-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '280748055062261144256829011522,611383529460203938529778578156,758347513009188164258740024377,765250997800956994707848705590,823846431983332137676234200864,1039274089804474093597857958789,1238562937903969951409626009350,1282837818040009240024855286894,1348181407903278300455154912266,1464657975284444413722897173919,1552420608577567086111406342419,1582368877998921861138644373484,2138559125594666019317156994573,2223480502397513415698859164048,2243741668027487750906381097292,2557021278110435340059260559549', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3418.1716943061765, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1]], [7, [1]], [17, [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1', 'coefficient_field': '1.1.1.1', 'conductor': 230823426529176822657882149835550112280127458568963096576, 'conductor_radical': 238, 'degree': 32, 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 1], [1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 16, 128, 688, 2808, 9296, 25984, 62960, 134684, 257744, 445568, 700912, 1008840, 1334032, 1625472, 1828656, 1901638, 1828656, 1625472, 1334032, 1008840, 700912, 445568, 257744, 134684, 62960, 25984, 9296, 2808, 688, 128, 16, 1], [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 12, 0, 0, 0, 14, 0, 0, 0, 12, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, -8, 36, -112, 266, -504, 784, -1016, 1106, -1008, 748, -392, 0, 392, -748, 1008, -1105, 1008, -748, 392, 0, -392, 748, -1008, 1106, -1016, 784, -504, 266, -112, 36, -8, 1], [1, -16, 120, -560, 1820, -4368, 8008, -11440, 12872, -11472, 8248, -5488, 5460, -9296, 16136, -22896, 25742, -22896, 16136, -9296, 5460, -5488, 8248, -11472, 12872, -11440, 8008, -4368, 1820, -560, 120, -16, 1], [1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, -4, 0, 0, 0, 10, 0, 0, 0, -16, 0, 0, 0, 19, 0, 0, 0, -16, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, 0, 1], [1, 0, -4, 0, 8, 0, -8, 0, 2, 0, 4, 0, 0, 0, -12, 0, 19, 0, -12, 0, 0, 0, 4, 0, 2, 0, -8, 0, 8, 0, -4, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1], [1, -8, 36, -112, 266, -504, 784, -1016, 1106, -1008, 748, -392, 0, 392, -748, 1008, -1105, 1008, -748, 392, 0, -392, 748, -1008, 1106, -1016, 784, -504, 266, -112, 36, -8, 1], [1, 0, -8, 0, 36, 0, -112, 0, 266, 0, -504, 0, 784, 0, -1016, 0, 1107, 0, -1016, 0, 784, 0, -504, 0, 266, 0, -112, 0, 36, 0, -8, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, -4, 0, 0, 0, 10, 0, 0, 0, -16, 0, 0, 0, 19, 0, 0, 0, -16, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 12, 0, 0, 0, 14, 0, 0, 0, 12, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 1], [1, 16, 136, 800, 3620, 13328, 41328, 110448, 258570, 536640, 996216, 1665456, 2520336, 3465840, 4343160, 4969152, 5196627, 4969152, 4343160, 3465840, 2520336, 1665456, 996216, 536640, 258570, 110448, 41328, 13328, 3620, 800, 136, 16, 1], [1, 0, -8, 0, 36, 0, -112, 0, 266, 0, -504, 0, 784, 0, -1016, 0, 1107, 0, -1016, 0, 784, 0, -504, 0, 266, 0, -112, 0, 36, 0, -8, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, -4, 0, 10, 0, -16, 0, 18, 0, -12, 0, 0, 0, 12, 0, -17, 0, 12, 0, 0, 0, -12, 0, 18, 0, -16, 0, 10, 0, -4, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 12, 0, 0, 0, 14, 0, 0, 0, 12, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 1]], 'euler_factors_factorization': [[[[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 2], [[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [1], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 1], 16], [[1, 0, 1], 8]], [[[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], 2]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1], 4], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 2]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, -1, 1], 8], [[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, -1], 16], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 2]], [[[1, 0, 0, 0, 0, 0, 0, 0, 1], 4]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 4]], [[[1, 0, -1, 0, 1], 4], [[1, 0, 0, 0, -1, 0, 0, 0, 1], 2]], [[[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], 2]], [[[1, -1, 1], 8], [[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, -1, 0, 1], 8]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 2]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 2], [[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 0, 0, 0, 0, 1], 4]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 4]], [[[1, 0, 0, 0, 1], 4], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 2]], [[[1, 1, 1], 16]], [[[1, 0, -1, 0, 1], 8]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, -1, 0, 1], 4], [[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1], 4], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '32-3332e16-1.1-c0e16-0-1', 'leading_term': '0.5833902542525506210380314535988459541632455393989629532950838784789910150519714504955089', 'load_key': 'CMFs-workshop', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/ce/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.003662109375', 'prec': 47}, 'plot_values': [0.5833902542525505, 0.5838400840973377, 0.5839790128403708, 0.5838163799491464, 0.5833615664766426, 0.5826239155706553, 0.581612653112913, 0.5803368084238988, 0.5788051349092785, 0.5770260304620255, 0.5750074573705857, 0.5727568614173647, 0.5702810897829821, 0.5675863072997015, 0.5646779072246823, 0.5615584361364698, 0.5582242853969996, 0.5546690025858263, 0.5508803278200064, 0.5468443848811014, 0.5425470683683588, 0.5379740789043737, 0.533110961226683, 0.527943145371625, 0.5224559911471133, 0.5166348360799606, 0.5104650470108935, 0.5039320754961653, 0.49702151730837524, 0.4897191733489105, 0.48201100939402675, 0.4738831041899468, 0.4653216869072505, 0.45631334093472886, 0.4468454947197348, 0.4369059478235853, 0.42648275460033785, 0.4155642748112071, 0.4041392272030892, 0.3921967460969832, 0.37972644102151415, 0.3667184594149405, 0.3531635473078652, 0.33905294709015155, 0.3243785257591395, 0.3091331611769662, 0.2933108564151717, 0.276906838354561, 0.2599176591952092, 0.24234122941470995, 0.22417675545552976, 0.2054251436459123, 0.186089199804578, 0.1661737476292045, 0.14568574726602368, 0.1246344133896701, 0.10303132840993565, 0.08089048394073783, 0.058228377533654625, 0.035064171503369386, 0.011419792378324994, -0.01267997797319116, -0.03720741828925852, -0.062131792049557134, -0.08741928096440706, -0.11303292146651871, -0.13893252447303225, -0.16507464363730434, -0.19141256332714018, -0.21789629851439368, -0.24447260167396348, -0.2710848962123366, -0.2976734055248339, -0.32417532336916677, -0.35052492376702526, -0.37665369346411576, -0.40249048936652876, -0.4279617219023197, -0.4529915651423271, -0.4775021943812038, -0.5014140517277323, -0.5246461053465765, -0.5471160575380113, -0.5687407839856055, -0.5894367795734248, -0.6091207981352076, -0.6277102614640103, -0.6451236473562713, -0.6612809778199543, -0.6761043285791748, -0.6895183572060706, -0.701450847288686, -0.7118332656961889, -0.720601329651564, -0.7276955799701799, -0.7330619564738696, -0.7366523712483084, -0.7384252597334046, -0.7383462144766596, -0.7363890897848154, -0.7325361773252608, -0.72677850184374, -0.7191162508441601, -0.7095591610108565, -0.6981268552861112, -0.6848491245635191, -0.6697661480236183, -0.6529286462705306, -0.6343979616317728, -0.614246060262307, -0.5925554510519967, -0.5694190168351999, -0.544939993150978, -0.5192321423357543, -0.49241863614096104, -0.4646313041168316, -0.4360099445136813, -0.4067015363377459, -0.3768593537831038, -0.346641985869199, -0.31621226530303426, -0.2857361118237131, -0.2553812965645244, -0.22531613527246488, -0.19570811954397493, -0.1667224976088896, -0.1385210228005742, -0.11126063654760582, -0.08509145446967077, -0.060155191955557664, -0.03658368564657208, -0.014497448778962368, 0.0059957025364834405, 0.024801939753314208, 0.04184261212779097, 0.05705531748668216, 0.07039483437803624, 0.0818338968262293, 0.09136379353986891, 0.09899477383916767, 0.10475623238897429, 0.10869675076760743, 0.11088390354991881, 0.11140372169863225, 0.11035989155895064, 0.10787269468174293, 0.10407768988798635, 0.09912410803872122, 0.09317299781234516, 0.08639512812110631, 0.07896865641363604, 0.07107658001449353, 0.06290399171793493, 0.054635167728683355, 0.046450580026506906, 0.038523713873296415, 0.03101772817587589, 0.02408217069593911, 0.017849719929155055, 0.012432997478855916, 0.007921501404386466, 0.004378713071493295, 0.00183943027645636, 0.00030738063231434444, -0.00024682670843281915, 0.00011263908752559185, 0.0012856095297752825, 0.003135182091811627, 0.005487501867643333, 0.008132137918105516, 0.010823106177579991, 0.01328053319104388, 0.01519298501975547, 0.016220474086038283, 0.01599814753718715, 0.01414065104557795, 0.010247151686127944, 0.003906992993194027, -0.0052940605517498495, -0.017767045974570825, -0.03391254254081379, -0.05411298649024945, -0.07872448274366134, -0.10806853312249233, -0.14242374037108185, -0.18201745643508796, -0.22701755962855175, -0.27752449304605914, -0.3335637011960559, -0.39507860555302254, -0.4619242616253826, -0.5338618400544747, -0.6105540720575033, -0.6915618497706085, -0.7763422219678311, -0.8642473911211888, -0.9545249283808527, -1.046320263064169, -1.138680717112939, -1.230561070875423, -1.3208308513590534, -1.4082833524405018, -1.491646370978713, -1.5695946160532879, -1.6407637206931662, -1.7037657568189075, -1.757206125082194, -1.79970166226788, -1.8298997803754085, -1.8464987978814087, -1.8482698642260011, -1.834077143457709, -1.8028983377870553, -1.7538451959058612, -1.686183376219247, -1.5993513325734259, -1.4929778846159498, -1.3668981344119893, -1.2211673956875195, -1.0560728123428154, -0.8721423588719085, -0.6701509371513709, -0.45112331335443967, -0.21633466931317047, 0.03269156236189904, 0.2941936193559059, 0.5661839758346876, 0.8464653887084157, 1.1326504816046055, 1.4221850185046099, 1.7123747318211704, 2.0004154777686365, 2.283426425994678, 2.5584859254460373, 2.822669625462448, 3.073090371303203, 3.3069393268962637, 3.5215267133459256, 3.7143231757744957, 3.883003258164245, 4.0254855843375825, 4.139971397316411, 4.224981922018419, 4.279388139159118, 4.302437251060973, 4.293774878812138, 4.253461768710926, 4.181984471597297, 4.08025953364409, 3.9496308245229845, 3.7918597320238816, 3.609108289276294, 3.403915113604246, 3.1791634739095658, 2.938042215282159, 2.6839999698011474, 2.4206931498780917, 2.1519290161133355, 1.881604950723041, 1.613639659946242, 1.3519032199912104, 1.1001461817036637, 0.8619282592142548, 0.6405479173838193, 0.4389742401622038, 0.25978258339474886, 0.10509476341807072, -0.02347422673789784, -0.12486125213103155, -0.19859086627427158, -0.2448007716386522, -0.2642558690171766, -0.2583500177834146, -0.229094788428789, -0.17909481583169382, -0.11150964278479165, -0.03000158125372091, 0.061329808789761346, 0.15802590165127695, 0.25535872936731796, 0.34843206426757795, 0.43229166099851263, 0.5020424433146996, 0.5529708344425485, 0.5806699013919737, 0.5811647616016287, 0.5510355192351344, 0.4875348598388049, 0.38869734184976873, 0.25343741789125485, 0.08163307857701317, -0.12580817208377684, -0.36690294398629625, -0.6385664404069946, -0.9366139861040322, -1.255789489206291, -1.5898212125312807, -1.931506399801189, -2.2728250712896356, -2.605082678918233, -2.919080642536045, -3.205313082268389, -3.4541873265596297, -3.6562650232893525, -3.8025199247230166, -3.8846088669029624, -3.895152242250437, -3.8280076733086688, -3.67854076032944, -3.443881934878482, -3.123161128342316, -2.7177126811856307, -2.2312421670178, -1.6699467171715776, -1.042580490710997, -0.36045715225281794, 0.3626183954112973, 1.1104962184831342, 1.8649119572481612, 2.605807371218906, 3.3117453638877614, 3.9604226016378052, 4.5292825236728484, 4.996231932253371, 5.340451772186958, 5.5433006995983725, 5.5893066531961315, 5.467238794219343, 5.171250116533232, 4.70207895396844, 4.068295560976375, 3.2875779498650033, 2.387999269562552, 1.409307245485131, 0.40417467950331837, -0.5606028816467921, -1.4029857729127102, -2.024665073938486, -2.310160350397704, -2.1260854263263385, -1.320583781065776, 0.27703903365821964, 2.856460206433723, 6.626240029383952, 11.813458014252156, 18.663067268225127, 27.43695235571383, 38.41267902448591, 51.881931217026754, 68.14863711753372, 87.52677433371312, 110.33786117518628, 136.908144211479, 167.56547645313307, 202.6358662363189, 242.4398796597506, 287.28881298710087, 337.4806668968272, 393.2959757464681, 454.9935342256305, 522.8060676334945, 596.9359020498242, 677.550874451468, 764.7803013607959, 858.710862573014, 959.3828280661459, 1066.7865684820854, 1180.8593971017606, 1301.4827984305011, 1428.4800658311647, 1561.6143764774126, 1700.5876018258032, 1845.0396337835887, 1994.5482944124699, 2148.629890267562, 2306.740508853917, 2468.2790704605486, 2632.590045390386, 2798.9660575110893, 2966.6518511246163, 3134.8489271373273, 3302.720799261503, 3469.3988329169333, 3633.988621040879, 3795.5768428788265, 3953.2386337771277, 4106.045556929662, 4253.0733719895925, 4393.410076967601, 4526.164460570399, 4650.4772008238715, 4765.5279811913815, 4870.541875802945, 4964.796957268504, 5047.6315467547165, 5118.451001778119, 5176.733956471496, 5222.037934142532, 5254.004258160558, 5272.362194516315, 5276.932267720576, 5267.628967665262, 5244.463107133184, 5207.5423966735925, 5157.074513382135, 5093.362746611234, 5016.801814291308, 4927.874415156033, 4827.14688284902, 4715.26398544754, 4592.942927647009, 4460.96662312145, 4320.176314011257, 4171.463622949196, 4015.7621303907017, 3854.0385761514626, 3687.283788878488, 3516.5046381209067, 3342.717944699011, 3166.9370122150917, 2990.1612125950514, 2813.367143397673, 2637.500186336188, 2463.466563049178, 2292.125976789539, 2124.284920131738, 1960.6907191570788, 1802.0263740087207, 1648.9062443717141, 1501.8726164989876, 1361.3931771080267, 1227.8599950776836, 1101.5895018933716, 982.8210539589905, 871.7179912757429, 768.3693043238321, 672.7923806847178, 584.936591863804, 504.6875458128263, 431.871926434818, 366.2628349823631, 307.58554329232544, 255.5235652959676, 209.72495123674003, 169.80871013475868, 135.37140004151527, 105.99350808268802, 81.24537179862394, 60.693221988312274, 43.904948195824915, 30.455471999321883, 19.93163600647063, 11.936617676476091, 6.093801386906733, 2.0500692405123777, -0.5215099907826118, -1.9196036367058986, -2.4131488869797586, -2.2404864872659105, -1.6090724016884224, -0.695746395090399, 0.3524937090265985, 1.4172581435140834, 2.4071122730044845, 3.255561888797984, 3.918738067823929, 4.372845594000701, 4.61144277308189, 4.64261566803899, 4.486111587910603, 4.170494143714222, 3.730378346592021, 3.203799725209054, 2.6297660980993522, 2.046033564401255, 1.4871433057905814, 0.9827486203906556, 0.5562529442899794, 0.22377210222747257, -0.006573698021711629, -0.13504016527271925, -0.1703206563630223, -0.12930483702733503, -0.03655789821588925, 0.07645168819742815, 0.17234399272837275, 0.20900299721579757, 0.14089779706943434, -0.07949305956272228, -0.5001977721297154, -1.1682485163738723, -2.128200753676804, -3.420713670350178, -5.081228087134545, -7.138774746754579, -9.614941820879316, -12.523025884039438, -15.867390404648981, -19.64305764322439, -23.83550374042916, -28.42068431801027, -33.36530606190236, -38.627301926920424, -44.15650310283045, -49.89550108817996, -55.78067376987211, -61.74335057878938, -67.7110891257226, -73.60903371732654, -79.3613248628303, -84.89252831799675, -90.12905236646245, -95.00052288768082, -99.44111152392861, -103.39083971119777, -106.79668183377473, -109.6134176540567, -111.80436832229127, -113.34198435895976, -114.20824917017063, -114.39489337195243, -113.90341937739159, -112.74493977050382, -110.93983687238739, -108.51725451808359, -105.51443633452709, -101.97592767856645, -97.95266081570199, -93.5009764339882, -88.68162417039817, -83.55858334079439, -78.19779720705709, -72.66598885585739, -67.0295264872576, -61.35333640699722, -55.69988374018413, -50.12823873745866, -44.69324408616933, -39.44479593455875, -34.42724845552157, -29.6789487888045, -25.231906229945515, -21.111605520148366, -17.33694390075314, -13.92026806416235, -10.867564324973998, -8.178764313498814, -5.848133070716576, -3.864758860135151, -2.21311833722208, -0.8736972716643475, 0.17634920655210298, 0.9625129000110445, 1.5122411102418358, 1.8542525461104753, 2.0178747369015504, 2.0324195485634675, 1.926601804553888, 1.7280046091832073, 1.4626136749244183, 1.1544222896980854, 0.8251106293338868, 0.4938010649538255, 0.17688829012338955, -0.1120539325939912, -0.362293600477765, -0.5658940208686642, -0.7176061316220421, -0.8147066845214777, -0.8567901851093126, -0.845522941126409, -0.7843685067523496, -0.6782926105685417, -0.5334563511640151, -0.3569067409266185, -0.15627255605784365, 0.060527276943859495, 0.2855564421199494, 0.5111102487077978, 0.7299357526557778, 0.9354190304209489, 1.121737781873226, 1.2839781086788997, 1.4182154343626208, 1.5215620254185853, 1.5921786788243004, 1.6292537218190808, 1.6329552585146303, 1.6043590582005334, 1.5453560587686759, 1.4585437345688086, 1.3471056835387054, 1.2146837677122229, 1.0652472858237463, 0.9029631464402841, 0.7320684056084557, 0.5567512919795851, 0.38104302704144044, 0.20872234877045073, 0.043232916284828504, -0.11238286575237508, -0.2555331999395827, -0.3841099672969663, -0.4965059183651866, -0.5916168044715924, -0.6688296344884911, -0.7279985433691893, -0.7694099918747068, -0.7937391807581169, -0.8019998891171839, -0.7954899321647546, -0.7757325379443554, -0.744418121532612, -0.7033448690691946, -0.6543621893959803, -0.5993186047012643, -0.5400146669957184, -0.47816177281256794, -0.41534749277771504, -0.35300778063542254, -0.2924061862241718, -0.234619975174174, -0.18053286002102412, -0.13083387708062078, -0.08602180366109623, -0.04641445449306617, -0.012161907344756282, 0.016737428499678474, 0.040417842381959806, 0.059125718003648464, 0.07319821123701258, 0.083041943529256, 0.0891123616482294, 0.0918943193142963, 0.0918843330844795, 0.08957485800025144, 0.08544082198407445, 0.07992855537127265, 0.0734471564762133, 0.06636229062874884, 0.058992260418996925, 0.05160600036046939, 0.044423065622168065, 0.037615148463507705, 0.03130897523676911, 0.025590250663413555, 0.020508336798912064, 0.016081388587054612, 0.012301691120362666, 0.009140973412484682, 0.0065555077046116645, 0.004490840173418572, 0.0028860366201987364, 0.001677364260493206, 0.0008013601339339906, 0.00019727959109373423, -0.00019105731418443767, -0.00041399272487353675, -0.0005152768343078506, -0.0005317630106203648, -0.0004934773250789502, -0.0004239847331159685, -0.0003409738038995687, -0.0002569862793576772, -0.00018022489769850834, -0.00011538202784380204, -6.444198611856711e-05, -2.7420683685048176e-05, -3.0169540990452287e-06, 1.0839310502183543e-05, 1.6548976799956646e-05, 1.6514502831929955e-05, 1.2912385726238357e-05, 7.55529688672465e-06, 1.8290645895947613e-06, -3.311735273547325e-06, -7.305851402739692e-06, -9.920424069983476e-06, -1.1172550547072389e-05, -1.1248469469428256e-05, -1.042881862134893e-05, -9.025721559772189e-06, -7.334846743561725e-06, -5.603377015074303e-06, -4.013080804950738e-06, -2.6762860099662876e-06, -1.6417405287422985e-06, -9.070049834920922e-07, -4.3410137192599235e-07, -1.6554918634683679e-07, -3.8556588580558e-08, 4.109758527847253e-09, 7.2776211266866985e-09, 5.342154731731253e-10, -1.1764201019290604e-09, 5.50931544900759e-09, 1.6750516295627347e-08, 2.6051198962348343e-08, 2.8025186037643167e-08, 2.0726078379262233e-08, 6.26997648152143e-09, -1.0134993055492112e-08, -2.230266008381955e-08, -2.5642081774295947e-08, -1.9408474473693296e-08, -7.907558210937968e-09, -1.379265909826338e-10, -7.692980569237787e-09, -4.1166784875595234e-08, -1.0575477344339712e-07, -1.971469546524621e-07, -2.9910835760546334e-07, -3.842644135598779e-07, -4.1950757968521417e-07, -3.7708565327029076e-07, -2.5181807027256575e-07, -8.404044657960776e-08, 1.3142122252676493e-08, -1.75182740114629e-07, -9.929578853415231e-07, -2.934055252911474e-06, -6.65174970751924e-06, -1.2951602200587897e-05, -2.2762977024841327e-05, -3.7085415288972246e-05, -5.690792940357387e-05, -8.31017606292997e-05, -0.0001162902057492692, -0.00015670267823294958, -0.0002040239799451712, -0.00025725354715209407, -0.00031459286574224204, -0.00037338195356770483, -0.00043010739444574933, -0.0004805045001276122, -0.0005197744343607668, -0.0005429338387688073, -0.0005453095018998541, -0.0005231783420566866, -0.0004745355736687198, -0.0003999791350640793, -0.00030367565483601906, -0.00019435835389904294, -8.6294486920124e-05, -1.4719981835829917e-07, 3.6353760444935106e-05, -1.197492148088892e-05, -0.0001877782453927392, -0.0005407000748120627, -0.0011263667144593445, -0.002004751771964225, -0.003237884595717235, -0.00488688960304493, -0.007008370930923126, -0.009650187614042889, -0.012846832666027654, -0.016614521321960368, -0.020946197145528003, -0.025806720952476728, -0.031128536285275316, -0.03680813225266112, -0.04270363849533279, -0.0486338848908436, -0.054379239096329, -0.05968457590161464, -0.0642645151309522, -0.06781084819820639, -0.07000240279104886, -0.07051717719592451, -0.06904648260514028, -0.06531071239179963, -0.05907621687650636, -0.05017251002238241, -0.03850901923777276, -0.024090465553232264, -0.007029879658170775, 0.012441771689499344, 0.03397035555120593, 0.05707871801719445, 0.08117313438615147, 0.10555639239892378, 0.12944778936054416, 0.15201008688415285, 0.17238301247531043, 0.18972246711347218, 0.203244204688156, 0.2122703382931788, 0.21627589620543783, 0.21493314086186197, 0.20815068052517677, 0.19610407885176095, 0.17925461605425633, 0.15835324107606358, 0.1344252452598113, 0.10873333652269304, 0.08271768664376757, 0.057911127816772136, 0.03582907772298796, 0.017834978119948035, 0.004983399005845359, -0.002155532894981841, -0.0036851242679696774, -0.0005776016689312697, 0.005132588794789246, 0.010167648210634985, 0.00984865543431955, -0.002026497927950261, -0.03325621043979572, -0.09324657298226594, -0.19294846396651594, -0.34470851169735073, -0.5620237286393808, -0.8591918715931899, -1.2508525169264133, -1.7514174482703262, -2.374393194120352, -3.131603352862224, -4.03232499997576, -5.082363548051639, -6.283082435608832, -7.6304244646860715, -9.113955010227029, -10.715967250027107, -12.41069503383585, -14.16367911246505, -15.931334622897724, -17.660767639069178, -19.289886757680595, -20.74785192364454, -21.955896884673972, -22.828553729712393, -23.275297907863568, -23.202620013889614, -22.516562469735515, -21.12577339096449, -18.94465719647718, -15.896856558392567, -11.918980556349565, -6.964445406613362, -1.0073156315471719, 5.953981420641267, 13.893207381347649, 22.753280163458516, 32.44381163388206, 42.8393717786641, 53.77863167959263, 65.06452833883382, 76.46563252041035, 87.71887105422117, 98.53332884519193, 108.59533328199268, 117.57536138428257, 125.13612392057267, 130.94180674053078, 134.6683934012953, 136.01486915154845, 134.71505266469762, 130.5497496804828, 123.35887369689695, 113.05313492195015, 99.62486321720782, 83.15763755649529, 63.834017242618025, 41.94056957578049, 17.87036167702681, -7.877727784985369, -34.70333597369367, -61.91295528741504, -88.7325032489482, -114.32428351185474, -137.8083962154934, -158.28853115947118, -174.88194213286044, -186.75325616800856, -193.1516249814738, -193.45073886402, -187.19061357473254, -174.1199077592378, -154.2381849443742, -127.83679016255029, -95.53702803103238, -58.324479399707855, -17.57830243566635, 24.90772724257763, 66.91233679979655, 105.78346823767272, 138.44602831504747, 161.42179054311416, 170.86239692643045, 162.59651164016677, 132.19092020761892, 75.02534246927223, -13.618591581264278, -138.4549363580498, -304.0785309355817, -514.8389041334462, -774.7046583313414, -1087.1200354679168, -1454.8550785797145, -1879.8548811991043, -2363.08971579756, -2904.408964347519, -3502.402908797269, -4154.280807692289, -4855.760764052602, -5600.974607023391, -6382.396398052656, -7190.795845890411, -8015.219519347632, -8843.002428241381, -9659.812103693148, -10449.726796927831, -11195.348837919773, -11877.952722426178, -12477.666987355722, -12973.69577191428, -13344.574921621079, -13568.478861928044, -13623.51761464382, -13488.05436888011, -13141.051344311343, -12562.427964632001, -11733.425610793363, -10636.97287379913, -9258.044925065742, -7584.010433752733, -5604.959393434717, -3314.005281123637, -707.5551635500026, 2214.458367148749, 5448.3881733764, 8986.736154611346, 12818.091941029017, 16927.11477659646, 21294.56919643427, 25897.42058922717, 30708.990950042855, 35699.174062527505, 40834.70827183295, 46079.50394113702, 51395.02164674519, 56740.696180802006, 62074.400517234346, 67352.94308236065, 72532.62242554023, 77569.8620441439, 82421.72376340728, 87046.42301636258, 91403.85927468013, 95456.13326792327, 99168.03715763053, 102507.50970098405, 105446.04900405406, 107959.07616937034, 110026.2439735471, 111631.68565193877, 112764.19990057903, 113417.36966206333, 113589.6861113771, 113284.61737957093, 112510.36902748555, 111279.71320752082, 109609.80422669329, 107521.85311080489, 105040.7771784364, 102194.8173746411, 99015.11663027266, 95535.26670474716, 91790.8313720514, 87818.85405835154, 83657.3581323441, 79344.84901153677, 74919.87990912082, 70420.58616014512, 65884.13354874657, 61346.29078497415, 56841.047698849325, 52400.28295515968, 48053.487975424316, 43827.48914110848, 39746.24409260633, 35830.69882120466, 32098.69640170999, 28564.936367070986, 25240.98286225501, 22135.319320847113, 19253.452990226775, 16598.040170386877, 14169.044088465871, 11963.939172311997, 9977.939841416046, 8204.247631228074, 6634.311200009915, 5258.094739408318, 4064.3489332695967, 3040.873687803205, 2174.778650978918, 1452.733769293964, 861.2049377800356, 386.671321188999, 15.81763199256929, -264.287975713863, -466.03697132594147, -601.1527788220845, -680.5881637501375, -714.4471338029012, -711.9304644360337, -681.3035534787609, -629.8849626176824, -564.053820164672, -489.2739438591198, -410.1316157688623, -330.3856856585452, -253.02747525427665, -180.34792919164337, -114.00867522659792, -55.11692439975367, -4.301670963641877, 38.21118749433956, 72.52638265424062, 99.0107802064723, 118.22992058233079, 130.890405158526, 137.78869074670945, 139.76662187705952, 137.6738366298632, 132.33698181827842, 124.53539219696621, 114.98319929886979, 104.31629814376721, 93.08466486530838, 81.74933234929782, 70.68311736160774, 60.174399792199225, 50.4332711547843, 41.5994042690199, 33.75104606198044, 26.914597188634072, 21.07431224138361, 16.181729380023594, 12.16451517063153, 8.93449278881919, 6.394678892838578, 4.445197780640811, 2.9881160903267174, 1.9311696844882973, 1.1904304652973188, 0.6920070940164259, 0.3728982301562486, 0.18113249685687607, 0.07533664825737661, 0.023873312790218277, 0.003683326168177371, -0.0010437375963014788, -0.0002624244149070944, 0.0005630221174896678, -0.0008081202178548527, -0.004508860800679539, -0.009495717896628092, -0.014279055880214725, -0.01745150891401365, -0.01802627421241537, -0.015606886070383052, -0.010416958313130635, -0.0032223952156884314, 0.004820076140957011, 0.012355193161495966, 0.018032354538265592, 0.020694277306252423, 0.019531311379291566, 0.014187359845114276, 0.004809267813213334, -0.007961344474157991, -0.023050241731323893, -0.039058706524227084, -0.05440606403245194, -0.06749284815703108, -0.07686999609884144, -0.08139960069083468, -0.08039396239851543, -0.07372177093055143, -0.06187300583494439, -0.04597735121688908, -0.02777433079389941, -0.009536779526396432, 0.0060473205244088194, 0.016027023671498903, 0.017364973388770903, 0.0071271766677928495, -0.017325880555757227, -0.058158821801565196, -0.11690283689509552, -0.19432841036891993, -0.29035709418438277, -0.404017713167181, -0.5334497736077999, -0.6759543094814279, -0.828093011386847, -0.9858255753838269, -1.1446752134328966, -1.2999191515206692, -1.446792439401141, -1.580694498341893, -1.6973879684043218, -1.7931800127396782, -1.8650784140424317, -1.9109165612536094, -1.9294329679401447, -1.9203101100014779, -1.8841711216912775, -1.8225352704214854, -1.7377408203927995, -1.6328226680325082, -1.5113616363957139, -1.3773204988438064, -1.234869953110199, -1.0882131031838636, -0.9414168255163764, -0.7982577095435813, -0.6620892110955694, -0.5357353095291852, -0.42141474469858914, -0.32069770727448527, -0.23449281211111686, -0.1630671054440181, -0.10609513009762425, -0.06273082160448475, -0.03169972068456506, -0.011404700354451704, -3.820699890981729e-05, 0.004305274825559011, 0.0035224485624623892, -0.0005946346848980082, -0.00643916181596547, -0.012651676709821444, -0.01816174856958003, -0.02220847989193361, -0.02434038646725271, -0.02439638095140164, -0.022470640815926913, -0.01886438210369438, -0.014028907685746734, -0.008504354741701841, -0.002858463019546237, 0.002370545625006769, 0.006723390033461302, 0.00985856835950603, 0.011578572431462916, 0.01184237498193663, 0.010764055319308338, 0.008598369219309796, 0.005714924515298469, 0.002563348269929085, -0.0003676373193565024, -0.0025939598171305835, -0.0036792872604527304, -0.003274183083605179, -0.0011483957771036921, 0.002786131064507955, 0.008463266218538516, 0.01566266775859543, 0.02402183784903627, 0.033059516405056305, 0.04220887665682161, 0.05085828726644019, 0.05839685162268478, 0.064261760404205, 0.06798406378255341, 0.06922869530828504, 0.06782657422313272, 0.06379612099868003, 0.05735203545594247, 0.04890042740645223, 0.03902004889595893, 0.028430272585764336, 0.017947369455398803, 0.008431451581117017, 0.0007271344002152118, -0.0043985063953751406, -0.006316788956707185, -0.004593043747817128, 0.0009667220693365837, 0.010281674602773669, 0.02297757190527516, 0.038385579632285165, 0.055559547454528145, 0.0733118321873928, 0.09026639841768892, 0.10492706536042533, 0.1157578021527682, 0.12127110671160513, 0.12011987797846188, 0.1111877918054211, 0.09367308402541924, 0.06716150669808527, 0.031682447858554535, -0.012256289764476576, -0.0636561611297535, -0.12104039653894579, -0.18249193769429042, -0.24571599944051972, -0.30812527647453264, -0.36694478196322916, -0.4193306318728882, -0.4624978803525292, -0.49385148751868096, -0.5111139398713236, -0.5124431543955236, -0.496535433423064, -0.4627066337257787, -0.4109462528052518, -0.3419423855033407, -0.25707533444382746, -0.15837943659814696, -0.04847425106059502, 0.06953220512568162, 0.19216405300766945, 0.3157167771574367, 0.4364094305641932, 0.5505412799500957, 0.6546454690769007, 0.7456326032373366, 0.8209163129919486, 0.8785178572935445, 0.917142589845882, 0.9362237930755961, 0.9359326416383298, 0.9171539536550811, 0.881429116303443, 0.8308692501085504, 0.7680432069140342, 0.6958462979702145, 0.617356649418106, 0.5356871557182002, 0.45384091230388446, 0.37457413822390495, 0.30027751109743445, 0.2328836979990582, 0.17380297675222842, 0.12388999372062637, 0.08344340135340717, 0.05223779060654822, 0.029585460758907705, 0.01442380716150473, 0.00542255382605228, 0.0011038021246074729, -3.301473770951447e-05, 0.0006103687291150725, 0.0018407563970417045, 0.0027635709349326876, 0.002846428498249728, 0.0019506666649253919, 0.0003273137954189931, -0.0014240619090976662, -0.0024330072611018993, -0.0016694528674082163, 0.0019164980664114198, 0.00923337592378075, 0.020874584398460357, 0.036942234810064124, 0.05687957105552898, 0.07932326388009107, 0.1019865447915282, 0.12158355296225162, 0.13380325139897542, 0.13333709953364534, 0.11396593095214425, 0.06870684375487109, -0.009981875562433008, -0.12994275574428546, -0.299015980475154, -0.524701671604582, -0.8138005578655944, -1.1720478062532929, -1.6037560220815823, -2.1114839642324483, -2.6957474399413015, -3.3548021133363166, -4.084510788622965, -4.878260000427227, -5.726974970374361, -6.619230985267114, -7.541461931470774, -8.478252359162566, -9.412712389451888, -10.326924425192724, -11.202446232135461, -12.020853112157763, -12.764299786445967, -13.416081271500731, -13.961173288831436, -14.386796279593842, -14.68287666377757, -14.842312200291154, -14.861210794040092, -14.739029228133676, -14.478600159781145, -14.086048947086052, -13.57060519533792, -12.94429085642367, -12.221524212655513, -11.41865093037904, -10.553416874521455, -9.64440295974858, -8.71044643002715, -7.770110724958868, -6.841108489223192, -5.939744177504718, -5.08048052807992, -4.2755903672471405, -3.5349025965841414, -2.865649070133313, -2.272414701778807, -1.7571891527938044, -1.3195134179396684, -0.956708721884042, -0.6641792589015411, -0.43577063442681446, -0.2641655951017049, -0.14129879249927413, -0.05876480278129799, -0.008211519753316772, 0.018299976868637192, 0.027987531191691936, 0.02710337783994697, 0.02076076496393875, 0.012835739156940038, 0.005944228875780639, 0.0014908070407699387, -0.00021794944148771468, 0.00019440835343841474, 0.0013840805463541308, 0.001524680763927458, -0.001442375648765845, -0.009559920561576743, -0.024624437614720454, -0.04798610403231267, -0.08039050975315307, -0.12187039669440852, -0.1716926706467239, -0.2283626320539377, -0.289684026712002, -0.3528703098159986, -0.4146996141948738, -0.4717034658961934, -0.5203773667535482, -0.5574001133691311, -0.579849249880916, -0.5853974817361116, -0.5724788092824166, -0.540414355442403, -0.4894896952528005, -0.42097843586028993, -0.3371098392258268, -0.24098144344569328, -0.1364207511350952, -0.027802946919931636, 0.08016587507238634, 0.18268848453645306, 0.2751264110526928, 0.35324679837948875, 0.4134541707951981, 0.45299173309275864, 0.47009575904015166, 0.4641011341742152, 0.43549101336174734, 0.3858865235683306, 0.31797642802770454, 0.23538988627057963, 0.1425185128442409, 0.04429669245898998, -0.05404859677449914, -0.1472654911571811, -0.2303484913055466, -0.29879980221049596, -0.34886767268469726, -0.3777447578867163, -0.38371810631777375, -0.3662631024465372, -0.3260740217926591, -0.2650311099903434, -0.18610581276367003, -0.09320877165152376, 0.009011583088012363, 0.11540937954771029, 0.2206080408757984, 0.3192794296404382, 0.4064206843783498, 0.4776121477220123, 0.5292457313465987, 0.5587143767235607, 0.5645456914856298, 0.5464753257623641, 0.5054568416479617, 0.443607626660806, 0.36409108171715193, 0.2709446257914028, 0.16886246854936043, 0.06294450959412803, -0.04157511695314897, -0.13960524406960625, -0.22646584503830997, -0.298136158112308, -0.3514621315540908, -0.3843109486118903, -0.3956727584169659, -0.3857006801648432, -0.3556868466504913, -0.30797594090804864, -0.24582126061475876, -0.1731910882861036, -0.09453452585849449, -0.014522152092627996, 0.06222450306901528, 0.1313998998305249, 0.18926303450785373, 0.23285451174323252, 0.26016888491335444, 0.2702708510994393, 0.26335035514400623, 0.24071354274483764, 0.2047098484493548, 0.1585990177280864, 0.10636517450424801, 0.0524879825441917, 0.0016835673757441911, -0.041370692559304506, -0.07231405581859643, -0.08736515992877487, -0.0835555051956965, -0.058921492950418076, -0.012641808690935513, 0.05488733421257695, 0.14204243210489276, 0.24602962562513905, 0.36300565630179554, 0.48825669659270504, 0.6164257644860752, 0.741776792615494, 0.8584814229536293, 0.9609133502458108, 1.0439347618506594, 1.1031600287012773, 1.1351817808450064, 1.1377493217927297, 1.1098832981533464, 1.0519256691341299, 0.9655235831333796, 0.8535474909560596, 0.7199483407795872, 0.5695619327113751, 0.4078712753844591, 0.2407399356375764, 0.07413078983043497, -0.0861748024852855, -0.23484260426524986, -0.3672221275026112, -0.4795442152302437, -0.5690729919909088, -0.6341889622308757, -0.6744126130039316, -0.6903694115048368, -0.6836985674350118, -0.6569125409412834, -0.6132169042559186, -0.5563021828973798, -0.4901205988511671, -0.41866114498910356, -0.345736115546795, -0.274791128545887, -0.2087488779650677, -0.14989523966624055, -0.09981116895699249, -0.05935013966071848, -0.02866641938716379, -0.007286658679328143, 0.005782466748776039, 0.011920149845770198, 0.012741810273621338, 0.009945502084016417, 0.005165867305418771, -0.00015376091428572202, -0.004862139129509438, -0.00816708474274478, -0.009664700228707775, -0.009330044903757327, -0.007471452303916326, -0.004653342473827054, -0.0015957434258448441, 0.0009394152995022432, 0.00226384039977347, 0.0018684705690836718, -0.0004920732142201853, -0.004746064689366792, -0.010489810269077247, -0.017015806017203025, -0.023384737367058036, -0.028538178868009866, -0.031444821499455586, -0.031269202239965106, -0.027548860253579676, -0.020363236435084645, -0.010475964861118162, 0.0005675982324327174, 0.010404578941975582, 0.01589485039672343, 0.013247660368613499, -0.0017604523684083362, -0.033477512432623396, -0.08598555933289878, -0.16264264516781576, -0.2655792368846826, -0.3951772542767126, -0.5495670619125684, -0.7241774992758199, -0.9113752405623342, -1.1002341260900617, -1.2764687743072167, -1.4225621082658102, -1.5181087898221128, -1.5403867381056786, -1.4651559730815211, -1.2676675287166896, -0.9238659809507939, -0.41174318798846365, 0.28720964394613063, 1.1865141671145016, 2.293262883519291, 3.606802659402903, 5.1176060098246925, 6.806413335494434, 8.643718924146599, 10.589662238653785, 12.594372059124037, 14.598793521151645, 16.536007615527776, 18.333030083221587, 19.913071073545602, 21.19821487064275, 22.11228168896431, 22.583922703586286, 22.549893657953852, 21.958094123148154, 20.770385336921606, 18.965106345535304, 16.539109527615455, 13.50919604820227, 9.912851133394108, 5.80820389032503, 1.2731661306910698, -3.5962618202742065, -8.68849438120892, -13.87961221615061, -19.037277540572667, -24.025242118386696, -28.708262568854387, -32.957038818104266, -36.6530792217193, -39.693331072305384, -41.99435482513024, -43.49585072887139, -44.16336736366084, -43.99005083625224, -42.99733007922744, -41.234476476086925, -38.77702318101738, -35.724079046366974, -32.19462186533629, -28.322964045983014, -24.253551032406893, -20.13493819490159, -16.113597219815087, -12.327856420134262, -8.902155833404539, -5.941856700973723, -3.5288445560174995, -1.71813483997314, -0.535649395554577, 0.022717087886682592, -0.009322432954934894, -0.5702227479134802, -1.5736785281220436, -2.912873958481213, -4.465744997191625, -6.10102495798755, -7.6847845322454935, -9.08717455975166, -10.189021056671743, -10.887973012501522, -11.103908958883773, -10.783331462214766, -9.902523485550457, -8.469294482263477, -6.523207148578836, -4.134245250956109, -1.3999558453798449, 1.5588331559504152, 4.603588819197585, 7.584645826572739, 10.348445183190401, 12.74513175305143, 14.636160653171535, 15.901558167042271, 16.446421976791715, 16.20637051793937, 15.151663900588305, 13.289766979035761, 10.6661989451617, 7.363591740429527, 3.498964547102272, -0.7806682637837083, -5.3043362768020454, -9.884462410858358, -14.325075579603658, -18.430593278728335, -22.014776589780574, -24.90944171386249, -26.972524561801652, -28.095120651788836, -28.207083727252805, -27.280955645654352, -25.33402027662536, -22.428350824502605, -18.668831519665694, -14.199363217554604, -9.196968816337028, -3.864206795742567, 1.5795065685468317, 6.907420898246893, 11.895394083161019, 16.331799024776586, 20.026938510527458, 22.82153145803821, 24.593866005127417, 25.265253141888376, 24.803579383229394, 23.224771569114065, 20.592097967800214, 17.013365874995223, 12.636005453038738, 7.64033368969541, 2.2313777812813163, -3.3703770788434606, -8.938879103321032, -14.252574557719814, -19.104172783321843, -23.309654558566393, -26.716104627145004, -29.20800733556063, -30.711768072960332, -31.1982861610858, -30.68312748123102, -29.224879112664244, -26.921208822830387, -23.90314829379875, -20.327979416888535, -16.371023375869523, -12.21675900362955, -8.049725965705527, -4.045673983272872, -0.3634014300357433, 2.8623138571067894, 5.526349757945314, 7.557177719782541, 8.918931846145965, 9.611548773977383, 9.669059331673122, 9.156039219975163, 8.1624461501613, 6.797234822625733, 5.181138473655504, 3.439045424594269, 1.692417825276919, 0.05219370210947767, -1.3874173473171547, -2.5538884692626325, -3.3997980568525876, -3.904529832398027, -4.074163006640858, -3.9395677669419435, -3.5528552730081597, -2.9824346931137655, -2.30694234337809, -1.6084597815428547, -0.9655172985869311, -0.4463702375978851, -0.1030340898783868, 0.033462638760217524, -0.04379333093763055, -0.31640823890825065, -0.7416378343037157, -1.2555815753733908, -1.7785700822923252, -2.2225590747996717, -2.5002149802971916, -2.5352676186219685, -2.2735660216972176, -1.6942059923235193, -0.8200510709397788, 0.27301966773559844, 1.448828285609332, 2.506196699257025, 3.1773511589888055, 3.129834291880716, 1.9721748300610318, -0.7366080254583123, -5.473776029807871, -12.736241950614517, -23.02106718284388, -36.803703313173784, -54.514804190955346, -76.51655883137576, -103.07957132755044, -134.36170420633513, -170.39078277003787, -211.04937789906975, -256.0642508390685, -305.00129975213025, -357.2663012928785, -412.1117645674237, -468.6500146298956, -525.8731383749097, -582.6779613948135, -637.8949403344178, -690.3214902591607, -738.7581231216096, -782.0461065946257, -819.1052733480028, -848.9705603940334, -870.8272895137254, -884.0454200613697, -888.1998226807959, -883.0865226574973, -868.7331576229949, -845.4019293660796, -813.5860811869007, -773.9958925681564, -727.5368003197975, -675.2820165060532, -618.4393990878083, -558.3137360666244, -496.2658081673759, -433.6697253987382, -371.8701039756808, -312.1406588241105, -255.64629907818698, -203.41008776693747, -156.2820060129903, -114.9165405812484, -79.75848772319, -51.03609197502239, -28.76257338749804, -12.745625419260925, -2.604133354181193, 2.2086907508800064, 2.3768003386984375, -1.311327246535367, -7.998085162121559, -16.793419361340124, -26.811311154409918, -37.20461107166117, -47.19683044466811, -56.10965940437797, -63.38566490903933, -68.60478141930668, -71.49423391288931, -71.93179018519083, -69.9424183321899, -65.68872610504727, -59.45580972297849, -51.63135757831298, -42.68203056999979, -33.12726900317643, -23.51175172865027, -14.37775444112267, -6.238621160767664, 0.445538428954869, 5.2889304579663525, 7.996839190810781, 8.377602926307775, 6.349579634227133, 1.9428963338537688, -4.703926475618776, -13.352152674068746, -23.67528630934553, -35.27510903715077, -47.70046745688196, -60.46788441328487, -73.08301834789515, -85.06199043795118, -95.95177886976018, -105.34878686262698, -112.91424001325464, -118.38666342744864, -121.59121950509206, -122.4434096206389, -120.94916460367409, -117.20130691208757, -111.37244442609638, -103.7047558982089, -94.49724890594082, -84.09116073975703, -72.85422811756452, -61.1645732045656, -49.39500336542472, -37.89821715586022, -26.99353118129955, -16.955940613219976, -8.007732401997513, -0.3129423602918001, 6.025271867876636, 10.964821779919548, 14.521889428297216, 16.76563969360841, 17.810921050867034, 17.809415952073103, 16.939749581760708, 15.39708673488911, 13.38273884970787, 11.094266845591038, 8.716544089230675, 6.414150690381328, 4.325372256168083, 2.5579867958732048, 1.1869238794671613, 0.2537816760160896, -0.2319067845924013, -0.28984277107360845, 0.035181068726953486, 0.6784173655421197, 1.5609492584922466, 2.5957699298013215, 3.6938399863925926, 4.7697345747123805, 5.746577763348542, 6.560090089947558, 7.161570558545393, 7.519715693363112, 7.6212486539217945, 7.470399061115816, 7.0873361469231515, 6.5057153570726465, 5.769536844787372, 4.929508107800489, 4.039197873882703, 3.1512211840288633, 2.313685439425901, 1.5670669698134971, 0.9417378743038142, 0.45626233982882436, 0.11652100625788864, -0.08431472993545845, -0.16498671649683244, -0.15460729517827626, -0.09048548900302952, -0.015470599000424376, 0.025014999208440337, -0.013930849577227834, -0.17365844667483563, -0.4891786841802174, -0.9867904652278663, -1.6822473916760783, -2.5795551529028926, -3.670460302375336, -4.9346468084847395, -6.3406176558851755, -7.847201329696805, -9.405589962495672, -10.961788904396021, -12.459337752177115, -13.842151277413477, -15.057325600667552, -16.057760280962444, -16.804502965280605, -17.26874842577267, -17.43303965364754, -17.29193970824914, -16.8521319590781, -16.13191925250508, -15.160163238181918, -13.974733055019847, -12.620555984993116, -11.14738046460333, -9.607373261918838, -8.052677304516536, -6.533054569119491, -5.0937299757065615, -3.7735443453761337, -2.6034757090149543, -1.6055848422814971, -0.7924878938202082, -0.1673195666204292, 0.2758230169162542, 0.5510072444385886, 0.6792286145654528, 0.686890658137726, 0.6040919008470094, 0.462816476522628, 0.29512562313260216, 0.1314428472158443, -0.0009835210844334414, -0.07937135922646524, -0.08640139366758888, -0.010867182413231957, 0.1520414423982834, 0.4008115333724829, 0.7280171609742284, 1.1210239060683418, 1.5629332773519908, 2.033706318714041, 2.5113981169766806, 2.9734327668573677, 3.3978500224619466, 3.7644600529228764, 4.055850863337367, 4.258201306486254, 4.361876790777702, 4.3617834174734025, 4.257465431495541, 4.052961890788069, 3.7564441093633016, 3.379668170763812, 2.937281336965739, 2.446003454561233, 1.9237627114898512, 1.3888271098838754, 0.8589725142292831, 0.3507269431489084, -0.1212761631571712, -0.544815884685557, -0.9104463963951323, -1.211694775914882, -1.4451056591667912, -1.6101390439777028, -1.7089380013469704, -1.745988740665051, -1.7276993424125415, -1.6619268972042338, -1.5574826706653102, -1.423632228229691, -1.2696274308913778, -1.1042903604116496, -0.9356646093350794, -0.7707469642666593, -0.6152970971866542, -0.4737339128179801, -0.3491161863230103, -0.24319596212488728, -0.15653310782505975, -0.08865725296804255, -0.0382621605827101, -0.0034174006203249465, 0.018217065470554124, 0.029186084105573436, 0.03205489159994866, 0.029254581197096566, 0.022961410966787242, 0.015012716191919693, 0.0068592234393037325, -0.00044842386664314075, -0.006243363474090541, -0.010202364264343828, -0.012288515719495638, -0.012683698343178347, -0.011717517118566135, -0.009798681015144516, -0.007353769506126977, -0.004777053205354195, -0.0023936468421653432, -0.00043688402920785837, 0.0009605136217887585, 0.0017629313731896475, 0.0020183007327189803, 0.00183749843402311, 0.0013698899821353529, 0.0007781109824087279, 0.0002148536286626462, -0.00019610529325190938, -0.0003730720551428533, -0.0002829823915940943, 5.874196817852851e-05, 0.0005944092932548863, 0.0012351598671098674, 0.0018753560453847978, 0.0024084390747377035, 0.0027423946676003465, 0.002813063164811342, 0.002593854023425605, 0.002100919001016846, 0.0013933141759190255, 0.0005681992332592446, -0.00024837471043952816, -0.0009141085616818019, -0.0012852272035515783, -0.0012318862393028796, -0.0006526735364113753, 0.0005132360512606063, 0.0022774839310218484, 0.004598370325144773, 0.007381626684780272, 0.010486067787642639, 0.013733679121999607, 0.01692337567326274, 0.019847008219372794, 0.022306286629361023, 0.024129158059394272, 0.025184182481458872, 0.025391638161649063, 0.02473037612619798, 0.023239814192640245, 0.021016885230447577, 0.018208195020285103, 0.014998101331057116, 0.011593632782657074, 0.008207548184984894, 0.005041192074240861, 0.00226854758037571, 2.2869295227720808e-05, -0.0016129712913985196, -0.002611605313681267, -0.0030011716922315164, -0.0028603001833674424, -0.0023085580429852946, -0.0014932346202609877, -0.0005736713115925655, 0.00029542622549724387, 0.0009801681463372318, 0.0013816180679512447, 0.0014464973417870914, 0.0011734324520424229, 0.0006140733780563993, -0.00013113169388551005, -0.0009222358846310326, -0.0015934360814594665, -0.0019699551929753998, -0.001886604405744609, -0.0012062846762416629, 0.0001633139272666493, 0.002256478836406512, 0.005041118007255525, 0.008416293108153295, 0.012216174763833272, 0.0162203907836092, 0.020170130074140192, 0.023788824600476068, 0.026805754815381787, 0.028980567876317594, 0.030126499363861792, 0.03013007295635912, 0.028965218532943822, 0.026700149952092512, 0.023495918776229162, 0.019595987638527424, 0.015307164854174965, 0.010972945077931078, 0.0069413915240456505, 0.0035298606282200442, 0.0009894154414668282, -0.0005278078544438608, -0.0009950581712718973, -0.0005282781188207776, 0.0006081998621481545, 0.002009278207307122, 0.0031507921553567773, 0.003424935440403524, 0.0021879167754768436, -0.0011827536998402657, -0.007225171099376267, -0.016328951796578603, -0.028675204142391282, -0.044185469984967224, -0.06248483177735097, -0.08288373893813282, -0.10438215544822478, -0.1256983566478222, -0.14532315296103, -0.16159857958986076, -0.17281827066769384, -0.17734495323414715, -0.173738875378575, -0.16088964602448483, -0.13814318572255066, -0.1054143737226407, -0.06327524099410602, -0.013013770297942106, 0.04334383503959008, 0.10305248938846628, 0.16271178031551878, 0.21837386996786423, 0.26569322050736044, 0.3001129561748911, 0.31708015630191866, 0.3122801640447959, 0.2818782451077168, 0.2227557649001572, 0.13272436712400737, 0.010699298604905986, -0.1431632023273668, -0.3273825528902851, -0.5391317492611387, -0.7742785250276192, -1.027490935086503, -1.2924046677200545, -1.5618459246332834, -1.828100569819557, -2.0832175351453994, -2.3193323476756698, -2.5289952448087494, -2.7054880244642003, -2.8431406525271745, -2.937604021556808, -2.9859929954269138, -2.98699886967837, -2.940938487246474, -2.8497343732056244, -2.7168084762128566, -2.5469147763040842, -2.3459175797808314, -2.120524907876279, -1.8779908945931814, -1.6258024860416855, -1.3713662557330561, -1.121711157467069, -0.8832316472499689, -0.6614529761152019, -0.46083659257170584, -0.2846687269087289, -0.13501305783415485, -0.012725008503249783, 0.08247674637344898, 0.1518894664907546, 0.19766458114359253, 0.22261591943962106, 0.2300117119580362, 0.22336317662599237, 0.20622175627942452, 0.18199588071326583, 0.1537978740528919, 0.12432199804507892, 0.09575961261859843, 0.06975733971581946, 0.04741439520242274, 0.02931486643488968, 0.01558884839727101, 0.005994954006295852, 1.5935159172589862e-05, -0.003041023003538846, -0.003947194279939315, -0.003465287215116654, -0.0022781329099696725, -0.0009368265682324894, 0.00016983508713940405, 0.0008250175697964453, 0.0009741687992812656, 0.0006992119028172053, 0.00018119777300137146, -0.0003434492704928156, -0.0006278367868720031, -0.0004557602025066733, 0.0003250127536477747, 0.0017803414482112324, 0.00387988370339672, 0.006500130870833208, 0.009439206232252454, 0.012441103170237208, 0.015226119628986885, 0.017523907082741663, 0.01910512089149928, 0.019807979016249536, 0.01955676693592132, 0.0183702623583278, 0.016359217652474528, 0.013713282731411638, 0.01067894606374937, 0.007531090836294282, 0.004541497883019664, 0.001947995196298755, -7.208995943469259e-05, -0.0014209907338043582, -0.0020896820486409145, -0.0021559590217506757, -0.001771500249595498, -0.0011393907470186005, -0.00048480247978864273, -2.2480550579702257e-05, 7.475613472923516e-05, -0.00029778204206128085, -0.0011595725257720119, -0.0024397666318498523, -0.003985473435450371, -0.005583136218210506, -0.006990826924632508, -0.007977519544130885, -0.008363935286694326, -0.00805841411236108, -0.007081133520121659, -0.005570906709854928, -0.0037703001102752727, -0.001987295456550476, -0.0005349797168546367, 0.0003455308512163764, 0.0005698708482665764, 0.0002902847121267347, -4.4864264055368014e-05, 0.0003310672859693653, 0.002470917716438248, 0.007612564892332009, 0.016998195198443377, 0.031610400291926494, 0.05182986916914406, 0.07702982232424606, 0.10513426941511733, 0.13217756154183175, 0.15191304459134936, 0.15552657676346232, 0.1315150365949969, 0.06578970121711859, -0.05794149048289064, -0.25747094325370146, -0.5510445965620576, -0.9559746046186361, -1.4869465426447521, -2.154085449498692, -2.9608850995930434, -3.902140129791589, -4.9620463596936, -6.112654485300497, -7.312942126730139, -8.508680925057867, -9.633293774096217, -10.60986689410291, -11.354419659732908, -11.780457121656198, -11.80473304882957, -11.354044000322753, -10.372696775601831, -8.830218056622524, -6.7287762486104015, -4.10961704428893, -1.0577377691415646, 2.296033386589329, 5.776402333129441, 9.16922473615957, 12.232109939388556, 14.710572837960807, 16.360043884827775, 16.973750713040882, 16.416120569860354, 14.660966875781776, 11.832986567880324, 8.25100104285011, 4.47090055882407, 1.325608437899341, -0.040935876224775035, 1.850921485750238, 8.828468444331502, 23.062226288676378, 47.04182249394384, 83.52909212152932, 135.48571077967767, 205.9734991112072, 298.0267780971723, 414.5002532680384, 557.8903719364428, 730.1321861247835, 932.3783228449805, 1164.7651468788365, 1426.173313081495, 1713.9912317734822, 2023.8911117248697, 2349.6281412501357, 2682.8739517626987, 3013.0957182091997, 3327.492905695165, 3611.0033797072956, 3846.388146753005, 4014.437026482897, 4094.205982566642, 4063.3420032684567, 3898.508853965432, 3575.8964126273954, 3071.806295291268, 2363.3031362527167, 1428.917590252732, 249.38402485666285, -1191.606897706223, -2906.6628591125127, -4903.975580861938, -7186.66244985989, -9752.188615299687, -12591.927562708428, -15690.893871451437, -19027.587873277243, -22573.995824360893, -26295.763948183107, -30152.552430646097, -34098.57015230909, -38083.285323863376, -42052.30142822576, -45948.382158305496, -49712.60357368647, -53285.606682955135, -56608.91945713734, -59626.426610707, -62285.97077185385, -64540.49335439638, -66349.26494023958, -67678.89260479252, -68504.2010262552, -68808.94379427578, -68586.29925976969, -67839.13282103394, -66580.01432687363, -64830.98656441715, -62623.08835056206, -59995.643310343934, -56995.334589912025, -53675.26861785693, -50093.81011757926, -46312.81492801259, -42396.08301939934, -38407.83546885223, -34411.22312689296, -30466.79988969678, -26631.148065583762, -22955.66408275377, -19485.520114555784, -16258.828746094196, -13306.03089665347, -10649.519707821526, -8303.506641867338, -6274.165340951588, -4559.928814584384, -3151.9548101888545, -2034.8674030222912, -1187.6590583390175, -584.7120025008666, -196.90053619222644, 7.266065154233221, 60.49864720665188, -4.381901325691147, -155.48148443518585, -362.76475086653517, -598.8560903281569, -839.689376454959, -1064.9916426099574, -1258.598786980399, -1408.5990577048512, -1507.3055965575359, -1551.0722448444592, -1539.9703941667626, -1477.3489064291646, -1369.3023743737015, -1224.0755588307593, -1051.432223571901, -862.0126098379052, -666.7113855117797, -476.09959972119856, -299.9111789248942, -146.6115354031337, -23.057846503798316, 65.73761230741677, 116.73761443786998, 128.9067943143841, 103.14144004565857, 42.112399615404875, -49.96559721099273, -167.6224980530399, -304.46209575799753, -453.5139855508916, -607.5910759023382, -759.6342646665089, -903.0297621205955, -1031.8897982674796, -1141.2761762389941, -1227.3637851224412, -1287.5429642456475, -1320.4584090133694, -1325.9869574162751, -1305.1593554304334, -1260.0334403393952, -1193.5280260680422, -1109.2280652468296, -1011.1723693086935, -903.6352898493545, -790.9135925591837, -677.1291329129774, -566.0542600713098, -460.9636766159158, -364.5252438838695, -278.7306937604529, -204.8656417817439, -143.51750042817366, -94.61806984402538, -57.51603712704714, -31.07340630046894, -13.779050345492177, -3.8721444711182555, 0.5317945735027327, 1.31919544178856, 0.2672769636231924, -1.051283277954851, -1.343570299529373, 0.35116673336073745, 4.633234679912047, 11.73822130381261, 21.555291235589543, 33.665466813653325, 47.3963605807455, 61.88912367899079, 76.17294023715736, 89.24224082637627, 100.13192207049015, 107.98622571898908, 112.117737169504, 112.05320978150046, 107.56323438460167, 98.67593711549073, 85.67432303200408, 69.07785153542959, 49.61011475251753, 28.154989899907015, 5.704184494456265, -16.700522234028828, -38.0268717532777, -57.31011232719304, -73.7061545914897, -86.5370649614203, -95.3271746168631, -99.82719829422713, -100.02416773229926, -96.13911781775809, -88.61243312496569, -78.07791192149017, -65.32723533592943, -51.2669456308116, -36.8704321542839, -23.12754283134637, -10.994470642555948, -1.3464597335179533, 5.06436137542513, 7.644058205979386, 5.983343769563771, -0.12572330055939898, -10.683451586465527, -25.48640228144439, -44.140775239329976, -66.08426333343812, -90.61497387551262, -116.92570997495199, -144.14166736183012, -171.35979127289656, -197.68780505813746, -222.281080554589, -244.37575349921102, -263.3168526585682, -278.5818566604119, -289.7956405236401, -296.7369400331528, -299.3387879507686, -297.6823434959209, -291.9848045814378, -282.58235650118166, -269.90928079773306, -254.47445070303237, -236.8362932710443, -217.5773218197805, -197.28086049528213, -176.50938409019145, -155.7856152941736, -135.57777584914743, -116.28669994960696, -98.23741344316882, -81.67555345135871, -66.76758790769816, -53.60441728492494, -42.2078220980868, -32.539133465741585, -24.509458144102247, -17.990782788273737, -12.827311508072572, -8.84642539169784, -5.868791597900754, -3.7173902448852245, -2.2248483264112866, -1.2389829191491861, -0.6266894531818957, -0.27615237126841735, -0.09749035460223016, -0.022051314550504977, -0.0006210250952736114, -0.0008364783507995462, -0.004101565679303504, -0.002290401010212735, 0.005504682177575388, 0.015964230102611922, 0.02410505975169284, 0.025303192777816196, 0.016717450759772306, -0.0018931745275503594, -0.027915130678438992, -0.05611056366055545, -0.07922746908441705, -0.08886909701765103, -0.07649690095716821, -0.03444611819450836, 0.04315365110355389, 0.15964054559098337, 0.3153283599748218, 0.5072964701549922, 0.729470774409908, 0.9729808633661196, 1.2267578643658166, 1.478313022729895, 1.7146411370032892, 1.923130024340861, 2.092435213713836, 2.2132557492763327, 2.2789526481944855, 2.285969894011983, 2.2340342264929585, 2.1261271257281544, 1.9682390122822084, 1.7689306546175525, 1.5387391878660315, 1.289479173434189, 1.0334831284789872, 0.7828269369075321, 0.5486112693216575, 0.3403379865657905, 0.1654155852917246, 0.028819133479581927, -0.0670729499829348, -0.12246948759388897, -0.1399959470402695, -0.12438279062990945, -0.08204087327535081, -0.020557605134347776, 0.051849361961195314, 0.12688364735537694, 0.19669148292096264, 0.2543219668030756, 0.2941010301183037, 0.3119012695703998, 0.3052977715595925, 0.27360884470704516, 0.2178265204341153, 0.1404418562633166, 0.0451932915357148, -0.06324163265411183, -0.17958859200981708, -0.2983289078331012, -0.4140397481607608, -0.5217071925629364, -0.6169850054228889, -0.6963867145700113, -0.757414395767703, -0.7986182902598503, -0.819589750029883, -0.820894151626846, -0.8039535894077637, -0.7708929810871803, -0.7243636973417265, -0.6673452746785872, -0.602952811033564, -0.5342597651108757, -0.46414405622534227, -0.39516576874025844, -0.3294739434232683, -0.268750053063683, -0.2141884916884586, -0.16650825421431065, -0.1259908474151306, -0.09253840657853196, -0.06574543438414471, -0.04497754293759253, -0.029451008298614537, -0.018307786659202595, -0.010681621541438275, -0.005752073177156258, -0.002785153750152087, -0.0011597510640654126, -0.00038043455894770867, -7.820571151498467e-05, -1.4025392420833207e-06, 5.962376163231229e-07, -1.8991579212076403e-06, 3.632391711927716e-06, -6.084837063480385e-06, -7.05220408550404e-05, -0.0002294523348365194, -0.0005115112814427676, -0.0009274127433461357, -0.0014675477513856337, -0.0021033311756058254, -0.002791383797172888, -0.0034794646295593806, -0.004113115362173121, -0.004642075490746295, -0.005025696852923604, -0.005236820348484533, -0.005263829647806853, -0.0051108419682279775, -0.004796210971758393, -0.004349683861926485, -0.003808663062450849, -0.0032140687869749605, -0.002606285358638395, -0.0020216095272968487, -0.0014895131175954462, -0.0010309216741115814, -0.0006575597522885147, -0.00037232223791696035, -0.00017048595560795518, -4.151539254143534e-05, 2.8814136282186012e-05, 5.625307300240502e-05, 5.6120435194681424e-05, 4.174421096551139e-05, 2.3419928154525426e-05, 7.931353980955298e-06, -1.3957968795016329e-06, -4.19764522234165e-06, -2.2671846863538076e-06, 1.4035776457940893e-06, 3.5761976862850914e-06, 1.5764848018350107e-06, -6.136008641549142e-06, -1.969348923728378e-05, -3.7845719177794256e-05, -5.824666554320865e-05, -7.792743144411782e-05, -9.38592664704322e-05, -0.00010350432279380849, -0.00010526106698278728, -9.873375620449099e-05, -8.478884858409294e-05, -6.539272717959048e-05, -4.3260989441503945e-05, -2.1389069986006128e-05, -2.544090109457609e-06, 1.1195253538956823e-05, 1.8772173345517972e-05, 2.030065772163156e-05, 1.7002488811772008e-05, 1.0940988740823994e-05, 4.594928196830342e-06, 3.4534886443244554e-07, -3.3084466315079934e-08, 4.220347483005897e-06, 1.2632019956732664e-05, 2.3521355857284697e-05, 3.429754701188376e-05, 4.200166905055068e-05, 4.402383533918848e-05, 3.8884495563862376e-05, 2.6941293025366438e-05, 1.087361615455821e-05, -4.190398324706137e-06, -1.1003640579309358e-05, -1.0284676985785696e-06, 3.426569908223049e-05, 0.0001017446422947762, 0.00020477760285917296, 0.0003414851575657431, 0.0005033574182962588, 0.0006745298366443578, 0.000831973429582955, 0.0009467769544423843, 0.000986583980924897, 0.0009191040973909901, 0.0007164585272959959, 0.00035996380959672726, -0.0001551771913851945, -0.0008159021361354946, -0.0015886847657232202, -0.002418896558722506, -0.0032326097908605654, -0.003941104490289182, -0.004448124802676737, -0.0046594610962145, -0.004494140726751141, -0.003896209554029847, -0.002845799605241949, -0.0013680105029468656, 0.0004618960675189959, 0.0025183499303508767, 0.004631411865074606, 0.006599331154702632, 0.00820760565492868, 0.009253632005756808, 0.009575021102287815, 0.009079268928794827, 0.007771161377517239, 0.005774227765460311, 0.003342369832928528, 0.00085788549335768, -0.001187223125984248, -0.0022286733079447344, -0.001686535023852033, 0.0009603717816081573, 0.006085967777221283, 0.013820286669639657, 0.023953016456866368, 0.03584752683845189, 0.04837745115318098, 0.05989911306924039, 0.06827045136144741, 0.0709281136786674, 0.06503149032542249, 0.047678594130202936, 0.016194145883809793, -0.031515355216913794, -0.09655102026783383, -0.1785733706170201, -0.2753408592017649, -0.3822651432477355, -0.4920177061402008, -0.5942253363381894, -0.6752931693020972, -0.7183924017384916, -0.7036452223056582, -0.6085390250886795, -0.40855103385130664, -0.07800423278231716, 0.4088574997987174, 1.076606299924707, 1.9472230750531616, 3.038604487624375, 4.363055366922153, 5.925847817674738, 7.723934657628087, 9.744906890552317, 11.966310184506032, 14.355402210544213, 16.86931756575068, 19.45575645614471, 22.054224364683414, 24.597856126024084, 27.01560039895046, 29.234802122067318, 31.184092533540216, 32.796447317555526, 34.01226944181845, 34.78234066253223, 35.07048096649307, 34.85576305614127, 34.13427423908229, 32.92005643225867, 31.244992934595576, 29.157997555845913, 26.723358920239058, 24.018270954223553, 21.129669370938146, 18.1505073992322, 15.175421172812868, 12.29630242535862, 9.597945738198458, 7.153970207073797, 5.023246227223784, 3.2470404048703183, 1.8470685535458387, 0.8245293471165764, 0.1602799911322452, -0.18380821378827567, -0.262407467174276, -0.1433207234440474, 0.09672544563252734, 0.376853861999855, 0.6171071048216079, 0.7435220353251836, 0.692887941450377, 0.41688879817379315, -0.1146335694940443, -0.9115139179844292, -1.962344589432048, -3.2349274079736565, -4.678085445045742, -6.224730446040391, -7.796027560981706, -9.306417716455812, -10.669196985832988, -11.802308503981314, -12.633979025378975, -13.107831343828154, -13.187151784216102, -12.858043807509814, -12.131011635741132, -11.04101795575602, -9.645994334202213, -8.023682180843135, -6.267088875157848, -4.478848426887351, -2.7648000893622715, -1.227190696415606, 0.042056078582691316, 0.9675511095324956, 1.4956998539668906, 1.598628909819215, 1.276474107250582, 0.5578255575086332, -0.5017566978998214, -1.8231020362467734, -3.3084866355165516, -4.848200981903066, -6.328104600626712, -7.637660023918562, -8.677905905476896, -9.368798193441213, -9.655369143073056, -9.512213514418322, -8.94590732301074, -7.995092261012752, -6.728111340767972, -5.238249426776588, -3.636805630612807, -2.0443929259091163, -0.5809810816354889, 0.6446742805378175, 1.5452553759791867, 2.064165995303272, 2.183104793787977, 1.9272216559183108, 1.3672951890626512, 0.6185380100715667, -0.16415777468040793, -0.7944908947969255, -1.066249117950876, -0.767506223786488, 0.3032340184167617, 2.319889442936995, 5.4117434255300205, 9.647639861927615, 15.022599986238337, 21.44805807240087, 28.746549511087043, 36.65152319683156, 44.81276848569756, 52.80759273139743, 60.157542791878164, 66.3501102004093, 70.8645172255156, 73.2003710660327, 72.90771705394373, 69.616845631497, 63.06590627142354, 53.12463174974889, 39.812749526124165, 23.311574612397944, 3.9676704309885795, -17.712508272139754, -41.07733273803979, -65.35290545943761, -89.673731694493, -113.1200199912132, -134.75995861075705, -153.69495584651102, -169.10560186133065, -180.29675755014716, -186.73762599761858, -188.0939719949124, -184.25250949133644, -175.3350455372118, -161.7011524997965, -143.9387562265126, -122.84288905930066, -99.38292968469199, -74.65765539909926, -49.84329831323783, -26.136373750321464, -4.693739600891838, 13.427071466100879, 27.32427119584386, 36.30180721610244, 39.90954746835719, 37.97165544314766, 30.601498739600245, 18.201979573858445, 1.4509098379515253, -18.72817557273645, -41.208605581770215, -64.71405395969232, -87.88008631239093, -109.32582906474214, -127.72655268638007, -141.88432671035537, -150.79459631595, -153.703100166114, -150.15054876792072, -140.0035134148307, -123.46939411425731, -101.09449359745489, -73.74507968126652, -42.57218114807246, -8.961692933745018, 25.52787825788434, 59.237056059028326, 90.482965685121, 117.63913019867515, 139.2135166883175, 153.92081427453235, 160.74570991306672, 158.99314051903613, 148.3233705343686, 128.7704124733594, 100.74298367392448, 65.00806449811145, 22.65798241597721, -24.937251328369307, -76.189920813129, -129.3638957935456, -182.64981554336595, -234.24251353146875, -282.4176259085207, -325.6050608997253, -362.45052432468026, -391.8659632939271, -413.06707335291964, -425.5960396837957, -429.3289303793702, -424.46793687350385, -411.51939772718356, -391.2592096212376, -364.68779116005834, -332.977195174769, -297.41324570631485, -259.33569784688143, -220.07958487108579, -180.92004246426382, -143.02261407576952, -107.40278638811743, -74.89431619221797, -46.12911937375403, -21.528395756748065, -1.3043955891936894, 14.52805638557304, 26.13161586282058, 33.819741416482664, 38.025210247248104, 39.26586895920946, 38.10965823134333, 35.14101664063143, 30.930001325128863, 26.00520652515487, 20.83247012007812, 15.799673154188717, 11.207785271119553, 7.2678522991695, 4.103725353443115, 1.7596366097523874, 0.21155927492366092, -0.6188080035287031, -0.8486396351946287, -0.6183379649245183, -0.0767110595164879, 0.6321224977612313, 1.379421342099396, 2.059672233096354, 2.595385004959069, 2.9388764929830065, 3.071309157890857, 2.9994318874326265, 2.7505963424822903, 2.3666402722148616, 1.8973508538413142, 1.3941393373226278, 0.9044681225005105, 0.46745489622349995, 0.11093115520489708, -0.14993261076480993, -0.3124513216048321, -0.38488982779908926, -0.3838845683295945, -0.3311952261015926, -0.2502105332718398, -0.16263414958552527, -0.08573799598297774, -0.030496926582138293, -0.0008154093918513783, 0.0060645463347040515, -0.001995023728036844, -0.014570086936335097, -0.021923837537560904, -0.01860117010868804, -0.006952245392839532, -0.0001546859734803966, -0.024329347965837966, -0.11940622215238102, -0.33849215506604824, -0.745613521299472, -1.4118455116768964, -2.4099846297507477, -3.8080609099714895, -5.662108184293397, -8.008706376489384, -10.85789253628139, -14.18704187004579, -17.9363682763879, -22.006391455000916, -26.257782340623404, -30.513878975116466, -34.565920989181, -38.18089020867255, -41.11166151703979, -43.108996114678355, -43.93476097134915, -43.375644365706925, -41.256566673687914, -37.452964043567185, -31.901173559304578, -24.606157421743198, -15.64559499124065, -5.170498610417615, 6.5977981037814475, 19.374387084213716, 32.821003956303734, 46.55925668943027, 60.186221437144404, 73.291615480069, 85.47565553404064, 96.3666597598691, 105.63745703825465, 113.01972747360888, 118.31551034526889, 121.4056061582617, 122.25460366939878, 120.91029812382081, 117.49904284578204, 112.21781562941104, 105.32318836246507, 97.11775289539237, 87.93478876713638, 78.12203821240546, 68.02548161115759, 57.973981440030656, 48.26558732955199, 39.15617454889701, 30.850931651861025, 23.499078711021752, 17.191816204941176, 11.963406317109486, 7.795479969052174, 4.6239120941143605, 2.3476450857903557, 0.8389014300158827, -0.04598567343462573, -0.45584538045076783, -0.5347060639287927, -0.41317033015582877, -0.20158413656043625, 0.014686371606084143, 0.17771283964195037, 0.2571956771481624, 0.24854544495385808, 0.16915477809698468, 0.05325745802755219, -0.05414148113959306, -0.10374607573598207, -0.04833590110440751, 0.1514691127207179, 0.5224591001142073, 1.0754214691413917, 1.803273454005659, 2.680825727054961, 3.6661388714314684, 4.703320130975907, 5.726565487046148, 6.665034703176652, 7.4480767015771585, 8.01051619436332, 8.297573185669064, 8.269051363041646, 7.902496438453444, 7.19512489678305, 6.164397741453697, 4.847066121346178, 3.2969582695015514, 1.5816588347447365, -0.2216894412838896, -2.031154771297667, -3.7650214623024194, -5.346745133252824, -6.709421839245758, -7.7994815283292755, -8.579418063592426, -9.029407813443155, -9.14774986708398, -8.95014427747078, -8.467903809749721, -7.745289593692485, -6.836203652773567, -5.80028196976763, -4.698902139261586, -3.591360106280848, -2.5314474724037073, -1.56458110810212, -0.7257222191756157, -0.0381782025862419, 0.4867103820181106, 0.8490392258890256, 1.0590659817769947, 1.1353401869156874, 1.1024196837186473, 0.9883746489704203, 0.8222829533361808, 0.6319099166562251, 0.4417358090710978, 0.2714363817740618, 0.13492375701838605, 0.03997327296156888, -0.011577187858808688, -0.023126618334125604, -0.0022161991979933807, 0.04082809857085538, 0.09437083380836796, 0.14691527804350205, 0.18839165568095392, 0.21117581353739756, 0.2107603417804293, 0.18603721513598948, 0.13919003458328524, 0.07523152922951275, 0.001254193395884674, -0.07451452939800493, -0.1437411878435448, -0.1989843896250632, -0.23455488936508864, -0.24714792812790426, -0.2361839056893953, -0.20382521121533065, -0.15467160019826307, -0.0951705725476404, -0.032809518638077316, 0.024819964451882098, 0.07098054952910622, 0.10066117766996593, 0.11126135771890737, 0.10300333710911419, 0.07901222033299948, 0.04504034880779074, 0.008850350232176672, -0.020691630090948623, -0.03472702408428008, -0.025607558294930846, 0.011940366938824753, 0.07982478077420577, 0.17589781087593295, 0.29367166611087947, 0.422513260084882, 0.5483486969993614, 0.6548509976807982, 0.7250309686560676, 0.7431224173542732, 0.6965968925633159, 0.5781136753226761, 0.38718276828682163, 0.131340552350035, -0.17334946106767354, -0.5026199899614568, -0.8252391914475454, -1.105187193911187, -1.3047119670291958, -1.3881239950775335, -1.3261222316317616, -1.1003162281203365, -0.7075911847830174, -0.1640017044649317, 0.492201298861591, 1.1987664733222545, 1.8691582622841505, 2.3940257422269178, 2.6446139924638405, 2.4780499612080797, 1.744380241987578, 0.2951033474636753, -2.007197497431622, -5.278630709679668, -9.60386151328511, -15.02676448138127, -21.542355808294648, -29.090676789758625, -37.553187097989486, -46.7521076017651, -56.45300673968956, -66.37075006926884, -76.17872349757768, -85.52103776590894, -94.02738123655438, -101.3297472951289, -107.08023672129606, -110.9691161753906, -112.74289396765373, -112.21935164602992, -109.29933125237088, -103.97548645578203, -96.33683381621952, -86.56866990446764, -74.94767059180347, -61.83224883408726, -47.64851213594199, -32.87241535267402, -18.0089393320957, -3.5692777265289433, 9.952842794447523, 22.104367183075333, 32.494725621379565, 40.81467257352748, 46.85086546902806, 50.49567226895024, 51.75163800999897, 50.73031709614122, 47.64548125276289, 42.80101955011767, 36.57413976674014, 29.39474297049107, 21.722060428791142, 14.0198010970618, 6.731152962051911, 0.2550400832981525, -5.0749705260169184, -9.008502940308146, -11.39131656600913, -12.172782199486635, -11.407615818947892, -9.251794045909461, -5.9528921124440375, -1.835387949294437, 2.7182519788227673, 7.289663065436915, 11.448638622324637, 14.777839368607555, 16.8968145471901, 17.484071726215124, 16.295826110018716, 13.18017474317053, 8.08646139790212, 1.0693184459184095, -7.712823111626721, -18.004627363827677, -29.46572795029815, -41.68690437632467, -54.20966666636151, -66.54819215805801, -78.21245514448202, -88.731350784568, -97.67464294963573, -104.67331318275014, -109.43691200461377, -111.76461204445158, -111.55271564279175, -108.79774875284797, -103.59426825169717, -96.12831641091803, -86.66694834679548, -75.54441547637674, -63.14580926027456, -49.88906317385387, -36.20625353719804, -22.52513154290062, -9.251762961377612, 3.244980450759292, 14.6467057957151, 24.695557120401535, 33.20063077227832, 40.04094458549325, 45.165102198143956, 48.587964151113134, 50.38439478934207, 50.680819769628975, 49.64520457912272, 47.476047636811906, 44.39100837035354, 40.61575842170128, 36.373590427182464, 31.876370337550995, 27.316723583593646, 22.861874254536385, 18.649662246365818, 14.786468609345727, 11.346925605481571, 8.375216651232037, 5.887711233738671, 3.876622920400726, 2.3143382995378006, 1.1581587482900202, 0.3551129255743156, -0.15344509214599802, -0.42768110001933124, -0.5257489015472073, -0.5009638885161435, -0.39976004943123783, -0.26044706341975976, -0.11270334695613793, 0.022287828985554224, 0.1311791362836939, 0.20741267301608693, 0.24992648992828384, 0.2617492276064522, 0.24860388012441414, 0.21761875691159435, 0.17622383434842656, 0.13128242966594397, 0.0884810730151049, 0.05197341293267431, 0.024262038304108467, 0.006279574253465414, -0.002380639207163077, -0.0031370108916449133, 0.0019526710843230943, 0.010561482047655668, 0.02042293001669457, 0.029591895522648872, 0.03662054528098148, 0.04064425306378476, 0.04138280147053668, 0.03906989820618398, 0.03433067371719039, 0.028028533360597574, 0.021105154302469186, 0.014434394289322156, 0.008706374086807833, 0.004352692983728465, 0.0015176557643293352, 7.437654271210585e-05, -0.0003207053639873332, -0.0001455143415146914, 8.451749285029057e-05, -8.634897306942513e-05, -0.0009700930539917667, -0.0026752672303483258, -0.005079636735105428, -0.007838854399903419, -0.010430321004525775, -0.012227148859146223, -0.012593576293248442, -0.010990605442920411, -0.007079303996294682, -0.0008092314886987307, 0.007519203967112898, 0.017227135563805177, 0.0272696249461917, 0.0362893053651479, 0.04270837385219105, 0.044852262150167424, 0.04109463828752117, 0.03000979261036641, 0.010519811070802536, -0.01797650633963022, -0.055505812511541214, -0.10146329316882662, -0.1546031454455562, -0.21307907852610078, -0.27453329084726213, -0.33622831153257543, -0.39521247606554294, -0.4485069427558687, -0.49330031019031373, -0.5271388001018689, -0.5480952097097411, -0.5548958444526662, -0.5470061228912332, -0.5246630673268051, -0.4888459866920198, -0.4412152589463007, -0.3840046292420561, -0.3198755086498837, -0.25174705519635554, -0.18261469095748442, -0.11537019587915366, -0.052635979336833, 0.0033753631221962064, 0.050967715395122695, 0.08902897459327645, 0.11705428571904061, 0.13512632395700447, 0.14385759768966014, 0.14430147484619166, 0.137843668951928, 0.12608399209542476, 0.1106948445974069, 0.09329843695996266, 0.07536432586387976, 0.05812972477257993, 0.04254658907614883, 0.029256996626138624, 0.018595899736543815, 0.010618041069997497, 0.005144464211967749, 0.0018223109646240587, 0.00019097296284947574, -0.00025210095095706044, 8.027258397985315e-06, 0.0005519662370466156, 0.0010595416607477777, 0.0013270480037879454, 0.001268581031283581, 0.0009027884613421498, 0.0003279546428905441, -0.0003104628666417732, -0.0008552717770890705, -0.0011713662227035725, -0.0011737727398739145, -0.0008468036682963552, -0.0002523711752887004, 0.00047317304892564654, 0.0011329783698806276, 0.0014925230437797745, 0.0013084831363099243, 0.0003601763841637779, -0.0015201170637977495, -0.004421451711314541, -0.008336148198504553, -0.013151638913409073, -0.018653555685525458, -0.024539777515387495, -0.030443974267482736, -0.035966480572149316, -0.0407094383851795, -0.044312716976573685, -0.046487038534869844, -0.0470410198297681, -0.045899452671411684, -0.04311102307132583, -0.03884472055955379, -0.033375308413028444, -0.0270592896323855, -0.020303825572168227, -0.013531697800461815, -0.007144870844304776, -0.0014913365755138235, 0.003161826794198898, 0.006646878919869499, 0.008903754088484503, 0.009977777417198417, 0.010007305322167646, 0.009202844425728588, 0.007820042283442954, 0.006129528492593025, 0.00438685780378325, 0.002805741284599811, 0.0015373639383839742, 0.0006578607225999452, 0.00016514983456909947, -1.4592272346056543e-05, -1.1824055359963572e-05, 8.225820904505034e-06, -0.00012842046198546783, -0.0005773770303847826, -0.0014508870334745728, -0.002797905923764581, -0.0045917220294690265, -0.006726750057841349, -0.00902513135275544, -0.011252685598091205, -0.013142760507854867, -0.01442551547373436, -0.014859179774396755, -0.014260068743575827, -0.012527893944283195, -0.00966322406933015, -0.005774923702406147, -0.001076305784564555, 0.00413008957930403, 0.009477937389658922, 0.014570490399710815, 0.019018617629159112, 0.022479640964714734, 0.02469285176239419, 0.025508050472664214, 0.02490336651354079, 0.022989379555866704, 0.01999954218183357, 0.016267127659086646, 0.0121905885504028, 0.008190534144321025, 0.004662519403458134, 0.0019306742923305203, 0.00020714727585600048, -0.0004380293556766679, -9.291412590340177e-05, 0.000996952275524115, 0.0024465324329832625, 0.003765574294591835, 0.004406313856165906, 0.0038203688533985205, 0.0015192629394290057, -0.002867515922739611, -0.00954302566221382, -0.0185074438032757, -0.029541028251918986, -0.04220819405056712, -0.05588308662900077, -0.06979502420974154, -0.08309012890387538, -0.09490362508839215, -0.10443607577293615, -0.11102717199834439, -0.11421724663124569, -0.1137901383208292, -0.10979436119177641, -0.10253930230278255, -0.09256640073809332, -0.08059793278395336, -0.06746848441962708, -0.05404618026944873, -0.04115206477725481, -0.029486326066160886, -0.019569175449049427, -0.011703621709848868, -0.005964202772570289, -0.002212658300634194, -0.00013778591219297683, 0.0006835862730517985, 0.0007143475061185303, 0.00038439013948059214, 2.7850279944584935e-05, -0.00016021041946118208, -0.0001404035078420347, -1.4932808738931271e-05, 1.7012046964554613e-05, -0.00027024272972200436, -0.0010414085317540685, -0.0023084054759018673, -0.0038489455051043163, -0.005149478513142193, -0.005386497049403761, -0.0034586845303238335, 0.0019235376709610583, 0.012091098970163097, 0.02822039811768041, 0.05110580719345992, 0.08092646460221337, 0.11704016527363956, 0.15784112427382713, 0.20071821059592831, 0.24214496245786088, 0.2779217762414903, 0.30355367671185496, 0.3147329119911549, 0.30805264703385826, 0.2816949646041012, 0.23602127907044587, 0.17399217508763293, 0.10132804884629923, 0.026338533952368088, -0.04062417472344907, -0.08809709393078126, -0.10479037951846414, -0.08114590847701439, -0.011049668096351512], 'positive_zeros': ['0.22147116485545379211991940324978', '0.48229656448719361807815991015851', '0.59823070558453120155209330107427', '0.60367659484654544932842997202837', '0.64990024209747212235750578380170', '0.819842699255900549429978681864314', '0.977053880368121569984014656509817', '1.01198060239078931750983454277992', '1.06352760584071827954714501542322', '1.15541141622206115605994105893260', '1.22464392656625361570815943219854', '1.24826894549178629095598830741059', '1.66534477869315113410535826088402', '1.68702568768526371249868466462089', '1.75401684186257254299049495232015', '1.77000008332226694898470075797003', '1.78608899108506902513280801516959', '2.01713412011958660145452404471288', '2.06395770512259787839920617769217', '2.10837191417237831268563741099339', '2.19459518481256367512294349061894', '2.29394091253661954429630664420249', '2.40032011223918237020799365134761', '2.44690739075334442720094291529924', '2.46949338274332776133257898387060', '2.52979156256918819522206930318963', '2.53821088947863823402635413078585', '2.54258319719018123820481719002977', '2.56485190531222502261392815147272', '2.58592260771443375082939016325082', '2.58592458138590962468269932353092', '2.62453778598338894169929945114653', '2.62681371545503231488382208506371', '2.72461772779227936799781960888947', '2.73148295245039150302352449949887', '2.83950699195700006263559722249341', '2.92822487682543696017621072012807', '2.93743532467631561619264879415194', '2.95127247097228980962300889174545', '3.07307609203687524867073333268417', '3.16662460160596091032345210623596', '3.23150405125451086065262583820464', '3.26612017678013790337823239918450', '3.39936150219773583379569857781804', '3.66228958969135815401008228742365', '3.72470528325408312983827773411189', '3.85448391008407747875979987941321', '3.86056835491549744986174093378439', '3.86582779322822783291438250629813', '3.89796419552825215956496036628845', '3.92360100004240393556871873786875', '3.97184813022316611645190348648844', '3.98570685806704546675783918055345', '4.13454049539280346580714133015094', '4.14508349696832526930309718056416', '4.18773484200273489544210493375930', '4.22191404972935413977719331419812', '4.23831885762843513765121234881356', '4.31072007649998197190173650290297', '4.32446071092424988454599106460495', '4.37892590356150507982910794287570', '4.44733029878195029435814610938777', '4.56234685467900187890377288372107', '4.56377832912830162424196794067417', '4.58561838389045615742111246947425', '4.59806758497276383273185319618331', '4.64317282190535450903510474883233', '4.83851897787974999691799190368559', '4.86593336724252748596573975081746', '4.86988060885505227118577981872753', '4.88039242449208098389527798715208', '4.96675401696034008984835789851659', '5.01872849020710526683188079426641', '5.06438398969168336197027458873928', '5.12181641146545939122589498297433', '5.17157349348225090287874028238466', '5.21863553421104417821659350050272', '5.24125893460928990671670706445425', '5.32271259723078474361568681365978', '5.40338506192221491182863516560835', '5.42347637440305190712171010385015', '5.45136593535720083868508903079346', '5.46330301635657547188545489749274', '5.50396010365371053366799135665707', '5.51850515245026087390320632187712', '5.58333119679956460816513509518357', '5.67358649989842701492300967138055', '5.77851115483670475186221545178243', '5.78235720572632013933111453280656', '5.84282170873255061320412300333412', '5.89534770204695788715587133381819', '5.95718901891157902315406312739985', '6.01098545523467612072935482162384', '6.07948821270604965305855747784720', '6.12683356032777993109415737127999', '6.17637032781591580148527526223724', '6.18057942113067458921039909734357', '6.22105422290068290969695633298581', '6.24310609679477875491648163159744', '6.42119760044200689669973488735155', '6.42968889500937148686319057706761', '6.50362921899892937668761051590517', '6.52341552466010246447804689387700', '6.62491961575907392005243518009445', '6.68485788875885263262762927395653', '6.69406988653687654377977071572669', '6.77672675544606691710693578942447', '6.79415029912883587373724708562757', '6.79992144257887720537175170016685', '6.92626807436048388404239918782474', '6.95797478193490372036708363066409', '6.96931963080234867251506297858995', '7.05957275007627465701454600803971', '7.14523907649296994017677319877460', '7.17382204953972127247286173737003', '7.21168515630980874764259205594220', '7.23801979795697310298088156609431', '7.25048524690780573808427788860129', '7.29010344642362522736107913713815', '7.30818117938839147256033400126445', '7.38651759458939951759948274414244', '7.41446417555298930882076927287436', '7.43713737851935356686464104084599', '7.45936714310642051751128910010607', '7.53503153514174717763960967800333', '7.54584185306729138932501855914319', '7.56490133324294757145032279516733', '7.63271119340785460147728478655616', '7.67606139161472491876847317464505', '7.79340509341281811360521437593856', '7.85523868428021230777218244579760', '7.87653896867605713838268584145487', '7.893031555386997958214225059610990', '7.905310852064726178443455150061542', '7.972257529097417686756458556081724', '7.998331199383159421327431725652520', '8.002998867522995334525600059840036', '8.054866074179485554406829590801463', '8.066816174828938853669735454700083', '8.069519295141987841187839695585606', '8.117423287844066368563383669775092', '8.200644890769423077189869803107331', '8.250156086789296288085640488634747', '8.251321262513451820172794383726895', '8.364944329986031289272731852377278', '8.561804097382279161561649167588336', '8.569192454929786548545562874967384', '8.643398774171405332026871177876913', '8.662704941939732012173802744626214', '8.781006203448787612187351015419160', '8.789741746053549602220589776945926', '8.799582035514301676223557652426608', '8.870553236397965026164987938949499', '8.932512137357172926157696315217521', '8.946477700741616817725971939326663', '9.119075198068544859131457406101784', '9.130987960533576005592362292252290', '9.151304463903882382231514920696675', '9.175430773720130262630782107947903', '9.291847758385328511654367751004977'], 'prelabel': '32-3332e16-1.1-c0e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2895288372476055, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e16-0', 'trace_hash': 1237747412014483673, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.22147116485545379211991940325', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.48229656448719361807815991016', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.59823070558453120155209330107', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3418.1716943061765, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 230823426529176822657882149835550112280127458568963096576, 'conductor_radical': 238, 'degree': 32, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler13': [1, 16, 128, 688, 2808, 9296, 25984, 62960, 134684, 257744, 445568, 700912, 1008840, 1334032, 1625472, 1828656, 1901638, 1828656, 1625472, 1334032, 1008840, 700912, 445568, 257744, 134684, 62960, 25984, 9296, 2808, 688, 128, 16, 1], 'euler17': [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler19': [1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler29': [1, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 12, 0, 0, 0, 14, 0, 0, 0, 12, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 1], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler31': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler37': [1, -8, 36, -112, 266, -504, 784, -1016, 1106, -1008, 748, -392, 0, 392, -748, 1008, -1105, 1008, -748, 392, 0, -392, 748, -1008, 1106, -1016, 784, -504, 266, -112, 36, -8, 1], 'euler41': [1, -16, 120, -560, 1820, -4368, 8008, -11440, 12872, -11472, 8248, -5488, 5460, -9296, 16136, -22896, 25742, -22896, 16136, -9296, 5460, -5488, 8248, -11472, 12872, -11440, 8008, -4368, 1820, -560, 120, -16, 1], 'euler43': [1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1], 'euler47': [1, 0, 0, 0, -4, 0, 0, 0, 10, 0, 0, 0, -16, 0, 0, 0, 19, 0, 0, 0, -16, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, 0, 1], 'euler5': [1, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 1], 'euler53': [1, 0, -4, 0, 8, 0, -8, 0, 2, 0, 4, 0, 0, 0, -12, 0, 19, 0, -12, 0, 0, 0, 4, 0, 2, 0, -8, 0, 8, 0, -4, 0, 1], 'euler59': [1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1], 'euler61': [1, -8, 36, -112, 266, -504, 784, -1016, 1106, -1008, 748, -392, 0, 392, -748, 1008, -1105, 1008, -748, 392, 0, -392, 748, -1008, 1106, -1016, 784, -504, 266, -112, 36, -8, 1], 'euler67': [1, 0, -8, 0, 36, 0, -112, 0, 266, 0, -504, 0, 784, 0, -1016, 0, 1107, 0, -1016, 0, 784, 0, -504, 0, 266, 0, -112, 0, 36, 0, -8, 0, 1], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler73': [1, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 1], 'euler79': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler83': [1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1], 'euler89': [1, 0, 0, 0, -4, 0, 0, 0, 10, 0, 0, 0, -16, 0, 0, 0, 19, 0, 0, 0, -16, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, 0, 1], 'euler97': [1, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 12, 0, 0, 0, 14, 0, 0, 0, 12, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 1], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 16, 128, 688, 2808, 9296, 25984, 62960, 134684, 257744, 445568, 700912, 1008840, 1334032, 1625472, 1828656, 1901638, 1828656, 1625472, 1334032, 1008840, 700912, 445568, 257744, 134684, 62960, 25984, 9296, 2808, 688, 128, 16, 1], [1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 12, 0, 0, 0, 14, 0, 0, 0, 12, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, -8, 36, -112, 266, -504, 784, -1016, 1106, -1008, 748, -392, 0, 392, -748, 1008, -1105, 1008, -748, 392, 0, -392, 748, -1008, 1106, -1016, 784, -504, 266, -112, 36, -8, 1], [1, -16, 120, -560, 1820, -4368, 8008, -11440, 12872, -11472, 8248, -5488, 5460, -9296, 16136, -22896, 25742, -22896, 16136, -9296, 5460, -5488, 8248, -11472, 12872, -11440, 8008, -4368, 1820, -560, 120, -16, 1], [1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, -4, 0, 0, 0, 10, 0, 0, 0, -16, 0, 0, 0, 19, 0, 0, 0, -16, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, 0, 1], [1, 0, -4, 0, 8, 0, -8, 0, 2, 0, 4, 0, 0, 0, -12, 0, 19, 0, -12, 0, 0, 0, 4, 0, 2, 0, -8, 0, 8, 0, -4, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1], [1, -8, 36, -112, 266, -504, 784, -1016, 1106, -1008, 748, -392, 0, 392, -748, 1008, -1105, 1008, -748, 392, 0, -392, 748, -1008, 1106, -1016, 784, -504, 266, -112, 36, -8, 1], [1, 0, -8, 0, 36, 0, -112, 0, 266, 0, -504, 0, 784, 0, -1016, 0, 1107, 0, -1016, 0, 784, 0, -504, 0, 266, 0, -112, 0, 36, 0, -8, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, -2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -2, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, -4, 0, 0, 0, 10, 0, 0, 0, -16, 0, 0, 0, 19, 0, 0, 0, -16, 0, 0, 0, 10, 0, 0, 0, -4, 0, 0, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 8, 0, 0, 0, 12, 0, 0, 0, 14, 0, 0, 0, 12, 0, 0, 0, 8, 0, 0, 0, 4, 0, 0, 0, 1]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/ce/a'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '32-3332e16-1.1-c0e16-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '32-3332e16-1.1-c0e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2895288372476055, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e16-0', 'trace_hash': 1237747412014483673, 'z1': {'__RealLiteral__': 0, 'data': '0.22147116485545379211991940325', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '280748055062261144256829011522,611383529460203938529778578156,758347513009188164258740024377,765250997800956994707848705590,823846431983332137676234200864,1039274089804474093597857958789,1238562937903969951409626009350,1282837818040009240024855286894,1348181407903278300455154912266,1464657975284444413722897173919,1552420608577567086111406342419,1582368877998921861138644373484,2138559125594666019317156994573,2223480502397513415698859164048,2243741668027487750906381097292,2557021278110435340059260559549', 'Lhash_array': ['280748055062261144256829011522', '611383529460203938529778578156', '758347513009188164258740024377', '765250997800956994707848705590', '823846431983332137676234200864', '1039274089804474093597857958789', '1238562937903969951409626009350', '1282837818040009240024855286894', '1348181407903278300455154912266', '1464657975284444413722897173919', '1552420608577567086111406342419', '1582368877998921861138644373484', '2138559125594666019317156994573', '2223480502397513415698859164048', '2243741668027487750906381097292', '2557021278110435340059260559549'], 'label': '32-3332e16-1.1-c0e16-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/ce/a'}