# Stored data for newform 882.6.a.b, downloaded from the LMFDB on 13 November 2024. {"Nk2": 31752, "analytic_conductor": 141.45852907504892, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, 1], [3, 1], [7, -1]], "atkin_lehner_string": "++-", "char_conductor": 1, "char_degree": 1, "char_is_minimal": true, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [882, 1, [785, 199], [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, [54, 1]], [11, [-594, 1]]], "hecke_orbit": 2, "hecke_orbit_code": 4503599728034674, "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": "882.6.a.b", "level": 882, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 3, 7], "level_radical": 42, "minimal_twist": "126.6.a.e", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q-4q^{2}+2^{4}q^{4}-54q^{5}-2^{6}q^{8}+6^{3}q^{10}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "5.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "882.6.a", "trace_display": [-4, 0, -54, 0], "trace_hash": 422478040141857600, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.959", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.908", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.807", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.002", "prec": 17}, "traces": [0, 1, -4, 0, 16, -54, 0, 0, -64, 0, 216, 594, 0, -26, 0, 0, 256, 534, 0, 3004, -864, 0, -2376, 3510, 0, -209, 104, 0, 0, 4296, 0, -8036, -1024, 0, -2136, 0, 0, -502, -12016, 0, 3456, -9870, 0, 9068, 9504, 0, -14040, -1140, 0, 0, 836, 0, -416, 28356, 0, -32076, 0, 0, -17184, 8196, 0, -29822, 32144, 0, 4096, 1404, 0, -62884, 8544, 0, 0, -34398, 0, -56990, 2008, 0, 48064, 0, 0, 49496, -13824, 0, 39480, 52512, 0, -28836, -36272, 0, -38016, 48282, 0, 0, 56160, 0, 4560, -162216, 0, 83938, 0, 0, -3344, 62694, 0, 30988, 1664, 0, -113424, 118218, 0, 207362, 128304, 0, 0, -136416, 0, -189540, 68736, 0, -32784, 0, 0, 191785, 119288, 0, -128576, 180036, 0, -128248, -16384, 0, -5616, -370296, 0, 0, 251536, 0, -34176, 12924, 0, 177760, 0, 0, 137592, -15444, 0, -231984, 227960, 0, -8032, 309564, 0, -300136, -192256, 0, 0, 433944, 0, -11726, -197984, 0, 55296, 0, 0, -269260, -157920, 0, -210048, -41604, 0, -370617, 115344, 0, 145088, -286962, 0, 0, 152064, 0, -193128, -420186, 0, 16918, 0, 0, -224640, 27108, 0, 317196, -18240, 0, 648864, -134742, 0, -314650, -335752, 0, 0, 596628, 0, 10096, 13376, 0, -250776, 0, 0, 532980, -123952, 0, -6656, 1784376, 0, -721324, 453696, 0, -472872, -489672, 0, 0, -829448, 0, -513216, -13884, 0, 536584, 0, 0, 545664, 1486980, 0, 1109566, 758160, 0, -274944, 1387956, 0, 61560, 131136, 0, 0, 1564062, 0, -1363190, -767140, 0, -477152, 0, 0, -78104, 514304, 0, -720144, 1548468, 0, 2084940, 512992, 0, 65536, 1541466, 0, 0, 22464, 0, 1481184, -2132514, 0, -1531224, 0, 0, -1006144, -386142, 0, 1175812, 136704, 0, -51696, -124146, 0, 417038, -711040, 0, 0, -523932, 0, 2367244, -550368, 0, 61776, 0, 0, -1134701, 927936, 0, -911840, 2446302, 0, -442584, 32128, 0, -1238256, -91260, 0, 0, 1200544, 0, 769024, 1610388, 0, 969316, 0, 0, -1735776, -2447652, 0, -2025410, 46904, 0, 791936, 2503788, 0, 2551824, -221184, 0, 0, 1604136, 0, 5434, 1077040, 0, 631680, 0, 0, 1286996, 840192, 0, 166416, 3395736, 0, -1406386, 1482468, 0, -461376, -4773384, 0, 0, -580352, 0, 1147848, -1253130, 0, -1668758, 0, 0, -608256, 2136870, 0, 1857492, 772512, 0, 1680744, 3609066, 0, 6547917, -67672, 0, 0, 3077460, 0, 1881904, 898560, 0, -108432, 0, 0, 4861862, -1268784, 0, 72960, -111696, 0, 251300, -2595456, 0, 538968, 567720, 0, 0, 1258600, 0, 1343008, -2345472, 0, 1874340, 0, 0, -2386512, -2672784, 0, 5257186, -40384, 0, -53504, -2341404, 0, 208936, 1003104, 0, 0, -298188, 0, -662318, -2131920, 0, 495808, 0, 0, -2835648, 26624, 0, -7137504, -5277516, 0, 1748174, 2885296, 0, -1814784, -111606, 0, 0, 1891488, 0, 1958688, -2655750, 0, 3120262, 0, 0, 3317792, 10544040, 0, 4021312, 2052864, 0, 55536, -766146, 0, -2607228, -2146336, 0, 0, -3019608, 0, -5862780, -2182656, 0, -5947920, 0, 0, -223114, -4438264, 0, -3032640, 4580502, 0, -4236544, 1099776, 0, -5551824, 2744988, 0, 0, -246240, 0, -524544, 5386392, 0, -627836, 0, 0, -6256248, 2676276, 0, 13052, 5452760, 0, 3068560, -4532652, 0, -7929592, 1908608, 0, 0, -7105674, 0, 2294064, 312416, 0, -2057216, 0, 0, -1313524, 2880576, 0, -6193872, -3646080, 0, -3385476, -8339760, 0, -2051968, -9654102, 0, 0, -262144, 0, -6165864, -1673352, 0, -677160, 0, 0, -89856, -7678698, 0, 9065104, -5924736, 0, 8530056, -4291224, 0, 5883757, 6124896, 0, 0, 256620, 0, -6383772, 4024576, 0, 1544568, 0, 0, 7331078, -4703248, 0, -546816, -11197548, 0, -3164980, 206784, 0, 496584, 12905184, 0, 0, -1668152, 0, 2844160, -118092, 0, -235768, 0, 0, 2095728, -6435444, 0, 7366464, -9468976, 0, 2201472, 3229764, 0, -228556, -247104, 0, 0, -733590, 0, -15081698, 4538804, 0, -3711744, 0, 0, 16843464, 3647360, 0, -9785208, -8900436, 0, -24140144, 1770336, 0, -128512, -1348698, 0, 0, 4953024, 0, 365040, 11844354, 0, 9626710, 0, 0, -4802176, -10356390, 0, 641512, -3076096, 0, -6441552, 29640, 0, 3729638, -3877264, 0, 0, -11857980, 0, -2606360, 6943104, 0, 9790608, 0, 0, -9068819, 8101640, 0, -187616, -268068, 0, 5155400, -3167744, 0, -10015152, 6925392, 0, 0, -10207296, 0, 884736, 14251716, 0, 12431044, 0, 0, -6416544, -5716428, 0, 4868424, -21736, 0, -4308160, -2484792, 0, 19995984, -2526720, 0, 0, 2874810, 0, 8182738, -5147984, 0, -3360768, 0, 0, 15078960, -665664, 0, -13582944, -17714268, 0, 15218654, 5625544, 0, -5929872, 18594246, 0, 0, 1845504, 0, 19093536, -1362, 0, -697896, 0, 0, 2321408, -737256, 0, -18351464, -4591392, 0, 5012520, -9599040, 0, -5270580, 6675032, 0, 0, -10044792, 0, -1508008, 2433024, 0, -8547480, 0, 0, -2111494, -7429968, 0, -3090048, -28206360, 0, 833976, -6722976, 0, -14436264, 296016, 0, 0, -26191668, 0, 270688, -897864, 0, 90220, 0, 0, -12309840, 4842312, 0, 14066398, -7527616, 0, -3594240, -37353096, 0, 22001780, 433728, 0, 0, 9429810, 0, -16716456, -19447448, 0, 5075136, 0, 0, 5064200, -291840, 0, 446784, 16207344, 0, -9414790, -1005200, 0, 10381824, 18102546, 0, 0, -2155872, 0, -2270880, -213096, 0, -23797034, 0, 0, -5034400, 9764526, 0, 1679524, -5372032, 0, 9381888, -29649480, 0, -20432412, -7497360, 0, 0, 633204, 0, 2693008, 9546048, 0, 10691136, 0, 0, 775372, -21028744, 0, 161536, 26983398, 0, -608760, 214016, 0, 9365616, -33852060, 0, 0, -835744, 0, -4012416, 13081344, 0, -21206288, 0, 0, 1192752, 14540040, 0, 27240272, 2649272, 0, 8527680, 37623660, 0, 4755824, -1983232, 0, 0, -22616694, 0, 24489574, 11342592, 0, -106496, 0, 0, 2246616, 28550016, 0, 21110064, -31310652, 0, -2055533, -6992696, 0, -11541184, 20013318, 0, 0, 7259136, 0, 446424, -1762020, 0, 15956482, 0, 0, -7565952, -6517998, 0, 17740540, -7834752, 0, 10623000, 8574366, 0, 15495948, -12481048, 0, 0, 29400624, 0, 1634984, -13271168, 0, -42176160, 0, 0, -38355058, -16085248, 0, -8211456, -39165066, 0, 17276636, -222144, 0, 3064584, -23335092, 0, 0, 10428912, 0, 8585344, -3424560, 0, 22690044, 0, 0, 12078432, -34522656, 0, 15142104, 23451120, 0, 8730624, -913572, 0, -31644940, 23791680, 0, 0, -2295510, 0, 31192128, 892456, 0, 17753056, 0, 0, -28061152, 12130560, 0, -18322008, 894348, 0, 104918, 16946176, 0, -4399104, -6790254, 0, 0, 22207296, 0, -10979952, -17128584, 0, -38316098, 0, 0, 984960, -11686782, 0, -34643700, 2098176, 0, -21545568, 20820066, 0, 1481740, 2511344, 0, 0, -14155560, 0, 7276068, 25024992, 0, -10705104, 0, 0, 35948145, -52208, 0, -21811040, 16991100, 0, 52955792, -12274240, 0, 18130608, -10784496, 0, 0, 31718368, 0, -7634432, -47822604, 0, 28679508, 0, 0, 28422696, 29666232, 0, -32217912, -9176256, 0, -1249664, 31828680, 0, -13926328, 8228864, 0, 0, -545184, 0, 3599986, 5254096, 0, -11522304, 0, 0, 4376664, 24775488, 0, 14584320, 85181424, 0, -23400358, 13541904, 0, 33359040, -41962986, 0, 0, 8207872, 0, 38616408, 54959994, 0, 24226498, 0, 0, 1048576, 2062830, 0, -1286896, 24663456, 0, 6693408, 38343186, 0, 45100346, 2708640, 0, 0, -15924948, 0, 21346984, 359424, 0, 30714792, 0, 0, -96356304, -36260416, 0, 23698944, 35992614, 0, -4771156, -34120224, 0, 17164896, 38951496, 0, 0, -23535028, 0, -24499584, -11893152, 0, -18765236, 0, 0, -1026480, 49859172, 0, -20070230, 25535088, 0, -16098304, -2156592, 0, -1895212, -6178272, 0, 0, -1365312, 0, -4001400, -29324312, 0, 18812992, 0, 0, 69464480, 2187264, 0, 44790192, 49627608, 0, -41689450, 12659920, 0, -827136, 20731686, 0, 0, -1986336, 0, -51620736, -42985554, 0, 749736, 0, 0, 6672608, -25857666, 0, 37240236, -11376640, 0, 472368, -28975536, 0, 36620210, 943072, 0, 0, 24620784, 0, 7720168, -8382912, 0, 25741776, 0, 0, 73962890, -29465856, 0, 37875904, 18406872, 0, -80296920, -8805888, 0, -12919056, -33580056, 0, 0, 914224, 0, 988416, -59916564, 0, 4034072, 0, 0, 2934360, 51887640, 0, -78351374, 60326792, 0, -18155216, -1255332, 0, -89585288, 14846976, 0, 0, 53188626, 0, -74949624, -67373856, 0, -14589440, 0, 0, -4060204, 39140832, 0, 35601744, 238260, 0, 70221492, 96560576, 0, -7081344, 39856350, 0, 0, 514048, 0, 5394792, 36597138, 0, -42401520, 0, 0, -19812096, 21880014, 0, -84459348, -1460160, 0, -47377416, 123173028, 0, -11023138, -38506840, 0, 0, 73612260, 0, -18368532, 19208704, 0, 41425560, 0, 0, -65214994, -2566048, 0, 12304384, 34584810, 0, 99529560, 25766208, 0, -118560, -39889884, 0, 0, -14918552, 0, 15509056, -54778092, 0, 45826384, 0, 0, 47431920, 4217616, 0, -1090610, 10425440, 0, -27772416, -30432660, 0, -81031104, -39162432, 0, 0, 38956128, 0, -26463974, 36275276, 0, -32406560, 0, 0, -83617272, 750464, 0, 1072272, 42430536, 0, -2182388, -20621600, 0, 12670976, -112586760, 0, 0, 40060608, 0, -27701568, 79315320, 0, -188903536, 0, 0, 40829184, 22545678, 0, -76648736, -3538944, 0, -57006864, -2648214, 0, -83239164, -49724176, 0, 0, 26370696, 0, -35836676, 25666176, 0, 22865712, 0, 0, 69201506, -19473696, 0, 86944, 14157354, 0, 88194056, 17232640, 0, 9939168, 84486288, 0, 0, -79983936, 0, 10106880, -1630044, 0, 115155756, 0, 0, -11499240, -78009204, 0, 8706550, -32730952, 0, 20591936, -5926404, 0, 3054968, 13443072, 0, 0, 18255996, 0, -72870448, -60315840, 0, 2662656, 0, 0, -805688, 54331776, 0, 70857072, 26430864, 0, 20851668, -60874616, 0, -22502176, -103331592, 0, 0, 23719488, 0, -74376984, -63493848, 0, 28767960, 0, 0, -7382016, -57585690, 0, -4897440, -76374144, 0, 5448, 72073830, 0, -69091953, 2791584, 0, 0, 100231296, 0, 106941384, -9285632, 0, 2949024, 0, 0, -33606550, 73405856, 0, 18365568, -22520052, 0, -171197960, -20050080, 0, 38396160, -3073668, 0, 0, 21082320, 0, -26700128, -76179312, 0, 139444660, 0, 0, 40179168, -104675220, 0, 28292328, 6032032, 0, -9732096, 19005264, 0, 28041408, 34189920, 0, 0, -127831176, 0, -5391412, 8445976, 0, 29719872, 0, 0, 57281816, 12360192, 0, 112825440, 117959592, 0, -32945350, -3335904, 0, 26891904, 78606930, 0, 0, 57745056, 0, -1184064, -21405738, 0, -219955824, 0, 0, 104766672, 61273854, 0, -22212500, -1082752, 0, 3591456, -146208162, 0, 52902674, -360880, 0, 0, 9161040, 0, 134671372, 49239360, 0, -19369248, 0, 0, -132100308, -56265592, 0, 30110464, 3546816, 0, 3462920, 14376960, 0, 149412384, -1712964, 0, 0, -88007120, 0, -1734912, 118779600, 0, 48154252, 0, 0, -37719240, 112643136, 0, -60237422, 66865824, 0, 77789792, -61512396, 0, 4928040, -20300544, 0, 0, -81898266, 0, 148685984, -20256800, 0, 1167360, 0, 0, 7676856, -1787136, 0, -64829376, -152818272, 0, 25782588, 37659160, 0, 4020800, 4954740, 0, 0, -41527296, 0, -72410184, 17663598, 0, 6232798, 0, 0, 8623488, 105589440, 0, -70505120, 9083520, 0, 852384, -52343064, 0, 121817376, 95188136, 0, 0, -220722840, 0, 37149328, 20137600, 0, -39058104, 0, 0, -87271126, -6718096, 0, 21488128, -50967222, 0, 132173208, -37527552, 0, 118597920, 188063580, 0, 0, 81729648, 0, 29989440, 109372140, 0, -21057068, 0, 0, -2532816, -70453020, 0, -4986410, -10772032, 0, -38184192, 157746048, 0, -140424364, -42764544, 0, 0, 63349398, 0, -135204552, -3101488, 0, 84114976, 0, 0, -4552136, -646144, 0, -107933592, -137798496, 0, -32258638, 2435040, 0, -856064, 169148670, 0, 0, -37462464, 0, 135408240, -107597742, 0, 94964386, 0, 0, 3342976, -28472562, 0, -86623344, 16049664, 0, -52325376, -35993166, 0, 48286550, 84825152, 0, 0, -4680936, 0, 103524268, -4771008, 0, -58160160, 0, 0, -120736980, -108961088, 0, -10597088, -154599138, 0, 183881016, -34110720, 0, -150494640, -227868816, 0, 0, -19023296, 0, 7932928, 44822892, 0, 3334448, 0, 0, 90466776, -69497784, 0, 33933382, -97958296, 0, -45370368, -178280784, 0, -88608928, 425984, 0, 0, 24052062, 0, 212881942, -8986464, 0, -114200064, 0, 0, 13142756, -84440256, 0, 125242608, -200034900, 0, -18439301, 8222132, 0, 27970784, 75944844, 0, 0, 46164736, 0, -80053272, 145039128, 0, -182830142, 0, 0, -29036544, -73540146, 0, 97111048, -1785696, 0, 7048080, 9627696, 0, 257762736, -63825928, 0, 0, -117361116, 0, 35210016, 30263808, 0, 26071992, 0, 0, 33478596, -70962160, 0, 31339008, 115070406, 0, 112731596, -42492000, 0, -34297464, -6965244, 0, 0, -61983792, 0, 49924192, 156936864, 0, 67669020, 0, 0, -117602496, 572280, 0, 33031090, -6539936, 0, 53084672, 90112932, 0, -4289524, 168704640, 0, 0, 16547592, 0, -78446318, 153420232, 0, 64340992, 0, 0, 76352408, 32845824, 0, 156660264, -89501160, 0, -115390980, -69106544, 0, 888576, -128115312, 0, 0, -12258336, 0, 93340368, 7189182, 0, -45935054, 0, 0, -41715648, -336024, 0, 156939892, -34341376, 0, 13698240, -199072278, 0, -214479526, -90760176, 0, 0, -159940440, 0, -194889564, -48313728, 0, 138090624, 0, 0, -74342626, -60568416, 0, -93804480, -353587518, 0, -4621760, -34922496, 0, 3654288, -33944028, 0, 0, 126579760, 0, -95166720, 173730960, 0, 63128412, 0, 0, 9182040, 225403512, 0, 11910910, -124768512, 0, -3569824, -65863056, 0, -37269640, -71012224, 0, 0, -101622816, 0, -24712776, 112244608, 0, -48522240, 0, 0, 252149752, 73288032, 0, -3577392, -95223432, 0, -64779819, -419672, 0, -67784704, 110731308, 0, 0, 17596416, 0, 27161016, -220146498, 0, -265194302, 0, 0, -88829184, -262540548, 0, -184640192, 43919808, 0, 68514336, -14867286, 0, 110613854, 153264392, 0, 0, -160661604, 0, -201293132, -3939840, 0, 46747128, 0, 0, 6031584, 138574800, 0, -8392704, 227316978, 0, 239649592, 86182272, 0, -83280264, -13570200, 0, 0, -5926960, 0, -10045376, 102497652, 0, -170455428, 0, 0, 56622240, -204828792, 0, 184317120, -29104272, 0, -100099968, -109318572, 0, -30656880, 42820416, 0, 0, 188332776, 0, -72846144, -143792580, 0, 208832, 0, 0, 11251800, 87244160, 0, -67964400, -239649684, 0, -264465922, -211823168, 0, 49096960, -8048664, 0, 0, -72522432, 0, 43137984, -270149664, 0, 126655488, 0, 0, -126873472, 29739318, 0, -305464928, 30537728, 0, 191290416, -101214360, 0, 93087952, -114718032, 0, 0, -14234712, 0, 7803536, -113690784, 0, -118664928, 0, 0, -249590484, 128871648, 0, 36705024, 113820306, 0, -10344664, 4998656, 0, -127314720, 240457380, 0, 0, 55705312, 0, -32915456, -283888044, 0, 259329208, 0, 0, 2180736, 10049292, 0, 33566374, -14399944, 0, -21016384, 67118088, 0, -50629984, 46089216, 0, 0, -96728214, 0, 126435816, -17506656, 0, -99101952, 0, 0, 172125908, -58337280, 0, -340725696, -11282544, 0, -55433698, 93601432, 0, -54167616, -10337520, 0, 0, -133436160, 0, 167851944, 241829046, 0, -192658850, 0, 0, -32831488, 355126872, 0, 16102152, -154465632, 0, -219839976, -27162486, 0, 304876, -96905992, 0, 0, 35765172, 0, 169469820, -4194304, 0, -8251320, 0, 0, 95212082, 5147584, 0, -98653824, 102413190, 0, -147773808, -26773632, 0, -153372744, 213097944, 0, 0, -180401384, 0, -10834560, 150515736, 0, 622915448, 0, 0, 63699792, -10975008, 0, 505335824, -85387936, 0, -1437696, 179562588, 0, 116299988, -122859168, 0, 0, 112487238, 0, -185673998, 385425216, 0, 145041664, 0, 0, 284985864, -94795776, 0, -143970456, 357456984, 0, -80036748, 19084624, 0, 136480896, -94401396, 0, 0, -68659584, 0, -155805984, -18993570, 0, 111260218, 0, 0, 94140112, -244829040, 0, 7000760, 97998336, 0, 47572608, -186902100, 0, 96139224, 75060944, 0, 0, 304308636, 0, -375746756, 4105920, 0, -199436688, 0, 0, -48832858, 80280920, 0, -102140352, -46337490, 0, 32703896, 64393216, 0, 8626368, -409793664, 0, 0, 7580848, 0, 24713088, 302226336, 0, 143410500, 0, 0, 5461248, -68484432, 0, 160038970, 16005600, 0, 117297248, -168494148, 0, 354397032, -75251968, 0, 0, 1081704, 0, -279873720, -277857920, 0, -8749056, 0, 0, 6478580, -179160768, 0, -198510432, -4114392, 0, -569378160, 166757800, 0, -50639680, 5997024, 0, 0, 3308544, 0, -82926744, -217150848, 0, 19289660, 0, 0, 7945344, 276422328, 0, -52593836, 206482944, 0, 171942216, 384346266, 0, -228045407, -2998944, 0, 0, 175970664, 0, 41371884, -26690432, 0, 103430664, 0, 0, 75099362, -148960944, 0, 45506560, -10090938, 0, -197738064, -1889472, 0, 115902144, 294622380, 0, 0, -146480840, 0, -3772288, 21064584, 0, 31429516, 0, 0, -98483136, -251825004, 0, 163058832, -30880672, 0, 33531648, 7461012, 0, -52399852, -102967104, 0, 0, 316590120, 0, 14970644, -295851560, 0, 117863424, 0, 0, 457971640, -151503616, 0, -73627488, 160487172, 0, -51616546, 321187680, 0, 35223552, -158818446, 0, 0, 51676224, 0, 134320224, 257132208, 0, -381150638, 0, 0, -3656896, 12048156, 0, 226232908, -3953664, 0, 239666256, 212634816, 0, -68891962, -16136288, 0, 0, 228871596, 0, 576122140, -11737440, 0, -207550560, 0, 0, -247347108, 313405496, 0, -241307168, 63422706, 0, 370750856, 72620864, 0, 5021328, 228773376, 0, 0, 358341152, 0, -59387904, -428466456, 0, 220055940, 0, 0, -212754504, 10924836, 0, 6901416, 299798496, 0, 269495424, 242841120, 0, -148229352, 58357760, 0, 0, -455601150, 0, -299489546, 16240816, 0, -156563328, 0, 0, 229144460, -142406976, 0, -953040, 81768840, 0, -439868, -280885968, 0, -386242304, -149187234, 0, 0, 28325376, 0, -159425400, 94923840, 0, -290865168, 0, 0, -2056192, 108767880, 0, -3751244, -21579168, 0, -146388552, 540828144, 0, 50919986, 169606080, 0, 0, 262574700, 0, -19173056, 79248384, 0, -87520056, 0, 0, -410320090, 337837392, 0, 5840640, 406211526, 0, -144518904, 189509664, 0, -492692112, -252684432, 0, 0, 44092552, 0, 154027360, -704808, 0, 225591552, 0, 0, -294449040, 177707424, 0, -385256992, 73474128, 0, -76834816, -299464488, 0, -80894520, -165702240, 0, 0, -449341854, 0, -17543042, 260859976, 0, 10264192, 0, 0, -8247096, -49217536, 0, -138339240, 428197968, 0, 109741622, -398118240, 0, -103064832, -149085078, 0, 0, 474240, 0, 159559536, 87086778, 0, -397749856, 0, 0, 59674208, 318730896, 0, 383706396, -62036224, 0, 219112368, 186944514, 0, 414945180, -183305536, 0, 0, -123879456, 0, -568204184, -189727680, 0, -16870464, 0, 0, -391693018, 4362440, 0, -41701760, 181392522, 0, 31567768, 111089664, 0, 121730640, 3503292, 0, 0, 324124416, 0, 156649728, -1112369184, 0, -32325840, 0, 0, -155824512, 70930296, 0, 883266120, 105855896, 0, -145101104, 294343140, 0, -404302264, 129626240, 0, 0, 727840620, 0, 8180900, 334469088, 0, -3001856, 0, 0, 196888320, -4289088, 0, -169722144, 659082204, 0, -62786482, 8729552, 0, 82486400, -13103046, 0, 0, -50683904, 0, 450347040, -163115442, 0, 165307176, 0, 0, -160242432, 74321328, 0, -49893644, 110806272, 0, -317261280, -185125230, 0, 521321508, 755614144, 0, 0, -507274692, 0, 424370188, -163316736, 0, -90182712, 0, 0, 540256502, 306594944, 0, 14155776, -15512328, 0, 824445864, 228027456, 0, 10592856, -160272624, 0, 0, 332956656, 0, 198896704, -421986432, 0, -6476492, 0, 0, -105482784, 227941944, 0, 207419472, 143346704, 0, -102664704, 36566640, 0, -262496, -91462848, 0, 0, 78505974, 0, 142365886, -276806024, 0, 77894784, 0, 0, -478820160, -347776, 0, -56629416, 38823696, 0, 414649692, -352776224, 0, -68930560, -394106322, 0, 0, -39756672, 0, -337945152, -489515616, 0, -544643942, 0, 0, 319935744, -532051506, 0, -270425896, -40427520, 0, 6520176, 17267796, 0, 929052828, -460623024, 0, 0, 366673056, 0, 231726096, 45996960, 0, 312036816, 0, 0, 533991040, -34826200, 0, 130923808, -317722878, 0, -210571864, -82367744, 0, 23705616, -809734860, 0, 0, -12219872, 0, -53772288, 489751128, 0, 395760880, 0, 0, -73023984, -27940056, 0, -13857480, 291481792, 0, 241263360, -6261684, 0, 405981752, -10650624, 0, 0, -24707562, 0, -358384202, 3222752, 0, -217327104, 0, 0, 319273868, -283428288, 0, -105723456, -44044908, 0, -650035102, -83406672, 0, 243498464, 507855666, 0, 0, 90008704, 0, 413326368, 492360018, 0, 28608980, 0, 0, -94877952, -395878212, 0, 196293676, 297507936, 0, 253975392, -288701022, 0, 180576854, -115071840, 0, 0, -46393776, 0, -43346792, 29528064, 0, 230342760, 0, 0, -43338658, 19589760, 0, 305496576, -140860722, 0, -449402212, -21792, 0, -288295320, 170908920, 0, 0, 276367812, 0, -11166336, 120362520, 0, 18754424, 0, 0, -400925184, 620665080, 0, -512053622, -427765536, 0, 37142528, 509620008, 0, -696879936, -11796096, 0, 0, -387994152, 0, 919789992, 134426200, 0, -293623424, 0, 0, -266264272, -73462272, 0, 90080208, -143784840, 0, -9343440, 684791840, 0, 80200320, -531626958, 0, 0, -153584640, 0, 12294672, 673165350, 0, 6376968, 0, 0, -84329280, 63469218, 0, -159853520, 106800512, 0, 304717248, 12731472, 0, 398116022, -557778640, 0, 0, 140494944, 0, 394627096, -160716672, 0, 418700880, 0, 0, 385867243, -113169312, 0, -24128128, 360597648, 0, 347513976, 38928384, 0, -76021056, 603600276, 0, 0, -112165632, 0, -136759680, 28510944, 0, 915630804, 0, 0, 511324704, 929930256, 0, -530835386, 21565648, 0, -33783904, 198919104, 0, -22216536, -118879488, 0, 0, 576871254, 0, -174407256, -229127264, 0, -49440768, 0, 0, -334579108, -451301760, 0, -471838368, 12342024, 0, 230759162, 131781400, 0, 13343616, -55560558, 0, 0, -107567616, 0, -314427720, 33997080, 0, -901608544, 0, 0, -230980224, -197909478, 0, 631926360, 4736256, 0, 85622952, 213942846, 0, -570232112, 879823296, 0, 0, 814411692, 0, 207827788, -419066688, 0, -245095416, 0, 0, -1266713316, 88850000, 0, 4331008, -855233154, 0, -13951184, -14365824, 0, 584832648, -431368308, 0, 0, -211610696, 0, 1443520, -541324872, 0, 339508260, 0, 0, -36644160, -909547056, 0, -516412262, -538685488, 0, -196957440, -450150480, 0, -24846992, 77476992, 0, 0, 52138722, 0, 269333424, 528401232, 0, 225062368, 0, 0, 480623544, -120441856, 0, -14187264, -306921624, 0, -153237708, -13851680, 0, -57507840, 1303567776, 0, 0, -597649536, 0, 6851856, -38661480, 0, 200361094, 0, 0, 352028480, 380090310, 0, -229368348, 6939648, 0, -475118400, -312667410, 0, 72829692, -192617008, 0, 0, -477450612, 0, -80134040, 150876960, 0, -450572544, 0, 0, -28848716, 240949688, 0, -267463296, 698432328, 0, -35224904, -311159168, 0, 246049584, 133124448, 0, 0, -19712160, 0, 81202176, 562491300, 0, -639595116, 0, 0, 327593064, -962436420, 0], "weight": 6, "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, -4, 0, 16, -54, 0, 0, -64, 0, 216, 594, 0, -26, 0, 0, 256, 534, 0, 3004, -864, 0, -2376, 3510, 0, -209, 104, 0, 0, 4296, 0, -8036, -1024, 0, -2136, 0, 0, -502, -12016, 0, 3456, -9870, 0, 9068, 9504, 0, -14040, -1140, 0, 0, 836, 0, -416, 28356, 0, -32076, 0, 0, -17184, 8196, 0, -29822, 32144, 0, 4096, 1404, 0, -62884, 8544, 0, 0, -34398, 0, -56990, 2008, 0, 48064, 0, 0, 49496, -13824, 0, 39480, 52512, 0, -28836, -36272, 0, -38016, 48282, 0, 0, 56160, 0, 4560, -162216, 0, 83938, 0, 0, -3344, 62694, 0, 30988, 1664, 0, -113424, 118218, 0, 207362, 128304, 0, 0, -136416, 0, -189540, 68736, 0, -32784, 0, 0, 191785, 119288, 0, -128576, 180036, 0, -128248, -16384, 0, -5616, -370296, 0, 0, 251536, 0, -34176, 12924, 0, 177760, 0, 0, 137592, -15444, 0, -231984, 227960, 0, -8032, 309564, 0, -300136, -192256, 0, 0, 433944, 0, -11726, -197984, 0, 55296, 0, 0, -269260, -157920, 0, -210048, -41604, 0, -370617, 115344, 0, 145088, -286962, 0, 0, 152064, 0, -193128, -420186, 0, 16918, 0, 0, -224640, 27108, 0, 317196, -18240, 0, 648864, -134742, 0, -314650, -335752, 0, 0, 596628, 0, 10096, 13376, 0, -250776, 0, 0, 532980, -123952, 0, -6656, 1784376, 0, -721324, 453696, 0, -472872, -489672, 0, 0, -829448, 0, -513216, -13884, 0, 536584, 0, 0, 545664, 1486980, 0, 1109566, 758160, 0, -274944, 1387956, 0, 61560, 131136, 0, 0, 1564062, 0, -1363190, -767140, 0, -477152, 0, 0, -78104, 514304, 0, -720144, 1548468, 0, 2084940, 512992, 0, 65536, 1541466, 0, 0, 22464, 0, 1481184, -2132514, 0, -1531224, 0, 0, -1006144, -386142, 0, 1175812, 136704, 0, -51696, -124146, 0, 417038, -711040, 0, 0, -523932, 0, 2367244, -550368, 0, 61776, 0, 0, -1134701, 927936, 0, -911840, 2446302, 0, -442584, 32128, 0, -1238256, -91260, 0, 0, 1200544, 0, 769024, 1610388, 0, 969316, 0, 0, -1735776, -2447652, 0, -2025410, 46904, 0, 791936, 2503788, 0, 2551824, -221184, 0, 0, 1604136, 0, 5434, 1077040, 0, 631680, 0, 0, 1286996, 840192, 0, 166416, 3395736, 0, -1406386, 1482468, 0, -461376, -4773384, 0, 0, -580352, 0, 1147848, -1253130, 0, -1668758, 0, 0, -608256, 2136870, 0, 1857492, 772512, 0, 1680744, 3609066, 0, 6547917, -67672, 0, 0, 3077460, 0, 1881904, 898560, 0, -108432, 0, 0, 4861862, -1268784, 0, 72960, -111696, 0, 251300, -2595456, 0, 538968, 567720, 0, 0, 1258600, 0, 1343008, -2345472, 0, 1874340, 0, 0, -2386512, -2672784, 0, 5257186, -40384, 0, -53504, -2341404, 0, 208936, 1003104, 0, 0, -298188, 0, -662318, -2131920, 0, 495808, 0, 0, -2835648, 26624, 0, -7137504, -5277516, 0, 1748174, 2885296, 0, -1814784, -111606, 0, 0, 1891488, 0, 1958688, -2655750, 0, 3120262, 0, 0, 3317792, 10544040, 0, 4021312, 2052864, 0, 55536, -766146, 0, -2607228, -2146336, 0, 0, -3019608, 0, -5862780, -2182656, 0, -5947920, 0, 0, -223114, -4438264, 0, -3032640, 4580502, 0, -4236544, 1099776, 0, -5551824, 2744988, 0, 0, -246240, 0, -524544, 5386392, 0, -627836, 0, 0, -6256248, 2676276, 0, 13052, 5452760, 0, 3068560, -4532652, 0, -7929592, 1908608, 0, 0, -7105674, 0, 2294064, 312416, 0, -2057216, 0, 0, -1313524, 2880576, 0, -6193872, -3646080, 0, -3385476, -8339760, 0, -2051968, -9654102, 0, 0, -262144, 0, -6165864, -1673352, 0, -677160, 0, 0, -89856, -7678698, 0, 9065104, -5924736, 0, 8530056, -4291224, 0, 5883757, 6124896, 0, 0, 256620, 0, -6383772, 4024576, 0, 1544568, 0, 0, 7331078, -4703248, 0, -546816, -11197548, 0, -3164980, 206784, 0, 496584, 12905184, 0, 0, -1668152, 0, 2844160, -118092, 0, -235768, 0, 0, 2095728, -6435444, 0, 7366464, -9468976, 0, 2201472, 3229764, 0, -228556, -247104, 0, 0, -733590, 0, -15081698, 4538804, 0, -3711744, 0, 0, 16843464, 3647360, 0, -9785208, -8900436, 0, -24140144, 1770336, 0, -128512, -1348698, 0, 0, 4953024, 0, 365040, 11844354, 0, 9626710, 0, 0, -4802176, -10356390, 0, 641512, -3076096, 0, -6441552, 29640, 0, 3729638, -3877264, 0, 0, -11857980, 0, -2606360, 6943104, 0, 9790608, 0, 0, -9068819, 8101640, 0, -187616, -268068, 0, 5155400, -3167744, 0, -10015152, 6925392, 0, 0, -10207296, 0, 884736, 14251716, 0, 12431044, 0, 0, -6416544, -5716428, 0, 4868424, -21736, 0, -4308160, -2484792, 0, 19995984, -2526720, 0, 0, 2874810, 0, 8182738, -5147984, 0, -3360768, 0, 0, 15078960, -665664, 0, -13582944, -17714268, 0, 15218654, 5625544, 0, -5929872, 18594246, 0, 0, 1845504, 0, 19093536, -1362, 0, -697896, 0, 0, 2321408, -737256, 0, -18351464, -4591392, 0, 5012520, -9599040, 0, -5270580, 6675032, 0, 0, -10044792, 0, -1508008, 2433024, 0, -8547480, 0, 0, -2111494, -7429968, 0, -3090048, -28206360, 0, 833976, -6722976, 0, -14436264, 296016, 0, 0, -26191668, 0, 270688, -897864, 0, 90220, 0, 0, -12309840, 4842312, 0, 14066398, -7527616, 0, -3594240, -37353096, 0, 22001780, 433728, 0, 0, 9429810, 0, -16716456, -19447448, 0, 5075136, 0, 0, 5064200, -291840, 0, 446784, 16207344, 0, -9414790, -1005200, 0, 10381824, 18102546, 0, 0, -2155872, 0, -2270880, -213096, 0, -23797034, 0, 0, -5034400, 9764526, 0, 1679524, -5372032, 0, 9381888, -29649480, 0, -20432412, -7497360, 0, 0, 633204, 0, 2693008, 9546048, 0, 10691136, 0, 0, 775372, -21028744, 0, 161536, 26983398, 0, -608760, 214016, 0, 9365616, -33852060, 0, 0, -835744, 0, -4012416, 13081344, 0, -21206288, 0, 0, 1192752, 14540040, 0, 27240272, 2649272, 0, 8527680, 37623660, 0, 4755824, -1983232, 0, 0, -22616694, 0, 24489574, 11342592, 0, -106496, 0, 0, 2246616, 28550016, 0, 21110064, -31310652, 0, -2055533, -6992696, 0, -11541184, 20013318, 0, 0, 7259136, 0, 446424, -1762020, 0, 15956482, 0, 0, -7565952, -6517998, 0, 17740540, -7834752, 0, 10623000, 8574366, 0, 15495948, -12481048, 0, 0, 29400624, 0, 1634984, -13271168, 0, -42176160, 0, 0, -38355058, -16085248, 0, -8211456, -39165066, 0, 17276636, -222144, 0, 3064584, -23335092, 0, 0, 10428912, 0, 8585344, -3424560, 0, 22690044, 0, 0, 12078432, -34522656, 0, 15142104, 23451120, 0, 8730624, -913572, 0, -31644940, 23791680, 0, 0, -2295510, 0, 31192128, 892456, 0, 17753056, 0, 0, -28061152, 12130560, 0, -18322008, 894348, 0, 104918, 16946176, 0, -4399104, -6790254, 0, 0, 22207296, 0, -10979952, -17128584, 0, -38316098, 0, 0, 984960, -11686782, 0, -34643700, 2098176, 0, -21545568, 20820066, 0, 1481740, 2511344, 0, 0, -14155560, 0, 7276068, 25024992, 0, -10705104, 0, 0, 35948145, -52208, 0, -21811040, 16991100, 0, 52955792, -12274240, 0, 18130608, -10784496, 0, 0, 31718368, 0, -7634432, -47822604, 0, 28679508, 0, 0, 28422696, 29666232, 0, -32217912, -9176256, 0, -1249664, 31828680, 0, -13926328, 8228864, 0, 0, -545184, 0, 3599986, 5254096, 0, -11522304, 0, 0, 4376664, 24775488, 0, 14584320, 85181424, 0, -23400358, 13541904, 0, 33359040, -41962986, 0, 0, 8207872, 0, 38616408, 54959994, 0, 24226498, 0, 0, 1048576, 2062830, 0, -1286896, 24663456, 0, 6693408, 38343186, 0, 45100346, 2708640, 0, 0, -15924948, 0, 21346984, 359424, 0, 30714792, 0, 0, -96356304, -36260416, 0, 23698944, 35992614, 0, -4771156, -34120224, 0, 17164896, 38951496, 0, 0, -23535028, 0, -24499584, -11893152, 0, -18765236, 0, 0, -1026480, 49859172, 0, -20070230, 25535088, 0, -16098304, -2156592, 0, -1895212, -6178272, 0, 0, -1365312, 0, -4001400, -29324312, 0, 18812992, 0, 0, 69464480, 2187264, 0, 44790192, 49627608, 0, -41689450, 12659920, 0, -827136, 20731686, 0, 0, -1986336, 0, -51620736, -42985554, 0, 749736, 0, 0, 6672608, -25857666, 0, 37240236, -11376640, 0, 472368, -28975536, 0, 36620210, 943072, 0, 0, 24620784, 0, 7720168, -8382912, 0, 25741776, 0, 0, 73962890, -29465856, 0, 37875904, 18406872, 0, -80296920, -8805888, 0, -12919056, -33580056, 0, 0, 914224, 0, 988416, -59916564, 0, 4034072, 0, 0, 2934360, 51887640, 0, -78351374, 60326792, 0, -18155216, -1255332, 0, -89585288, 14846976, 0, 0, 53188626, 0, -74949624, -67373856, 0, -14589440, 0, 0, -4060204, 39140832, 0, 35601744, 238260, 0, 70221492, 96560576, 0, -7081344, 39856350, 0, 0, 514048, 0, 5394792, 36597138, 0, -42401520, 0, 0, -19812096, 21880014, 0, -84459348, -1460160, 0, -47377416, 123173028, 0, -11023138, -38506840, 0, 0, 73612260, 0, -18368532, 19208704, 0, 41425560, 0, 0, -65214994, -2566048, 0, 12304384, 34584810, 0, 99529560, 25766208, 0, -118560, -39889884, 0, 0, -14918552, 0, 15509056, -54778092, 0, 45826384, 0, 0, 47431920, 4217616, 0, -1090610, 10425440, 0, -27772416, -30432660, 0, -81031104, -39162432, 0, 0, 38956128, 0, -26463974, 36275276, 0, -32406560, 0, 0, -83617272, 750464, 0, 1072272, 42430536, 0, -2182388, -20621600, 0, 12670976, -112586760, 0, 0, 40060608, 0, -27701568, 79315320, 0, -188903536, 0, 0, 40829184, 22545678, 0, -76648736, -3538944, 0, -57006864, -2648214, 0, -83239164, -49724176, 0, 0, 26370696, 0, -35836676, 25666176, 0, 22865712, 0, 0, 69201506, -19473696, 0, 86944, 14157354, 0, 88194056, 17232640, 0, 9939168, 84486288, 0, 0, -79983936, 0, 10106880, -1630044, 0, 115155756, 0, 0, -11499240, -78009204, 0, 8706550, -32730952, 0, 20591936, -5926404, 0, 3054968, 13443072, 0, 0, 18255996, 0, -72870448, -60315840, 0, 2662656, 0, 0, -805688, 54331776, 0, 70857072, 26430864, 0, 20851668, -60874616, 0, -22502176, -103331592, 0, 0, 23719488, 0, -74376984, -63493848, 0, 28767960, 0, 0, -7382016, -57585690, 0, -4897440, -76374144, 0, 5448, 72073830, 0, -69091953, 2791584, 0, 0, 100231296, 0, 106941384, -9285632, 0, 2949024, 0, 0, -33606550, 73405856, 0, 18365568, -22520052, 0, -171197960, -20050080, 0, 38396160, -3073668, 0, 0, 21082320, 0, -26700128, -76179312, 0, 139444660, 0, 0, 40179168, -104675220, 0, 28292328, 6032032, 0, -9732096, 19005264, 0, 28041408, 34189920, 0, 0, -127831176, 0, -5391412, 8445976, 0, 29719872, 0, 0, 57281816, 12360192, 0, 112825440, 117959592, 0, -32945350, -3335904, 0, 26891904, 78606930, 0, 0, 57745056, 0, -1184064, -21405738, 0, -219955824, 0, 0, 104766672, 61273854, 0, -22212500, -1082752, 0, 3591456, -146208162, 0, 52902674, -360880, 0, 0, 9161040, 0, 134671372, 49239360, 0, -19369248, 0, 0, -132100308, -56265592, 0, 30110464, 3546816, 0, 3462920, 14376960, 0, 149412384, -1712964, 0, 0, -88007120, 0, -1734912, 118779600, 0, 48154252, 0, 0, -37719240, 112643136, 0, -60237422, 66865824, 0, 77789792, -61512396, 0, 4928040, -20300544, 0, 0, -81898266, 0, 148685984, -20256800, 0, 1167360, 0, 0, 7676856, -1787136, 0, -64829376, -152818272, 0, 25782588, 37659160, 0, 4020800, 4954740, 0, 0, -41527296, 0, -72410184, 17663598, 0, 6232798, 0, 0, 8623488, 105589440, 0, -70505120, 9083520, 0, 852384, -52343064, 0, 121817376, 95188136, 0, 0, -220722840, 0, 37149328, 20137600, 0, -39058104, 0, 0, -87271126, -6718096, 0, 21488128, -50967222, 0, 132173208, -37527552, 0, 118597920, 188063580, 0, 0, 81729648, 0, 29989440, 109372140, 0, -21057068, 0, 0, -2532816, -70453020, 0, -4986410, -10772032, 0, -38184192, 157746048, 0, -140424364, -42764544, 0, 0, 63349398, 0, -135204552, -3101488, 0, 84114976, 0, 0, -4552136, -646144, 0, -107933592, -137798496, 0, -32258638, 2435040, 0, -856064, 169148670, 0, 0, -37462464, 0, 135408240, -107597742, 0, 94964386, 0, 0, 3342976, -28472562, 0, -86623344, 16049664, 0, -52325376, -35993166, 0, 48286550, 84825152, 0, 0, -4680936, 0, 103524268, -4771008, 0, -58160160, 0, 0, -120736980, -108961088, 0, -10597088, -154599138, 0, 183881016, -34110720, 0, -150494640, -227868816, 0, 0, -19023296, 0, 7932928, 44822892, 0, 3334448, 0, 0, 90466776, -69497784, 0, 33933382, -97958296, 0, -45370368, -178280784, 0, -88608928, 425984, 0, 0, 24052062, 0, 212881942, -8986464, 0, -114200064, 0, 0, 13142756, -84440256, 0, 125242608, -200034900, 0, -18439301, 8222132, 0, 27970784, 75944844, 0, 0, 46164736, 0, -80053272, 145039128, 0, -182830142, 0, 0, -29036544, -73540146, 0, 97111048, -1785696, 0, 7048080, 9627696, 0, 257762736, -63825928, 0, 0, -117361116, 0, 35210016, 30263808, 0, 26071992, 0, 0, 33478596, -70962160, 0, 31339008, 115070406, 0, 112731596, -42492000, 0, -34297464, -6965244, 0, 0, -61983792, 0, 49924192, 156936864, 0, 67669020, 0, 0, -117602496, 572280, 0, 33031090, -6539936, 0, 53084672, 90112932, 0, -4289524, 168704640, 0, 0, 16547592, 0, -78446318, 153420232, 0, 64340992, 0, 0, 76352408, 32845824, 0, 156660264, -89501160, 0, -115390980, -69106544, 0, 888576, -128115312, 0, 0, -12258336, 0, 93340368, 7189182, 0, -45935054, 0, 0, -41715648, -336024, 0, 156939892, -34341376, 0, 13698240, -199072278, 0, -214479526, -90760176, 0, 0, -159940440, 0, -194889564, -48313728, 0, 138090624, 0, 0, -74342626, -60568416, 0, -93804480, -353587518, 0, -4621760, -34922496, 0, 3654288, -33944028, 0, 0, 126579760, 0, -95166720, 173730960, 0, 63128412, 0, 0, 9182040, 225403512, 0, 11910910, -124768512, 0, -3569824, -65863056, 0, -37269640, -71012224, 0, 0, -101622816, 0, -24712776, 112244608, 0, -48522240, 0, 0, 252149752, 73288032, 0, -3577392, -95223432, 0, -64779819, -419672, 0, -67784704, 110731308, 0, 0, 17596416, 0, 27161016, -220146498, 0, -265194302, 0, 0, -88829184, -262540548, 0, -184640192, 43919808, 0, 68514336, -14867286, 0, 110613854, 153264392, 0, 0, -160661604, 0, -201293132, -3939840, 0, 46747128, 0, 0, 6031584, 138574800, 0, -8392704, 227316978, 0, 239649592, 86182272, 0, -83280264, -13570200, 0, 0, -5926960, 0, -10045376, 102497652, 0, -170455428, 0, 0, 56622240, -204828792, 0, 184317120, -29104272, 0, -100099968, -109318572, 0, -30656880, 42820416, 0, 0, 188332776, 0, -72846144, -143792580, 0, 208832, 0, 0, 11251800, 87244160, 0, -67964400, -239649684, 0, -264465922, -211823168, 0, 49096960, -8048664, 0, 0, -72522432, 0, 43137984, -270149664, 0, 126655488, 0, 0, -126873472, 29739318, 0, -305464928, 30537728, 0, 191290416, -101214360, 0, 93087952, -114718032, 0, 0, -14234712, 0, 7803536, -113690784, 0, -118664928, 0, 0, -249590484, 128871648, 0, 36705024, 113820306, 0, -10344664, 4998656, 0, -127314720, 240457380, 0, 0, 55705312, 0, -32915456, -283888044, 0, 259329208, 0, 0, 2180736, 10049292, 0, 33566374, -14399944, 0, -21016384, 67118088, 0, -50629984, 46089216, 0, 0, -96728214, 0, 126435816, -17506656, 0, -99101952, 0, 0, 172125908, -58337280, 0, -340725696, -11282544, 0, -55433698, 93601432, 0, -54167616, -10337520, 0, 0, -133436160, 0, 167851944, 241829046, 0, -192658850, 0, 0, -32831488, 355126872, 0, 16102152, -154465632, 0, -219839976, -27162486, 0, 304876, -96905992, 0, 0, 35765172, 0, 169469820, -4194304, 0, -8251320, 0, 0, 95212082, 5147584, 0, -98653824, 102413190, 0, -147773808, -26773632, 0, -153372744, 213097944, 0, 0, -180401384, 0, -10834560, 150515736, 0, 622915448, 0, 0, 63699792, -10975008, 0, 505335824, -85387936, 0, -1437696, 179562588, 0, 116299988, -122859168, 0, 0, 112487238, 0, -185673998, 385425216, 0, 145041664, 0, 0, 284985864, -94795776, 0, -143970456, 357456984, 0, -80036748, 19084624, 0, 136480896, -94401396, 0, 0, -68659584, 0, -155805984, -18993570, 0, 111260218, 0, 0, 94140112, -244829040, 0, 7000760, 97998336, 0, 47572608, -186902100, 0, 96139224, 75060944, 0, 0, 304308636, 0, -375746756, 4105920, 0, -199436688, 0, 0, -48832858, 80280920, 0, -102140352, -46337490, 0, 32703896, 64393216, 0, 8626368, -409793664, 0, 0, 7580848, 0, 24713088, 302226336, 0, 143410500, 0, 0, 5461248, -68484432, 0, 160038970, 16005600, 0, 117297248, -168494148, 0, 354397032, -75251968, 0, 0, 1081704, 0, -279873720, -277857920, 0, -8749056, 0, 0, 6478580, -179160768, 0, -198510432, -4114392, 0, -569378160, 166757800, 0, -50639680, 5997024, 0, 0, 3308544, 0, -82926744, -217150848, 0, 19289660, 0, 0, 7945344, 276422328, 0, -52593836, 206482944, 0, 171942216, 384346266, 0, -228045407, -2998944, 0, 0, 175970664, 0, 41371884, -26690432, 0, 103430664, 0, 0, 75099362, -148960944, 0, 45506560, -10090938, 0, -197738064, -1889472, 0, 115902144, 294622380, 0, 0, -146480840, 0, -3772288, 21064584, 0, 31429516, 0, 0, -98483136, -251825004, 0, 163058832, -30880672, 0, 33531648, 7461012, 0, -52399852, -102967104, 0, 0, 316590120, 0, 14970644, -295851560, 0, 117863424, 0, 0, 457971640, -151503616, 0, -73627488, 160487172, 0, -51616546, 321187680, 0, 35223552, -158818446, 0, 0, 51676224, 0, 134320224, 257132208, 0, -381150638, 0, 0, -3656896, 12048156, 0, 226232908, -3953664, 0, 239666256, 212634816, 0, -68891962, -16136288, 0, 0, 228871596, 0, 576122140, -11737440, 0, -207550560, 0, 0, -247347108, 313405496, 0, -241307168, 63422706, 0, 370750856, 72620864, 0, 5021328, 228773376, 0, 0, 358341152, 0, -59387904, -428466456, 0, 220055940, 0, 0, -212754504, 10924836, 0, 6901416, 299798496, 0, 269495424, 242841120, 0, -148229352, 58357760, 0, 0, -455601150, 0, -299489546, 16240816, 0, -156563328, 0, 0, 229144460, -142406976, 0, -953040, 81768840, 0, -439868, -280885968, 0, -386242304, -149187234, 0, 0, 28325376, 0, -159425400, 94923840, 0, -290865168, 0, 0, -2056192, 108767880, 0, -3751244, -21579168, 0, -146388552, 540828144, 0, 50919986, 169606080, 0, 0, 262574700, 0, -19173056, 79248384, 0, -87520056, 0, 0, -410320090, 337837392, 0, 5840640, 406211526, 0, -144518904, 189509664, 0, -492692112, -252684432, 0, 0, 44092552, 0, 154027360, -704808, 0, 225591552, 0, 0, -294449040, 177707424, 0, -385256992, 73474128, 0, -76834816, -299464488, 0, -80894520, -165702240, 0, 0, -449341854, 0, -17543042, 260859976, 0, 10264192, 0, 0, -8247096, -49217536, 0, -138339240, 428197968, 0, 109741622, -398118240, 0, -103064832, -149085078, 0, 0, 474240, 0, 159559536, 87086778, 0, -397749856, 0, 0, 59674208, 318730896, 0, 383706396, -62036224, 0, 219112368, 186944514, 0, 414945180, -183305536, 0, 0, -123879456, 0, -568204184, -189727680, 0, -16870464, 0, 0, -391693018, 4362440, 0, -41701760, 181392522, 0, 31567768, 111089664, 0, 121730640, 3503292, 0, 0, 324124416, 0, 156649728, -1112369184, 0, -32325840, 0, 0, -155824512, 70930296, 0, 883266120, 105855896, 0, -145101104, 294343140, 0, -404302264, 129626240, 0, 0, 727840620, 0, 8180900, 334469088, 0, -3001856, 0, 0, 196888320, -4289088, 0, -169722144, 659082204, 0, -62786482, 8729552, 0, 82486400, -13103046, 0, 0, -50683904, 0, 450347040, -163115442, 0, 165307176, 0, 0, -160242432, 74321328, 0, -49893644, 110806272, 0, -317261280, -185125230, 0, 521321508, 755614144, 0, 0, -507274692, 0, 424370188, -163316736, 0, -90182712, 0, 0, 540256502, 306594944, 0, 14155776, -15512328, 0, 824445864, 228027456, 0, 10592856, -160272624, 0, 0, 332956656, 0, 198896704, -421986432, 0, -6476492, 0, 0, -105482784, 227941944, 0, 207419472, 143346704, 0, -102664704, 36566640, 0, -262496, -91462848, 0, 0, 78505974, 0, 142365886, -276806024, 0, 77894784, 0, 0, -478820160, -347776, 0, -56629416, 38823696, 0, 414649692, -352776224, 0, -68930560, -394106322, 0, 0, -39756672, 0, -337945152, -489515616, 0, -544643942, 0, 0, 319935744, -532051506, 0, -270425896, -40427520, 0, 6520176, 17267796, 0, 929052828, -460623024, 0, 0, 366673056, 0, 231726096, 45996960, 0, 312036816, 0, 0, 533991040, -34826200, 0, 130923808, -317722878, 0, -210571864, -82367744, 0, 23705616, -809734860, 0, 0, -12219872, 0, -53772288, 489751128, 0, 395760880, 0, 0, -73023984, -27940056, 0, -13857480, 291481792, 0, 241263360, -6261684, 0, 405981752, -10650624, 0, 0, -24707562, 0, -358384202, 3222752, 0, -217327104, 0, 0, 319273868, -283428288, 0, -105723456, -44044908, 0, -650035102, -83406672, 0, 243498464, 507855666, 0, 0, 90008704, 0, 413326368, 492360018, 0, 28608980, 0, 0, -94877952, -395878212, 0, 196293676, 297507936, 0, 253975392, -288701022, 0, 180576854, -115071840, 0, 0, -46393776, 0, -43346792, 29528064, 0, 230342760, 0, 0, -43338658, 19589760, 0, 305496576, -140860722, 0, -449402212, -21792, 0, -288295320, 170908920, 0, 0, 276367812, 0, -11166336, 120362520, 0, 18754424, 0, 0, -400925184, 620665080, 0, -512053622, -427765536, 0, 37142528, 509620008, 0, -696879936, -11796096, 0, 0, -387994152, 0, 919789992, 134426200, 0, -293623424, 0, 0, -266264272, -73462272, 0, 90080208, -143784840, 0, -9343440, 684791840, 0, 80200320, -531626958, 0, 0, -153584640, 0, 12294672, 673165350, 0, 6376968, 0, 0, -84329280, 63469218, 0, -159853520, 106800512, 0, 304717248, 12731472, 0, 398116022, -557778640, 0, 0, 140494944, 0, 394627096, -160716672, 0, 418700880, 0, 0, 385867243, -113169312, 0, -24128128, 360597648, 0, 347513976, 38928384, 0, -76021056, 603600276, 0, 0, -112165632, 0, -136759680, 28510944, 0, 915630804, 0, 0, 511324704, 929930256, 0, -530835386, 21565648, 0, -33783904, 198919104, 0, -22216536, -118879488, 0, 0, 576871254, 0, -174407256, -229127264, 0, -49440768, 0, 0, -334579108, -451301760, 0, -471838368, 12342024, 0, 230759162, 131781400, 0, 13343616, -55560558, 0, 0, -107567616, 0, -314427720, 33997080, 0, -901608544, 0, 0, -230980224, -197909478, 0, 631926360, 4736256, 0, 85622952, 213942846, 0, -570232112, 879823296, 0, 0, 814411692, 0, 207827788, -419066688, 0, -245095416, 0, 0, -1266713316, 88850000, 0, 4331008, -855233154, 0, -13951184, -14365824, 0, 584832648, -431368308, 0, 0, -211610696, 0, 1443520, -541324872, 0, 339508260, 0, 0, -36644160, -909547056, 0, -516412262, -538685488, 0, -196957440, -450150480, 0, -24846992, 77476992, 0, 0, 52138722, 0, 269333424, 528401232, 0, 225062368, 0, 0, 480623544, -120441856, 0, -14187264, -306921624, 0, -153237708, -13851680, 0, -57507840, 1303567776, 0, 0, -597649536, 0, 6851856, -38661480, 0, 200361094, 0, 0, 352028480, 380090310, 0, -229368348, 6939648, 0, -475118400, -312667410, 0, 72829692, -192617008, 0, 0, -477450612, 0, -80134040, 150876960, 0, -450572544, 0, 0, -28848716, 240949688, 0, -267463296, 698432328, 0, -35224904, -311159168, 0, 246049584, 133124448, 0, 0, -19712160, 0, 81202176, 562491300, 0, -639595116, 0, 0, 327593064, -962436420, 0]}