 0, -514181548995788, 0, 0, 0, 357131932938996, 0, -631644906594224, 0, 0, 0, 278183150638332, 0, 643055378471100, 0, 0, 0, 657675299336832, 0, -459050093742500, 0, 0, 0, -915702867160632, 0, -547563289234428, 0, 0, 0, -1085622825947550, 0, 1128396568973408, 0, 0, 0, 313508424111168, 0, 534397974645888, 0, 0, 0, 163924983100278, 0, -46912694264588, 0, 0, 0, -312644050476912, 0, 1771411394027257, 0, 0, 0, -1171062072574716, 0, -32943913479144, 0, 0, 0, -1338774929540244, 0, -1281958508682538, 0, 0, 0, 286410908541660, 0, -1105639461244004, 0, 0, 0, 1798413579015000, 0, -2188178205046400, 0, 0, 0, -2121608950717374, 0, 1702868413681976, 0, 0, 0, -2448882915166092, 0, 1025209624720428, 0, 0, 0, 738094760695590, 0, 21010268758708, 0, 0, 0, 813255095444568, 0, 1132487353279874, 0, 0, 0, -1676472946435392, 0, 167487253491384, 0, 0, 0, -2912545182972516, 0, -874362184968800, 0, 0, 0, -1529013546440658, 0, -2265842187193536, 0, 0, 0, 2715166624101000, 0, -2591038342922998, 0, 0, 0, 680810093727762, 0, -1687610876689304, 0, 0, 0, -1787073724314048, 0, -535763782489282, 0, 0, 0, 2843668860910086, 0, -814487455941980, 0, 0, 0, -1856152315755360, 0, -1380597697898339, 0, 0, 0, 2038935328952004, 0, 1458684356311168, 0, 0, 0, -2731397653360176, 0, 4476980851091574, 0, 0, 0, 1162971435762798, 0, -4734612318417668, 0, 0, 0, 5475272623688664, 0, 1178942391294480, 0, 0, 0, 887970661792482, 0, -971996603059512, 0, 0, 0, 3144543068000100, 0, 1329822392592302, 0, 0, 0, -6336812495126400, 0, 6189233080942800, 0, 0, 0, -2343994774618296, 0, -6844380693513502, 0, 0, 0, -888819607540614, 0, 4488242870012384, 0, 0, 0, 2224018428599628, 0, -4621329421958916, 0, 0, 0, -560092073833764, 0, -4597206126295892, 0, 0, 0, 3026223045270120, 0, 4643729120252628, 0, 0, 0, 2587014691966818, 0, 5702228929394600, 0, 0, 0, -6881482169802912, 0, 2520806909453870, 0, 0, 0, -3009113934125376, 0, 3224693788401744, 0, 0, 0, 3037163189811840, 0, 3940005973775872, 0, 0, 0, 1847656654594350, 0, -6520856018525024, 0, 0, 0, -6752553793487208, 0, -1482084159648202, 0, 0, 0, 1592145897639312, 0, -5393426983129460, 0, 0, 0, 8961919068060168, 0, 7247978628132420, 0, 0, 0, -414021461386176, 0, 7787200900914568, 0, 0, 0, -2837549273252928, 0, -2419224924478786, 0, 0, 0, 5025522575565318, 0, 3599458910260640, 0, 0, 0, -3942486816793080, 0, 12105571636854530, 0, 0, 0, 7456300773991722, 0, -898303442786552, 0, 0, 0, 12986977151152200, 0, 3711567099707424, 0, 0, 0, 5749230246012636, 0, 11257989560649676, 0, 0, 0, 12884285509146912, 0, 7838524227988516, 0, 0, 0, 10466895892615986, 0, 7086461501899584, 0, 0, 0, 6368065799411256, 0, -21808114651830528, 0, 0, 0, 12817970979489270, 0, -9792950640539852, 0, 0, 0, -2791562631378792, 0, -18884663501469200, 0, 0, 0, -7084100698669542, 0, -19856913386391008, 0, 0, 0, -20553656994225396, 0, -14592049502444170, 0, 0, 0, -17753018252327442, 0, -13350445449487344, 0, 0, 0, 6549633589083960, 0, 1860979369616671, 0, 0, 0, -450062185459482, 0, 8556056647916848, 0, 0, 0, 19624197869017392, 0, 19924415074625198, 0, 0, 0, -15914882431310394, 0, 1190195095374820, 0, 0, 0, -1733431366649952, 0, 19440450464710068, 0, 0, 0, -12348905671744800, 0, -5324275603460152, 0, 0, 0, -26912052959163456, 0, 11660223223786454, 0, 0, 0, 16609123048628718, 0, 12820490726271532, 0, 0, 0, -221358390467016, 0, -34326742898559104, 0, 0, 0, 19818493117161600, 0, -9490703533876440, 0, 0, 0, -6836488840909200, 0, 2220988907587212, 0, 0, 0, -15811371085786932, 0, 24836086882256116, 0, 0, 0, 8102951455624752, 0, -9461115291715344, 0, 0, 0, -12215532751318848, 0, 33381374096334400, 0, 0, 0, -12411806096965104, 0, 5858363921599634, 0, 0, 0, -35671257106709970, 0, -49649330621253300, 0, 0, 0, -12787199585565552, 0, 39624761192998394, 0, 0, 0, -5371931506709022, 0, 44694629501954544, 0, 0, 0, 22224103394043684, 0, -21295370874808676, 0, 0, 0, -7668673573745178, 0, -23548861835880192, 0, 0, 0, -58078393207220064, 0, -22084676748206367, 0, 0, 0, 25787800690539252, 0, -28047373147337984, 0, 0, 0, -24342728765789268, 0, 38031950529388480, 0, 0, 0, 21914442147874206, 0, -10475129405270520, 0, 0, 0, -7045855376252712, 0, -42496855590691836, 0, 0, 0, -64991493296988384, 0, -40487293131612392, 0, 0, 0, 15528325596024000, 0, 17960734932482174, 0, 0, 0, 40526224537416576, 0, 15633535801481640, 0, 0, 0, 6211372681063800, 0, -11702091187813390, 0, 0, 0, -20255731606089078, 0, -49546456439457600, 0, 0, 0, -17953019169671220, 0, -13325880316933018, 0, 0, 0, 13342578724040538, 0, 41295824267730800, 0, 0, 0, -16615423460382168, 0, -24898739350723942, 0, 0, 0, -31082881146758028, 0, 8688156920124040, 0, 0, 0, 91088713719907680, 0, -35761575351304800, 0, 0, 0, 36801180581909430, 0, 41225248580309428, 0, 0, 0, 38254975067856792, 0, -35660799607526912, 0, 0, 0, -10392717675269862, 0, -25876540988235488, 0, 0, 0, 25329238590276888, 0, 20542789971481910, 0, 0, 0, 44584755738843900, 0, -19401751963736468, 0, 0, 0, 31638799813442424, 0, 68205264154175232, 0, 0, 0, 24088757122036992, 0, 32571111393047416, 0, 0, 0, 70719001461061572, 0, -7709542602506002, 0, 0, 0, 3467432584492326, 0, 72253246712982944, 0, 0, 0, -43713598626699312, 0, 42761517578853192, 0, 0, 0, -23227844334941910, 0, -38835399237918984, 0, 0, 0, -34570566253755312, 0, 56574365174603894, 0, 0, 0, 43721837985786000, 0, 14352699322266412, 0, 0, 0, -170867971146009816, 0, 24649781792845850, 0, 0, 0, 22235283215992704, 0, 44682474769215336, 0, 0, 0, 21112880557799016, 0, -35082864120747968, 0, 0, 0, -21668860564171860, 0, -21676451345227888, 0, 0, 0, -3963592283528448, 0, 35143101344748098, 0, 0, 0, 35029751995884420, 0, -86928556078862200, 0, 0, 0, 88582120297047228, 0, 52048288693946268, 0, 0, 0, -167781248534798976, 0, 83223982371916348, 0, 0, 0, 20361151138556064, 0, -2336515353706032, 0, 0, 0, 137966990526431538, 0, -5656140514591728, 0, 0, 0, -134152095060825516, 0, 101542959996792300, 0, 0, 0, 3798867130950342, 0, 23194847699154720, 0, 0, 0, 20313418006641480, 0, -84050834285187118, 0, 0, 0, 86488081869051348, 0, 49217771420676432, 0, 0, 0, 244317170044181472, 0, -168310223389326442, 0, 0, 0, 40066904983228926, 0, 21376414037509776, 0, 0, 0, 124015727712314088, 0, -51008798637273057, 0, 0, 0, -2131291789073790, 0, -44984833738573352, 0, 0, 0, 119589846298990800, 0, 15844807169430974, 0, 0, 0, 84444655986943308, 0, 72712005829026984, 0, 0, 0, -147655963983307800, 0, 162741821329134050, 0, 0, 0, -119274079236701760, 0, 84654576318180888, 0, 0, 0, 8999311647631500, 0, -84703196660802548, 0, 0, 0, -123073317380172096, 0, -198708843975106528, 0, 0, 0, -49368691054714416, 0, 59045756179728400, 0, 0, 0, 202231843237520226, 0, -21705993438649400, 0, 0, 0, -148449678792021372, 0, -94837057460214516, 0, 0, 0, -196382200948376250, 0, -157352925535162892, 0, 0, 0, -157096921728540864, 0, 141375782023592114, 0, 0, 0, -33830751560047062, 0, -61678022712370448, 0, 0, 0, 100256533229719884, 0, -160702676165179008, 0, 0, 0, 129868983125018364, 0, 113485366885238352, 0, 0, 0, 108480794052093720, 0, -161002457425886278, 0, 0, 0, 6381448740294102, 0, -192277681510144184, 0, 0, 0, 164963437664387064, 0, 71788154181326176, 0, 0, 0, -295949483884013568, 0, -74356738373329984, 0, 0, 0, -163754446658216400, 0, -66985994856897900, 0, 0, 0, 137645856663616800, 0, 324087268338403808, 0, 0, 0, 43059775938162672, 0, 150468529140810720, 0, 0, 0, 99624957234174078, 0, 154957418525534400, 0, 0, 0, -128786130232745256, 0, -36552761688005817, 0, 0, 0, -181514757671739438, 0, -151877211215830992, 0, 0, 0, -534077721734979744, 0, -308612723936939218, 0, 0, 0, -92004854348910324, 0, 236163822100734200, 0, 0, 0, 7813512388087272, 0, 195151679845696000, 0, 0, 0, -193721749487744928, 0, -91117323486571760, 0, 0, 0, -299164275247833744, 0, 228399873932814012, 0, 0, 0, 337312640638704270, 0, -125460485369917992, 0, 0, 0, 86490365632369608, 0, -67929852456367580, 0, 0, 0, -388199650654975950, 0, -316411313659900328, 0, 0, 0, 74651090584915284, 0, 229791332488503470, 0, 0, 0, -97092978950700138, 0, -357792392811123648, 0, 0, 0, 219837678138606960, 0, -68937923487336336, 0, 0, 0, 28045247724262542, 0, 258063384035888896, 0, 0, 0, 118778880166104252, 0, -304382007240123322, 0, 0, 0, -75338013802875648, 0, 411431754219789580, 0, 0, 0, -449432326787539200, 0, 223867793440385028, 0, 0, 0, -243155328470936364, 0, -210271058520051032, 0, 0, 0, 44919002974709940, 0, 480768039076859968, 0, 0, 0, 130517470271183718, 0, 210123859962675892, 0, 0, 0, 63467017382750304, 0, -509623482831413230, 0, 0, 0, -312983174920463478, 0, 411567973849470816, 0, 0, 0, 201540458065605180, 0, -457967121267860000, 0, 0, 0, 520274184129452928, 0, -327763341042534648, 0, 0, 0, 114914735516093112, 0, -138906965931250860, 0, 0, 0, 321962206483783572, 0, 188736950561013624, 0, 0, 0, 261734398238477748, 0, -89308781354596438, 0, 0, 0, 214631956628013360, 0, -445474684490664332, 0, 0, 0, 437174466748221144, 0, 48565663921451700, 0, 0, 0, 203205731818937568, 0, -465425911169227088, 0, 0, 0, 537403851861605568, 0, 609340521265687190, 0, 0, 0, -116730399068772018, 0, 461226141079172208, 0, 0, 0, 35615779412746440, 0, -434464362298322048, 0, 0, 0, 395325107681022852, 0, 647055491047505656, 0, 0, 0, -414292261114696908, 0, -161471954588649106, 0, 0, 0, -350871554881510800, 0, -242960848146750140, 0, 0, 0, 416052631215682128, 0, 36780804380243124, 0, 0, 0, 561545413055223744, 0, -468172682439605992, 0, 0, 0, -279613660134733200, 0, 762616350786184694, 0, 0, 0, -307382736368212002, 0, -272322634741961440, 0, 0, 0, -686455847754551976, 0, 116268128190559130, 0, 0, 0, 475166098538839122, 0, -474221533384796400, 0, 0, 0, -582351703687607580, 0, 545986087871836862, 0, 0, 0, 507890722575729432, 0, 151278318826737556, 0, 0, 0, 654115017675706272, 0, 473707660717158336, 0, 0, 0, -664456031680881654, 0, 514055907738032760, 0, 0, 0, -23611910250410064, 0, -546001274335878144, 0, 0, 0, 335882025491145084, 0, 647822530703075888, 0, 0, 0, 513295049005874472, 0, -605806952504896726, 0, 0, 0, -201250450953561984, 0, 142957828772881672, 0, 0, 0, -704131521310867596, 0, -540575250102259570, 0, 0, 0, 291500423807066880, 0, 60662511451222036, 0, 0, 0, 812756841542711184, 0, 182948406091456363, 0, 0, 0, -822236251671800364, 0, 1086935893957498592, 0, 0, 0, -388476921450339000, 0, 744304489133340998, 0, 0, 0, -683108602342054674, 0, -456815868387114740, 0, 0, 0, 230534465918636856, 0, 135944041835156544, 0, 0, 0, 197074108939689090, 0, 341853596406999000, 0, 0, 0, 541662200883061440, 0, -514982418847629012, 0, 0, 0, 486076389539161398, 0, -410692476746993948, 0, 0, 0, 407758621339988808, 0, 1502941141555683200, 0, 0, 0, -666260695924218438, 0, 771063962539732056, 0, 0, 0, 491323400274014016, 0, 516828561732819062, 0, 0, 0, 363531551257058460, 0, -27003850416956324, 0, 0, 0, 294854183529377472, 0, -550261614478750582, 0, 0, 0, 1063893378134002752, 0, 355353872129372440, 0, 0, 0, -1066275662538564744, 0, -167069262803833332, 0, 0, 0, -679679558203557300, 0, -1546719540519734784, 0, 0, 0, 141414792464570472, 0, -1448984185105737646, 0, 0, 0, 1096069375933973508, 0, -462450276029168048, 0, 0, 0, -1485231550797244836, 0, -889233721608771130, 0, 0, 0, -197988892642576176, 0, -249730282819630800, 0, 0, 0, -1191861347866282464, 0, 1474490674340495642, 0, 0, 0, -654558224577729246, 0, -717748098394643560, 0, 0, 0, 720652006132000932, 0, -1230864415268751858, 0, 0, 0, -1576092001311307200, 0, -30983699205833976, 0, 0, 0, 953175477964555248, 0, 242630317392203318, 0, 0, 0, -166204181830954080, 0, -1712780347249156832, 0, 0, 0, -648507283062587376, 0, -946867493180185632, 0, 0, 0, 1426223313557390208, 0, 939351128710736600, 0, 0, 0, 1161609992732962344, 0, 621202334594822877, 0, 0, 0, 269369012432065140, 0, -171123878045961792, 0, 0, 0, -31920227301297996, 0, -1516543280423300578, 0, 0, 0, -749277362147684628, 0, -524982966143094764, 0, 0, 0, -1699374363573461328, 0, -675441855996783982, 0, 0, 0, -696897612011317974, 0, 86984061871675360, 0, 0, 0, -841844108794701600, 0, 935052617512582200, 0, 0, 0, 445633418223604350, 0, 330450187055963216, 0, 0, 0, -545107098974858520, 0, 541152203188175488, 0, 0, 0, 585195659798426178, 0, 1378795237017386904, 0, 0, 0, 1460216178589822884, 0, -1207523041404021216, 0, 0, 0, -1180794104421709578, 0, -314314718927044608, 0, 0, 0, -1440235796194633800, 0, 964208051826423012, 0, 0, 0, -461738411602536768, 0, 1119002034501352512, 0, 0, 0, -170857229953143108, 0, 2159935697066332118, 0, 0, 0, -1719048067417883460, 0, -1156267735958972896, 0, 0, 0, 461668699956600600, 0, -294861386039072220, 0, 0, 0, 1094877826772342610, 0, 752082053291587048, 0, 0, 0, -1632031495073648928, 0, 824609800713212800, 0, 0, 0, 153987123440112588, 0, 672999169100108864, 0, 0, 0, 2870407295294386848, 0, -673119012967690320, 0, 0, 0, 346053446017105722, 0, -470506900675999400, 0, 0, 0, 903910736492027100, 0, 1086964595071805632, 0, 0, 0, 280939188189177276, 0, 725740000885495516, 0, 0, 0, -1121406275197779096, 0, -1414650959108111782, 0, 0, 0, 969546271744134306, 0, -1829796233650709240, 0, 0, 0, -2409174599808446652, 0, 2170365553488517452, 0, 0, 0, -2803326249295067706, 0, 1224421008710763268, 0, 0, 0, -454608805921542624, 0, -807967937676947326, 0, 0, 0, -1627166709625160832, 0, 352457653675157968, 0, 0, 0, 7816708904514924, 0, -1888987041042515290, 0, 0, 0, -86651176936532400, 0, -886570875842395248, 0, 0, 0, -424558721405158680, 0, -1363580613384763868, 0, 0, 0, -1801685947561051260, 0, -1336941758825099280, 0, 0, 0, 2813450534835945312, 0, 556568780484739358, 0, 0, 0, 640300830492124998, 0, 1076229483908641200, 0, 0, 0, 116954162135604048, 0, -1204540583152314240, 0, 0, 0, -1542961933124293350, 0, 753336191473061000, 0, 0, 0, -360478908105087732, 0, -224456519866163552, 0, 0, 0, 3123230878284992718, 0, -218912053400294948, 0, 0, 0, 1973431257311506824, 0, 722815882527358010, 0, 0, 0, 5172365878776977664, 0, -1624449945663601560, 0, 0, 0, -250019222755824060, 0, -1670180359011365376, 0, 0, 0, 1735934094138963948, 0, 4076381461722700116, 0, 0, 0, -1949902172302828368, 0, 2838361504990670978, 0, 0, 0, 1846524657829005300, 0, 662092231883995496, 0, 0, 0, 1828974942212044056, 0, -2013989688134645256, 0, 0, 0, 2196443375737298670, 0, -1491945548375084612, 0, 0, 0, 2394889566762090048, 0, 1915155187039060874, 0, 0, 0, -3468363697973798622, 0, -328788443515463048, 0, 0, 0, 2696571572922733800, 0, 5494174567888154176, 0, 0, 0, 3817563235271321622, 0, -1999038585839277312, 0, 0, 0, -2568875229617420304, 0, 2887633181986219442, 0, 0, 0, -2781203965393837548, 0, -3014048577888006408, 0, 0, 0, 3166407991330213872, 0, 350709744987512316, 0, 0, 0, 5796443129927356032, 0, -1684143866545985540, 0, 0, 0, 1083915006979224360, 0, -4564253251561147200, 0, 0, 0, 1101331546278672000, 0, 4968234235691578208, 0, 0, 0, 685773952844887200, 0, -2344139242833398180, 0, 0, 0, -523246918316531904, 0, -1320458545753748348, 0, 0, 0, -3534934728088471776, 0, -764530575967837967, 0, 0, 0, -3820274549019263718, 0, 1152705651937252632, 0, 0, 0, 462241451371824096, 0, 3824911764772361222, 0, 0, 0, -399113962132766310, 0, -914161288013158248, 0, 0, 0, 3232773121976609232, 0, -3514034732570812800, 0, 0, 0, 3146096510497479666, 0, 3074360927157587560, 0, 0, 0, 1043856971846783508, 0, -2921643236726143380, 0, 0, 0, -4610812271352405684, 0, 4843393060882229188, 0, 0, 0, -2019188610279909936, 0, -2155059595151188172, 0, 0, 0, -5959762260699945600, 0, -897753082637655376, 0, 0, 0, -405411094614422916, 0, 1234733784699398150, 0, 0, 0, -1774632809611932738, 0, 1544093769120626528, 0, 0, 0, -509975142305355576, 0, 4890241339815743162, 0, 0, 0, 2091722799228650916, 0, -1758549236607793064, 0, 0, 0, -3580766835384990000, 0, 258122103627654158, 0, 0, 0, -3008809560594903834, 0, 1790710017773952700, 0, 0, 0, -4277954856637572768, 0, 378518211997970292, 0, 0, 0, -373936655270348790, 0, 1241674262332516768, 0, 0, 0, -1192110948731661072, 0, 6450817279077642688, 0, 0, 0, 2713197284781460176, 0, -4956565685546056176, 0, 0, 0, 2250969050187477720, 0, -4346353108039006764, 0, 0, 0, 349691909009575362, 0, 2187625490478019656, 0, 0, 0, 4283912663853865380, 0, -4986631895357370418, 0, 0, 0, -1626715912641219456, 0, 1002235388995789636, 0, 0, 0, 480398658022484832, 0, 3750080995375755316, 0, 0, 0, 6757705809471782106, 0, -10333424859719969056, 0, 0, 0, 2846158050523407480, 0, 2936148805632748896, 0, 0, 0, 2837891304312320256, 0, 5590007299270324828, 0, 0, 0, -5632464208213304400, 0, -102574883987692486, 0, 0, 0, -4401733416400065102, 0, -3217834503723390728, 0, 0, 0, 1708471912511755776, 0, 947179372841759150, 0, 0, 0, -7316222315124719178, 0, -2121538411106088480, 0, 0, 0, -2056217698603200000, 0, 334136890422180881, 0, 0, 0, 2964770811509713608, 0, -2743404862168762200, 0, 0, 0, -7501167586020432708, 0, -7184295863792189600, 0, 0, 0, -3865378124832479394, 0, 2468645086637144520, 0, 0, 0, -2706412624754532072, 0, 965071874576092814, 0, 0, 0, 9690318935393538624, 0, 3032819474650859376, 0, 0, 0, 3642064531422295584, 0, -4900487271833353666, 0, 0, 0, 1128641367126598278, 0, 4568669845697447840, 0, 0, 0, -6777810296717820336, 0, 1740916077694340800, 0, 0, 0, -2451884136028568736, 0, -1604004046580622312, 0, 0, 0, 3254021198034541500, 0, -298209676047903648, 0, 0, 0, -3707857312264362600, 0, -7970892224851495604, 0, 0, 0, -2099637020433052128, 0, -3112579213416359302, 0, 0, 0, -62748428347749774, 0, 1463812688808977384, 0, 0, 0, 5585229690349053696, 0, -3792155775976173312, 0, 0, 0, -2556607298241565200, 0, 535192954161766848, 0, 0, 0, 2646882840519255000, 0, 3169061514381039408, 0, 0, 0, -4908205206796427004, 0, -3220791829103839088, 0, 0, 0, 2592603465488868720, 0, -6116252711889087476, 0, 0, 0, -3138476450614243200, 0, 5279942732048204112, 0, 0, 0, -1536843078390037080, 0, -3943960525834823158, 0, 0, 0, -1479671463825069402, 0, -8226137215712898384, 0, 0, 0, 3031935763824096132, 0, 6816712586576499180, 0, 0, 0, -3589713851276136720, 0, 543329071284646420, 0, 0, 0, 903299859205708848, 0, 6259701214413573300, 0, 0, 0, 3359446848990512250, 0, -5383280789614316672, 0, 0, 0, -6506334616700670528, 0, 446905004045592854, 0, 0, 0, 10079242947952713468, 0, 3691474777109250504, 0, 0, 0, -2668710662437240512, 0, -8150092223351947904, 0, 0, 0, 1333803023692528224, 0, 847188768762505312, 0, 0, 0, -1239967050742857900, 0, -3037434811457188500, 0, 0, 0, -3081338721808190208, 0, -3682949340174712000, 0, 0, 0, 4751578074687943392, 0, 4591987389432664418, 0, 0, 0, -1340766513894697974, 0, 9280240195586368176, 0, 0, 0, -12155314628229468600, 0, -945191452556202948, 0, 0, 0, 3072301297424469630, 0, -9416516609550783712, 0, 0, 0, 270498595129614408, 0, 5432419431004609994, 0, 0, 0, -2096615537220283662, 0, 7137134580874053944, 0, 0, 0, 3412400222852236368, 0, 1645072247116532160, 0, 0, 0, -2824627523652547818, 0, 1802705595049874592, 0, 0, 0, 11751240526436308800, 0, 7959764364701902000, 0, 0, 0, -10213958097961163862, 0, 4602339699152000416, 0, 0, 0, 6134083958408742744, 0, -6850614086041302080, 0, 0, 0, 8402243779399192926, 0, 5739830186416149340, 0, 0, 0, -2994169485176660952, 0, 6752343910465812456, 0, 0, 0, 5407142072550358644, 0, 7285396657311662728, 0, 0, 0, -89023807183943196, 0, 1986334812778411934, 0, 0, 0, -3950139055208005632, 0, 6037276435562893012, 0, 0, 0, -12765138150408196656, 0, 4967533717401603650, 0, 0, 0, -10648918291590061158, 0, 7719376243729046904, 0, 0, 0, 8742477802174965180, 0, 5854774700088714892, 0, 0, 0, 7391772761063514108, 0, 588580654445318956, 0, 0, 0, -9793433203540936008, 0, -9384925383157116502, 0, 0, 0, 8481794738862242400, 0, -14307401610479114840, 0, 0, 0, -3705659985767486880, 0, 773963588555819690, 0, 0, 0, -5505684519959490090, 0, -6626536477982477612, 0, 0, 0, 6375117133532927064, 0, -20510497790325510912, 0, 0, 0, 4463254599962277738, 0, -9073169822034009496, 0, 0, 0, 3333872101334097288, 0, 9700274686151140550, 0, 0, 0, 1025610767721816462, 0, -10369652696600490000, 0, 0, 0, 1476756052910035920, 0, 6004044342033894864, 0, 0, 0, 12617035530297542400, 0, 7034632395355929016, 0, 0, 0, -2625460297533973368, 0, 3767221970810386560, 0, 0, 0, 10850271213634638726, 0, 3530693259268217504, 0, 0, 0, 6162721305992639304, 0, 12233197209836378484, 0, 0, 0, 1245618175429363050, 0, 9213042523036976368, 0, 0, 0, -9818739273290273616, 0, 12696347761702258694, 0, 0, 0, 13325804933030518398, 0, -1032001375537107188, 0, 0, 0, 27275991929932696608, 0, -9101299518993967433, 0, 0, 0, 7344626311069896900, 0, 14120258888847686472, 0, 0, 0, 12938785174065067140, 0, -5713280005601572096, 0, 0, 0, 2770407468803418402, 0, -6726227015997191448, 0, 0, 0, 19064094462733107000, 0, -12345235460607425422, 0, 0, 0, -508136083391917974, 0, -12556073106878461776, 0, 0, 0, -6431745152806050852, 0, -4255854390170771940, 0, 0, 0, -11141947961679384192, 0, 16571838082416077308, 0, 0, 0, -121145209662710328, 0, -2848427163485392006, 0, 0, 0, -6607910601811835982, 0, -22642624090194939040, 0, 0, 0, -7490059463135474112, 0, -7463502607194108800, 0, 0, 0, -423282782934238878, 0, -19384102862364629088, 0, 0, 0, 10222045903152800640, 0, -4847860441876941968, 0, 0, 0, -6529922079011753484, 0, 11518428124968809296, 0, 0, 0, -9437652401052081780, 0, 8048840412241493856, 0, 0, 0, 12546283762866351006, 0, 8199315720578062256, 0, 0, 0, 1522886092073707848, 0, 9666543009146470272, 0, 0, 0, -7806583354261934190, 0, 7771831729925605776, 0, 0, 0, -965731503631320144, 0, -12815825551443467746, 0, 0, 0, -24724725248024985792, 0, -11353535402758843600, 0, 0, 0, -13287618358368538416, 0, -11260958122650206700, 0, 0, 0, -20415216937663410240, 0, 16793735525019527256, 0, 0, 0, 1596973749288565020, 0, 18283713317964400572, 0, 0, 0, 5041572358530100800, 0, 21816290010004488992, 0, 0, 0, -10597619811036868968, 0, -22285563625386365542, 0, 0, 0, 7914425535182500626, 0, -4750917208591516200, 0, 0, 0, -19491558272647821132, 0, 8816292108776834028, 0, 0, 0, 6362335448985826710, 0, -3224420266210609052, 0, 0, 0, -6122948875204571424, 0, 5139338122687780180, 0, 0, 0, 3053973161699574816, 0, 15121991126266430600, 0, 0, 0, 6447483431458555200, 0, 18764112713293926006, 0, 0, 0, 13334404177151962044, 0, -15655650754566366000, 0, 0, 0, 17879340898072239240, 0]}